See the following article for a detailed description of all options and their input:
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"value": "<p><strong>Load transferring devices</strong> contain two entities the base plate and single anchor. Let's start with the Base plate. To specify the position, a reference surface and edge must be selected. These define the origin of the coordinates from which the X and Y distances are measured. There are two shape definition options, Rectangular and Polygon.</p>\n<figure data-asset-id=\"11cd27f6-009d-4db7-8317-0f09336fca36\" data-image-id=\"11cd27f6-009d-4db7-8317-0f09336fca36\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f525cda5-6fb0-4656-b554-83760c0b1cbf/3D%20Detail%20in%2024.1_8.png\" data-asset-id=\"11cd27f6-009d-4db7-8317-0f09336fca36\" data-image-id=\"11cd27f6-009d-4db7-8317-0f09336fca36\" alt=\"\"></figure>\n<p>The base plate is connected to the concrete element by a contact that transfers compressive stresses and, if the user chooses, can also transmit shear stresses. There are three shear transfer mechanisms that can be selected:</p>\n<ul>\n <li><strong>by friction</strong></li>\n <li><strong>by anchors</strong></li>\n <li><strong>by shear lug</strong></li>\n</ul>\n<p>The software does not allow you to combine these shear transfer mechanisms.</p>\n<p>For the option by friction, the design value of the friction coefficient needs to be entered. For the option by shear lug, the steel profile, including geometry and position, needs to be inputted.</p>\n<p>All the possible configuration of base plates can be found in the article: <a data-item-id=\"2a4f94ba-b8bb-4cab-abfc-d5c6d81e4f16\" href=\"\">Base Plates Options</a>.</p>\n<p>The base plate can transmit either a point load or a group of forces. For a point load, the model can be loaded with six internal forces (Fx, Fy, Fz, Mx, My, and Mz) at any position on the base plate. For a group of forces, users can input the forces’ positions, intensities, and directions into a table, allowing for a general positioning on the base plate. It is important to mention that the base plate is point-loaded and doesn't have any stiffener or member welded on its upper face. Thus, for correct load distribution, it is important to use a relatively stiff base plate with relatively high thickness. Another option is to use <a data-item-id=\"b01780a3-d07a-4184-bc1a-29a87b138150\" href=\"\">Stub</a>, that handless the issue with the plate stiffness.</p>\n<p>A second load transfer device, the single anchor, can be added and interconnected with the base plate to create, for example, a base plate of the column anchored with four anchors (see the figure below). It is also possible to model separate anchors without a base plate.</p>\n<figure data-asset-id=\"173535b3-f5bc-4054-8097-28f3511f801f\" data-image-id=\"173535b3-f5bc-4054-8097-28f3511f801f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a3bed85a-cfe8-4e4e-8ff0-f583b813e845/3D%20Detail%20in%2024.1_9.png\" data-asset-id=\"173535b3-f5bc-4054-8097-28f3511f801f\" data-image-id=\"173535b3-f5bc-4054-8097-28f3511f801f\" alt=\"\"></figure>\n<p>More information about the interconnection with the base plate can be found in the <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Theoretical background</a>.</p>\n<p>In terms of position and geometry, the anchors are referenced to the surface and edge of the block, including the determination of the relative position as with the base plate. Of course, it is possible to specify the length of the anchor in the concrete and the length above the concrete surface.</p>\n<figure data-asset-id=\"d863d248-0da0-4d70-be58-409733d42f62\" data-image-id=\"d863d248-0da0-4d70-be58-409733d42f62\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/faa9fa38-dfc7-420c-8d12-59a0d69eb30d/3D%20Detail%20in%2024.1_10.png\" data-asset-id=\"d863d248-0da0-4d70-be58-409733d42f62\" data-image-id=\"d863d248-0da0-4d70-be58-409733d42f62\" alt=\"\"></figure>\n<p>The anchors are implemented in two variants:</p>\n<ul>\n <li>Cast-in-place </li>\n <li>Adhesive anchors</li>\n</ul>\n<p>For the Cast-in-place Reinforcement, the Bond strength is used according to EN 1992-1-1 chap. 8.4.2. In addition, it is possible to specify the Anchorage type for this type of anchor as for conventional reinforcement.</p>\n<p>For Adhesive anchors, it is possible to directly input the bond strength, which the user can find out from the technical data sheet of the applied adhesive mortar. Note that <strong>it is necessary to input the design value of the bond strength. </strong>The following <a data-item-id=\"28fda422-6776-422c-95fb-6a969235d0c0\" href=\"\">article</a> will help you find the value. </p>\n<figure data-asset-id=\"b48eec47-5b68-4835-8312-09aeb774a144\" data-image-id=\"b48eec47-5b68-4835-8312-09aeb774a144\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/09d0bd61-f206-4b5d-a968-5f34b828e48a/3D%20Detail%20in%2024.1_11.png\" data-asset-id=\"b48eec47-5b68-4835-8312-09aeb774a144\" data-image-id=\"b48eec47-5b68-4835-8312-09aeb774a144\" alt=\"\"></figure>\n<p>See all anchors options in the article: <a data-item-id=\"10e87806-c370-4f36-97fd-c9eb0824350f\" href=\"\">Single Anchor Options</a></p>\n<p>A thorough description of the behavior of the interconnection between the anchor and base plate is described in the <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Theoretical background</a>.</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 </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 <em>IDEA StatiCa Detail</em> 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 𝜂<sub>𝑓𝑐</sub> reduction factor defined in <em>fib</em> 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 <em>f</em><em><sub>bd</sub></em> 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. </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. </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>. </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 is a mathematical model describing the response of<strong> </strong>brittle materials, to 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 compressive strength far exceeds the 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 structural engineering, it is used to determine failure load as well as the angle of fracture for displacement of fracture surface in concrete and similar materials. Coulomb's friction hypothesis is used to determine the combination of shear and normal stress that will cause a fracture of the material. Mohr's circle 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 principle of normality, the stress introduced at failure will be perpendicular to the line describing the fracture condition. </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 angle of friction. This makes the strength of the material determinable by comparing the external mechanical work introduced by the displacement and the external load with the internal mechanical work introduced by the strain and stress at the line of failure. By conservation of energy, 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. </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. </p>\n<p>\\[\\kappa = \\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": "<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. 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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>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>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>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 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 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 > 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><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. </p>\n<p>The analysis by CSFM takes into account all relevant non-linear and inelastic effects (except shrinkage) defined in 6.6.3. </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: 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. 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 & Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&genre=book&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 load factors in IDEA StatiCa Detail.}}}\\]</em></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": "<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> 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 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 compressive strength 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). </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) 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": "<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 stress reduction factors, exactly as in conventional concrete analysis.</p>\n<p>Values of <strong>stress reduction factors</strong> are prescribed in AUS 3600 Cl. 2.2.3. The default values for concrete and reinforcement are set according to Table 2.2.3</p>\n<figure data-asset-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" data-image-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1d32796c-ae70-42fb-a3d3-4542e785f5b1/Stress%20reduction%20factors_AUS.png\" data-asset-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" data-image-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 50\\qquad The setting of stress 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 AS 3600 Cl. 4.2.2. Load factors for Serviceability combinations shall be determined according to Table 4.1. For all templates, load factors are already predefined.</p>\n<figure data-asset-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" data-image-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/887ee546-c598-41fd-b494-c43ccbc55194/Load%20factors%20AUS.png\" data-asset-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" data-image-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 51\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></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 Equivalent principal stress <em>f</em><em><sub>c,eq</sub></em> (also σ<em><sub>c,eq</sub></em> 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> 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 <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 <em>f</em><em><sub>sy,lim</sub></em> is determined. </p>\n<p>In the current version, the code checks for anchors in shear and shear with tension<strong> </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> is the load bearing area of the head of the fastener (without the shank area). </li>\n <li><em>f</em><em><sub>c</sub></em><em>'</em> is the specified compressive strength of concrete</li>\n <li><em>k</em><em><sub>2</sub></em> 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. </p>\n<h4>Anchorage - 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> (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> (<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 anchorage force <em>F</em><em><sub>a </sub></em>and the bond force <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 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) 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. </p>"
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"value": "<h1>Structural design of concrete 3D discontinuities in IDEA StatiCa Detail</h1>\n<h2>Introduction to the 3D CSFM method</h2>\n<p><a href=\"#general-introduction\">General introduction for the structural design of concrete 3D details</a><br>\n<a href=\"#main-assumptions-and-limitations\">Main assumptions and limitations</a><br>\n<a href=\"#mohr-coulomb-plasticity-theory-implementation-in-3D-CSFM\">Mohr-Coulomb plasticity theory implementation in 3D CSFM</a><br>\n<a href=\"#general-mechanics-assumptions-for-3D-CSFM\">General mechanics assumptions for 3D CSFM</a></p>\n<h2>Analysis model of IDEA StatiCa 3D Detail</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">Introduction to finite element implementation</a><br>\n<a href=\"#general-finite-element-types\">General finite element types</a><br>\n<a href=\"#load-transfer-devices\">Load transfer devices</a><br>\n<a href=\"#concrete-meshing-in-3D-CSFM\">Meshing in 3D CSFM</a><br>\n<a href=\"#solution-method-and-load-control-algorithm-for-3D-CSFM\">Solution method and load-control algorithm for 3D CSFM</a><br>\n<a href=\"#presentation-of-3D-results\">Presentation of 3D results</a><br>\n<a href=\"#model-imported-from-idea-statica-connection\">Model imported from IDEA StatiCa Connection</a></p>\n<h2>Model verification</h2>\n<p><a href=\"#limit-states\">Limit states</a></p>\n<h3>Structural verifications according to EUROCODE</h3>\n<p>- <a href=\"#material-models-in-3D-CSFM-EN\">Material models in 3D CSFM (EN)</a><br>\n- <a href=\"#partial-safety-factors\">Partial safety factors</a><br>\n- <a href=\"#ultimate-limit-state-checks\">Ultimate limit state checks</a></p>\n<h3>Structural verifications according to ACI 318-19</h3>\n<p>- <a href=\"#material-models-in-3D-CSFM-ACI\">Material models in 3D CSFM (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></p>\n<h3>Structural verifications according to AS 3600</h3>\n<p>- <a href=\"#material-models-in-3D-CSFM-AUS\">Material models in 3D CSFM (AUS)</a><br>\n- <a href=\"#stress-and-strength-reduction-factors-and-load-factors\">Stress and strength reduction factors and load factors</a><br>\n- <a href=\"#strength-and-anchorage-verifications\">Strength and anchorage verifications</a></p>\n<p><br></p>\n<p><br></p>\n<h1>Introduction to the 3D CSFM method</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"b03faaef_b4f1_010d_1fd1_edf6dd647e42\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_3d_detail___general_introdu\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d2c23365_3b66_01a0_abd7_41cc7a5d855b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" 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In order for the 3D 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_3d\">Verifications: Detail 3D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n9f39b9ca_50c0_015a_2c43_8759ed607707\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models_3d\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1d1efe19_0968_013b_6544_5bd3d06f14aa\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail_3d___strength_reduct\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"b9c02246_d04c_0146_3699_3c2b4bf9c86d\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail_3d___strength_analys\"></object>\n<p><br></p>\n<p><br></p>\n<h1>Structural verifications according to Australian standard AS 3600</h1>\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. </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. 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_3d\">Verifications: Detail 3D</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'c</em> is used for calculations, as is described in the next chapter.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n9420be53_2547_0180_5def_d6e20b5be7b1\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail_3d___material_models\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n0a6ca427_5a30_01fc_5334_3f6d024f40b9\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail_3d__stress_reduction\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cd5aad70_8155_0111_d25f_c72e153f21e5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail_3d___strength_analys_f37d2d9\"></object>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"take_idea_statica_24_0_for_a_test_drive_today\"></object>\n<h2>Verifications and validations</h2>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail_3d\">Verifications: Detail 3D</a></li>\n</ul>\n<h3>References</h3>\n<ol>\n <li>Wu, D.; Wang, Y.; Qiu, Y.; Zhang, J.; Wan, Y.-K. Determination of Mohr–Coulomb Parameters from Nonlinear Strength Criteria for 3D Slopes. <em>Math. Probl. Eng.</em> <strong>2019</strong>, 6927654.</li>\n <li>Lelovic, S.; Vasovic, D.; Stojic, D. Determination of the Mohr-Coulomb Material Parameters for Concrete under Indirect Tensile Test. <em>Tech. Gaz.</em> <strong>2019</strong>, <em>26</em>, 412–419.</li>\n <li>Galic, M.; Marovic, P.; Nikolic, Ž. Modified Mohr-Coulomb—Rankine material model for concrete. <em>Eng. Comput.</em> <strong>2011</strong>, <em>28</em>, 853–887.</li>\n <li>Fan, Q.; Gu, S.C.; Wang, B.N.; Huang, R.B. Two Parameter Parabolic Mohr Strength Criterion Applied to Analyze The Results of the Brazilian Test. <em>Appl. Mech. Mater.</em> <strong>2014</strong>, <em>624</em>, 630–634.</li>\n</ol>"
