Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.
Ultimate limit state analysis
The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).
To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:
- Choose a selection of the most critical load combinations.
- Calculate only Ultimate Limit State (ULS) load combinations.
- Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).
\[ \textsf{\textit{\footnotesize{Fig. 19\qquad Mesh multiplier.}}}\]
Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).
The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.
Serviceability limit state analysis
SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.
The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.
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"description": "Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.",
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"value": "<h4>Crack width calculation</h4>\n<p>There are two ways of computing crack widths - stabilized and non-stabilized cracking. According to the geometrical reinforcement ratio in each part of the structure is decided, which type of crack calculation model will be used (TCM for stabilized cracking and POM for non-stabilized cracking model).</p>\n<figure data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/62ba3929-8689-4973-8782-fcdd0780002b/Crack%20width%20calculation.PNG\" data-asset-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" data-image-id=\"4a11f2de-770f-43aa-840a-4c41d9c2abf9\" alt=\"Fig. 24\tCrack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar for non-stabilized cracking.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 20 \\qquad Crack width calculation: (a) considered crack kinematics; (b) projection of crack kinematics into the principal}}}\\) \\( \\textsf{\\textit{\\footnotesize{directions of the reinforcing bar; (c) crack width in the direction of the reinforcing bar for stabilized cracking; (d) cases with}}}\\) \\( \\textsf{\\textit{\\footnotesize{local non-stabilized cracking regardless of the reinforcement amount; (e) crack width in the direction of the reinforcing bar}}}\\)\\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking.}}}\\)</em></p>\n<p><br></p>\n<p>While the CSFM yields a direct result for most verifications (e.g., member capacity, deflections…), crack width results are calculated from the reinforcement strain results directly provided by FE analysis following the methodology described in Fig. 20. A crack kinematic without slip (pure crack opening) is considered (Fig. 20a), which is consistent with the main assumptions of the model. The principal directions of stresses and strains define the inclination of the cracks (θ<em><sub>r</sub></em> = θ<sub>s</sub>= θ<sub>e</sub>). According to (Fig. 20b), the crack width (<em>w</em>) can be projected in the direction of the reinforcing bar (<em>w</em><em><sub>b</sub></em>), leading to:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(θ_r + θ_b - \\frac{π}{2}\\right)}\\]</p>\n<p>where θ<em><sub>b</sub></em> is the bar inclination.</p>\n<p>Please note, that the program displays values of θ<em><sub>r</sub></em> and θ<em><sub>b</sub></em> < <em>π/2</em>. It means that the previous equation works for cases, where the reinforcement and crack go through the different quadrants of the Cartesian coordinate system as shown in Fig. 20, where reinforcement goes through I. and III. quadrants and crack through II and IV. For cases where the reinforcement and crack go through the same quadrants, the equation has to be modified as follows:</p>\n<p>\\[w = \\frac{w_b}{\\cos\\left(-θ_r + θ_b + \\frac{π}{2}\\right)}\\]</p>\n<p>The component <em>w</em><em><sub>b</sub></em> is consistently calculated based on the tension stiffening models by integrating the reinforcement strains. For those regions with fully developed crack patterns, the calculated average strains (e<em><sub>m</sub></em>) along the reinforcing bars are directly integrated along the crack spacing (<em>s</em><em><sub>r</sub></em>), as indicated in (Fig. 20c). While this approach to calculating the crack directions does not correspond to the real position of the cracks, it still provides representative values that lead to crack width results that can be compared to code-required crack width values at the position of the reinforcing bar.</p>\n<p>Special situations are observed at concave corners of the calculated structure. In this case, the corner predefines the position of a single crack that behaves in a non-stabilized fashion before additional adjacent cracks develop. These additional cracks generally develop after the serviceability range (Mata-Falcón 2015), which justifies calculating the crack widths in such a region as if they were non-stabilized (Fig. 21).</p>\n<figure data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5a46a740-1622-47eb-b7f3-186fee0f6fbc/Concave%20corner.png\" data-asset-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" data-image-id=\"cb811a73-9dfe-4b06-8a93-34019678e846\" alt=\"Fig. 25\tDefinition of the region at concave corners in which the crack width is computed as if it were non-stabilized.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 21\\qquad Definition of the region at concave corners in which the crack width is computed as if it were non-stabilized.}}}\\]</em></p>\n<h4>Tension stiffening</h4>\n<p>The implementation of tension stiffening distinguishes between cases of stabilized and non-stabilized crack patterns. In both cases, the concrete is considered fully cracked before loading by default.</p>\n<figure data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/80e8fffe-3c98-4677-af35-7c2ce025e0bb/Tension%20stiffening%20model.PNG\" data-asset-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" data-image-id=\"bcb3e177-6a83-42bd-a51a-7294e4a7d6e8\" alt=\"Fig. 3\tTension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear, steel and concrete stresses, and steel strains between cracks, considering average crack spacing (λ=0.67); (b) pull-out assumption for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel; (d) detail of the initial branches of the tension chord response.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 22\\qquad Tension stiffening model: (a) tension chord element for stabilized cracking with distribution of bond shear,}}}\\) </em>\\( \\textsf{\\textit{\\footnotesize{steel and concrete stresses, and steel strains between cracks, considering average crack spacing); (b) pull-out assumption}}}\\) \\( \\textsf{\\textit{\\footnotesize{for non-stabilized cracking with distribution of bond shear and steel stresses and strains around the crack; (c) resulting}}}\\) \\( \\textsf{\\textit{\\footnotesize{tension chord behavior in terms of reinforcement stresses at the cracks and average strains for European B500B steel;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) detail of the initial branches of the tension chord response.}}}\\)</p>\n<p><br></p>\n<p><strong>Stabilized cracking</strong></p>\n<p>In fully developed crack patterns, tension stiffening is introduced using the Tension Chord Model (TCM) (Marti et al. 1998; Alvarez 1998) – Fig. 22a – which has been shown to yield excellent response predictions in spite of its simplicity (Burns 2012). The TCM assumes a stepped, rigid-perfectly plastic bond shear stress-slip relationship with τ<em><sub>b </sub></em>= τ<em><sub>b</sub></em><sub>0</sub> =2 <em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s</sub></em> ≤ <em>f</em><em><sub>y</sub></em> and τ<em><sub>b</sub></em> =τ<em><sub>b</sub></em><sub>1</sub> = <em>f</em><em><sub>ctm</sub></em> for σ<em><sub>s </sub></em>> <em>f</em><em><sub>y</sub></em>. Treating every reinforcing bar as a tension chord – Fig. 22b and Fig. 22a – the distribution of bond shear, steel, and concrete stresses and hence the strain distribution between two cracks can be determined for any given value of the maximum steel stresses (or strains) at the cracks.</p>\n<p>For <em>s</em><em><sub>r</sub></em> = <em>s</em><em><sub>r</sub></em><sub>0</sub>, a new crack may or may not form because at the center between two cracks σ<em><sub>c</sub></em><sub>1</sub> = <em>f</em><em><sub>ct</sub></em>. Consequently, the crack spacing may vary by a factor of two, i.e., <em>s</em><em><sub>r</sub></em> = λ<em>s</em><em><sub>r</sub></em><sub>0</sub>, with l = 0.5…1.0. Assuming a certain value for λ, the average strain of the chord (ε<em><sub>m</sub></em>) can be expressed as a function of the maximum reinforcement stresses (i.e., stresses at the cracks, σ<em><sub>sr</sub></em>). For the idealized bilinear stress-strain diagram for the reinforcing bare bars considered by default in the CSFM, the following closed-form analytical expressions are obtained (Marti et al. 1998):</p>\n<p>\\[\\varepsilon_m = \\frac{\\sigma_{sr}}{E_s} - \\frac{\\tau_{b0}s_r}{E_s Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\sigma_{sr} \\le f_y\\]</p>\n<p><br></p>\n<p>\\[{\\varepsilon_m} = \\frac{{{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}^2}Ø}}{{4{E_{sh}}{\\tau _{b1}}{s_r}}}\\left( {1 - \\frac{{{E_{sh}}{\\tau_{b0}}}}{{{E_s}{\\tau_{b1}}}}} \\right) + \\frac{{\\left( {{\\sigma_{sr}} - {f_y}} \\right)}}{{{E_s}}}\\frac{{{\\tau_{b0}}}}{{{\\tau_{b1}}}} + \\left( {{\\varepsilon_y} - \\frac{{{\\tau_{b0}}{s_r}}}{{{E_s}Ø}}} \\right)\\]</p>\n<p><em>\\[\\textrm{for}\\qquad\\qquad{f_y} \\le {\\sigma _{sr}} \\le \\left( {{f_y} + \\frac{{2{\\tau _{b1}}{s_r}}}{Ø}} \\right)\\]</em></p>\n<p><br></p>\n<p>\\[ \\varepsilon_m = \\frac{f_s}{E_s} + \\frac{\\sigma_{sr}-f_y}{E_{sh}} - \\frac{\\tau_{b1} s_r}{E_{sh} Ø}\\]</p>\n<p>\\[\\textrm{for}\\qquad\\qquad\\left(f_y + \\frac{2\\tau_{b1}s_r}{Ø}\\right) \\le \\sigma_{sr} \\le f_t\\]</p>\n<p>where:<br>\n <em>E</em><em><sub>sh</sub></em> the steel hardening modulus <em>E</em><em><sub>sh</sub></em> = (<em>f</em><em><sub>t</sub></em> – <em>f</em><em><sub>y</sub></em>)/(ε<em><sub>u</sub></em> – <em>f</em><em><sub>y</sub></em> /<em>E</em><em><sub>s</sub></em>) ,</p>\n<p><em>E</em><em><sub>s</sub></em> modulus of elasticity of reinforcement,</p>\n<p><em>Ø</em> reinforcing bar diameter,</p>\n<p>s<em><sub>r</sub></em><em><sup> </sup></em>crack spacing,</p>\n<p>σ<em><sub>sr</sub></em><em> </em>reinforcement stresses at the cracks,</p>\n<p>σ<em><sub>s</sub></em><em> </em>actual reinforcement stresses,</p>\n<p><em>f</em><em><sub>y </sub></em>yield strength of reinforcement.</p>\n<p><br></p>\n<p>The Idea StatiCa Detail implementation of the CSFM considers average crack spacing by default when performing computer-aided stress field analysis. The average crack spacing is considered to be 2/3 of the maximum crack spacing (λ = 0.67), which follows recommendations made on the basis of bending and tension tests (Broms 1965; Beeby 1979; Meier 1983). It should be noted that calculations of crack widths consider a maximum crack spacing (λ = 1.0) in order to obtain conservative values.</p>\n<p>The application of the TCM depends on the reinforcement ratio, and hence the assignment of an appropriate concrete area acting in tension between the cracks to each reinforcing bar is crucial. An automatic numerical procedure has been developed to define the corresponding effective reinforcement ratio (ρ<em><sub>eff</sub></em><em> = A</em><em><sub>s</sub></em><em>/A</em><em><sub>c,eff</sub></em>) for any configuration, including skewed reinforcement (Fig. 23).</p>\n<figure data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2c0d58ae-1639-4b2a-a99c-a5e274a318ac/Effective%20area%20of%20concrete.png\" data-asset-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" data-image-id=\"7a370722-a56b-438d-8cf3-21d62a938811\" alt=\"Fig. 4\tEffective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated; (b) cover and global symmetry condition; (c) resultant effective area.\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 23\\qquad Effective area of concrete in tension for stabilized cracking: (a) maximum concrete area that can be activated;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(b) cover and global symmetry condition; (c) resultant effective area.