根据 EN 1992-1-1 和 EN 1992-2 进行钢筋混凝土截面设计。
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Name: Theoretical background RCS - 2D - Types of 2D members
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"value": "<h3>板</h3>\n<p>根据 EN 1992-1-1 第 5.3.1(4) 条,板是最小板格尺寸不小于板总厚度 5 倍的构件。板仅承受弯矩和垂直于板形心平面的剪力。构造规定校核依据 EN 1992-1-1 第 9.3 条执行。</p>\n<h3>壳作为板 – 壳-板</h3>\n<p>几何形状的定义方式与板的几何定义类似。 与板不同,壳-板可承受弯曲和薄膜作用。构造规定依据板的规则进行校核(EN 1992-1-1 第 9.3 条)。</p>\n<h3>墙</h3>\n<p>根据 EN 1992-1-1 第 5.3.1(7) 条,墙是不满足以下条件的构件:</p>\n<ul>\n <li>截面高度不超过其宽度的 4 倍</li>\n <li>高度至少为截面高度的 3 倍</li>\n</ul>\n<p>墙仅承受薄膜作用,构造规定依据 EN 1992-1-1 第 9.6 条进行校核。</p>\n<h3>壳作为墙 – 壳-墙</h3>\n<p>几何形状的定义方式与墙的几何定义类似。与墙不同,壳-墙可承受弯曲和薄膜作用。构造规定依据墙的构造规定进行校核(EN 1992-1-1 第 9.6 条)。</p>\n<h3>深梁</h3>\n<p>根据 EN 1992-1-1 第 5.3.1(3) 条,深梁是跨度小于截面总高度 3 倍的构件。深梁与墙相同,仅承受薄膜作用。构造规定依据 EN 1992-1-1 第 9.7 条进行校核。</p>"
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Name: Theoretical background RCS - 2D - Reinforcement for 2D elements
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"value": "<p>为校核定义了一个1m x 1m的壳单元。钢筋输入到该壳单元中。每延米的钢筋用于二维构件的校核。</p>\n<p>可使用预定义的钢筋模板将钢筋输入到上边缘和下边缘。也可以向板中输入一般钢筋。</p>\n<h3>使用钢筋模板输入钢筋</h3>\n<figure data-asset-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\" data-image-id=\"fd2f905c-016a-4e31-9f0d-8abcb10aa60d\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9d173812-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 提供两种模板用于向二维单元输入钢筋。一种模板用于在上表面输入钢筋,另一种用于在下表面输入钢筋。</p>\n<p>两种模板均支持在二维单元表面输入正交钢筋。两种模板均可实现钢筋绕二维单元局部x轴的旋转。</p>\n<figure data-asset-id=\"13318037-6d3f-4502-9179-cda963311c47\" data-image-id=\"13318037-6d3f-4502-9179-cda963311c47\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8a578ffb-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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>一般钢筋的输入</h3>\n<p>每个钢筋层在截面和平面中定义。</p>\n<figure data-asset-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\" data-image-id=\"6e8ee58a-a6a2-4dcd-a4e4-76a01e56bb51\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/31561fe5-9548-4c5e-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>钢筋类型</h3>\n<p>必须定义钢筋的类型,以便能够执行构造规定的校核。对于以下类型的二维单元</p>\n<ul>\n <li>板和壳-板 – 按 EN 1992-1-1 第 9.3.1.1 条进行校核\n <ul>\n <li>主钢筋</li>\n <li>分布钢筋</li>\n </ul>\n </li>\n <li>墙、壳-墙和深梁 – 按 EN 1992-1-1 第 9.6.2 和 9.6.3 条进行校核\n <ul>\n <li>水平钢筋</li>\n <li>竖向钢筋</li>\n </ul>\n </li>\n</ul>\n<table><tbody>\n <tr><td><strong>备注:</strong></td></tr>\n <tr><td>板和壳-板的<strong>分布钢筋</strong>仅用于构造规定的校核,不用于二维单元的其他校核。</td></tr>\n</tbody></table>"