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"value": "<h3>Introducción</h3>\n<p>Comencemos definiendo el uso o la casuística de usos de IDEA StatiCa Detail 3D, en nuestra versión actual, desarrollamos herramientas y verificamos la solución sólo para el <strong>anclaje de estructuras de acero en bloques simples de hormigón armado</strong>.</p>\n<p>El siguiente texto se divide en dos partes: limitaciones de la aplicación y del método en sí, y limitaciones de la importación desde IDEA StatiCa Connection.</p>\n<h3>Limitaciones de la aplicación</h3>\n<h4>Hormigón armado</h4>\n<p>El <strong>CSFM 3D no está diseñado para hormigón simple u hormigón ligeramente armado</strong>. En este caso, el resultado del cálculo puede dar lugar a resultados engañosos o a divergencias del cálculo no lineal.</p>\n<p>Puede obtener más información en <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Antecedentes teóricos</a>.</p>\n<p>La razón principal por la que en la aplicación <strong>sólo</strong> se pueden modelizar elementos de <strong>hormigón armado</strong> es que la resistencia a tracción del hormigón es despreciable. Por tanto, todos los esfuerzos de tracción deben transmitirse mediante armaduras de acero de refuerzo.</p>\n<p>La segunda razón es: En IDEA StatiCa Detail 3D, no se utiliza la mecánica de fractura. El modelo no simula la propagación explícita de grietas, ni emplea parámetros de mecánica de fractura del hormigón (G_f, K_IC, forma de la superficie de fractura). El hormigón se modela como un material dúctil con una rama plástica horizontal en compresión - una vez que se alcanza la tensión de compresión límite, la tensión permanece constante, y sólo las deformaciones continúan aumentando hasta un límite prescrito. Como consecuencia, Detail 3D puede capturar la redistribución plástica de tensiones y deformaciones en las regiones D, pero no modela explícitamente los mecanismos de fallo frágil gobernados por la mecánica de fractura (por ejemplo, fallo por cizallamiento puro del hormigón simple, propagación inestable de una única grieta dominante, etc.).</p>\n<figure data-asset-id=\"28eb5f80-45f6-4497-b319-314454d49641\" data-image-id=\"28eb5f80-45f6-4497-b319-314454d49641\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8423cd38-726f-4cf5-a0c4-ae7b5dbf1725/Reinforced%20concrete_v3.png\" data-asset-id=\"28eb5f80-45f6-4497-b319-314454d49641\" data-image-id=\"28eb5f80-45f6-4497-b319-314454d49641\" alt=\"\"></figure>\n<p>En resumen, sus modelos deberán ajustarse a la definición de hormigón armado presentada en las normas internacionales. <strong>Seguir las reglas de detallado conllevará a resultados correctos.</strong></p>\n<h4>Estado límite último</h4>\n<p>Todos los cálculos y comprobaciones del código se aplican <strong>únicamente</strong> para <strong>el</strong> estado límite <strong>último</strong>. La definición de los materiales y la forma de cálculo en sí deben ser diferentes para el ELS. Puede ver esta diferencia en el Detail 2D.</p>\n<h4>Ablandamiento por compresión</h4>\n<p>En primer lugar, definamos qué es el ablandamiento por compresión:<strong> El hormigón en compresión pierde resistencia y rigidez cuando al mismo tiempo está fuertemente fisurado en tracción, es decir, cuando existen grandes tensiones transversales de tracción.</strong></p>\n<p>En los casos en que la resistencia se rige por un puntal de compresión (diagonal de compresión) que atraviesa el hormigón muy fisurado, Detail 3D tiende a sobrestimar la capacidad (es decir, a ser ligeramente no conservador) si el resultado se interpreta directamente como la capacidad última real.</p>\n<p>Por estos motivos, el módulo 3D sólo es adecuado para verificar la resistencia de los anclajes en bloques de hormigón armado sencillos.</p>\n<p>Aunque es posible modelizar, por ejemplo, un encepado mediante apoyos en una superficie pequeña, la verificación no es fiable porque el efecto de ablandamiento llega a ser significativo, sobre todo en problemas relacionados con el punzonamiento. La misma situación puede darse en el caso de una losa delgada con un pilar colocado sobre ella, y en otros casos similares.</p>\n<figure data-asset-id=\"23cbdc1a-c706-47f9-9e86-6d9372816c99\" data-image-id=\"23cbdc1a-c706-47f9-9e86-6d9372816c99\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c1a13eda-0ba7-4d6f-a7c0-4effe0eb0d97/boolein_07.png\" data-asset-id=\"23cbdc1a-c706-47f9-9e86-6d9372816c99\" data-image-id=\"23cbdc1a-c706-47f9-9e86-6d9372816c99\" alt=\"\"></figure>\n<p>Para estas situaciones, es necesario implementar el ablandamiento del hormigón, que actualmente sólo está disponible en el módulo 2D. <strong>Por lo tanto, el módulo 3D sólo puede utilizarse para comprobar fallos en los que este efecto no tenga influencia.</strong></p>\n<h4>Comprobación de anclajes</h4>\n<p>El elemento del anclaje se define como capaz de transferir fuerzas normales de tracción o compresión, así como fuerzas de cortante, considerando también la rigidez a flexión, tal y como se describe en los <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Antecedentes teóricos</a>.</p>\n<p>Apoyamos las comprobaciones basadas en el código de acuerdo con las normas pertinentes <strong>(sólo EN</strong>), por lo tanto, IDEA StatiCa Detail se puede utilizar independientemente para la evaluación de anclajes (anclajes, armaduras, hormigón).</p>\n<p>Códigos implementados: <strong>EN 1992-4, EN 1993-1-8, EN 1994-1-1</strong></p>\n<p>Para verificar otros componentes de la unión (soldaduras, placas, etc.), es necesario utilizar IDEA StatiCa Connection, donde también se puede realizar la comprobación completa de anclajes para hormigón simple. El anclaje en Connection -junto con las fuerzas aplicadas- puede exportarse al Detail para el diseño adicional de la armadura.</p>\n<p><strong>Para los códigos ACI y australiano</strong> las comprobaciones de anclajes en cortante y en cortante - tracción<strong> no están implementadas </strong>todavía, por lo que siempre es necesario utilizar ambas aplicaciones para comprobaciones completas de anclajes.</p>\n<h4>Vuelco</h4>\n<p>Si la aplicación de carga provoca el vuelco del modelo, el modelo calculará hasta la divergencia o el alcance del criterio de convergencia. Esto suele llevar mucho tiempo y se obtiene el siguiente resultado:</p>\n<figure data-asset-id=\"84491111-cc1f-4723-953a-509b892d8976\" data-image-id=\"84491111-cc1f-4723-953a-509b892d8976\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2db19218-8483-49ec-8c9e-d0a41d4a9fbb/OT%20result.png\" data-asset-id=\"84491111-cc1f-4723-953a-509b892d8976\" data-image-id=\"84491111-cc1f-4723-953a-509b892d8976\" alt=\"\"></figure>\n<p>Se le mostrará el porcentaje de la carga transferida, además, en Resultados auxiliares se muestra la deformación extrema.</p>\n<p>Solución: Se recomienda calcular cualquier modelo primero con el Multiplicador del tamaño de malla por defecto ajustado a un valor alto (4-5). Este multiplicador se encuentra en Ajustes -> Ajustes de malla. El cálculo será rápido y podrá ver si el vuelco es el problema o no.</p>\n<p>Es necesario comprobar si el peso propio del bloque de hormigón está incluido, ya que puede evitar el vuelco del modelo. Tenga en cuenta que, al importar desde la aplicación Connection, el peso propio <strong>no</strong> se introduce automáticamente en el modelo - para más detalles, consulte el texto que aparece a continuación.</p>\n<h3>Limitaciones de la importación desde Connection</h3>\n<h4>Contactos</h4>\n<p>En general, no se admite la importación de fuerzas que actúan sobre la placa base a través del <strong>contacto </strong>con otra placa de acero. Esto se aplica tanto a los tipos de contacto borde-superficie como superficie-superficie. Más información <a href=\"https://www.ideastatica.com/support-center/10-most-important-questions-about-3d-anchoring-in-detail#contact-stress\" title=\"in this article\">en este artículo</a>.</p>\n<figure data-asset-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" data-image-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ed18b6d3-c35c-4edb-9919-9c108856ca5c/10%20most%20important%20questions%20about%203D%20anchoring%20in%20Detail%2003.png\" data-asset-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" data-image-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" alt=\"\"></figure>\n<h4>Anclajes en el elemento</h4>\n<p>Sólo los modelos anclados a través de la placa base pueden importarse correctamente a la aplicación Detail. Para modelos en los que los elementos están conectadas directamente a bloques de hormigón, la placa de conexión del elemento con anclajes se importa sin cargas.</p>\n<figure data-asset-id=\"a6bc790a-51f0-4da8-a0ba-1af51e7a603d\" data-image-id=\"a6bc790a-51f0-4da8-a0ba-1af51e7a603d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8d3c9d76-58eb-43af-ba9b-e66a0aa1e621/Anchorage%20by%20member.png\" data-asset-id=\"a6bc790a-51f0-4da8-a0ba-1af51e7a603d\" data-image-id=\"a6bc790a-51f0-4da8-a0ba-1af51e7a603d\" alt=\"\"></figure>\n<h4>El peso propio no se añade automáticamente</h4>\n<p>El peso propio no se calcula/añade automáticamente. Debe incluirse manualmente en el proyecto de Detail. Esto puede afectar principalmente a la verificación del anclaje a la cimentación, donde la no consideración del peso propio podría provocar el vuelco de la cimentación, tal y como se menciona en el párrafo anterior.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"b1849b38_7111_01c7_0349_b96c060ed706\"></object>\n<h4>Tipos de anclaje no soportados para exportación</h4>\n<p>Los anclajes de gancho no están soportados en Detail. En su lugar se utilizará una placa washer en el archivo exportado.</p>\n<p>La placa arandela se modela como un elemento de placa directamente unido al vástago del anclaje, transfiriendo la carga al hormigón exclusivamente a través del contacto de compresión. La propia placa se modela linealmente, sin plasticidad, y no se somete a comprobaciones de resistencia. Dado que el vástago tiene una <strong>resistencia de adherencia nula</strong>, toda la carga se transfiere al hormigón a través de la placa de anclaje. Encontrará más información sobre los tipos de anclajes en el artículo: <a data-item-id=\"10e87806-c370-4f36-97fd-c9eb0824350f\" href=\"\">Definición de anclaje</a> simple.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n9d01d0ee_37ff_0136_829a_408f6d1b0837\"></object>\n<h4>Combinaciones de tipos de anclajes no soportadas</h4>\n<p>La aplicación Detail no admite la combinación de pernos con cabeza o armadura con otros tipos de anclaje. Estos tipos de anclaje no se incluirán en el modelo exportado. Puede encontrar más información sobre las opciones de placas en el artículo: <a data-item-id=\"2a4f94ba-b8bb-4cab-abfc-d5c6d81e4f16\" href=\"\">Opciones de placas de anclaje</a>.</p>\n<h4>Combinación de cargas importadas y cargas introducidas por el usuario</h4>\n<p>Las<strong>cargas importadas y las cargas introducidas por el usuario no pueden combinarse en un modelo</strong>. Por las razones descritas en el apartado <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Antecedentes teóricos</a>. Los anclajes se importan desconectados de las placas base. Si se crea un caso de carga definido por el usuario, es obvio que la carga no se transferirá correctamente.</p>\n<p>Solución: Copie el elemento de Proyecto importado, borre todas las cargas importadas, interconecte todos los anclajes con la placa base, y entonces podrá introducir su caso de carga definido por el usuario.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n975e54ed_2b6d_019e_6772_44375c7605ba\"></object>\n<h4>Más bloques de hormigón</h4>\n<p><strong>Sólo</strong> se admite <strong>un bloque de hormigón</strong> en Detail. Sin embargo, el bloque de hormigón puede modificarse utilizando el Volumen negativo, el Plano de corte y la operación Cortar. Así es posible modelar formas más complejas, como pedestales, extensiones de la banda de cimentación, anclajes junto a aberturas, etc.</p>\n<p>También es posible importar dos bloques de hormigón independientes desde Conexión, que se importan a Detail como dos entidades de modelo que pueden modificarse y unirse posteriormente utilizando la operación de corte.</p>\n<figure data-asset-id=\"9f96c79c-33d3-4273-b411-1ad4e393715e\" data-image-id=\"9f96c79c-33d3-4273-b411-1ad4e393715e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/356bd5ec-b0a6-4db9-8eaa-91337f3b2f42/2%20independent%20blocks.png\" data-asset-id=\"9f96c79c-33d3-4273-b411-1ad4e393715e\" data-image-id=\"9f96c79c-33d3-4273-b411-1ad4e393715e\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n6c1bba61_2d83_01d4_a3da_8726ec9e068b\"></object>\n<h4>Más de una placa base en un bloque</h4>\n<p>Se admite la exportación de más placas base en un bloque, <strong>aunque no se recomienda importar los denominados anclajes de borde</strong>.</p>\n<figure data-asset-id=\"6169236b-b86e-4aa9-92c8-39b25fed9f8b\" data-image-id=\"6169236b-b86e-4aa9-92c8-39b25fed9f8b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c6b296ed-b436-4264-8411-72c6bf7b3be9/Design.png\" data-asset-id=\"6169236b-b86e-4aa9-92c8-39b25fed9f8b\" data-image-id=\"6169236b-b86e-4aa9-92c8-39b25fed9f8b\" alt=\"\"></figure>\n<p>En la aplicación Connection, el hormigón se modela de forma simplificada utilizando el modelo de sub-sólido de Winkler. Por otro lado, el modelo de la parte de acero sobre el bloque de hormigón se modela en detalle, incluyendo la plasticidad de los materiales. Para una verificación más detallada del hormigón armado bajo la placa base, es posible exportar la placa base, los anclajes y las cargas a la aplicación Detail. Allí, el hormigón se modela plásticamente.</p>\n<p>Los anclajes se exportan axialmente desconectados, y la carga entre ellos se sustituye por un par de fuerzas iguales pero opuestas (precisamente debido a la falta de rigidez de la parte de acero por encima de la placa base). Por lo tanto, no es posible que las fuerzas axiales en los anclajes cambien si la capa de recubrimiento en la esquina del bloque de hormigón se vuelve plástica. Del mismo modo, las soldaduras de las placas base se exportan desconectadas, sustituyéndose la conexión por fuerzas iguales pero opuestas. Por lo tanto, no puede haber ningún cambio en la tensión sobre la soldadura en caso de plastificación de la esquina de hormigón.</p>\n<p>De ello se deduce que, tras la exportación, aunque todas las fuerzas que actúan sobre las placas base estén en equilibrio, no se cumplirán las condiciones de deformación.</p>\n<p><em>Se aplica a la versión actual 25.1.2. Puede diferir en versiones anteriores, ya que estamos trabajando gradualmente para eliminar estas limitaciones. Puede encontrar más información sobre cada versión en las </em><a data-item-id=\"e0447990-4817-41b4-8d3e-37393eb4b691\" href=\"\"><em>notas de la versión</em></a><em>.</em><br>\n</p>"
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"value": "<h2>1 Nuevo proyecto</h2>\n<p>Ejecute el <strong>IDEA StatiCa Connection</strong>. Lo podrá conseguir en la pestaña de <strong>Acero (Steel)</strong>.</p>\n<figure data-asset-id=\"f6f4ad54-796a-4cb1-ab65-5c1b999f00df\" data-image-id=\"f6f4ad54-796a-4cb1-ab65-5c1b999f00df\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/caf94706-976b-405e-9d9c-8e8d72445714/Connection_to_Detail_01-01.png\" data-asset-id=\"f6f4ad54-796a-4cb1-ab65-5c1b999f00df\" data-image-id=\"f6f4ad54-796a-4cb1-ab65-5c1b999f00df\" alt=\"\"></figure>\n<p><strong>Mantenga la configuración por defecto </strong>de anclaje y entre en la aplicación.</p>\n<figure data-asset-id=\"d847e266-d4b7-42aa-89b1-1023999e6b95\" data-image-id=\"d847e266-d4b7-42aa-89b1-1023999e6b95\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d0c9de48-d056-4155-ac8d-8270c4120a0e/Connection_to_Detail_01-02.png\" data-asset-id=\"d847e266-d4b7-42aa-89b1-1023999e6b95\" data-image-id=\"d847e266-d4b7-42aa-89b1-1023999e6b95\" alt=\"\"></figure>\n<h2>2 Diseño</h2>\n<p><strong>Después de crear el modelo </strong>desde la plantilla, para mover la zapata al borde, tenemos que <strong>desglosar la plantilla para separar las operaciones y se nos permita editarlas de forma más sencilla.</strong></p>\n<figure data-asset-id=\"b8e0bcb1-858b-49ae-8da0-abd0ef7b2d4b\" data-image-id=\"b8e0bcb1-858b-49ae-8da0-abd0ef7b2d4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7fea954d-3d4b-4484-8cc8-1623c694e003/1.png\" data-asset-id=\"b8e0bcb1-858b-49ae-8da0-abd0ef7b2d4b\" data-image-id=\"b8e0bcb1-858b-49ae-8da0-abd0ef7b2d4b\" alt=\"\"></figure>\n<p>Vamos a ajustar la placa base y establecer <strong>La transferencia de la fuerza a cortante</strong> como<strong> Fricción</strong>.</p>\n<figure data-asset-id=\"2dbac565-c634-4e13-a8a0-f17e70b14eeb\" data-image-id=\"2dbac565-c634-4e13-a8a0-f17e70b14eeb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bb0a2659-325f-463c-bb89-36164d79ec4d/Connection_to_Detail_02-02.png\" data-asset-id=\"2dbac565-c634-4e13-a8a0-f17e70b14eeb\" data-image-id=\"2dbac565-c634-4e13-a8a0-f17e70b14eeb\" alt=\"\"></figure>\n<p><em>Nota: Desde el lanzamiento de la </em><em><strong>versión 24.1, IDEA StatiCa Detail </strong></em><a data-item-id=\"b871eedc-885b-4f1b-993d-578acfe45641\" href=\"\"><em>ha salido de su versión BETA</em></a><em> para el </em><em><strong>diseño de anclajes 3D</strong></em><em>. Con esta nueva versión, el cortante puede ser transferido también a través de </em><a data-item-id=\"9cbe085e-7b89-4860-a28d-33fe19f1c4ae\" href=\"\"><em>anclajes, llave de cortante y fricción</em></a><em>.</em></p>\n<p><strong>Introduzca las fuerzas internas</strong> para anclajes con carga biaxial. Las fuerzas internas causan esfuerzos de compresión en el contacto entre el suelo y el bloque de hormigón. Por defecto, se supone que el <a data-item-id=\"28992afa-3044-47f1-be8d-ad2a00d75f7a\" href=\"\">bloque de</a> hormigón está agrietado.</p>\n<figure data-asset-id=\"5c643873-8d30-4580-b2f2-f8497c31cff6\" data-image-id=\"5c643873-8d30-4580-b2f2-f8497c31cff6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ea2a2dd7-5b26-4310-a828-5e8ff91cc544/Connection_to_Detail_02-03.png\" data-asset-id=\"5c643873-8d30-4580-b2f2-f8497c31cff6\" data-image-id=\"5c643873-8d30-4580-b2f2-f8497c31cff6\" alt=\"\"></figure>\n<h2>3 Verificación</h2>\n<p><strong>Pase</strong> a la pestaña <strong>Verificación</strong>. Acá podrá ver cómo se realiza el chequeo normativo de los anclajes, comentemos un poco más en detalle esto.</p>\n<figure data-asset-id=\"f568a2d0-aef8-4e7a-8be1-95dfbb4309e4\" data-image-id=\"f568a2d0-aef8-4e7a-8be1-95dfbb4309e4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/75069198-6791-4be5-9929-ba1d6ae109d5/Connection_to_Detail_03-01.png\" data-asset-id=\"f568a2d0-aef8-4e7a-8be1-95dfbb4309e4\" data-image-id=\"f568a2d0-aef8-4e7a-8be1-95dfbb4309e4\" alt=\"\"></figure>\n<p>Hablemos un poco más sobre los fallos potenciales por tracción, cortante e interacción mutua según <a data-item-id=\"c57cf277-3f01-4ec8-82bc-470f3f631a73\" href=\"\">EN 1992-4</a>.