}}}\\)</em></p>\n<p><br></p>\n<p><strong>Non-stabilized cracking</strong></p>\n<p>Cracks existing in regions with geometric reinforcement ratios lower than ρ<em><sub>cr</sub></em>, i.e., the minimum reinforcement amount for which the reinforcement is able to carry the cracking load without yielding, are generated by either non-mechanical actions (e.g. shrinkage) or the progression of cracks controlled by other reinforcement. The value of this minimum reinforcement is obtained as follows:</p>\n<p>\\[{\\rho _{cr}} = \\frac{{{f_{ct}}}}{{{f_y} - \\left( {n - 1} \\right){f_{ct}}}}\\]</p>\n<p>where:</p>\n<p><em>f</em><em><sub>y</sub></em> reinforcement yield strength,</p>\n<p><em>f</em><em><sub>ct</sub></em> concrete tensile strength,</p>\n<p><em>n</em> modular ratio, <em>n</em> = <em>E</em><em><sub>s</sub></em> / <em>E</em><em><sub>c</sub></em> .</p>\n<p>For conventional concrete and reinforcing steel, ρ<em><sub>cr</sub></em> amounts to approximately 0.6%.</p>\n<p>For stirrups with reinforcement ratios below ρ<em><sub>cr</sub></em>, cracking is considered to be non-stabilized and tension stiffening is implemented by means of the Pull-Out Model (POM) described in Fig. 22b. This model analyzes the behavior of a single crack considering no mechanical interaction between separate cracks, neglecting the deformability of concrete in tension and assuming the same stepped, rigid-perfectly plastic bond shear stress-slip relationship used by the TCM. This allows the reinforcement strain distribution (ε<em><sub>s</sub></em>) in the vicinity of the crack to be obtained for any maximum steel stress at the crack (σ<em><sub>sr</sub></em>) directly from equilibrium. Given the fact that the crack spacing is unknown for a non-fully developed crack pattern, the average strain (ε<em><sub>m</sub></em>) is computed for any load level over the distance between points with zero slip when the reinforcing bar reaches its tensile strength (<em>f</em><em><sub>t</sub></em>) at the crack (<em>l</em><sub>ε,</sub><em><sub>avg</sub></em> in Fig. 22b), leading to the following relationships:</p>\n<figure data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/43adc17b-b9e9-4a81-ab9f-ff4c13297b34/Equation%201.2.4.2.PNG\" data-asset-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" data-image-id=\"cd3ad82c-e048-4baa-abd9-c0957e0a7f4b\" alt=\"\"></figure>\n<p>The proposed models allow the computation of the behavior of bonded reinforcement, which is finally considered in the analysis. This behavior (including tension stiffening) for the most common European reinforcing steel (B500B, with <em>f</em><em><sub>t</sub></em> / <em>f</em><em><sub>y</sub></em> = 1.08 and ε<em><sub>u</sub></em> = 5%) is illustrated in Fig. 22c-d.</p>"
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"value": "<p>The CSFM considers continuous stress fields in the concrete (2D finite elements), complemented by discrete “rod” elements representing the reinforcement (1D finite elements). Therefore, the reinforcement is not diffusely embedded into the concrete 2D finite elements but explicitly modeled and connected to them. A plane stress state is considered in the calculation model.</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"Fig. 8\t Visualization of the calculation model of a structural element (trimmed beam) in Idea StatiCa Detail.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 6\\qquad Visualization of the calculation model of a structural element (trimmed beam) in Idea StatiCa Detail.}}}\\]</em></p>\n<p>Both entire <a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">walls</a> and beams, as well as details (parts) of beams (isolated discontinuity region, also called trimmed end), can be modeled. In the case of walls and entire beams, supports must be defined in such a way that an (externally) isostatic (statically determinate) or hyperstatic (statically indeterminate) structure results. The load transfer at the trimmed ends of beams is introduced by means of a special Saint-Venant transfer zone, which ensures a realistic stress distribution in the analyzed detail region.</p>"
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"value": "<h3>Workflow and goals</h3>\n<p>The goal of reinforcement design tools in the <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">CSFM</a> is to help designers determine the location and required amount of reinforcing bars efficiently. The following tools are available to help/ guide the user in this process: linear calculation and <a data-item-id=\"decdf07d-a46b-5894-9a22-793436e318c7\" href=\"\">topology optimization</a>.</p>\n<p>Reinforcement design tools consider more simplified constitutive models than the models used for the final verification of the structure. Therefore, the definition of the reinforcement in this step should be considered a pre-design to be confirmed/refined during the final verification step. The use of the different reinforcement design tools will be depicted in the model shown in Fig. 5, which consists of one end of a simply supported beam with variable depth subjected to a uniformly distributed load.</p>\n<figure data-asset-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" data-image-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9b0c4840-5a55-46f3-95ba-86a9baabbf0c/Model%20used%20to%20illustrate%20the%20use%20of%20the%20reinforcement%20design%20tools.png\" data-asset-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" data-image-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 5\\qquad Model used to illustrate the use of the reinforcement design tools.}}}\\]</em></p>\n<h3>Linear analysis</h3>\n<p>The linear analysis considers linear elastic material properties and neglects reinforcement in the concrete region. It is, therefore, a very fast calculation that provides a first insight into the locations of tension and compression areas. An example of such a calculation is shown in Fig. 6.</p>\n<figure data-asset-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" data-image-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ea7896d1-8276-4d08-b811-066cca73b455/Results%20from%20the%20linear%20analysis%20tool.jpg\" data-asset-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" data-image-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 6\\qquad Results from the linear analysis tool for defining reinforcement layout}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(red: areas in compression, blue: areas in tension).}}}\\]</em></p>\n<h3>Topology optimization</h3>\n<p>Topology optimization is a method that aims to find the optimal distribution of material in a given volume for a certain load configuration. The topology optimization implemented in <em>Idea StatiCa Detail</em> uses a linear finite element model. Each finite element may have a relative density from 0 to 100 %, representing the relative amount of material used. These element densities are the optimization parameters in the optimization problem. The resulting material distribution is considered optimal for the given set of loads if it minimizes the total strain energy of the system. By definition, the optimal distribution is also the geometry that has the largest possible stiffness for the given loads.</p>\n<p>The iterative optimization process starts with a homogeneous density distribution.<em> </em>The calculation is performed for multiple total volume fractions (20%, 40%, 60%, and 80%), which allows the user to select the most practical result. The resulting shape consists of trusses with struts and ties and represents the optimum shape for the given load cases (Fig. 7).</p>\n<figure data-asset-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" data-image-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f4d37064-76c7-4413-b1aa-87455a32852c/Results%20from%20the%20topology%20optimization%201.jpg\" data-asset-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" data-image-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" alt=\"\"></figure>\n<figure data-asset-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" data-image-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d81f2841-8274-414a-8f30-b55427216169/Results%20from%20the%20topology%20optimization%202.png\" data-asset-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" data-image-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 7\\qquad Results from the topology optimization design tool with 20\\% and 40\\% effective volume}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(red: areas in compression, blue: areas in tension).}}}\\]</em></p>\n<p><br></p>"
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"value": "<p>The design and assessment of concrete elements are normally performed at the sectional (1D-element) or point (2D-element) level. This procedure is described in all standards for structural design, e.g., in (EN 1992-1-1), and it is used in everyday structural engineering practice. However, it is not always known or respected that the procedure is only acceptable in areas where the Bernoulli-Navier hypothesis of plane strain distribution applies (referred to as B-regions). The places where this hypothesis does not apply are called discontinuity or disturbed regions (D-Regions). Examples of B and D regions of 1D-elements are given in (Fig. 1). These are, e.g., bearing areas, parts where concentrated loads are applied, locations where an abrupt change in the cross-section occurs, openings, etc. When designing concrete structures, we meet a lot of other D-Regions such as walls, bridge diaphragms, corbels, etc. </p>\n<figure data-asset-id=\"874c8092-fb41-44c6-804d-52727044d470\" data-image-id=\"874c8092-fb41-44c6-804d-52727044d470\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dc96c2fd-25aa-43fd-b6d5-556b5242b9cf/Discontinuity%20regions.png\" data-asset-id=\"874c8092-fb41-44c6-804d-52727044d470\" data-image-id=\"874c8092-fb41-44c6-804d-52727044d470\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 1\\qquad Discontinuity regions (Navrátil et al. 2017)}}}\\]</em></p>\n<p>In the past, semi-empirical design rules were used for dimensioning discontinuity regions. Fortunately, these rules have been largely superseded over the past decades by strut-and-tie models (Schlaich et al., 1987) and stress fields (Marti 1985), which are featured in current design codes and frequently used by designers today. These models are mechanically consistent and powerful tools. Note that stress fields can generally be continuous or discontinuous and that strut-and-tie models are a special case of discontinuous stress fields.</p>\n<p>Despite the evolution of computational tools over the past decades, Strut-and-Tie models are essentially still used as hand calculations. Their application for real-world structures is tedious and time-consuming since iterations are required, and several load cases need to be considered. Furthermore, this method is not suitable for verifying serviceability criteria (deformations, crack widths, etc.).</p>\n<p>The interest of structural engineers in a reliable and fast tool to design D-regions led to the decision to develop the new Compatible Stress Field Method, a method for computer-aided stress field design that allows the automatic design and assessment of structural concrete members subjected to in-plane loading.</p>\n<p>The Compatible Stress Field Method is a continuous FE-based stress field analysis method in which classic stress field solutions are complemented with kinematic considerations, i.e., the state of strain is evaluated throughout the structure. Hence, the effective compressive strength of concrete can be automatically computed based on the state of transverse strain in a similar manner as in compression field analyses that account for compression softening (Vecchio and Collins 1986; Kaufmann and Marti 1998) and the EPSF method (Fernández Ruiz and Muttoni 2007). Moreover, the CSFM considers tension stiffening, providing realistic stiffnesses to the elements, and covers all design code prescriptions (including serviceability and deformation capacity aspects) not consistently addressed by previous approaches. The CSFM uses common uniaxial constitutive laws provided by design standards for concrete and reinforcement. These are known at the design stage, which allows the partial safety factor method to be used. Hence, designers do not have to provide additional, often arbitrary material properties as are typically required for non-linear FE-analyses, making the method perfectly suitable for engineering practice.</p>\n<p>To foster the use of computer-aided stress fields by structural engineers, these methods should be implemented in user-friendly software environments. To this end, the CSFM has been implemented in <em>IDEA StatiCa Detail</em>; a new user-friendly commercial software developed jointly by ETH Zurich and the software company IDEA StatiCa in the framework of the DR-Design Eurostars-10571 project.</p>"