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Name: Theoretical background RCS - 2D - Internal forces
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"value": "<h3>内力的输入</h3>\n<p>二维构件内力的输入取决于二维单元的类型:</p>\n<ul>\n <li><strong>壳-板</strong> – 可输入薄膜力(n<sub>x</sub>、n<sub>y</sub> 和 n<sub>xy</sub>)、弯矩(m<sub>x</sub>、m<sub>y</sub> 和 m<sub>xy</sub>)和剪力(v<sub>x</sub> 和 v<sub>y</sub>)</li>\n <li><strong>壳-墙 </strong>–<strong> </strong>可输入薄膜力(n<sub>x</sub>、n<sub>y</sub> 和 n<sub>xy</sub>)、弯矩(m<sub>x</sub>、m<sub>y</sub> 和 m<sub>xy</sub>)和剪力(v<sub>x</sub> 和 v<sub>y</sub>)</li>\n <li><strong>板</strong> – 仅可输入弯矩(m<sub>x</sub>、m<sub>y</sub> 和 m<sub>xy</sub>)和剪力(v<sub>x</sub> 和 v<sub>y</sub>)</li>\n <li><strong>墙</strong> – 仅可输入薄膜力(n<sub>x</sub>、n<sub>y</sub> 和 n<sub>xy</sub>)</li>\n <li><strong>深梁</strong> – 仅可输入薄膜力(n<sub>x</sub>、n<sub>y</sub> 和 n<sub>xy</sub>)</li>\n</ul>\n<table><tbody>\n <tr><td><br></td><td><strong>说明</strong></td></tr>\n <tr><td>m<sub>x(y)</sub></td><td>沿 x(y)轴方向的弯矩。正值在二维单元下表面产生拉力。</td></tr>\n <tr><td>m<sub>xy(yx)</sub></td><td>绕 y(x)轴作用于平行于 x(y)轴边缘的扭矩。正值在二维单元下表面产生拉剪应力。由于在二维单元每一点处水平剪应力相等定理成立,扭矩 m<sub>xy</sub> = m<sub>yx</sub> 在二维单元每一点处也相等。因此程序中仅输入 m<sub>xy </sub>的值。</td></tr>\n <tr><td>n<sub>x(y)</sub></td><td>沿 x(y)轴方向的法向力。正值沿 x(y)轴方向作用,在截面中产生拉力。</td></tr>\n <tr><td>n<sub>xy(yx)</sub></td><td>作用于中面内、沿 y(x)轴方向、作用于平行于 x(y)轴边缘的法向力。正值沿 x(y)轴方向作用。由于在二维单元每一点处水平剪应力相等定理成立,法向力 n<sub>xy</sub> = n<sub>yx</sub> 在二维单元每一点处也相等。因此程序中仅输入 n<sub>xy </sub>的值。</td></tr>\n <tr><td>v<sub>x(y)</sub></td><td>垂直于中面、作用于平行于 x(y)轴边缘的剪力。正值沿 z 轴方向作用。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/791c30e3-49b2-4e45-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>校核时需定义以下组合类型:</p>\n<ul>\n <li><strong>承载能力极限状态/偶然</strong> – 为该组合类型定义的内力分量用于二维单元的承载能力极限状态校核:\n <ul>\n <li>承载力 N-M-M</li>\n <li>响应 N-M-M</li>\n <li>相关性</li>\n </ul>\n </li>\n</ul>\n<p>以及构造规定的校核</p>\n<ul>\n <li><strong>标准组合</strong> – 为该组合类型定义的内力分量用于应力限值校核(正常使用极限状态)</li>\n <li><strong>准永久组合</strong> – 为该组合类型定义的内力分量用于裂缝宽度校核(正常使用极限状态)</li>\n</ul>\n<figure data-asset-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\" data-image-id=\"6de3e1e7-cd01-4834-b305-61d4dfbcb1a1\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8f8a0710-3804-47a2-9316-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>备注:</strong></td></tr>\n <tr><td>内力分量 v<sub>x</sub> 和 v<sub>y</sub> 对于<strong>标准组合</strong>和<strong>准永久组合</strong>类型无需输入,因为这些值在校核中不使用。