</p>\n<figure data-asset-id=\"43ce57a5-2fb3-448e-99c2-5e93ff9f8a4a\" data-image-id=\"43ce57a5-2fb3-448e-99c2-5e93ff9f8a4a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f53625ee-a0a5-452a-8e20-685e7aadb0f7/Connection_to_Detail_03-02.png\" data-asset-id=\"43ce57a5-2fb3-448e-99c2-5e93ff9f8a4a\" data-image-id=\"43ce57a5-2fb3-448e-99c2-5e93ff9f8a4a\" alt=\"\"></figure>\n<p><strong>Por favor, revise la Comprobación Detallada</strong> <strong>de los Anclajes</strong> ya que podrá evidenciar más información sobre el chequeo en la primera página del reporte. <strong>En este texto se le informará de las comprobaciones normativas que necesita realizar manualmente o utilizando otros métodos</strong>, ya que no están incluidas en IDEA StatiCa Connection. Se recomienda llevar a cabo dichas verificaciones.</p>\n<figure data-asset-id=\"71bb7b2c-3ad4-4fb8-9c68-4f11208d71c3\" data-image-id=\"71bb7b2c-3ad4-4fb8-9c68-4f11208d71c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7844715a-b9c5-4dc1-86cf-b00bf7b78ac8/Connection_to_Detail_03-03.png\" data-asset-id=\"71bb7b2c-3ad4-4fb8-9c68-4f11208d71c3\" data-image-id=\"71bb7b2c-3ad4-4fb8-9c68-4f11208d71c3\" alt=\"\"></figure>\n<p>El fallo de <strong>Chequeo de los Anclajes </strong>se deriva de:</p>\n<ul>\n <li>La <strong>Resistencia a la rotura del hormigón de los anclajes en tracción y cortante</strong>.</li>\n <li><strong>Este problema puede resolverse fácilmente en IDEA StatiCa Detail con el método 3D CSFM</strong>. Esta metodología le permite hacer un análisis más avanzado que el modelo de hormigón simple o sin reforzar planteado en IDEA StatiCa Connection.</li>\n</ul>\n<h2>4 Exportación</h2>\n<p>Ahora nuestro aplicativo<strong> IDEA StatiCa Connection cuenta con un potente </strong><a data-item-id=\"270b17d4-280e-4c4b-b83e-ae25015afb38\" href=\"\"><strong>enlace BIM a Detail</strong></a>, que permite diseñar y comprobar bloques de hormigón armado con múltiples combinaciones.</p>\n<p>Requisitos previos para la exportación:</p>\n<ul>\n <li>El modelo tiene que estar<strong> pre-calculado y los resultados incluidos</strong></li>\n</ul>\n<p>Vaya a la pestaña <strong>Verificación-> Chequeo CR -> Guardar.</strong></p>\n<figure data-asset-id=\"ea91e94f-e32f-4298-a975-2ef961da9400\" data-image-id=\"ea91e94f-e32f-4298-a975-2ef961da9400\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f831ecc3-5a2e-4717-b78b-1acf29b2d736/Connection_to_Detail_04-01.png\" data-asset-id=\"ea91e94f-e32f-4298-a975-2ef961da9400\" data-image-id=\"ea91e94f-e32f-4298-a975-2ef961da9400\" alt=\"\"></figure>\n<p>La exportación sólo se permite para modelos que contemplen anclajes al hormigón y permitirá la transferencia del: </p>\n<ul>\n <li>El bloque de hormigón</li>\n <li>Los anclajes</li>\n <li>La placa base</li>\n <li>Las cargas</li>\n</ul>\n<p>Información adicional y parámetros que se establecen según los ajustes correspondientes en la Conexión:</p>\n<ul>\n <li>Transferencia a cortante (mediante anclajes, llave de cortante y fricción)</li>\n <li>Material</li>\n <li>Tipo de anclaje Post instalado (Adhesivo) /Vaciado in situ</li>\n <li>Tipo de acabo de anclaje Arandela/Recto/Gancho</li>\n <li>Coeficiente de fricción</li>\n</ul>\n<h2>5 Diseño</h2>\n<p>Esta sección le permitirá modificar Elementos, Apoyos, Cargas, Combinaciones, e introducir los aceros de refuerzo.</p>\n<h3>Soporte</h3>\n<p>El terreno tiene cierta rigidez, que debe ser considerada para un diseño preciso. El <strong>Apoyo superficial</strong> permite introducir la rigidez en las tres direcciones y <strong>por defecto se considera que no trabaja a tracción</strong> (no linealidad de la condición de contorno).</p>\n<ul>\n <li>Tenga cuidado al hacer suposiciones sobre las condiciones de contorno. En caso de no linealidad, si los momentos son bastante elevados, el bloque de hormigón en tensión puede volcarse durante el análisis, provocando grandes rotaciones. Esto puede conducir a un modelo divergente debido al movimiento del cuerpo flexible.</li>\n</ul>\n<figure data-asset-id=\"c592a8ce-8a91-428f-a116-310ffa4ee934\" data-image-id=\"c592a8ce-8a91-428f-a116-310ffa4ee934\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9ffc00ad-d001-4dbc-976c-89adf199d300/Connection_to_Detail_05-01.png\" data-asset-id=\"c592a8ce-8a91-428f-a116-310ffa4ee934\" data-image-id=\"c592a8ce-8a91-428f-a116-310ffa4ee934\" alt=\"\"></figure>\n<figure data-asset-id=\"005baf6f-c14a-43a7-9f2d-134b8e007b00\" data-image-id=\"005baf6f-c14a-43a7-9f2d-134b8e007b00\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/360a420a-db3c-434f-baea-bc0f6dae83e6/2.png\" data-asset-id=\"005baf6f-c14a-43a7-9f2d-134b8e007b00\" data-image-id=\"005baf6f-c14a-43a7-9f2d-134b8e007b00\" alt=\"\"></figure>\n<h3>Dispositivos de transferencia</h3>\n<p>Los anclajes son tomados de IDEA StatiCa Connection. Se pueden seleccionar dos tipos de anclajes.</p>\n<p>Anclajes vaciados in situ:</p>\n<ul>\n <li>Anclajes preinstalados con las mismas propiedades de adherencia que las barras de refuerzo.</li>\n</ul>\n<p>Anclajes adhesivos:</p>\n<ul>\n <li>Post-instalados (anclajes químicos) con la opción de personalizar su fuerza de adherencia en función de la fuerza de adherencia real.</li>\n</ul>\n<figure data-asset-id=\"bc241e0b-3ef8-4695-a828-bffd387dc495\" data-image-id=\"bc241e0b-3ef8-4695-a828-bffd387dc495\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/58083a9d-6c17-43a7-817d-9b7252101989/3.png\" data-asset-id=\"bc241e0b-3ef8-4695-a828-bffd387dc495\" data-image-id=\"bc241e0b-3ef8-4695-a828-bffd387dc495\" alt=\"\"></figure>\n<p>Por favor tenga especial cuidado en el correcto ajuste de la <strong>Interconexión de los anclajes con la placa base</strong>. En el caso de importar la zapata desde la aplicación Connection, la <strong>Transferencia de</strong> <strong>fuerzas axiales</strong> debe estar en <strong>OFF</strong>, y la <strong>Transferencia de cortante</strong> <strong>en ON</strong>. La razón es que los anclajes se cargan a tracción directamente con la fuerza derivada del análisis de la conexión. Puede leer más sobre esto <a data-item-id=\"270b17d4-280e-4c4b-b83e-ae25015afb38\" href=\"\">aquí</a>.</p>\n<p>Si diseñara una zapata desde cero en la aplicación Detail, ambas opciones estarían en ON. Cuando se transfiere el esfuerzo cortante a través de los anclajes, el usuario debe determinar qué anclajes soportarán el esfuerzo cortante y seleccionar la casilla de verificación correspondiente. Esto debe estar alineado con las condiciones establecidas en EN, que especifican que el cortante sólo debe asignarse a los anclajes efectivos para la comprobación del fallo del borde del hormigón.</p>\n<h3>Armaduras de refuerzo</h3>\n<p>Ajuste el recubrimiento de hormigón a 40 mm, que se utilizará como valor por defecto para el acero de refuerzo.</p>\n<figure data-asset-id=\"92ab352d-ac09-4a0a-8d84-6f329f595dcc\" data-image-id=\"92ab352d-ac09-4a0a-8d84-6f329f595dcc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3ec6a0bb-ec40-4702-bbb2-89bd511df9d1/4.png\" data-asset-id=\"92ab352d-ac09-4a0a-8d84-6f329f595dcc\" data-image-id=\"92ab352d-ac09-4a0a-8d84-6f329f595dcc\" alt=\"\"></figure>\n<p>Seleccione el <strong>Armado del acero de refuerzo(1)-->Grupo de armaduras 3D(2) </strong>y rellene el <strong>Diámetro</strong>, <strong>Propiedades</strong> y <strong>Geometría(3)</strong>.</p>\n<figure data-asset-id=\"6b6e717e-e109-4f48-b496-df5ced1c5eb8\" data-image-id=\"6b6e717e-e109-4f48-b496-df5ced1c5eb8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9a742dd2-0e9f-47e2-88e4-679d4f671661/5.png\" data-asset-id=\"6b6e717e-e109-4f48-b496-df5ced1c5eb8\" data-image-id=\"6b6e717e-e109-4f48-b496-df5ced1c5eb8\" alt=\"\"></figure>\n<p><strong>Copie</strong> la operación y cambie la <strong>Superficie</strong>. El resto de opciones se mantendrán.</p>\n<figure data-asset-id=\"7b6bcb85-b5c7-47a7-962b-2575cf579cdf\" data-image-id=\"7b6bcb85-b5c7-47a7-962b-2575cf579cdf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e3e3e1fc-04a7-45c7-a210-b57ae5627327/6.png\" data-asset-id=\"7b6bcb85-b5c7-47a7-962b-2575cf579cdf\" data-image-id=\"7b6bcb85-b5c7-47a7-962b-2575cf579cdf\" alt=\"\"></figure>\n<p><strong>Copie</strong> la operación y cambie las opciones que se muestran a continuación.</p>\n<figure data-asset-id=\"43726e22-af07-4ac1-be92-d112fcfe62ca\" data-image-id=\"43726e22-af07-4ac1-be92-d112fcfe62ca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8cff2846-d288-4186-9fe9-4ce360205c78/7.png\" data-asset-id=\"43726e22-af07-4ac1-be92-d112fcfe62ca\" data-image-id=\"43726e22-af07-4ac1-be92-d112fcfe62ca\" alt=\"\"></figure>\n<p><strong>Copie </strong>la operación y cambie las opciones que se muestran a continuación.</p>\n<figure data-asset-id=\"ec52d83a-da74-4b51-a743-2f945f7e7c31\" data-image-id=\"ec52d83a-da74-4b51-a743-2f945f7e7c31\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e4d0b63b-967f-4ef3-b686-453fd0e5dd73/8.png\" data-asset-id=\"ec52d83a-da74-4b51-a743-2f945f7e7c31\" data-image-id=\"ec52d83a-da74-4b51-a743-2f945f7e7c31\" alt=\"\"></figure>\n<h3>Cargas y combinaciones</h3>\n<p>Las combinaciones se toman de IDEA StatiCa Connection. Todo el proceso de importación se en detalla en el siguiente artículo - <a data-item-id=\"270b17d4-280e-4c4b-b83e-ae25015afb38\" href=\"\">Importación de anclajes desde Conexión a Detalle</a>.</p>\n<figure data-asset-id=\"e242070b-37a1-4f37-845b-56353fd83ff5\" data-image-id=\"e242070b-37a1-4f37-845b-56353fd83ff5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c1b8c32a-7e07-41fd-a4f3-aea3f359852a/9.png\" data-asset-id=\"e242070b-37a1-4f37-845b-56353fd83ff5\" data-image-id=\"e242070b-37a1-4f37-845b-56353fd83ff5\" alt=\"\"></figure>\n<p>Vamos a crear el <strong>Peso Propio</strong>:</p>\n<figure data-asset-id=\"195865cb-685a-4e18-9a16-f3e2e2647dda\" data-image-id=\"195865cb-685a-4e18-9a16-f3e2e2647dda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fb2740fa-c440-49ca-b7d6-e9f86b03ef58/10.png\" data-asset-id=\"195865cb-685a-4e18-9a16-f3e2e2647dda\" data-image-id=\"195865cb-685a-4e18-9a16-f3e2e2647dda\" alt=\"\"></figure>\n<p>Creamos una combinación con el Peso Propio, y agregamos el coeficiente para el peso propio = 1.35 de acuerdo con la normativa EN 1991-1-1</p>\n<figure data-asset-id=\"b2c448ed-67d4-485d-b14c-4bae5f5b5a2c\" data-image-id=\"b2c448ed-67d4-485d-b14c-4bae5f5b5a2c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/06acbace-d08f-472b-affe-3a17eebc3c17/10_1.png\" data-asset-id=\"b2c448ed-67d4-485d-b14c-4bae5f5b5a2c\" data-image-id=\"b2c448ed-67d4-485d-b14c-4bae5f5b5a2c\" alt=\"\"></figure>\n<h2>6 Verificación</h2>\n<p><strong>Antes de ejecutar el análisis</strong>, recomendamos <strong>cambiar el multiplicador del tamaño de elemento finito por defecto</strong> a dos para acelerar el cálculo. Este paso no es obligatorio, pero puede reducir el tiempo de cálculo y ayudar a detectar cualquier problema de divergencia. <strong>Si todo funciona correctamente y no surgen problemas, puede volver a cambiar a un multiplicador a uno</strong>.</p>\n<figure data-asset-id=\"cc5fdfb5-6bd5-40cd-8bd7-3551bc62168f\" data-image-id=\"cc5fdfb5-6bd5-40cd-8bd7-3551bc62168f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f4a01a9c-572f-4669-b241-be23f304ca61/11.png\" data-asset-id=\"cc5fdfb5-6bd5-40cd-8bd7-3551bc62168f\" data-image-id=\"cc5fdfb5-6bd5-40cd-8bd7-3551bc62168f\" alt=\"\"></figure>\n<figure data-asset-id=\"2f6ba38e-66d6-456e-b747-9ca3a13f0956\" data-image-id=\"2f6ba38e-66d6-456e-b747-9ca3a13f0956\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/54b18351-6be3-448e-ab4f-791346c5d876/12.png\" data-asset-id=\"2f6ba38e-66d6-456e-b747-9ca3a13f0956\" data-image-id=\"2f6ba38e-66d6-456e-b747-9ca3a13f0956\" alt=\"\"></figure>\n<h2>Resultados</h2>\n<h3>Tensión principal equivalente</h3>\n<p>La <strong>tensión equivalente principal (EPS)</strong> en el hormigón se determina basándose en el comportamiento volumétrico del bloque de hormigón. Se identifican y destacan las zonas que experimentan la mayor carga. Para conocer el efecto de confinamiento comparado con la compresión uniaxial, la tensión equivalente se calcula utilizando el factor kappa. En <a href=\"https://www.ideastatica.com/support-center/idea-statica-detail-structural-design-of-concrete-3d-discontinuities#ultimate-limit-state-checks\">este artículo de la base teórica</a> se muestra más información sobre la tensión principal <a href=\"https://www.ideastatica.com/support-center/idea-statica-detail-structural-design-of-concrete-3d-discontinuities#ultimate-limit-state-checks\">equivalente.</a></p>\n<figure data-asset-id=\"2a343b97-e6e5-42fc-9d86-73de11409b52\" data-image-id=\"2a343b97-e6e5-42fc-9d86-73de11409b52\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/db01ad39-5fd5-419f-8bc6-0e23abaf7048/13.png\" data-asset-id=\"2a343b97-e6e5-42fc-9d86-73de11409b52\" data-image-id=\"2a343b97-e6e5-42fc-9d86-73de11409b52\" alt=\"\"></figure>\n<h3>Tensiones en el acero de refuerzo</h3>\n<p><strong>Durante la comprobación de la armadura</strong>, es fundamental tener en cuenta que el anclaje cercano a la esquina se tiene una mayor utilización, practicamente al límite.</p>\n<figure data-asset-id=\"a5742641-b90e-4e0d-8938-2767aad96c7f\" data-image-id=\"a5742641-b90e-4e0d-8938-2767aad96c7f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a1b8292e-f1fc-4a86-972a-7ff94afa5f1b/14.png\" data-asset-id=\"a5742641-b90e-4e0d-8938-2767aad96c7f\" data-image-id=\"a5742641-b90e-4e0d-8938-2767aad96c7f\" alt=\"\"></figure>\n<p>Al visualizar la utilización de la armadura, el usuario puede ver claramente qué armadura contribuye a transferir la carga y evitar el fallo del cono de hormigón.</p>\n<figure data-asset-id=\"9b7eaa77-c046-423e-9707-6581b91fdfbe\" data-image-id=\"9b7eaa77-c046-423e-9707-6581b91fdfbe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f9e481ac-f232-4402-8a66-7d886ea4dfd8/15.png\" data-asset-id=\"9b7eaa77-c046-423e-9707-6581b91fdfbe\" data-image-id=\"9b7eaa77-c046-423e-9707-6581b91fdfbe\" alt=\"\"></figure>\n<h3>Adherencia</h3>\n<p>Compruebe los resultados de <strong>Adherencia </strong>y active la <strong>Fuerza Total en los Anclajes</strong>. Las fuerzas en los anclajes pueden variar ligeramente debido a los diferentes enfoques de cálculo relativos al bloque de hormigón. Sin embargo, las diferencias no son significativas.</p>\n<figure data-asset-id=\"69b59fab-b9b8-4ee2-b37f-4e51eb3be02c\" data-image-id=\"69b59fab-b9b8-4ee2-b37f-4e51eb3be02c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/09a8f55d-3f15-4843-9549-240567d9b8b3/16.png\" data-asset-id=\"69b59fab-b9b8-4ee2-b37f-4e51eb3be02c\" data-image-id=\"69b59fab-b9b8-4ee2-b37f-4e51eb3be02c\" alt=\"\"></figure>\n<h3>Deformaciones</h3>\n<p>Vaya a <strong>Auxiliar</strong> y active la <strong>Deformación</strong>.</p>\n<p>No es necesario realizar una comprobación de la deformación para ULS, pero es muy recomendable comprobar la deformación después del análisis para asegurarse de que el modelo no está experimentando una gran deformación, una gran rotación o que cualquier elemento finito esté presentando un comportamiento anómalo. Esto le proporcionará una visión general de los resultados del análisis y ayudará a identificar cualquier problema que pueda haber surgido durante el análisis.</p>\n<figure data-asset-id=\"10b137bd-2790-4edf-a3b4-0b376dfc5498\" data-image-id=\"10b137bd-2790-4edf-a3b4-0b376dfc5498\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9711f3e5-6748-433d-9579-7c4af49e46a4/17.png\" data-asset-id=\"10b137bd-2790-4edf-a3b4-0b376dfc5498\" data-image-id=\"10b137bd-2790-4edf-a3b4-0b376dfc5498\" alt=\"\"></figure>\n<h2>7 Reporte</h2>\n<p>Por último, vaya a la <strong>Vista de informe/Impresión</strong>. 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"value": "<p>El Eurocódigo especifica varios métodos de fallo de anclajes y zapatas de hormigón y los divide además según el tipo de carga. En <a data-item-id=\"b1a3015d-e75a-48e6-8495-70450fde4ba9\" href=\"\">IDEA StatiCa</a> Connection, hemos sido capaces de evaluar los anclajes hasta ahora, pero con algunas limitaciones, las evaluaciones tuvieron que hacerse manualmente.</p>\n<figure data-asset-id=\"2eee8876-6b85-40a8-a229-92cc736bfab2\" data-image-id=\"2eee8876-6b85-40a8-a229-92cc736bfab2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8b6d2b74-2ded-4e4e-96a2-79c016d63b11/Connection.png\" data-asset-id=\"2eee8876-6b85-40a8-a229-92cc736bfab2\" data-image-id=\"2eee8876-6b85-40a8-a229-92cc736bfab2\" alt=\"\"></figure>\n<p>Al mismo tiempo, era imposible contabilizar el refuerzo de los bloques de hormigón. Esto está cambiando ahora con IDEA StatiCa Detail 3D, que añade más posibilidades. IDEA StatiCa Detail 3D no ofrece valoraciones como estamos acostumbrados en la norma que las define para el hormigón liso. Sin embargo, con el análisis por elementos finitos, podemos comprobar que el hormigón armado satisfará la carga especificada y, en este caso, <strong>evitará el fallo del hormigón, que correspondería</strong> a esas condiciones. Las aplicaciones funcionan de forma independiente y pueden utilizarse por separado, pero gracias al <a data-item-id=\"270b17d4-280e-4c4b-b83e-ae25015afb38\" href=\"\">vínculo entre Conexión y Detalle</a>, también es posible utilizar Detalle únicamente como cálculo complementario.</p>\n<p>Repasemos ahora una por una las condiciones del Eurocódigo y las posibilidades que nos ofrecen las aplicaciones.</p>\n<h2>Fuerza de tracción</h2>\n<p>El Eurocódigo divide el primer tipo de carga<strong>(fuerza de tracción</strong>) en 6 posibles casos de fallo de anclajes o bloques de hormigón (a, b, c, d, e, f) y dos más para zapatas reforzadas (g, h).</p>\n<p>La figura inferior muestra esquemáticamente qué tipo de fallo se puede evaluar con la app Connection y qué comportamiento puede cubrir el uso de hormigón armado y, por tanto, el análisis en Detalle. IDEA StatiCa Connection utiliza fórmulas empíricas del Eurocódigo ( EN 1992-4-7.2.1) para el diseño de anclajes <strong>(CBFEM)</strong>, mientras que IDEA StatiCa Detail se basa completamente en el método de elementos finitos <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\"><strong>(3D CSFM)</strong></a>. Por lo tanto, algunas opciones de evaluación se solapan en ambas aplicaciones, pero siempre con un método diferente.