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"value": "<p>Assessment of the structure using the CSFM is performed by two different analyses: one for serviceability and one for ultimate limit state load combinations. The serviceability analysis assumes that the ultimate behavior of the element is satisfactory, and the yield conditions of the material will not be reached at serviceability load levels. This approach enables the use of simplified constitutive models (with a linear branch of concrete stress-strain diagram) for serviceability analysis to enhance numerical stability and calculation speed. Therefore, it is recommended the use the workflow presented below, in which the ultimate limit state analysis is carried out as the first step.</p>\n<h3>Ultimate limit state analysis</h3>\n<p>The different verifications required by specific design codes are assessed based on the direct results provided by the model. ULS verifications are carried out for concrete strength, reinforcement strength, and anchorage (bond shear stresses).</p>\n<p>To ensure a structural element has an efficient design, it is highly recommended to run a preliminary analysis which takes into account the following steps:</p>\n<ul>\n <li>Choose a selection of the most critical load combinations.</li>\n <li>Calculate only Ultimate Limit State (ULS) load combinations.</li>\n <li>Use a coarse mesh (by increasing the multiplier of the default mesh size in Setup (Fig. 19)).</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"Fig. 23\tMesh multiplier.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>Such a model will calculate very quickly, allowing designers to review the detailing of the structural element efficiently and re-run the analysis until all verification requirements are fulfilled for the most critical load combinations. Once all the verification requirements of this preliminary analysis are fulfilled, it is suggested that the complete ultimate load combinations be included and the use of fine mesh size (the mesh size recommended by the program). User can change mesh size by the multiplier, which can reach values from 0.5 to 5 (Fig. 19).</p>\n<p>The basic results and verifications (stress, strain, and utilization (i.e., the calculated value/limit value from the code), as well as the direction of principal stresses in the case of concrete elements) are displayed by means of different plots where compression is generally presented in red and tension in blue. Global minimum and maximum values for the entire structure can be highlighted as well as minimum and maximum values for every user-defined part. In a separate tab of the program, advanced results such as tensor values, deformations of the structure, and reinforcement ratios (effective and geometric) used for computing the tension stiffening of reinforcing bars can be shown. Furthermore, loads and reactions for selected combinations or load cases can be presented.</p>\n<h3>Serviceability limit state analysis</h3>\n<p>SLS assessments are carried out for stress limitation, crack width, and deflection limits. Stresses are checked in concrete and reinforcement elements according to the applicable code in a similar manner to that specified for the ULS.</p>\n<p>The serviceability analysis contains certain simplifications of the constitutive models which are used for ultimate limit state analysis. A perfect bond is assumed, i.e., the anchorage length is not verified at serviceability. Furthermore, the plastic branch of the stress-strain curve of concrete in compression is disregarded, while the elastic branch is linear and infinite. These simplifications enhance the numerical stability and calculation speed, and do not reduce the generality of the solution as long as the resultant material stress limits at serviceability are clearly below their yielding points (as required by standards). Therefore, the simplified models used for serviceability are only valid if all verification requirements are fulfilled.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
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"value": "<p>The non-linear (inelastic) finite element analysis model is created by several types of finite elements used to model concrete, reinforcement, and the bond between them. Concrete and reinforcement elements are first meshed independently and then connected to each other using multi-point constraints (MPC elements). This allows the reinforcement to occupy an arbitrary, relative position in relation to the concrete. If anchorage length verification is to be calculated, bond and anchorage end spring elements are inserted between the reinforcement and the MPC elements.</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"Fig. 15\tFinite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>Concrete</h3>\n<p>Concrete is modeled using quadrilateral and trilateral shell elements, CQUAD4 and CTRIA3. These can be defined by four or three nodes, respectively. Only plane stress is assumed to exist in these elements, i.e., stresses or strains in the z-direction are not considered.</p>\n<p>Each element has four or three integration points which are placed at approximately 1/4 of its size. At each integration point in every element, the directions of principal strains α<sub>1</sub>, α<sub>2</sub> are calculated. In both of these directions, the principal stresses σ<em><sub>c</sub></em><sub>1</sub>, σ<em><sub>c</sub></em><sub>2</sub> and stiffnesses <em>E</em><sub>1</sub>, <em>E</em><sub>2</sub> are evaluated according to the specified concrete stress-strain diagram, as per Fig. 2. It should be noted that the impact of the compression softening effect couples the behavior of the main compressive direction to the actual state of the other principal direction.</p>\n<h3>Reinforcement</h3>\n<p>Rebars are modeled by two-node 1D “rod” elements (CROD), which only have axial stiffness. These elements are connected to special “bond” elements which were developed in order to model the slip behavior between a reinforcing bar and the surrounding concrete. These bond elements are subsequently connected by MPC (multi-point constraint) elements to the mesh representing the concrete. This approach allows the independent meshing of reinforcement and concrete, while their interconnection is ensured later.</p>\n<h3>Bond elements</h3>\n<p>The anchorage length is verified by implementing the bond shear stresses between concrete elements (2D) and reinforcing bar elements (1D) in the finite element model. To this end, a “bond” finite element type was developed.</p>\n<p>The definition of the bond element is similar to that of a shell element (CQUAD4). It is also defined by 4 nodes, but in contrast to a shell, it only has a non-zero stiffness in shear between the two upper and two lower nodes. In the model, the upper nodes are connected to the elements representing reinforcement and the lower nodes to those representing concrete. The behavior of this element is described by the bond stress, τ<em><sub>b</sub></em>, as a bilinear function of the slip between the upper and lower nodes, δ<em><sub>u</sub></em>, see Fig. 14.</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"Fig. 16 \t(a) conceptual illustration of the deformation of a bond element, (b) a stress-deformation function. \"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>The elastic stiffness modulus of the bond-slip relationship, <em>G</em><em><sub>b</sub></em>, is defined as follows:</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>where:</p>\n<p><em>k</em><em><sub>g</sub></em> coefficient depending on the reinforcing bar surface (by default <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2)</p>\n<p><em>E</em><em><sub>c</sub></em> modulus of elasticity of concrete (taken as <em>E</em><em><sub>cm</sub></em> in case of EN)</p>\n<p>Ø the diameter of the reinforcing bar</p>\n<p>The design values (factored values) of ultimate bond shear stress, <em>f</em><em><sub>bd</sub></em>, provided in the respective selected design codes EN 1992-1-1 or ACI 318-19 are used to verify the anchorage length. The hardening of the plastic branch is calculated by default as <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>.</p>\n<h3>Anchorage spring</h3>\n<p>The provision of anchorage ends to the reinforcing bars (i.e., bends, hooks, loops…), which fulfills the prescriptions of design codes, allows the reduction of the basic anchorage length of the bars (<em>l</em><em><sub>b,net</sub></em>) by a certain factor β (referred to as the ‘anchorage coefficient’ below). The design value of the anchorage length (<em>l</em><em><sub>b</sub></em>) is then calculated as follows:</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p>The intended reduction in <em>l</em><em><sub>b,net</sub></em> is equivalent to the activation of the reinforcing bar at its end at a percentage of its maximum capacity given by the anchorage reduction coefficient, as shown in Fig. 15a.</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"Fig. 19\t Model for the reduction of the anchorage length: (a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship. \"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>The reduction of the anchorage length is included in the finite element model by means of a spring element at the end of the bar (Fig. 15), which is defined by the constitutive model shown in Fig. 15b. The maximum force transmitted by this spring (<em>F</em><em><sub>au</sub></em>) is:</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>where :</p>\n<p><em>β</em> the anchorage coefficient based on anchorage type,</p>\n<p><em>A</em><em><sub>s</sub></em> the cross-section of the reinforcing bar,</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em> the design value (factored value) of the yield strength of the reinforcement.</p>"
