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    "value": "<p>In practice, engineers may encounter different types of finite elements (from simple 1D bar elements to more complicated 3D brick elements) that are used in a variety of applications for the analysis and design of structural elements. A common feature of most of the computations in practice tends to be the linear behavior of the models, the advantages of which are undoubtedly speed, clarity, and simply the fact that for a large variety of problems, this solution is quite sufficient.</p>\n<p>Especially in the world of concrete structures, it often happens that the linear approach is not sufficient simply because after the first cracks appear in the loaded element, the stresses are redistributed and the problem becomes significantly non-linear.</p>\n<p>For these cases, it is necessary to choose one of the more sophisticated approaches. For 1D cases, analytical methods defined directly in codes can often be found. For example, popular Strut and Tie models can be built for 2D planar elements and discontinuity regions (D-regions), or the more sophisticated stress field method implemented in IDEA StatiCa Detail, CSFM, can be used.</p>\n<p>However, if the engineer encounters a problem that cannot be simplified into planar behavior, the options are very limited. Of course, a 3D Strut and Tie model can be built or semi-scientific software can be used for accurate analysis. These procedures are often time-consuming, not code-compliant, and require an engineer knowledgeable in advanced modeling methods.</p>\n<p>For this reason, IDEA StatiCa has developed and implemented the 3D CSFM (Compatible Stress Field Method) in the Detail application. 3D CSFM extends the established CSFM into a third dimension, offering a fast and code-compliant solution that is primarily applicable to the everyday engineer, giving them a unique new ability to safely tackle the complex details of concrete structures.</p>"
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    "value": "<p>3D CSFM defines the concrete behavior based on the<strong> Modified Mohr-Coulomb</strong> plasticity theory for monotonic loading. The method <strong>considers principal concrete stresses in compression and reinforcement stresses (σ</strong><em><strong><sub>sr</sub></strong></em><strong>) at the cracks while neglecting the concrete tensile strength (tension cut-off), except for its stiffening effect on the reinforcement (</strong><a data-item-id=\"3b2ffddf-80fb-4ad0-822b-89d98e3fee43\" href=\"\"><strong>Tension stiffening</strong></a><strong>).</strong></p>\n<p><strong>σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>1</sub></strong><em><strong><sub>r</sub></strong></em><em><strong>, </strong></em><strong>σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>2</sub></strong><em><strong><sub>r</sub></strong></em><em><strong>, </strong></em><strong>σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>3</sub></strong><em><strong><sub>r</sub></strong></em><em><strong> ≤ 0 MPa</strong></em></p>\n<p>The reinforcement bars are linked to concrete volume finite elements through bond elements, allowing for slip between the concrete and reinforcement. It should be noted that 3D CSFM <strong>is not suitable for simulating plain concrete</strong> due to the absence of tension, which may result in misleading deformation and model divergence. Generally, the Mohr-Coulomb theory includes two fundamental properties governing the evolution of the plasticity surface in compression and partially in tension: the internal friction angle <em>φ</em> and cohesion parameter <em>c</em>. <strong>3D CSFM assumes a zero angle of internal friction </strong>(Fig. 1e), leading to a conservative design due to the plasticity surface resembling the Tresca model, which is independent of the first stress invariant.</p>\n<figure data-asset-id=\"749c6949-1e95-4bb3-a7d6-c4d9e61543b7\" data-image-id=\"749c6949-1e95-4bb3-a7d6-c4d9e61543b7\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/893fb5c9-66fd-4188-a343-c6b088d0d26b/Main%20assumptions%203D.png\" data-asset-id=\"749c6949-1e95-4bb3-a7d6-c4d9e61543b7\" data-image-id=\"749c6949-1e95-4bb3-a7d6-c4d9e61543b7\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 1\\qquad Basic assumptions of the 3D CSFM: (a) principal stresses in concrete; (b) stresses in the reinforcement direction;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(c) stress-strain diagram of concrete in terms of maximum stresses; (d) stress-strain diagram of reinforcement}}}\\) \\( \\textsf{\\textit{\\footnotesize{in terms of stresses at cracks and average strains; (e) Mohr's circles for concrete model in 3D CSFM; (f) bond shear stress-slip}}}\\) \\( \\textsf{\\textit{\\footnotesize{relationship for anchorage length verifications.}}}\\)</em></p>\n<h4>Concrete&nbsp;</h4>\n<p>The presented material model is a multisurface plasticity model given by the combination of the Mohr-Coulomb and Rankine models for monotonic loading. It’s important to note that this model does not address unloading, therefore, state variables are not stored, as they would be in classical plasticity models used for cyclic loading.</p>\n<figure data-asset-id=\"2be61213-d2e5-4d37-80c1-67f0a7176b6f\" data-image-id=\"2be61213-d2e5-4d37-80c1-67f0a7176b6f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c818225e-7dac-4bd4-81f0-8ccbe2ee0200/Mohrs%20plasticity%20surfaces.png\" data-asset-id=\"2be61213-d2e5-4d37-80c1-67f0a7176b6f\" data-image-id=\"2be61213-d2e5-4d37-80c1-67f0a7176b6f\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 2\\qquad Mohr-Coulomb multi-surface plasticity model for friction angle 0 degree}}}\\]</em></p>\n<p>As already mentioned, the material model is intended for use in applications that calculate the response of reinforced concrete (not suitable for plain concrete). This is due to the exclusion of concrete in tension. Therefore, the model is not even suitable for structural elements where the design rules for reinforced concrete such as minimum reinforcement ratio, maximum bar spacing, etc., are not fulfilled. It should also be added that, for numerical stability reasons, a very small tensile capacity is defined in the model. The tensile part is restricted by planes corresponding to the Rankine model.</p>\n<p>3D CSFM in&nbsp;<em>IDEA StatiCa Detail</em>&nbsp;does not consider an explicit failure criterion in terms of strains for concrete in compression (i.e., it considers an infinitely plastic branch after the peak stress is reached). This simplification does not allow the deformation capacity of structures failing in compression to be verified. However, their ultimate capacity is properly predicted when the increase in the brittleness of concrete as its strength rises is considered by means of the&nbsp;𝜂<sub>𝑓𝑐</sub>&nbsp;reduction factor defined in&nbsp;<em>fib</em>&nbsp;Model Code 2010 as follows:</p>\n<p>\\[f_{c,red} = \\eta _{fc} \\cdot f_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>c</sub></em> is the concrete cylinder characteristic strength (in MPa for the definition of <em>\\( \\eta_{fc} \\)</em>).</p>\n<p>The <em>f</em><em><sub>c,red</sub></em> is then compared with the Equivalent Principal Stress σ<em><sub>c,eq</sub></em> in concrete, which will be defined further, of course, with consideration of all safety factors prescribed by code.</p>\n<p>A detailed description of the concrete model can be found at the following link:</p>\n<ul>\n  <li><a data-asset-id=\"ab4d6a64-e6e3-474a-a358-8ba882f37669\" href=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/efa87501-bbfc-4fef-abe1-bc1de8123991/Concrete%20material%20model%20designated%20for%203D%20version.pdf\"><strong>Concrete Material Model for 3D Detail</strong></a></li>\n</ul>\n<h4>Reinforcement</h4>\n<p>The bilinear stress-strain diagram for reinforcement bars, as defined by design codes (Fig. 1d), represents an idealized model. This model necessitates knowledge of the basic properties of the reinforcement during the design phase, specifically the strength and ductility class. Alternatively, users have the option to define a customized stress-strain relationship.</p>\n<p>Tension stiffening is considered by modifying the stress-strain relationship of the bare reinforcing bar to capture the average stiffness of the bars embedded in the concrete (ε<sub>m</sub>) (Fig 1b).</p>\n<h4>Anchorage</h4>\n<p>Bond-slip between reinforcement and concrete is introduced in the finite element model by considering the simplified rigid-perfectly plastic constitutive relationship presented in (Fig. 1f), with&nbsp;<em>f</em><em><sub>bd</sub></em>&nbsp;being the design value (factored value) of the ultimate bond stress specified by the design code for the specific bond conditions.</p>\n<p>This is a simplified model with the sole purpose of verifying bond prescriptions according to design codes (i.e., anchorage of reinforcement). The reduction of the anchorage length when using hooks, loops, and similar bar shapes can be considered by defining a certain capacity at the end of the reinforcement, as will be described further.</p>\n<h4>Anchors</h4>\n<p>The element of the anchor is defined as being able to transfer normal tensile or compression forces, as well as shear forces, considering the bending stiffness.&nbsp;</p>\n<p>The following types of anchors are available:</p>\n<ul>\n  <li>Cast-in-place anchors\n    <ul>\n      <li>Reinforcement</li>\n      <li>Washer plate</li>\n      <li>Headed stud</li>\n    </ul>\n  </li>\n  <li>Cast-in-place reinforcement\n    <ul>\n      <li>Reinforcement</li>\n      <li>Threaded rods</li>\n    </ul>\n  </li>\n</ul>\n<p><br></p>\n<p><strong>Cast-in-place - Reinforcement</strong></p>\n<p>Modeled as ribbed reinforcement embedded in concrete. Bond strength is calculated according to selected code rules in the same way as for standard reinforcement. At the anchor end, an <strong>Anchorage type</strong> can be defined, working identically to reinforcement - an anchorage spring is applied with the β-factor set according to the chosen code. Three geometric shapes are available: <strong>Straight, L-shape, U-shape</strong>.</p>\n<figure data-asset-id=\"f0dc574b-a09f-4237-8d2d-a97d9b04216a\" data-image-id=\"f0dc574b-a09f-4237-8d2d-a97d9b04216a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b7dc2b3e-f3e4-4741-8826-118ea9a6372a/Cast-in-reinforcement%20shapes.png\" data-asset-id=\"f0dc574b-a09f-4237-8d2d-a97d9b04216a\" data-image-id=\"f0dc574b-a09f-4237-8d2d-a97d9b04216a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 3\\qquad Cast-in reinforcement anchor - shapes}}}\\]</em></p>\n<p><strong>Cast-in-place - Washer plate and Headed stud</strong></p>\n<p>The washer plate and the head of the headed stud are modeled as a plate-shell element from the corresponding material attached directly to the anchor shank. It transfers load to the concrete through compression-only contact. Available shapes: circular and square (only circular for headed stud), with customizable dimensions. The washer plate and head model is elastic and is not checked for resistance.&nbsp;</p>\n<p>At the finite element model level, the <strong>pull-out</strong> of the anchor is directly checked. The compression contact has stop criteria set so that it is not able to transfer greater contact stress to the concrete than prescribed by the selected standard. In practical terms, this means that if the anchor were to be loaded with a force that does not comply with the pull-out assessment, the result would be premature termination of the calculation because this stop criterion would be exceeded during further loading.</p>\n<p>The anchor shank has <strong>zero bond strength</strong> – all load is transferred to the concrete through the plate or head into the concrete.</p>\n<p><strong>Post-installed - Reinforcement and Threaded rod</strong></p>\n<p>Designed as bars installed into drilled holes and bonded with adhesive. The engineer specifies the <strong>design bond strength</strong> directly from the technical specification of the adhesive product.</p>\n<p>More information about connecting individual anchor types to the base plate or cast-in plate can be found in the chapter Finite elements types - <a href=\"https://www.ideastatica.com/support-center/idea-statica-detail-structural-design-of-concrete-3d-discontinuities#load-transfer-devices\" title=\"Load transferring devices\">Load transferring devices</a>.&nbsp;</p>"
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    "value": "<p>In the following chapter, we will take a look at how the Mohr-Coulomb theory is implemented in 3D CSFM. We will explain how the confinement effect (triaxial stress) is considered and how the Equivalent Principal Stress σ<em><sub>c,eq</sub></em> is calculated, which is used to determine the load-bearing capacity from the point of view of concrete.</p>\n<h3>Introduction to the theory</h3>\n<p>Mohr–Coulomb theory&nbsp;is a&nbsp;mathematical model&nbsp;describing the response of<strong> </strong>brittle materials, to&nbsp;shear and normal stress. Most of the classical engineering materials follow this rule in at least a part of their shear failure envelope. Generally, the theory applies to materials for which the&nbsp;compressive strength&nbsp;far exceeds the&nbsp;tensile strength.</p>\n<figure data-asset-id=\"0efd9940-94f4-4a5c-845f-4e8a444c8cc4\" data-image-id=\"0efd9940-94f4-4a5c-845f-4e8a444c8cc4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7282915e-1152-48e3-92ed-76a5464967cf/Mohr%20intro.png\" data-asset-id=\"0efd9940-94f4-4a5c-845f-4e8a444c8cc4\" data-image-id=\"0efd9940-94f4-4a5c-845f-4e8a444c8cc4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 4\\qquad Mohr-Coulomb Plasticity Model }}}\\]</em></p>\n<p>In&nbsp;structural engineering,&nbsp;it is used to determine failure load as well as the angle of&nbsp;fracture&nbsp;for displacement of fracture surface in concrete and similar materials.&nbsp;Coulomb's&nbsp;friction&nbsp;hypothesis is used to determine the combination of shear and&nbsp;normal stress&nbsp;that will cause a fracture of the material.&nbsp;Mohr's circle&nbsp;is used to determine which principal stresses will produce this combination of shear and normal stress and the angle of the plane in which this will occur. According to the&nbsp;principle of normality,&nbsp;the stress introduced at failure will be perpendicular to the line describing the fracture condition.&nbsp;</p>\n<figure data-asset-id=\"4962a8ef-007d-48ec-9fb5-8de7f68c9dc0\" data-image-id=\"4962a8ef-007d-48ec-9fb5-8de7f68c9dc0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/cd1f2b6a-98ff-4114-b442-f1ae9463d0c2/01.png\" data-asset-id=\"4962a8ef-007d-48ec-9fb5-8de7f68c9dc0\" data-image-id=\"4962a8ef-007d-48ec-9fb5-8de7f68c9dc0\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 5\\qquad Meridian plane and tension cut-off}}}\\]</em></p>\n<p>It can be shown that a material failing according to Coulomb's friction hypothesis will show the displacement introduced at failure forming an angle to the line of fracture equal to the&nbsp;angle of friction. This makes the strength of the material determinable by comparing the external&nbsp;mechanical work&nbsp;introduced by the displacement and the external load with the internal mechanical work introduced by the&nbsp;strain&nbsp;and stress at the line of failure. By&nbsp;conservation of energy,&nbsp;the sum of these must be zero and this will make it possible to calculate the failure load of the construction.</p>\n<h3>Implementation in 3D CSFM</h3>\n<p>In general, for a given angle of internal friction of the concrete, which is around <em>φ = 30-40° </em>in Reference [1], [2], [3], [4], the tensile and compressive strengths of the concrete Mohr's circles can be constructed as in Figure 6.</p>\n<figure data-asset-id=\"f0359fcd-2033-4b19-a6dd-154dc0bbfa82\" data-image-id=\"f0359fcd-2033-4b19-a6dd-154dc0bbfa82\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7ca2aece-2d9e-4ac9-a3e2-fb9938b610e0/Mohrs%20circles%20for%20real%20concrete.png\" data-asset-id=\"f0359fcd-2033-4b19-a6dd-154dc0bbfa82\" data-image-id=\"f0359fcd-2033-4b19-a6dd-154dc0bbfa82\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 6\\qquad Mohr's circles for concrete}}}\\]</em></p>\n<p>Where <em>f</em><em><sub>c</sub></em> is concrete strength in compression, <em>f</em><em><sub>ct</sub></em> is concrete strength in tension, <em>φ</em> is the angle of internal friction, and σ<em><sub>c</sub></em><sub>1</sub><em>, </em>σ<em><sub>c</sub></em><sub>3</sub> are the principal stresses of concrete under triaxial compression.</p>\n<p>It can be noticed that as the principal stress σ<em><sub>c</sub></em><sub>3</sub> increases, the maximal possible difference between the values of σ<em><sub>c</sub></em><sub>3</sub> and σ<em><sub>c</sub></em><sub>1</sub>, which we define as maximal σ<em><sub>c,eq</sub></em> (see below), also increases. This difference corresponds to twice the deviatoric stress defined in the literature as a radius of the mohr circles.</p>\n<p>In 3D CSFM implemented in IDEA StatiCa Detail, the angle of internal friction is considered as <em>φ = 0°, </em>as shown in Figure 7.</p>\n<figure data-asset-id=\"4ada49d8-d60e-44d9-a343-a0b88366cb7a\" data-image-id=\"4ada49d8-d60e-44d9-a343-a0b88366cb7a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a356c004-fcd0-4557-9209-da5d8264edae/Mohrs%20circles%20for%20concrete%20in%20Detail.png\" data-asset-id=\"4ada49d8-d60e-44d9-a343-a0b88366cb7a\" data-image-id=\"4ada49d8-d60e-44d9-a343-a0b88366cb7a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 7\\qquad Mohr's circles for concrete implemented in IDEA StatiCa Detail}}}\\]</em></p>\n<p>The practical consequence of this implementation is that the maximum difference between σ<em><sub>c</sub></em><sub>3</sub> and σ<em><sub>c</sub></em><sub>1</sub> is constant as σ<em><sub>c</sub></em><sub>3</sub> increases.&nbsp;</p>\n<p><strong>Equivalent Principal Stress expresses the equivalent uni-axial stress for a general tri-axial stress state.</strong></p>\n<p>\\[\\sigma_{c,eq} = \\sigma_{c3} - \\sigma_{c1}\\]</p>\n<p>The σ<em><sub>c,eq</sub></em> value can, therefore, be directly compared with uniaxial strength limits according to codes.</p>\n<p>\\[\\frac{\\sigma_{c,eq} }{ \\sigma_{c,lim}} \\le 1\\]</p>\n<p>Where σ<em><sub>c</sub></em><sub>,lim</sub> is the design (factored) uniaxial strength of concrete <em>f</em><em><sub>c</sub></em>.</p>\n<p>Comparing Figure 6, where the real angle of internal friction is used, and Figure 7, which shows the Mohr-Coulomb theory implementation with zero angle of internal friction, it can be seen that the approach chosen for the calculations in Detail is very conservative for the assessment of triaxial stress state.</p>\n<p>For a better understanding of the areas affected by tri-axial compression stress, the expression of the increase of the effective material strength due to tri-axial compression has been added to the IDEA StatiCa Detail application as a ratio σ<em><sub>c</sub></em><sub>3</sub>/σ<em><sub>c,lim</sub></em>. You can find this ratio in the Strength code check.</p>\n<p>In the Auxiliary results, the user can also find the <em>κ</em> factor, which explains the tri-axiality in a different way.&nbsp;</p>\n<p>\\[\\kappa = &nbsp;&nbsp;\\frac{ \\sigma_{c3}}{ \\sigma_{c,eq}}\\]</p>\n<p>The concrete strength check can be then rewritten as:</p>\n<p>\\[\\frac{\\sigma_{c,eq} }{ \\sigma_{c,lim}} = \\frac{\\sigma_{c,3} }{ \\kappa \\cdot \\sigma_{c,lim}} \\le 1\\]</p>\n<p>It follows from the previous that if the element is under hydrostatic stress - σ<em><sub>c</sub></em><sub>3</sub>=σ<em><sub>c</sub></em><sub>2</sub>=σ<em><sub>c</sub></em><sub>1</sub>, the Equivalent Principal Stress σ<em><sub>c,eq</sub></em> will have the zero value, and the kappa factor will reach infinity.</p>\n<p>More can be found here: <a data-item-id=\"738c9a41-0902-4013-8dd7-87b062dea2a5\" href=\"\"><strong>Tri-axial stress – the active confinement effect</strong></a></p>"
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    "value": "<h3>Equilibrium equations</h3>\n<p>The theory of small deformations enables the assembly of the equilibrium equation based on the undeformed volume using a first-order approach.&nbsp;</p>\n<figure data-asset-id=\"dc9faa89-b191-44d3-b878-b79ed47c82b5\" data-image-id=\"dc9faa89-b191-44d3-b878-b79ed47c82b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c69bee50-7a44-4db5-82f1-11c8bfdb294b/05.png\" data-asset-id=\"dc9faa89-b191-44d3-b878-b79ed47c82b5\" data-image-id=\"dc9faa89-b191-44d3-b878-b79ed47c82b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 8\\qquad Equilibrium equations and graphical representation on infinitesimal element}}}\\]</em></p>\n<h3>Compatibility equations</h3>\n<p>A solid body comprises infinitesimal volumes or material points, each of which is interconnected without gaps or overlaps. Mathematical conditions must be adhered to in order to prevent the occurrence of gaps or overlaps when a continuum body undergoes deformation.</p>\n<h3>Constitutive equations</h3>\n<p>The constitutive equations governing the behavior of 3D elements play a pivotal role in the analysis of material behavior in structural mechanics. These equations are formulated to accommodate the non-linear <strong>isotropic behavior</strong>, which is valid for <strong>solid block </strong>members in IDEA StatiCa Detail.&nbsp;</p>\n<figure data-asset-id=\"e8a9a447-3458-470a-addd-709405e6ba22\" data-image-id=\"e8a9a447-3458-470a-addd-709405e6ba22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/95c6d00e-0cfa-45e0-ac79-d367c7db7960/06.png\" data-asset-id=\"e8a9a447-3458-470a-addd-709405e6ba22\" data-image-id=\"e8a9a447-3458-470a-addd-709405e6ba22\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 9\\qquad Linearly elastic isotropic compliance matrix}}}\\]</em></p>"
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    "value": "<p>El CSFM 3D considera campos de tensión continuos en el hormigón (elementos finitos 3D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 3D del hormigón, sino que se modela explícitamente y se conecta a ellos.</p>\n<figure data-asset-id=\"93c4b062-c8bc-4047-8086-f0c532dee15d\" data-image-id=\"93c4b062-c8bc-4047-8086-f0c532dee15d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97debac7-edd7-4330-8a1a-5ebb7a19e65a/11.png\" data-asset-id=\"93c4b062-c8bc-4047-8086-f0c532dee15d\" data-image-id=\"93c4b062-c8bc-4047-8086-f0c532dee15d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 9\\qquad Representación del modelo de cálculo para bloque de hormigón y muro fuera del plano}}}]</em></p>"
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    "value": "<p>El modelo de análisis de elementos finitos no lineal (inelástico) se crea mediante varios tipos de elementos finitos utilizados para modelizar el hormigón, la armadura y la unión entre ellos. Los elementos de hormigón y armadura se mallan primero de forma independiente y luego se interconectan mediante restricciones multipunto (elementos MPC). Esto permite que la armadura ocupe cualquier posición no limitada a los nodos de la malla tetraédrica. Para verificar la longitud de anclaje, la unión y el extremo de anclaje se insertan elementos de muelle entre la armadura y los elementos MPC.</p>\n<figure data-asset-id=\"4edc33ee-6deb-467c-a229-355e726e5505\" data-image-id=\"4edc33ee-6deb-467c-a229-355e726e5505\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4fdc48d7-668c-4525-8066-92c0cf98fec2/FE%203D%20model.png\" data-asset-id=\"4edc33ee-6deb-467c-a229-355e726e5505\" data-image-id=\"4edc33ee-6deb-467c-a229-355e726e5505\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 10\\qquad Modelo de elementos finitos: elementos de refuerzo mapeados a la malla de hormigón utilizando elementos MPC y de enlace}} {}]</em></p>\n<h4>Hormigón</h4>\n<p>El hormigón se analiza utilizando <strong>elementos tetraédricos mixtos con rotaciones nodales</strong>. Los elementos tetraédricos nos permiten mallar regiones de cualquier topología mientras que la formulación implementada garantiza resultados de deformación precisos (sin esfuerzos cortantes espurios conocidos como efecto shear lock) incluso para la malla gruesa que no sería adecuada para la formulación de elementos tetraédricos lineales.</p>\n<p>Se utiliza la integración completa. Esto significa que cada elemento está equipado con cuatro puntos de integración situados dentro del volumen. Esta integración permite obtener un campo de deformaciones y tensiones preciso, lo que permite evaluar y presentar los resultados de forma suficiente en todo el volumen. Posteriormente, los criterios de parada se establecen en función del valor en el punto de integración.</p>\n<h4>Refuerzo</h4>\n<p>Las armaduras se modelizan mediante elementos \"varilla\" 1D de dos nodos (CROD), que sólo tienen rigidez axial. Estos elementos están conectados a elementos especiales de \"unión\" que se desarrollaron para modelar el comportamiento de deslizamiento entre una barra de refuerzo y el hormigón circundante. Estos elementos de unión se conectan posteriormente mediante elementos MPC (restricción multipunto) a la malla que representa el hormigón. Este planteamiento permite el mallado independiente de la armadura y el hormigón, mientras que su interconexión se garantiza posteriormente.</p>\n<h4>Elementos de unión</h4>\n<p>La longitud de anclaje se verifica implementando los esfuerzos cortantes de enlace entre los elementos de hormigón (3D) y los elementos de armadura (1D) en el modelo de elementos finitos. Para ello, se ha desarrollado el tipo de elemento finito \"enlace\".</p>\n<p>El elemento de unión se define como un elemento finito de cáscara conectado a los elementos que representan el refuerzo por la primera capa y por la segunda capa a la malla de hormigón mediante restricciones multipunto (elementos MPC). Cabe señalar que el elemento de unión siempre se muestra en este artículo con una altura distinta de cero, que, sin embargo, se define como infinitesimal en el modelo.</p>\n<p>El comportamiento de este elemento se describe por la tensión de adherencia, <em><sub>τb</sub></em>, como una función bilineal del deslizamiento entre los nudos superior e inferior, <em>δu</em>, ver (Fig. 11).</p>\n<figure data-asset-id=\"248b8a69-ac53-4d77-ae02-42c07ac5fdb6\" data-image-id=\"248b8a69-ac53-4d77-ae02-42c07ac5fdb6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a833cda6-cf17-4c1f-9f83-c345621c0267/14.png\" data-asset-id=\"248b8a69-ac53-4d77-ae02-42c07ac5fdb6\" data-image-id=\"248b8a69-ac53-4d77-ae02-42c07ac5fdb6\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 11\\qquad (a) Ilustración conceptual de la deformación de un elemento de unión; (b) función cizalladura-deformación}}}]</em></p>\n<p>El módulo de rigidez elástica de la relación adherencia-deslizamiento, <em>Gb</em>, se define como sigue:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}]</p>\n<p>coeficiente <em>kg</em> en función de la superficie de la barra de armadura (por defecto <em>kg</em> = 0,2)</p>\n<p><em><sub>Ec</sub></em> módulo de elasticidad del hormigón (tomado como <em>Ecm</em> en el caso de EN)</p>\n<p>Ø diámetro de la armadura</p>\n<p>Para verificar la longitud de anclaje se utilizan los valores de cálculo (valores factorizados) del esfuerzo cortante último de adherencia, <em><sub>fbd</sub></em>, proporcionados en los respectivos códigos de cálculo seleccionados EN 1992-1-1 o ACI 318-19. El endurecimiento de la rama plástica se calcula por defecto como <em>Gb/105</em>.</p>\n<h4>Muelle de anclaje</h4>\n<p>La provisión de extremos de anclaje a las barras de armadura (es decir, codos, ganchos, lazos...), que cumple las prescripciones de los códigos de diseño, permite reducir la longitud de anclaje básica de las barras<em>(lb</em><em><sub>,net</sub></em>) en un determinado factor β (denominado a continuación \"coeficiente de anclaje\"). El valor de diseño de la longitud de anclaje<em>(lb</em>) se calcula entonces de la siguiente manera:</p>\n<figure data-asset-id=\"72456c32-3fb6-4671-91fa-f288cbc7e1fc\" data-image-id=\"72456c32-3fb6-4671-91fa-f288cbc7e1fc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/92e32489-804f-495a-937e-40b647a0abf1/15.png\" data-asset-id=\"72456c32-3fb6-4671-91fa-f288cbc7e1fc\" data-image-id=\"72456c32-3fb6-4671-91fa-f288cbc7e1fc\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 12\\qquad Modelo para la reducción de la longitud de anclaje: a) Fuerza de anclaje a lo largo de la longitud de anclaje de }}}]. \\[ \\textsf{textit{footnotesize{la barra de refuerzo, b) ley constitutiva de la fuerza de deslizamiento-anclaje}}}]</em></p>\n<p>La reducción de la longitud de anclaje se incluye en el modelo de elementos finitos mediante un elemento muelle en el extremo de la barra (Fig. 12a), que viene definido por el modelo constitutivo mostrado en (Fig. 12b). La fuerza máxima transmitida por este muelle<em>(</em><em><sub>Fau</sub></em>) es:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>donde :</p>\n<p><em>β</em> el coeficiente de anclaje en función del tipo de anclaje</p>\n<p><em><sub>Como</sub></em> la sección transversal de la barra de refuerzo</p>\n<p><em><sub>fyd</sub></em><em> </em>el valor de cálculo (valor factorizado) del límite elástico de la armadura</p>"