</p>\n<figure data-asset-id=\"408fd958-1746-4e52-af3b-5e812aaeed7d\" data-image-id=\"408fd958-1746-4e52-af3b-5e812aaeed7d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0a7cb357-e90c-448e-9e0d-6e3dbf48c7ff/24.png\" data-asset-id=\"408fd958-1746-4e52-af3b-5e812aaeed7d\" data-image-id=\"408fd958-1746-4e52-af3b-5e812aaeed7d\" alt=\"\"></figure>\n<p>Por la naturaleza de los métodos implementados en el software, en Conexión sólo se puede considerar el hormigón simple, mientras que en <strong>Detalle sólo se puede considerar la zapata de hormigón armado</strong>.</p>\n<figure data-asset-id=\"38eba50f-4f9e-4fd6-9380-7300c20715de\" data-image-id=\"38eba50f-4f9e-4fd6-9380-7300c20715de\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/504267ed-44f6-46ae-9b15-33d57f0af506/failures.png\" data-asset-id=\"38eba50f-4f9e-4fd6-9380-7300c20715de\" data-image-id=\"38eba50f-4f9e-4fd6-9380-7300c20715de\" alt=\"\"></figure>\n<p>Los principales supuestos y limitaciones del análisis para el IDEA StatiCa Detail 3D se mencionan en el artículo <a data-item-id=\"4c908003-c3bb-4c0d-80ca-2c29cc8eef92\" href=\"\">Limitaciones conocidas</a>.</p>\n<h4>a) Rotura del acero</h4>\n<p>El fallo del acero de los anclajes<strong> cargados a tracción</strong> por sí solos se verifica en ambas aplicaciones. La resistencia a tracción de los anclajes se comprueba en Conexión según la siguiente fórmula:</p>\n<figure data-asset-id=\"1a72d337-d1eb-4b26-a77d-fda6504f8dfb\" data-image-id=\"1a72d337-d1eb-4b26-a77d-fda6504f8dfb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5cb675be-68cc-4cf6-9f70-8c3f4c32d193/16.png\" data-asset-id=\"1a72d337-d1eb-4b26-a77d-fda6504f8dfb\" data-image-id=\"1a72d337-d1eb-4b26-a77d-fda6504f8dfb\" alt=\"\"></figure>\n<p>En detalle, los anclajes se comprueban como las barras reforzadas regulares de acuerdo con los diagramas de tensión-deformación definidos para materiales particulares mientras se utiliza el valor de la deformación límite como máximo 5% (calculado en base al efecto de rigidización por tensión leer más en TB)</p>\n<h4>b) Rotura del cono de hormigón</h4>\n<p>El fallo del cono de hormigón puede verificarse en Connection. Sin embargo, en Connection, la aplicación sólo puede considerar <strong>el hormigón simple</strong>.</p>\n<figure data-asset-id=\"790a2f96-5d7d-48ed-b807-d461283656b1\" data-image-id=\"790a2f96-5d7d-48ed-b807-d461283656b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/07234199-279f-463f-8463-6480fc07aba5/17.png\" data-asset-id=\"790a2f96-5d7d-48ed-b807-d461283656b1\" data-image-id=\"790a2f96-5d7d-48ed-b807-d461283656b1\" alt=\"\"></figure>\n<p>Por lo tanto, en caso de que falle el cono de hormigón, es apropiado proceder a IDEA StatiCa Detail, donde se proporciona un análisis de todo el bloque reforzado. La resistencia a tracción del hormigón se desprecia de forma conservadora, lo que significa que la capacidad portante en caso de fallo del cono viene determinada, en gran medida, por la cantidad de armadura especificada. En la imagen inferior, se pueden ver las <strong>direcciones de las tensiones principales</strong> que indican la forma del cono mencionado anteriormente. En la parte derecha, se pueden ver los valores de las tensiones del hormigón, que se evalúan con los valores límite.</p>\n<figure data-asset-id=\"cbb46b36-986e-4279-9a26-b6f7daca9c28\" data-image-id=\"cbb46b36-986e-4279-9a26-b6f7daca9c28\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/60dbba5d-4619-4258-87aa-1a8bc97565c7/concrete%20cone%20failure.png\" data-asset-id=\"cbb46b36-986e-4279-9a26-b6f7daca9c28\" data-image-id=\"cbb46b36-986e-4279-9a26-b6f7daca9c28\" alt=\"\"></figure>\n<h4>c) Rotura por arrancamiento</h4>\n<p>Esta comprobación de código está en Conexión sólo para determinados casos (véase la primera imagen de ese artículo). Una evaluación adicional es necesaria para los anclajes mecánicos post-instalados.</p>\n<figure data-asset-id=\"37d9800f-de2f-41cf-82e7-d95bf4d20ce6\" data-image-id=\"37d9800f-de2f-41cf-82e7-d95bf4d20ce6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7b5d9cb3-361a-45a4-b93b-077ba189fa8e/18.png\" data-asset-id=\"37d9800f-de2f-41cf-82e7-d95bf4d20ce6\" data-image-id=\"37d9800f-de2f-41cf-82e7-d95bf4d20ce6\" alt=\"\"></figure>\n<p>En Detalle, es posible configurar los denominados anclajes <a data-item-id=\"d07820f8-072b-44dc-a35a-94b73e2e284b\" href=\"\">adhesivos</a> y especificar la resistencia de adherencia de diseño en función de sus parámetros técnicos. A continuación, los anclajes se verificarán en función de estos parámetros. (Aplicable sólo para hormigón armado).</p>\n<figure data-asset-id=\"641efac9-5d36-4d5e-b077-ed9196890a39\" data-image-id=\"641efac9-5d36-4d5e-b077-ed9196890a39\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8369e3e5-4360-4ce3-becf-0d648b6d8ea9/Design%20%285%29.png\" data-asset-id=\"641efac9-5d36-4d5e-b077-ed9196890a39\" data-image-id=\"641efac9-5d36-4d5e-b077-ed9196890a39\" alt=\"\"></figure>\n<h4>d) Combinación de arrancamiento y fallo del hormigón de los anclajes adheridos</h4>\n<p>Este fallo sólo puede detectarse en Detalle, donde las tensiones del hormigón y las zonas de anclaje se evalúan utilizando CSFM 3D. El mecanismo de fallo combinado de extracción y hormigón se encuentra en Detalle basado en los principios definidos anteriormente, y su evaluación forma parte de la comprobación de la resistencia del hormigón y del anclaje. (Aplicable únicamente al hormigón armado).</p>\n<h4>e) Rotura del hormigón</h4>\n<p>No es posible evaluarlo en Conexión. En Detalle, el fallo por fisuración suele ser un problema del hormigón simple, en el que el uso de armadura impide que se produzca. Al mismo tiempo, es posible ver las tensiones y deformaciones tanto de la armadura bajo compresión o tensión como del hormigón bajo compresión en la aplicación Detalle.</p>\n<figure data-asset-id=\"e065a9a9-29db-42d7-81d0-a2df2b1d2968\" data-image-id=\"e065a9a9-29db-42d7-81d0-a2df2b1d2968\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e3a47f6f-0ed5-46a2-9b45-4187da316e49/steel.png\" data-asset-id=\"e065a9a9-29db-42d7-81d0-a2df2b1d2968\" data-image-id=\"e065a9a9-29db-42d7-81d0-a2df2b1d2968\" alt=\"\"></figure>\n<h4>f) Rotura del hormigón</h4>\n<p>Para hormigón liso, es posible la comprobación empírica según el Eurocódigo en Conexión.</p>\n<figure data-asset-id=\"925cc023-af68-47ba-9b26-aa1bf5f77f16\" data-image-id=\"925cc023-af68-47ba-9b26-aa1bf5f77f16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b14e42c8-42d1-4dd4-8108-a71aa8430cf2/19.png\" data-asset-id=\"925cc023-af68-47ba-9b26-aa1bf5f77f16\" data-image-id=\"925cc023-af68-47ba-9b26-aa1bf5f77f16\" alt=\"\"></figure>\n<p>Para elementos estructurales reforzados, es posible utilizar Detail. El fallo por reventamiento del hormigón está cubierto en el análisis de resistencia del hormigón. Cuando las tensiones de tracción se transfieren sólo por el refuerzo (como se ha mencionado varias veces anteriormente).</p>\n<h4>Comprobaciones adicionales para bloques de hormigón armado:</h4>\n<p>En el caso de las zapatas reforzadas, se requiere una evaluación adicional de la armadura. El fallo del acero de la armadura y el fallo del anclaje de la armadura forman parte de la evaluación de la armadura en Detalle.</p>\n<p><strong>g) Rotura de la armadura de acero</strong></p>\n<p><strong>h) Rotura del anclaje de la armadura</strong></p>\n<h2>Carga cortante</h2>\n<p>El Eurocódigo divide el segundo tipo de carga<strong>(esfuerzo cortante</strong>) en 4 posibles casos de fallo del anclaje o del bloque de hormigón (a, b, c, d) y dos más para zapatas reforzadas (e, f).</p>\n<figure data-asset-id=\"4ff30694-4f30-4052-ba21-42b94f8d1235\" data-image-id=\"4ff30694-4f30-4052-ba21-42b94f8d1235\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/180de776-7c82-455f-9f59-7a09e8ae0b6e/27.png\" data-asset-id=\"4ff30694-4f30-4052-ba21-42b94f8d1235\" data-image-id=\"4ff30694-4f30-4052-ba21-42b94f8d1235\" alt=\"\"></figure>\n<p>La figura inferior muestra <strong>esquemáticamente</strong> qué tipo de fallo se puede evaluar con la app Connection y también qué comportamiento puede cubrir el uso de hormigón armado y, por tanto, el análisis en Detalle. IDEA StatiCa Connection utiliza fórmulas empíricas del Eurocódigo ( EN 1992-4-7.2.2) <strong>para el diseño de anclajes </strong><a data-item-id=\"d4aa2923-a94a-4c40-8fd8-93608acbf893\" href=\"\"><strong>(CBFEM)</strong></a><strong>.</strong> Todos los tipos de fallo causados por fuerza cortante pueden ser cubiertos en la aplicación Conexión.</p>\n<figure data-asset-id=\"457df143-9dfb-4d48-8087-e37ff0514ea1\" data-image-id=\"457df143-9dfb-4d48-8087-e37ff0514ea1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5929bf71-34da-46ae-b406-852cc91bcfc6/28.png\" data-asset-id=\"457df143-9dfb-4d48-8087-e37ff0514ea1\" data-image-id=\"457df143-9dfb-4d48-8087-e37ff0514ea1\" alt=\"\"></figure>\n<p>En el IDEA StatiCa Detail 3D, el cortante puede ser transferido por fricción, anclajes o orejetas de cortante. Es importante decir que sólo se evalúa la zapata. Los anclajes / orejetas de cizallamiento deben comprobarse en la conexión o en otro lugar. Una vez más, debe hacerse hincapié en que sólo se requiere hormigón armado.</p>\n<h4>a) Fallo del acero sin brazo de palanca</h4>\n<p>El fallo del acero sin el brazo de palanca de los anclajes cargados a cortante se verifica sólo en Connection. La resistencia al corte de los anclajes se verifica en IDEA StatiCa Connection de acuerdo con la siguiente fórmula:</p>\n<figure data-asset-id=\"09debd54-4504-4d1e-bfab-1c116b6a7a94\" data-image-id=\"09debd54-4504-4d1e-bfab-1c116b6a7a94\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2ca381f9-13f1-4aeb-9660-2d32c87b74da/20.png\" data-asset-id=\"09debd54-4504-4d1e-bfab-1c116b6a7a94\" data-image-id=\"09debd54-4504-4d1e-bfab-1c116b6a7a94\" alt=\"\"></figure>\n<p>La evaluación no es posible en Detalle.</p>\n<h4>b) Fallo de acero con brazo de palanca</h4>\n<p>El fallo del acero con el brazo de palanca de los anclajes cargados a cortante se verifica sólo en Conexión. La resistencia al corte del anclaje se verifica en IDEA StatiCa Connection de acuerdo con la siguiente fórmula:</p>\n<figure data-asset-id=\"b1f57fe5-e5be-4ff1-a457-079ff22926d7\" data-image-id=\"b1f57fe5-e5be-4ff1-a457-079ff22926d7\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8aed3ac3-c0c7-46a6-b1c7-f829adf97c81/21.png\" data-asset-id=\"b1f57fe5-e5be-4ff1-a457-079ff22926d7\" data-image-id=\"b1f57fe5-e5be-4ff1-a457-079ff22926d7\" alt=\"\"></figure>\n<p>La evaluación no es posible en Detalle.</p>\n<h4>c) Rotura por arrancamiento del hormigón</h4>\n<p>El fallo por arrancamiento del hormigón de los anclajes cargados a cortante se verifica sólo en Conexión. La resistencia a cortante de los anclajes se comprueba en IDEA StatiCa Connection de acuerdo con la siguiente fórmula:</p>\n<figure data-asset-id=\"c1e6f12a-45a5-4a95-8237-46dd4129a930\" data-image-id=\"c1e6f12a-45a5-4a95-8237-46dd4129a930\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/50dbe5ee-716e-42bf-b01b-bb3128305f72/22.png\" data-asset-id=\"c1e6f12a-45a5-4a95-8237-46dd4129a930\" data-image-id=\"c1e6f12a-45a5-4a95-8237-46dd4129a930\" alt=\"\"></figure>\n<p>La capacidad de corte del hormigón a través de la placa base se evalúa entonces en la aplicación Detalle.</p>\n<h4>d) Fallo de borde de hormigón</h4>\n<p>El fallo del borde del hormigón de los anclajes cargados a cortante se verifica en Connection sólo para hormigón liso. La resistencia a cortante de los anclajes se verifica en IDEA StatiCa Connection de acuerdo con la siguiente fórmula:</p>\n<figure data-asset-id=\"9b8d7c48-0539-441f-8c97-63be3393d355\" data-image-id=\"9b8d7c48-0539-441f-8c97-63be3393d355\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ef3d36b2-d22b-4bda-b857-29a636c8bc21/23.png\" data-asset-id=\"9b8d7c48-0539-441f-8c97-63be3393d355\" data-image-id=\"9b8d7c48-0539-441f-8c97-63be3393d355\" alt=\"\"></figure>\n<p>El fallo del borde del hormigón se puede comprobar en el Detalle (sólo hormigón armado).</p>\n<h4>Comprobaciones adicionales para bloques de hormigón armado:</h4>\n<p>Para zapatas reforzadas, se requiere una evaluación adicional de la armadura. El fallo del acero y del anclaje de la armadura forma parte de la evaluación de la armadura en IDEA StatiCa Detail.</p>\n<p><strong>e) Fallo del acero de la armadura suplementaria</strong></p>\n<p><strong>f) Fallo de anclaje de la armadura suplementaria</strong></p>\n<h2>Conclusión</h2>\n<p>La ventaja más significativa se encuentra en ejemplos como el anclaje cerca de un borde y otros casos en los que el hormigón simple no cumple la carga requerida. Hay que tener en cuenta que los anclajes y las orejetas de cizallamiento deben evaluarse más en profundidad en Conexión, pero juntas, estas dos herramientas de software proporcionan una solución completa.</p>\n<p>Debido al método y a la forma en que está diseñada la aplicación, la <strong>aplicación Detalle sólo es adecuada para zapatas reforzadas.</strong></p>"
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"value": "<h2>1. ¿Por qué se detuvo el cálculo antes de tiempo?</h2>\n<p>Los criterios de detención en el modelo 3D CSFM aseguran que las simulaciones se detienen en los límites definidos, podrás conocer más sobre esto límites en el siguiente artículo <a href=\"https://www.ideastatica.com/support-center-knowledge-base?article=idea-statica-detail-structural-design-of-concrete-3d-discontinuities&type=support_center_article#solution-method-and-load-control-algorithm-for-3D-CSFM\">Método de solución y algoritmo de control de carga para CSFM 3D</a>, también puedes buscar más información en la base de conocimientos de IDEA StatiCa Detail. </p>\n<p>Por defecto, la opción \"Stop at Limit Strain\" está activada, deteniendo los cálculos cuando se alcanzan algunos de los criterios ULS, por ejemplo, en el software se comprueba la utilización del hormigón, la armadura y el anclaje; la deformación del hormigón se limita al 5% en compresión y al 7% en tracción debido a las necesidades de convergencia. La deformación plástica de la armadura se limita al 5 %, mientras que el anclaje utiliza límites basados en el deslizamiento, no en la tensión de adherencia. </p>\n<p>La detención del cálculo del modelo, por lo tanto, puede deberse a varias razones, la razón más común es la falta de armadura, los errores de divergencia o también pueden deberse a un modelo mal apoyado, que provoque una deformación excesiva, otra razón puede ser que el diseño no sea satisfactorio para la carga especificada y simplemente esté sobrecargado.</p>\n<figure data-asset-id=\"0d2e9bb5-b1a2-47e7-bc38-5a1ac66545ce\" data-image-id=\"0d2e9bb5-b1a2-47e7-bc38-5a1ac66545ce\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a647eea7-a4e9-4b88-ad67-1d3076d93079/fig_1.png\" data-asset-id=\"0d2e9bb5-b1a2-47e7-bc38-5a1ac66545ce\" data-image-id=\"0d2e9bb5-b1a2-47e7-bc38-5a1ac66545ce\" alt=\"\"></figure>\n<h2>2. ¿Qué tipos de apoyos pueden utilizarse en Detail?</h2>\n<p>En el Detail 3D, los apoyos superficiales pueden añadir rigidez en todas las direcciones, por defecto, los apoyos son sólo de compresión (botón gris), lo que puede hacer que las estructuras \"vuelen\" debido a la falta de resistencia a la tracción, para permitir la tracción, se debe cambiar el botón a blanco. Se sugieren dos enfoques diferentes:</p>\n<p>1) Utilizar el apoyo por defecto sólo a compresión para las zapatas apoyadas en el suelo, pero recuerde aplicar manualmente el peso propio, ya que no se exporta desde IDEA StatiCa Connection.</p>\n<p>2) Para submodelos (por ejemplo, balcones, pedestales...) con barras de refuerzo continuas, utilice el apoyo estándar (con tracción incluida) y el anclaje de barras continuas; esto añade restricciones de punto único, garantizando una transferencia de fuerza adecuada y evitando errores como el desprendimiento de la cubierta de hormigón o la divergencia del modelo. Sin ello, los modelos pueden fallar debido a los límites de deformación (por ejemplo, 7 % de deformación en el hormigón en tracción).</p>\n<p>Para obtener información detallada sobre las funcionalidades de <a href=\"https://www.ideastatica.com/support-center-knowledge-base?article=full-functionalities-of-detail-3d&type=support_center_article#ultimate-limit-state-checks\">Detail 3D</a>, consulte el artículo <a href=\"https://www.ideastatica.com/support-center-knowledge-base?article=full-functionalities-of-detail-3d&type=support_center_article#ultimate-limit-state-checks\">Funcionalidades completas de Detail 3D</a>.</p>\n<figure data-asset-id=\"37cd7a92-6714-478f-be31-a95a18f81bd0\" data-image-id=\"37cd7a92-6714-478f-be31-a95a18f81bd0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4047322b-1886-4030-90eb-6df30a861a00/fig_2.png\" data-asset-id=\"37cd7a92-6714-478f-be31-a95a18f81bd0\" data-image-id=\"37cd7a92-6714-478f-be31-a95a18f81bd0\" alt=\"\"></figure>\n<h2>3. ¿Por qué es tan importante respetar las reglas de detallado?</h2>\n<p>La armadura diseñada debe seguir las reglas de detallado basadas en códigos (por ejemplo, armadura suplementaria para la transferencia de fuerzas de tracción y cortante según EN 1992-4), Detail 3D garantiza un flujo de fuerzas adecuado: zonas de compresión en el hormigón y tensión en las armaduras, sin embargo, el refuerzo adecuado es esencial, ya que el hormigón no transfiere la tracción y las reglas de detallado no están automatizadas: los usuarios deben aplicarlas manualmente, y es responsabilidad del ingeniero estructural reforzar el bloque de hormigón de la forma correcta.</p>\n<figure data-asset-id=\"68f9c4ab-80c2-4901-ba4d-94849cd52d38\" data-image-id=\"68f9c4ab-80c2-4901-ba4d-94849cd52d38\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a5c9f11-12d7-432f-95aa-517d420810ce/fig_3.png\" data-asset-id=\"68f9c4ab-80c2-4901-ba4d-94849cd52d38\" data-image-id=\"68f9c4ab-80c2-4901-ba4d-94849cd52d38\" alt=\"\"></figure>\n<h2>4. 