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"value": "<p>In the calculation for the results of SLS, only the elastic behavior of concrete is taken into account. In other words, an infinite linear stress-strain diagram is considered for concrete. You can display <strong>long-term</strong> or <strong>short-term</strong> effects for SLS checks. What is the difference between these two effects? Read the article below (paragraph Concrete SLS) to learn more.</p>\n<ul>\n <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Material models (EN)</a></li>\n</ul>\n<h2>Stress</h2>\n<p>There are two options for displaying results for concrete and reinforcement: </p>\n<ul>\n <li>the ratio of the stress and the limit stress </li>\n <li>the stress itself </li>\n</ul>\n<p>Stresses are calculated for the <strong>Characteristic</strong> and for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of the stress and limit stress</h4>\n<p>The results are clear at first sight: Green color means the utilization is up to 90%, orange is 90-100% of utilization, and red is above 100%.</p>\n<p>Read about how the limit value is determined in the following article.</p>\n<ul>\n <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Serviceability limit state analysis</a></li>\n</ul>\n<figure data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d12601c9-32a1-408f-9b41-e031d5b6fc45/RC-D_06_20.png\" data-asset-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" data-image-id=\"9a616d2b-74cb-45c4-b2c1-c2c4e126973d\" alt=\"\"></figure>\n<figure data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/45cd98c6-57b5-4373-a001-6e5c3ed8f5b8/RC-D_06_21.png.png\" data-asset-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" data-image-id=\"1ae8c1e4-5d61-421b-8f05-b54df99ec4c6\" alt=\"\"></figure>\n<h4>Stress</h4>\n<p>The display method is similar to the ULS results (in this case, the stress is from the calculation with the elastic behavior of concrete). You can display the distribution of concrete stress <em>σ</em><em><sub>c</sub></em><sub> </sub>for an applied portion of the load. Also known as principal stresses <em>σ</em><em><sub>2</sub></em>.</p>\n<figure data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6f65c964-8c56-4aac-a14c-4307bfde6a8d/RC-D_06_22.png\" data-asset-id=\"9d57f668-7250-467a-b305-817be6809f9c\" data-image-id=\"9d57f668-7250-467a-b305-817be6809f9c\" alt=\"\"></figure>\n<figure data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16c8bb7b-6bc7-4b9a-b27f-cf1075f7715a/RC-D_06_23.png\" data-asset-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" data-image-id=\"02dda510-4b1e-4b1e-bb64-81077f8e3a1d\" alt=\"\"></figure>\n<h2>Crack</h2>\n<p>In this section, you will learn about all four options for displaying results for crack checks. Read the further articles to learn about the calculation.</p>\n<ul>\n <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Main assumptions and limitations for CSFM</a></li>\n <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Structural element verification in IDEA StatiCa Detail</a></li>\n</ul>\n<p>Cracks are calculated only for the <strong>Quasi-permanent</strong> load combinations.</p>\n<h4>Ratio of crack width and limit crack width</h4>\n<p>The limit value w<sub>lim</sub> can be set in the top ribbon. The w<sub>lim</sub> = 0.3 mm is set by default according to Eurocode. The results are again differentiated by color (green/orange/red) so that the check is obvious at first sight.</p>\n<figure data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9fa5bdd1-ec85-4575-9e0f-6d26ce70c206/RC-D_06_24.png\" data-asset-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" data-image-id=\"0b4f0d29-6d96-4cc6-a8fe-ea633f20f628\" alt=\"\"></figure>\n<h4>Crack width</h4>\n<p>This functionality is used to display the crack width for every single element of the reinforcement. </p>\n<figure data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/97bc905a-76c9-4b12-abe1-3a93c71cdf2b/RC-D_06_25.png\" data-asset-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" data-image-id=\"46fb1a3f-e513-4d03-9c50-04a9f4ca4c16\" alt=\"\"></figure>\n<h4>The distance between stabilized cracks</h4>\n<p>See the links at the beginning of the section. The article explains the method of calculating the distance between stabilized cracks.</p>\n<figure data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bcb4dbbc-29b3-48bb-a1f1-72cdb456b0b6/RC-D_06_26.png\" data-asset-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" data-image-id=\"62e5dda7-3887-421b-a4ec-b4afe26fcbda\" alt=\"\"></figure>\n<p>The presentation of crack spacing is schematic only. It does not represent the crack spacing computed for the calculation.</p>\n<h4>Unreinforced area</h4>\n<p>The crack width is checked only in the vicinity of the reinforcement. Control of cracking is not performed in non-reinforced zones.</p>\n<p>This result simply shows the non-reinforced areas where cracks will probably appear. It is recommended to design some reinforcement to that areas.</p>\n<figure data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/4f60ea99-7197-4ee8-865e-2e282fdf60ef/RC-D_06_27.png\" data-asset-id=\"60363106-9502-4217-9931-e493c71e7e5b\" data-image-id=\"60363106-9502-4217-9931-e493c71e7e5b\" alt=\"\"></figure>\n<h2>Deflection</h2>\n<p>See the options below:</p>\n<ul>\n <li><em>u</em><em><sub>z,st</sub></em> - Immediate deflection caused by <strong>total load</strong> - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n <li><em>u</em><em><sub>z,lt</sub></em> - Long-term deflection caused by <strong>long-term loads </strong>(permanent and prestressing load type) - calculated with <strong>long-term stiffnesses </strong><em><strong>Ec,eff</strong></em><strong>. </strong>In other words, the creep coefficients are included.</li>\n <li><em>Δu</em><em><sub>z</sub></em> - Deflection increment caused by <strong>short-term loads</strong> (variable load type) - calculated with <strong>short-term stiffnesses </strong><em><strong>Ec</strong></em><strong>.</strong></li>\n <li><em>u</em><em><sub>z,tot</sub></em><em> = u</em><em><sub>z,lt</sub></em><em> + Δu</em><em><sub>z</sub></em><sub> </sub></li>\n</ul>\n<p>Deflections are calculated only for the <strong>Characteristic</strong> load combinations.</p>\n<figure data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/815bac57-2809-4383-b0cc-abfa3349b443/RC-D_06_29.png\" data-asset-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" data-image-id=\"e4454c67-f23e-461a-baac-97d2a3b92614\" alt=\"\"></figure>\n<p>Besides the table values in the Data section, you can display the deformed shape. You can also modify the scale of the deformation.</p>\n<p>Finally, in addition to displaying deformations, it is also possible to do a <strong>deflection check</strong>. You can choose between two checks - <strong>Increment</strong> and <strong>Total.</strong></p>\n<ul>\n <li><em>Δu</em><em><sub>z</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - Increment</li>\n <li><em>u</em><em><sub>z,tot</sub></em><em> / Δu</em><em><sub>z,lim</sub></em> - Total</li>\n</ul>\n<p><em>Δu</em><em><sub>z,lim</sub></em>, and <em>Δu</em><em><sub>z,lim</sub></em> can be manually set in the Deflection check bar in the top ribbon.</p>\n<figure data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9efce2e8-54f2-4fe3-8fcb-700d0bc1bd32/RC-D_06_30.png\" data-asset-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" data-image-id=\"929831b6-68db-4720-bfd3-e7c27d1cfd85\" alt=\"\"></figure>\n<p>The deflection check is not allowed for trimmed ends. </p>\n<h2>Practical example</h2>\n<p>For a practical example of displaying the results, continue to the <a href=\"https://www.youtube.com/embed/77fFYFUvv5c/?start=2408\">video</a> from the previously streamed webinar. 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"value": "<p>As per Eurocode 1990, the limit states that concern:</p>\n<ul>\n <li>the functioning of the structure or structural members under normal use;</li>\n <li>the comfort of people;</li>\n <li>the appearance of the construction works;</li>\n</ul>\n<p>shall be classified as <strong>serviceability limit states (SLS)</strong>. This includes <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">deformations</a>, vibrations, and damage affecting the appearance or durability, such as, e.g. <a data-item-id=\"9e7e995c-6e74-422f-af6e-88a8d7fe047f\" href=\"\">cracking</a>.</p>\n<p>In other words, these <a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">limit state checks</a> are not restricted by the strength resistance of the structure’s elements, but it is more about the overall durability of the structure and also the psychological comfort of people.</p>\n<p>Let me explain this in greater detail. Where would you feel more comfortable? In a new building with already cracked walls and bent ceilings or beams where the state could worsen in time? Or in a building with nice and smooth walls, and you can’t notice the slight deflection of the floor? I’m not even going to guess that everybody chooses the second example. And this is exactly why we should pay attention to <a data-item-id=\"52fea93a-1c63-4303-9fb3-89047991db8b\" href=\"\">SLS checks</a>.</p>\n<p>However, we all know that structural engineers' time is precious, so they want to be as efficient as possible with their designs. As a solution, we have developed new features in the <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\">IDEA StatiCa Detail</a> app to make sure that engineers using our tools have the design and assessments done fast, economically, and safely.</p>\n<h2>Stress limitation check – not that limiting anymore</h2>\n<p>How often have you dealt with unsatisfying results for the stress limitation check? In my case, I must say many times. And I had already known in most cases that they could have been neglected because of the nature of the results.</p>\n<p>One of the most typical issues is stress peaks - singularities usually occurring in sharp corners. Let’s take a look at what it is and why it is important not to confuse a singularity with stress concentration.</p>\n<figure data-asset-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" data-image-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dd6606c3-1024-4b08-9714-682a8ac4ee91/RN_23_limited%20stress%20check_01.png\" data-asset-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" data-image-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" alt=\"\"></figure>\n<p>At first glance, you may remark that you don’t see the difference between those two. Nevertheless, there are distinctions, and you should always be aware of them. Because, in the end, the overall design is always up to the responsible engineer and their judgment.</p>\n<p>So, what is a singularity, and how can structural engineers <a data-item-id=\"706e907a-540d-4b2b-8c13-af84c1593c7c\" href=\"\">recognize it from stress concentration</a>?</p>\n<p>A <a href=\"https://blogs.solidworks.com/tech/2018/07/what-is-a-stress-singularity-in-solidworks-simulation.html\">stress singularity</a> is a mesh point where the stress does not converge towards a specific value, i.e., that theoretically, the stress value at the singularity is infinite.</p>\n<p>It’s typically:</p>\n<ul>\n <li>An area where the point load is applied.</li>\n <li>A sharp corner of the structure.</li>\n <li>A point restraint.</li>\n <li>Corners of bodies in contact.</li>\n</ul>\n<p>And you can be sure it is a singularity when:</p>\n<ul>\n <li>There is a rapid change in stress in one mesh element.</li>\n <li>The value of the stress in one node of the mesh is higher than the limit value.</li>\n <li>It affects only a small structure area and doesn’t reach adjacent elements.</li>\n</ul>\n<p>Back in the days when I dealt with structures with singularities, I knew that in almost all cases, they could have been neglected because of the reasons mentioned above, but there was no way to do it if I wanted to have satisfying checks in the used app. This meant I had to modify the model in various ways, so I spent a lot of time with it or possibly increase the material grade or input additional <a data-item-id=\"6fa5f6f4-dd62-4a8b-a85b-77dc223d2e05\" href=\"\">reinforcement</a>.</p>\n<p>And this is where the Detail app comes in with its new <strong>Limited stress check functionality</strong>.</p>\n<figure data-asset-id=\"9df73250-0838-4920-a30b-042b662a8ea9\" data-image-id=\"9df73250-0838-4920-a30b-042b662a8ea9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f23934d1-5d6a-4a79-a9b3-cafbe5cdc34d/RN_23_limited%20stress%20check_03.png\" data-asset-id=\"9df73250-0838-4920-a30b-042b662a8ea9\" data-image-id=\"9df73250-0838-4920-a30b-042b662a8ea9\" alt=\"\"></figure>\n<p>Let’s see how the feature works in a practical example. We have a beam with a trimmed end and opening. The load is a combination of a line load and a point load. After running the analysis, we can see that the stress limitation check for concrete is not OK with all the necessary information.</p>\n<figure data-asset-id=\"299e8246-a8c3-4ba7-856d-d5a6cca40286\" data-image-id=\"299e8246-a8c3-4ba7-856d-d5a6cca40286\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3d9df3e2-4642-4f23-858a-4347434d9174/Stress%20limitation%20check_not%20OK.png\" data-asset-id=\"299e8246-a8c3-4ba7-856d-d5a6cca40286\" data-image-id=\"299e8246-a8c3-4ba7-856d-d5a6cca40286\" alt=\"\"></figure>\n<p>After closer examination, it’s clear that both situations I previously described have occurred. There is a stress concentration at the top of the beam under the point load-bearing plate and a singularity in the sharp corner of the opening.