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    "value": "<h3>Placa base</h3>\n<p>La placa base se modela como un elemento de envolvente lineal. El material de acero utilizado para las placas base se define en la pestaña Materiales. La única propiedad física es el módulo de elasticidad <em>E</em>.</p>\n<figure data-asset-id=\"26c9d9a5-1064-44e2-8707-eb635d75347f\" data-image-id=\"26c9d9a5-1064-44e2-8707-eb635d75347f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/371f790c-72d7-49be-8247-ade39e45d4d9/Linear%20steel.png\" data-asset-id=\"26c9d9a5-1064-44e2-8707-eb635d75347f\" data-image-id=\"26c9d9a5-1064-44e2-8707-eb635d75347f\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 13\\qquad Definición del material de la placa base}}]</em></p>\n<p>La placa base puede ser cargada por la carga puntual (Fx, Fy, Fz, Mx, My, Mz) y grupo de fuerzas (Fx, Fy, Fz), principalmente utilizado para cargar modelos exportados desde la Conexión IDEA StatiCa. Tenga en cuenta que las cargas y momentos puntuales cargan directamente el nodo correspondiente de la placa base. Esto significa que no hay redistribución, sólo por la rigidez de la placa base.</p>\n<p>Esta implementación permite importar efectos de carga desde IDEA StatiCa Connection que se aplican a la placa base en la ubicación de los elementos finitos de soldadura individuales con el valor y la dirección determinados a partir de la tensión general de ese elemento finito de soldadura. Se puede leer más en el capítulo correspondiente de este documento.</p>\n<p>Entre la placa base y el hormigón se define un contacto de sólo compresión por fricción. Para la <strong>transferencia a cortante</strong> el usuario puede elegir entre tres opciones:</p>\n<ul>\n  <li><strong>Por anclajes</strong></li>\n  <li><strong>Por fricción</strong></li>\n  <li><strong>Por orejeta de cizallamiento</strong></li>\n</ul>\n<p>El software no permite la combinación de estos mecanismos de transferencia de cizalladura.</p>\n<p><strong>El</strong> coeficiente de fricción debe introducirse como valor de diseño (factorizado). En caso de que la fuerza cortante resultante <em><sub>Fxy</sub></em><em> </em>exceda la fuerza de presión <em><sub>Fz</sub></em> veces el coeficiente de fricción <em>μ</em> el cálculo se detendrá y no todas las cargas se aplicarán al modelo. La condición se escribe de la siguiente manera:</p>\n<p>\\[\\frac {F_{xy}}{ \\mu \\cdot F_{z}}le 1\\]</p>\n<p>Esto se puede ver en el siguiente ejemplo en el que se consideran dos casos de carga.</p>\n<ul>\n  <li>LC1 - Tipo permanente - <sub>Fz</sub> = 100 kN</li>\n  <li>LC2 - Tipo variable - <sub>Fx</sub> = 100 kN</li>\n</ul>\n<figure data-asset-id=\"2937e4c9-29aa-4613-9d4e-c44bbc628457\" data-image-id=\"2937e4c9-29aa-4613-9d4e-c44bbc628457\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c9f5d8cb-31be-436c-881b-1ed934e28860/Friction%20-%20load%20input.png\" data-asset-id=\"2937e4c9-29aa-4613-9d4e-c44bbc628457\" data-image-id=\"2937e4c9-29aa-4613-9d4e-c44bbc628457\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 14\\qquad Entrada de carga para el ejemplo que explica la transferencia de cortante por fricción}}]</em></p>\n<p>En el primer paso del cálculo, se aplica toda la carga permanente. A continuación, se aplica gradualmente la carga variable hasta alcanzar el valor de la carga de presión multiplicado por el coeficiente de fricción.</p>\n<figure data-asset-id=\"d506d242-bb4e-41a7-8847-3211617b017d\" data-image-id=\"d506d242-bb4e-41a7-8847-3211617b017d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e430f86d-007d-4b58-8ac3-6c561def378d/Friction%20-%20result.png\" data-asset-id=\"d506d242-bb4e-41a7-8847-3211617b017d\" data-image-id=\"d506d242-bb4e-41a7-8847-3211617b017d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 15\\qquad Resultados del ejemplo que explica la transferencia de cizalladura por fricción}}]</em></p>\n<p>El gráfico de la Figura 16 define el comportamiento del contacto por fricción entre la placa base y el hormigón.</p>\n<figure data-asset-id=\"19efc159-8105-4a48-b356-24e75616f28d\" data-image-id=\"19efc159-8105-4a48-b356-24e75616f28d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e64e31cd-772c-4b95-84c2-b3442e790aa6/Friction%20contact%20graph.png\" data-asset-id=\"19efc159-8105-4a48-b356-24e75616f28d\" data-image-id=\"19efc159-8105-4a48-b356-24e75616f28d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 16\\qquad Gráfico fuerza-desplazamiento que describe el comportamiento del contacto por rozamiento}}]</em></p>\n<p>El valor de <em>Fzμ</em> difiere para cada incremento del cálculo, mientras que el valor de la deformación máxima por cizalladura <em><sub>uxy</sub></em> es constante.</p>\n<p>Si la fuerza normal de compresión <em><sub>Fz</sub></em> y la fuerza de corte <em><sub>Fxy</sub></em> se introducen en un tipo de caso de carga (por ejemplo, sólo permanente), y la condición de <em><sub>Fxy</sub></em><em> / (</em><em><sub>Fzμ</sub></em><em>) ≤ 1</em> no se cumple<em>, </em>no se aplicará ninguna carga al modelo porque la condición no se cumple en ningún incremento del cálculo.</p>\n<p><strong>La orejeta de cortante</strong> está conectada con la malla de hormigón mediante restricciones que sólo permiten la transferencia de tensiones normales a compresión.</p>\n<figure data-asset-id=\"ae58f4f5-1a75-4eac-99f5-9964a720abe5\" data-image-id=\"ae58f4f5-1a75-4eac-99f5-9964a720abe5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f5a88134-312b-4689-9bcd-a77eb0e834e3/Shear%20lug%20transfer.png\" data-asset-id=\"ae58f4f5-1a75-4eac-99f5-9964a720abe5\" data-image-id=\"ae58f4f5-1a75-4eac-99f5-9964a720abe5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 17\\qquad Transferencia de la orejeta de cortante del mecanismo de cortante}}]</em></p>\n<p>La orejeta de cizallamiento se modela a partir de elementos lineales de concha, donde el módulo de elasticidad E define el material.</p>\n<p>Los resultados no se evalúan y se muestran tanto para la placa base como para la orejeta de cizallamiento.</p>\n<h3>Anclajes</h3>\n<p>Los elementos finitos que representan los anclajes se modelan para poder transferir fuerzas normales y cortantes al hormigón, teniendo en cuenta también la rigidez a flexión de los anclajes. Para modelizar el deslizamiento entre el anclaje y el hormigón circundante, se utilizan los mismos elementos de adherencia y MPC que para la armadura. Con la diferencia de que para los anclajes adhesivos es posible especificar la resistencia de adherencia de diseño.</p>\n<p>Los anclajes pueden interconectarse con placas base. Para esta interconexión, se utiliza una restricción totalmente no lineal para conectar el extremo del anclaje y un nodo de la placa base. Este elemento nos permite controlar todos los grados de libertad para garantizar, por ejemplo, que los anclajes no transmitan presión a la placa base sin separación, o que el anclaje no transmita cizalladura al modelar una orejeta de cizalladura, etc.</p>\n<p>Los ajustes de<strong>interconexión con la</strong> placa base para anclajes permiten al usuario controlar si el anclaje se conectará con la placa base mediante la restricción mencionada anteriormente y cómo.</p>\n<figure data-asset-id=\"c07375e3-202a-449e-a4ef-aa55f268fdee\" data-image-id=\"c07375e3-202a-449e-a4ef-aa55f268fdee\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dc2938e5-b707-4f53-a0b6-b795bfef8d4d/Interconnection%20with%20base%20plate%20settings.png\" data-asset-id=\"c07375e3-202a-449e-a4ef-aa55f268fdee\" data-image-id=\"c07375e3-202a-449e-a4ef-aa55f268fdee\" alt=\"\"></figure>\n<p>En la versión actual <strong>sólo</strong> <strong>se admite</strong> <strong>el contacto directo</strong> entre la placa base y el hormigón <strong>.</strong></p>\n<p>La fuerza de compresión no se transfiere de la placa base al anclaje en el caso de Contacto directo. La compresión se transfiere sólo por el contacto entre la placa base y el hormigón.</p>\n<p>La casilla de verificación <strong>Transferencia de fuerzas axiales</strong> puede utilizarse para controlar si el anclaje y la placa base estarán conectados o no en términos de tensión. Esto se utiliza principalmente para la exportación de la función Conexión (véase el capítulo correspondiente). Para el modelado manual, tiene sentido tener esta casilla de verificación siempre marcada.</p>\n<p>La casilla de verificación <strong>Transferencia de cortante</strong> puede utilizarse para controlar si el anclaje y la placa base se conectarán o no en términos de cortante. Tenga en cuenta que no se admite la combinación de mecanismos de transferencia de esfuerzo cortante, por lo que para la transferencia por fricción y la orejeta de esfuerzo cortante, esta casilla de verificación es irrelevante. Por otro lado, para la transferencia a cortante mediante anclajes, este campo da la opción de excluir algunos anclajes de la transferencia a cortante.</p>"
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    "value": "<p>Los elementos finitos se implementan internamente, y el modelo de análisis se genera automáticamente sin necesidad de una interacción competente del usuario. Una parte importante de este proceso es el mallado.</p>\n<h4>Hormigón</h4>\n<p>Todos los elementos de hormigón se mallan juntos. La aplicación calcula automáticamente un tamaño de elemento recomendado basándose en el tamaño y la forma de la estructura y teniendo en cuenta el diámetro de la barra de refuerzo más grande. Además, el tamaño de elemento recomendado garantiza la generación de un mínimo de cuatro elementos en las partes delgadas de la estructura, como pilares esbeltos o muros finos, para garantizar resultados fiables en estas zonas. Los diseñadores siempre pueden seleccionar un tamaño de elemento de hormigón definido por el usuario modificando el multiplicador del tamaño de malla por defecto.</p>\n<h4>Armadura</h4>\n<p>La armadura se divide en elementos con aproximadamente la misma longitud que el tamaño del elemento de hormigón. Una vez generadas las mallas de armadura y hormigón, se interconectan con elementos de unión, como se muestra en la Fig. 9.</p>\n<h4>Refinado</h4>\n<p>La malla de hormigón se refina automáticamente bajo la placa base, alrededor de los anclajes y alrededor de las orejetas de cortante. El tamaño de la malla refinada es por defecto dos veces menor que la malla básica de hormigón. El radio del área refinada se define como el tamaño del elemento multiplicado por dos.</p>"
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        "url": "https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1178a514-d8d2-4a37-a0f2-517809af1881/16.png",
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    "value": "<p>Se utiliza un algoritmo Newton-Raphson (NR) estándar completo para encontrar la solución a un problema MEF no lineal.</p>\n<p>Generalmente, el algoritmo NR no suele converger cuando se aplica toda la carga en un solo paso. Un enfoque habitual, que también se utiliza aquí, es aplicar la carga secuencialmente en múltiples incrementos y utilizar el resultado del incremento de carga anterior para iniciar la solución Newton del siguiente. Para ello, se implementó un algoritmo de control de carga sobre el Newton-Raphson. En caso de que las iteraciones NR no converjan, el incremento de carga actual se reduce a la mitad de su valor y se vuelven a intentar las iteraciones NR.</p>\n<p>Un segundo objetivo del algoritmo de control de carga es encontrar la carga crítica, que corresponde a determinados \"criterios de parada\", en concreto, la deformación máxima del hormigón, el deslizamiento máximo de los elementos de unión, el desplazamiento máximo de los elementos de anclaje y la deformación máxima de las barras de refuerzo. La carga crítica se determina mediante el método de bisección. En caso de que se supere el criterio de parada en algún punto del modelo, se descartan los resultados del último incremento de carga y se calcula un nuevo incremento de la mitad de tamaño que el anterior. Este proceso se repite hasta que se encuentra la carga crítica con una cierta tolerancia de error.</p>\n<p>Para el hormigón, el criterio de parada se fijó en una deformación del 5% en compresión (es decir, alrededor de un orden de magnitud mayor que la deformación de fallo real del hormigón) y del 7% en tracción en los puntos de integración de los elementos de cáscara. En tracción, el valor se fijó para permitir que se alcanzara primero la deformación límite en la armadura, que suele estar en torno al 5% sin tener en cuenta la rigidización por tracción. En compresión, el valor se eligió entre varias alternativas como uno lo suficientemente grande para que los efectos del aplastamiento sean visibles en los resultados, pero lo suficientemente pequeño para no causar demasiados problemas con la estabilidad numérica.</p>\n<figure data-asset-id=\"f52823d4-6603-4d3a-8405-71c3d8d92ddd\" data-image-id=\"f52823d4-6603-4d3a-8405-71c3d8d92ddd\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1178a514-d8d2-4a37-a0f2-517809af1881/16.png\" data-asset-id=\"f52823d4-6603-4d3a-8405-71c3d8d92ddd\" data-image-id=\"f52823d4-6603-4d3a-8405-71c3d8d92ddd\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig 13\\qquad Ley constitutiva de los elementos de enlace y anclaje utilizados para la verificación de la longitud de anclaje: a) Tensión de cizalladura de enlace}}] \\respuesta al deslizamiento de un elemento de unión, b) respuesta fuerza-desplazamiento de un elemento de anclaje}}.</em></p>\n<p>Para el refuerzo, el criterio de parada se define en términos de tensiones. Dado que se modelizan las tensiones en la fisura, el criterio en tracción corresponde a la resistencia a tracción de la armadura teniendo en cuenta el coeficiente de seguridad. El mismo valor se utiliza para el criterio en compresión.</p>\n<p>El criterio de detención en elementos de unión y muelles de anclaje es <em><sub>α-δumax</sub></em>, donde <em><sub>δumax</sub></em> es el deslizamiento máximo utilizado en las comprobaciones del código y α = 10.</p>"
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    "value": "<p>Los resultados se presentan independientemente para el hormigón y para los elementos de refuerzo. Los valores de tensión y deformación en el hormigón se calculan en los puntos de integración de los elementos de volumen. Sin embargo, como no resulta práctico presentar los datos de esta manera, los resultados se presentan por defecto en nudos, como el valor máximo de la tensión de compresión a partir de puntos de integración de Gauss adyacentes en elementos conectados. Debe tenerse en cuenta que esta representación podría subestimar localmente los resultados en los bordes comprimidos de las barras en un caso en el que el tamaño del elemento finito sea similar a la profundidad de la zona de compresión.</p>\n<p>Los resultados de los elementos finitos de refuerzo son constantes para cada elemento (un valor - por ejemplo, para las tensiones del acero) o lineales (dos valores - para los resultados de las uniones). Para los elementos auxiliares, como los elementos de las placas de apoyo, sólo se presentan las deformaciones.</p>"
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    "value": "<p>El modelo IDEA Statica Detail no siempre tiene que ser modelado desde cero o desde una plantilla. También existe la opción de importar el modelo incluyendo los efectos de carga desde IDEA StatiCa Connection. La geometría del bloque de hormigón, los anclajes, la placa base, los materiales y los efectos de carga se transfieren.</p>\n<figure data-asset-id=\"10a571a8-c649-479f-a6a1-775847ff787b\" data-image-id=\"10a571a8-c649-479f-a6a1-775847ff787b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4d9e99b1-b39c-4b40-876a-1bb351b6f5c8/Connection%20export.png\" data-asset-id=\"10a571a8-c649-479f-a6a1-775847ff787b\" data-image-id=\"10a571a8-c649-479f-a6a1-775847ff787b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 16\\qquad Cargas importadas desde IDEA StatiCa Connection}}}]</em></p>\n<p>La placa base está cargada por un grupo de fuerzas determinadas a partir de la tensión general de cada elemento finito de las soldaduras que conectan el miembro de acero y la placa base.</p>\n<p>Dado que la definición de los componentes individuales es diferente en Conexión y Detalle (por ejemplo, la placa base se modela mediante un material lineal en Detalle mientras que en Conexión se modela mediante un material plástico), habría una redistribución diferente de las cargas entre el contacto placa base-hormigón y los anclajes, o entre los propios anclajes. En otras palabras, habría diferentes fuerzas normales de tracción en los anclajes en Conexión y Detalle. Por este motivo, los anclajes se importan desconectados para fuerzas normales (en la dirección del anclaje) de la placa base, y los anclajes se cargan directamente con las fuerzas de tracción aplicadas. Además, deben añadirse las fuerzas opuestas que cargan la placa base situada en la ubicación del anclaje para que el modelo alcance el equilibrio. Estas dos fuerzas opuestas se muestran en la figura 16.</p>\n<p>Sin embargo, las fuerzas de cizallamiento se transfieren mediante la interconexión de la placa base y el anclaje (o orejeta de cizallamiento, o fricción). Este comportamiento es posible porque existe una restricción que conecta la placa base y el anclaje que nos permite controlar todos los grados de libertad de esta interconexión.</p>"
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    "value": "<h3>Estado límite último</h3>\n<p>Las diferentes verificaciones exigidas por los códigos de diseño específicos se evalúan a partir de los resultados directos proporcionados por el modelo. Las verificaciones de los estados límite últimos se realizan para la resistencia del hormigón, la resistencia de la armadura y el anclaje (esfuerzos cortantes de adherencia).</p>\n<p>Para garantizar que un elemento estructural tiene un diseño eficiente, es muy recomendable ejecutar un análisis preliminar que tenga en cuenta los siguientes pasos:</p>\n<ul>\n  <li>Elegir una selección de las combinaciones de carga más críticas.</li>\n  <li>Calcular sólo las combinaciones de carga de Estado Límite Último (ELU).</li>\n  <li>Para acelerar el tiempo de cálculo y resolver cualquier problema, considere la posibilidad de utilizar una malla gruesa aumentando el multiplicador del tamaño de malla por defecto en la Configuración (Fig. 14). Si el modelo funciona bien, revierta el multiplicador a un factor de 1.</li>\n</ul>\n<figure data-asset-id=\"ef499945-27e1-4fef-94af-ddfedd4e15bd\" data-image-id=\"ef499945-27e1-4fef-94af-ddfedd4e15bd\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1633c630-1610-428f-9f76-d50d4d8ce8c2/18.png\" data-asset-id=\"ef499945-27e1-4fef-94af-ddfedd4e15bd\" data-image-id=\"ef499945-27e1-4fef-94af-ddfedd4e15bd\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig 14\\qquad Multiplicador de malla}}}]</em></p>\n<p>Un modelo de este tipo calculará muy rápidamente, permitiendo a los diseñadores revisar el detallado del elemento estructural de manera eficiente y volver a ejecutar el análisis hasta que se cumplan todos los requisitos de verificación para las combinaciones de carga más críticas. Una vez cumplidos todos los requisitos de verificación de este análisis preliminar, se sugiere incluir todas las combinaciones de carga última y utilizar un tamaño de malla fino (el tamaño de malla recomendado por el programa). Los usuarios pueden cambiar el tamaño de malla mediante el multiplicador, que puede alcanzar valores de 0,5 a 5 (Fig. 14).</p>\n<p>Los resultados básicos y las verificaciones (tensión, deformación y utilización (es decir, el valor calculado/valor límite del código)), así como la dirección de las tensiones principales en el caso de elementos de hormigón) se muestran mediante diferentes gráficos donde la compresión se presenta generalmente en rojo y la tensión en azul. Se pueden resaltar los valores mínimos y máximos globales de toda la estructura, así como los valores mínimos y máximos de cada parte definida por el usuario. En una pestaña separada del programa, pueden mostrarse resultados avanzados como los valores de los tensores, las deformaciones de la estructura y las relaciones de armadura (efectiva y geométrica) utilizadas para calcular la rigidez a tracción de las barras de armadura. Además, pueden presentarse las cargas y reacciones para combinaciones o casos de carga seleccionados.</p>"
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    "value": "<h3>Hormigón - ULS</h3>\n<p>El modelo de hormigón implementado en 3D CSFM se basa en las leyes constitutivas de compresión uniaxial prescritas por EN 1992-1-1 para el cálculo de secciones transversales, que sólo dependen de la resistencia a la compresión. El diagrama parábola-rectángulo especificado en EN 1992-1-1 Cl. 3.1.7 (1) (Fig. 15a) se utiliza por defecto en 3D CSFM, pero los diseñadores también pueden elegir una relación plástica ideal elástica más simplificada de acuerdo con EN 1992-1-1 Cl. 3.1.7 (2) (Fig. 15b). La resistencia a la tracción se desprecia, como en el diseño clásico de hormigón armado.</p>\n<figure data-asset-id=\"b2fb51e7-b2de-4a4f-a36c-fe77b2c4d056\" data-image-id=\"b2fb51e7-b2de-4a4f-a36c-fe77b2c4d056\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/48e6b672-8f00-481a-8f1c-87d1c46a175d/SS%20diagrams%20conc.png\" data-asset-id=\"b2fb51e7-b2de-4a4f-a36c-fe77b2c4d056\" data-image-id=\"b2fb51e7-b2de-4a4f-a36c-fe77b2c4d056\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig 15\\qquad Diagramas tensión-deformación del hormigón para ULS: a) diagrama parábola-rectángulo; b) diagrama bilineal}}}]</em></p>\n<p>La implementación de CSFM 3D en <em>IDEA StatiCa Detail</em> no considera un criterio de fallo explícito en términos de deformaciones para el hormigón en compresión (es decir, después de alcanzar la tensión máxima, considera una rama plástica con <sub>εcu2</sub> (<sub>εcu3</sub>) en un valor del 5% mientras que EN 1992-1-1 asume una deformación última inferior al 0,35%). Esta simplificación no permite verificar la capacidad de deformación de las estructuras que fallan en compresión. Sin embargo, su capacidad última <em><sub>fcd</sub></em> según EN 1992-1-1 3.1.3 se predice correctamente cuando el aumento de la fragilidad del hormigón a medida que aumenta su resistencia se considera mediante el factor de reducción \\ <em>(\\eta_{fc}\\)</em> definido en el Código Modelo <em>fib</em> 2010 de la siguiente manera:</p>\n<p>\\[f_{cd}={\\alpha_{cc}} \\cdot \\frac{f_{ck,red}}{γ_c} = {\\alpha_{cc}} \\...frac... feta...fc... \\f_{ck}{γ_c}]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{ck}}}}} \\right)^{\\frac{1}{3}} \\le 1\\]</p>\n<p>donde:</p>\n<p><em><sub>αcc</sub></em> es el coeficiente que tiene en cuenta los efectos a largo plazo sobre la resistencia a la compresión y los efectos desfavorables derivados de la forma de aplicar la carga. Es conforme a la norma EN 1992-1-1 Cl. 3.1.6 (1). El valor por defecto es 1,0.</p>\n<p><em><sub>fck</sub></em> es la resistencia característica del cilindro de hormigón (en MPa para la definición de \\ <em>( \\eta_{fc} \\)</em>).</p>\n<h3>Refuerzo</h3>\n<p>Por defecto, se considera el diagrama tensión-deformación bilineal idealizado para las armaduras desnudas definido en EN 1992-1-1, sección 3.2.7 (Fig. 16). La definición de este diagrama sólo requiere conocer las propiedades básicas de la armadura durante la fase de diseño (clase de resistencia y ductilidad). Siempre que se conozcan, se puede considerar la relación tensión-deformación real de la armadura (laminada en caliente, trabajada en frío, templada y autotemplada, ...). El diagrama tensión-deformación de la armadura puede ser definido por el usuario, pero en este caso es imposible asumir el efecto de rigidización por tracción (es imposible calcular la anchura de la fisura). La utilización del diagrama tensión-deformación con una rama superior horizontal no permite verificar la durabilidad estructural. Por lo tanto, es necesaria la verificación manual de los requisitos de ductilidad estándar.</p>\n<figure data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/47fb26f0-9509-403c-ac42-7d68821d59d1/Steel%20stress-strain%20diagram%20CSFM.PNG\" data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 16 \\qquad Diagrama tensión-deformación de la armadura: a) diagrama bilineal con una rama superior inclinada; b) diagrama bilineal}}]. \\con una rama superior horizontal.</em></p>\n<p>La rigidización por tracción (Fig. 17) se tiene en cuenta automáticamente modificando la relación tensión-deformación de entrada de la barra de refuerzo desnuda para capturar la rigidez media de las barras embebidas en el hormigón (<em><sub>εm</sub></em>).</p>\n<figure data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/111ff130-8480-486a-adca-4c0068bcf66e/Tension%20stiffening%20CSFM.PNG\" data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 17\\qquad Esquema de rigidización a tracción.}}]</em></p>"