</td></tr>\n</tbody></table>\n<h3>校核方向的确定</h3>\n<p>为正确校核二维单元,需确定校核方向。校核方向可针对每种组合类型分别输入,采用以下两种方法:</p>\n<ul>\n <li><strong>用户自定义方向</strong> – 用户以相对于二维单元平面内 x 轴的角度定义校核方向。该选项为承载能力极限状态组合类型的默认设置,预设角度值为 0 度。校核在以下方向进行:\n <ul>\n <li>定义方向</li>\n <li>垂直于定义方向的方向</li>\n <li>上表面压力斜杆方向</li>\n <li>下表面压力斜杆方向</li>\n </ul>\n </li>\n <li><strong>主应力方向</strong> – 校核方向自动计算为二维单元上、下表面主应力方向。该选项为标准组合和准永久组合类型的默认设置。校核在以下方向进行:\n <ul>\n <li>下表面主应力方向</li>\n <li>垂直于下表面主应力方向的方向</li>\n <li>下表面压力斜杆方向</li>\n <li>上表面主应力方向</li>\n <li>垂直于上表面主应力方向的方向</li>\n <li>上表面压力斜杆方向</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/66f0d110-3ed4-45d4-908e-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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/65ec297a-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>承载能力极限状态校核方向分析</h4>\n<p><strong>分析 1</strong></p>\n<p>对于仅承受弯矩(m<sub>x</sub> = 20 kNm/m,m<sub>y</sub> = 10 kNm/m,m<sub>xy</sub> = 5 kNm/m)的二维单元,改变钢筋角度和承载能力极限状态校核方向角度,结果显示在以下图表中:</p>\n<figure data-asset-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\" data-image-id=\"d8412f9c-3f08-428c-84c0-ac41984e950b\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/35ebc4ca-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>分析表明:</p>\n<ul>\n <li>若钢筋相互垂直,不同校核方向角度下的校核结果相近,与所定义的钢筋角度无关,校核最大值出现在 0°、45° 和 90° 方向。因此,可采用预设校核角度 0° 进行校核。</li>\n <li>若钢筋不相互垂直,各校核结果差异显著,最大校核值大致出现在与平均钢筋方向对应的方向。因此,当钢筋不相互垂直时,建议更改预设校核方向或在多个方向进行校核。</li>\n</ul>\n<p><strong>分析 2</strong></p>\n<p>对于正交钢筋,改变弯矩值和角度进行承载能力极限状态规范校核,结果以图表表示:</p>\n<figure data-asset-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\" data-image-id=\"2c7ebe3f-ec72-4a8a-a262-56b08ca5d29b\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/94e37635-06c1-4972-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>分析表明,即使弯矩值不同,承载能力极限状态校核的最大值仍出现在 0°、45° 和 90° 校核方向。因此,可采用预设校核角度 0° 进行校核。对于仅承受法向力或法向力与弯矩组合作用的二维单元,同样适用类似结论。</p>\n<h3>内力向校核方向的换算</h3>\n<p>所定义的内力采用 Baumann 变换公式换算至校核方向,该公式见 Baumann, Th.:\"Zur Frage der Netzbewehrung von Flächentragwerken\",载于:Der Bauingenieur 47(1972),Berlin 1975。计算步骤如下:</p>\n<ol>\n <li>计算二维单元两个表面的法向力</li>\n <li>计算二维单元两个表面的主力</li>\n <li>将各表面的力换算至定义的校核方向</li>\n <li>将各表面的力换算至中心</li>\n <li>将剪力换算至定义的校核方向</li>\n</ol>\n<h4>计算二维单元两个表面的法向力</h4>\n<p>所定义的内力采用以下公式换算至两个表面:</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>内力换算时需确定内力力臂(z)。内力力臂由沿主弯矩 m<sub>1</sub> 方向在两个表面加载时的极限应变法确定。