</p>\n<figure data-asset-id=\"9f238560-5e2c-4a2e-b7bd-6595ec9f6a72\" data-image-id=\"9f238560-5e2c-4a2e-b7bd-6595ec9f6a72\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8614cc67-f9ec-4e7c-b0c5-82a3c2dc0d96/Stress%20limitation%20check_not%20OK_detailed%20results.png\" data-asset-id=\"9f238560-5e2c-4a2e-b7bd-6595ec9f6a72\" data-image-id=\"9f238560-5e2c-4a2e-b7bd-6595ec9f6a72\" alt=\"\"></figure>\n<p>Now is the right time to use engineering judgment! The singularity in the corner can be neglected without question in the design. But what about the small area with stress concentration? What should I do? The first thing is to turn on the mesh, which might help evaluate the impact. If it is still unclear, I can go to <a data-item-id=\"4bb80e0f-cb69-4f4d-9406-42fb6211bc1c\" href=\"\">Settings</a>, set the mesh to be finer, and assess again.</p>\n<p>Nevertheless, in our case, it is visible at first sight that the stress concentration area is very small, so, from my point of view, it is acceptable to exclude it from the calculation as well.</p>\n<p>And it can be done pretty easily! For this purpose, we have developed a feature called Limited Check. The functionality allows you to neglect the unsatisfactory areas. What does this mean?</p>\n<ol>\n <li>Instead of the red areas with utilization over 100%, you see them in white, and the limit check value is 100% in the case of a stress ratio or the limit stress value in MPa.</li>\n <li>On top of that, in the overall check table, the red circle with a cross sign is changed to a yellow triangle with an exclamation point representing an informative matter, and a nonconformity with a thorough description appears.</li>\n <li>As the cherry on top, you can display only the neglected regions while the rest of the element remains in white.</li>\n</ol>\n<figure data-asset-id=\"eb177d3f-555d-458b-a017-23610286b350\" data-image-id=\"eb177d3f-555d-458b-a017-23610286b350\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dcf347d9-0107-4f02-b012-f65ff6c67a0b/Stress%20limitation%20check_limited%20check_all.png\" data-asset-id=\"eb177d3f-555d-458b-a017-23610286b350\" data-image-id=\"eb177d3f-555d-458b-a017-23610286b350\" alt=\"\"></figure>\n<p>All the options can be included in the <a data-item-id=\"659d5379-de12-4897-9f8e-46497a7d70b0\" href=\"\">report</a> after you’re done with the modeling process and are happy with your design. So you will have bulletproof documentation to silence any doubters.</p>\n<h2>Prestressed structures in IDEA StatiCa</h2>\n<p>Every structural engineer dealing with prestressed concrete structures is aware that it is very important to pay attention to particular stages of structures’ working lives, especially the beginning and end.</p>\n<p>It’s because no prestressing force is constant. The value is variable along the length of the prestressing tendon and, last but not least, in time. It is obvious that the correct evaluation of the precise value of the prestressing force, hence, the stresses in tendons, has a significant impact on the structure’s behavior.</p>\n<p>The changes in the prestressing force (a decrease of the prestressing force might not necessarily appear!) are caused by many factors and are referred to as prestressing losses. Yes, I used the plural correctly. The prestressing losses are distinguished as:</p>\n<ul>\n <li>Short-term losses</li>\n <li>Long-term losses</li>\n</ul>\n<h3>Short-term losses</h3>\n<p>Short-term losses usually happen during the manufacturing process. Short-term loss can be caused by, e.g., friction, a slip in the anchorage set, immediate elastic strain in concrete, relaxation of the tendons, etc.</p>\n<h3>Long-term losses</h3>\n<p>Long-term losses occur after the application of the prestressing and can affect the structure during its whole working life. The cause of the long-term losses can be considered – creep, shrinkage, long-term relaxation, and elastic strain in concrete caused by the application of a variable load.</p>\n<h3>Not an easy task. Or is it?</h3>\n<p>Considering all of this (which is a must in the design!) may lead to having several combinations taking into account various prestressing coefficients.</p>\n<p>Here <a data-item-id=\"a0e85d28-23e6-4006-94d6-f334c2be9b67\" href=\"\"><strong>IDEA StatiCa Detail</strong></a> enters the spotlight for the second time. Thanks to new functionality called <a data-item-id=\"11765fc5-842e-4fe5-afed-c54104da47d5\" href=\"\"><strong>Long-term losses for SLS check</strong></a>, you don’t need to have a bunch of combinations and spend hours with your model while stressing if you haven't forgotten something.</p>\n<p>All you need to do in the Detail app is to set one combination, and you are able to cover short-term and long-term effects for both pre-tensioned and post-tensioned tendons.</p>\n<figure data-asset-id=\"91d05e27-c506-4ef2-a660-41c5e1936935\" data-image-id=\"91d05e27-c506-4ef2-a660-41c5e1936935\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7e118ef5-b989-41bc-8d9d-34200540892c/Long-term%20losses_general.png\" data-asset-id=\"91d05e27-c506-4ef2-a660-41c5e1936935\" data-image-id=\"91d05e27-c506-4ef2-a660-41c5e1936935\" alt=\"\"></figure>\n<p>Are you pumped to learn how it works? Let’s find out!</p>\n<p>It’s important to for knowing the stress limitation check and getting the results for short-term and long-term effects in the Detail application, we use an infinite linear stress-strain diagram.</p>\n<figure data-asset-id=\"e05c49f0-c5ec-44dc-91c6-3309766288c3\" data-image-id=\"e05c49f0-c5ec-44dc-91c6-3309766288c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/fc29949d-bb8d-4378-94b7-ad2468831f3f/RN_23_long%20term%20losses_02.png\" data-asset-id=\"e05c49f0-c5ec-44dc-91c6-3309766288c3\" data-image-id=\"e05c49f0-c5ec-44dc-91c6-3309766288c3\" alt=\"\"></figure>\n<p>We distinguish two branches. One for short-term effects using modulus of elasticity E<sub>cm</sub>. And the other one is for long-term effects, where the stress in tendons is reduced in increments for prestressing and permanent load by the defined value of long-term losses. The increment of variable load considers E<sub>cm</sub>.</p>\n<p>How to set the value of long-term losses correctly? We may provide you with some default settings; however, it is again up to structural engineers which value they will eventually use for the calculation.</p>\n<p>Please be aware that the value differs for pre-stressed tendons and post-stressed tendons. It is because of the exact time for which you ought to set the loss value. Check the <a data-item-id=\"11765fc5-842e-4fe5-afed-c54104da47d5\" href=\"\">Implementation of long-term losses in Detail </a>article, where you can find a more detailed description of the topic and, more importantly, what is the proper time for setting the long-term losses estimation to the calculation.</p>\n<p>If you are interested in more new features of IDEA StatiCa 23.0 (maybe not only for concrete but steel or BIM links as well), visit our <a data-item-id=\"9a275699-6cf5-48a3-ac7c-1154c4c1331a\" href=\"\">Release notes page</a>. </p>\n<p>IDEA StatiCa Detail is a great tool to solve your concrete details and other discontinuity regions. Find out more about its possibilities in our <a data-item-id=\"68527d02-6aa1-4a1a-87c2-363edf00b0bb\" href=\"\">Support Center</a>, where you can also learn how to use it in <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&label=detail\" data-new-window=\"true\" target=\"_blank\" rel=\"noopener noreferrer\">many tutorials</a>, see our product engineers in action in one of our <a href=\"https://www.ideastatica.com/support-center-webinars?label=detail\" data-new-window=\"true\" target=\"_blank\" rel=\"noopener noreferrer\">webinars</a> or download a <a href=\"https://www.ideastatica.com/support-center/sample-projects-for-reinforced-concrete-design\" data-new-window=\"true\" target=\"_blank\" rel=\"noopener noreferrer\">sample project</a>.</p>\n<p>If you are starting with the software or just want to improve your skills, check out our self-paced learning <a data-item-id=\"9b649ffb-9cc1-48a3-b827-442f7cdd2af5\" href=\"\">Campus courses</a> and select the one that suits your needs the best.</p>\n<figure data-asset-id=\"ecc4042a-a260-4f73-8e5f-83efbe36cfdc\" data-image-id=\"ecc4042a-a260-4f73-8e5f-83efbe36cfdc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/78122945-95f0-4621-be7b-2e4f4b73148a/preview_wall_cracks.png\" data-asset-id=\"ecc4042a-a260-4f73-8e5f-83efbe36cfdc\" data-image-id=\"ecc4042a-a260-4f73-8e5f-83efbe36cfdc\" alt=\"IDEA StatiCa Detail is structural engineering software for the structural design and code-check of concrete discontinuity regions.\"></figure>\n<p>For those interested even more in theory and the <a data-item-id=\"86ad7678-0f7f-452a-8e0d-376ea5797b27\" href=\"\">CSFM method</a> behind the Detail application, go to the <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">Theoretical background for IDEA StatiCa Detail</a>, and go wild with studying.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n6de9747b_c244_01af_3701_bf6bb9d99cd4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n664053b1_d4b4_0135_9a14_8bf39e660317\"></object>"
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"value": "<p><strong>Common 3D models</strong> in FEA software <strong>cannot</strong> fully <strong>capture</strong> the behavior of this critical part, especially in cases where the coupling beam is a deep beam or weakened by an opening.</p>\n<p>Looking for safe and economical solution to this problem? Don't want to waste time with a complex assessment? Do you want to see the results for the <strong>ultimate limit state</strong> and the <strong>serviceable limit state</strong>, including, e.g., the <strong>crack width check</strong>?</p>\n<h3>Fast assessment of coupling beam? No problem for IDEA StatiCa Detail!</h3>\n<figure data-asset-id=\"4260af1a-23dc-4453-84a8-026c142d1d65\" data-image-id=\"4260af1a-23dc-4453-84a8-026c142d1d65\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f44e0c1c-2eb3-454a-ad17-c8f1eec6d245/2022-11-23%20Coupling%20beam.png\" data-asset-id=\"4260af1a-23dc-4453-84a8-026c142d1d65\" data-image-id=\"4260af1a-23dc-4453-84a8-026c142d1d65\" alt=\"\"></figure>\n<p>We will speak about the importance and possibilities of modeling the coupling beam. Then we will set the correct <strong>load </strong>on the selected cut-off <strong>beam</strong>, input the <strong>reinforcement</strong>, and go through the detailed results.</p>\n<h3>The ultimate solution for concrete details and structural parts</h3>\n<p>Common 3D FEA software considers the linear behavior of concrete. Design and code-checks of reinforcement are limited, especially for the <strong>serviceability limit state,</strong> which may lead to the development of <strong>excessive cracks</strong>. All of that is covered within the <a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">CSFM-based</a> application IDEA StatiCa Detail. Now, all engineers can efficiently design and code-check structures of any shape and many more.</p>\n<p>If you want to see more of <strong>IDEA StatiCa Detail </strong>in action, there are other <a href=\"https://www.ideastatica.com/support-center-webinars?product=concrete&label=detail\" data-new-window=\"true\" title=\"recorded webinars\" target=\"_blank\" rel=\"noopener noreferrer\">recorded webinars</a> to watch, or browse our Support center for <a href=\"https://www.ideastatica.com/support-center-tutorials?product=concrete&label=detail\" title=\"IDEA StatiCa Detail\">tutorials</a> and read the <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">theoretical background.</a></p>\n<h3>Webinar recording</h3>"
