IDEA StatiCa RCS – Structural design of 2D concrete members

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    "value": "<h3>Slab</h3>\n<p>According to EN 1992-1-1, art. 5.3.1(4) a slab is a member, for which the minimum panel dimension is not less than 5 times the overall slab thickness. The slab is loaded only by bending moments and shear forces perpendicular to the centroidal plane of the slab. Detailing provisions check is performed according to EN 1992-1-1, art. 9.3.</p>\n<h3>Shell as a slab – Shell-slab</h3>\n<p>The geometry is defined similarly to the slab geometry definition.&nbsp; Unlike the slab, the shell-slab can be loaded by bending and membrane actions. Detailing provisions are checked according to rules for slab (EN 1992-1-1, art. 9.3).</p>\n<h3>Wall</h3>\n<p>According to EN 1992-1-1, art. 5.3.1(7) a wall is a member, for which the following principles are not fulfilled:</p>\n<ul>\n  <li>the section depth does not exceed 4 times its width</li>\n  <li>the height is at least 3 times the section depth</li>\n</ul>\n<p>The wall is loaded only by membrane action and detailing provisions are checked according to EN 1992-1-1, art. 9.6.</p>\n<h3>Shell as wall – Shell-wall</h3>\n<p>The geometry is defined similarly to the wall geometry definition. Unlike the wall, the shell-wall can be loaded by bending and membrane actions. Detailing provisions are checked according to detailing provisions for wall (EN 1992-1-1, art. 9.6).</p>\n<h3>Deep beam</h3>\n<p>According to EN 1992-1-1, art. 5.3.1(3) a deep beam is a member for which the span is less than 3 times the overall section depth. The deep beam can be loaded as the wall only by membrane actions. Detailing provisions are checked according to EN 1992-1-1, art. 9.7.</p>"
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    "value": "<p>A shell element measuring 1m x 1m is defined for the check. Reinforcement is input into this shell element. Reinforcement per linear meter is taken into account for the check of the 2D member.</p>\n<p>Predefined reinforcement templates can be used to input the reinforcement to the upper and the lower edges. It is possible to input general reinforcement into the slab.</p>\n<h3>The input of reinforcement using reinforcement templates</h3>\n<figure data-asset-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\" data-image-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/9d173812-b9e7-43b0-8a57-710bed97f254/Template.png\" data-asset-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\" data-image-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\" alt=\"\"></figure>\n<p>IDEA RCS supplies two templates for the input of reinforcement into a 2D element. One template is for the input of reinforcement at the upper surface, the other one is for the input of reinforcement at the lower surface.</p>\n<p>Both templates allow input of orthogonal reinforcement at the surfaces of the 2D element. Both templates enable the rotation of reinforcement about the local x-axis of the 2D element.</p>\n<figure data-asset-id=\"13318037-6d3f-4502-9179-cda963311c47\" data-image-id=\"13318037-6d3f-4502-9179-cda963311c47\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8a578ffb-961c-4c18-ad8f-1b4146d6be89/Dialog%20for%20definition%20of%202D%20reinforcement.png\" data-asset-id=\"13318037-6d3f-4502-9179-cda963311c47\" data-image-id=\"13318037-6d3f-4502-9179-cda963311c47\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Dialog for the definition of 2D reinforcement}}}\\]</em></p>\n<p><br></p>\n<figure data-asset-id=\"06f2122f-e1cf-423d-aa79-744094c2a218\" data-image-id=\"06f2122f-e1cf-423d-aa79-744094c2a218\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/c1697edd-176d-4719-871e-f0be624844e6/Schema%20of%20defined%20reinforcement%20at%20the%20lower%20surface%20of%202D%20element.png\" data-asset-id=\"06f2122f-e1cf-423d-aa79-744094c2a218\" data-image-id=\"06f2122f-e1cf-423d-aa79-744094c2a218\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Schema of defined reinforcement at the lower surface of 2D element}}}\\]</em></p>\n<h3>The input of general reinforcement</h3>\n<p>Each reinforcement layer is defined in the section and in the plan.</p>\n<figure data-asset-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\" data-image-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/31561fe5-9548-4c5e-acd2-7976ab4133be/general%20input.png\" data-asset-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\" data-image-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{General input}}}\\]</em></p>\n<h3>Type of reinforcement</h3>\n<p>The type of reinforcement bar has to be defined to be able to perform the check of detailing provisions. For 2D elements of type</p>\n<ul>\n  <li>Slab and shell–slab – for checks according to EN 1992-1-1, art. 9.3.1.1\n    <ul>\n      <li>Main reinforcement</li>\n      <li>Distribution reinforcement</li>\n    </ul>\n  </li>\n  <li>Wall, Shell-wall, and Deep beam – for check according to EN 1992-1-1, art 9.6.2 and 9.6.3\n    <ul>\n      <li>Horizontal reinforcement</li>\n      <li>Vertical reinforcement</li>\n    </ul>\n  </li>\n</ul>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td><strong>The distribution reinforcement </strong>of slabs and shell-slabs is taken into account only for the check of detailing provisions, it is not used in other checks of the 2D elements.</td></tr>\n</tbody></table>"