4. ¿Cómo puedo modelar correctamente la transferencia de fuerza cortante?</h2>\n<p>El esfuerzo cortante en las placas base puede transferirse mediante fricción, anclajes o llave de cortante, pero sólo puede utilizarse un método a la vez, veamos sus consideraciones:</p>\n<p>Para la fricción, asegúrese de que la secuencia de casos de carga es correcta: aplique primero la compresión (permanente) y después el cizallamiento (variable). Si se hace incorrectamente, la placa base puede \"salir volando\", con una secuencia de carga correcta y el coeficiente de fricción ajustado a 0,25, la fuerza de cizallamiento puede transferirse por un 25% de la fuerza de compresión. </p>\n<p>En el caso de la llave de cortante, toda la fuerza de cortante se transfiere a través de esta llave, pero no se comprueba en IDEA StatiCa Detail, por lo tanto, se deberá comprobar la llave de cortante en IDEA StatiCa Connection y, a continuación, importar el modelo dentro de IDEA StatiCa Detail; la transferencia de carga en el bloque de hormigón seguirá la trayectoria de tensión típica (alas/alma) en función de la dirección de la carga de cortante.</p>\n<p>En el caso de los anclajes, el usuario puede definir qué anclajes son eficaces para la transferencia a cortante, sin embargo, no se comprueba su capacidad en Detail, por lo que se debe verificar su capacidad en Connection antes de simularla en Detail.</p>\n<figure data-asset-id=\"c334ada2-8202-4972-98e7-633c2cf2b65f\" data-image-id=\"c334ada2-8202-4972-98e7-633c2cf2b65f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/341548e5-af27-4363-b1e6-1b85cf7303a2/fig_4.png\" data-asset-id=\"c334ada2-8202-4972-98e7-633c2cf2b65f\" data-image-id=\"c334ada2-8202-4972-98e7-633c2cf2b65f\" alt=\"\"></figure>\n<h2>5. ¿Qué hay que tener en cuenta al exportar de Connection a Detail?</h2>\n<p>Las cargas pueden aplicarse directamente a los anclajes (tracción, compresión, cortante) o a la placa base (se permiten los seis grados de libertad). Los anclajes y las placas base se modelan como elementos separados, por lo que la transferencia de fuerzas entre ellos debe activarse manualmente mediante restricciones.</p>\n<ul>\n <li>Cuando se exporta el modelo de anclaje desde IDEA StatiCa Connection (por ejemplo, véase el <a href=\"https://www.ideastatica.com/support-center/bim-link-connection-to-3d-detail-eccentrically-loaded-anchoring\">enlace BIM Conexión a detalle - Anclaje con carga excéntrica</a>), la transferencia de fuerza axial entre los anclajes y la placa base se desactiva para evitar un empuje adicional no deseado de la placa base.</li>\n <li>Alternativamente, cuando se modela desde cero y se aplica la carga directamente sobre la placa base, el usuario tiene que activar la transferencia axial y de esfuerzo cortante entre la placa base y los anclajes.</li>\n</ul>\n<figure data-asset-id=\"d7699790-0998-4ffd-8fc8-86d824451d7c\" data-image-id=\"d7699790-0998-4ffd-8fc8-86d824451d7c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/cc49b2be-049e-43f6-bf2d-ecacfcb6eb0a/fig_5.png\" data-asset-id=\"d7699790-0998-4ffd-8fc8-86d824451d7c\" data-image-id=\"d7699790-0998-4ffd-8fc8-86d824451d7c\" alt=\"\"></figure>\n<h2>6. ¿Qué rigidez debe tener la placa base?</h2>\n<p>También es importante establecer la rigidez correcta de la placa base. En la siguiente figura se comparan tres modelos:</p>\n<ul>\n <li>una placa base flexible exportada desde Connection,</li>\n <li>una placa base flexible modelada directamente en Detail 3D con una carga aplicada en un único punto,</li>\n <li>y una placa base rígida con mayor espesor, con una carga aplicada en un único punto.</li>\n</ul>\n<p>Los resultados mostraron que las placas flexibles modeladas directamente en Detail 3D producen distribuciones de tensiones imprecisas y efectos de apalancamiento artificiales. La placa rígida elimina estos problemas, dando resultados coherentes con la exportación de Connection. Las fuerzas de anclaje fueron similares en el primer y el tercer modelo, pero el segundo (placa base flexible en Detail 3D) sobrestimó las fuerzas de anclaje en más de un 30 %, lo que lo convierte en un enfoque incorrecto. Por lo tanto, si no se exporta desde Connection, y se carga en un único punto, para obtener la interacción entre la placa base y el hormigón lo más cercana posible a la realidad, la sugerencia es utilizar la placa base rígida.</p>\n<figure data-asset-id=\"03a4b8aa-c047-4799-87d5-0df195a891e5\" data-image-id=\"03a4b8aa-c047-4799-87d5-0df195a891e5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f9ea68dd-7d49-4224-8b0c-5c9a91bf4202/fig_6.png\" data-asset-id=\"03a4b8aa-c047-4799-87d5-0df195a891e5\" data-image-id=\"03a4b8aa-c047-4799-87d5-0df195a891e5\" alt=\"\"></figure>\n<h2>7. ¿Qué ocurre con la tensión de contacto?</h2>\n<p>En Connection, es posible establecer un contacto entre dos placas y mostrar la tensión de contacto. Sin embargo, es una limitación conocida (ver <a data-item-id=\"4c908003-c3bb-4c0d-80ca-2c29cc8eef92\" href=\"\">Limitación conocida para Detalle 3D</a>) de la exportación de anclajes desde Connection a Detail.</p>\n<figure data-asset-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" data-image-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ed18b6d3-c35c-4edb-9919-9c108856ca5c/10%20most%20important%20questions%20about%203D%20anchoring%20in%20Detail%2003.png\" data-asset-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" data-image-id=\"156a7ab4-17b4-46d6-8bbd-5169130f0963\" alt=\"\"></figure>\n<p>Hay dos consecuencias en esto para el modelo en Detail:</p>\n<ul>\n <li>Parte de las cargas se pierden completamente.</li>\n <li>Las cargas importadas no están en equilibrio, y el modelo no puede ser calculado debido a deformaciones excesivas en la placa base y divergencias en el análisis.</li>\n</ul>\n<p>¿Cómo resolver esta limitación? Hay dos opciones:</p>\n<ul>\n <li>Modificar su modelo en Connection haciendo que no haya contracto entre las placas que generen tensiones de contacto. Operaciones como <strong>Placa Frontal</strong>, <strong>Cubrejuntas, </strong>y <strong>Placa de Rigidización </strong>(creada con el input de<strong> Doblar</strong>) generan contactos automáticamente en el modelo de elementos finitos.</li>\n <li>Borrar los efectos de cargas exportados desde el modelo de Connection; seleccionar la placa base y cambiar el <strong>Tipo de carga</strong> a <strong>Columna</strong>; agregar un nuevo <strong>Caso de Carga</strong> y un <strong>Impulso de Carga</strong>, e introduzca las fuerzas internas como en el modelo de Connection.</li>\n</ul>\n<figure data-asset-id=\"5d5f9721-c273-45b9-9af4-e36504b8656d\" data-image-id=\"5d5f9721-c273-45b9-9af4-e36504b8656d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6faacfec-06c2-4cfc-b034-bdd42090afea/What%20about%20the%20contact%20stress%2002.png\" data-asset-id=\"5d5f9721-c273-45b9-9af4-e36504b8656d\" data-image-id=\"5d5f9721-c273-45b9-9af4-e36504b8656d\" alt=\"\"></figure>\n<h2>8. ¿Por qué la tensión de unión supera el 99,9 % tan rápidamente?</h2>\n<p>En la mayoría de los modelos, la tensión de adherencia en el anclaje supera el 99,9% de utilización para niveles de carga de tensión muy bajos, la razón se encuentra en el diagrama tensión-deformación de la unión entre el anclaje/refuerzo y el hormigón, como se muestra en la siguiente figura, la unión alcanza rápidamente su tensión límite, y cualquier carga adicional conduce a la deformación plástica de la unión. </p>\n<p>Para determinar la tensión límite de adherencia de los anclajes adhesivos, consulte el artículo <a href=\"https://www.ideastatica.com/support-center-knowledge-base?article=bond-strength-for-anchors-in-detail-3d&type=support_center_article#ultimate-limit-state-checks\">Resistencia de adherencia de los anclajes en Detail 3D</a>.</p>\n<figure data-asset-id=\"a2e731b9-a69a-4518-b6e9-da26b921acfc\" data-image-id=\"a2e731b9-a69a-4518-b6e9-da26b921acfc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/694b1acb-ba85-43dd-90ef-f356cf56cd1b/fig_8.png\" data-asset-id=\"a2e731b9-a69a-4518-b6e9-da26b921acfc\" data-image-id=\"a2e731b9-a69a-4518-b6e9-da26b921acfc\" alt=\"\"></figure>\n<h2>9. ¿Cómo debo gestionar la configuración de la malla?</h2>\n<p>La calidad de la malla es crucial para las simulaciones 3D, especialmente para problemas no lineales, ya que afecta directamente al tiempo de cálculo, el mallado puede ser influenciado a partir del factor multiplicador de malla, el cual oscila entre 0,5 y 5, siendo 1 el valor por defecto. </p>\n<p>Utilizar un factor de 5 acelera las simulaciones y ayuda a identificar errores, pero los resultados pueden ser imprecisos (más de un 30% de error), por lo cual, tras verificar el modelo, el factor sugerido es 1 o inferior para obtener tensiones y deformaciones precisas, lo que aumenta el tiempo de análisis. </p>\n<p>En resumen, una malla gruesa (factor más alto) se utiliza para el diseño previo, mientras que una malla más fina (factor más bajo) proporciona resultados más precisos en la simulación final, especialmente alrededor de los anclajes.</p>\n<figure data-asset-id=\"bdd9c4e0-a0cd-47e3-998a-362d57009d1a\" data-image-id=\"bdd9c4e0-a0cd-47e3-998a-362d57009d1a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c52342a2-48e4-4c7e-8ce0-a6d60dbae041/fig_9.png\" data-asset-id=\"bdd9c4e0-a0cd-47e3-998a-362d57009d1a\" data-image-id=\"bdd9c4e0-a0cd-47e3-998a-362d57009d1a\" alt=\"\"></figure>\n<h2>10. ¿Es posible importar múltiples placas ancladas?</h2>\n<p>Sí, es posible; la pregunta ahora es ¿Qué ocurre después de exportar las multiples placas del Connection al Detail? </p>\n<p>Se importan dos o más bloques de hormigón a Detail dependiendo del número de placas base en Connection, donde cada placa base tiene sus propios bloques de hormigón. La limitación conocida (véase <a data-item-id=\"4c908003-c3bb-4c0d-80ca-2c29cc8eef92\" href=\"\">Limitación conocida para Detail 3D</a>) es que los bloques sólidos múltiples no son posible de modelar en Detail. Por lo tanto, el usuario tiene que eliminar todos los bloques excepto uno, y relacionar todas las demás placas base con ese bloque, generando así el modelo adecuado para la distribución correcta de las fuerzas de anclaje y soldaduras.</p>\n<figure data-asset-id=\"67bdf601-8d7f-4e71-aaf5-161af569fa02\" data-image-id=\"67bdf601-8d7f-4e71-aaf5-161af569fa02\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/00939d59-945e-4675-8580-7b5672439d54/fig_10.png\" data-asset-id=\"67bdf601-8d7f-4e71-aaf5-161af569fa02\" data-image-id=\"67bdf601-8d7f-4e71-aaf5-161af569fa02\" alt=\"\"></figure>\n<h2>Conclusión</h2>\n<p>El CSFM 3D de IDEA StatiCa Detail es una potente herramienta para modelar el comportamiento no lineal del hormigón y las barras de refuerzo, garantizando el cumplimiento del Eurocódigo y el ACI. Maneja eficazmente las interacciones de adherencia, zonas de tensión y compresión, y disposiciones de armadura, ofreciendo soluciones robustas de anclaje y transferencia de carga. </p>\n<p>Los criterios garantizan que los cálculos se detienen cuando se alcanzan los límites críticos de deformación, y el detallado adecuado de las armaduras es esencial para obtener resultados realistas. </p>\n<p>La calidad de la malla es crucial para obtener simulaciones precisas, ya que las mallas más finas proporcionan mayor precisión a costa de tiempos de análisis más largos. </p>\n<p>El refuerzo suplementario, la transferencia del esfuerzo cortante y los ajustes correctos de exportación son también factores clave para lograr diseños precisos y conformes a la normativa.</p>\n<p>Para obtener información más detallada, eche un vistazo al seminario web <a data-item-id=\"fe18abc4-7d3c-45ac-97e6-002bf87224ef\" href=\"\">10 preguntas más frecuentes sobre anclajes 3D</a>.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"fbcaf745_da91_019b_7a47_296ac910234f\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n3cd4f0f8_7be2_0129_3c28_244f77795d19\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n507ab528_1047_01d5_bbae_b4ba321f5f7b\"></object>"
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"value": "IDEA StatiCa ofrece diseño estructural de vigas, muros y columnas de concreto, con módulos para zonas de discontinuidad y anclajes. Permite calcular hormigón armado y pretensado y hacer todas las verificaciones ULS y SLS de norma."
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"value": "<h2>Introducción</h2>\n<p>El efecto de confinamiento en estructuras de hormigón se refiere al fenómeno en el que la resistencia y la ductilidad del hormigón mejoran significativamente debido a la presión lateral (activa) o al confinamiento proporcionado por los materiales circundantes (pasiva), como la armadura de acero o las camisas externas. Este efecto es especialmente importante para mejorar el comportamiento del hormigón en compresión, sobre todo bajo cargas elevadas.</p>\n<p>He aquí los aspectos clave del efecto de confinamiento en las estructuras de hormigón:</p>\n<ol>\n <li><strong>Aumento de la resistencia</strong>: El confinamiento aumenta la resistencia a la compresión del hormigón. Cuando se aplica presión lateral, se frena la expansión lateral del hormigón, lo que le permite soportar mayores cargas axiales antes de fallar.</li>\n <li><strong>Mayor ductilidad</strong>: El hormigón confinado presenta una mayor ductilidad, lo que significa que puede sufrir mayores deformaciones antes de fallar.</li>\n <li><strong>Comportamiento bajo carga</strong>: El confinamiento modifica el modo de fallo del hormigón, que pasa de ser frágil y repentino a ser más dúctil y gradual. Este cambio en el modo de fallo es beneficioso para la seguridad e integridad de las estructuras en condiciones de carga extremas.</li>\n <li><strong>Consideraciones de diseño</strong>: El diseño de elementos de hormigón confinado implica calcular la cantidad y disposición de la armadura de confinamiento para conseguir la resistencia y ductilidad deseadas. Las normas y códigos, como las directrices EN (Eurocódigo), proporcionan fórmulas y directrices para el diseño de elementos de hormigón confinado.</li>\n <li><strong>Aplicaciones</strong>: El confinamiento activo se tiene en cuenta a la hora de diseñar, por ejemplo, zonas parcialmente cargadas, bisagras de hormigón, etc.</li>\n</ol>\n<p>En la siguiente figura se puede observar cómo el diagrama tensión-deformación y la capacidad portante pueden diferir para el hormigón no confinado y el confinado.</p>\n<figure data-asset-id=\"267e3d53-b814-4a9e-8ece-f1295cb99094\" data-image-id=\"267e3d53-b814-4a9e-8ece-f1295cb99094\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4c82248d-2921-4a12-8752-4ed3b69cb201/32.png\" data-asset-id=\"267e3d53-b814-4a9e-8ece-f1295cb99094\" data-image-id=\"267e3d53-b814-4a9e-8ece-f1295cb99094\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 1\\qquad Efecto del confinamiento e influencia en la capacidad portante de las estructuras}}]</em></p>\n<p>Antes de entrar en el ejemplo en sí, recordemos cómo se define el material de hormigón en la aplicación.</p>\n<h2>Definición del material de hormigón en IDEA StatiCa Detalle</h2>\n<p>3D CSFM define el comportamiento del hormigón basándose en la <strong>teoría de plasticidad de Mohr-Coulomb</strong> para cargas monótonas.</p>\n<p>En general, para un ángulo dado de fricción interna del hormigón, que está alrededor de φ <em>= 30°</em>, las resistencias a tracción y compresión de los círculos de Mohr del hormigón pueden construirse como en la Figura 2.</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. 2\\qquad Círculos de Mohr para hormigón}}]</em></p>\n<p>Donde <em><sub>fc</sub></em> es la resistencia del hormigón en compresión, <em><sub>fct</sub></em> es la resistencia del hormigón en tracción, <em>φ</em> es el ángulo de fricción interna, y <sub>σc1</sub><em>, </em><sub>σc3</sub> son las tensiones principales del hormigón bajo compresión triaxial.</p>\n<p>Puede observarse que a medida que aumenta la tensión principal <sub>σc3</sub>, también aumenta la diferencia máxima posible entre los valores de <sub>σc3</sub> y <sub>σc1</sub>, que definimos como σc<em><sub>,eq</sub></em> máxima (véase más adelante).</p>\n<p>En 3D CSFM como se implementa en IDEA StatiCa Detail, el ángulo de fricción interna se considera como φ <em>= 0°, </em>como se muestra en la Figura 3.</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. 3\\qquad Círculos de Mohr para hormigón implementados en IDEA StatiCa Detail}}]</em></p>\n<p>La consecuencia práctica de esta implementación es que la diferencia máxima entre <sub>σc3</sub> y <sub>σc1</sub> es constante a medida que aumenta <sub>σc3</sub>.</p>\n<p><strong>Tensión principal equivalente expresa la tensión uniaxial \"perjudicial\" 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>,</sub></em> eq puede, por tanto, compararse directamente con los límites de resistencia uniaxial según los códigos.</p>\n<p>Comparando la Figura 2, en la que se utiliza el ángulo real de rozamiento interno, y la Figura 3, que muestra la aplicación de la teoría de Mohr-Coulomb con un ángulo de rozamiento interno nulo, puede observarse que el enfoque elegido para los cálculos en la aplicación Detalle es muy conservador para la evaluación del estado tensional triaxial. Obsérvese que el modelo con ángulo de rozamiento nulo se asemeja al modelo de Tresca, con corte de tensión.</p>\n<p>Leer más en <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\"><strong>Diseño estructural de discontinuidades 3D de hormigón en IDEA StatiCa Detail</strong></a></p>\n<h2>Ensayo triaxial - un ejemplo de confinamiento activo</h2>\n<p>En el ejemplo, simularemos un ensayo triaxial para explicar cómo se implementa el efecto de presión triaxial en 3D CSFM en IDEA StatiCa Detail. Este será, por lo tanto, un ejemplo de <strong>confinamiento activo</strong>. Todos los cálculos serán en valores característicos.