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"value": "<p><strong>Stress peaks (singularities) can be neglected from the stress limitation check! </strong>Before we explain this option in detail, let's recall how the singularity, which can be neglected, and stress concentration, which cannot be neglected, differ. In the figure below, you can see a typical stress peak (singularity) in a sharp corner and a typical stress concentration around an opening.</p>\n<figure data-asset-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" data-image-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/dd6606c3-1024-4b08-9714-682a8ac4ee91/RN_23_limited%20stress%20check_01.png\" data-asset-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" data-image-id=\"d22a59ea-0d22-4084-a81d-b8d1c340d0ad\" alt=\"\"></figure>\n<p>It looks very similar, so how can you recognize the singularity from the stress concentration? When can you use the limited stress check? Well, the fact is that the decision is always up to the responsible engineer. We can offer you advice and name some typical singularities to help you.</p>\n<ul>\n <li>When there is a rapid change in stress in one element of the mesh – there is a singularity.</li>\n <li>If the stress is high above the limit only in one node of the mesh – there is a singularity.</li>\n <li>Only the very small areas of unsatisfactory stress should be neglected.</li>\n <li>Typical singularities – <strong>sharp corners</strong>, the point of the mesh that is near to the anchorage or bearing plate and is not included in the partially loaded area.</li>\n</ul>\n<p>Now, let's explain how the feature works. There is a wall with an opening with an unsatisfactory stress limitation check in the right sharp corner.</p>\n<figure data-asset-id=\"fb76e23c-24d1-44d5-b803-995f28fce547\" data-image-id=\"fb76e23c-24d1-44d5-b803-995f28fce547\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a22d9d40-1503-4476-809e-32e4260164f2/RN_23_limited%20stress%20check_02.png\" data-asset-id=\"fb76e23c-24d1-44d5-b803-995f28fce547\" data-image-id=\"fb76e23c-24d1-44d5-b803-995f28fce547\" alt=\"\"></figure>\n<p>As you can see, the area is very small according to the whole structure. There is a option in the top ribbon that allows you to neglect the unsatisfactory areas.</p>\n<figure data-asset-id=\"eaeccc88-5e2a-4811-830e-1aa31447c4c3\" data-image-id=\"eaeccc88-5e2a-4811-830e-1aa31447c4c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/1e20eacd-ef0b-4972-abf5-f34835074fb6/RN_23_limited%20stress%20check_03_1.png\" data-asset-id=\"eaeccc88-5e2a-4811-830e-1aa31447c4c3\" data-image-id=\"eaeccc88-5e2a-4811-830e-1aa31447c4c3\" alt=\"\"></figure>\n<p>The utilization is then 100%, and nonconformity appears.</p>\n<figure data-asset-id=\"ad66635b-62ad-4766-98a4-c7bb36b489dd\" data-image-id=\"ad66635b-62ad-4766-98a4-c7bb36b489dd\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3fe91946-2d79-435c-ae6d-2e28a0db2be1/RN_23_limited%20stress%20check_04.png\" data-asset-id=\"ad66635b-62ad-4766-98a4-c7bb36b489dd\" data-image-id=\"ad66635b-62ad-4766-98a4-c7bb36b489dd\" alt=\"\"></figure>\n<p>You can also display the neglected areas. </p>\n<figure data-asset-id=\"b1a8e608-a3fe-4e3a-b0da-83b29fe774c5\" data-image-id=\"b1a8e608-a3fe-4e3a-b0da-83b29fe774c5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/531431e5-2aa9-4535-a4cb-56d0d5a7261e/RN_23_limited%20stress%20check_05.png\" data-asset-id=\"b1a8e608-a3fe-4e3a-b0da-83b29fe774c5\" data-image-id=\"b1a8e608-a3fe-4e3a-b0da-83b29fe774c5\" alt=\"\"></figure>\n<p>All of these checks and images can be added to the report. So it will be shown that some areas were neglected, or how large these areas are. You can choose if you want to report original values or not, etc.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5a01670a_a78f_01f6_334d_c862e365c52d\"></object>"
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"value": "<p>The sharp corner created at the junction of the coupling beam and shear wall creates a local stress peak that skews the model results. This peak is caused by the singularities at the point of the sharp re-entrant corner. The question is how to deal with these peaks in the models themselves.</p>\n<h3>Singularities</h3>\n<p>A <a href=\"https://blogs.solidworks.com/tech/2018/07/what-is-a-stress-singularity-in-solidworks-simulation.html\">stress singularity</a> is a point of the mesh where the stress does not converge towards a specific value. As we keep refining the mesh, the stress at this point keeps increasing. Theoretically, the stress at the singularity is infinite. Typical situations where stress singularities occur are the appliance of a point load, <strong>sharp re-entrant corners</strong>, corners of bodies in contact, and point restraints.</p>\n<p>In reality, no corner is perfectly sharp. Even if detailed this way, a manufactured sharp corner will always present a small fillet radius. This means that the stress will not be infinite anymore and the corner singularity will disappear. Instead, stress concentration takes over.</p>\n<figure data-asset-id=\"79b044c2-1d9a-40d3-9932-7b771832d283\" data-image-id=\"79b044c2-1d9a-40d3-9932-7b771832d283\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5db665f8-3046-4afd-aeca-e609116da478/06_singulerities_linear.png\" data-asset-id=\"79b044c2-1d9a-40d3-9932-7b771832d283\" data-image-id=\"79b044c2-1d9a-40d3-9932-7b771832d283\" alt=\"The relationship between mesh stress concentration behavior\"></figure>\n<p><em>Figure 6. A sensitivity study was performed on the material linear model to find the relationship between mesh stress concentration behavior. </em></p>\n<h3>Stress concentration</h3>\n<p>Stress concentration behaves similarly to stress singularities, but the stress will converge towards a finite value, not infinite, given that the mesh is sufficiently refined. Features such as holes, filleted corners, changes of cross-section, etc., will lead to stress concentrations.</p>\n<ul>\n <li>A <strong>coarse mesh will not capture local effects </strong>such as stress concentrations.</li>\n <li>The more we refine the mesh, the more accurate the results are. However, the model is not computationally efficient. The Saint Venant's principle says that the effect should be local. Therefore, the <strong>mesh could be refined locally</strong> rather than globally, subdividing all the elements in the mesh.</li>\n <li><strong>Plasticity</strong> helps to ensure correct behavior and suppress the singularity effect.</li>\n</ul>\n<figure data-asset-id=\"3b146157-4f4c-407b-9631-fd414336afcc\" data-image-id=\"3b146157-4f4c-407b-9631-fd414336afcc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a22608f8-cc30-4a3f-b68c-70303ec3e045/07_plasticity.png\" data-asset-id=\"3b146157-4f4c-407b-9631-fd414336afcc\" data-image-id=\"3b146157-4f4c-407b-9631-fd414336afcc\" alt=\"\"></figure>\n<figure data-asset-id=\"0297a245-6b77-4782-9842-bb2ea2a57263\" data-image-id=\"0297a245-6b77-4782-9842-bb2ea2a57263\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/21ccfcec-31ef-4d84-b2e1-40065d4724b4/07_1_plasticity.png\" data-asset-id=\"0297a245-6b77-4782-9842-bb2ea2a57263\" data-image-id=\"0297a245-6b77-4782-9842-bb2ea2a57263\" alt=\"Relationship between mesh size and sharp and fillet corner equivalent stress\"></figure>\n<p><em>Figure 7. A sensitivity study was performed on the material nonlinear model to find the relationship between mesh size and sharp and fillet corner equivalent stress. </em></p>\n<h3>How to deal with singularities and stress concentrations</h3>\n<ul>\n <li><strong>Ignore the singularities</strong>. If we are interested in the stresses far away from any singularities, the Saint Venant's principle applies – the stresses will be correct.</li>\n <li>The <strong>mesh</strong> must be <strong>locally refined</strong> to capture the <strong>stress concentration effect</strong>.</li>\n <li>Typical geometric-induced singularities, such as sharp<strong> re-entrant corners,</strong> can be <strong>avoided</strong> by modeling fillets instead. Effectively, the stress singularity becomes a stress concentration.</li>\n <li><strong>Plasticity</strong> allows the model to behave according to reality, and the singularity effect vanishes.</li>\n <li>The mesh should be refined to verify that stresses do converge. This requires a <strong>mesh sensitivity study.</strong></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n3253192c_ec6f_01e9_93e6_067f6cb84fb6\"></object>"
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"value": "<p>From frequent customer inquiries and our own experience, we have put together the following topics:</p>\n<ul>\n <li>How to input compressive load under the anchoring plate to the model</li>\n <li>How to input the load from the ceiling</li>\n <li>How to input the load from the shear connection</li>\n <li>How to input the partial factors for ULS and SLS</li>\n</ul>\n<p>Each issue is briefly described and then explained as part of an already streamed webinar.</p>\n<p><em>Note: If you need a reminder of what types of load can be used in the application, continue to the article </em><a data-item-id=\"38cbe005-0e1e-4d75-ae8a-2ef9dcee4c2b\" href=\"\"><em>General Description of Load impulses in Detail application</em></a><em>.</em></p>\n<h2>How to input compressive load under the anchoring plate to the model</h2>\n<figure data-asset-id=\"68f349db-e4be-4378-a5be-c6ed60084ecf\" data-image-id=\"68f349db-e4be-4378-a5be-c6ed60084ecf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/3724fe58-e2c2-4408-b9fd-c8a68186aa77/How%20to%20input%20compressive%20load%20under_MainPicture.png\" data-asset-id=\"68f349db-e4be-4378-a5be-c6ed60084ecf\" data-image-id=\"68f349db-e4be-4378-a5be-c6ed60084ecf\" alt=\"How to input compressive load under the anchoring plate to the model\"></figure>\n<p>The stress in the concrete receives from the analysis in the IDEA StatiCa Connection. Due to the possibility of displaying the effective areas, we are able to integrate the stress on each effective area and get the forces. Due to the fact that the stress is constant along with the height of the effective area, we use uniform load to simulate the effect of stress under the anchoring plate.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"b903004b_a526_0119_31fd_3c10466b3ffb\"></object>\n<h2>How to input the load from the ceiling</h2>\n<figure data-asset-id=\"248999d5-7aae-41e1-a77b-15ab22780d7c\" data-image-id=\"248999d5-7aae-41e1-a77b-15ab22780d7c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ce2c5dac-bde1-453b-873c-82947eca7a8d/How%20to%20input%20the%20load%20from%20the%20ceiling_MainPicture.png\" data-asset-id=\"248999d5-7aae-41e1-a77b-15ab22780d7c\" data-image-id=\"248999d5-7aae-41e1-a77b-15ab22780d7c\" alt=\"How to input the load from the ceiling\"></figure>\n<p>The monolithic junction of the ceiling to the wall induces load, which can not be neglected. According to the shape of the shear force in the place of the junction from the FEA, we can adjust the equivalent load to the model.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"de14d9be_e2f5_0137_7c49_dd516c67400e\"></object>\n<h2>How to input the load from the shear connection</h2>\n<p>The shear connection is possible modeled using a special load device called \"Patch load\". This entity is capable of distributed point load over an effective radius (area) which is defined by the user. </p>\n<figure data-asset-id=\"4455c845-919f-4dbe-a02d-fda43670a9ac\" data-image-id=\"4455c845-919f-4dbe-a02d-fda43670a9ac\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/06cf789c-5902-461d-85ef-31d63ecc82cd/How%20to%20input%20the%20load%20from%20the%20shear%20connection.png\" data-asset-id=\"4455c845-919f-4dbe-a02d-fda43670a9ac\" data-image-id=\"4455c845-919f-4dbe-a02d-fda43670a9ac\" alt=\"How to input the load from the shear connection\"></figure>\n<p>The option when the force is transferred directly to the concrete or reinforcement bars is derived from the realization of the connection in the wall. We have used the option for direct transfer to the reinforcement bars due to the effect of welding the anchors to the wire fabrics. It is really important to realize that the shear joint transfers, apart from the vertical load, also bending moment out of the plane of the wall. This effect cannot be covered in the 2D model in IDEA StatiCa Detail.