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    "value": "<p>The Compatible Stress Field Method is compliant with modern design codes. As the calculation models only use standard material properties, the partial safety factor format prescribed in the design codes can be applied without any adaptation. In this way, the input loads are factored, and the characteristic material properties are reduced using the respective safety coefficients prescribed in design codes, exactly as in conventional concrete analysis. Values of material safety factors prescribed in EN 1992-1-1 chap. 2.4.2.4 are set by default, but the user can change safety factors in the Code and calculation settings (Fig. 18).</p>\n<figure data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4cadae4a-9a8a-4f9b-935c-51395116ed4e/Material%20factors.png\" data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 18\\qquad The setting of &nbsp;material safety factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p>Load safety factors have to be defined by the user in Combination rules for each non-linear combination of load cases (Fig. 19). For all templates implemented in <a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\">Idea StatiCa Detail</a>, partial safety factors are already predefined.</p>\n<figure data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2d2607d1-29e9-4dfd-80ef-db2ba7d172bf/Combination%20factors.png\" data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad The setting of&nbsp; load partial factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p>By using appropriate user-defined combinations of partial safety factors, users can also compute with 3D CSFM using the global resistance factor method (Navrátil, et al. 2017), but this approach is hardly ever used in design practice. Some guidelines recommend using the global resistance factor method for non-linear analysis. However, in simplified non-linear analyses (such as 3D CSFM), which only require those material properties that are used in conventional hand calculations, it is still more desirable to use the partial safety format.</p>"
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    "value": "<p>Las diferentes verificaciones exigidas por la norma EN 1992-1-1 se evalúan a partir de los resultados directos proporcionados por el modelo. Las verificaciones ULS se llevan a cabo para la resistencia del hormigón, la resistencia de la armadura y el anclaje (esfuerzos cortantes de adherencia).</p>\n<p>La <strong>resistencia</strong> del <strong>hormigón</strong> en compresión se evalúa como la relación entre la tensión principal equivalente máxima σc<em><sub>,eq </sub></em>obtenida del análisis de EF y el valor límite σc<em><sub>,lim</sub></em> = <em><sub>fcd</sub></em>.</p>\n<p><strong>La tensión principal equivalente expresa la tensión uniaxial equivalente para un estado de tensión triaxial general.</strong></p>\n<p>\\[\\sigma_{c,eq} = \\sigma_{c3} - \\sigma_{c1}\\]</p>\n<p>El valor σc<em><sub>,eq</sub></em> puede, por tanto, compararse directamente con los límites de resistencia uniaxial según 1992-1-1 Cl. 3.1.7 (1).</p>\n<p>Esta expresión se deriva de la aplicación de la teoría de la plasticidad de Mohr-Coulomb, suponiendo de forma conservadora el ángulo de rozamiento interno φ <em>= 0°.</em></p>\n<p>La <strong>resistencia de la armadura</strong> se evalúa tanto en tracción como en compresión como la relación entre la tensión en la armadura en las fisuras <em><sub>σsr</sub></em> y el valor límite especificado σs<em><sub>,lim</sub></em>:</p>\n<p>\\(σ_{s,lim} = \\frac{k \\cdot f_{yk}}{γ_s}{qquad\\qquad\\textsf{\\small{para diagrama bilineal con rama superior inclinada}})</p>\n<p>\\(σ_{s,lim} = \\frac{f_{yk}{γ_s}qquad\\qquad\\textsf{\\small{para diagrama bilineal con rama superior horizontal})</p>\n<p>donde:</p>\n<p><em><sub>fyk</sub></em> es el límite elástico de la armadura según EN 1992-1-1 Cl. 3.2.3,</p>\n<p><em>k</em> es la relación entre la resistencia a la tracción<em><sub>ftk</sub></em> y el límite elástico,<br>\\(k = \\frac{f_{tk}}{f_{yk}})</p>\n<p><em>γs</em><sub> es </sub>el factor de seguridad parcial de la armadura.</p>\n<p>El <strong>esfuerzo cortante</strong> de adherencia se evalúa independientemente como la relación entre el esfuerzo de adherencia <em><sub>τb</sub></em> calculado mediante el análisis de EF y la resistencia última de adherencia <em><sub>fbd</sub></em><sub>,</sub> de acuerdo con la norma EN 1992-1-1 cap. 8.4.2: \"Esfuerzos de adherencia\". 8.4.2:</p>\n<p>\\[\\frac{τ_{b}}{f_{bd}}le 1\\].</p>\n<p>\\[f_{bd} = 2,25 \\cdot η_1\\cdot η_2\\cdot f_{ctd}\\]</p>\n<p>donde:</p>\n<p><em><sub>fctd</sub></em><sub> </sub>es el valor de cálculo de la resistencia a tracción del hormigón según EN 1992-1-1 Cl. 3.1.6 (2). Debido a la creciente fragilidad del hormigón de mayor resistencia, <em>fctk</em><em><sub>,0.05</sub></em><sub> </sub>se limita al valor para C60/75 según EN 1992-1-1 Cl. 8.4.2 (2)</p>\n<p><sub>η1</sub> es un coeficiente relacionado con la calidad del estado de adherencia y la posición de la barra durante el hormigonado (Fig. 31).</p>\n<p><sub>η1</sub> = 1,0 cuando se obtienen condiciones \"buenas\" y</p>\n<p><sub>η1</sub> = 0,7 para todos los demás casos y para barras en elementos estructurales construidos con encofrados deslizantes, a menos que pueda demostrarse que existen \"buenas\" condiciones de adherencia</p>\n<p><sub>η2</sub> está relacionado con el diámetro de la barra:</p>\n<p><sub>η2</sub> = 1,0 para Ø ≤ 32 mm</p>\n<p><sub>η2</sub> = (132 - Ø)/100 para Ø &gt; 32 mm</p>\n<figure data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7aa307dc-3cd6-4d42-8dd8-d0ff97994677/Bond%20conditions.PNG\" data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 20\\qquad EN 1992-1-1 Figura 8.2 - Descripción de las condiciones de adherencia.}}]</em></p>\n<p>En IDEA StatiCa Detail, las condiciones de adherencia se tienen en cuenta según la Fig. 20 c) y d). La dirección del hormigonado puede establecerse en la aplicación para cada elemento del proyecto de la siguiente manera:</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 21\\qquadirección del hormigonado}}]</em></p>\n<p>Estas comprobaciones se realizan con respecto a los valores límite apropiados para las respectivas partes de la estructura (es decir, a pesar de tener una única calidad tanto para el hormigón como para el material de la armadura, los diagramas tensión-deformación finales diferirán en cada parte de la estructura debido a los efectos de rigidización por tracción y ablandamiento por compresión).</p>\n<p><strong>Fuerza total </strong><strong><em><sub>Ftot</sub></em></strong><strong> y fuerza límite </strong><strong><em><sub>Flim</sub></em></strong></p>\n<p>La fuerza total <strong><em><sub>Ftot</sub></em></strong> es el resultado del análisis de elementos finitos y puede definirse de dos maneras.</p>\n<p>\\[F_{tot}=A_{s}\\cdot \\sigma_{s}\\]</p>\n<p>donde<em><sub>As</sub></em> es el área de la barra de refuerzo y <em><sub>σs</sub></em> es la tensión en la barra.</p>\n<p>O como suma de la fuerza de anclaje<em><sub>Fa y </sub></em>la fuerza de adherencia <em><sub>Fbond</sub></em><em>.</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>donde<em><sub>Fa</sub></em> es la fuerza real en el muelle de anclaje y <em><sub>Fbond</sub></em> es la fuerza de adherencia que puede obtenerse integrando la tensión de adherencia <em><sub>τb</sub></em> a lo largo de la longitud de la barra de armadura <em>l.</em></p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p><sub>Cs</sub> es la circunferencia de la barra de refuerzo.</p>\n<p>La fuerza límite<strong><em><sub>Flim</sub></em></strong> es la fuerza máxima en el elemento de la barra de refuerzo teniendo en cuenta la <strong>resistencia última</strong> de la barra de refuerzo y también <strong>las condiciones de anclaje </strong>(unión entre el hormigón y la armadura y ganchos de anclaje, bucles, etc.).</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=k\\cdot f_{yd}\\cdot A_{s}]</p>\n<p>\\F_{au}=beta k\\cdot f_{yd}\\cdot A_{s}]</p>\n<p>\\F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bd}\\cdot A_{s}]</p>\n<p>donde <sub>Cs</sub> es la circunferencia de la barra de refuerzo, y <em>l</em> es la longitud desde el comienzo de la barra de refuerzo hasta el punto de interés.</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 22\\qquad Definición de la fuerza límite Flim}}}]</em></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>donde<em><sub>Flim,add</sub></em> es la fuerza adicional calculada a partir de la magnitud del ángulo entre elementos vecinos.<em><sub>Flim,2</sub></em> debe ser siempre inferior a<em><sub>Fu</sub></em>.</p>\n<p>Los <strong>tipos de anclaje</strong> disponibles en 3D CSFM incluyen una barra recta (es decir, sin reducción del extremo del anclaje), curva, gancho, bucle, barra transversal soldada, unión perfecta y barra continua. Todos estos tipos, junto con los respectivos coeficientes de anclaje β, se muestran en la Fig. 23 para la armadura longitudinal y en la Fig. 24 para los estribos. Los valores de los coeficientes de anclaje adoptados están de acuerdo con la norma EN 1992-1-1 sección 8.4.4 Tab. 8.2. Cabe señalar que a pesar de las diferentes opciones disponibles, 3D CSFM distingue tres tipos de extremos de anclaje: (i) sin reducción de la longitud de anclaje, (ii) una reducción del 30% de la longitud de anclaje en el caso de un anclaje normalizado, y (iii) unión perfecta.</p>\n<figure data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b16975dc-aeea-4e7e-bfc7-23a8f8b28c7e/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 23\\qquad Tipos de anclaje disponibles y coeficientes de anclaje respectivos para barras de refuerzo longitudinal en el CSFM 3D:}}}]</em></p>\n<p><em>\\(a) barra recta; (b) curva; (c) gancho; (d) bucle; (e) barra transversal soldada; (f) unión perfecta; (g) barra continua.</em></p>\n<figure data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/86ffb525-5912-4a7f-9576-fff17481b7a1/Available%20anchorage%20types%20for%20stirrups.png\" data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 24\\qquad Tipos de anclaje disponibles y coeficientes de anclaje respectivos para estribos.}}]</em></p>\n<p><em>\\Estribos cerrados: (a) gancho; (b) curva; (c) solapamiento. Estribos abiertos: (d) gancho; (e) barra continua.]</em></p>\n<p>Para cumplir con la norma EN 1992-1-1, se debe utilizar el muelle de anclaje en el cálculo, el muelle de anclaje se modifica por el coeficiente β por lo que el usuario debe utilizar uno de los tipos de anclaje disponibles al definir las condiciones de inicio y final de la armadura.</p>"
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    "value": "<h3>Hormigón - Resistencia</h3>\n<p>El modelo de hormigón implementado para los cálculos de resistencia en el CSFM se basa en la curva de tensión-deformación parabólico-plástica para hormigón basada en la curva de tensión-deformación parabólica de la Asociación de Cemento Portland descrita en las Notas de PCA sobre los Requisitos del Código de Construcción ACI 318-99 para el Hormigón Estructural, Figura 6-8. La resistencia a la tracción se desprecia, al igual que en el diseño clásico de hormigón armado. La resistencia a la tracción se desprecia, como en el diseño clásico del hormigón armado.</p>\n<figure data-asset-id=\"839fc455-78ea-4fa5-b0a2-d05127192ead\" data-image-id=\"839fc455-78ea-4fa5-b0a2-d05127192ead\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dade5431-c749-41c4-a9be-e4e5ebb96462/SS%20diagrams%20conc%20-%20ACI.png\" data-asset-id=\"839fc455-78ea-4fa5-b0a2-d05127192ead\" data-image-id=\"839fc455-78ea-4fa5-b0a2-d05127192ead\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 38\\qquad Diagrama tensión-deformación del hormigón para el análisis de resistencia}}]</em></p>\n<p>La implementación del CSFM en <em>IDEA StatiCa Detail</em> no considera un criterio de fallo explícito en términos de deformaciones para el hormigón en compresión (es decir, después de alcanzar la tensión pico considera una rama plástica con <sub>εc0</sub> en valor máximo 5% mientras que ACI 318-19 Cl. 22.2.2.1 asume una deformación última menor que 0.3%). Esta simplificación no permite verificar la capacidad de deformación de las estructuras que fallan en compresión. Sin embargo, la resistencia se predice correctamente cuando el aumento de la fragilidad del hormigón a medida que aumenta su resistencia se considera mediante el factor de reducción \\ <em>(\\eta_{fc}\\)</em> definido en el Código Modelo <em>fib</em> 2010 de la siguiente manera:</p>\n<p>\\[f'_{c,lim}=\\alpha_{1}\\cdot\\phi_{c}\\cdot \\eta _{fc}\\cdot f'_{c}\\].</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}} \\le 1\\]</p>\n<p>donde:</p>\n<p><sub>α1</sub> es el factor de reducción de la resistencia a compresión del hormigón definido en ACI 318-19 Cl. 22.2.2.4.1. Cuando se utiliza un diagrama tensión-deformación parábola-rectángulo, es necesario reducir la tensión máxima de compresión por este factor. Esto promedia la distribución de la tensión en la zona de compresión de tal manera que la resistencia a la compresión resultante es menor o igual a la resistencia a la compresión calculada utilizando un diagrama tensión-deformación con una rama plástica decreciente<em>.</em></p>\n<p><em>Φc</em><em><sub>es </sub></em>el factor de reducción de la resistencia del hormigón. El valor por defecto se establece de acuerdo con ACI 318-19 Tabla 24.2.1 (b)(f).</p>\n<p><em>f'</em><em><sub>c</sub></em> es la resistencia cilíndrica del hormigón (en MPa para la definición de \\ <em>( \\eta_{fc} \\)</em>).</p>\n<h3>Refuerzo</h3>\n<p>Se considera un diagrama tensión-deformación perfectamente elasto-plástico con un límite elástico definido para la armadura no pretensada. Véase ACI 319-19 CL. 20.2.1. La definición de este diagrama sólo requiere conocer las propiedades básicas de la armadura: resistencia y módulo de elasticidad.</p>\n<p>El diagrama tensión-deformación de la armadura también puede ser definido por el usuario, pero en este caso, es imposible asumir el efecto de rigidización por tracción.</p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 42 \\qquad Diagrama tensión-deformación de la armadura}}]</em></p>\n<p>donde:</p>\n<p><em>Φs</em><em><sub>es </sub></em>el factor de reducción de resistencia de la armadura. El valor por defecto se establece de acuerdo con ACI 318-19 Tabla 24.2.1.</p>\n<p><em><sub>fy</sub></em> es el límite elástico de la armadura</p>\n<p><em><sub>Es</sub></em> el módulo de elasticidad de la armadura</p>\n<p>Se selecciona el 10% como deformación límite en la que se detiene el cálculo. Este valor se considera seguro según el artículo 7 de ASTM A955/A955M-20c.</p>\n<p>La rigidez por tracción (Fig. 43) se tiene en cuenta automáticamente modificando la relación tensión-deformación de entrada de la barra de refuerzo desnuda para capturar la rigidez media de las barras embebidas en el hormigón (<em><sub>εm</sub></em>).</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 43\\qquad Esquema de rigidización a tracción.}}]</em></p>"
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                    "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                    "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. IDEA StatiCa offers a fully customizable report to print out or save in an editable format.</p>\n<figure data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6e3c18c1-a97e-4301-8ee4-31b1ed278382/6_1%20Report.png\" data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" alt=\"\"></figure>\n<figure data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/33137b76-efe1-4357-a046-99a24413aa88/6_2%20Report.png\" data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" alt=\"\"></figure>\n<p>You have designed, optimized, and code-checked a pier cap according to Eurocode.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"idea_statica_tutorial___pier_cap_from_dxf_2495f70\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"campus_cta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0d61cad8_c463_0160_5df5_bb66b7a55152\"></object>"
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                            "value": "Los muros de hormigón y las vigas profundas son elementos portantes habituales en las estructuras de los edificios. Sin embargo, debido a los requisitos de trazado, estas estructuras portantes se ven muy a menudo debilitadas por puertas, ventanas y otras aberturas."
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                            "value": "<h4>¿Muro de hormigón armado o vigas profundas con verificación de códigos completa? No hay problema.</h4>\n<p>El objetivo del webinar es presentar cómo realizar en minutos la comprobación de código de una <strong>viga profunda de forma general</strong> en <strong>IDEA StatiCa Detail</strong> en conexión con los resultados de la aplicación de AEF. Mostraremos el flujo de trabajo en un ejemplo de un edificio residencial de hormigón - exportando la geometría, creando el submodelo en IDEA StatiCa Detail, aplicando las <strong>cargas correctas</strong>, el diseño de la armadura, y el código de comprobación final para los <strong>estados</strong> <strong>límite últimos y de servicio</strong>.</p>\n<p>Pruébelo usted mismo - obtenga la <a data-item-id=\"0c872071-6a3f-4b99-8cd4-66440db9cc0d\" href=\"\">licencia de prueba gratuita</a> y siga el tutorial paso a paso en <a data-item-id=\"1dc3667d-ddd6-5483-8b97-e7b69923fef7\" href=\"\">Muro de hormigón</a>.</p>\n<figure data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/177694cc-5c91-42cb-b88c-568f900670fe/Code-check%20of%20walls%20and%20deep%20beams.png\" data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\" alt=\"\"></figure>\n<h4>La solución definitiva para detalles y piezas estructurales de hormigón</h4>\n<p>El software de AEF 3D habitual tiene en cuenta el comportamiento lineal del hormigón. El diseño y las comprobaciones de código de la armadura son limitados, especialmente para el <strong>estado límite de servicio</strong> que puede conducir al desarrollo de <strong>grietas excesivas</strong>. Todo esto está cubierto dentro de la aplicación IDEA StatiCa Detail <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">basada en CSFM</a>. Ahora, todos los ingenieros pueden diseñar y comprobar eficientemente muros o vigas profundas de cualquier forma y muchas más.</p>\n<p>Si desea ver más de <strong>IDEA StatiCa Detail </strong>en acción, hay otros dos seminarios web grabados para ver:</p>\n<ul>\n  <li><a data-item-id=\"1300fb1c-8e32-47f3-8b21-0e8e77e1f238\" href=\"\">¿Cómo diseñar fácilmente una viga pretensada con aberturas?</a></li>\n  <li><a data-item-id=\"73d449cf-610e-5c7c-9e8c-da8093630d24\" href=\"\">Muro colado in situ - Ruzomberok (Eslovaquia)</a></li>\n</ul>\n<p>O navegue por nuestro Centro de soporte para ver <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&amp;label=detail\" title=\"IDEA StatiCa Detail\">tutoriales</a> y leer los <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">fundamentos teóricos.</a></p>\n<h3>Grabación del seminario web</h3>"
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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    "value": "<p>The Compatible Stress Field Method is compliant with modern design codes. As the calculation models only use standard material properties, the partial safety factor format prescribed in the design codes can be applied without any adaptation. In this way, the input loads are factored, and the characteristic material properties are reduced using the respective strength reduction factors, exactly as in conventional concrete analysis.</p>\n<p>Values of <strong>strength reduction factors</strong> are prescribed in ACI 318-19 Cl. 21.2. The default values for concrete and reinforcement are chosen based on the assumption that the typical example solved in the application is shear-controlled (based on Table 21.2.1 (b), (f), (g)). However, it is possible to model any type of element. Therefore, if a compression or tension-controlled element is assessed, the user has the option to change the strength reduction factor value in the Preferences.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 42\\qquad The setting of strength reduction factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p><strong>Load factors</strong> for Strength combinations shall be defined according to ACI 318-19 Table 5.3.1.</p>\n<p>Except as stated in Chapter 34, service-level load combinations are not defined in ACI 318-19. It is recommended to use combination rules based on Appendix C of ASCE/SEI 7-16. For all templates, load factors are already predefined.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 43\\qquad The setting of&nbsp;load factors in IDEA StatiCa Detail.}}}\\]</em></p>"
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                    "value": "<h4>Crack width calculation</h4>\n<p>There are two ways of computing crack widths - stabilized and non-stabilized cracking. According to the geometrical reinforcement ratio in each part of the structure is decided, which type of crack calculation model will be used (TCM for stabilized cracking and POM for non-stabilized cracking model).</p>\n<figure data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62ba3929-8689-4973-8782-fcdd0780002b/Crack%20width%20calculation.PNG\" data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" alt=\"Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 20 \\qquad Crack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal}}}\\) \\( \\textsf{\\textit{\\footnotesize{directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with}}}\\) \\( \\textsf{\\textit{\\footnotesize{local&nbsp;non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar}}}\\)\\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking.}}}\\)</em></p>\n<p><br></p>\n<p>While the CSFM yields a direct result for most verifications (e.g., member capacity, deflections…), crack width results are calculated from the reinforcement strain results directly provided by FE analysis following the methodology described in Fig. 20. A crack kinematic without slip (pure crack opening) is considered (Fig. 20a), which is consistent with the main assumptions of the model. The principal directions of stresses and strains define the inclination of the cracks (θ<em><sub>r</sub></em>&nbsp;=&nbsp;θ<sub>s</sub>=&nbsp;θ<sub>e</sub>). According to (Fig. 20b), the crack width (<em>w</em>) can be projected in the direction of the reinforcing bar (<em>w</em><em><sub>b</sub></em>), leading to:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(θ_r + θ_b - \\frac{π}{2}\\right)}\\]</p>\n<p>where θ<em><sub>b</sub></em>&nbsp;is the bar inclination.</p>\n<p>Please note, that the program displays values of θ<em><sub>r</sub></em> and θ<em><sub>b</sub></em> &lt; <em>π/2</em>. It means that the previous equation works for cases, where the reinforcement and crack go through the different quadrants of the Cartesian coordinate system as shown in Fig. 20, where reinforcement goes through I. and III. quadrants and crack through II and IV. For cases where the reinforcement and crack go through the same quadrants, the equation has to be modified as follows:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(-θ_r + θ_b + \\frac{π}{2}\\right)}\\]</p>\n<p>The component <em>w</em><em><sub>b</sub></em> is consistently calculated based on the tension stiffening models by integrating the reinforcement strains. For those regions with fully developed crack patterns, the calculated average strains (e<em><sub>m</sub></em>) along the reinforcing bars are directly integrated along the crack spacing (<em>s</em><em><sub>r</sub></em>), as indicated in (Fig. 20c). While this approach to calculating the crack directions does not correspond to the real position of the cracks, it still provides representative values that lead to crack width results that can be compared to code-required crack width values at the position of the reinforcing bar.</p>\n<p>Special situations are observed at concave corners of the calculated structure. In this case, the corner predefines the position of a single crack that behaves in a non-stabilized fashion before additional adjacent cracks develop. These additional cracks generally develop after the serviceability range (Mata-Falcón 2015), which justifies calculating the crack widths in such a region as if they were non-stabilized (Fig. 21).</p>\n<figure data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a46a740-1622-47eb-b7f3-186fee0f6fbc/Concave%20corner.png\" data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" alt=\"Fig. 25\tDefinition of the region at concave corners in which the crack width is computed as if it were non-stabilized.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 21\\qquad Definition of the region at concave corners in which the crack width is computed as if it were non-stabilized.}}}\\]</em></p>\n<h4>Tension stiffening</h4>\n<p>The implementation of tension stiffening distinguishes between cases of stabilized and non-stabilized crack patterns. In both cases, the concrete is considered fully cracked before loading by default.</p>\n<figure data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/80e8fffe-3c98-4677-af35-7c2ce025e0bb/Tension%20stiffening%20model.PNG\" data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" alt=\"Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 22\\qquad Tension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear,}}}\\) </em>\\( \\textsf{\\textit{\\footnotesize{steel and concrete stresses, and steel strains between cracks, considering average crack spacing); (b) pull-out assumption}}}\\) \\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting}}}\\) \\( \\textsf{\\textit{\\footnotesize{tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) detail of the initial branches of the tension chord response.}}}\\)</p>\n<p><br></p>\n<p><strong>Stabilized cracking</strong></p>\n<p>In fully developed crack patterns, tension stiffening is introduced using the Tension Chord Model (TCM) (Marti et al. 1998; Alvarez 1998)&nbsp;– Fig. 22a – which has been shown to yield excellent response predictions in spite of its simplicity (Burns 2012). The TCM assumes a stepped, rigid-perfectly plastic bond shear stress-slip relationship with τ<em><sub>b&nbsp;</sub></em>=&nbsp;τ<em><sub>b</sub></em><sub>0</sub>&nbsp;=2&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s</sub></em>&nbsp;≤&nbsp;<em>f</em><em><sub>y</sub></em> and τ<em><sub>b</sub></em>&nbsp;=τ<em><sub>b</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s&nbsp;</sub></em>&gt;&nbsp;<em>f</em><em><sub>y</sub></em>. Treating every reinforcing bar as a tension chord ­– Fig. 22b and Fig. 22a – the distribution of bond shear, steel, and concrete stresses and hence the strain distribution between two cracks can be determined for any given value of the maximum steel stresses (or strains) at the cracks.