</p>\n<p>El modelo es del tipo de bloque sólido con dimensiones en planta de 1.0 x 1.0 m y una altura de 3.0 m hecho de concreto C30/37 soportado por un soporte rígido de superficie en la dirección Z. Sólo en aras de la estabilidad del modelo de análisis, se incluyen también las direcciones X e Y en el apoyo superficial con un valor de rigidez despreciable. La carga se aplica en dos etapas. En el primer paso, se aplica al modelo una presión hidrostática (σc<sub><em>,</em></sub><sub>1</sub> = σc<sub><em>,</em></sub><sub>2</sub> = σc<sub><em>,</em></sub><sub>3</sub>) de 20 MPa. Este alto valor, relativo a la resistencia del hormigón, se eligió principalmente para demostrar la estabilidad del modelo computacional.</p>\n<figure data-asset-id=\"0745573b-ce79-4aca-84fe-1d43cf4802c3\" data-image-id=\"0745573b-ce79-4aca-84fe-1d43cf4802c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c7494607-2b43-4caa-a8e1-0f4288da7e11/Tri-axial%20test.png\" data-asset-id=\"0745573b-ce79-4aca-84fe-1d43cf4802c3\" data-image-id=\"0745573b-ce79-4aca-84fe-1d43cf4802c3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 4\\qquad Configuración de ensayo triaxial - modelo, carga y condiciones de contorno}}]</em></p>\n<p>Después de calcular el modelo, obtenemos el valor σc<sub><em>,eq</em></sub> = 0 MPa en todo el modelo. Esto corresponde a la definición anterior de la aplicación de la teoría de la plasticidad de Mohr-Coulomb en Detalle.</p>\n<figure data-asset-id=\"bcefe73a-3380-47e4-8de0-53a0ad3fbe85\" data-image-id=\"bcefe73a-3380-47e4-8de0-53a0ad3fbe85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/eb50b0f7-cced-42a8-ae95-53f49b768cdb/Eq%20stress%20step%201.png\" data-asset-id=\"bcefe73a-3380-47e4-8de0-53a0ad3fbe85\" data-image-id=\"bcefe73a-3380-47e4-8de0-53a0ad3fbe85\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 5\\qquad Tensión Principal Equivalente - primer paso de cálculo}}]</em></p>\n<p>En el segundo paso, se aplica una carga superficial de 50 MPa a la superficie superior del modelo. Obsérvese que esta carga es superior a la resistencia a compresión axial del hormigón considerada de 30 MPa. El objetivo de la prueba es demostrar que en este paso no se aplicará ninguna carga superior a la resistencia a compresión del hormigón. Por lo tanto, el cálculo debe detenerse de modo que la carga aplicada sea igual al valor resultante de σc<sub><em>,eq.</em></sub></p>\n<p>Veamos ahora los resultados. Como era de esperar, el cálculo se detuvo porque se superó el criterio de deformación plástica en el hormigón, que es del 5%.</p>\n<figure data-asset-id=\"64847678-e025-4afd-b504-f78296ce7881\" data-image-id=\"64847678-e025-4afd-b504-f78296ce7881\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0aeb3a83-a813-4b7e-ab8a-2c5be92749fe/Stop%20criterion%20after%202.%20step.png\" data-asset-id=\"64847678-e025-4afd-b504-f78296ce7881\" data-image-id=\"64847678-e025-4afd-b504-f78296ce7881\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 7\\qquad Resultado del cálculo tras el segundo paso}}}]</em></p>\n<p>Si repasamos los resultados, comprobamos que coinciden con los supuestos definidos anteriormente. Esto demuestra que el modelo concreto en Detalle funciona correctamente en términos de confinamiento activo.</p>\n<figure data-asset-id=\"7e5e0cbf-2c7d-456c-a7e3-5b0eae9eae90\" data-image-id=\"7e5e0cbf-2c7d-456c-a7e3-5b0eae9eae90\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/399058ba-db6c-445e-8468-98eb0a4d4607/Load%20stress%20step%202.png\" data-asset-id=\"7e5e0cbf-2c7d-456c-a7e3-5b0eae9eae90\" data-image-id=\"7e5e0cbf-2c7d-456c-a7e3-5b0eae9eae90\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{footnotesize{Fig. 7\\qquad a) Carga aplicada en el paso 2; b) Tensión principal equivalente; c) Tensiones principales σc,3 a σc,1}}}]</em></p>\n<p>Los picos de tensión que se observan en las superficies superior e inferior se deben a la forma de aplicar la carga superficial y el apoyo superficial en los bordes de la malla a partir de elementos tetraédricos con rotaciones nodales. Y también al hecho de que los valores nodales máximos de los elementos finitos adyacentes se muestran siempre en la aplicación Detalle. Sin embargo, el tema de este artículo no es la especificación de este método, por lo que no profundizaremos en él.</p>\n<h4>Verificación ABAQUS</h4>\n<p>En el siguiente paso, veremos una comparación con modelos creados en ABAQUS, donde también se utiliza la teoría de plasticidad de Mohr-Coulomb para definir el hormigón. Compararemos los resultados de Detail con un modelo de hormigón real con un ángulo de rozamiento interno de 30°. De este modo, demostramos la conservabilidad del enfoque en 3D CSFM.</p>\n<figure data-asset-id=\"6a5d81a7-da32-45e1-bee7-3b2769615a5d\" data-image-id=\"6a5d81a7-da32-45e1-bee7-3b2769615a5d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d8d6859d-2d6f-4ac9-ab6c-1d1aa11c4d42/Tri-axial%20ABAQUS.png\" data-asset-id=\"6a5d81a7-da32-45e1-bee7-3b2769615a5d\" data-image-id=\"6a5d81a7-da32-45e1-bee7-3b2769615a5d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 7\\qquad Modelo ABAQUS: a) Malla de hormigón 2; b) Definición de cargas; c) Tensiones principales σc,3}}]</em></p>\n<p>En ABAQUS, creamos un modelo similar al modelo en Detalle. Las definiciones de material, condiciones de contorno y cargas son idénticas. Por otra parte, la malla de hormigón se ha simplificado. Los resultados de dos cálculos, uno utilizando φ <em>= 0°; c = 15 MPa y el segundo φ = 30°; c = 8,65 MPa</em>, se muestran en el gráfico siguiente, así como la comparación con otros ángulos de rozamiento interno φ <em>= </em>10°, 20°, 40°.</p>\n<figure data-asset-id=\"3431843e-a5eb-41d4-aa9f-b0b57492f2a6\" data-image-id=\"3431843e-a5eb-41d4-aa9f-b0b57492f2a6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d7b7d8b7-4c82-42de-bcb4-f3c0c8b93f48/Tri-axial%20ABAQUS%20comparison.png\" data-asset-id=\"3431843e-a5eb-41d4-aa9f-b0b57492f2a6\" data-image-id=\"3431843e-a5eb-41d4-aa9f-b0b57492f2a6\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 7\\qquad Comparación de 3D CSFM, un modelo ABAQUS con varios ángulos de fricción interna }}}]</em></p>\n<p>El gráfico muestra la coincidencia entre los modelos 3D CSFM y ABAQUS para φ <em>= 0°</em>. También se ilustra claramente que las simplificaciones en la definición del material de hormigón en 3D CSFM (la rama plástica horizontal del diagrama tensión-deformación y la envolvente lineal horizontal de Mohr-Coulomb), que conducen a una mayor claridad y, lo que es más importante, a un cálculo más rápido, también conducen, al menos en términos de tensión triaxial, a resultados conservadores.</p>\n<p>Como último punto, cabe mencionar que si consideramos una tensión hidrostática superior a 20 MPa, la diferencia entre los modelos φ <em>= 0°</em> y otros ángulos sería aún mayor.</p>\n<h2>Conclusión</h2>\n<p>Se demostró y explicó que el cálculo en 3D CSFM es consistente con los supuestos reportados en los <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Antecedentes Teóricos</a>. Esto se verificó mediante la comparación con los modelos ABAQUS y se demostró el conservadurismo del enfoque 3D CSFM para el fenómeno de la tensión triaxial.</p>"
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"value": "<h2>Introduction</h2>\n<p>The passive confinement effect in concrete structures refers to the phenomenon where the strength and ductility of concrete are significantly improved due to confinement provided by surrounding materials, such as steel reinforcement or external jackets. This effect is particularly important in enhancing the performance of concrete in compression, especially under high loads.</p>\n<p>Here are the key aspects of the confinement effect in concrete structures:</p>\n<ol>\n <li><strong>Increased strength</strong>: Confinement increases the compressive strength of concrete. When lateral pressure is applied, it restrains the lateral expansion of the concrete, allowing it to sustain higher axial loads before failing.</li>\n <li><strong>Enhanced ductility</strong>: Confined concrete exhibits greater ductility, meaning it can undergo larger deformations before failure. </li>\n <li><strong>Mechanisms of passive confinement</strong>:\n <ul>\n <li><strong>Internal confinement</strong>: Achieved through transverse reinforcement such as ties, stirrups, or spirals within reinforced concrete. These reinforcements prevent the concrete from cracking and bulging outward.</li>\n <li><strong>External confinement</strong>: Involves the use of external materials like fiber-reinforced polymer (FRP) wraps, steel jackets, or concrete jackets applied around the structural member. This method is often used for retrofitting and strengthening existing structures.</li>\n </ul>\n </li>\n <li><strong>Behavior under load</strong>: Confinement changes the failure mode of concrete from a brittle, sudden failure to a more ductile, gradual one. This change in failure mode is beneficial for the safety and integrity of structures under extreme loading conditions.</li>\n <li><strong>Design considerations</strong>: The design of confined concrete members involves calculating the amount and arrangement of confining reinforcement to achieve the desired strength and ductility. Standards and codes, such as EN (Eurocode) guidelines, provide formulas and guidelines for designing confined concrete elements.</li>\n <li><strong>Applications</strong>: Confinement is widely used in the design of columns, bridge piers, and other critical structural elements. It is also used in retrofitting and strengthening existing structures to improve their load-carrying capacity.</li>\n</ol>\n<p>In the following figure, you can observe how the stress-strain diagram and bearing capacity can differ for unconfined and confined concrete.</p>\n<figure data-asset-id=\"1758cca9-168a-4db0-98c7-75c52d5e06fd\" data-image-id=\"1758cca9-168a-4db0-98c7-75c52d5e06fd\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ff38065e-58f4-4de6-ae36-7f859e63e19f/Passive%20confinment%20model.png\" data-asset-id=\"1758cca9-168a-4db0-98c7-75c52d5e06fd\" data-image-id=\"1758cca9-168a-4db0-98c7-75c52d5e06fd\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 1\\qquad Stress-strain model proposed for monotonic loading of confined and unconfined concrete [2]}}}\\]</em></p>\n<h2>Columns subjected to high compressive loading – a passive confinement example</h2>\n<p>In this example, we compare several differently shaped columns subjected to high compressive loading with different topologies and reinforcement ratios, calculated in IDEA StatiCa Detail and calculated by different analytical approaches by Morger, et al. [1], which are given in several current standards – <em>fib</em> Model Code for Concrete Structures 2010 (MC 2010) [3], SIA 262:2013 Concrete Structures (SIA 262) [4], and Eurocode 2 - Design of concrete structures EN 1992-1-1:2023 (EC 2) [5].</p>\n<p>Before we get into the verification itself, let's recall the theoretical basics of 3D CSFM implemented in the application IDEA StatiCa Detail – <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\"><strong>Structural design of concrete 3D discontinuities in IDEA StatiCa Detail</strong></a></p>\n<h3>Analytical methods</h3>\n<p>The whole verification is based on the analytical approaches already mentioned in [1]. In this text, we will only give a basic description of the analytical methods of calculation including the relevant formulas. For a better understanding, we recommend studying the paper [1] in more detail.</p>\n<p>The load-bearing resistance of an RC member in compression can be obtained by summing up the three individual components with their associated cross-sectional areas: (i) the uniaxial concrete compressive strength of the entire concrete cross-section, (ii) the compressive strength of the longitudinal reinforcement, and (iii) the increase in concrete compressive strength due to a triaxial stress state provided by confining reinforcement:</p>\n<p>\\[N_{R}=\\underset{(i)}{\\underbrace{f_{c}\\cdot A_{c}}}+\\underset{(ii)}{\\underbrace{(f_{sy.l}-f_{c})\\cdot A_{s.l}}}+\\underset{(iii)}{\\underbrace{\\Delta f_{conf}\\cdot A_{conf}}}\\]</p>\n<p>where <em>f</em><em><sub>c</sub></em> = uniaxial concrete compressive strength, <em>A</em><em><sub>c</sub></em> = concrete cross-section area, <em>f</em><em><sub>sy,l</sub></em> and <em>A</em><em><sub>s,l</sub></em> = yield strength and total cross-sectional area of longitudinal reinforcement, <em>Δf</em><em><sub>conf</sub></em> = concrete compressive strength increase due to confinement, and <em>A</em><em><sub>conf</sub></em> = governing confined concrete area.</p>\n<p>In this article, the coordinate system of an RC member in compression is chosen such that the loading direction coincides with the x-axis, which is referred to as the longitudinal direction. The y and z-directions are, thus, referred to as lateral directions.</p>\n<figure data-asset-id=\"91ad8e59-e06c-411f-8fe8-811fbb184a38\" data-image-id=\"91ad8e59-e06c-411f-8fe8-811fbb184a38\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6623bde0-2bef-429d-bdc7-8619c947b2a0/most%20important%20geometrical%20parameters.png\" data-asset-id=\"91ad8e59-e06c-411f-8fe8-811fbb184a38\" data-image-id=\"91ad8e59-e06c-411f-8fe8-811fbb184a38\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 2\\qquad Definition of most important geometrical parameters [1]}}}\\]</em></p>\n<p>The increase of the concrete compressive strength <em>Δf</em><em><sub>conf</sub></em> due to confinement is approximately four times the lateral compressive stress [6].</p>\n<p>\\[\\Delta f_{conf}=4\\cdot min(\\sigma_{confy},\\sigma_{confz})\\]</p>\n<p>Assuming yielding of the confining reinforcement and full dispersion of the confining forces, the confining stresses follow equilibrium as:</p>\n<p>\\[\\sigma_{confy}=\\frac{\\sum A_{s.confy}\\cdot f_{sy.conf}}{s_{x}\\cdot b_{csz}};\\sigma_{confz}=\\frac{\\sum A_{s.confz}\\cdot f_{sy.conf}}{s_{x}\\cdot b_{csy}}\\]</p>\n<p>Where <em>f</em><em><sub>sy.conf</sub></em> is the yield strength of confining reinforcement.</p>\n<p>The following sub-sections present the different existing approaches to determine the governing confined concrete area <em>A</em><em><sub>conf</sub></em> (and the corresponding effectiveness factor k) according to current design guidelines (EC 2, SIA 262, and MC 2010) and according to a new model approach for passive confinement presented in [1].</p>\n<h4>Design approaches according to design guidelines</h4>\n<p><strong>EC2 </strong>determines the governing confined concrete area <em>A</em><em><sub>conf,EC2</sub></em> based on arching action between the discretely distributed load introduction points of the confining reinforcement.</p>\n<p>\\[A_{conf.EC2}=\\underset{A}{\\underbrace{\\left( b_{csy}\\cdot b_{csz}-\\frac{\\sum s^{2}_{i}}{6}\\right)}}\\cdot \\underset{B}{\\underbrace{\\left( \\frac{(b_{csy}\\cdot s_{x}/2)\\cdot(b_{csz}-s_{x}/2)}{b_{csy}\\cdot b_{csz}}\\right)}}\\]</p>\n<p>\\[= \\left( b_{csy}\\cdot b_{csz}-\\frac{\\sum s^{2}_{i}}{6}\\right) \\cdot \\left(1-\\frac{s_{x}}{2\\cdot b_{csy}} \\right) \\cdot \\left(1-\\frac{s_{x}}{2\\cdot b_{csz}} \\right)\\]</p>\n<p>This equation, applicable to rectangular crosssections, is based on the work of Mander [2]. For more information and an understanding of parts A and B, refer to [1].</p>\n<figure data-asset-id=\"f135df00-0be5-4566-bf2f-4f98374d4b15\" data-image-id=\"f135df00-0be5-4566-bf2f-4f98374d4b15\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/38782f2d-a9f4-4eb7-a10b-16a298b9d0bc/Confined%20concrete%20area%20according%20to%20EC2.png\" data-asset-id=\"f135df00-0be5-4566-bf2f-4f98374d4b15\" data-image-id=\"f135df00-0be5-4566-bf2f-4f98374d4b15\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 3\\qquad Definition of confined concrete area according to EC 2: (a) confined concrete area at the section of a confining }}}\\) \\( \\textsf{\\textit{\\footnotesize{reinforcement layer (e.g., x = sx/2), (b) and (c) longitudinal dispersion of confining forces, (d) governing confined concrete }}}\\) \\( \\textsf{\\textit{\\footnotesize{area at the center between two confining reinforcement layers (e.g., x=0, dotted lines indicating section from (a) as reference).}}}\\)</em></p>\n<p>It is worth mentioning that in EC2, the effectiveness factor of the confining reinforcement <em>k</em> is used to express the load-bearing resistance. Factor <em>k</em> is the ratio between the governing confined concrete area <em>A</em><em><sub>conf</sub></em> and the cross-sectional area Ac.</p>\n<p>\\[k=\\frac{A_{conf}}{A_{c}}\\]</p>\n<p>Using this factor, the load-bearing resistance <em>N</em><em><sub>R</sub></em> can be rewritten as:</p>\n<p>\\[N_{R}=\\left( f_{c}+k\\cdot \\Delta f_{conf}\\right)\\cdot A_{c}+(f_{sy.l}-f_{c})\\cdot A_{s.l}\\]</p>\n<p>The effective factor is then defined as:</p>\n<p>\\[k=\\left(\\frac{b_{csy}\\cdot b_{csz}-\\frac{1}{6} \\sum b_{i}^{2}}{b_{cy}\\cdot b_{cz}}\\right)\\cdot \\left(1-\\frac{s_{x}}{2\\cdot b_{csy}} \\right)\\cdot \\left(1-\\frac{s_{x}}{2\\cdot b_{csz}} \\right)\\]</p>\n<p>For the purposes of this article, however, we will stick to the load-bearing resistance <em>N</em><em><sub>R</sub></em> expression from the beginning of the chapter over the use of the governing confined concrete area <em>A</em><em><sub>conf</sub></em>.</p>\n<p><br></p>\n<p><strong>SIA 262</strong> defines the governing confined concrete area <em>A</em><em><sub>conf,SIA262</sub></em> based on the stress field illustrated in Figure 4, proposed by Sigrist [7].