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    "value": "<h3>The input of internal forces</h3>\n<p>The input of internal forces of 2D members depends on the type of 2D element:</p>\n<ul>\n  <li><strong>Shell-slab</strong> – membrane forces (n<sub>x</sub>, n<sub>y</sub> and n<sub>xy</sub>), bending moments (m<sub>x</sub>, m<sub>y</sub> and m<sub>xy</sub>) and shear forces (v<sub>x</sub> and v<sub>y</sub>) can be entered</li>\n  <li><strong>Shell- wall </strong>–<strong> </strong>membrane forces (n<sub>x</sub>, n<sub>y</sub> and n<sub>xy</sub>), bending moments (m<sub>x</sub>, m<sub>y</sub> and m<sub>xy</sub>) and shear forces (v<sub>x</sub> and v<sub>y</sub>) can be entered</li>\n  <li><strong>Slab</strong> – only bending moments (m<sub>x</sub>, m<sub>y</sub> and m<sub>xy</sub>) and shear forces (v<sub>x</sub> and v<sub>y</sub>) can be entered</li>\n  <li><strong>Wall</strong> – only membrane forces (n<sub>x</sub>, n<sub>y</sub> and n<sub>xy</sub>) can be entered</li>\n  <li><strong>Deep beam</strong> – only membrane forces (n<sub>x</sub>, n<sub>y</sub> and n<sub>xy</sub>) can be entered</li>\n</ul>\n<table><tbody>\n  <tr><td><br></td><td><strong>Description</strong></td></tr>\n  <tr><td>m<sub>x(y)</sub></td><td>Bending moment in the direction of x (y)-axis. A positive value causes tension at the lower surface of a 2D element.</td></tr>\n  <tr><td>m<sub>xy(yx)</sub></td><td>Torsional moment about y (x)-axis acting on the edge parallel to the axis x (y). Positive value causes tensional shear stress at the lower surface of a 2D element. Because in each point of the 2D element theorem the equality of horizontal shear stresses is valid, torsional moments m<sub>xy</sub> = m<sub>yx</sub> are equal in each point of 2D element too. Thus only value of m<sub>xy </sub>is entered in the program.</td></tr>\n  <tr><td>n<sub>x(y)</sub></td><td>Normal force in direction of x (y)-axis. Positive value acts in direction of x(y) axis and causes tension in section.</td></tr>\n  <tr><td>n<sub>xy(yx)</sub></td><td>Normal force acting in the centre plane in direction of y(x)-axis on edge parallel to x(y)-axis. Positive value acts in direction of x(y)-axis. Because in each point of the 2D element theorem the equality of horizontal shear stresses is valid, normal forces n<sub>xy</sub> = n<sub>yx</sub> are equal in each point of 2D element too. Thus only value of n<sub>xy </sub>is entered in the program.</td></tr>\n  <tr><td>v<sub>x(y)</sub></td><td>Shear force acting perpendicular to centre plane on edge parallel to x(y)-axis. Positive value acts in direction of z-axis.</td></tr>\n</tbody></table>\n<figure data-asset-id=\"d7527b12-91e9-4cad-95d9-c33e4c359259\" data-image-id=\"d7527b12-91e9-4cad-95d9-c33e4c359259\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/791c30e3-49b2-4e45-b7cd-b301bc788d70/Sign%20convention%20of%20internal%20forces.png\" data-asset-id=\"d7527b12-91e9-4cad-95d9-c33e4c359259\" data-image-id=\"d7527b12-91e9-4cad-95d9-c33e4c359259\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Sign convention of internal forces}}}\\]</em></p>\n<p>The following types of combinations have to be defined for checks:</p>\n<ul>\n  <li><strong>Ultimate limit state/Accidental</strong> – internal force components defined for this type of combinations are used for ULS checks of 2D elements:\n    <ul>\n      <li>Capacity N-M-M</li>\n      <li>Response N-M-M</li>\n      <li>Interaction</li>\n    </ul>\n  </li>\n</ul>\n<p>and the check of detailing provisions</p>\n<ul>\n  <li><strong>Characteristic</strong> – internal force components defined for this type of combination are used for check of stress limitation (SLS)</li>\n  <li><strong>Quasi-permanent </strong>– internal force components defined for this type of combination are used for check of crack width (SLS)</li>\n</ul>\n<figure data-asset-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\" data-image-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8f8a0710-3804-47a2-9316-ce40bc4dd087/Table%20of%20internal%20forces.png\" data-asset-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\" data-image-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\" alt=\"\"></figure>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>Internal forces components v<sub>x</sub> and v<sub>y</sub> are not required to be entered for combination types <strong>Characteristic</strong> and <strong>Quasi-permanent</strong>, because these values are not used in checks.</td></tr>\n</tbody></table>\n<h3>Determining the direction of the check</h3>\n<p>The direction of the check has to be determined for the proper check of the 2D element. The direction of the check can be entered for each combination type separately, using the following two methods:</p>\n<ul>\n  <li><strong>User defined direction </strong>– the user defines the check direction as an angle relative to the x-axis in plane of the 2D element. This option is set as default for combination type ULS and the predefined value of the angle is 0 degrees. Checks are performed in the following directions:\n    <ul>\n      <li>Defined direction</li>\n      <li>Direction perpendicular to defined direction</li>\n      <li>Direction of compression diagonal at the upper surface</li>\n      <li>Direction of compression diagonal at the lower surface</li>\n    </ul>\n  </li>\n  <li><strong>Direction of principal stresses</strong> – the check direction is calculated automatically as the direction of principal stresses at the upper and at the lower surface of the 2D element. This