</p>\n<p>For <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;<em>s</em><em><sub>r</sub></em><sub>0</sub>, a new crack may or may not form because at the center between two cracks σ<em><sub>c</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ct</sub></em>. Consequently, the crack spacing may vary by a factor of two, i.e., <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;λ<em>s</em><em><sub>r</sub></em><sub>0</sub>, with l&nbsp;=&nbsp;0.5…1.0. Assuming a certain value for λ, the average strain of the chord (ε<em><sub>m</sub></em>) can be expressed as a function of the maximum reinforcement stresses (i.e., stresses at the cracks, σ<em><sub>sr</sub></em>). For the idealized bilinear stress-strain diagram for the reinforcing bare bars considered by default in the CSFM, the following closed-form analytical expressions are obtained (Marti et al. 1998):</p>\n<p>\\[\\varepsilon_m = \\frac{\\sigma_{sr}}{E_s} - \\frac{\\tau_{b0}s_r}{E_s Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\sigma_{sr} \\le f_y\\]</p>\n<p><br></p>\n<p>\\[{\\varepsilon_m} = \\frac{{{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}^2}Ø}}{{4{E_{sh}}{\\tau _{b1}}{s_r}}}\\left( {1 - \\frac{{{E_{sh}}{\\tau_{b0}}}}{{{E_s}{\\tau_{b1}}}}} \\right) + \\frac{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}}{{{E_s}}}\\frac{{{\\tau_{b0}}}}{{{\\tau_{b1}}}} + \\left( {{\\varepsilon_y} - \\frac{{{\\tau_{b0}}{s_r}}}{{{E_s}Ø}}} \\right)\\]</p>\n<p><em>\\[\\textrm{for}\\qquad\\qquad{f_y} \\le {\\sigma _{sr}} \\le \\left( {{f_y} + \\frac{{2{\\tau _{b1}}{s_r}}}{Ø}} \\right)\\]</em></p>\n<p><br></p>\n<p>\\[ \\varepsilon_m = \\frac{f_s}{E_s} + \\frac{\\sigma_{sr}-f_y}{E_{sh}} - \\frac{\\tau_{b1} s_r}{E_{sh} Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\left(f_y + \\frac{2\\tau_{b1}s_r}{Ø}\\right) \\le \\sigma_{sr} \\le f_t\\]</p>\n<p>where:<br>\n <em>E</em><em><sub>sh</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;the steel hardening modulus <em>E</em><em><sub>sh</sub></em>&nbsp;=&nbsp;(<em>f</em><em><sub>t</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>)/(ε<em><sub>u</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;/<em>E</em><em><sub>s</sub></em>)&nbsp;,</p>\n<p><em>E</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of reinforcement,</p>\n<p><em>Ø</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reinforcing bar diameter,</p>\n<p>s<em><sub>r</sub></em><em><sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sup></em>crack spacing,</p>\n<p>σ<em><sub>sr</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>reinforcement stresses at the cracks,</p>\n<p>σ<em><sub>s</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>actual reinforcement stresses,</p>\n<p><em>f</em><em><sub>y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</sub></em>yield strength of reinforcement.</p>\n<p><br></p>\n<p>The Idea StatiCa Detail implementation of the CSFM considers average crack spacing by default when performing computer-aided stress field analysis. The average crack spacing is considered to be 2/3 of the maximum crack spacing (λ&nbsp;=&nbsp;0.67), which follows recommendations made on the basis of bending and tension tests (Broms 1965; Beeby 1979; Meier 1983). It should be noted that calculations of crack widths consider a maximum crack spacing (λ&nbsp;=&nbsp;1.0) in order to obtain conservative values.</p>\n<p>The application of the TCM depends on the reinforcement ratio, and hence the assignment of an appropriate concrete area acting in tension between the cracks to each reinforcing bar is crucial. An automatic numerical procedure has been developed to define the corresponding effective reinforcement ratio (ρ<em><sub>eff</sub></em><em> = A</em><em><sub>s</sub></em><em>/A</em><em><sub>c,eff</sub></em>) for any configuration, including skewed reinforcement (Fig. 23).</p>\n<figure data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2c0d58ae-1639-4b2a-a99c-a5e274a318ac/Effective%20area%20of%20concrete.png\" data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" alt=\"Fig. 4\tEffective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated; (b) cover and global symmetry condition; (c) resultant effective area.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 23\\qquad Effective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(b) cover and global symmetry condition; (c) resultant effective area.}}}\\)</em></p>\n<p><br></p>\n<p><strong>Non-stabilized cracking</strong></p>\n<p>Cracks existing in regions with geometric reinforcement ratios lower than ρ<em><sub>cr</sub></em>, i.e., the minimum reinforcement amount for which the reinforcement is able to carry the cracking load without yielding, are generated by either non-mechanical actions (e.g. shrinkage) or the progression of cracks controlled by other reinforcement. The value of this minimum reinforcement is obtained as follows:</p>\n<p>\\[{\\rho _{cr}} = \\frac{{{f_{ct}}}}{{{f_y} - \\left( {n - 1} \\right){f_{ct}}}}\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>y</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;reinforcement yield strength,</p>\n<p><em>f</em><em><sub>ct</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;concrete tensile strength,</p>\n<p><em>n</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modular ratio, <em>n</em>&nbsp;=&nbsp;<em>E</em><em><sub>s</sub></em>&nbsp;/&nbsp;<em>E</em><em><sub>c</sub></em>&nbsp;.</p>\n<p>For conventional concrete and reinforcing steel, ρ<em><sub>cr</sub></em> amounts to approximately 0.6%.</p>\n<p>For stirrups with reinforcement ratios below ρ<em><sub>cr</sub></em>, cracking is considered to be non-stabilized and tension stiffening is implemented by means of the Pull-Out Model (POM) described in Fig. 22b. This model analyzes the behavior of a single crack considering no mechanical interaction between separate cracks, neglecting the deformability of concrete in tension and assuming the same stepped, rigid-perfectly plastic bond shear stress-slip relationship used by the TCM. This allows the reinforcement strain distribution (ε<em><sub>s</sub></em>) in the vicinity of the crack to be obtained for any maximum steel stress at the crack (σ<em><sub>sr</sub></em>) directly from equilibrium. Given the fact that the crack spacing is unknown for a non-fully developed crack pattern, the average strain (ε<em><sub>m</sub></em>) is computed for any load level over the distance between points with zero slip when the reinforcing bar reaches its tensile strength (<em>f</em><em><sub>t</sub></em>) at the crack (<em>l</em><sub>ε,</sub><em><sub>avg</sub></em> in Fig. 22b), leading to the following relationships:</p>\n<figure data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/43adc17b-b9e9-4a81-ab9f-ff4c13297b34/Equation%201.2.4.2.PNG\" data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" alt=\"\"></figure>\n<p>The proposed models allow the computation of the behavior of bonded reinforcement, which is finally considered in the analysis. This behavior (including tension stiffening) for the most common European reinforcing steel (B500B, with <em>f</em><em><sub>t</sub></em>&nbsp;/&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;=&nbsp;1.08 and ε<em><sub>u</sub></em>&nbsp;=&nbsp;5%) is illustrated in Fig. 22c-d.</p>"
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                            "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                            "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                            "value": "<p>In the calculation for the results of SLS, only the elastic behavior of concrete is taken into account. In other words, an infinite linear stress-strain diagram is considered for concrete. You can display <strong>long-term</strong> or <strong>short-term</strong> effects for SLS checks. What is the difference between these two effects? Read the article below (paragraph Concrete SLS) to learn more.</p>\n<ul>\n  <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Material models (EN)</a></li>\n</ul>\n<h2>Stress</h2>\n<p>There are two options for displaying results for concrete and reinforcement:&nbsp;</p>\n<ul>\n  <li>the ratio of the stress and the limit stress&nbsp;</li>\n  <li>the stress itself&nbsp;</li>\n</ul>\n<p>Stresses are calculated for the <strong>Characteristic</strong> and for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of the stress and limit stress</h4>\n<p>The results are clear at first sight: Green color means the utilization is up to 90%, orange is 90-100% of utilization, and red is above 100%.</p>\n<p>Read about how the limit value is determined in the following article.</p>\n<ul>\n  <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Serviceability limit state analysis</a></li>\n</ul>\n<figure data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d12601c9-32a1-408f-9b41-e031d5b6fc45/RC-D_06_20.png\" data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" alt=\"\"></figure>\n<figure data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/45cd98c6-57b5-4373-a001-6e5c3ed8f5b8/RC-D_06_21.png.png\" data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" alt=\"\"></figure>\n<h4>Stress</h4>\n<p>The display method is similar to the ULS results (in this case, the stress is from the calculation with the elastic behavior of concrete). You can display the distribution of concrete stress <em>σ</em><em><sub>c</sub></em><sub> </sub>for an applied portion of the load. Also known as principal stresses <em>σ</em><em><sub>2</sub></em>.</p>\n<figure data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6f65c964-8c56-4aac-a14c-4307bfde6a8d/RC-D_06_22.png\" data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\" alt=\"\"></figure>\n<figure data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16c8bb7b-6bc7-4b9a-b27f-cf1075f7715a/RC-D_06_23.png\" data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" alt=\"\"></figure>\n<h2>Crack</h2>\n<p>In this section, you will learn about all four options for displaying results for crack checks. Read the further articles to learn about the calculation.</p>\n<ul>\n  <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Main assumptions and limitations for CSFM</a></li>\n  <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Structural element verification in IDEA StatiCa Detail</a></li>\n</ul>\n<p>Cracks are calculated only for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of crack width and limit crack width</h4>\n<p>The limit value w<sub>lim</sub> can be set in the top ribbon. The w<sub>lim</sub> = 0.3 mm is set by default according to Eurocode. The results are again differentiated by color (green/orange/red) so that the check is obvious at first sight.</p>\n<figure data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9fa5bdd1-ec85-4575-9e0f-6d26ce70c206/RC-D_06_24.png\" data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" alt=\"\"></figure>\n<h4>Crack width</h4>\n<p>This functionality is used to display the crack width for every single element of the reinforcement.&nbsp;</p>\n<figure data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97bc905a-76c9-4b12-abe1-3a93c71cdf2b/RC-D_06_25.png\" data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" alt=\"\"></figure>\n<h4>The distance between stabilized cracks</h4>\n<p>See the links at the beginning of the section. The article explains the method of calculating the distance between stabilized cracks.</p>\n<figure data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bcb4dbbc-29b3-48bb-a1f1-72cdb456b0b6/RC-D_06_26.png\" data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" alt=\"\"></figure>\n<p>The presentation of crack spacing is schematic only. It does not represent the crack spacing computed for the calculation.</p>\n<h4>Unreinforced area</h4>\n<p>The crack width is checked only in the vicinity of the reinforcement. Control of cracking is not performed in non-reinforced zones.</p>\n<p>This result simply shows the non-reinforced areas where cracks will probably appear. It is recommended to design some reinforcement to that areas.</p>\n<figure data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f60ea99-7197-4ee8-865e-2e282fdf60ef/RC-D_06_27.png\" data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\" alt=\"\"></figure>\n<h2>Deflection</h2>\n<p>See the options below:</p>\n<ul>\n  <li><em>u</em><em><sub>z,st</sub></em> - Immediate deflection caused by <strong>total load</strong> - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,lt</sub></em> - Long-term deflection caused by <strong>long-term loads </strong>(permanent and prestressing load type) - calculated with <strong>long-term stiffnesses </strong><em><strong>Ec,eff</strong></em><strong>. </strong>In other words, the creep coefficients are included.</li>\n  <li><em>Δu</em><em><sub>z</sub></em> - Deflection increment caused by <strong>short-term loads</strong> (variable load type) - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> = u</em><em><sub>z,lt</sub></em><em>&nbsp;+ Δu</em><em><sub>z</sub></em><sub>&nbsp;</sub></li>\n</ul>\n<p>Deflections are calculated only for the <strong>Characteristic</strong> load combinations.</p>\n<figure data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/815bac57-2809-4383-b0cc-abfa3349b443/RC-D_06_29.png\" data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" alt=\"\"></figure>\n<p>Besides the table values in the Data section, you can display the deformed shape. You can also modify the scale of the deformation.</p>\n<p>Finally, in addition to displaying deformations, it is also possible to do a <strong>deflection check</strong>. You can choose between two checks - <strong>Increment</strong> and <strong>Total.</strong></p>\n<ul>\n  <li><em>Δu</em><em><sub>z</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - &nbsp;Increment</li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> / Δu</em><em><sub>z,lim</sub></em>&nbsp;- Total</li>\n</ul>\n<p><em>Δu</em><em><sub>z,lim</sub></em>, and <em>Δu</em><em><sub>z,lim</sub></em> can be manually set in the Deflection check bar in the top ribbon.</p>\n<figure data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9efce2e8-54f2-4fe3-8fcb-700d0bc1bd32/RC-D_06_30.png\" data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" alt=\"\"></figure>\n<p>The deflection check is not allowed for trimmed ends.&nbsp;</p>\n<h2>Practical example</h2>\n<p>For a practical example of displaying the results, continue to the <a href=\"https://www.youtube.com/embed/77fFYFUvv5c/?start=2408\">video</a> from the previously streamed webinar. 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            "value": "<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.</p>\n<h3>Ultimate limit state analysis</h3>\n<p>The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<p>To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:</p>\n<ul>\n  <li>Choose a selection of the most critical load combinations.</li>\n  <li>Calculate only Ultimate Limit State (ULS) load combinations.</li>\n  <li>Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"Fig. 23\tMesh multiplier.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).</p>\n<p>The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.</p>\n<h3>Serviceability limit state analysis</h3>\n<p>SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.</p>\n<p>The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. 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                            "value": "<h4>¿Muro de hormigón armado o vigas profundas con verificación de códigos completa? No hay problema.</h4>\n<p>El objetivo del webinar es presentar cómo realizar en minutos la comprobación de código de una <strong>viga profunda de forma general</strong> en <strong>IDEA StatiCa Detail</strong> en conexión con los resultados de la aplicación de AEF. Mostraremos el flujo de trabajo en un ejemplo de un edificio residencial de hormigón - exportando la geometría, creando el submodelo en IDEA StatiCa Detail, aplicando las <strong>cargas correctas</strong>, el diseño de la armadura, y el código de comprobación final para los <strong>estados</strong> <strong>límite últimos y de servicio</strong>.</p>\n<p>Pruébelo usted mismo - obtenga la <a data-item-id=\"0c872071-6a3f-4b99-8cd4-66440db9cc0d\" href=\"\">licencia de prueba gratuita</a> y siga el tutorial paso a paso en <a data-item-id=\"1dc3667d-ddd6-5483-8b97-e7b69923fef7\" href=\"\">Muro de hormigón</a>.</p>\n<figure data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/177694cc-5c91-42cb-b88c-568f900670fe/Code-check%20of%20walls%20and%20deep%20beams.png\" data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\" alt=\"\"></figure>\n<h4>La solución definitiva para detalles y piezas estructurales de hormigón</h4>\n<p>El software de AEF 3D habitual tiene en cuenta el comportamiento lineal del hormigón. El diseño y las comprobaciones de código de la armadura son limitados, especialmente para el <strong>estado límite de servicio</strong> que puede conducir al desarrollo de <strong>grietas excesivas</strong>. Todo esto está cubierto dentro de la aplicación IDEA StatiCa Detail <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">basada en CSFM</a>. Ahora, todos los ingenieros pueden diseñar y comprobar eficientemente muros o vigas profundas de cualquier forma y muchas más.</p>\n<p>Si desea ver más de <strong>IDEA StatiCa Detail </strong>en acción, hay otros dos seminarios web grabados para ver:</p>\n<ul>\n  <li><a data-item-id=\"1300fb1c-8e32-47f3-8b21-0e8e77e1f238\" href=\"\">¿Cómo diseñar fácilmente una viga pretensada con aberturas?</a></li>\n  <li><a data-item-id=\"73d449cf-610e-5c7c-9e8c-da8093630d24\" href=\"\">Muro colado in situ - Ruzomberok (Eslovaquia)</a></li>\n</ul>\n<p>O navegue por nuestro Centro de soporte para ver <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&amp;label=detail\" title=\"IDEA StatiCa Detail\">tutoriales</a> y leer los <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">fundamentos teóricos.</a></p>\n<h3>Grabación del seminario web</h3>"
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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    "value": "<p>Las distintas verificaciones exigidas por la norma ACI 318-19 se evalúan a partir de los resultados directos proporcionados por el modelo. Las verificaciones se llevan a cabo para la resistencia del hormigón, la resistencia de la armadura y el anclaje (esfuerzos cortantes de adherencia).</p>\n<p>La <strong>resistencia</strong> del <strong>hormigón</strong> en compresión se evalúa como la relación entre la tensión principal equivalente máxima <em>fc</em><em><sub>,eq</sub></em> (también σc<em><sub>,eq</sub></em> en el texto anterior) obtenida a partir del análisis de EF y el valor límite <em>f'</em><em><sub>c,lim</sub></em>.</p>\n<p><strong>La tensión principal equivalente expresa la tensión uniaxial equivalente para un estado de tensión triaxial general.</strong></p>\n<p>\\[f_{c,eq} = \\sigma_{c3}} - \\sigma_{c1}\\].</p>\n<p>El valor de fc<em><sub>,</sub></em> eq puede, por tanto, compararse directamente con los límites de resistencia uniaxial. Esta expresión se deriva de la aplicación de la teoría de la plasticidad de Mohr-Coulomb, asumiendo de forma conservadora el ángulo de fricción interna φ <em>= 0°.</em></p>\n<p>La <strong>resistencia de la armadura</strong> se evalúa tanto en tracción como en compresión como la relación entre la tensión en la armadura en las fisuras <em><sub>fs</sub></em> y el valor límite especificado <em>fy</em><em><sub>,lim</sub></em>.</p>\n<p>\\[f_{y,lim} = \\phi_{s} \\cdot f_{y}\\]</p>\n<p>El <strong>esfuerzo cortante</strong> de adherencia se evalúa independientemente como la relación entre el esfuerzo de adherencia <sub><em>τb</em></sub> calculado mediante el análisis de EF y la resistencia de adherencia <sub><em>fbu</em></sub>.</p>\n<p>Aunque la resistencia de adherencia no se define explícitamente en ACI 318-19, el cálculo de la longitud de desarrollo se puede encontrar en la Sección 25.4.2. Sin embargo, dado que la resistencia de adherencia es el dato básico para determinar la longitud de desarrollo, véase R25.4.1.1 y ACI Comité 408 1966, la resistencia de adherencia puede calcularse como sigue:</p>\n<p>Supongamos que si anclamos la barra de armadura en un bloque de hormigón hasta la longitud de desarrollo <em><sub>ld</sub></em> o mayor, el arrancamiento de la armadura producirá la rotura de la armadura y no el arrancamiento del hormigón. Esto se puede escribir con la siguiente fórmula.</p>\n<p>\\[\\pi\\cdot d_{b} \\cdot l_{d} \\cdot f_{bu}=f_{y}\\cdot A_{s}]</p>\n<p>donde:</p>\n<p><em><sub>db</sub></em> es el diámetro de la barra de armadura, <em><sub>ld</sub></em> es la longitud de desarrollo, <em><sub>fbu</sub></em> es el límite de adherencia, <em><sub>fy</sub></em> es el límite elástico de la armadura y<em><sub>As</sub></em> es el área de la barra de armadura.</p>\n<p>De lo anterior se deduce fácilmente la fórmula para calcular la fuerza de adherencia:</p>\n<p>\\f_{bu}=frac{f_{y}\\cdot A_{s}}{pi\\cdot d_{b} \\cdot l_{d} }].</p>\n<p>La longitud de desarrollo <em><sub>ld</sub></em> se determina entonces de acuerdo con ACI 318-19 Tabla 25.4.2.3 de la siguiente manera:</p>\n<p>\\[l_{d}=\\left( \\frac{f_{y}\\cdot\\psi_{t}\\cdot\\psi_{e}\\cdot\\psi_{g}}{C\\cdot\\lambda\\sqrt{f'_{c}}} \\d_{b}]</p>\n<p>donde:</p>\n<p><em>C = 25</em> (2,1 para métrica) para no. 6 y barras más pequeñas y alambres deformados, <em>C = 20</em> (1,7 para el sistema métrico) para no. 7 y barras mayores, λ = 1,0 para hormigón de peso normal, <em><sub>ψt</sub></em>, <em><sub>ψe</sub></em><sub>,</sub> <em><sub>ψg</sub></em> se determinan de acuerdo con ACI 318-19 Tabla 25.4.2.3.</p>\n<p>Sólo se soportan las armaduras no revestidas o revestidas de zinc (galvanizadas), por lo que <em><sub>ψe</sub></em><em> = 1,0</em>. <em><sub>ψg</sub></em> se determina automáticamente a partir del grado de la armadura, y <em><sub>ψt</sub></em> se deriva automáticamente de la posición de la armadura en el modelo y de la dirección de hormigonado que puede establecerse en la aplicación para cada elemento del proyecto de la siguiente manera.</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 46\\qquadirección del hormigonado}}}]</em></p>\n<p>Estas comprobaciones se realizan con respecto a los valores límite apropiados para las respectivas partes de la estructura (es decir, a pesar de tener una única calidad tanto para el hormigón como para el material de la armadura, los diagramas tensión-deformación finales diferirán en cada parte de la estructura debido a los efectos de rigidización por tracción y ablandamiento por compresión).</p>\n<p><strong>Fuerza total </strong><strong><em><sub>Ftot</sub></em></strong><strong> y fuerza límite </strong><strong><em><sub>Flim</sub></em></strong></p>\n<p>La fuerza total <strong><em><sub>Ftot</sub></em></strong> es el resultado del análisis de elementos finitos y puede definirse de dos maneras.</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>donde<em><sub>As</sub></em> es el área de la barra de refuerzo y <em><sub>fs</sub></em> es la tensión en la barra.</p>\n<p>O como suma de la fuerza de anclaje<em><sub>Fa y </sub></em>la fuerza de adherencia <em><sub>Fbond</sub></em><em>.</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>donde<em><sub>Fa</sub></em> es la fuerza real en el muelle de anclaje y <em><sub>Fbond</sub></em> es la fuerza de adherencia que puede obtenerse integrando la tensión de adherencia <em><sub>τb</sub></em> a lo largo de la longitud de la barra de armadura <em>l.</em></p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p><sub>Cs</sub> es la circunferencia de la barra de refuerzo.</p>\n<p>La fuerza límite<strong><em><sub>Flim</sub></em></strong> es la fuerza máxima en el elemento de la barra de refuerzo teniendo en cuenta la <strong>resistencia</strong> de la barra de refuerzo y también <strong>las condiciones de anclaje </strong>(unión entre el hormigón y la armadura y ganchos de anclaje, bucles, etc.).</p>\n<p>\\[F_{lim}=min_left( F_{lim,bond}+F_{au},F_{u} \\right)\\}]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}]</p>\n<p>\\F_{au}=f_{y,lim}dot A_{s}]</p>\n<p>\\F_{lim,bond}=C_{s}{cdot l}{cdot f_{bu}{]</p>\n<p>donde <sub>Cs</sub> es la circunferencia de la barra de refuerzo, y <em>l</em> es la longitud desde el comienzo de la barra de refuerzo hasta el punto de interés.</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 47\\qquad Definición de la fuerza límite Flim}}]</em></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>donde<em><sub>Flim,add</sub></em> es la fuerza adicional calculada a partir de la magnitud del ángulo entre elementos vecinos.<em><sub>Flim,2</sub></em> debe ser siempre inferior a<em><sub>Fu</sub></em>.</p>\n<p>Los <strong>tipos de anclaje</strong> disponibles en CSFM incluyen una barra recta (es decir, sin reducción del extremo del anclaje), gancho de 90 grados, gancho de 180 grados, unión perfecta y barra continua. Todos estos tipos, junto con los respectivos coeficientes de anclaje β, se muestran en la Fig. 48 para la armadura longitudinal. Los valores de los coeficientes de anclaje adoptados se derivan de la comparación de la ecuación de la sección ACI 318-19 25.4.3.1 y ecuaciones tomadas de la sección ACI 318-19 25.4.2.3. Cabe señalar que, a pesar de las diferentes opciones disponibles, el CSFM distingue tres tipos de extremos de anclaje: (i) ninguna reducción de la longitud de anclaje, (ii) una reducción del 30% de la longitud de anclaje en el caso de un anclaje normalizado, y (iii) unión perfecta.</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 48\\qquad Tipos de anclaje disponibles y coeficientes de anclaje respectivos para barras de refuerzo longitudinal en CSFM:}}]</em></p>\n<p><em>\\(a) barra recta; (b) gancho de 90 grados; (c) gancho de 180 grados; (d) unión perfecta; (e) barra continua}}].</em></p>\n<p>El coeficiente de anclaje de los estribos es siempre - β = 1,0.</p>\n<p>Para cumplir con ACI, el resorte de anclaje debe ser utilizado en el cálculo, el resorte de anclaje es modificado por el coeficiente β por lo que el usuario debe utilizar uno de los tipos de anclaje disponibles al definir las condiciones de inicio y final de la armadura.</p>"
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                    "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                    "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. IDEA StatiCa offers a fully customizable report to print out or save in an editable format.</p>\n<figure data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6e3c18c1-a97e-4301-8ee4-31b1ed278382/6_1%20Report.png\" data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" alt=\"\"></figure>\n<figure data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/33137b76-efe1-4357-a046-99a24413aa88/6_2%20Report.png\" data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" alt=\"\"></figure>\n<p>You have designed, optimized, and code-checked a pier cap according to Eurocode.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"idea_statica_tutorial___pier_cap_from_dxf_2495f70\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"campus_cta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0d61cad8_c463_0160_5df5_bb66b7a55152\"></object>"
                                  },
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                                    "name": "Support center article",
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                                  "expertise_levels": {
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                                        "name": "Beginner",