</p>\n<p>\\[A_{conf.SIA262}=(b_{csy}-s_{x})\\cdot (b_{csz}-s_{x})\\]</p>\n<figure data-asset-id=\"a4484eb3-42a1-447a-8e18-eaf6ff15d0d3\" data-image-id=\"a4484eb3-42a1-447a-8e18-eaf6ff15d0d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/347a80eb-2fa9-45fb-905b-0467fd46546f/Confined%20concrete%20area%20according%20to%20SIA%20262.png\" data-asset-id=\"a4484eb3-42a1-447a-8e18-eaf6ff15d0d3\" data-image-id=\"a4484eb3-42a1-447a-8e18-eaf6ff15d0d3\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 4\\qquad Definition of the confined concrete area according to SIA 262: (a) stress field and (b) lateral section at the level }}}\\) \\( \\textsf{\\textit{\\footnotesize{of the confining reinforcement (e.g., x = sx/2). }}}\\)</em></p>\n<p><br></p>\n<p><strong>MC 2010</strong> defines the governing confined concrete area as a combination of the two models forming the basis of the EC 2 and SIA 262 formulation:</p>\n<p>\\[A_{conf.MC2010}=\\left( b_{csy}\\cdot b_{csz}-\\frac{\\sum s^{2}_{i}}{6}\\right)\\cdot \\left( \\frac{(b_{csy}\\cdot s_{x})\\cdot(b_{csz}-s_{x})}{b_{csy}\\cdot b_{csz}}\\right)\\]</p>\n<p>\\[= \\left( b_{csy}\\cdot b_{csz}-\\frac{\\sum s^{2}_{i}}{6}\\right) \\cdot \\left(1-\\frac{s_{x}}{b_{csy}} \\right) \\cdot \\left(1-\\frac{s_{x}}{b_{csz}} \\right)\\]</p>\n<p><br></p>\n<p><strong>The new model approach for passive confinement</strong> introduced in [1] defines the simplified confined concrete area <em>A</em><em><sub>conf,simp</sub></em> as a function of the confining reinforcement geometry and spacing.</p>\n<p>\\[A_{conf.simp}=\\left(b_{csy}-\\frac{\\sqrt{s_{x}^{2}+s_{z}^{2}}}{2}\\right)\\cdot \\left(b_{csz}-\\frac{\\sqrt{s_{x}^{2}+s_{y}^{2}}}{2}\\right)\\]</p>\n<h3>IDEA StatiCa Detail models</h3>\n<p>Models are of the solid block type with various plan dimensions <em>b</em><em><sub>cy</sub></em> x <em>b</em><em><sub>cz</sub></em>, height <em>h</em><em><sub>x</sub></em>, and stirrups distance <em>s</em><em><sub>x</sub></em> made of C30/37 concrete supported by rigid surface support in the X, Y, Z direction at the bottom surface. For the sake of the stability of the top concrete cover in the model, the top surface is also supported in horizontal directions by rigid support. Concrete cover <em>c</em> is 30 mm for all models. There are always four longitudinal rebars with the diameter <em>Φ</em><em><sub>s,l</sub></em><em> = 10 mm</em>. Stirrups, the confining reinforcement, and longitudinal bars are modeled from steel B500B. All calculations are in characteristic values.</p>\n<figure data-asset-id=\"a4a34e14-4c79-4e2f-bb7a-3bca03837987\" data-image-id=\"a4a34e14-4c79-4e2f-bb7a-3bca03837987\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6056a8a4-94ea-43e1-974d-f85cd120b862/Passive%20confinement%20models.png\" data-asset-id=\"a4a34e14-4c79-4e2f-bb7a-3bca03837987\" data-image-id=\"a4a34e14-4c79-4e2f-bb7a-3bca03837987\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 5\\qquad IDEA StatiCa Detail models a) 0.75 x 1.5 x 4.0; b) 1.0 x 1.0 x 4.0; c) 0.75 x 2.5 x 5.0; d) 2.0 x 2.0 x 6.0}}}\\]</em></p>\n<p>A load greater than the expected load capacity is always applied. The program then searches for the maximum possible applicable load so that one of the defined criteria is not exceeded. In this case, it is always the limit strain criterion of the stirrup reinforcement, which is a maximum of 5%, but due to the implemented Tension stiffening, the limiting value is usually lower. For more details, see <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Theoretical Background</a>. </p>\n<p>In the following figure, it can be seen that the calculation of model 0.75 x 1.5 x 4.0 was stopped and a multiple of the applied load was found as the maximum load that the element can resist.</p>\n<figure data-asset-id=\"b17363b9-988c-4c1d-adeb-334b40074b8c\" data-image-id=\"b17363b9-988c-4c1d-adeb-334b40074b8c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/358337a5-e90c-487d-b844-b595f16be1f0/Passive%20confinement%20limit%20strain.png\" data-asset-id=\"b17363b9-988c-4c1d-adeb-334b40074b8c\" data-image-id=\"b17363b9-988c-4c1d-adeb-334b40074b8c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 6\\qquad IDEA StatiCa Detail – limit strain in reinforcement}}}\\]</em></p>\n<h3>Comparison of individual models</h3>\n<p>In the following tables and graphs, we present a comparison of all models created in the IDEA StatiCa Detail application and analytical approaches, including all intermediate results for one rectangular and one square model. However, there are auxiliary variables that need to be defined first.</p>\n<p><em>Φ</em><em><sub>s,l</sub></em> and <em>Φ</em><em><sub>s,conf</sub></em> are the diameters of longitudinal and confining reinforcement, <em>n</em><em><sub>y</sub></em> and <em>n</em><em><sub>z</sub></em> are the numbers of spaces <em>s</em><em><sub>y</sub></em> and <em>s</em><em><sub>z</sub></em> (meaning that the number of stirrup legs is <em>n+1</em>), <em>N</em><em><sub>R,uncf</sub></em> and <em>N</em><em><sub>R,conf</sub></em> are defined as follows:</p>\n<p>\\[N_{R,uncf}=f_{c}\\cdot A_{c}+(f_{sy.l}-f_{c})\\cdot A_{s.l}; N_{R,conf}=\\Delta f_{conf}\\cdot A_{conf}\\]</p>\n<h4>Rectangular model a) 0.75 x 1.5 x 4.0</h4>\n<figure data-asset-id=\"ce160464-4bac-46e8-a9d2-e675977689f4\" data-image-id=\"ce160464-4bac-46e8-a9d2-e675977689f4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/03c627fb-abc9-460a-8076-320591572b40/0.75_1.5_4%20-%20intermidi.png\" data-asset-id=\"ce160464-4bac-46e8-a9d2-e675977689f4\" data-image-id=\"ce160464-4bac-46e8-a9d2-e675977689f4\" alt=\"\"></figure>\n<figure data-asset-id=\"c61d0a6b-cc7b-4175-b4e1-4d46fe902907\" data-image-id=\"c61d0a6b-cc7b-4175-b4e1-4d46fe902907\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/abdce0f1-fc7d-4ee0-8e9e-ff7e68387e74/0.75_1.5_4%20-%20capacity.png\" data-asset-id=\"c61d0a6b-cc7b-4175-b4e1-4d46fe902907\" data-image-id=\"c61d0a6b-cc7b-4175-b4e1-4d46fe902907\" alt=\"\"></figure>\n<figure data-asset-id=\"4c4703b5-ace8-4e07-a9b4-879844b1d63c\" data-image-id=\"4c4703b5-ace8-4e07-a9b4-879844b1d63c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5975a9e8-2bfb-4d3d-82af-b7e0195c1cfc/0.75_1.5_4%20-%20ratios.png\" data-asset-id=\"4c4703b5-ace8-4e07-a9b4-879844b1d63c\" data-image-id=\"4c4703b5-ace8-4e07-a9b4-879844b1d63c\" alt=\"\"></figure>\n<figure data-asset-id=\"6443c137-40de-4dea-b2e4-9223682ee184\" data-image-id=\"6443c137-40de-4dea-b2e4-9223682ee184\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e0d6eed8-4316-4d91-a606-60b0d0a404f1/0.75_1.5_4%20-%20lbc.png\" data-asset-id=\"6443c137-40de-4dea-b2e4-9223682ee184\" data-image-id=\"6443c137-40de-4dea-b2e4-9223682ee184\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ee09da0c_0ef6_0164_bae7_ba88270dd704\"></object>\n<h4>Square model b) 1.0 x 1.0 x 4.0</h4>\n<figure data-asset-id=\"dd3afef2-c364-4e17-bfb8-fe1e5a289f8f\" data-image-id=\"dd3afef2-c364-4e17-bfb8-fe1e5a289f8f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9043e607-1941-47ac-9832-5d5306eda1f0/1_1_4%20-%20intermidi.png\" data-asset-id=\"dd3afef2-c364-4e17-bfb8-fe1e5a289f8f\" data-image-id=\"dd3afef2-c364-4e17-bfb8-fe1e5a289f8f\" alt=\"\"></figure>\n<figure data-asset-id=\"63a0291a-cf92-4539-a6e5-677d1a92c0d9\" data-image-id=\"63a0291a-cf92-4539-a6e5-677d1a92c0d9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4d08268c-6815-4628-84dc-361c064a4978/1_1_4%20-%20capacity.png\" data-asset-id=\"63a0291a-cf92-4539-a6e5-677d1a92c0d9\" data-image-id=\"63a0291a-cf92-4539-a6e5-677d1a92c0d9\" alt=\"\"></figure>\n<figure data-asset-id=\"cdd67cfb-6c53-42bf-b850-273dd1b214e3\" data-image-id=\"cdd67cfb-6c53-42bf-b850-273dd1b214e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f6dee50d-146e-4694-8aaa-1538379b1645/1_1_4%20-%20ratios.png\" data-asset-id=\"cdd67cfb-6c53-42bf-b850-273dd1b214e3\" data-image-id=\"cdd67cfb-6c53-42bf-b850-273dd1b214e3\" alt=\"\"></figure>\n<figure data-asset-id=\"1b69693e-5d58-431f-96fa-a3da72f2d05a\" data-image-id=\"1b69693e-5d58-431f-96fa-a3da72f2d05a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a5bbd9cb-0d03-41a0-9606-d1ca3265c9df/1_1_4%20-%20lbc.png\" data-asset-id=\"1b69693e-5d58-431f-96fa-a3da72f2d05a\" data-image-id=\"1b69693e-5d58-431f-96fa-a3da72f2d05a\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n3da22c56_c93b_0195_202d_02df21b941f6\"></object>\n<h4>Rectangular model c) 0.75 x 2.5 x 5.0</h4>\n<figure data-asset-id=\"bf61b109-5f6a-441b-8302-58a2b09cb384\" data-image-id=\"bf61b109-5f6a-441b-8302-58a2b09cb384\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7dde6f32-d58c-4e19-8835-c0101e6c7e62/0.75_2_5%20-%20lbc.png\" data-asset-id=\"bf61b109-5f6a-441b-8302-58a2b09cb384\" data-image-id=\"bf61b109-5f6a-441b-8302-58a2b09cb384\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n14a40d45_5e31_01fa_7d34_725af70e1e3f\"></object>\n<h4>Square model d) 2.0 x 2.0 x 6.0</h4>\n<figure data-asset-id=\"07db6188-a465-47f0-9d10-615bb8df7eac\" data-image-id=\"07db6188-a465-47f0-9d10-615bb8df7eac\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/222fccb8-f601-41fe-b2aa-290ae7e5351c/2_2_6%20-%20lbc.png\" data-asset-id=\"07db6188-a465-47f0-9d10-615bb8df7eac\" data-image-id=\"07db6188-a465-47f0-9d10-615bb8df7eac\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1bc8ae97_dcc3_0117_d9fb_2be2c6543497\"></object>\n<h2>Conclusion</h2>\n<p>Several conclusions can be drawn from the results presented above. In general, the 3D CSFM results have been shown to be quite conservative, especially for square models where the increase in load capacity due to the confinement is less than half in some examples. Good conformity, within 2% deviation, can be observed for rectangular models. Among the analytical methods investigated, the EC2 approach shows the best match in all models. This verification demonstrates that the use of 3D CSFM is safe from a passive confinement point of view and in accordance with the established methods of standards.</p>\n<h2>References</h2>\n<p>[1] MORGER, Fabian; KENEL, Albin a KAUFMANN, Walter. Passive confinement of reinforced concrete members revisited. Online. <em>Structural Concrete</em>. ISSN 1464-4177. <a href=\"https://doi.org/10.1002/suco.202400209\">https://doi.org/10.1002/suco.202400209</a>.</p>\n<p>[2] Mander JB, Priestley MJN, Park R. Observed stress-strain behavior of confined concrete. J Struct Eng. 1988;114:1827–49. <a href=\"https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1827)\">https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1827)</a></p>\n<p>[3] International Federation for Structural Concrete (fib). Model code for concrete structures 2010; 2013.</p>\n<p>[4] SIA. Swisscode SIA 262: concrete structures. Zurich, Switzerland: Swiss society of engineers and architects (SIA); 2013.</p>\n<p>[5] EN 1992-1-1:2023. Eurocode 2—Design of concrete structures—Part 1-1: General rules and rules for buildings, bridges and civil engineering structures; 2023.</p>\n<p>[6] Nielsen MP, Hoang LC. Limit analysis and concrete plasticity. 3rd ed. Boca Raton, FL: CRC Press; 2011. <a href=\"https://doi.org/10.1201/b10432\">https://doi.org/10.1201/b10432</a></p>\n<p>[7] Sigrist V. Zum Verformungsvermögen von Stahlbetonträgern [On the deformation capacity of structural concrete girders]. Doctoral Thesis. ETH Zürich; 1995. <a href=\"https://doi.org/10.3929/ethz-a-001492371\">https://doi.org/10.3929/ethz-a-001492371</a></p>"
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Verification of the presented approach is based on (I) comparison with other well-established software for numerical simulations of material behavior and (II) compliance with standard design codes. </p>\n<h2>Experiment description</h2>\n<p>The experimental campaign [1] involves testing full-size anchors bonded in a concrete block. The rods are made of ribbed bar (FeE500B) and are 20 mm in diameter. For the ribbed bar, the steel yield strength is 585 MPa, the ultimate strength is 700 MPa, the ultimate strain at failure is 16%, and the elastic modulus is 210 GPa. Three different depths (100, 150, 200 mm) are being tested to observe bond, concrete cone, or rod failure. The anchors are cast in a reinforced concrete block (2250x1850x600 mm) to prevent splitting failure and edge effects. The EDF(Electricity of France)-recommended minimum reinforcement is installed, consisting of one layer of 20 and 25 mm diameter ribbed bars in both directions on the upper and lower parts of the block.</p>\n<p>Additionally, some 12 mm diameter stirrups are installed to support the two layers of reinforcement. The reinforcement rate is 0.64%. The concrete grade used is C40/50. The concrete block is secured using two metal sections connected to the test slab with four prestressing bars. No confining pressure is applied around the anchorage. The hydraulic jack is fixed to the anchorage by two symmetrical rods. The quasi-static tensile loading is displacement-controlled with a loading rate of 1 mm/min, and the load is applied until the anchor fails. </p>\n<figure data-asset-id=\"4fb4349f-bda8-4e02-b925-e51650f5673a\" data-image-id=\"4fb4349f-bda8-4e02-b925-e51650f5673a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bed29f4e-6668-4ca4-86ae-b73971bc6a1a/01.png\" data-asset-id=\"4fb4349f-bda8-4e02-b925-e51650f5673a\" data-image-id=\"4fb4349f-bda8-4e02-b925-e51650f5673a\" alt=\"\"></figure>\n<p><em>1) Pull out test setup - coming from article: Pullout behavior of cast-in-place headed and bonded anchors with different embedment depths - Fabien Delhomme, Thierry Roure ,Benjamin Arrieta, Ali Limam</em></p>\n<figure data-asset-id=\"e74201c9-829d-4a9e-90c7-de43902745b2\" data-image-id=\"e74201c9-829d-4a9e-90c7-de43902745b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0476497e-3f50-471c-9816-a328f41dd074/02.png\" data-asset-id=\"e74201c9-829d-4a9e-90c7-de43902745b2\" data-image-id=\"e74201c9-829d-4a9e-90c7-de43902745b2\" alt=\"\"></figure>\n<p><em>2) Reinforcements and anchor layout</em></p>\n<h2>3D CSFM -Compatible Stress Field Method</h2>\n<h3>Theory </h3>\n<p>3D CSFM defines the concrete behavior based on the Mohr-Coulomb plasticity theory for monotonic loading. The method examines concrete behavior in terms of principal stresses, while neglecting the concrete tensile strength. The effect of concrete tension is only taken into account in Tension stiffening of steel rebars.<br>\nThe 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 is not suitable for simulating plain concrete due to the absence of tension, which may result in misleading deformation and model divergence. <br>\nGenerally, 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>. 3D CSFM assumes a zero angle of internal friction, leading to a conservative design due to the plasticity surface resembling the Tresca model, which is independent of the first stress invariant. More can be found in <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\"><strong>Theoretical Background</strong></a><strong> </strong>[2].</p>\n<h3>Model assembly</h3>\n<p>The FEA model is constructed using concrete tetrahedral elements of higher order, with embedded 1D rod representing reinforcements interconnected via MPC( Multi-Point-Constraints) and bond elements to allow slip. The reinforcement bars are split into two surface layers with a cover of 60 mm and shear links (see Fig. 2). The model utilizes surface support with restricted X, Y, Z degrees of freedom over a width of 200 mm. Casted anchors are positioned in the middle of the testing specimen, and the length of the anchor varies from 100-200 mm to test all possible failure modes.</p>\n<figure data-asset-id=\"57ceca96-ad6f-441d-9aab-48456f5b4d56\" data-image-id=\"57ceca96-ad6f-441d-9aab-48456f5b4d56\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8b1fe644-ce49-46f0-8ad6-bd895d4a83f4/04.png\" data-asset-id=\"57ceca96-ad6f-441d-9aab-48456f5b4d56\" data-image-id=\"57ceca96-ad6f-441d-9aab-48456f5b4d56\" alt=\"\"></figure>\n<p><em>3) Model assembly</em></p>\n<h3>Anchor model</h3>\n<p>The anchor is modeled using a ROD element that can only transfer compression and tension. The important aspect is the bond model and how the anchor is connected to the surrounding concrete to ensure the flow of forces and stress during an interaction between the concrete, anchor, and reinforcements. The connection has a specific linear shear stiffness G<sub>b</sub>, which depends on the modulus of elasticity of concrete E<sub>cm</sub> and the diameter of the anchor. More about the bond model can be found in <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">Theoretical Background</a> [2].</p>\n<figure data-asset-id=\"b6ba5280-0fed-4b32-a52b-7e3fdc634fb3\" data-image-id=\"b6ba5280-0fed-4b32-a52b-7e3fdc634fb3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f22d2a3-3f60-40ee-b28d-24bd2439a719/03.png\" data-asset-id=\"b6ba5280-0fed-4b32-a52b-7e3fdc634fb3\" data-image-id=\"b6ba5280-0fed-4b32-a52b-7e3fdc634fb3\" alt=\"\"></figure>\n<p><em>4) Bond model and MPC</em></p>\n<h2>Design standards</h2>\n<h3>CEB-FIB mode code 2020</h3>\n<p>The engineers have the support in the code and valid standards. This statement evokes the impulse to compare the experimental solution with code - solutions to verify the safety of current standards and codes. The concrete properties C40/50 have been taken from code properties. Material properties for reinforcement bars and anchors were experimentally tested and the data were provided. We have verified the solution for unconfined concrete and the subcategory of good/other bond conditions. The CEB-FIB mode code [3] provides a clear definition of how the bond works. The inputs have been used for numerical simulation of anchor in ABAQUS [4]. </p>\n<figure data-asset-id=\"1f47192f-5327-435a-8873-2996db5cd28e\" data-image-id=\"1f47192f-5327-435a-8873-2996db5cd28e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ceffed56-48bf-4482-81b0-c17fd1ed0a14/05.png\" data-asset-id=\"1f47192f-5327-435a-8873-2996db5cd28e\" data-image-id=\"1f47192f-5327-435a-8873-2996db5cd28e\" alt=\"\"></figure>\n<p><em>4) CEB-FIB mode code 2020 - Bond model</em></p>\n<h3>Eurocode 1992-1-1</h3>\n<p>The Eurocode 1992-1-1 [5] assumption has been used as a prerequisite for <a data-item-id=\"66c6fbb8-b380-43c7-8b4f-9d41d29a42f2\" href=\"\">3D CSFM</a>. The rigidly-plastic model with a characteristic and experimental calculated bond model has been used for simulation and comparison with an experimental solution. </p>\n<figure data-asset-id=\"a3897e35-b1b0-4544-9dff-c9686c6380f3\" data-image-id=\"a3897e35-b1b0-4544-9dff-c9686c6380f3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e19364e8-9cdf-44a0-902f-f9c8fd581f01/06.png\" data-asset-id=\"a3897e35-b1b0-4544-9dff-c9686c6380f3\" data-image-id=\"a3897e35-b1b0-4544-9dff-c9686c6380f3\" alt=\"\"></figure>\n<p><em>5) Eurocode 1992-1-1 and 3D CSFM - Bond model</em></p>\n<h2>Eurocode 1992-4</h2>\n<p>The characteristic values have also been compared with Eurocode 1992-4 [6], which is implemented in <a data-item-id=\"13cc5bee-7ec7-422b-8dbe-8a57ef0073a9\" href=\"\">IDEA StatiCa Connection</a>. This provides insight into how the reinforcement in the concrete block affects the local behavior of the anchor. It allows checking for effects such as anchor failure in tension and concrete cone breakout.