option is set as default for combination types Characteristic and Quasi-permanent. Checks are performed in the following directions:\n    <ul>\n      <li>Direction of principal stresses at the lower surface</li>\n      <li>Direction perpendicular to the direction of principal stresses at the lower surface</li>\n      <li>Direction of compression diagonal at the lower surface</li>\n      <li>Direction of principal stresses at the upper surface</li>\n      <li>Direction perpendicular to the direction of principal stresses at the upper surface</li>\n      <li>Direction of compression diagonal at the upper surface</li>\n    </ul>\n  </li>\n</ul>\n<figure data-asset-id=\"13cb2bfb-b44c-4539-9d68-86811373ef08\" data-image-id=\"13cb2bfb-b44c-4539-9d68-86811373ef08\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/66f0d110-3ed4-45d4-908e-8ac0da8ad84c/Direction%20of%20check.png\" data-asset-id=\"13cb2bfb-b44c-4539-9d68-86811373ef08\" data-image-id=\"13cb2bfb-b44c-4539-9d68-86811373ef08\" alt=\"\"></figure>\n<figure data-asset-id=\"e09a5997-025d-450e-999f-78485d3f25fa\" data-image-id=\"e09a5997-025d-450e-999f-78485d3f25fa\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/65ec297a-9bab-454b-b1c3-b030525c6f49/Recalculated%20internal%20forces%20in%20input%20direction%20by%20theory%20of%20Baumann.png\" data-asset-id=\"e09a5997-025d-450e-999f-78485d3f25fa\" data-image-id=\"e09a5997-025d-450e-999f-78485d3f25fa\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Recalculated internal forces in input direction by theory of Baumann}}}\\]</em></p>\n<h4>Analysis of check direction for ultimate limit state</h4>\n<p><strong>Analysis 1</strong></p>\n<p>For a 2D element loaded only by bending moments (m<sub>x</sub> = 20 kNm/m, m<sub>y</sub> = 10 kNm/m, m<sub>xy</sub> = 5 kNm/m ) with the angle of reinforcement and angle of check direction changed for the ultimate limit state - the results are displayed in the following graph:</p>\n<figure data-asset-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\" data-image-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/35ebc4ca-5001-4d06-aedd-92f9a0262685/Analysis%201.png\" data-asset-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\" data-image-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\" alt=\"\"></figure>\n<p>The analysis implies:</p>\n<ul>\n  <li>If reinforcement bars are perpendicular to each other, check results are similar for different check direction angles, they are not dependent on the defined reinforcement angle and the maximum value of the check is found for angles 0, 45, and 90 degrees. Thus this check can be performed for a predefined direction of a check angle of 0 degrees.</li>\n  <li>If reinforcement bars are not perpendicular to each other, the results of the checks differ significantly and the maximum check value is achieved approximately in the direction corresponding with the direction of average reinforcement.&nbsp;Thus it is recommended to change the predefined check direction or to perform checks in more directions in cases when reinforcement bars are not perpendicular to each other.</li>\n</ul>\n<p><strong>Analysis 2</strong></p>\n<p>For the orthogonal reinforcement, the values of bending moments and the angle have been changed&nbsp;for the ULS code-check. Results are represented in the graph:</p>\n<figure data-asset-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\" data-image-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/94e37635-06c1-4972-b08f-650691e78a4e/Analysis%202.png\" data-asset-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\" data-image-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\" alt=\"\"></figure>\n<p>The analysis implies that even for different values of bending moments the maximum value of the ultimate limit state check is found for check directions 0, 45, and 90 degrees. Thus the check can be performed for a predefined check angle of 0 degrees. A similar conclusion is valid for 2D elements loaded by normal force only or loaded by normal force combined with bending moments.</p>\n<h3>Recalculation of internal forces to directions of check</h3>\n<p>The defined internal forces are recalculated to the check directions using the Baumann transformation formula, described in Baumann, Th. : \"Zur Frage der Netzbewehrung von Flächentragwerken\". In : Der Bauingenieur 47 (1972), Berlin 1975. The calculation procedure is as follows:</p>\n<ol>\n  <li>Calculation of normal forces at both surfaces of the 2D element</li>\n  <li>Calculation of principal forces at both surfaces of the 2D element</li>\n  <li>Calculation of recalculated forces for each surface to the defined direction of check</li>\n  <li>Calculation of recalculated forces for each surface to the center</li>\n  <li>Recalculation of shear forces to the defined direction of check</li>\n</ol>\n<h4>Calculation of normal forces at both surfaces of the 2D element</h4>\n<p>Defined internal forces are recalculated to both surfaces using the following formulas:</p>\n<p>\\[{{n}_{x,low\\left( upp \\right)}}=\\frac{{{n}_{x}}}{2}+\\left( - \\right)\\frac{{{m}_{x}}}{z}\\]</p>\n<p>\\[{{n}_{y,low\\left( upp \\right)}}=\\frac{{{n}_{y}}}{2}+\\left( - \\right)\\frac{{{m}_{y}}}{z}\\]</p>\n<p>\\[~~~~~{{n}_{xy,low\\left( upp \\right)}}=\\frac{{{n}_{xy}}}{2}+\\left( - \\right)\\frac{{{m}_{xy}}}{z}\\]</p>\n<p>The lever arm of internal forces (z) has to be determined for the recalculation of internal forces. The lever arm of internal forces is determined from the method of limit strain at loading by the principal bending moment in directions of the principal moments m<sub>1</sub> at both surfaces. If the principal moments are equal to zero or if the equilibrium is not found in the direction of principal moments, the lever arm of internal forces is determined according to the formula:</p>\n<p>\\[z=x\\cdot d\\]</p>\n<table><tbody>\n  <tr><td><br></td><td><strong>Description</strong></td></tr>\n  <tr><td>x</td><td>The coefficient for calculation of the internal forces arm is defined in the National code setup.