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. 3, 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=\"Fig. 5\tModel used to illustrate the use of the reinforcement design tools.\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 3\\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. 4.</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=\"Fig. 6\tResults from the linear analysis tool for defining reinforcement layout (red: areas in compression, blue: areas in tension).\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 4\\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. 5).</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=\"Fig. 7\tResults from the topology optimization design tool with 20% and 40% effective volume (red: areas in compression, blue: areas in tension).\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 5\\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 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": "Každá betonová konstrukce obsahuje části s určitou formou nespojitosti – krátkou konzolu, otvor, apod. Navzdory tomu, že se diskontinuity nacházejí v každé betonové konstrukci, doposud neexistovalo žádné jasné a jednoznačné řešení pro kompletní návrh a posouzení betonových detailů, stěn a příčníků."
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"value": "<p>V současné době se pro posouzení oblastí nespojitosti používají jednoúčelové specializované programy nebo excelovské tabulkové procesory založené na metodě příhradové analogie. Nebo naopak mohou být výjimečně využity vědecky orientované programy bez vazby na národní normy a předpisy a bez možnosti návrhu a optimalizace výztuže. Tato praxe vede k přílišnému zjednodušování nebo naopak k pokusu zbytečně simulovat realitu. Nová metoda a softwarový nástroj umožňují inženýrům efektivně, bezpečně a hospodárně navrhnout vhodné dimenze betonového prvku, umístění a množství výztuže, a to na základě platných norem. </p>\n<p>Metoda je založena na počítačové implementaci modelu tlakových polí. Uvažují se podobné zjednodušené předpoklady jako pro ruční výpočty, přitom však vylepšení modelu umožňuje řešení mezních stavů použitelnosti včetně deformací a je založeno na jasných materiálových vlastnostech. Model tlakových polí lze považovat za zobecněnou metodu příhradové analogie, ve které jsou však uvažovány skutečné oblasti namáhané napětím namísto výslednic sil. Ověření metody bylo provedeno vůči případům nezávislým na normách, jakož i porovnáním s výpočty podle existujících norem s materiálovými zákony definovanými těmito normami.</p>\n<p>Tento článek byl publikován autory J. Navrátil, P. Ševčík, L. Michalčík, P. Foltyn a J. Kabeláč na konferenci 24. Betonářské dny (2017).</p>"
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"value": "<p>Při výpočtu výsledků MSP se bere v úvahu pouze pružné chování betonu. Jinými slovy, pro beton se uvažuje nekonečný lineární diagram napětí a deformace. Při kontrole MSP lze zobrazit dlouhodobé nebo krátkodobé účinky. Jaký je rozdíl mezi těmito dvěma účinky? Přečtěte si článek níže (odstavec Beton MSP), kde se dozvíte více.</p>\n<ul>\n <li><a data-item-id=\"1838439f-0398-4754-b0c9-6f627127a407\" href=\"\">Materiálový model (EN)</a></li>\n</ul>\n<h2>Napětí</h2>\n<p>Existují dvě možnosti zobrazení výsledků pro beton a výztuž: </p>\n<ul>\n <li>poměr napětí a mezního napětí </li>\n <li>samotné napětí </li>\n</ul>\n<p>Napětí se vypočítají pro <strong>charakteristické</strong> a<strong> kvazistálé</strong> kombinace zatížení.</p>\n<h4>Poměr napětí a limitního napětí</h4>\n<p>Výsledky jsou jasné na první pohled: Zelená barva znamená využití do 90 %, oranžová 90-100 % využití a červená nad 100 %.</p>\n<p>O tom, jak se mezní hodnota určuje, se dočtete v následujícím článku.</p>\n<ul>\n <li><a data-item-id=\"70b033ed-8364-4692-a84d-8eda80f00dce\" href=\"\">Mezní stav použitelnosti</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>Napětí</h4>\n<p>Způsob zobrazení je podobný výsledkům MSÚ (v tomto případě je napětí z výpočtu s pružným chováním betonu). Lze zobrazit rozložení napětí v betonu σ<sub>c</sub> pro aplikovanou část zatížení. Známé také jako hlavní napětí σ<sub>2</sub>.</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>Trhliny</h2>\n<p>V této části se seznámíte se všemi čtyřmi možnostmi zobrazení výsledků kontroly trhlin. Přečtěte si další články, kde se dozvíte více o výpočtu.</p>\n<ul>\n <li><a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">Hlavní předpoklady a limity CSFM</a></li>\n <li><a data-item-id=\"b42f7f51-b2ee-464e-bfeb-5170776cbd10\" href=\"\">Konstrukční ověření prvků v IDEA StatiCa Detail</a></li>\n</ul>\n<p>Trhliny se počítají pouze pro kombinace <strong>kvazistálého</strong> zatížení.</p>\n<h4>Poměr šířky trhliny a limitní šířky trhliny</h4>\n<p>Mezní hodnotu w<sub>lim</sub> lze nastavit na horním pásu karet. Standardně je podle Eurokódu nastavena hodnota w<sub>lim</sub> = 0,3 mm. Výsledky jsou opět barevně odlišeny (zelená/oranžová/červená), aby byla kontrola zřejmá na první pohled.</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>Šířka trhliny </h4>\n<p>Tato funkce slouží k zobrazení šířky trhliny pro každý jednotlivý prvek výztuže. </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>Vzdálenost mezi trhlinami</h4>\n<p>Viz odkazy na začátku stránky. Článek vysvětluje metodu výpočtu vzdálenosti mezi stabilizovanými trhlinami.</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>Prezentace vzdálenosti trhlin je pouze schematická. Nezobrazuje vzdálenost trhlin vypočtenou pro výpočet.</p>\n<h4>Nevyztužená oblast</h4>\n<p>Šířka trhliny se kontroluje pouze v blízkosti výztuže. Kontrola trhlin se neprovádí v nevyztužených zónách.</p>\n<p>Tento výsledek jednoduše ukazuje nevyztužené oblasti, kde se pravděpodobně objeví trhliny. Doporučuje se navrhnout zesílení těchto oblastí.</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>Průhyby</h2>\n<p>See the options below:</p>\n<ul>\n <li><em>u</em><em><sub>z,st</sub></em> - <strong>Okamžitý průhyb</strong> způsobený celkovým zatížením - vypočtený <strong>s krátkodobými tuhostmi Ec.</strong></li>\n <li><em>u</em><em><sub>z,lt</sub></em> -<strong>Dlouhodobý průhyb</strong> způsobený dlouhodobým zatížením (trvalý a předpínací typ zatížení) - vypočtený s <strong>dlouhodobými tuhostmi Ec,eff</strong>. Jinými slovy, jsou zahrnuty součinitele dotvarování.</li>\n <li><em>Δu</em><em><sub>z</sub></em> - <strong>Přírůstek průhybu</strong> způsobený krátkodobým zatížením (proměnný typ zatížení) - vypočtený s <strong>krátkodobými tuhostmi Ec.</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>Průhyby se počítají pouze pro <strong>charakteristické</strong> kombinace zatížení.</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>Kromě tabulkových hodnot v části Data můžete zobrazit deformovaný tvar. 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