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                                        "name": "Detail 2D",
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                                        "name": "EN (Eurocode)",
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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    "value": "<h3>Concrete - Strength</h3>\n<p>The concrete model implemented for strength calculations in CSFM is based on the parabolic-plastic stress-strain curve. The tensile strength is neglected, as it is in classic reinforced concrete design.</p>\n<figure data-asset-id=\"52146a6b-a36a-4782-8d86-9f21cc21cb86\" data-image-id=\"52146a6b-a36a-4782-8d86-9f21cc21cb86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/22a6013d-68bc-406c-b92a-f500a9ba191e/SS%20diagrams%20conc%20-%20AUS.png\" data-asset-id=\"52146a6b-a36a-4782-8d86-9f21cc21cb86\" data-image-id=\"52146a6b-a36a-4782-8d86-9f21cc21cb86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 47\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p>The implementation of CSFM in <em>IDEA StatiCa Detail</em> does not consider an explicit failure criterion in terms of strains for concrete in compression (i.e., after the peak stress is reached, it considers a plastic branch with ε<em><sub>cp</sub></em> in maximum value 5%, while AS 3600 Cl. 8.3.1 assumes ultimate strain of less than 0.3%). This simplification does not allow the deformation capacity of structures failing in compression to be verified. However, the strength is properly predicted when the increase in the brittleness of concrete as its strength rises is considered by means of the <em>\\(\\eta_{fc}\\)</em>&nbsp;reduction factor defined in <em>fib</em> Model Code 2010 as follows:</p>\n<p>\\[f'_{c,lim}=\\alpha_{2}\\cdot\\phi_{s} \\cdot \\eta_{fc}\\cdot f'_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>where:</p>\n<p><em>α</em><sub>2</sub> is the reduction factor of concrete compressive strength defined in AS 3600 Cl. 8.3.1 <br>\nWhen using a parabola-rectangle&nbsp;stress-strain diagram, it is necessary to reduce the maximum compressive stress by this factor. This averages the stress distribution in the compression zone in such a way that the resulting compressive strength is less than or equal to the&nbsp;compressive strength&nbsp;calculated using a stress-strain diagram with a decreasing plastic branch<em>. </em>An analogous approach is defined for the Rectangular stress block in Chapter 8.1.3.</p>\n<p><em>Φ</em><em><sub>s </sub></em>is the stress reduction factor for concrete. The default value is set according to AS 3600 Table 2.2.3.</p>\n<p><em>f'</em><em><sub>c</sub></em> is the concrete cylinder strength (in MPa for the definition of <em>\\( \\eta_{fc} \\)</em>).</p>\n<h3>Reinforcement</h3>\n<p>A perfectly elasto-plastic stress-strain diagram with a defined yield point for the non-prestresses reinforcement is considered, see AS 3600 Section 3.2. The definition of this diagram only requires the basic properties of the reinforcement to be known – the strength and modulus of elasticity.</p>\n<p>The reinforcement stress-strain diagram can be also defined by the user, but in this case, it is impossible to assume the tension stiffening effect (it is impossible to calculate crack width).&nbsp;</p>\n<figure data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4e33b934-9d0f-4ba7-9764-4f31801c752b/Steel%20stress-strain%20diagram%20CSFM%20-%20AUS.png\" data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 48 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>where:</p>\n<p><em>Φ</em><em><sub>s </sub></em>is the strength reduction factor for reinforcement. Where the default value is set according to AS 3600 Table 2.2.3.</p>\n<p><em>f</em><em><sub>y</sub></em> is the yield strength of reinforcement</p>\n<p><em>E</em><em><sub>s</sub></em> modulus of elasticity of reinforcement</p>\n<p>Tension stiffening (Fig. 49) &nbsp;is accounted for automatically by modifying the input stress-strain relationship of the bare reinforcing bar in order to capture the average stiffness of the bars embedded in the concrete (ε<em><sub>m</sub></em>).</p>\n<figure data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b27b5ab6-24ea-410b-901a-fccbd7e4005f/Tension%20stiffening%20CSFM%20-%20AUS.png\" data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 49\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
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                    "value": "<h4>Crack width calculation</h4>\n<p>There are two ways of computing crack widths - stabilized and non-stabilized cracking. According to the geometrical reinforcement ratio in each part of the structure is decided, which type of crack calculation model will be used (TCM for stabilized cracking and POM for non-stabilized cracking model).</p>\n<figure data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62ba3929-8689-4973-8782-fcdd0780002b/Crack%20width%20calculation.PNG\" data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" alt=\"Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 20 \\qquad Crack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal}}}\\) \\( \\textsf{\\textit{\\footnotesize{directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with}}}\\) \\( \\textsf{\\textit{\\footnotesize{local&nbsp;non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar}}}\\)\\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking.}}}\\)</em></p>\n<p><br></p>\n<p>While the CSFM yields a direct result for most verifications (e.g., member capacity, deflections…), crack width results are calculated from the reinforcement strain results directly provided by FE analysis following the methodology described in Fig. 20. A crack kinematic without slip (pure crack opening) is considered (Fig. 20a), which is consistent with the main assumptions of the model. The principal directions of stresses and strains define the inclination of the cracks (θ<em><sub>r</sub></em>&nbsp;=&nbsp;θ<sub>s</sub>=&nbsp;θ<sub>e</sub>). According to (Fig. 20b), the crack width (<em>w</em>) can be projected in the direction of the reinforcing bar (<em>w</em><em><sub>b</sub></em>), leading to:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(θ_r + θ_b - \\frac{π}{2}\\right)}\\]</p>\n<p>where θ<em><sub>b</sub></em>&nbsp;is the bar inclination.</p>\n<p>Please note, that the program displays values of θ<em><sub>r</sub></em> and θ<em><sub>b</sub></em> &lt; <em>π/2</em>. It means that the previous equation works for cases, where the reinforcement and crack go through the different quadrants of the Cartesian coordinate system as shown in Fig. 20, where reinforcement goes through I. and III. quadrants and crack through II and IV. For cases where the reinforcement and crack go through the same quadrants, the equation has to be modified as follows:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(-θ_r + θ_b + \\frac{π}{2}\\right)}\\]</p>\n<p>The component <em>w</em><em><sub>b</sub></em> is consistently calculated based on the tension stiffening models by integrating the reinforcement strains. For those regions with fully developed crack patterns, the calculated average strains (e<em><sub>m</sub></em>) along the reinforcing bars are directly integrated along the crack spacing (<em>s</em><em><sub>r</sub></em>), as indicated in (Fig. 20c). While this approach to calculating the crack directions does not correspond to the real position of the cracks, it still provides representative values that lead to crack width results that can be compared to code-required crack width values at the position of the reinforcing bar.</p>\n<p>Special situations are observed at concave corners of the calculated structure. In this case, the corner predefines the position of a single crack that behaves in a non-stabilized fashion before additional adjacent cracks develop. These additional cracks generally develop after the serviceability range (Mata-Falcón 2015), which justifies calculating the crack widths in such a region as if they were non-stabilized (Fig. 21).</p>\n<figure data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a46a740-1622-47eb-b7f3-186fee0f6fbc/Concave%20corner.png\" data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" alt=\"Fig. 25\tDefinition of the region at concave corners in which the crack width is computed as if it were non-stabilized.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 21\\qquad Definition of the region at concave corners in which the crack width is computed as if it were non-stabilized.}}}\\]</em></p>\n<h4>Tension stiffening</h4>\n<p>The implementation of tension stiffening distinguishes between cases of stabilized and non-stabilized crack patterns. In both cases, the concrete is considered fully cracked before loading by default.</p>\n<figure data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/80e8fffe-3c98-4677-af35-7c2ce025e0bb/Tension%20stiffening%20model.PNG\" data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" alt=\"Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 22\\qquad Tension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear,}}}\\) </em>\\( \\textsf{\\textit{\\footnotesize{steel and concrete stresses, and steel strains between cracks, considering average crack spacing); (b) pull-out assumption}}}\\) \\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting}}}\\) \\( \\textsf{\\textit{\\footnotesize{tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) detail of the initial branches of the tension chord response.}}}\\)</p>\n<p><br></p>\n<p><strong>Stabilized cracking</strong></p>\n<p>In fully developed crack patterns, tension stiffening is introduced using the Tension Chord Model (TCM) (Marti et al. 1998; Alvarez 1998)&nbsp;– Fig. 22a – which has been shown to yield excellent response predictions in spite of its simplicity (Burns 2012). The TCM assumes a stepped, rigid-perfectly plastic bond shear stress-slip relationship with τ<em><sub>b&nbsp;</sub></em>=&nbsp;τ<em><sub>b</sub></em><sub>0</sub>&nbsp;=2&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s</sub></em>&nbsp;≤&nbsp;<em>f</em><em><sub>y</sub></em> and τ<em><sub>b</sub></em>&nbsp;=τ<em><sub>b</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s&nbsp;</sub></em>&gt;&nbsp;<em>f</em><em><sub>y</sub></em>. Treating every reinforcing bar as a tension chord ­– Fig. 22b and Fig. 22a – the distribution of bond shear, steel, and concrete stresses and hence the strain distribution between two cracks can be determined for any given value of the maximum steel stresses (or strains) at the cracks.</p>\n<p>For <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;<em>s</em><em><sub>r</sub></em><sub>0</sub>, a new crack may or may not form because at the center between two cracks σ<em><sub>c</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ct</sub></em>. Consequently, the crack spacing may vary by a factor of two, i.e., <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;λ<em>s</em><em><sub>r</sub></em><sub>0</sub>, with l&nbsp;=&nbsp;0.5…1.0. Assuming a certain value for λ, the average strain of the chord (ε<em><sub>m</sub></em>) can be expressed as a function of the maximum reinforcement stresses (i.e., stresses at the cracks, σ<em><sub>sr</sub></em>). For the idealized bilinear stress-strain diagram for the reinforcing bare bars considered by default in the CSFM, the following closed-form analytical expressions are obtained (Marti et al. 1998):</p>\n<p>\\[\\varepsilon_m = \\frac{\\sigma_{sr}}{E_s} - \\frac{\\tau_{b0}s_r}{E_s Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\sigma_{sr} \\le f_y\\]</p>\n<p><br></p>\n<p>\\[{\\varepsilon_m} = \\frac{{{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}^2}Ø}}{{4{E_{sh}}{\\tau _{b1}}{s_r}}}\\left( {1 - \\frac{{{E_{sh}}{\\tau_{b0}}}}{{{E_s}{\\tau_{b1}}}}} \\right) + \\frac{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}}{{{E_s}}}\\frac{{{\\tau_{b0}}}}{{{\\tau_{b1}}}} + \\left( {{\\varepsilon_y} - \\frac{{{\\tau_{b0}}{s_r}}}{{{E_s}Ø}}} \\right)\\]</p>\n<p><em>\\[\\textrm{for}\\qquad\\qquad{f_y} \\le {\\sigma _{sr}} \\le \\left( {{f_y} + \\frac{{2{\\tau _{b1}}{s_r}}}{Ø}} \\right)\\]</em></p>\n<p><br></p>\n<p>\\[ \\varepsilon_m = \\frac{f_s}{E_s} + \\frac{\\sigma_{sr}-f_y}{E_{sh}} - \\frac{\\tau_{b1} s_r}{E_{sh} Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\left(f_y + \\frac{2\\tau_{b1}s_r}{Ø}\\right) \\le \\sigma_{sr} \\le f_t\\]</p>\n<p>where:<br>\n <em>E</em><em><sub>sh</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;the steel hardening modulus <em>E</em><em><sub>sh</sub></em>&nbsp;=&nbsp;(<em>f</em><em><sub>t</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>)/(ε<em><sub>u</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;/<em>E</em><em><sub>s</sub></em>)&nbsp;,</p>\n<p><em>E</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of reinforcement,</p>\n<p><em>Ø</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reinforcing bar diameter,</p>\n<p>s<em><sub>r</sub></em><em><sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sup></em>crack spacing,</p>\n<p>σ<em><sub>sr</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>reinforcement stresses at the cracks,</p>\n<p>σ<em><sub>s</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>actual reinforcement stresses,</p>\n<p><em>f</em><em><sub>y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</sub></em>yield strength of reinforcement.</p>\n<p><br></p>\n<p>The Idea StatiCa Detail implementation of the CSFM considers average crack spacing by default when performing computer-aided stress field analysis. The average crack spacing is considered to be 2/3 of the maximum crack spacing (λ&nbsp;=&nbsp;0.67), which follows recommendations made on the basis of bending and tension tests (Broms 1965; Beeby 1979; Meier 1983). It should be noted that calculations of crack widths consider a maximum crack spacing (λ&nbsp;=&nbsp;1.0) in order to obtain conservative values.</p>\n<p>The application of the TCM depends on the reinforcement ratio, and hence the assignment of an appropriate concrete area acting in tension between the cracks to each reinforcing bar is crucial. An automatic numerical procedure has been developed to define the corresponding effective reinforcement ratio (ρ<em><sub>eff</sub></em><em> = A</em><em><sub>s</sub></em><em>/A</em><em><sub>c,eff</sub></em>) for any configuration, including skewed reinforcement (Fig. 23).</p>\n<figure data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2c0d58ae-1639-4b2a-a99c-a5e274a318ac/Effective%20area%20of%20concrete.png\" data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" alt=\"Fig. 4\tEffective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated; (b) cover and global symmetry condition; (c) resultant effective area.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 23\\qquad Effective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(b) cover and global symmetry condition; (c) resultant effective area.}}}\\)</em></p>\n<p><br></p>\n<p><strong>Non-stabilized cracking</strong></p>\n<p>Cracks existing in regions with geometric reinforcement ratios lower than ρ<em><sub>cr</sub></em>, i.e., the minimum reinforcement amount for which the reinforcement is able to carry the cracking load without yielding, are generated by either non-mechanical actions (e.g. shrinkage) or the progression of cracks controlled by other reinforcement. The value of this minimum reinforcement is obtained as follows:</p>\n<p>\\[{\\rho _{cr}} = \\frac{{{f_{ct}}}}{{{f_y} - \\left( {n - 1} \\right){f_{ct}}}}\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>y</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;reinforcement yield strength,</p>\n<p><em>f</em><em><sub>ct</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;concrete tensile strength,</p>\n<p><em>n</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modular ratio, <em>n</em>&nbsp;=&nbsp;<em>E</em><em><sub>s</sub></em>&nbsp;/&nbsp;<em>E</em><em><sub>c</sub></em>&nbsp;.</p>\n<p>For conventional concrete and reinforcing steel, ρ<em><sub>cr</sub></em> amounts to approximately 0.6%.</p>\n<p>For stirrups with reinforcement ratios below ρ<em><sub>cr</sub></em>, cracking is considered to be non-stabilized and tension stiffening is implemented by means of the Pull-Out Model (POM) described in Fig. 22b. This model analyzes the behavior of a single crack considering no mechanical interaction between separate cracks, neglecting the deformability of concrete in tension and assuming the same stepped, rigid-perfectly plastic bond shear stress-slip relationship used by the TCM. This allows the reinforcement strain distribution (ε<em><sub>s</sub></em>) in the vicinity of the crack to be obtained for any maximum steel stress at the crack (σ<em><sub>sr</sub></em>) directly from equilibrium. Given the fact that the crack spacing is unknown for a non-fully developed crack pattern, the average strain (ε<em><sub>m</sub></em>) is computed for any load level over the distance between points with zero slip when the reinforcing bar reaches its tensile strength (<em>f</em><em><sub>t</sub></em>) at the crack (<em>l</em><sub>ε,</sub><em><sub>avg</sub></em> in Fig. 22b), leading to the following relationships:</p>\n<figure data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/43adc17b-b9e9-4a81-ab9f-ff4c13297b34/Equation%201.2.4.2.PNG\" data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" alt=\"\"></figure>\n<p>The proposed models allow the computation of the behavior of bonded reinforcement, which is finally considered in the analysis. This behavior (including tension stiffening) for the most common European reinforcing steel (B500B, with <em>f</em><em><sub>t</sub></em>&nbsp;/&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;=&nbsp;1.08 and ε<em><sub>u</sub></em>&nbsp;=&nbsp;5%) is illustrated in Fig. 22c-d.</p>"
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                            "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                            "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                            "value": "<p>In the calculation for the results of SLS, only the elastic behavior of concrete is taken into account. In other words, an infinite linear stress-strain diagram is considered for concrete. You can display <strong>long-term</strong> or <strong>short-term</strong> effects for SLS checks. What is the difference between these two effects? Read the article below (paragraph Concrete SLS) to learn more.</p>\n<ul>\n  <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Material models (EN)</a></li>\n</ul>\n<h2>Stress</h2>\n<p>There are two options for displaying results for concrete and reinforcement:&nbsp;</p>\n<ul>\n  <li>the ratio of the stress and the limit stress&nbsp;</li>\n  <li>the stress itself&nbsp;</li>\n</ul>\n<p>Stresses are calculated for the <strong>Characteristic</strong> and for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of the stress and limit stress</h4>\n<p>The results are clear at first sight: Green color means the utilization is up to 90%, orange is 90-100% of utilization, and red is above 100%.</p>\n<p>Read about how the limit value is determined in the following article.</p>\n<ul>\n  <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Serviceability limit state analysis</a></li>\n</ul>\n<figure data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d12601c9-32a1-408f-9b41-e031d5b6fc45/RC-D_06_20.png\" data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" alt=\"\"></figure>\n<figure data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/45cd98c6-57b5-4373-a001-6e5c3ed8f5b8/RC-D_06_21.png.png\" data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" alt=\"\"></figure>\n<h4>Stress</h4>\n<p>The display method is similar to the ULS results (in this case, the stress is from the calculation with the elastic behavior of concrete). You can display the distribution of concrete stress <em>σ</em><em><sub>c</sub></em><sub> </sub>for an applied portion of the load. Also known as principal stresses <em>σ</em><em><sub>2</sub></em>.</p>\n<figure data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6f65c964-8c56-4aac-a14c-4307bfde6a8d/RC-D_06_22.png\" data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\" alt=\"\"></figure>\n<figure data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16c8bb7b-6bc7-4b9a-b27f-cf1075f7715a/RC-D_06_23.png\" data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" alt=\"\"></figure>\n<h2>Crack</h2>\n<p>In this section, you will learn about all four options for displaying results for crack checks. Read the further articles to learn about the calculation.</p>\n<ul>\n  <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Main assumptions and limitations for CSFM</a></li>\n  <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Structural element verification in IDEA StatiCa Detail</a></li>\n</ul>\n<p>Cracks are calculated only for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of crack width and limit crack width</h4>\n<p>The limit value w<sub>lim</sub> can be set in the top ribbon. The w<sub>lim</sub> = 0.3 mm is set by default according to Eurocode. The results are again differentiated by color (green/orange/red) so that the check is obvious at first sight.</p>\n<figure data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9fa5bdd1-ec85-4575-9e0f-6d26ce70c206/RC-D_06_24.png\" data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" alt=\"\"></figure>\n<h4>Crack width</h4>\n<p>This functionality is used to display the crack width for every single element of the reinforcement.&nbsp;</p>\n<figure data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97bc905a-76c9-4b12-abe1-3a93c71cdf2b/RC-D_06_25.png\" data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" alt=\"\"></figure>\n<h4>The distance between stabilized cracks</h4>\n<p>See the links at the beginning of the section. The article explains the method of calculating the distance between stabilized cracks.</p>\n<figure data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bcb4dbbc-29b3-48bb-a1f1-72cdb456b0b6/RC-D_06_26.png\" data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" alt=\"\"></figure>\n<p>The presentation of crack spacing is schematic only. It does not represent the crack spacing computed for the calculation.</p>\n<h4>Unreinforced area</h4>\n<p>The crack width is checked only in the vicinity of the reinforcement. Control of cracking is not performed in non-reinforced zones.</p>\n<p>This result simply shows the non-reinforced areas where cracks will probably appear. It is recommended to design some reinforcement to that areas.</p>\n<figure data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f60ea99-7197-4ee8-865e-2e282fdf60ef/RC-D_06_27.png\" data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\" alt=\"\"></figure>\n<h2>Deflection</h2>\n<p>See the options below:</p>\n<ul>\n  <li><em>u</em><em><sub>z,st</sub></em> - Immediate deflection caused by <strong>total load</strong> - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,lt</sub></em> - Long-term deflection caused by <strong>long-term loads </strong>(permanent and prestressing load type) - calculated with <strong>long-term stiffnesses </strong><em><strong>Ec,eff</strong></em><strong>. </strong>In other words, the creep coefficients are included.</li>\n  <li><em>Δu</em><em><sub>z</sub></em> - Deflection increment caused by <strong>short-term loads</strong> (variable load type) - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> = u</em><em><sub>z,lt</sub></em><em>&nbsp;+ Δu</em><em><sub>z</sub></em><sub>&nbsp;</sub></li>\n</ul>\n<p>Deflections are calculated only for the <strong>Characteristic</strong> load combinations.</p>\n<figure data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/815bac57-2809-4383-b0cc-abfa3349b443/RC-D_06_29.png\" data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" alt=\"\"></figure>\n<p>Besides the table values in the Data section, you can display the deformed shape. You can also modify the scale of the deformation.</p>\n<p>Finally, in addition to displaying deformations, it is also possible to do a <strong>deflection check</strong>. You can choose between two checks - <strong>Increment</strong> and <strong>Total.</strong></p>\n<ul>\n  <li><em>Δu</em><em><sub>z</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - &nbsp;Increment</li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> / Δu</em><em><sub>z,lim</sub></em>&nbsp;- Total</li>\n</ul>\n<p><em>Δu</em><em><sub>z,lim</sub></em>, and <em>Δu</em><em><sub>z,lim</sub></em> can be manually set in the Deflection check bar in the top ribbon.</p>\n<figure data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9efce2e8-54f2-4fe3-8fcb-700d0bc1bd32/RC-D_06_30.png\" data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" alt=\"\"></figure>\n<p>The deflection check is not allowed for trimmed ends.&nbsp;</p>\n<h2>Practical example</h2>\n<p>For a practical example of displaying the results, continue to the <a href=\"https://www.youtube.com/embed/77fFYFUvv5c/?start=2408\">video</a> from the previously streamed webinar. 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            "value": "<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.</p>\n<h3>Ultimate limit state analysis</h3>\n<p>The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<p>To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:</p>\n<ul>\n  <li>Choose a selection of the most critical load combinations.</li>\n  <li>Calculate only Ultimate Limit State (ULS) load combinations.</li>\n  <li>Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"Fig. 23\tMesh multiplier.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).</p>\n<p>The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.</p>\n<h3>Serviceability limit state analysis</h3>\n<p>SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.</p>\n<p>The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. IDEA StatiCa offers a fully customizable report to print out or save in an editable format.</p>\n<figure data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6e3c18c1-a97e-4301-8ee4-31b1ed278382/6_1%20Report.png\" data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" alt=\"\"></figure>\n<figure data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/33137b76-efe1-4357-a046-99a24413aa88/6_2%20Report.png\" data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" alt=\"\"></figure>\n<p>You have designed, optimized, and code-checked a pier cap according to Eurocode.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"idea_statica_tutorial___pier_cap_from_dxf_2495f70\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"campus_cta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0d61cad8_c463_0160_5df5_bb66b7a55152\"></object>"
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                            "value": "Los muros de hormigón y las vigas profundas son elementos portantes habituales en las estructuras de los edificios. Sin embargo, debido a los requisitos de trazado, estas estructuras portantes se ven muy a menudo debilitadas por puertas, ventanas y otras aberturas."