</td></tr>\n  <tr><td>d</td><td>The effective height of the cross-section calculated separately for the upper and the lower surfaces of the 2D element. For the lower surface, it is a distance from the centroid of reinforcement bars at the lower surface to the upper edge of the cross-section. For the upper surface, it is a distance from the centroid of reinforcement bars at the upper surface to the lower edge of the cross-section.</td></tr>\n</tbody></table>\n<figure data-asset-id=\"7c8907f2-b9aa-403c-b675-ce3bfad367a4\" data-image-id=\"7c8907f2-b9aa-403c-b675-ce3bfad367a4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d4a45e04-e8ff-4789-8693-772188e274de/Arm%20of%20internal%20forces.png\" data-asset-id=\"7c8907f2-b9aa-403c-b675-ce3bfad367a4\" data-image-id=\"7c8907f2-b9aa-403c-b675-ce3bfad367a4\" alt=\"\"></figure>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>The arm of internal forces can be verified in the Response N-M-M check. Only the bending moments have to be entered and the check direction has to correspond with the direction of the principal moment.</td></tr>\n</tbody></table>\n<p>In the following diagram, a verification of the internal forces lever arm is displayed for bending moments m<sub>x</sub> = 20 kNm/m, m<sub>y</sub> = 10 kNm/m,&nbsp;m<sub>xy</sub> = 5 kNm/m. The direction of principal moments has been calculated as α<sub>m1</sub> = 22.5 degrees and the response of cross-section was calculated to determine the internal forces lever arm.</p>\n<figure data-asset-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\" data-image-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/29d59e0b-33e4-42d3-991a-ef8d4cedc1bf/Verification%20of%20the%20internal%20forces_1.png\" data-asset-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\" data-image-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\" alt=\"\"></figure>\n<figure data-asset-id=\"2f3fb7b4-7943-4e3a-8959-646ff48030e3\" data-image-id=\"2f3fb7b4-7943-4e3a-8959-646ff48030e3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/867a7d2a-480a-45ec-8ac0-0bfb2870f33f/Verification%20of%20the%20internal%20forces_2.png\" data-asset-id=\"2f3fb7b4-7943-4e3a-8959-646ff48030e3\" data-image-id=\"2f3fb7b4-7943-4e3a-8959-646ff48030e3\" alt=\"\"></figure>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>Internal force lever arms for recalculation of internal forces in the direction of the check and internal force lever arms for checks can be different, because the internal force lever arm for recalculation is determined on a cross-section loaded by principal moments in the direction of principal moments, and the internal force lever arm for the check is determined on a cross-section loaded by bending moments and normal forces in the direction of the check. Values of internal force lever arms for all combination types are displayed in the table <strong>Recalculated forces</strong> in the navigator <strong>Internal forces in section</strong>.</td></tr>\n</tbody></table>\n<figure data-asset-id=\"febfc639-2888-43a0-9c80-db523b8beb10\" data-image-id=\"febfc639-2888-43a0-9c80-db523b8beb10\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a778abd2-823d-479c-a9ed-bded913dcd41/Recalculated%20forces.png\" data-asset-id=\"febfc639-2888-43a0-9c80-db523b8beb10\" data-image-id=\"febfc639-2888-43a0-9c80-db523b8beb10\" alt=\"\"></figure>\n<h4>Calculation of internal forces at both surfaces</h4>\n<p>Principal forces at both surfaces of the 2D element are calculated using the formula:</p>\n<p>\\[{{n}_{1,bot\\left( top \\right)}}=\\frac{{{n}_{x,low\\left( upp \\right)+}}{{n}_{y,low\\left( upp \\right)}}}{2}+\\frac{1}{2}\\sqrt{{{\\left( {{n}_{x,low\\left( upp \\right)-}}{{n}_{y,low\\left( upp \\right)}} \\right)}^{2}}+4\\cdot {{n}_{xy,low\\left( upp \\right)}}}\\]</p>\n<p>\\[{{n}_{2,bot\\left( top \\right)}}=\\frac{{{n}_{x,low\\left( upp \\right)+}}{{n}_{y,low\\left( upp \\right)}}}{2}-\\frac{1}{2}\\sqrt{{{\\left( {{n}_{x,low\\left( upp \\right)-}}{{n}_{y,low\\left( upp \\right)}} \\right)}^{2}}+4\\cdot {{n}_{xy,low\\left( upp \\right)}}}\\]</p>\n<p>And the direction of principal forces is calculated using the formula:</p>\n<p>\\[{{\\alpha }_{n1,low\\left( upp \\right)}}=0,5\\cdot {{\\tan }^{-1}}\\left( \\frac{2\\cdot {{n}_{xy,low\\left( upp \\right)}}}{{{n}_{x,low\\left( upp \\right)}}-{{n}_{y,low\\left( upp \\right)}}} \\right)\\]</p>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>Principal forces and the direction of principal forces for both surfaces of the 2D element are displayed for all combination types in the table <strong>Recalculated forces </strong>in the navigator<strong> Internal forces in section.