</p>\n<figure data-asset-id=\"1ca88ae5-0164-42fe-a362-d5b86d385bc7\" data-image-id=\"1ca88ae5-0164-42fe-a362-d5b86d385bc7\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/56e0ddb4-bec2-4b4d-a27f-1f99e44effcc/07.png\" data-asset-id=\"1ca88ae5-0164-42fe-a362-d5b86d385bc7\" data-image-id=\"1ca88ae5-0164-42fe-a362-d5b86d385bc7\" alt=\"\"></figure>\n<p><em>6) a) Rod failure in tension; b) Concrete cone breakout</em></p>\n<h2>ABAQUS - Concrete Damage Plasticity</h2>\n<h3>Assumptions</h3>\n<p><a href=\"https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt05ch18s05abm36.html\">Concrete Damage Plasticity</a> (hereafter CDP) is based on the Drucker-Prager plasticity condition [7]. This model is suitable for materials with internal friction, such as soils or concrete. The tensile strength is significantly lower than the compressive strength and the hydrostatic part of the stress tensor plays a role in the evolution of the plasticity surface. Under general stress, the plasticity condition has the surface of a rotating cone. The material model for compressive and tensile stresses also considers post-critical behavior, which is controlled by the so-called damage parameters, taking values from zero (undamaged) to one (for near-zero stiffness of concrete in compression or tension in the post-critical condition). The larger the damage parameter number, the more the element is violated and does not contribute to the stiffness contribution.</p>\n<h3>Material models</h3>\n<p>The uniaxial material model in compression and tension for concrete is based on Thorenfeldt's theory [8]. All inputs are characteristic values that follow the reliability approach of EN 1992-1-1 [5]. The parameters for material model of reinforcement and anchor are taken from chapter \" Experimental description,\" with linear hardening considered in the plastic branch of the diagram. </p>\n<h3>FEA elements</h3>\n<p>The C3D8, or hexa-element with a linear basis function and eight integration points, was used for the FEM model of concrete. The concrete and reinforcement comprise T3D2 elements that transmit only axial effects. The interaction between the reinforcement and the concrete is provided by MPC constraints on which tension-stiffening is taken into account, which covers, to some extent, the cohesion model or dowel effect. </p>\n<h3>Model assembly</h3>\n<p>The FEA model is designed with symmetry boundary conditions to minimize computation costs and improve the efficiency and speed of the solution. It's important to note that due to the reduced model, the forces on the anchor will reach one-quarter of the maximum force. The mesh has been uniformly distributed using a bias ratio, which consistently decreases the mesh size of the concrete towards the anchor location. The mesh size for concrete is in range ( 5 - 100 mm). Local mesh seeding helps with a gradient of the stresses close to the anchor and more precise results. </p>\n<figure data-asset-id=\"3d926b31-f8fb-48e2-8d4c-bcab1bf67247\" data-image-id=\"3d926b31-f8fb-48e2-8d4c-bcab1bf67247\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fb507258-c29b-4abc-bd7c-965939bfcdfe/08.png\" data-asset-id=\"3d926b31-f8fb-48e2-8d4c-bcab1bf67247\" data-image-id=\"3d926b31-f8fb-48e2-8d4c-bcab1bf67247\" alt=\"\"></figure>\n<p><em>7) Model assembly</em></p>\n<h3>Anchor</h3>\n<p>The anchor is modeled using 3D volume elements. Contact cohesive behavior has been used to model the bond between the concrete and the anchor. The surface interaction enables delamination based on the linear elastic traction-separation law before damage occurs. Hard contact has been used in compression and frictionless behavior in tangential movements. Cohesive behavior in the normal and shear directions has been introduced using volumetric stiffness and damage parameters to represent post-critical behavior. The initiation of post-critical behavior is expressed by maximal bond stress in the normal and shear directions and fracture energy with linear or exponential softening [7].</p>\n<figure data-asset-id=\"0b558401-e4df-4f40-ae5c-6d513d69147f\" data-image-id=\"0b558401-e4df-4f40-ae5c-6d513d69147f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8c810bb1-8a44-4b29-88f8-d9533f343f91/09.png\" data-asset-id=\"0b558401-e4df-4f40-ae5c-6d513d69147f\" data-image-id=\"0b558401-e4df-4f40-ae5c-6d513d69147f\" alt=\"\"></figure>\n<p><em>8) Cohesive contact</em></p>\n<h2>Results - Anchor 100 mm</h2>\n<figure data-asset-id=\"828d1e8e-4740-4e18-bb98-fdf01857a3ff\" data-image-id=\"828d1e8e-4740-4e18-bb98-fdf01857a3ff\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/804d7639-a2a4-47f2-b8b0-6d2cc5999848/10.png\" data-asset-id=\"828d1e8e-4740-4e18-bb98-fdf01857a3ff\" data-image-id=\"828d1e8e-4740-4e18-bb98-fdf01857a3ff\" alt=\"\"></figure>\n<figure data-asset-id=\"7e0dfe68-6858-45fe-ac04-54464cbd773a\" data-image-id=\"7e0dfe68-6858-45fe-ac04-54464cbd773a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/61567b62-8af3-439c-b8b1-4a20da9bd210/11.png\" data-asset-id=\"7e0dfe68-6858-45fe-ac04-54464cbd773a\" data-image-id=\"7e0dfe68-6858-45fe-ac04-54464cbd773a\" alt=\"\"></figure>\n<p><em>9) Input-output necessary properties for simulation</em></p>\n<figure data-asset-id=\"2dd133bb-b4b6-4526-9272-23b2c129482e\" data-image-id=\"2dd133bb-b4b6-4526-9272-23b2c129482e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/cec61f81-adfb-4c88-bc1e-99e1099f4ede/12.png\" data-asset-id=\"2dd133bb-b4b6-4526-9272-23b2c129482e\" data-image-id=\"2dd133bb-b4b6-4526-9272-23b2c129482e\" alt=\"\"></figure>\n<p><em>10) Maximal force and utilization versus experiment for anchor 100 mm</em></p>\n<figure data-asset-id=\"abe57714-1c00-4e47-8646-0a53f6754ac9\" data-image-id=\"abe57714-1c00-4e47-8646-0a53f6754ac9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bd9635c8-63d2-42c8-8d6b-348378f45c67/13.png\" data-asset-id=\"abe57714-1c00-4e47-8646-0a53f6754ac9\" data-image-id=\"abe57714-1c00-4e47-8646-0a53f6754ac9\" alt=\"\"></figure>\n<p><em>11) Load deformation curve - T103-100 experimental data comparison </em></p>\n<figure data-asset-id=\"fecc0f84-15ac-4fda-a636-36dcee62a119\" data-image-id=\"fecc0f84-15ac-4fda-a636-36dcee62a119\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f0d8648d-88fc-4b5f-94ab-eba6ce276ed1/14.png\" data-asset-id=\"fecc0f84-15ac-4fda-a636-36dcee62a119\" data-image-id=\"fecc0f84-15ac-4fda-a636-36dcee62a119\" alt=\"\"></figure>\n<p><em>12) Load deformation curve - T103-100 characteristic code data comparison </em></p>\n<h2>Results - Anchor 150 mm</h2>\n<figure data-asset-id=\"1d43f39e-a9b6-4a62-be20-ee13e042889f\" data-image-id=\"1d43f39e-a9b6-4a62-be20-ee13e042889f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b52615a4-f2bf-4f06-9753-8a8269cc93d6/15.png\" data-asset-id=\"1d43f39e-a9b6-4a62-be20-ee13e042889f\" data-image-id=\"1d43f39e-a9b6-4a62-be20-ee13e042889f\" alt=\"\"></figure>\n<figure data-asset-id=\"6a703bf5-af1a-4928-a9f0-83ee5f150b9a\" data-image-id=\"6a703bf5-af1a-4928-a9f0-83ee5f150b9a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dd13fb04-aec5-485e-bca7-c6314e2742df/16.png\" data-asset-id=\"6a703bf5-af1a-4928-a9f0-83ee5f150b9a\" data-image-id=\"6a703bf5-af1a-4928-a9f0-83ee5f150b9a\" alt=\"\"></figure>\n<p><em>12) Input-output necessary properties for simulation</em></p>\n<figure data-asset-id=\"6309453d-90ab-4fde-ab4e-74043aae65e3\" data-image-id=\"6309453d-90ab-4fde-ab4e-74043aae65e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d8e058ce-8c24-49f9-8871-73534be84f69/17.png\" data-asset-id=\"6309453d-90ab-4fde-ab4e-74043aae65e3\" data-image-id=\"6309453d-90ab-4fde-ab4e-74043aae65e3\" alt=\"\"></figure>\n<p><em>13) Maximal force and utilization versus experiment for anchor 150 mm</em></p>\n<figure data-asset-id=\"5982b418-f72e-4f17-8cad-e10910d747ff\" data-image-id=\"5982b418-f72e-4f17-8cad-e10910d747ff\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7da761ce-c9a4-4134-b706-8360175152b6/18.png\" data-asset-id=\"5982b418-f72e-4f17-8cad-e10910d747ff\" data-image-id=\"5982b418-f72e-4f17-8cad-e10910d747ff\" alt=\"\"></figure>\n<p><em>14) Load deformation curve - T103-150 experimental data comparison </em></p>\n<figure data-asset-id=\"785db38d-6970-443c-ae65-c4f0b661be8c\" data-image-id=\"785db38d-6970-443c-ae65-c4f0b661be8c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3812fab2-6857-4a01-9a22-a735de4a447f/19.png\" data-asset-id=\"785db38d-6970-443c-ae65-c4f0b661be8c\" data-image-id=\"785db38d-6970-443c-ae65-c4f0b661be8c\" alt=\"\"></figure>\n<p><em>15) Load deformation curve - T103-100 characteristic code data comparison </em></p>\n<h2>Results - Anchor 200 mm</h2>\n<figure data-asset-id=\"03a951bf-d440-4a99-a796-3def5f476464\" data-image-id=\"03a951bf-d440-4a99-a796-3def5f476464\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/b31adf4a-cd86-4e05-bf27-bdb4eabf3e9d/20.png\" data-asset-id=\"03a951bf-d440-4a99-a796-3def5f476464\" data-image-id=\"03a951bf-d440-4a99-a796-3def5f476464\" alt=\"\"></figure>\n<figure data-asset-id=\"1eea570b-29c7-419d-92ce-b8d4d4a55e96\" data-image-id=\"1eea570b-29c7-419d-92ce-b8d4d4a55e96\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/345ce74d-6b1f-4caa-95c8-8e3805edddec/21.png\" data-asset-id=\"1eea570b-29c7-419d-92ce-b8d4d4a55e96\" data-image-id=\"1eea570b-29c7-419d-92ce-b8d4d4a55e96\" alt=\"\"></figure>\n<p><em>16) Input-output necessary properties for simulation</em></p>\n<figure data-asset-id=\"697d30eb-617b-4c05-b073-4201449f779a\" data-image-id=\"697d30eb-617b-4c05-b073-4201449f779a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/0fbdeb33-1c2b-48f9-a3d7-cdb7d77557e4/22.png\" data-asset-id=\"697d30eb-617b-4c05-b073-4201449f779a\" data-image-id=\"697d30eb-617b-4c05-b073-4201449f779a\" alt=\"\"></figure>\n<p><em>17) Maximal force and utilization versus experiment for anchor 200 mm</em></p>\n<figure data-asset-id=\"67aac596-644e-44f2-8bb5-9ca0994a2590\" data-image-id=\"67aac596-644e-44f2-8bb5-9ca0994a2590\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8a3f8fee-48f7-47aa-9a14-d54adfbafafb/23.png\" data-asset-id=\"67aac596-644e-44f2-8bb5-9ca0994a2590\" data-image-id=\"67aac596-644e-44f2-8bb5-9ca0994a2590\" alt=\"\"></figure>\n<p><em>18) Load deformation curve - T103-200 experimental data comparison </em></p>\n<figure data-asset-id=\"f80e5468-2277-4cb7-9641-8c172fc10185\" data-image-id=\"f80e5468-2277-4cb7-9641-8c172fc10185\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a7380fbf-4d0a-4a3a-815f-2adf2e2ba902/24.png\" data-asset-id=\"f80e5468-2277-4cb7-9641-8c172fc10185\" data-image-id=\"f80e5468-2277-4cb7-9641-8c172fc10185\" alt=\"\"></figure>\n<p><em>19) Load deformation curve - T103-200 characteristic code data comparison </em></p>\n<h2>Conclusion</h2>\n<p>The experimental campaign successfully investigated the behavior of full-size anchors bonded in a reinforced concrete block, using a comprehensive approach that integrated both experimental testing and numerical modeling. By varying the embedment depths of the anchors (100, 150, 200 mm), the study was able to observe different failure modes, including bond failure, concrete cone breakout, and rod failure. The results were rigorously compared with predictions from the CEB-FIB model code and Eurocodes, validating the safety and reliability of current design standards for such anchorage systems.</p>\n<p>The use of advanced modeling techniques, such as 3D CSFM and ABAQUS simulations with Concrete Damage Plasticity, provided deeper insights into the interaction between the concrete and reinforcement, as well as the bond behavior under quasi-static tensile loading. The findings confirmed the effectiveness of the proposed methods in predicting anchor performance, emphasizing the importance of accurate material modeling and appropriate boundary conditions in such simulations.</p>\n<p>The comparison between the actual behavior observed during the experiment and the numerical solution derived using 3D CSFM and ABAQUS shows an approximate 85% correlation. It can be concluded that no numerical solution exceeds the experimental data and maintains a 15% margin of error compared to the experiment, which is considered acceptable from an engineering perspective. The important aspect is also the failure modes which are fitting, except for the anchor length of 200 mm where in 3D CSFM, a combined mode of concrete cone and pull-out occurred before the steel rod failure. This is because, in this case, the peak loads corresponding to these two failure modes are very close.</p>\n<p>The results obtained from CEB-FIB mode code 2020 and Eurocode 1992-1-1 match the experimental results within the range of 30-40%. This indicates that the approach used in the code ensures safety. It's important to note that the values obtained are characteristic values, not design values, so the actual design strength is even lower.</p>\n<p><strong>The findings of the report should convey to the engineers that the 3D CSFM method yields safe outcomes in compliance with Eurocode 1992-1-1[5], and results in a conservative design that is integrated within the code itself.</strong></p>\n<p>Overall, this study contributes valuable data for improving anchorage design practices, offering evidence that can be used to refine existing codes and ensure that safety margins are adequately maintained in real-world applications. The experimental results, combined with theoretical and numerical analyses, provide a robust framework for understanding the complex interactions in anchored systems, ultimately leading to safe and efficient structural designs.</p>\n<h3>References</h3>\n<p>[1]Delhomme, F. & Roure, Thierry & Arrieta, Benjamin & Limam, Ali. (2015). Pullout behavior of cast-in-place headed and bonded anchors with different embedment depths. Materials and Structures. 49. 10.1617/s11527-015-0616-4. </p>\n<p>[2] \"IDEA StatiCa Detail – Structural Design of Concrete 3D Discontinuities (BETA).\" <em>IDEA StatiCa Support Center</em>, 2023. <a href=\"https://www.ideastatica.com/support-center/idea-statica-detail-structural-design-of-concrete-3d-discontinuities-beta\">https://www.ideastatica.com/support-center/idea-statica-detail-structural-design-of-concrete-3d-discontinuities-beta</a></p>\n<p>[3]<strong>International Federation for Structural Concrete (fib).</strong> <em>fib Model Code 2020 for Concrete Structures</em>. Berlin: Ernst & Sohn, 2021.</p>\n<p>[4] ABAQUS Standard User's Manual, Version 6.6*. Washington University in St. Louis, 2006. [<a href=\"https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm](https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm).\">https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm]</a></p>\n<p>[5] <strong>European Committee for Standardization (CEN).</strong> <em>EN 1992-1-1:2004: Eurocode 2 – Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings</em>. December 2004. <a href=\"https://www.phd.eng.br/wp-content/uploads/2015/12/en.1992.1.1.2004.pdf\">https://www.phd.eng.br/wp-content/uploads/2015/12/en.1992.1.1.2004.pdf</a>.</p>\n<p>[6] <strong>European Committee for Standardization (CEN).</strong> <em>EN 1992-4:2018: Eurocode 2 – Design of Concrete Structures – Part 4: Design of Fastenings for Use in Concrete</em>. Brussels: CEN, April 2018</p>\n<p>[7]<strong>ABAQUS, Inc.</strong> <em>ABAQUS User Subroutines Reference Manual, Version 6.6</em>. Washington University in St. Louis, 2006. <a href=\"https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt05ch18s05abm36.html\">https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt05ch18s05abm36.html</a>.</p>\n<p>[8] Massone, L. M.; et al. Shear-Flexure Interaction for Structural Walls, 2006. ResearchGate. <a href=\"https://www.researchgate.net/publication/284079633_Shear-flexure_interaction_for_structural_walls\">https://www.researchgate.net/publication/284079633_Shear-flexure_interaction_for_structural_walls</a> (accessed Jan 01, 2006).</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2a28a4d6_9d45_0195_3fa3_bf8595bc294b\"></object>"
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}Known limitations
Since Detail is just a tool and cannot replace engineering judgment, a safe understanding of its functions, benefits, and limitations is necessary. Read the following limitations, which must be taken into account:
- In Detail, the anchors are only checked for tensile strength. It is necessary to use Connection for shear and interaction checks.
- Only models anchored via the base plate and only Direct contact can be imported to Detail (from Connection).
For a full list of limitations with further explanation, see the article: Known limitations for 3D Detail
Released in IDEA StatiCa version 24.1
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