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                            "value": "<h4>¿Muro de hormigón armado o vigas profundas con verificación de códigos completa? No hay problema.</h4>\n<p>El objetivo del webinar es presentar cómo realizar en minutos la comprobación de código de una <strong>viga profunda de forma general</strong> en <strong>IDEA StatiCa Detail</strong> en conexión con los resultados de la aplicación de AEF. Mostraremos el flujo de trabajo en un ejemplo de un edificio residencial de hormigón - exportando la geometría, creando el submodelo en IDEA StatiCa Detail, aplicando las <strong>cargas correctas</strong>, el diseño de la armadura, y el código de comprobación final para los <strong>estados</strong> <strong>límite últimos y de servicio</strong>.</p>\n<p>Pruébelo usted mismo - obtenga la <a data-item-id=\"0c872071-6a3f-4b99-8cd4-66440db9cc0d\" href=\"\">licencia de prueba gratuita</a> y siga el tutorial paso a paso en <a data-item-id=\"1dc3667d-ddd6-5483-8b97-e7b69923fef7\" href=\"\">Muro de hormigón</a>.</p>\n<figure data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/177694cc-5c91-42cb-b88c-568f900670fe/Code-check%20of%20walls%20and%20deep%20beams.png\" data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\" alt=\"\"></figure>\n<h4>La solución definitiva para detalles y piezas estructurales de hormigón</h4>\n<p>El software de AEF 3D habitual tiene en cuenta el comportamiento lineal del hormigón. El diseño y las comprobaciones de código de la armadura son limitados, especialmente para el <strong>estado límite de servicio</strong> que puede conducir al desarrollo de <strong>grietas excesivas</strong>. Todo esto está cubierto dentro de la aplicación IDEA StatiCa Detail <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">basada en CSFM</a>. Ahora, todos los ingenieros pueden diseñar y comprobar eficientemente muros o vigas profundas de cualquier forma y muchas más.</p>\n<p>Si desea ver más de <strong>IDEA StatiCa Detail </strong>en acción, hay otros dos seminarios web grabados para ver:</p>\n<ul>\n  <li><a data-item-id=\"1300fb1c-8e32-47f3-8b21-0e8e77e1f238\" href=\"\">¿Cómo diseñar fácilmente una viga pretensada con aberturas?</a></li>\n  <li><a data-item-id=\"73d449cf-610e-5c7c-9e8c-da8093630d24\" href=\"\">Muro colado in situ - Ruzomberok (Eslovaquia)</a></li>\n</ul>\n<p>O navegue por nuestro Centro de soporte para ver <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&amp;label=detail\" title=\"IDEA StatiCa Detail\">tutoriales</a> y leer los <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">fundamentos teóricos.</a></p>\n<h3>Grabación del seminario web</h3>"
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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                        "description": "Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.",
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                        "description": "Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.",
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                    "value": "<h4>Crack width calculation</h4>\n<p>There are two ways of computing crack widths - stabilized and non-stabilized cracking. According to the geometrical reinforcement ratio in each part of the structure is decided, which type of crack calculation model will be used (TCM for stabilized cracking and POM for non-stabilized cracking model).</p>\n<figure data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62ba3929-8689-4973-8782-fcdd0780002b/Crack%20width%20calculation.PNG\" data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" alt=\"Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 20 \\qquad Crack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal}}}\\) \\( \\textsf{\\textit{\\footnotesize{directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with}}}\\) \\( \\textsf{\\textit{\\footnotesize{local&nbsp;non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar}}}\\)\\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking.}}}\\)</em></p>\n<p><br></p>\n<p>While the CSFM yields a direct result for most verifications (e.g., member capacity, deflections…), crack width results are calculated from the reinforcement strain results directly provided by FE analysis following the methodology described in Fig. 20. A crack kinematic without slip (pure crack opening) is considered (Fig. 20a), which is consistent with the main assumptions of the model. The principal directions of stresses and strains define the inclination of the cracks (θ<em><sub>r</sub></em>&nbsp;=&nbsp;θ<sub>s</sub>=&nbsp;θ<sub>e</sub>). According to (Fig. 20b), the crack width (<em>w</em>) can be projected in the direction of the reinforcing bar (<em>w</em><em><sub>b</sub></em>), leading to:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(θ_r + θ_b - \\frac{π}{2}\\right)}\\]</p>\n<p>where θ<em><sub>b</sub></em>&nbsp;is the bar inclination.</p>\n<p>Please note, that the program displays values of θ<em><sub>r</sub></em> and θ<em><sub>b</sub></em> &lt; <em>π/2</em>. It means that the previous equation works for cases, where the reinforcement and crack go through the different quadrants of the Cartesian coordinate system as shown in Fig. 20, where reinforcement goes through I. and III. quadrants and crack through II and IV. For cases where the reinforcement and crack go through the same quadrants, the equation has to be modified as follows:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(-θ_r + θ_b + \\frac{π}{2}\\right)}\\]</p>\n<p>The component <em>w</em><em><sub>b</sub></em> is consistently calculated based on the tension stiffening models by integrating the reinforcement strains. For those regions with fully developed crack patterns, the calculated average strains (e<em><sub>m</sub></em>) along the reinforcing bars are directly integrated along the crack spacing (<em>s</em><em><sub>r</sub></em>), as indicated in (Fig. 20c). While this approach to calculating the crack directions does not correspond to the real position of the cracks, it still provides representative values that lead to crack width results that can be compared to code-required crack width values at the position of the reinforcing bar.</p>\n<p>Special situations are observed at concave corners of the calculated structure. In this case, the corner predefines the position of a single crack that behaves in a non-stabilized fashion before additional adjacent cracks develop. These additional cracks generally develop after the serviceability range (Mata-Falcón 2015), which justifies calculating the crack widths in such a region as if they were non-stabilized (Fig. 21).</p>\n<figure data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a46a740-1622-47eb-b7f3-186fee0f6fbc/Concave%20corner.png\" data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" alt=\"Fig. 25\tDefinition of the region at concave corners in which the crack width is computed as if it were non-stabilized.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 21\\qquad Definition of the region at concave corners in which the crack width is computed as if it were non-stabilized.}}}\\]</em></p>\n<h4>Tension stiffening</h4>\n<p>The implementation of tension stiffening distinguishes between cases of stabilized and non-stabilized crack patterns. In both cases, the concrete is considered fully cracked before loading by default.</p>\n<figure data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/80e8fffe-3c98-4677-af35-7c2ce025e0bb/Tension%20stiffening%20model.PNG\" data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" alt=\"Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 22\\qquad Tension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear,}}}\\) </em>\\( \\textsf{\\textit{\\footnotesize{steel and concrete stresses, and steel strains between cracks, considering average crack spacing); (b) pull-out assumption}}}\\) \\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting}}}\\) \\( \\textsf{\\textit{\\footnotesize{tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) detail of the initial branches of the tension chord response.}}}\\)</p>\n<p><br></p>\n<p><strong>Stabilized cracking</strong></p>\n<p>In fully developed crack patterns, tension stiffening is introduced using the Tension Chord Model (TCM) (Marti et al. 1998; Alvarez 1998)&nbsp;– Fig. 22a – which has been shown to yield excellent response predictions in spite of its simplicity (Burns 2012). The TCM assumes a stepped, rigid-perfectly plastic bond shear stress-slip relationship with τ<em><sub>b&nbsp;</sub></em>=&nbsp;τ<em><sub>b</sub></em><sub>0</sub>&nbsp;=2&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s</sub></em>&nbsp;≤&nbsp;<em>f</em><em><sub>y</sub></em> and τ<em><sub>b</sub></em>&nbsp;=τ<em><sub>b</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s&nbsp;</sub></em>&gt;&nbsp;<em>f</em><em><sub>y</sub></em>. Treating every reinforcing bar as a tension chord ­– Fig. 22b and Fig. 22a – the distribution of bond shear, steel, and concrete stresses and hence the strain distribution between two cracks can be determined for any given value of the maximum steel stresses (or strains) at the cracks.</p>\n<p>For <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;<em>s</em><em><sub>r</sub></em><sub>0</sub>, a new crack may or may not form because at the center between two cracks σ<em><sub>c</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ct</sub></em>. Consequently, the crack spacing may vary by a factor of two, i.e., <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;λ<em>s</em><em><sub>r</sub></em><sub>0</sub>, with l&nbsp;=&nbsp;0.5…1.0. Assuming a certain value for λ, the average strain of the chord (ε<em><sub>m</sub></em>) can be expressed as a function of the maximum reinforcement stresses (i.e., stresses at the cracks, σ<em><sub>sr</sub></em>). For the idealized bilinear stress-strain diagram for the reinforcing bare bars considered by default in the CSFM, the following closed-form analytical expressions are obtained (Marti et al. 1998):</p>\n<p>\\[\\varepsilon_m = \\frac{\\sigma_{sr}}{E_s} - \\frac{\\tau_{b0}s_r}{E_s Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\sigma_{sr} \\le f_y\\]</p>\n<p><br></p>\n<p>\\[{\\varepsilon_m} = \\frac{{{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}^2}Ø}}{{4{E_{sh}}{\\tau _{b1}}{s_r}}}\\left( {1 - \\frac{{{E_{sh}}{\\tau_{b0}}}}{{{E_s}{\\tau_{b1}}}}} \\right) + \\frac{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}}{{{E_s}}}\\frac{{{\\tau_{b0}}}}{{{\\tau_{b1}}}} + \\left( {{\\varepsilon_y} - \\frac{{{\\tau_{b0}}{s_r}}}{{{E_s}Ø}}} \\right)\\]</p>\n<p><em>\\[\\textrm{for}\\qquad\\qquad{f_y} \\le {\\sigma _{sr}} \\le \\left( {{f_y} + \\frac{{2{\\tau _{b1}}{s_r}}}{Ø}} \\right)\\]</em></p>\n<p><br></p>\n<p>\\[ \\varepsilon_m = \\frac{f_s}{E_s} + \\frac{\\sigma_{sr}-f_y}{E_{sh}} - \\frac{\\tau_{b1} s_r}{E_{sh} Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\left(f_y + \\frac{2\\tau_{b1}s_r}{Ø}\\right) \\le \\sigma_{sr} \\le f_t\\]</p>\n<p>where:<br>\n <em>E</em><em><sub>sh</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;the steel hardening modulus <em>E</em><em><sub>sh</sub></em>&nbsp;=&nbsp;(<em>f</em><em><sub>t</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>)/(ε<em><sub>u</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;/<em>E</em><em><sub>s</sub></em>)&nbsp;,</p>\n<p><em>E</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of reinforcement,</p>\n<p><em>Ø</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reinforcing bar diameter,</p>\n<p>s<em><sub>r</sub></em><em><sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sup></em>crack spacing,</p>\n<p>σ<em><sub>sr</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>reinforcement stresses at the cracks,</p>\n<p>σ<em><sub>s</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>actual reinforcement stresses,</p>\n<p><em>f</em><em><sub>y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</sub></em>yield strength of reinforcement.</p>\n<p><br></p>\n<p>The Idea StatiCa Detail implementation of the CSFM considers average crack spacing by default when performing computer-aided stress field analysis. The average crack spacing is considered to be 2/3 of the maximum crack spacing (λ&nbsp;=&nbsp;0.67), which follows recommendations made on the basis of bending and tension tests (Broms 1965; Beeby 1979; Meier 1983). It should be noted that calculations of crack widths consider a maximum crack spacing (λ&nbsp;=&nbsp;1.0) in order to obtain conservative values.</p>\n<p>The application of the TCM depends on the reinforcement ratio, and hence the assignment of an appropriate concrete area acting in tension between the cracks to each reinforcing bar is crucial. An automatic numerical procedure has been developed to define the corresponding effective reinforcement ratio (ρ<em><sub>eff</sub></em><em> = A</em><em><sub>s</sub></em><em>/A</em><em><sub>c,eff</sub></em>) for any configuration, including skewed reinforcement (Fig. 23).</p>\n<figure data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2c0d58ae-1639-4b2a-a99c-a5e274a318ac/Effective%20area%20of%20concrete.png\" data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" alt=\"Fig. 4\tEffective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated; (b) cover and global symmetry condition; (c) resultant effective area.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 23\\qquad Effective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(b) cover and global symmetry condition; (c) resultant effective area.}}}\\)</em></p>\n<p><br></p>\n<p><strong>Non-stabilized cracking</strong></p>\n<p>Cracks existing in regions with geometric reinforcement ratios lower than ρ<em><sub>cr</sub></em>, i.e., the minimum reinforcement amount for which the reinforcement is able to carry the cracking load without yielding, are generated by either non-mechanical actions (e.g. shrinkage) or the progression of cracks controlled by other reinforcement. The value of this minimum reinforcement is obtained as follows:</p>\n<p>\\[{\\rho _{cr}} = \\frac{{{f_{ct}}}}{{{f_y} - \\left( {n - 1} \\right){f_{ct}}}}\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>y</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;reinforcement yield strength,</p>\n<p><em>f</em><em><sub>ct</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;concrete tensile strength,</p>\n<p><em>n</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modular ratio, <em>n</em>&nbsp;=&nbsp;<em>E</em><em><sub>s</sub></em>&nbsp;/&nbsp;<em>E</em><em><sub>c</sub></em>&nbsp;.</p>\n<p>For conventional concrete and reinforcing steel, ρ<em><sub>cr</sub></em> amounts to approximately 0.6%.</p>\n<p>For stirrups with reinforcement ratios below ρ<em><sub>cr</sub></em>, cracking is considered to be non-stabilized and tension stiffening is implemented by means of the Pull-Out Model (POM) described in Fig. 22b. This model analyzes the behavior of a single crack considering no mechanical interaction between separate cracks, neglecting the deformability of concrete in tension and assuming the same stepped, rigid-perfectly plastic bond shear stress-slip relationship used by the TCM. This allows the reinforcement strain distribution (ε<em><sub>s</sub></em>) in the vicinity of the crack to be obtained for any maximum steel stress at the crack (σ<em><sub>sr</sub></em>) directly from equilibrium. Given the fact that the crack spacing is unknown for a non-fully developed crack pattern, the average strain (ε<em><sub>m</sub></em>) is computed for any load level over the distance between points with zero slip when the reinforcing bar reaches its tensile strength (<em>f</em><em><sub>t</sub></em>) at the crack (<em>l</em><sub>ε,</sub><em><sub>avg</sub></em> in Fig. 22b), leading to the following relationships:</p>\n<figure data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/43adc17b-b9e9-4a81-ab9f-ff4c13297b34/Equation%201.2.4.2.PNG\" data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" alt=\"\"></figure>\n<p>The proposed models allow the computation of the behavior of bonded reinforcement, which is finally considered in the analysis. This behavior (including tension stiffening) for the most common European reinforcing steel (B500B, with <em>f</em><em><sub>t</sub></em>&nbsp;/&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;=&nbsp;1.08 and ε<em><sub>u</sub></em>&nbsp;=&nbsp;5%) is illustrated in Fig. 22c-d.</p>"
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                            "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                            "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                            "value": "<p>In the calculation for the results of SLS, only the elastic behavior of concrete is taken into account. In other words, an infinite linear stress-strain diagram is considered for concrete. You can display <strong>long-term</strong> or <strong>short-term</strong> effects for SLS checks. What is the difference between these two effects? Read the article below (paragraph Concrete SLS) to learn more.</p>\n<ul>\n  <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Material models (EN)</a></li>\n</ul>\n<h2>Stress</h2>\n<p>There are two options for displaying results for concrete and reinforcement:&nbsp;</p>\n<ul>\n  <li>the ratio of the stress and the limit stress&nbsp;</li>\n  <li>the stress itself&nbsp;</li>\n</ul>\n<p>Stresses are calculated for the <strong>Characteristic</strong> and for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of the stress and limit stress</h4>\n<p>The results are clear at first sight: Green color means the utilization is up to 90%, orange is 90-100% of utilization, and red is above 100%.</p>\n<p>Read about how the limit value is determined in the following article.</p>\n<ul>\n  <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Serviceability limit state analysis</a></li>\n</ul>\n<figure data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d12601c9-32a1-408f-9b41-e031d5b6fc45/RC-D_06_20.png\" data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" alt=\"\"></figure>\n<figure data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/45cd98c6-57b5-4373-a001-6e5c3ed8f5b8/RC-D_06_21.png.png\" data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" alt=\"\"></figure>\n<h4>Stress</h4>\n<p>The display method is similar to the ULS results (in this case, the stress is from the calculation with the elastic behavior of concrete). You can display the distribution of concrete stress <em>σ</em><em><sub>c</sub></em><sub> </sub>for an applied portion of the load. Also known as principal stresses <em>σ</em><em><sub>2</sub></em>.</p>\n<figure data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6f65c964-8c56-4aac-a14c-4307bfde6a8d/RC-D_06_22.png\" data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\" alt=\"\"></figure>\n<figure data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16c8bb7b-6bc7-4b9a-b27f-cf1075f7715a/RC-D_06_23.png\" data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" alt=\"\"></figure>\n<h2>Crack</h2>\n<p>In this section, you will learn about all four options for displaying results for crack checks. Read the further articles to learn about the calculation.</p>\n<ul>\n  <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Main assumptions and limitations for CSFM</a></li>\n  <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Structural element verification in IDEA StatiCa Detail</a></li>\n</ul>\n<p>Cracks are calculated only for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of crack width and limit crack width</h4>\n<p>The limit value w<sub>lim</sub> can be set in the top ribbon. The w<sub>lim</sub> = 0.3 mm is set by default according to Eurocode. The results are again differentiated by color (green/orange/red) so that the check is obvious at first sight.</p>\n<figure data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9fa5bdd1-ec85-4575-9e0f-6d26ce70c206/RC-D_06_24.png\" data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" alt=\"\"></figure>\n<h4>Crack width</h4>\n<p>This functionality is used to display the crack width for every single element of the reinforcement.&nbsp;</p>\n<figure data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97bc905a-76c9-4b12-abe1-3a93c71cdf2b/RC-D_06_25.png\" data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" alt=\"\"></figure>\n<h4>The distance between stabilized cracks</h4>\n<p>See the links at the beginning of the section. The article explains the method of calculating the distance between stabilized cracks.</p>\n<figure data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bcb4dbbc-29b3-48bb-a1f1-72cdb456b0b6/RC-D_06_26.png\" data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" alt=\"\"></figure>\n<p>The presentation of crack spacing is schematic only. It does not represent the crack spacing computed for the calculation.</p>\n<h4>Unreinforced area</h4>\n<p>The crack width is checked only in the vicinity of the reinforcement. Control of cracking is not performed in non-reinforced zones.</p>\n<p>This result simply shows the non-reinforced areas where cracks will probably appear. It is recommended to design some reinforcement to that areas.</p>\n<figure data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f60ea99-7197-4ee8-865e-2e282fdf60ef/RC-D_06_27.png\" data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\" alt=\"\"></figure>\n<h2>Deflection</h2>\n<p>See the options below:</p>\n<ul>\n  <li><em>u</em><em><sub>z,st</sub></em> - Immediate deflection caused by <strong>total load</strong> - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,lt</sub></em> - Long-term deflection caused by <strong>long-term loads </strong>(permanent and prestressing load type) - calculated with <strong>long-term stiffnesses </strong><em><strong>Ec,eff</strong></em><strong>. </strong>In other words, the creep coefficients are included.</li>\n  <li><em>Δu</em><em><sub>z</sub></em> - Deflection increment caused by <strong>short-term loads</strong> (variable load type) - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> = u</em><em><sub>z,lt</sub></em><em>&nbsp;+ Δu</em><em><sub>z</sub></em><sub>&nbsp;</sub></li>\n</ul>\n<p>Deflections are calculated only for the <strong>Characteristic</strong> load combinations.</p>\n<figure data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/815bac57-2809-4383-b0cc-abfa3349b443/RC-D_06_29.png\" data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" alt=\"\"></figure>\n<p>Besides the table values in the Data section, you can display the deformed shape. You can also modify the scale of the deformation.</p>\n<p>Finally, in addition to displaying deformations, it is also possible to do a <strong>deflection check</strong>. You can choose between two checks - <strong>Increment</strong> and <strong>Total.</strong></p>\n<ul>\n  <li><em>Δu</em><em><sub>z</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - &nbsp;Increment</li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> / Δu</em><em><sub>z,lim</sub></em>&nbsp;- Total</li>\n</ul>\n<p><em>Δu</em><em><sub>z,lim</sub></em>, and <em>Δu</em><em><sub>z,lim</sub></em> can be manually set in the Deflection check bar in the top ribbon.</p>\n<figure data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9efce2e8-54f2-4fe3-8fcb-700d0bc1bd32/RC-D_06_30.png\" data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" alt=\"\"></figure>\n<p>The deflection check is not allowed for trimmed ends.&nbsp;</p>\n<h2>Practical example</h2>\n<p>For a practical example of displaying the results, continue to the <a href=\"https://www.youtube.com/embed/77fFYFUvv5c/?start=2408\">video</a> from the previously streamed webinar. Due to the fact that we have two identical models, which vary in the usage method, we can check and compare results for both.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2d2a3d75_fd83_01e8_404c_a86288f83049\"></object>"
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            "value": "<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.</p>\n<h3>Ultimate limit state analysis</h3>\n<p>The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<p>To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:</p>\n<ul>\n  <li>Choose a selection of the most critical load combinations.</li>\n  <li>Calculate only Ultimate Limit State (ULS) load combinations.</li>\n  <li>Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"Fig. 23\tMesh multiplier.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).</p>\n<p>The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.</p>\n<h3>Serviceability limit state analysis</h3>\n<p>SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.</p>\n<p>The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. IDEA StatiCa offers a fully customizable report to print out or save in an editable format.</p>\n<figure data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6e3c18c1-a97e-4301-8ee4-31b1ed278382/6_1%20Report.png\" data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" alt=\"\"></figure>\n<figure data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/33137b76-efe1-4357-a046-99a24413aa88/6_2%20Report.png\" data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" alt=\"\"></figure>\n<p>You have designed, optimized, and code-checked a pier cap according to Eurocode.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"idea_statica_tutorial___pier_cap_from_dxf_2495f70\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"campus_cta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0d61cad8_c463_0160_5df5_bb66b7a55152\"></object>"
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                            "value": "Los muros de hormigón y las vigas profundas son elementos portantes habituales en las estructuras de los edificios. Sin embargo, debido a los requisitos de trazado, estas estructuras portantes se ven muy a menudo debilitadas por puertas, ventanas y otras aberturas."