</strong></td></tr>\n</tbody></table>\n<figure data-asset-id=\"d4c26cbc-15a3-44fc-a1e0-5a5eeed6326c\" data-image-id=\"d4c26cbc-15a3-44fc-a1e0-5a5eeed6326c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/d181818c-be1a-4f18-a1a9-5abdc2709210/Normal%20forces.png\" data-asset-id=\"d4c26cbc-15a3-44fc-a1e0-5a5eeed6326c\" data-image-id=\"d4c26cbc-15a3-44fc-a1e0-5a5eeed6326c\" alt=\"\"></figure>\n<h4>Calculation of recalculated internal forces at surfaces to the defined check direction</h4>\n<p>Recalculation of principal forces to the check directions is performed separately for each surface using the Baumann transformation formula:</p>\n<p>\\[{{n}_{surface,i,low\\left( upp \\right)}}=\\frac{{{n}_{1,low\\left( upp \\right)}}\\cdot \\sin \\left( {{\\alpha }_{j,low\\left( upp \\right)}} \\right)\\cdot \\sin \\left( {{\\alpha }_{k,low\\left( upp \\right)}} \\right)+{{n}_{2,low\\left( upp \\right)}}\\cdot \\cos \\left( {{\\alpha }_{j,low\\left( upp \\right)}} \\right)\\cdot \\cos \\left( {{\\alpha }_{k,low\\left( upp \\right)}} \\right)}{\\sin \\left( {{\\alpha }_{j,low\\left( upp \\right)}}-{{\\alpha }_{i,low\\left( upp \\right)}} \\right)\\cdot \\sin \\left( {{\\alpha }_{k,low\\left( upp \\right)}}-{{\\alpha }_{i,low\\left( upp \\right)}} \\right)}\\]</p>\n<table><tbody>\n  <tr><td><br></td><td><strong>Description</strong></td></tr>\n  <tr><td>i, j, k, i</td><td><p>Index of check direction (internal forces recalculation direction) i, j, k, i = 1, 2, 3, 1 . E. G. For lower surface and calculation of force in j-direction (angle α<sub>2</sub>) the formula is:</p>\n<p>\\[{{n}_{surface,2,low}}=\\frac{{{n}_{1,low}}\\cdot \\sin {{\\alpha }_{3,low}}\\cdot \\sin {{\\alpha }_{1,low}}+{{n}_{2,low}}\\cdot \\cos {{\\alpha }_{3,low}}\\cdot \\cos {{\\alpha }_{1,low}}}{\\sin \\left( {{\\alpha }_{3,low}}-{{\\alpha }_{2,low}} \\right)\\cdot \\sin \\left( {{\\alpha }_{1,low}}-{{\\alpha }_{2,low}} \\right)}\\]</p>\n</td></tr>\n  <tr><td>&nbsp;\\[{{\\alpha }_{i,j,k,low\\left( upp \\right)}}\\]</td><td><p>The angle between the defined check direction or the direction of compressive strut and the direction of principal forces at the lower or upper surface of the 2D element.</p>\n<p>Defined check direction &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;α<sub>1, low(upp)</sub> = α<sub>1</sub> – α<sub> low(upp)</sub></p>\n<p>Dir. perpendicular to the defined direction &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;α<sub>2, low(upp)</sub> = α<sub>2</sub> – α<sub> low(upp)</sub></p>\n<p>The direction of check for compressive strut &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;α<sub>3, low(upp)</sub> = α<sub>3</sub> – α<sub> low(upp)</sub></p>\n</td></tr>\n  <tr><td>α<sub>1</sub></td><td>Defined check direction for the particular combination</td></tr>\n  <tr><td>α<sub>2</sub></td><td>The direction perpendicular to the defined direction, α<sub>2 </sub>= α<sub>1</sub> + 90 degrees</td></tr>\n  <tr><td>α<sub>3</sub></td><td>Check the direction in the direction of the compressive strut in the plane of the 2D element. This direction is optimized to minimize the force in this direction.</td></tr>\n</tbody></table>\n<p><br></p>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td><p>If the <strong>check direction </strong>is identical to the <strong>Principal stresses direction</strong>, the forces in the compressive strut are zero, thus this direction is neglected in the check</p>\n<p>The direction of the compressive strut for all states of stress except the hyperbolic state of stress (n<sub>1,low(upp)</sub> &gt; 0 and&nbsp;n<sub>1,low(upp)</sub> &lt; 0) can be calculated according to the formula:</p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;α<sub>3</sub> = 0,5(α<sub>1</sub> + α<sub>2</sub>)</p>\n<p>Recalculated internal forces for both surfaces of 2D element and all check directions including the direction of the compressive strut are displayed in the table <strong>Recalculated forces</strong></p>\n</td></tr>\n</tbody></table>\n<figure data-asset-id=\"c0a48427-2332-47ed-8401-3860e31463c1\" data-image-id=\"c0a48427-2332-47ed-8401-3860e31463c1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/a3e8d96c-ad72-41eb-9945-994dc90baa6e/Normal%20forces%20-%20angle.png\" data-asset-id=\"c0a48427-2332-47ed-8401-3860e31463c1\" data-image-id=\"c0a48427-2332-47ed-8401-3860e31463c1\" alt=\"\"></figure>\n<h4>Transformation of recalculated internal forces to the centroid of the cross-section</h4>\n<p>For the check of the 2D element, the surface forces in a particular direction have to be recalculated to the centroid of the cross-section. The result is normal force n<sub>d,i</sub> and bending moment m<sub>d,I</sub> acting in the centroid of the 2D element cross-section.</p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; m<sub>d,i</sub> = n<sub>lower,i</sub>·z<sub>s,low </sub>+ n<sub>upper,i</sub>·z<sub>s,upp</sub></p>\n<p><sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; n<sub>d,i</sub> = n<sub>lower,i</sub> + n<sub>upper,i</sub></p>\n<table><tbody>\n  <tr><td><br></td><td><strong>Description</strong></td></tr>\n  <tr><td>n<sub>lower,i</sub></td><td>Recalculated surface forces at lower surface in the i<sup>th</sup> check direction, when n<sub>lower,i</sub> = n<sub>surface,low,i</sub>.</td></tr>\n  <tr><td>n<sub>upper,i</sub></td><td>Recalculated internal forces at upper surface in the i<sup>th</sup> check direction, when&nbsp;n<sub>upper,i</sub> = n<sub>surface,upp,i</sub>.