</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n84a805ec_c0d5_0194_d92a_22e6c77a3ab9\"></object>\n<h2>How to input the partial factors for ULS and SLS</h2>\n<p>Load cases as self–weight or ceiling are added in the characteristic values. If we input the load cases from the joints, we apply the partial factor of 1 due to the design value extracted from the IDEA StatiCa Connection. Nevertheless, in SLS, the situation is not so simple due to the fact that design values cannot be separated from the point of view of permanent and variable loads and divided by appropriate partial factors. The reason is the non-linear analysis in IDEA StatiCa Connection, so we cannot use the superposition of the loads. 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"value": "<h2>Reinforcement in Partially Loaded Area</h2>\n<p>You can design the reinforcement in the partially loaded area in a more effective way since version 20.1. The reinforcing bars are part of the CSFM model, and the bond between concrete and bars is treated as perfect. </p>\n<figure data-asset-id=\"3ab51e56-2e14-40b7-9f70-7ee929f7adeb\" data-image-id=\"3ab51e56-2e14-40b7-9f70-7ee929f7adeb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f589881a-d9fc-4105-a625-e64020697db3/Partially%20loaded%20areas-reinf.PNG\" data-asset-id=\"3ab51e56-2e14-40b7-9f70-7ee929f7adeb\" data-image-id=\"3ab51e56-2e14-40b7-9f70-7ee929f7adeb\" alt=\"partially loaded areas with reinforcement\"></figure>\n<h2>About Partially Loaded Area</h2>\n<p>This feature is suitable mainly for precast and bridge structural engineers who are dealing with significant reactions in the bearings or concentrated prestressed forces from the tendons in the beams. The benefit is hidden beyond non - conservative design, saving material and money.</p>\n<p>We have figured out how to deal with triaxial stress in partially loaded areas. In these areas crushing of concrete is allowed, and the resistance of concrete in compression can be raised due to transverse confinement according to valid standards (Eurocode). The increase of the resistance can be up to 3 times the cylinder strength of concrete.</p>\n<figure data-asset-id=\"b72f7533-5eae-4ccc-8386-af616f712ff6\" data-image-id=\"b72f7533-5eae-4ccc-8386-af616f712ff6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/25769cf9-c38a-4738-860c-948de6a17400/Partially%20loaded%20area%201.PNG\" data-asset-id=\"b72f7533-5eae-4ccc-8386-af616f712ff6\" data-image-id=\"b72f7533-5eae-4ccc-8386-af616f712ff6\" alt=\"\"></figure>\n<p>The partially loaded area can be found on every structure. Some typical examples are bridge diaphragms with an area above the bearings, areas under the anchor, or concentrated load on the edge of the wall. Partially loaded areas are designed according to the requirements of the Eurocode and simultaneously are restrained by model geometry (openings, thickness, edges, abrupt change of cross-section).</p>\n<figure data-asset-id=\"db666445-daab-4bbd-8f4c-dd0917b61eba\" data-image-id=\"db666445-daab-4bbd-8f4c-dd0917b61eba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/88696c5a-2fa2-4f08-b3d7-2ae565699c02/Partially%20loaded%20area%202.png\" data-asset-id=\"db666445-daab-4bbd-8f4c-dd0917b61eba\" data-image-id=\"db666445-daab-4bbd-8f4c-dd0917b61eba\" alt=\"Triaxial stress is covered by new feature, which artificially increase the area of the cone and cover this effect.\"></figure>\n<p>The increase of concrete resistance can be considered if the confinement is kept. Due to this condition, reinforcement bars are automatically added to pass the condition regarding confinement and Eurocode provision.</p>\n<figure data-asset-id=\"802e353e-22eb-4418-a1c6-c7c47e4f890c\" data-image-id=\"802e353e-22eb-4418-a1c6-c7c47e4f890c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7fecad0b-e34f-415a-86ce-0b5ddf1b674c/Partially%20loaded%20area%20cone.png\" data-asset-id=\"802e353e-22eb-4418-a1c6-c7c47e4f890c\" data-image-id=\"802e353e-22eb-4418-a1c6-c7c47e4f890c\" alt=\"\"></figure>\n<p>This functionality guarantees that models are getting converge and simultaneously comply with design criteria for valid standards (Eurocode). The implemented method is independent of the finite element mesh. <strong>The bearing capacity is increased with</strong> the <strong>changing of the concrete area. The consequence of this state is constant stress along with the height of a cone. </strong>Dispersed fictitious struts affect artificially the stiffness of the cone and correctly redistribute the transverse stress, which appears in this area. The density of each dispersed strut is increased to the direction of the applied load.</p>\n<figure data-asset-id=\"62cc432f-b87c-4de2-b8ca-afd16981510a\" data-image-id=\"62cc432f-b87c-4de2-b8ca-afd16981510a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2a98ab65-1aab-4c54-839b-25a89481479e/Dispersed%20fictitious%20struts.png\" data-asset-id=\"62cc432f-b87c-4de2-b8ca-afd16981510a\" data-image-id=\"62cc432f-b87c-4de2-b8ca-afd16981510a\" alt=\"\"></figure>\n<p>Known limitations come out from the standards valid in Eurocode.</p>\n<ul>\n <li>Cones cannot coincide</li>\n <li>The area A<sub>c1</sub> and A<sub>c0 </sub>lie on the resultant of the acting force</li>\n</ul>\n<p><br></p>"
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"value": "<p><strong>Compatible Stress Field Method </strong>(CSFM) is an innovative method implemented in IDEA StatiCa Concrete used for the design of reinforced concrete structures. Let’s take a look behind the scenes of our software and see for yourselves that there is no need to be afraid of using CSFM calculations in your projects. </p>\n<figure data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7fd8d041-20d1-40a8-9a71-eb9cdce27155/7.png\" data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" alt=\"\"></figure>\n<p><em>Fig: a) Wall with openings b) Shear wall c) Beam with dapped ends and openings d) Bridge pier e) Bridge diaphragm </em></p>\n<p>See the <strong>introduction video about CSFM and IDEA StatiCa Detail</strong>:</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n9cf4be9e_1a16_013b_08ac_786b868df709\"></object>\n<p>CSFM offers much more than just ULS checks. The advanced state of the method is based on <strong>modified compression field theory</strong>, implementation of <strong>tension stiffening</strong>, and distinguishing between stabilized or non-stabilized cracking; hence we <strong>perform SLS checks</strong> of the concrete member. Thus, we can observe <strong>crack width</strong>, <strong>deformation</strong>, and <strong>stresses</strong> corresponding to SLS combinations.</p>\n<p>Watch the recording of a webinar where the theory behind the CSFM was explained in detail. </p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4a95bf6f_e0a2_0145_b0f4_e9fe78b96928\"></object>\n<p>If you are interested in the method itself, see some more resources:</p>\n<p><strong>Article summarizing the principles</strong> of the method: <a data-item-id=\"eaab962d-ba44-4ee0-8fa7-45193c9f52b5\" href=\"\">CSFM explained</a></p>\n<p><strong>Extensive theoretical background</strong> where you will find in detail the material methods used, how the model is built and meshed, and how the individual values are calculated: <a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">Theoretical Background</a></p>\n<p><br></p>\n<p>The method (CSFM) is implemented in <a data-item-id=\"4d79cdf4-c6ee-47e8-b4f2-58f4281194bf\" href=\"\">IDEA StatiCa Detail</a>.</p>\n<p><br></p>"
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"value": "<p>Four types of load impulses can be defined for reinforced concrete discontinuity regions:</p>\n<ul>\n <li><strong>Point load</strong></li>\n <li><strong>Line load</strong></li>\n <li><strong>Surface load</strong></li>\n <li><strong>Self-weight</strong></li>\n</ul>\n<p>Now, let's have a look at each of the options.</p>\n<h3>Point load</h3>\n<p>This simple load impulse is defined by its value, direction, inclination, position, and effective radius. The way how a point load is set can influence the method of how the load is applied to the model.</p>\n<p>The first option is to set the load <strong>on edge</strong>. See the figure below.</p>\n<figure data-asset-id=\"7e99a13e-2fe2-4cb1-a62c-1b15c2340daf\" data-image-id=\"7e99a13e-2fe2-4cb1-a62c-1b15c2340daf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7fba1061-90ff-47f6-a815-d9f65c830f37/RC-D_04_10.png\" data-asset-id=\"7e99a13e-2fe2-4cb1-a62c-1b15c2340daf\" data-image-id=\"7e99a13e-2fe2-4cb1-a62c-1b15c2340daf\" alt=\"\"></figure>\n<p>The second option is to set the load generally <strong>into the model</strong>. The value of every applied load is calculated by weighted average where the weight is the distance from a point of application. In other words, the applied loads are variably distributed, not uniformly.</p>\n<figure data-asset-id=\"e49527a2-df9f-4065-85e9-28b65779a847\" data-image-id=\"e49527a2-df9f-4065-85e9-28b65779a847\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/571ac7e5-b45a-4e9b-be3d-e855c3633cb5/RC-D_04_11.png\" data-asset-id=\"e49527a2-df9f-4065-85e9-28b65779a847\" data-image-id=\"e49527a2-df9f-4065-85e9-28b65779a847\" alt=\"\"></figure>\n<p>The third option is to adjust the load to the <strong>patch load </strong>-<strong> </strong>one of the <a data-item-id=\"50ed723b-9b87-4870-a69f-e05b5a8a8150\" href=\"\">load-transferring devices</a>, by using the functionality in the Geometry section. </p>\n<figure data-asset-id=\"fe5fd12b-c28b-4ee8-9411-bc6409c8c4f6\" data-image-id=\"fe5fd12b-c28b-4ee8-9411-bc6409c8c4f6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ecc36345-2762-40af-94f9-4bba0b1666a5/QRC-D_03%20Patch%20load.png\" data-asset-id=\"fe5fd12b-c28b-4ee8-9411-bc6409c8c4f6\" data-image-id=\"fe5fd12b-c28b-4ee8-9411-bc6409c8c4f6\" alt=\"\"></figure>\n<p>The load application is shown in the image below.</p>\n<figure data-asset-id=\"8b12881b-a598-447c-972c-0ad8d296c1d3\" data-image-id=\"8b12881b-a598-447c-972c-0ad8d296c1d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d03a5a23-8992-4269-9528-98d9f60bc8c2/RC-D_04_12.png\" data-asset-id=\"8b12881b-a598-447c-972c-0ad8d296c1d3\" data-image-id=\"8b12881b-a598-447c-972c-0ad8d296c1d3\" alt=\"\"></figure>\n<p>Let's compare the images for the load placed into the model, and set using the patch load. Without patch load, the point load is applied to the elements of the concrete mesh. On the other hand, with patch load, the point load is applied straight to the reinforcement bars.</p>\n<p>The patch load can be connected to the adjacent reinforcement automatically by the software. However, for that, you have to turn on the checkbox for the corresponding bars in the Reinforcement section.</p>\n<figure data-asset-id=\"0ee90871-78b5-429a-b983-01939f512d05\" data-image-id=\"0ee90871-78b5-429a-b983-01939f512d05\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ab55b953-305b-41b6-875b-324abd5f8677/RC-D_04_13--Reinforcement_--_patch_load_--_interconnect_automaticly.png\" data-asset-id=\"0ee90871-78b5-429a-b983-01939f512d05\" data-image-id=\"0ee90871-78b5-429a-b983-01939f512d05\" alt=\"\"></figure>\n<p>In the figure below, you can see the case where the horizontal reinforcement was excluded from the patch load area, hence not considered for the load transmission.</p>\n<figure data-asset-id=\"9c727e53-a09e-4d4d-bd22-58e981060c36\" data-image-id=\"9c727e53-a09e-4d4d-bd22-58e981060c36\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9d831094-cb38-4e46-944e-9c175969534a/RC-D_04_14.png\" data-asset-id=\"9c727e53-a09e-4d4d-bd22-58e981060c36\" data-image-id=\"9c727e53-a09e-4d4d-bd22-58e981060c36\" alt=\"\"></figure>\n<p>The point loads can also be transferred via some other load-transmitting devices like bearing plates, hanging loads, and more. Do you want to know more about that? Read the article <a data-item-id=\"50ed723b-9b87-4870-a69f-e05b5a8a8150\" href=\"\">Support and load transmitting components</a>.</p>\n<p>The main principle is that point loads are applied to the model by elastic links with different stiffnesses. The stiffnesses are evaluated by weighted averages based on the length of the links. These links are connected to the points of the concrete or reinforcement mesh (where the blue arrows were drawn) and transfer the loads to the structure.