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                            "value": "<h4>¿Muro de hormigón armado o vigas profundas con verificación de códigos completa? No hay problema.</h4>\n<p>El objetivo del webinar es presentar cómo realizar en minutos la comprobación de código de una <strong>viga profunda de forma general</strong> en <strong>IDEA StatiCa Detail</strong> en conexión con los resultados de la aplicación de AEF. Mostraremos el flujo de trabajo en un ejemplo de un edificio residencial de hormigón - exportando la geometría, creando el submodelo en IDEA StatiCa Detail, aplicando las <strong>cargas correctas</strong>, el diseño de la armadura, y el código de comprobación final para los <strong>estados</strong> <strong>límite últimos y de servicio</strong>.</p>\n<p>Pruébelo usted mismo - obtenga la <a data-item-id=\"0c872071-6a3f-4b99-8cd4-66440db9cc0d\" href=\"\">licencia de prueba gratuita</a> y siga el tutorial paso a paso en <a data-item-id=\"1dc3667d-ddd6-5483-8b97-e7b69923fef7\" href=\"\">Muro de hormigón</a>.</p>\n<figure data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/177694cc-5c91-42cb-b88c-568f900670fe/Code-check%20of%20walls%20and%20deep%20beams.png\" data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\" alt=\"\"></figure>\n<h4>La solución definitiva para detalles y piezas estructurales de hormigón</h4>\n<p>El software de AEF 3D habitual tiene en cuenta el comportamiento lineal del hormigón. El diseño y las comprobaciones de código de la armadura son limitados, especialmente para el <strong>estado límite de servicio</strong> que puede conducir al desarrollo de <strong>grietas excesivas</strong>. Todo esto está cubierto dentro de la aplicación IDEA StatiCa Detail <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">basada en CSFM</a>. Ahora, todos los ingenieros pueden diseñar y comprobar eficientemente muros o vigas profundas de cualquier forma y muchas más.</p>\n<p>Si desea ver más de <strong>IDEA StatiCa Detail </strong>en acción, hay otros dos seminarios web grabados para ver:</p>\n<ul>\n  <li><a data-item-id=\"1300fb1c-8e32-47f3-8b21-0e8e77e1f238\" href=\"\">¿Cómo diseñar fácilmente una viga pretensada con aberturas?</a></li>\n  <li><a data-item-id=\"73d449cf-610e-5c7c-9e8c-da8093630d24\" href=\"\">Muro colado in situ - Ruzomberok (Eslovaquia)</a></li>\n</ul>\n<p>O navegue por nuestro Centro de soporte para ver <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&amp;label=detail\" title=\"IDEA StatiCa Detail\">tutoriales</a> y leer los <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">fundamentos teóricos.</a></p>\n<h3>Grabación del seminario web</h3>"
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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    "value": "<p>The different verifications required by AS 3600 are assessed based on the direct results provided by the model. Verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<h4>Strength - Concrete</h4>\n<p>The <strong>concrete strength</strong> in compression is evaluated as the ratio between the maximum&nbsp;Equivalent principal stress <em>f</em><em><sub>c,eq</sub></em> (also σ<em><sub>c,eq</sub></em>&nbsp;in previous text) obtained from FE analysis and the limit value <em>f'</em><em><sub>c,lim</sub></em>.</p>\n<p><strong>Equivalent Principal Stress expresses the equivalent uni-axial stress for a general tri-axial stress state.</strong></p>\n<p>\\[f_{c,eq} = \\sigma_{c3} - \\sigma_{c1}\\]</p>\n<p>The f<em><sub>c,eq</sub></em>&nbsp;value can, therefore, be directly compared with uniaxial strength limits. This expression is derived from the implementation of the Mohr-Coulomb plasticity theory, conservatively assuming the angle of internal friction&nbsp;<em>φ = 0°.</em></p>\n<h4>Strength - Reinforcement</h4>\n<p>The <strong>strength of the reinforcement</strong> is evaluated in both tension and compression as the ratio between the stress in the reinforcement at the cracks <em>f</em><em><sub>s</sub></em> and the specified limit value <em>f</em><em><sub>sy,lim</sub></em>.</p>\n<p>\\[f_{sy,lim} = \\phi_{s} \\cdot f_{sy}\\]</p>\n<h4>Strength - Anchors</h4>\n<p>Anchors are checked for normal stresses in a similar way to reinforcement, where the limit value&nbsp;<em>f</em><em><sub>sy,lim</sub></em>&nbsp;is determined.&nbsp;</p>\n<p>In the current version, the code checks for anchors in shear and shear with tension<strong>&nbsp;</strong>are not available.</p>\n<p><strong>Pull-out check for headed anchors (Washer plates and Headed studs)</strong></p>\n<p>For headed anchors, an additional stop criterion is implemented to check the concrete bearing (crushing) above the anchor head - pull-out. During the analysis, the compressive force transferred through the head-to-concrete contact is monitored and compared with the limit value given by AS 5216:2021 Cl. 6.3.4 (pull-out failure of headed fastenings).</p>\n<p>\\[N_{Rd,p} = \\Phi_{Mp} \\cdot k_{2} \\cdot A_{h} \\cdot f'_{c}\\]<br>\n​</p>\n<p>where:</p>\n<ul>\n  <li>\\( \\Phi_{Mp}\\) is the strength reduction factor - Table 3.2.4</li>\n  <li><em>A</em><em><sub>h</sub></em>&nbsp;is the load bearing area of the head of the fastener (without the shank area).&nbsp;</li>\n  <li><em>f</em><em><sub>c</sub></em><em>'</em>&nbsp;is the specified compressive strength of concrete</li>\n  <li><em>k</em><em><sub>2</sub></em>&nbsp;is always taken as 7.5, i.e. the value for cracked concrete. This is consistent with the CSFM approach used in Detail, where the tensile strength of concrete is neglected and the concrete is assumed to be cracked in tension.</li>\n</ul>\n<p>Once the contact force reaches this code-based limit, the stop criterion is triggered and the analysis is terminated before the design pull-out resistance is exceeded.​&nbsp;</p>\n<h4>Anchorage - &nbsp;Bond stress</h4>\n<p>The <strong>bond shear stress</strong> is evaluated independently as the ratio between the bond stress τ<em><sub>b</sub></em> calculated by FE analysis and the design ultimate bond stress <em>f</em><em><sub>bu</sub></em>.</p>\n<p>For the determination of the design ultimate bond stress <em>f</em><em><sub>bu</sub></em>, the formula C13.1.2.2 defined in AS3600:2018 Sup 1:2022 is considered in the application.</p>\n<p>\\[f_{bu}=\\frac{k_{2}}{k_{1} \\cdot k_{3}} \\cdot (0.5 \\cdot \\sqrt{f'_{c}})\\]</p>\n<p>Where <em>f'</em><em><sub>c</sub></em><em> ≤ 65 MPa</em> (in the formula is in MPa), and <em>k</em> factors are determined from AS 3600 Cl. 13.1.2.2 as follows:</p>\n<p><em>k</em><em><sub>3</sub></em><em> = 0.7</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(conservative value for all reinforcement)<br>\n<em>k</em><em><sub>2</sub></em><em> = (132 - d</em><em><sub>b</sub></em><em>) / 100</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(<em>d</em><em><sub>b</sub></em> is diameret of rebar in millimeters)<br>\n = 1.3 for a horizontal bar with more than 300 mm of concrete cast below the bar, or 1.0 otherwise</p>\n<p><em>k</em><em><sub>1</sub></em> is automatically derived from the position of the reinforcement in the model and from the direction of concreting that can be set in the application for each project item as follows.</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 52\\qquad Direction of concreting}}}\\]</em></p>\n<p>The basic development length <em>L</em><em><sub>sy,tb</sub></em> is calculated according to formula 13.1.2.2 in AS 3600 as follows:</p>\n<p>\\[L_{sy,tb}=\\frac{0.5\\cdot k_{1}\\cdot k_{3}\\cdot f_{sy}\\cdot d_{b}}{k_{2}\\cdot \\sqrt{f'_{c}}}\\ge 29 \\cdot k_{1}\\cdot d_{b}\\]</p>\n<p>As can be seen in the formula, the basic development length <em>L</em><em><sub>sy,tb</sub></em> is limited from below, and therefore the design ultimate bond stress <em>f</em><em><sub>bu</sub></em> must be limited in the same way in the application, so the following applies:</p>\n<p>\\[f_{bu}\\le \\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p>Where <em>f</em><em><sub>sy</sub></em> is in MPa.</p>\n<p>The derivation of the <em>f</em><em><sub>bu</sub></em> limitation is as follows:</p>\n<p>\\[f_{bu}= \\frac{f_{sy}\\cdot A_{s}}{ \\pi \\cdot d_{b} \\cdot L_{sy,tb}}=\\frac{f_{sy}\\cdot \\pi \\cdot d_{b}^{2}}{4 \\cdot \\pi \\cdot d_{b} \\cdot 29 \\cdot k{1} \\cdot d_{b}} =\\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p><br></p>\n<p><strong>Total force </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> and limit force </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>The total force <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> is a result of the finite element analysis and can be defined in two ways.</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>where <em>A</em><em><sub>s</sub></em> is the area of the reinforcement bar and <em>f</em><em><sub>s</sub></em> is the stress in the bar.</p>\n<p>Or as a sum of the&nbsp;anchorage force&nbsp;<em>F</em><em><sub>a </sub></em>and the&nbsp;bond force&nbsp;<em>F</em><em><sub>bond</sub></em><em>.</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>where <em>F</em><em><sub>a</sub></em> is the actual force in the anchorage spring and <em>F</em><em><sub>bond</sub></em> is the bond force that can be obtained by integrating the bond stress <em>τ</em><em><sub>b</sub></em> along the length of reinforcement bar <em>l.</em></p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> is the circumference of the reinforcement bar.</p>\n<p>The limit force <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> is the maximum force in the element of the rebar considering the <strong>strength</strong> of the rebar and also <strong>anchoring conditions </strong>(bond between concrete and reinforcement and anchorage hooks, loops, etc.).</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>where C<sub>s</sub> is the circumference of the reinforcement bar, and <em>l</em> is the length from the beginning of the rebar to the point of interest.</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 53\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>where <em>F</em><em><sub>lim,add</sub></em> is the additional force calculated from the magnitude of the angle between neighboring elements. <em>F</em><em><sub>lim,2</sub></em> must always be lower than <em>F</em><em><sub>u</sub></em>.</p>\n<p><br></p>\n<p>The available <strong>anchorage types</strong> in CSFM include a straight bar (i.e., no anchor end reduction), Standard cog, Standard hook, perfect bond, and continuous bar. All these types, along with the respective anchorage coefficients β, are shown in Fig. 54 for longitudinal reinforcement. The values of the adopted anchorage coefficients are derived from AS 3600 Cl. 13.1.2. It should be noted that CSFM distinguishes three types of anchorage ends: (i) no reduction in the anchorage length, (ii) a reduction of 50% of the anchorage length in the case of a normalized anchorage, and (iii) perfect bond.</p>\n<figure data-asset-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" data-image-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/021688e6-24c8-441b-8210-9f0bb4377e75/Available%20anchorage%20types%20for%20longitudinal%20rebars_AUS.png\" data-asset-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" data-image-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 54\\qquad &nbsp;Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b)&nbsp;Standard cog; (c) Standard hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>The anchorage coefficient for stirrups is always - β = 1.0.</p>\n<p>In order to comply with AS 3600, the anchorage spring should be used in the calculation. The anchorage spring is modified by the β coefficient, so the user must use one of the available anchorage types when defining the reinforcement start and end conditions.&nbsp;</p>"
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                    "value": "<h4>Crack width calculation</h4>\n<p>There are two ways of computing crack widths - stabilized and non-stabilized cracking. According to the geometrical reinforcement ratio in each part of the structure is decided, which type of crack calculation model will be used (TCM for stabilized cracking and POM for non-stabilized cracking model).</p>\n<figure data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62ba3929-8689-4973-8782-fcdd0780002b/Crack%20width%20calculation.PNG\" data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" alt=\"Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 20 \\qquad Crack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal}}}\\) \\( \\textsf{\\textit{\\footnotesize{directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with}}}\\) \\( \\textsf{\\textit{\\footnotesize{local&nbsp;non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar}}}\\)\\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking.}}}\\)</em></p>\n<p><br></p>\n<p>While the CSFM yields a direct result for most verifications (e.g., member capacity, deflections…), crack width results are calculated from the reinforcement strain results directly provided by FE analysis following the methodology described in Fig. 20. A crack kinematic without slip (pure crack opening) is considered (Fig. 20a), which is consistent with the main assumptions of the model. The principal directions of stresses and strains define the inclination of the cracks (θ<em><sub>r</sub></em>&nbsp;=&nbsp;θ<sub>s</sub>=&nbsp;θ<sub>e</sub>). According to (Fig. 20b), the crack width (<em>w</em>) can be projected in the direction of the reinforcing bar (<em>w</em><em><sub>b</sub></em>), leading to:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(θ_r + θ_b - \\frac{π}{2}\\right)}\\]</p>\n<p>where θ<em><sub>b</sub></em>&nbsp;is the bar inclination.</p>\n<p>Please note, that the program displays values of θ<em><sub>r</sub></em> and θ<em><sub>b</sub></em> &lt; <em>π/2</em>. It means that the previous equation works for cases, where the reinforcement and crack go through the different quadrants of the Cartesian coordinate system as shown in Fig. 20, where reinforcement goes through I. and III. quadrants and crack through II and IV. For cases where the reinforcement and crack go through the same quadrants, the equation has to be modified as follows:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(-θ_r + θ_b + \\frac{π}{2}\\right)}\\]</p>\n<p>The component <em>w</em><em><sub>b</sub></em> is consistently calculated based on the tension stiffening models by integrating the reinforcement strains. For those regions with fully developed crack patterns, the calculated average strains (e<em><sub>m</sub></em>) along the reinforcing bars are directly integrated along the crack spacing (<em>s</em><em><sub>r</sub></em>), as indicated in (Fig. 20c). While this approach to calculating the crack directions does not correspond to the real position of the cracks, it still provides representative values that lead to crack width results that can be compared to code-required crack width values at the position of the reinforcing bar.</p>\n<p>Special situations are observed at concave corners of the calculated structure. In this case, the corner predefines the position of a single crack that behaves in a non-stabilized fashion before additional adjacent cracks develop. These additional cracks generally develop after the serviceability range (Mata-Falcón 2015), which justifies calculating the crack widths in such a region as if they were non-stabilized (Fig. 21).</p>\n<figure data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a46a740-1622-47eb-b7f3-186fee0f6fbc/Concave%20corner.png\" data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" alt=\"Fig. 25\tDefinition of the region at concave corners in which the crack width is computed as if it were non-stabilized.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 21\\qquad Definition of the region at concave corners in which the crack width is computed as if it were non-stabilized.}}}\\]</em></p>\n<h4>Tension stiffening</h4>\n<p>The implementation of tension stiffening distinguishes between cases of stabilized and non-stabilized crack patterns. In both cases, the concrete is considered fully cracked before loading by default.</p>\n<figure data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/80e8fffe-3c98-4677-af35-7c2ce025e0bb/Tension%20stiffening%20model.PNG\" data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" alt=\"Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 22\\qquad Tension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear,}}}\\) </em>\\( \\textsf{\\textit{\\footnotesize{steel and concrete stresses, and steel strains between cracks, considering average crack spacing); (b) pull-out assumption}}}\\) \\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting}}}\\) \\( \\textsf{\\textit{\\footnotesize{tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) detail of the initial branches of the tension chord response.}}}\\)</p>\n<p><br></p>\n<p><strong>Stabilized cracking</strong></p>\n<p>In fully developed crack patterns, tension stiffening is introduced using the Tension Chord Model (TCM) (Marti et al. 1998; Alvarez 1998)&nbsp;– Fig. 22a – which has been shown to yield excellent response predictions in spite of its simplicity (Burns 2012). The TCM assumes a stepped, rigid-perfectly plastic bond shear stress-slip relationship with τ<em><sub>b&nbsp;</sub></em>=&nbsp;τ<em><sub>b</sub></em><sub>0</sub>&nbsp;=2&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s</sub></em>&nbsp;≤&nbsp;<em>f</em><em><sub>y</sub></em> and τ<em><sub>b</sub></em>&nbsp;=τ<em><sub>b</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s&nbsp;</sub></em>&gt;&nbsp;<em>f</em><em><sub>y</sub></em>. Treating every reinforcing bar as a tension chord ­– Fig. 22b and Fig. 22a – the distribution of bond shear, steel, and concrete stresses and hence the strain distribution between two cracks can be determined for any given value of the maximum steel stresses (or strains) at the cracks.</p>\n<p>For <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;<em>s</em><em><sub>r</sub></em><sub>0</sub>, a new crack may or may not form because at the center between two cracks σ<em><sub>c</sub></em><sub>1</sub>&nbsp;=&nbsp;<em>f</em><em><sub>ct</sub></em>. Consequently, the crack spacing may vary by a factor of two, i.e., <em>s</em><em><sub>r</sub></em>&nbsp;=&nbsp;λ<em>s</em><em><sub>r</sub></em><sub>0</sub>, with l&nbsp;=&nbsp;0.5…1.0. Assuming a certain value for λ, the average strain of the chord (ε<em><sub>m</sub></em>) can be expressed as a function of the maximum reinforcement stresses (i.e., stresses at the cracks, σ<em><sub>sr</sub></em>). For the idealized bilinear stress-strain diagram for the reinforcing bare bars considered by default in the CSFM, the following closed-form analytical expressions are obtained (Marti et al. 1998):</p>\n<p>\\[\\varepsilon_m = \\frac{\\sigma_{sr}}{E_s} - \\frac{\\tau_{b0}s_r}{E_s Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\sigma_{sr} \\le f_y\\]</p>\n<p><br></p>\n<p>\\[{\\varepsilon_m} = \\frac{{{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}^2}Ø}}{{4{E_{sh}}{\\tau _{b1}}{s_r}}}\\left( {1 - \\frac{{{E_{sh}}{\\tau_{b0}}}}{{{E_s}{\\tau_{b1}}}}} \\right) + \\frac{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}}{{{E_s}}}\\frac{{{\\tau_{b0}}}}{{{\\tau_{b1}}}} + \\left( {{\\varepsilon_y} - \\frac{{{\\tau_{b0}}{s_r}}}{{{E_s}Ø}}} \\right)\\]</p>\n<p><em>\\[\\textrm{for}\\qquad\\qquad{f_y} \\le {\\sigma _{sr}} \\le \\left( {{f_y} + \\frac{{2{\\tau _{b1}}{s_r}}}{Ø}} \\right)\\]</em></p>\n<p><br></p>\n<p>\\[ \\varepsilon_m = \\frac{f_s}{E_s} + \\frac{\\sigma_{sr}-f_y}{E_{sh}} - \\frac{\\tau_{b1} s_r}{E_{sh} Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\left(f_y + \\frac{2\\tau_{b1}s_r}{Ø}\\right) \\le \\sigma_{sr} \\le f_t\\]</p>\n<p>where:<br>\n <em>E</em><em><sub>sh</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;the steel hardening modulus <em>E</em><em><sub>sh</sub></em>&nbsp;=&nbsp;(<em>f</em><em><sub>t</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>)/(ε<em><sub>u</sub></em>&nbsp;–&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;/<em>E</em><em><sub>s</sub></em>)&nbsp;,</p>\n<p><em>E</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of reinforcement,</p>\n<p><em>Ø</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reinforcing bar diameter,</p>\n<p>s<em><sub>r</sub></em><em><sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sup></em>crack spacing,</p>\n<p>σ<em><sub>sr</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>reinforcement stresses at the cracks,</p>\n<p>σ<em><sub>s</sub></em><em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </em>actual reinforcement stresses,</p>\n<p><em>f</em><em><sub>y&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</sub></em>yield strength of reinforcement.</p>\n<p><br></p>\n<p>The Idea StatiCa Detail implementation of the CSFM considers average crack spacing by default when performing computer-aided stress field analysis. The average crack spacing is considered to be 2/3 of the maximum crack spacing (λ&nbsp;=&nbsp;0.67), which follows recommendations made on the basis of bending and tension tests (Broms 1965; Beeby 1979; Meier 1983). It should be noted that calculations of crack widths consider a maximum crack spacing (λ&nbsp;=&nbsp;1.0) in order to obtain conservative values.</p>\n<p>The application of the TCM depends on the reinforcement ratio, and hence the assignment of an appropriate concrete area acting in tension between the cracks to each reinforcing bar is crucial. An automatic numerical procedure has been developed to define the corresponding effective reinforcement ratio (ρ<em><sub>eff</sub></em><em> = A</em><em><sub>s</sub></em><em>/A</em><em><sub>c,eff</sub></em>) for any configuration, including skewed reinforcement (Fig. 23).</p>\n<figure data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2c0d58ae-1639-4b2a-a99c-a5e274a318ac/Effective%20area%20of%20concrete.png\" data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" alt=\"Fig. 4\tEffective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated; (b) cover and global symmetry condition; (c) resultant effective area.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 23\\qquad Effective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(b) cover and global symmetry condition; (c) resultant effective area.}}}\\)</em></p>\n<p><br></p>\n<p><strong>Non-stabilized cracking</strong></p>\n<p>Cracks existing in regions with geometric reinforcement ratios lower than ρ<em><sub>cr</sub></em>, i.e., the minimum reinforcement amount for which the reinforcement is able to carry the cracking load without yielding, are generated by either non-mechanical actions (e.g. shrinkage) or the progression of cracks controlled by other reinforcement. The value of this minimum reinforcement is obtained as follows:</p>\n<p>\\[{\\rho _{cr}} = \\frac{{{f_{ct}}}}{{{f_y} - \\left( {n - 1} \\right){f_{ct}}}}\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>y</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;reinforcement yield strength,</p>\n<p><em>f</em><em><sub>ct</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;concrete tensile strength,</p>\n<p><em>n</em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modular ratio, <em>n</em>&nbsp;=&nbsp;<em>E</em><em><sub>s</sub></em>&nbsp;/&nbsp;<em>E</em><em><sub>c</sub></em>&nbsp;.</p>\n<p>For conventional concrete and reinforcing steel, ρ<em><sub>cr</sub></em> amounts to approximately 0.6%.</p>\n<p>For stirrups with reinforcement ratios below ρ<em><sub>cr</sub></em>, cracking is considered to be non-stabilized and tension stiffening is implemented by means of the Pull-Out Model (POM) described in Fig. 22b. This model analyzes the behavior of a single crack considering no mechanical interaction between separate cracks, neglecting the deformability of concrete in tension and assuming the same stepped, rigid-perfectly plastic bond shear stress-slip relationship used by the TCM. This allows the reinforcement strain distribution (ε<em><sub>s</sub></em>) in the vicinity of the crack to be obtained for any maximum steel stress at the crack (σ<em><sub>sr</sub></em>) directly from equilibrium. Given the fact that the crack spacing is unknown for a non-fully developed crack pattern, the average strain (ε<em><sub>m</sub></em>) is computed for any load level over the distance between points with zero slip when the reinforcing bar reaches its tensile strength (<em>f</em><em><sub>t</sub></em>) at the crack (<em>l</em><sub>ε,</sub><em><sub>avg</sub></em> in Fig. 22b), leading to the following relationships:</p>\n<figure data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/43adc17b-b9e9-4a81-ab9f-ff4c13297b34/Equation%201.2.4.2.PNG\" data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" alt=\"\"></figure>\n<p>The proposed models allow the computation of the behavior of bonded reinforcement, which is finally considered in the analysis. This behavior (including tension stiffening) for the most common European reinforcing steel (B500B, with <em>f</em><em><sub>t</sub></em>&nbsp;/&nbsp;<em>f</em><em><sub>y</sub></em>&nbsp;=&nbsp;1.08 and ε<em><sub>u</sub></em>&nbsp;=&nbsp;5%) is illustrated in Fig. 22c-d.</p>"
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                            "value": "<p>El CSFM considera campos de tensión continuos en el hormigón (elementos finitos 2D), complementados por elementos discretos de \"varilla\" que representan la armadura (elementos finitos 1D). Por lo tanto, la armadura no se incrusta difusamente en los elementos finitos 2D del hormigón, sino que se modela explícitamente y se conecta a ellos. En el modelo de cálculo se considera un estado de tensiones plano.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 6\\qquad Visualización del modelo de cálculo de un elemento estructural (viga recortada) en Idea StatiCa Detail.}}]</em></p>\n<p>Se pueden modelizar tanto <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">muros</a> y vigas enteras, como detalles (partes) de vigas (región de discontinuidad aislada, también llamada extremo recortado). En el caso de muros y vigas enteras, los apoyos deben definirse de tal manera que resulte una estructura (externamente) isostática (estáticamente determinada) o hiperestática (estáticamente indeterminada). La transferencia de carga en los extremos recortados de las vigas se introduce mediante una zona de transferencia especial de Saint-Venant, que garantiza una distribución de tensiones realista en la región de detalle analizada.</p>"
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                            "value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad &nbsp;Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the design value (factored value) of the yield strength of the reinforcement.</p>"
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                            "value": "<p>In the calculation for the results of SLS, only the elastic behavior of concrete is taken into account. In other words, an infinite linear stress-strain diagram is considered for concrete. You can display <strong>long-term</strong> or <strong>short-term</strong> effects for SLS checks. What is the difference between these two effects? Read the article below (paragraph Concrete SLS) to learn more.</p>\n<ul>\n  <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Material models (EN)</a></li>\n</ul>\n<h2>Stress</h2>\n<p>There are two options for displaying results for concrete and reinforcement:&nbsp;</p>\n<ul>\n  <li>the ratio of the stress and the limit stress&nbsp;</li>\n  <li>the stress itself&nbsp;</li>\n</ul>\n<p>Stresses are calculated for the <strong>Characteristic</strong> and for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of the stress and limit stress</h4>\n<p>The results are clear at first sight: Green color means the utilization is up to 90%, orange is 90-100% of utilization, and red is above 100%.</p>\n<p>Read about how the limit value is determined in the following article.</p>\n<ul>\n  <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Serviceability limit state analysis</a></li>\n</ul>\n<figure data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d12601c9-32a1-408f-9b41-e031d5b6fc45/RC-D_06_20.png\" data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" alt=\"\"></figure>\n<figure data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/45cd98c6-57b5-4373-a001-6e5c3ed8f5b8/RC-D_06_21.png.png\" data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" alt=\"\"></figure>\n<h4>Stress</h4>\n<p>The display method is similar to the ULS results (in this case, the stress is from the calculation with the elastic behavior of concrete). You can display the distribution of concrete stress <em>σ</em><em><sub>c</sub></em><sub> </sub>for an applied portion of the load. Also known as principal stresses <em>σ</em><em><sub>2</sub></em>.</p>\n<figure data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6f65c964-8c56-4aac-a14c-4307bfde6a8d/RC-D_06_22.png\" data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\" alt=\"\"></figure>\n<figure data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16c8bb7b-6bc7-4b9a-b27f-cf1075f7715a/RC-D_06_23.png\" data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" alt=\"\"></figure>\n<h2>Crack</h2>\n<p>In this section, you will learn about all four options for displaying results for crack checks. Read the further articles to learn about the calculation.</p>\n<ul>\n  <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Main assumptions and limitations for CSFM</a></li>\n  <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Structural element verification in IDEA StatiCa Detail</a></li>\n</ul>\n<p>Cracks are calculated only for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of crack width and limit crack width</h4>\n<p>The limit value w<sub>lim</sub> can be set in the top ribbon. The w<sub>lim</sub> = 0.3 mm is set by default according to Eurocode. The results are again differentiated by color (green/orange/red) so that the check is obvious at first sight.</p>\n<figure data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9fa5bdd1-ec85-4575-9e0f-6d26ce70c206/RC-D_06_24.png\" data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" alt=\"\"></figure>\n<h4>Crack width</h4>\n<p>This functionality is used to display the crack width for every single element of the reinforcement.&nbsp;</p>\n<figure data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97bc905a-76c9-4b12-abe1-3a93c71cdf2b/RC-D_06_25.png\" data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" alt=\"\"></figure>\n<h4>The distance between stabilized cracks</h4>\n<p>See the links at the beginning of the section. The article explains the method of calculating the distance between stabilized cracks.</p>\n<figure data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bcb4dbbc-29b3-48bb-a1f1-72cdb456b0b6/RC-D_06_26.png\" data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" alt=\"\"></figure>\n<p>The presentation of crack spacing is schematic only. It does not represent the crack spacing computed for the calculation.</p>\n<h4>Unreinforced area</h4>\n<p>The crack width is checked only in the vicinity of the reinforcement. Control of cracking is not performed in non-reinforced zones.</p>\n<p>This result simply shows the non-reinforced areas where cracks will probably appear. It is recommended to design some reinforcement to that areas.</p>\n<figure data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f60ea99-7197-4ee8-865e-2e282fdf60ef/RC-D_06_27.png\" data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\" alt=\"\"></figure>\n<h2>Deflection</h2>\n<p>See the options below:</p>\n<ul>\n  <li><em>u</em><em><sub>z,st</sub></em> - Immediate deflection caused by <strong>total load</strong> - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,lt</sub></em> - Long-term deflection caused by <strong>long-term loads </strong>(permanent and prestressing load type) - calculated with <strong>long-term stiffnesses </strong><em><strong>Ec,eff</strong></em><strong>. </strong>In other words, the creep coefficients are included.</li>\n  <li><em>Δu</em><em><sub>z</sub></em> - Deflection increment caused by <strong>short-term loads</strong> (variable load type) - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> = u</em><em><sub>z,lt</sub></em><em>&nbsp;+ Δu</em><em><sub>z</sub></em><sub>&nbsp;</sub></li>\n</ul>\n<p>Deflections are calculated only for the <strong>Characteristic</strong> load combinations.</p>\n<figure data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/815bac57-2809-4383-b0cc-abfa3349b443/RC-D_06_29.png\" data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" alt=\"\"></figure>\n<p>Besides the table values in the Data section, you can display the deformed shape. You can also modify the scale of the deformation.</p>\n<p>Finally, in addition to displaying deformations, it is also possible to do a <strong>deflection check</strong>. You can choose between two checks - <strong>Increment</strong> and <strong>Total.</strong></p>\n<ul>\n  <li><em>Δu</em><em><sub>z</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - &nbsp;Increment</li>\n  <li><em>u</em><em><sub>z,tot</sub></em><em> / Δu</em><em><sub>z,lim</sub></em>&nbsp;- Total</li>\n</ul>\n<p><em>Δu</em><em><sub>z,lim</sub></em>, and <em>Δu</em><em><sub>z,lim</sub></em> can be manually set in the Deflection check bar in the top ribbon.</p>\n<figure data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9efce2e8-54f2-4fe3-8fcb-700d0bc1bd32/RC-D_06_30.png\" data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" alt=\"\"></figure>\n<p>The deflection check is not allowed for trimmed ends.&nbsp;</p>\n<h2>Practical example</h2>\n<p>For a practical example of displaying the results, continue to the <a href=\"https://www.youtube.com/embed/77fFYFUvv5c/?start=2408\">video</a> from the previously streamed webinar. 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            "value": "<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.</p>\n<h3>Ultimate limit state analysis</h3>\n<p>The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<p>To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:</p>\n<ul>\n  <li>Choose a selection of the most critical load combinations.</li>\n  <li>Calculate only Ultimate Limit State (ULS) load combinations.</li>\n  <li>Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"Fig. 23\tMesh multiplier.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).</p>\n<p>The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.</p>\n<h3>Serviceability limit state analysis</h3>\n<p>SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.</p>\n<p>The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