&nbsp;</td></tr>\n  <tr><td>z<sub>s,low (upp)</sub></td><td>Distance of centroid of compressed concrete or centroid of reinforcement at the lower (upper) surface, when z = z<sub>s,low </sub>+ z<sub>s,upp</sub></td></tr>\n</tbody></table>\n<p><br></p>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>If the directions of compressive struts at the lower and the upper surface are different, for the recalculation of forces to the centroid it is necessary to calculate virtual forces at the bottom surface in the direction of the compressive strut at the upper surface and vice versa.</td></tr>\n</tbody></table>\n<figure data-asset-id=\"3f29f801-2349-42f8-9b4e-c83e55261963\" data-image-id=\"3f29f801-2349-42f8-9b4e-c83e55261963\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/8b4256d5-68ca-4407-842f-814f36674336/Recalculated%20design%20forces.png\" data-asset-id=\"3f29f801-2349-42f8-9b4e-c83e55261963\" data-image-id=\"3f29f801-2349-42f8-9b4e-c83e55261963\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Recalculated design forces}}}\\]</em></p>\n<h4>Recalculation of shear forces to the defined direction of check</h4>\n<p>Shear forces are recalculated to the direction of the check using the formula:</p>\n<p>\\[{{v}_{d,i}}={{v}_{x}}\\cdot \\cos ({{\\alpha }_{i}})+{{v}_{y}}\\cdot \\sin ({{\\alpha }_{i}})\\]</p>\n<p>and the maximal shear force is:</p>\n<p>\\[{{v}_{d,max~}}=\\sqrt{{{v}_{x}}^{2}+{{v}_{y}}^{2}}\\]</p>\n<p>and it acts in the direction</p>\n<p>\\[\\beta ={{\\tan }^{-1}}\\left( \\frac{{{v}_{y}}}{{{v}_{x}}} \\right)\\]</p>\n<table><tbody>\n  <tr><td><br></td><td>Description</td></tr>\n  <tr><td>α<sub>i</sub></td><td>Check the angle in the i<sup>th</sup> direction</td></tr>\n</tbody></table>\n<p><br></p>\n<table><tbody>\n  <tr><td><strong>Remark:</strong></td></tr>\n  <tr><td>When checking a 2D element with relatively large shear forces it is suitable to check the 2D element in the direction of maximal shear force, which means that the defined direction check corresponds to angle β</td></tr>\n</tbody></table>\n<p><br></p>\n<h2>Comparison of internal forces recalculation using various methods</h2>\n<h4>Recalculation of forces acc. to EN 1992-1-1</h4>\n<p>The method described in EN 1992-1-1 is used in several programs and in practice to calculate design internal forces. EN 1992-1-1 takes into account only perpendicular reinforcement directions. Calculation of dimensioning forces with the influence of torsional moment is described in the following flowchart, where m<sub>y</sub>³ m<sub>x</sub>. A similar diagram can be created for moments m<sub>y</sub> &lt; m<sub>x</sub></p>\n<figure data-asset-id=\"aad2766e-2051-417c-b519-2289649459fc\" data-image-id=\"aad2766e-2051-417c-b519-2289649459fc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f4010414-2958-4772-824c-0b420cd7a19e/Diagram.png\" data-asset-id=\"aad2766e-2051-417c-b519-2289649459fc\" data-image-id=\"aad2766e-2051-417c-b519-2289649459fc\" alt=\"\"></figure>\n<table><tbody>\n  <tr><td><br></td><td><strong>Description</strong></td></tr>\n  <tr><td>m<sub>xd+, </sub>m<sub>xd-</sub></td><td>Dimensioning bending moment in the x-axis direction for design and check of reinforcement at the lower (-) or the upper (+) surface</td></tr>\n  <tr><td><p>m<sub>yd+</sub></p>\n<p>m<sub>yd-</sub></p>\n</td><td>Dimensioning bending moment in the y-axis direction for design and check of reinforcement at the lower (-) or the upper (+) surface</td></tr>\n  <tr><td>m<sub>cd+, </sub>m<sub>cd-</sub></td><td>Dimensioning bending moment in the compressive concrete strut at the lower (-) or the upper (+) surface, which has to be carried by concrete</td></tr>\n</tbody></table>\n<p><br></p>\n<p>Values of recalculated dimensioning forces for the type of member = Slab, calculated using the method described in EN, are displayed in the following table:</p>\n<figure data-asset-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\" data-image-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7b530370-d7d5-49bd-af9f-dc6890fb9709/Table%201.png\" data-asset-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\" data-image-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\" alt=\"\"></figure>\n<p>In IDEA StatiCa RCS values of moments at the upper and lower surface are not displayed, but values of normal forces at both surfaces and values of moments recalculated to the centroid of the cross-section.</p>\n<figure data-asset-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\" data-image-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/86dc5414-e18b-4110-8b41-48e7abcee21b/Recalculated%20design%20forces_2.png\" data-asset-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\" data-image-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\" alt=\"\"></figure>\n<p>Moments at the lower and upper surfaces can be calculated using surface forces, which are displayed in the numerical output, using the formula:</p>\n<p>\\[{{m}_{surface,i,dlow\\left( upp \\right)}}={{n}_{surface,i,low\\left( upp \\right)}}\\cdot z\\]</p>\n<p>Values of surface forces and recalculated moments are displayed in the following tables:</p>\n<figure data-asset-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\" data-image-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/16817eac-7184-4a8b-8714-c4a818f06087/Table%202.png\" data-asset-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\" data-image-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\" alt=\"\"></figure>\n<figure data-asset-id=\"8c5c70a5-af7e-4fd3-bd9f-2248215a3c57\" data-image-id=\"8c5c70a5-af7e-4fd3-bd9f-2248215a3c57\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/ab2907f6-e819-4cc4-8e18-0098ee6ef830/Table%203.png\" data-asset-id=\"8c5c70a5-af7e-4fd3-bd9f-2248215a3c57\" data-image-id=\"8c5c70a5-af7e-4fd3-bd9f-2248215a3c57\" alt=\"\"></figure>\n<p>The tables show, that moments at slab surfaces calculated in IDEA Concrete and calculated according to the method described in EN, correspond only at one surface. This difference is caused by different optimization of the concrete strut. The method used in IDEA StatiCa RCS searches for the angle of the compressive strut at the minimal force in the strut. The method described in EN searches for a minimal sum of negative forces from all directions.