</p>\n<h3>Line load</h3>\n<p>Line load can be defined as uniform or trapezoidal. The used type depends on the numerical load definition. When applying the linear line load, simply enter only one value to the corresponding cell in the data window. Nevertheless, if you need to specify the trapezoidal load, fill in values at one and the other end of the load. See the practical examples:</p>\n<figure data-asset-id=\"ef199929-5587-4a94-a365-7dfe83bf2c9f\" data-image-id=\"ef199929-5587-4a94-a365-7dfe83bf2c9f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7ac4c6f3-c3d9-4034-94d8-63ee73fe3922/QRC-D_04%20Line%20load.png\" data-asset-id=\"ef199929-5587-4a94-a365-7dfe83bf2c9f\" data-image-id=\"ef199929-5587-4a94-a365-7dfe83bf2c9f\" alt=\"\"></figure>\n<p><em>Example of a uniform load</em></p>\n<p><br></p>\n<figure data-asset-id=\"290fcd80-c299-4698-bb0d-d7e4f71d4a38\" data-image-id=\"290fcd80-c299-4698-bb0d-d7e4f71d4a38\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/26bf6cbb-7f40-4ee7-90c2-2a1bea4eb2df/RC-D_04_03.png\" data-asset-id=\"290fcd80-c299-4698-bb0d-d7e4f71d4a38\" data-image-id=\"290fcd80-c299-4698-bb0d-d7e4f71d4a38\" alt=\"\"></figure>\n<p><em>Example of a trapezoidal load</em></p>\n<p><br></p>\n<p>The principle of applying the load is almost identical to the point load.</p>\n<figure data-asset-id=\"16569610-8b1e-45b3-9c82-dd16ce3ac518\" data-image-id=\"16569610-8b1e-45b3-9c82-dd16ce3ac518\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/265bd9ae-1dba-4f65-87d6-d810c098d1a2/RC-D_04_15.png\" data-asset-id=\"16569610-8b1e-45b3-9c82-dd16ce3ac518\" data-image-id=\"16569610-8b1e-45b3-9c82-dd16ce3ac518\" alt=\"\"></figure>\n<h3>Surface load</h3>\n<p>The application of the surface load works the same way. It is applied to the nodes of the elements of the concrete structure's mesh.</p>\n<figure data-asset-id=\"d05754be-13c0-456f-9480-51ee0053ed3b\" data-image-id=\"d05754be-13c0-456f-9480-51ee0053ed3b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/44d85026-322e-49b1-966b-d78da3280066/RC-D_04_16.png\" data-asset-id=\"d05754be-13c0-456f-9480-51ee0053ed3b\" data-image-id=\"d05754be-13c0-456f-9480-51ee0053ed3b\" alt=\"\"></figure>\n<h3>Self-weight</h3>\n<p>The <a data-item-id=\"0e81f59d-e89c-424e-8e89-d2b86855097e\" href=\"\">self-weight</a> is a version of the surface load. The intensities are automatically calculated according to the selected cross-section.</p>\n<figure data-asset-id=\"c85e1189-a9e4-4ba3-a54e-964352995583\" data-image-id=\"c85e1189-a9e4-4ba3-a54e-964352995583\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/6c2fed57-fee4-4e62-af95-ff97d681523c/RC-D_04_17.png\" data-asset-id=\"c85e1189-a9e4-4ba3-a54e-964352995583\" data-image-id=\"c85e1189-a9e4-4ba3-a54e-964352995583\" alt=\"\"></figure>"
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"value": "<p>The end forces of a member of the frame analysis model are transferred to the ends of member segments. Eccentricities of the members caused by the joint design are respected during transfer.</p>\n<p>The analysis model created by the CBFEM method corresponds to the real joint very precisely, whereas the analysis of internal forces is performed on a much idealized 3D FEM bar model, where individual beams are modeled using center lines, and the joints are modeled using immaterial nodes.</p>\n<figure data-asset-id=\"10096aab-7085-4165-96a7-c5a05676a1af\" data-image-id=\"10096aab-7085-4165-96a7-c5a05676a1af\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5627020e-d90c-42b3-be1e-dd6ad0cc2ba1/Structural%20design%20of%20steel%20connections%20-%20Loads.png\" data-asset-id=\"10096aab-7085-4165-96a7-c5a05676a1af\" data-image-id=\"10096aab-7085-4165-96a7-c5a05676a1af\" alt=\"The article is focusing on the internal forces in the steel connections. Structural design of welded and bolted connections. IDEA StatiCa - structural analysis software.\"></figure>\n<p><em>Joint of a vertical column and a horizontal beam</em></p>\n<p>The internal forces are analyzed using 1D members in the 3D model. There is an example of the internal forces in the following figure.</p>\n<figure data-asset-id=\"0bfcbcb4-ae12-4731-a21e-87704c4a6d9a\" data-image-id=\"0bfcbcb4-ae12-4731-a21e-87704c4a6d9a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f94c9234-06f3-455f-b8c0-0718fb1f3082/M_V.png\" data-asset-id=\"0bfcbcb4-ae12-4731-a21e-87704c4a6d9a\" data-image-id=\"0bfcbcb4-ae12-4731-a21e-87704c4a6d9a\" alt=\"\"></figure>\n<p><em>Internal forces in horizontal beam; M and V are the end forces at joint</em></p>\n<p>The effects caused by a member on the joint are important to designing the joint (connection). The effects are illustrated in the following figure:</p>\n<figure data-asset-id=\"8d26d59b-f842-4e4d-b55b-f667ee2a2e6a\" data-image-id=\"8d26d59b-f842-4e4d-b55b-f667ee2a2e6a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/bf7d9959-a914-4692-92b9-9c8e34bec9d7/1D_CBFEM.png\" data-asset-id=\"8d26d59b-f842-4e4d-b55b-f667ee2a2e6a\" data-image-id=\"8d26d59b-f842-4e4d-b55b-f667ee2a2e6a\" alt=\"\"></figure>\n<p><em>Effects of the member on the joint; CBFEM model is drawn in dark blue color</em></p>\n<p>Moment M and shear force V act in the theoretical joint. The point of the theoretical joint does not exist in the CBFEM model, thus the load cannot be applied here. The model must be loaded by actions M and V, which have to be transferred to the end of the segment in the distance r</p>\n<p><em>M</em><sub>c</sub> = <em>M</em> – <em>V</em> ∙ <em>r</em></p>\n<p><em>V</em><sub>c</sub> = <em>V</em></p>\n<p>In the CBFEM model, the end section of the segment is loaded by moment <em>M</em><sub>c</sub> and force <em>V</em><sub>c</sub>.</p>\n<p>When designing the joint, its real position relative to the theoretical point of the joint must be determined and respected. The internal forces in the position of the real joint are mostly different from the internal forces in the theoretical point of joint. Thanks to the precise CBFEM model, the design is performed on reduced forces – see moment <em>M</em><sub>r</sub> in the following figure:</p>\n<figure data-asset-id=\"9dea301a-b4b0-45ac-a201-17d2166608e9\" data-image-id=\"9dea301a-b4b0-45ac-a201-17d2166608e9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/41b9b039-09df-4358-a5df-193329807c2b/Mr.png\" data-asset-id=\"9dea301a-b4b0-45ac-a201-17d2166608e9\" data-image-id=\"9dea301a-b4b0-45ac-a201-17d2166608e9\" alt=\"\"></figure>\n<p><em>Bending moment on CBFEM model: The arrow points to the real position of the connection</em></p>\n<p>When loading the joint, it must be respected that the solution of the real joint must correspond to the theoretical model used for the calculation of internal forces. This is fulfilled for rigid joints, but the situation may be completely different for hinges.</p>\n<figure data-asset-id=\"e622907f-9a02-4a70-ac5d-40dcd37bce98\" data-image-id=\"e622907f-9a02-4a70-ac5d-40dcd37bce98\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/73a64f02-d658-4e3e-a965-dc3c77832767/pinned.png\" data-asset-id=\"e622907f-9a02-4a70-ac5d-40dcd37bce98\" data-image-id=\"e622907f-9a02-4a70-ac5d-40dcd37bce98\" alt=\"\"></figure>\n<p><em>Position of hinge in theoretical 3D FEM model and in the real structure</em></p>\n<p>It is illustrated in the previous figure that the position of the hinge in the theoretical 1D members model differs from the real position in the structure. The theoretical model does not correspond to reality. When applying the calculated internal forces, a significant bending moment is applied to the shifted joint, and the designed joint is overlarge or cannot be designed either. The solution is simple – both models must correspond. Either the hinge in 1D member model must be defined in the proper position, or the shear force must be shifted to get a zero moment in the position of the hinge.</p>\n<figure data-asset-id=\"74ae8357-4575-43b3-b11f-ecefebe5b415\" data-image-id=\"74ae8357-4575-43b3-b11f-ecefebe5b415\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d108966f-a62c-4b08-8a51-ed0db6d10eee/M_r_CBFEM.png\" data-asset-id=\"74ae8357-4575-43b3-b11f-ecefebe5b415\" data-image-id=\"74ae8357-4575-43b3-b11f-ecefebe5b415\" alt=\"\"></figure>\n<p><em>Shifted distribution of bending moment on beam: zero moment is at the position of the hinge</em></p>\n<p>The shift of the shear force can be defined in the table for the definition of the internal force.</p>\n<p>The location of the load effect has a big influence on the correct design of the connection. To avoid all misunderstandings, we allow the user to select from three options – <strong>Node</strong> / <strong>Bolts</strong> / <strong>Position</strong>.</p>\n<figure data-asset-id=\"412d71c8-6632-4943-90cb-5f4465a1e332\" data-image-id=\"412d71c8-6632-4943-90cb-5f4465a1e332\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/2f8a04e0-e53d-471b-862f-5a3cf91af8db/node_bolts_position.png\" data-asset-id=\"412d71c8-6632-4943-90cb-5f4465a1e332\" data-image-id=\"412d71c8-6632-4943-90cb-5f4465a1e332\" alt=\"\"></figure>\n<p>Note that when selecting the Node option, the forces are applied at the end of a selected member, which is usually at the theoretical node unless the offset of the selected member is set in geometry.</p>\n<h4>Import loads from FEA programs</h4>\n<p>IDEA StatiCa enables to import of internal forces from <a data-item-id=\"4a9855d4-6081-4707-86d5-7f4ad2bb3a57\" href=\"\">third-party FEA programs</a>. FEA programs use an envelope of internal forces from combinations. IDEA StatiCa Connection is a program that resolves steel joint nonlinearly (elastic/plastic material model). Therefore, the envelope combinations cannot be used. IDEA StatiCa searches for extremes of internal forces (<em>N, V</em><em><sub>y</sub></em><em>, V</em><em><sub>z</sub></em><em>, M</em><em><sub>x</sub></em><em>, M</em><em><sub>y</sub></em><em>, M</em><em><sub>z</sub></em>) in all combinations at the ends of all members connected to the joint. For each such extreme value, also all other internal forces from that combination in all remaining members are used. Idea StatiCa determines the worst combination for each component (plate, weld, bolt etc.) in the connection.</p>\n<p>The user can modify this list of load cases. He can work with combinations in the wizard (or BIM), or he can delete some cases directly in <a data-item-id=\"b0a659df-8f92-4d1f-abb6-2efa02bad946\" href=\"\">IDEA StatiCa Connection</a>.</p>\n<p><strong>Warning!</strong></p>\n<p>It is necessary to take into account unbalanced internal forces during the import. This can happen in the following cases:</p>\n<ul>\n <li>Nodal force was applied to the position of the investigated node. The software cannot detect which member should transfer this nodal force and, therefore, it is not taken into account in the analysis model. <em>Solution: Do not use nodal forces in global analysis. If necessary, the force must be manually added to a selected member as a normal or shear force.</em></li>\n <li>Loaded, non-steel (usually timber or concrete) member is connected to the investigated node. Such member is not considered in the analysis, and their internal forces are ignored in the analysis. <em>Solution: Replace the concrete member with a concrete block and anchorage.</em></li>\n <li>The node is a part of a slab or a wall (usually from concrete). The slab or the wall is not part of the model, and its internal forces are ignored. <em>Solution: Replace the concrete slab or wall with a concrete block and anchorage.</em></li>\n <li>Some members are connected to the investigated node via rigid links. Such members are not included in the model, and their internal forces are ignored. <em>Solution: Add these members into the list of connected members manually.</em></li>\n <li>Seismic load cases are analyzed in the software. Most FEA software offer the modal analysis to solve seismicity. The results of internal forces of seismic load cases provide usually only internal force envelopes in sections. Due to the evaluation method (square root of the sum of squares – SRSS), the internal forces are all positive and it is not possible to find the forces matching to the selected extreme. It is not possible to achieve a balance of internal forces. <em>Solution: Change the positive sign of some internal forces manually.</em></li>\n</ul>"
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