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                    "value": "<p>El Método del Campo de Tensiones Compatible cumple los códigos de diseño modernos. Dado que los modelos de cálculo sólo utilizan propiedades de material estándar, el formato de factor de seguridad parcial prescrito en los códigos de diseño puede aplicarse sin ninguna adaptación. De este modo, las cargas de entrada se factorizan y las propiedades características del material se reducen utilizando los factores de reducción de resistencia respectivos, exactamente igual que en el análisis convencional del hormigón.</p>\n<p>Los valores de los <strong>factores de reducción de resistencia</strong> se prescriben en ACI 318-19 Cl. 21.2. Los valores por defecto para el hormigón y la armadura se eligen basándose en la suposición de que el ejemplo típico resuelto en la aplicación es a cortante controlado (basado en la Tabla 21.2.1 (b), (f), (g)). Sin embargo, es posible modelizar cualquier tipo de elemento. Por lo tanto, si se evalúa un elemento controlado por compresión o tracción, el usuario tiene la opción de cambiar el valor del factor de reducción de resistencia en las Preferencias.</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 44\\qquad Ajuste de los factores de reducción de resistencia en IDEA StatiCa Detail.}}]</em></p>\n<p>Los<strong>factores de carga</strong> para las combinaciones de resistencia se definirán de acuerdo con ACI 318-19 Tabla 5.3.1.</p>\n<p>Excepto lo indicado en el Capítulo 34, las combinaciones de carga a nivel de servicio no están definidas en ACI 318-19. Se recomienda utilizar reglas de combinación basadas en el Apéndice C de ASCE/SEI 7-16. Para todas las plantillas, los factores de carga ya están predefinidos.</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 45\\qquad La configuración de factores de carga en Idea StatiCa Detail.}}]</em></p>"
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                                    "value": "<h2>1 New project</h2>\n<p>Let’s launch the <strong>IDEA StatiCa </strong>(<a data-item-id=\"0dff6482-3e17-4ca2-bb66-b4abc6a8dde4\" href=\"\">download the newest version</a>) and select the application <strong>Detail</strong>. Set up a new project by clicking 2D Detail with General input section, select proper concrete grade and cover. Finish setting by clicking <strong>Create</strong>.</p>\n<figure data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fe21d78b-0647-4837-8b89-24e8ce24ca29/1_1%20New%20project.png\" data-asset-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" data-image-id=\"51ba599d-8de7-4cc0-bb50-27eac77cab6c\" alt=\"\"></figure>\n<figure data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97919dd3-c3af-412c-a7c6-7f236eab183d/1_2%20New%20project.png\" data-asset-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" data-image-id=\"cc9ecd14-d5ec-4563-afca-429b96ad5c22\" alt=\"\"></figure>\n<p>This will load a blank project where we start from scratch.</p>\n<h2>2 Geometry</h2>\n<p>Start with the addition of a wall element by the <strong>DXF</strong> <strong>Import </strong>button.</p>\n<figure data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6778c05d-0b68-4c71-9e34-a83db2822936/2_1%20Geometry.png\" data-asset-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" data-image-id=\"b56414c4-957f-4a00-9fd2-216223d4b60f\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in source files), you will land in a dialog for selection. Select the part of the outline of the pier cap (if you used lines in DXF continue with Consecutive button) and click on <strong>Outline</strong>. Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7ac3717-3e8a-4d71-bef7-53a90dbb06db/2_2%20Geometry.png\" data-asset-id=\"ed360367-4110-4723-b943-94c2958aea56\" data-image-id=\"ed360367-4110-4723-b943-94c2958aea56\" alt=\"\"></figure>\n<p>Then <strong>import</strong> the upper part of the pier cap from the same DXF file.</p>\n<figure data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f79bfee-8f3e-40d2-b06e-9b5f370ed524/2_3%20Geometry.png\" data-asset-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" data-image-id=\"49b8bcec-0c83-4f13-869a-9af90392ebf4\" alt=\"\"></figure>\n<p>The shapes of the wall elements have been generated by DXF, but the 2D DXF reference lacks the information about thickness, thus you need to adjust it manually now. Set the <strong>Thickness</strong> for both <strong>W1</strong> and <strong>W2</strong> members to <strong>1,20 m</strong>.</p>\n<figure data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56914c67-b574-4458-9c75-6300515250cc/2_4%20Geometry.png\" data-asset-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" data-image-id=\"7dabe2fa-1b90-4805-a503-8a1f665d1091\" alt=\"\"></figure>\n<p>Right now, our structure is statically overdetermined, you need to add boundary conditions. To create <a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>line support</strong></a>, click on the <strong>Model Entity</strong> button and select the third type in <strong>Supports</strong> section.</p>\n<figure data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/902146d1-35d7-494d-ad33-0c533d6371d8/2_5%20Geometry.png\" data-asset-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" data-image-id=\"85d75495-728d-45ce-a0c9-55f8e7da6594\" alt=\"\"></figure>\n<p><strong>Constraint</strong> the support in <strong>X</strong>, <strong>Z</strong> and <strong>Ry</strong> directions and change the <strong>edge</strong> number to <strong>7</strong>. Also, switch off the <strong>Compression only</strong> functionality. The edge numbers can be seen in the <strong>Main window</strong>.</p>\n<figure data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6b851c91-a374-48ef-910b-f714f94bf4ae/2_6%20Geometry.png\" data-asset-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" data-image-id=\"28cd534b-fe6b-4603-ac41-d43e0436916f\" alt=\"\"></figure>\n<p>As a Point force-placed directly on the edge of a pier cap would crash the concrete locally in compression, we will use bearing plates to distribute the load more evenly. To add one, press&nbsp;<strong>Model Entity button</strong>&nbsp;once again, and in&nbsp;the <strong>Load transfer devices</strong>&nbsp;section, pick the first -&nbsp;<a data-item-id=\"1d52ff19-b6b3-5290-905a-178825f7cdc1\" href=\"\"><strong>Bearing plate</strong></a>.</p>\n<figure data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f214f09d-65b0-4caf-9a4b-42a77221348d/2_7%20Geometry.png\" data-asset-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" data-image-id=\"0bcce3af-dc3d-45e0-875e-0899ae84ff19\" alt=\"\"></figure>\n<p>Change the <strong>Width</strong> to <strong>0,40 m</strong> and the <strong>Thickness</strong> to <strong>0,04 m</strong>, then the <strong>Edge</strong> number to <strong>3</strong> and shift its <strong>X-Position</strong> to <strong>0,45 m</strong>.</p>\n<figure data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50355c70-edcd-43fd-a8db-dea4af49c1f1/2_8%20Geometry.png\" data-asset-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" data-image-id=\"9b55b426-71ca-42eb-a271-401c9c34edf5\" alt=\"\"></figure>\n<p>Then <strong>copy</strong> the <strong>Bearing plate</strong> and change its position to be measured <strong>From end</strong>.</p>\n<figure data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0eac1da7-c569-4dc1-ad01-4c005e088d98/2_9%20Geometry.png\" data-asset-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" data-image-id=\"53bbefc5-dda4-4ed2-81ef-d036116d43f0\" alt=\"\"></figure>\n<h2>3 Loads</h2>\n<p>Load Case will be created by clicking <strong>Load Case</strong> button and its for <strong>Permanent</strong> effects by default. You need two load cases to distinguish between permanent and variable loads and three combinations to cover one <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">ULS</a> and two <a data-item-id=\"6fbebc50-77e1-42e3-b7e8-9079c605a805\" href=\"\">SLS</a> combinations (Characteristic and Quasi-permanent) for all checks.</p>\n<figure data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/64b6b1b0-2105-4f7d-89db-9588533f35d8/3_1%20Loads.png\" data-asset-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" data-image-id=\"b2f03b16-0201-4e17-b574-de607fbf91a8\" alt=\"\"></figure>\n<p>Let's modify the automatically added load case <strong>LC1</strong> for permanent effects. In the <strong>Load impulses</strong> tab, click on the <strong>Plus</strong> button and apply a <strong>Point load</strong>. It will be automatically placed on one of the bearing plates.</p>\n<figure data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73eccf54-b16e-4d04-a79d-975a253174d4/3_2%20Loads.png\" data-asset-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" data-image-id=\"133d1a9c-9ec2-4d5c-b546-f7e6cb3e40e5\" alt=\"\"></figure>\n<p>As the last step, change its value to <strong>-2500 kN</strong>.</p>\n<figure data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e8e5a8b2-e039-4b6d-a19b-bd1ab5215a04/3_3%20Loads.png\" data-asset-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" data-image-id=\"7613b782-5d53-4adb-a49a-53ab1e9e90c8\" alt=\"\"></figure>\n<p>Copy that Point load to the other bearing plate <strong>BP2</strong>.</p>\n<figure data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ee28dab2-90d2-42f3-b772-475d518de122/3_4%20Loads.png\" data-asset-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" data-image-id=\"5552e8cd-23e8-462c-9e93-ae416d4aff63\" alt=\"\"></figure>\n<p>Copy Load Case 1 and change the LC type to the <strong>variable</strong>. Click on Point Load and change force to <strong>-1000 kN.</strong></p>\n<figure data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d574c49-bd02-4af9-9011-0a3b1130d9e6/3_5%20Loads.png\" data-asset-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" data-image-id=\"50f3925c-d1e3-43c5-b069-28e6b57cc7ad\" alt=\"\"></figure>\n<p>Repeat the steps for the last point load.</p>\n<figure data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/20e05d97-1652-4bf4-b997-f6fcda13a155/3_6%20Loads.png\" data-asset-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" data-image-id=\"79bdbc02-821f-4f20-b7d3-37e64d2f547d\" alt=\"\"></figure>\n<p>Create the first nonlinear combination by <strong>Combination</strong> button, and set it as ULS limit state.</p>\n<figure data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/17bb129d-f8dd-4c81-97ca-18f6fb7fecc3/3_7%20Loads.png\" data-asset-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" data-image-id=\"d0815179-0b84-44f0-84b0-7437351d3dc5\" alt=\"\"></figure>\n<p>Copy C1 and choose <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\"><strong>SLS</strong></a><strong> Characteristic. </strong>In addition, the option is available to check the combination on deflection and crack width both for a given combination and individually. For <strong>Characteristic</strong> combination choose Active for <strong>deflection</strong> check according to the picture below. &nbsp;</p>\n<figure data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7e8dcb4-07a9-44ba-b7db-5dae47d39f18/3_8%20Loads.png\" data-asset-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" data-image-id=\"fa5ca9d3-4f8a-4824-b425-29a218e3a820\" alt=\"\"></figure>\n<p>Now you can repeat the steps, <strong>copy</strong> C2 and choose <strong>SLS Quasi-Permanent </strong>for new C3. Activate <strong>Quasi-Permanent </strong>combination only for <strong>crack width</strong> calculation.&nbsp;</p>\n<figure data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/49282476-6070-4ee9-a3da-8ba806c532db/3_9%20Loads.png\" data-asset-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" data-image-id=\"5b924e5f-43c1-41f0-818a-7cb1bfc7eafc\" alt=\"\"></figure>\n<p>Now, change the partial factors for all combinations. To do that, click on the <strong>pen icon</strong> in any combination you defined and change the partial factors you see in the following picture.</p>\n<figure data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/87b44d74-eede-4ef9-aab9-5b75c7ad351b/3_10%20Loads.png\" data-asset-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" data-image-id=\"3bc7fadd-3912-48f8-8000-0d91cb0af453\" alt=\"\"></figure>\n<p>Note that the calculations are performed only for combinations of load cases that are ticked in the operation tree, not for individual load cases.</p>\n<h2>4 Reinforcement</h2>\n<p>The next step is to <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>reinforce</strong></a> the model. Combine the definition from scratch in IDEA StatiCa with the batch import of the reinforcement from the <strong>DXF</strong> file. In this tutorial, we assume that the user knows how to reinforce a pier cap and prepared some <a data-item-id=\"792f89a1-cc17-54fb-8eaa-611f8a0ea070\" href=\"\">reinforcement</a> in DXF in advance from drawings thus, we leave the tools for <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">reinforcement design</a> for another tutorial.</p>\n<p>Click on <strong>DXF</strong> <strong>Import </strong>and choose Group of bars entity.</p>\n<figure data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e51e193e-5772-4e02-9724-efe612a9955f/4_1%20Reinforcement.png\" data-asset-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" data-image-id=\"f5126442-836e-4f7b-929a-d56d2b4c1162\" alt=\"\"></figure>\n<p>A dialog to locate and open the desired DXF file will pop-up. After the selection of <strong>pier_cap.dxf</strong> (available in the source files), you will land in a dialog for selection. Select all the polylines (rebars shape) you need in order shown on the following picture and click on <strong>Select</strong> after each polyline (the order is not important in general, we just want to keep track in this tutorial when we talk about the specific name of an item). Finish the selection by <strong>OK</strong> button.</p>\n<figure data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7433e93f-9795-495a-a20d-9e4f2ef5f1d5/4_3%20Reinforcement.png\" data-asset-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" data-image-id=\"2e870d3c-beb7-4d83-96f3-92739983e310\" alt=\"\"></figure>\n<p>The 2D DXF file transfers the global width of a polyline as the diameter for each <a data-item-id=\"e891a412-d4f5-4473-8e9c-bded813ee5e3\" href=\"\">rebar</a>, but it does not contain information about the number of bars in the perpendicular direction, and we need to adjust them manually. Thanks to the <a data-item-id=\"c6a63f28-f703-4125-993e-8b2b00d61479\" href=\"\">multi-editing</a> feature, we can provide all changes for all reinforcement entities at once. &nbsp;</p>\n<p>Hold <strong>Ctrl</strong> and select all imported reinforcement, change the number of bars in a layer <strong>10 </strong>and diameter to <strong>20 mm</strong>.</p>\n<figure data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/522a97b6-22e0-4aa6-956d-ea0b8ffb70ee/4_4%20Reinforcement.png\" data-asset-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" data-image-id=\"33ec1295-68ad-494c-a3c3-a5f71e4f89cc\" alt=\"\"></figure>\n<p>To finish the reinforcement in this example, combine the reference from DXF with reinforcement defined in IDEA StatiCa Detail. In this case, add some horizontal and longitudinal reinforcement into the pier cap and a few layers of reinforcement representing the stirrups in the pier. Click on the <strong>Rebar assembly</strong> button and select the first reinforcement item <strong>Group of bars</strong>.</p>\n<figure data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3027cb33-110c-4b80-a470-01af1345750a/4_5%20Reinforcement.png\" data-asset-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" data-image-id=\"fa4a932c-e111-4839-a1c5-55cbb6c7975b\" alt=\"\"></figure>\n<p>Change the definition to <strong>On outline or opening edge</strong>. Then adjust the number of layers, their distances, the diameter, the number of bars in a layer, <a data-item-id=\"2b523983-1e01-41c9-bad0-5807b5485059\" href=\"\">anchorage</a> type for both ends and edges according to the following picture:</p>\n<figure data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/233bba37-5214-421f-9646-9fa9cf49e2ca/4_6%20Reinforcement.png\" data-asset-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" data-image-id=\"26fd362e-faa0-46f2-bee8-f94379378482\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> function to create <strong>GB6,</strong> which will represent the stirrups, and switch the edge to <strong>7</strong>. Set all parameters according to the picture below:</p>\n<figure data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a628132-4994-469e-9917-872f31fcbc0b/4_7%20Reinforcement.png\" data-asset-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" data-image-id=\"53ae292c-4fb6-4f31-b595-85c4fc4c8c29\" alt=\"\"></figure>\n<p>The last reinforcement items will introduce the longitudinal reinforcement of the pier cap. To do that, <strong>add a new group of bars</strong>. Change the properties as follows:</p>\n<figure data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a78bd3ba-73dd-4b26-98a0-692b54ad5b09/4_8%20Reinforcement.png\" data-asset-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" data-image-id=\"293450a5-ac45-42f9-99f6-fff86ba8cde1\" alt=\"\"></figure>\n<p>Use the <strong>copy</strong> button for the last time. Change the edge to <strong>8</strong>.</p>\n<figure data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62b5c0a1-9129-4b33-ae51-650f7cc3ac20/4_9%20Reinforcement.png\" data-asset-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" data-image-id=\"9fc368d8-b05f-4e7e-b35d-325ab88796e3\" alt=\"\"></figure>\n<p>After all reinforcement added and edited we can start the calculation by clicking on <strong>Calculate</strong> button.</p>\n<figure data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fa95121e-d453-4304-80e6-85dda909891c/4_10%20Reinforcement.png\" data-asset-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" data-image-id=\"33ee2cb4-19a0-4435-bf05-ea1f263be8ba\" alt=\"\"></figure>\n<h2>5 Calculation and Check</h2>\n<p>Start the analysis by clicking <strong>Calculation</strong> in the ribbon. The analysis model is automatically generated, the calculations are performed and you can see the summary of checks displayed together with the values of check results.</p>\n<figure data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7c9cdd56-cdb0-4c8b-963f-6b0dc4669234/5_1%20Check.png\" data-asset-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" data-image-id=\"c310c8a9-405a-407d-bae2-0f380acbe2e5\" alt=\"\"></figure>\n<p>To go through the detailed checks of each component, start with the <strong>Strength</strong> tab. This will show concrete checks such as utilization in stress, principal stresses, strains, and a map of reduction factor k<sub>c,</sub> which can be switched on the ribbon.</p>\n<figure data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c4aa00e-48cc-409e-bc79-21d28e55a786/5_2%20Check.png\" data-asset-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" data-image-id=\"87bd3bff-ee4a-4cf7-9490-a685fe5e1c3e\" alt=\"\"></figure>\n<p>For detailed results of reinforcement, you need to click on the row <a data-item-id=\"0e906322-2262-4075-a13c-2f864a41b7ee\" href=\"\"><strong>Reinforcement</strong></a>. This will change the ribbon icons and unroll the table for results. You can display the results for <a data-item-id=\"64fe8853-4024-409f-9e71-8e2007782f5b\" href=\"\">strains and stresses</a> in each bar and their utilization.</p>\n<figure data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aa19009c-39f5-4c08-bba0-493ac6d5a4ef/5_3%20Check.png\" data-asset-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" data-image-id=\"4dac15a1-9f3a-4039-b532-47ac9a19e21a\" alt=\"\"></figure>\n<p>All results can be displayed in the same way. Let´s show the difference in the ribbon for SLS checks of <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">crack-width</a> and deflection. Besides the icons to switch between the results, there are settings in the ribbon to set the limit value of cracks or to display the results of deflections from short/long-term models.</p>\n<figure data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/79b005fd-2d09-4e79-a97b-d45dc3c4fbd4/5_4%20Check.png\" data-asset-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" data-image-id=\"61faf394-9e26-4c85-b7c3-0c450dbcb495\" alt=\"\"></figure>\n<figure data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bea7f38c-6c84-49f0-8502-66bfb347093e/5_5%20Check.png\" data-asset-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" data-image-id=\"67aab4ff-4acd-45be-883c-775f9612870f\" alt=\"\"></figure>\n<h2>6 Report</h2>\n<p>At last, go to the <strong>Report</strong>. IDEA StatiCa offers a fully customizable report to print out or save in an editable format.</p>\n<figure data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6e3c18c1-a97e-4301-8ee4-31b1ed278382/6_1%20Report.png\" data-asset-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" data-image-id=\"982806dc-d702-4e8e-8c84-cfa8336ce687\" alt=\"\"></figure>\n<figure data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/33137b76-efe1-4357-a046-99a24413aa88/6_2%20Report.png\" data-asset-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" data-image-id=\"c4a06b84-478b-437a-ac93-3cb615623ae6\" alt=\"\"></figure>\n<p>You have designed, optimized, and code-checked a pier cap according to Eurocode.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"idea_statica_tutorial___pier_cap_from_dxf_2495f70\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"campus_cta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0d61cad8_c463_0160_5df5_bb66b7a55152\"></object>"
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                            "value": "<h4>¿Muro de hormigón armado o vigas profundas con verificación de códigos completa? No hay problema.</h4>\n<p>El objetivo del webinar es presentar cómo realizar en minutos la comprobación de código de una <strong>viga profunda de forma general</strong> en <strong>IDEA StatiCa Detail</strong> en conexión con los resultados de la aplicación de AEF. Mostraremos el flujo de trabajo en un ejemplo de un edificio residencial de hormigón - exportando la geometría, creando el submodelo en IDEA StatiCa Detail, aplicando las <strong>cargas correctas</strong>, el diseño de la armadura, y el código de comprobación final para los <strong>estados</strong> <strong>límite últimos y de servicio</strong>.</p>\n<p>Pruébelo usted mismo - obtenga la <a data-item-id=\"0c872071-6a3f-4b99-8cd4-66440db9cc0d\" href=\"\">licencia de prueba gratuita</a> y siga el tutorial paso a paso en <a data-item-id=\"1dc3667d-ddd6-5483-8b97-e7b69923fef7\" href=\"\">Muro de hormigón</a>.</p>\n<figure data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/177694cc-5c91-42cb-b88c-568f900670fe/Code-check%20of%20walls%20and%20deep%20beams.png\" data-asset-id=\"2a799851-47a8-48ba-a994-6142976c5204\" data-image-id=\"2a799851-47a8-48ba-a994-6142976c5204\" alt=\"\"></figure>\n<h4>La solución definitiva para detalles y piezas estructurales de hormigón</h4>\n<p>El software de AEF 3D habitual tiene en cuenta el comportamiento lineal del hormigón. El diseño y las comprobaciones de código de la armadura son limitados, especialmente para el <strong>estado límite de servicio</strong> que puede conducir al desarrollo de <strong>grietas excesivas</strong>. Todo esto está cubierto dentro de la aplicación IDEA StatiCa Detail <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">basada en CSFM</a>. Ahora, todos los ingenieros pueden diseñar y comprobar eficientemente muros o vigas profundas de cualquier forma y muchas más.</p>\n<p>Si desea ver más de <strong>IDEA StatiCa Detail </strong>en acción, hay otros dos seminarios web grabados para ver:</p>\n<ul>\n  <li><a data-item-id=\"1300fb1c-8e32-47f3-8b21-0e8e77e1f238\" href=\"\">¿Cómo diseñar fácilmente una viga pretensada con aberturas?</a></li>\n  <li><a data-item-id=\"73d449cf-610e-5c7c-9e8c-da8093630d24\" href=\"\">Muro colado in situ - Ruzomberok (Eslovaquia)</a></li>\n</ul>\n<p>O navegue por nuestro Centro de soporte para ver <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&amp;label=detail\" title=\"IDEA StatiCa Detail\">tutoriales</a> y leer los <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">fundamentos teóricos.</a></p>\n<h3>Grabación del seminario web</h3>"
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            "value": "<p><br></p>\n<p>The theoretical background is based on COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>\n(Kaufmann et al., 2020)</p>\n<h1>Structural design of concrete discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#design-tools-for-reinforcement\">Design tools for reinforcement</a></p>\n<h2>Analysis model of IDEA StatiCa Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#supports-and-load-transmitting-components\">Supports and load transmitting components</a><br>\n<a href=\"#load-transfer-at-trimmed-ends-of-beams\">Load transfer at trimmed ends of beams</a><br>\n<a href=\"#geometric-modification-of-cross-sections\">Geometric modification of cross-sections</a><br>\n<a href=\"#finite-element-types\">Finite element types</a><br>\n<a href=\"#meshing\">Meshing</a><br>\n<a href=\"#solution-method-and-load-control-algorithm\">Solution method and load-control algorithm</a><br>\n<a href=\"#presentation-of-results\">Presentation of results</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">Limit states, crack width calculation, and Tension stiffening</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-en\">Material models (EN)</a><br>\n- <a href=\"#safety-factors\">Safety factors</a><br>\n- <a href=\"#ultimate-limit-state-analysis\">Ultimate limit state analysis</a><br>\n- <a href=\"#partially-loaded-areas\">Partially loaded areas (PLA)<br>\n</a>- <a href=\"#serviceability-limit-state-analysis\">Serviceability limit state analysis</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-aci\">Material models (ACI)</a><br>\n- <a href=\"#strength-reduction-and-load-factors\">Strength reduction and load factors</a><br>\n- <a href=\"#strength-verifications\">Strength verifications</a><br>\n- <a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">Bearing and anchorage zones - Partially loaded areas<br>\n</a>- <a href=\"#serviceability-verifications\">Serviceability verifications</a></p>\n<p><br></p>\n<p><a href=\"#prestressing-in-detail-model-description\">Prestressing in Detail - Model description</a></p>\n<p><br></p>\n<h1>Introduction to the CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cdb17447_c070_01e2_1868_5c93c7251a4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4bcb2f0b_7383_010b_62f3_4436f719f938\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n629861c9_4749_01c9_91dd_65dd5c708245\"></object>\n<h1><br></h1>\n<h1>Analysis model of IDEA StatiCa Detail</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8c1341d1_edce_0175_23df_7ea947f7a9d9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n61511896_8acd_0196_f8fb_6e63bbebccd5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d6bad769_e632_0191_97c9_24b4a061bb3a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ab526be1_f133_01fb_b0bd_46acfd258f99\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec938fd0_e352_0162_8f9f_c0a6d1d97a2b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a0372b9_1e05_016c_d262_a340d921d273\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2f94d4e9_7013_01de_3046_66ee8ff97945\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a7b0ae9_80a0_01d4_187b_223185df4f64\"></object>\n<h1><br></h1>\n<h1>Model verification</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n89d6744c_775b_0188_c550_bd58c34aca49\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to Eurocode</h1>\n<p>Assessment of the structure using CSFM is performed by two different analyses: one for serviceability, and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84551104_4716_01b3_2661_a33671e672e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2922991_2d4f_01b7_5c69_db02b78d2725\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5fdc9c6e_d109_0126_a311_d9521c50c167\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c9c4750e_ba89_01a4_512b_90bb78915c0b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5faa75ec_67de_018e_11e9_a393dfef4d18\"></object>\n<h1><br></h1>\n<h1>Structural verifications according to ACI 318-19</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>CSFM is in accordance with ACI 318-19, chapter 6.8.1.1. In order for the CSFM to meet the requirements from ACI 318-19 Section 6.8.1.2, a lot of verification testing was done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e1f0c5c5_9dff_01e5_e38a_1f18b65c7441\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f2868ffa_224a_0186_8cdc_2705a1bdf957\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8ddf022c_a92f_01f8_1ee9_04eb823e80b5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d1f8707b_966e_01d5_5c42_4318a980fccb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f6c353a5_88bf_0166_aec5_12ad2979125f\"></object>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600 (2018)</h1>\n<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability, and one for strength load combinations. The serviceability analysis assumes that the behavior under factored loads is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed.</p>\n<p>The CSFM is a structural analysis method that satisfies the general rules in Chapters 6.1.1 and 6.1.2 and is defined as (f) non-linear stress analysis in Chapter 6.1.3 - further in Chapter 6.6.&nbsp;</p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3.&nbsp;</p>\n<p>In order to satisfy the requirements in Sections 6.6.4 and 6.6.5 - more can be found in AS3600:2018 Sup 1:2022 Section C6.6 - verification and validations of the method were done at various universities. Individual articles summarizing the results of verification and validation can be found at the following link.</p>\n<ul>\n  <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">Verifications: Detail 2D</a></li>\n</ul>\n<p>Since IDEA StatiCa Detail is a practical design program, factored characteristic compressive cylinder strength at 28 days <em>f'</em><em><sub>c</sub></em> is used for calculations as is described in the next chapter.</p>\n<p><br></p>\n<h1><br></h1>\n<p><br></p>\n<h1>Prestressing - model description</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de32c6b6_4392_0114_385a_1b749e8bfbee\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d485cadd_6bc3_01f5_0594_18b585741fe9\"></object>\n<h1><br></h1>\n<h1>References</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1:&nbsp; General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova.&nbsp;2020. “<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst &amp; Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&amp;genre=book&amp;isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” <em>ACI Journal</em> 83 (2): 219–31.</p>"
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