</p>\n<h4>Comparison of internal forces calculation with programs RFEM and SCIA Engineer</h4>\n<p>To compare the results of recalculated internal forces in programs IDEA Concrete, RFEM, and SCIA Engineer (SEN) a simple model of slab of dimensions 6 m x 4 m and thickness 200 mm was prepared. The slab is supported with line support at the edges and loaded with a uniform load of 10 kN/m<sup>2</sup>.</p>\n<p>To simplify the presentation only values of recalculated internal forces in one longitudinal section are displayed. The section distance from the slab edge is 1.5m. The internal forces calculated in the program RFEM were used as input values for IDEA Concrete.</p>\n<figure data-asset-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\" data-image-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/f95edfd4-6432-48af-a762-3d52735c7fc8/Table%204.png\" data-asset-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\" data-image-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\" alt=\"\"></figure>\n<p>The table shows good compliance of forces calculated in particular programs.</p>"
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    "value": "<p>Tal y como se describe en <a data-item-id=\"08114e5b-38b9-4a22-8909-df5524080155\" href=\"\"><strong>Esfuerzos internos</strong></a><strong> </strong>en el capítulo <strong>Transformación de los esfuerzos internos recalculados al</strong> centroide de la sección transversal, los esfuerzos de acotación superficial se transforman al centroide de una sección transversal de elemento 2D. El resultado de esta transformación es un momento flector y una fuerza normal, actuando en el centroide de una sección transversal rectangular, en la que la longitud del borde es de 1 m y la altura corresponde al espesor de la losa.</p>\n<p>Las comprobaciones del elemento 2D se realizan en todas las direcciones definidas a la vez. El programa convierte automáticamente la armadura a la dirección de comprobación mediante la fórmula:</p>\n<p>\\[{{A}_{Si,\\{alfa }}={{A}_{S}}\\cdot {{\\cos }^{2}}({{{alfa }_{i}})\\]</p>\n<table><tbody>\n  <tr><td></td><td><strong>Descripción</strong></td></tr>\n  <tr><td><sub>Asi,a</sub></td><td>Área de la <sup>i-ésima</sup> capa de refuerzo recalculada en la dirección a</td></tr>\n  <tr><td>Como</td><td>Área de la <sup>i-ésima</sup> capa de armadura del elemento 2D</td></tr>\n  <tr><td><sub>αi</sub></td><td>Ángulo entre la <sup>i-ésima</sup> capa de armadura y la dirección de comprobación</td></tr>\n</tbody></table>\n<table><tbody>\n  <tr><td><strong>Observación:</strong></td></tr>\n  <tr><td><strong>La distribución de la armadura</strong> en elementos 2D de tipo losa y cascarón-losa sólo se tiene en cuenta en la comprobación de la disposición de detalle, no se utiliza en otras comprobaciones de elementos 2D.</td></tr>\n</tbody></table>\n<h3>Resultados de las comprobaciones en direcciones definidas</h3>\n<p>Todas las comprobaciones activadas se realizan automáticamente en todas las direcciones requeridas. La presentación de los resultados es similar a la presentación de los resultados de los elementos 1D. La presentación para elementos 2D permite establecer la dirección a presentar. Los resultados de los elementos 2D se presentan en las direcciones de comprobación. Todas las direcciones, en las que se calcularon las comprobaciones, se dibujan en la presentación gráfica.</p>\n<p>Las flechas de la imagen representan las direcciones de comprobación, donde la naranja es la dirección del valor de comprobación máximo y la roja es la dirección de comprobación actual. Para cambiar la dirección actual, haga clic en la flecha o en el botón correspondiente de la cinta.</p>\n<figure data-asset-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\" data-image-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/e2212446-973e-4606-a3b1-03443cc33fe1/Arrows%20direction.png\" data-asset-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\" data-image-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\" alt=\"\"></figure>\n<table><tbody>\n  <tr><td><strong>Nota:</strong></td></tr>\n  <tr><td>Una vez finalizado el cálculo, las direcciones de comprobación de todas las comprobaciones se establecen en la dirección de utilización máxima de la sección transversal.</td></tr>\n</tbody></table>\n<p>Los resultados de las comprobaciones particulares se presentan en la dirección actual. El ángulo de la comprobación se muestra encima de la tabla con el resumen de la comprobación.</p>\n<p>Los resultados en la dirección extrema se imprimen en el informe.</p>\n<h3>Estado límite último</h3>\n<p>Los principios de la comprobación del estado límite último se describen en el manual de <a data-item-id=\"08dd67a9-0d8a-4013-a59a-b02f8feafceb\" href=\"\"><strong>fundamentos teóricos</strong></a> para elementos 1D. En los siguientes capítulos sólo se describen las diferencias para elementos 2D.</p>\n<h4>Comprobación de capacidad</h4>\n<p>La comprobación de capacidad no difiere de las comprobaciones de elementos 1D. La carga actúa sólo en un plano, por lo que el tipo de comprobación es N + M.</p>\n<h4>Comprobación de respuesta</h4>\n<p>Las comprobaciones de respuesta para determinadas direcciones de comprobación utilizan los mismos algoritmos que las comprobaciones de elementos 1D.</p>\n<h4>Comprobación de interacción</h4>\n<p>A diferencia de los elementos 1D, la comprobación de interacción se realiza sólo para evaluar la explotación V + M, la interacción de cortante y momento flector. Los valores<sub>VRd,c </sub>y<sub>VRd,max </sub>pueden verificarse en la tabla resumen de la comprobación de interacción.</p>\n<h4>Comparación de la comprobación de capacidad entre IDEA Concrete, RFEM y SCIA Engineer</h4>\n<p>Para comparar los resultados de la comprobación de capacidad con RFEM y SCIA Engineer se utilizaron los mismos datos descritos en <a data-item-id=\"08114e5b-38b9-4a22-8909-df5524080155\" href=\"\"><strong>Esfuerzos internos</strong></a><strong> </strong>en el capítulo <strong>Comparación del cálculo de esfuerzos internos</strong> con los programas RFEM y SCIA Engineer. La comparación se realizó en dos puntos de la losa.</p>\n<p>Debido a que los programas RFEM y SEN no comprueban la armadura real en la losa, sino que sólo diseñan el área de armadura necesaria, se utilizaron dos métodos para comparar el cálculo. El primero compara el aprovechamiento de la sección para la armadura necesaria diseñada en RFEM y SEN, asumiendo que la sección se aprovecha al 100% justo cuando se utiliza el área de armadura necesaria calculada.</p>\n<p>La explotación de la sección reforzada en hormigón IDEA se puede expresar relativamente entonces.</p>\n<p>Aprovechamiento relativo =<sub>As, req</sub> /<sub>As, RCS</sub> × 100 [%].</p>\n<table><tbody>\n  <tr><td></td><td><strong>Descripción</strong></td></tr>\n  <tr><td><sub>As, req</sub></td><td>Área de refuerzo requerida calculada en RFEM o SEN</td></tr>\n  <tr><td><sub>As, RCS</sub></td><td>Área de armadura en hormigón IDEA</td></tr>\n  <tr><td>100 [%]</td><td>Porcentaje</td></tr>\n</tbody></table>\n<p>La sección transversal en el Hormigón IDEA fue reforzada en la superficie inferior utilizando armadura d=10 mm en distancias de 200 mm en ambas direcciones, el área de la armadura en ambas direcciones es de 314 <sup>mm2</sup>.</p>\n<figure data-asset-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\" data-image-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/733f88e0-a150-4b07-a58d-6cadf3acfdb7/Table%205.png\" data-asset-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\" data-image-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\" alt=\"\"></figure>\n<p>La tabla muestra un buen cumplimiento de la explotación para todos los programas.</p>\n<p>La armadura con aproximadamente la misma área se definió en IDEA Concrete como la armadura requerida calculada en RFEM y SEN para el segundo método. Después, se comparó la explotación de la sección. Los resultados se muestran en la siguiente tabla:</p>\n<figure data-asset-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\" data-image-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/7d869414-d171-4e1b-a4b4-d7c0b44e184d/Table%206.png\" data-asset-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\" data-image-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\" alt=\"\"></figure>\n<p>La buena conformidad de los resultados también se muestra aquí.</p>\n<h3>Estado límite de servicio</h3>\n<h4>Limitación de tensión</h4>\n<p>La comprobación de la limitación de esfuerzos no difiere de la comprobación de elementos 1D.</p>\n<h4>Comprobación de la anchura de la grieta</h4>\n<p>Los elementos 1D comprueban de antemano la dirección de la grieta que se puede dibujar para elementos 2D.</p>\n<h3>Disposiciones de detalle</h3>\n<p>La comprobación de las disposiciones de detalle de los elementos 2D puede dividirse en dos grupos básicos:</p>\n<ul>\n  <li>Comprobación del porcentaje de armadura</li>\n  <li>Comprobación de las distancias entre barras</li>\n</ul>\n<p>La comprobación de las disposiciones de detalle depende también del tipo de elemento 2D. Las comprobaciones separadas para la armadura principal y de distribución se realizan para elementos de forjado y losa. La armadura vertical y horizontal se distingue para elementos de muro.</p>\n<p>La comprobación del porcentaje de armadura se realiza en la dirección de las tensiones principales. La armadura definida en el corte del elemento 2D (excepto la armadura de distribución) se transforma a las direcciones de las tensiones principales.</p>\n<p>La comprobación de la distancia entre barras se realiza perpendicularmente a la dirección de la armadura definida. Esta comprobación se realiza para todas las capas de armadura definidas y los valores límite dependen del tipo de elemento comprobado y del tipo de armadura definida.</p>\n<figure data-asset-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\" data-image-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\"><img src=\"https://assets-us-01.kc-usercontent.com:443/28eac049-c8ed-00e2-220c-12142a968dff/5219c67f-2812-4d58-962b-e81884616f01/Check%20of%20detailing.png\" data-asset-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\" data-image-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\" alt=\"\"></figure>"
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