若主弯矩等于零,或在主弯矩方向未找到平衡,则内力力臂按以下公式确定:</p>\n<p>\\[z=x\\cdot d\\]</p>\n<table><tbody>\n <tr><td><br></td><td><strong>说明</strong></td></tr>\n <tr><td>x</td><td>内力力臂计算系数在国家规范设置中定义。</td></tr>\n <tr><td>d</td><td>截面有效高度,分别针对二维单元的上、下表面单独计算。对于下表面,为下表面钢筋重心至截面上边缘的距离。对于上表面,为上表面钢筋重心至截面下边缘的距离。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>备注:</strong></td></tr>\n <tr><td>内力力臂可在响应 N-M-M 校核中验证。仅需输入弯矩,且校核方向须与主弯矩方向一致。</td></tr>\n</tbody></table>\n<p>下图显示了弯矩 m<sub>x</sub> = 20 kNm/m、m<sub>y</sub> = 10 kNm/m、m<sub>xy</sub> = 5 kNm/m 时内力力臂的验证结果。主弯矩方向计算为 α<sub>m1</sub> = 22.5 度,并通过截面响应计算确定内力力臂。</p>\n<figure data-asset-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\" data-image-id=\"7d8b7af5-36c4-4f06-bb39-4825f5a1ee9d\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/29d59e0b-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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/867a7d2a-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>备注:</strong></td></tr>\n <tr><td>用于内力换算的内力力臂与用于校核的内力力臂可能不同,因为用于换算的内力力臂是在主弯矩方向上由主弯矩加载的截面上确定的,而用于校核的内力力臂是在校核方向上由弯矩和法向力加载的截面上确定的。所有组合类型的内力力臂值显示在导航栏<strong>截面内力</strong>中的<strong>换算力</strong>表格中。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>计算两个表面的内力</h4>\n<p>二维单元两个表面的主力采用以下公式计算:</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>主力方向采用以下公式计算:</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>备注:</strong></td></tr>\n <tr><td>二维单元两个表面的主力及主力方向对所有组合类型均显示在导航栏<strong>截面内力</strong>中的<strong>换算力</strong>表格中。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>将表面内力换算至定义的校核方向</h4>\n<p>主力向校核方向的换算针对每个表面分别采用 Baumann 变换公式进行:</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>说明</strong></td></tr>\n <tr><td>i, j, k, i</td><td><p>校核方向(内力换算方向)的索引 i, j, k, i = 1, 2, 3, 1。例如,对于下表面计算 j 方向(角度 α<sub>2</sub>)的力,公式为:</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> \\[{{\\alpha }_{i,j,k,low\\left( upp \\right)}}\\]</td><td><p>定义的校核方向或压杆方向与二维单元下表面或上表面主力方向之间的夹角。</p>\n<p>定义的校核方向 α<sub>1, low(upp)</sub> = α<sub>1</sub> – α<sub> low(upp)</sub></p>\n<p>垂直于定义方向的方向 α<sub>2, low(upp)</sub> = α<sub>2</sub> – α<sub> low(upp)</sub></p>\n<p>压杆的校核方向 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>特定组合的定义校核方向</td></tr>\n <tr><td>α<sub>2</sub></td><td>垂直于定义方向的方向,α<sub>2 </sub>= α<sub>1</sub> + 90 度</td></tr>\n <tr><td>α<sub>3</sub></td><td>沿二维单元平面内压杆方向的校核方向。该方向经优化以使该方向的力最小。</td></tr>\n</tbody></table>\n<p><br></p>\n<table><tbody>\n <tr><td><strong>备注:</strong></td></tr>\n <tr><td><p>若<strong>校核方向</strong>与<strong>主应力方向</strong>相同,则压杆中的力为零,因此该方向在校核中忽略不计。</p>\n<p>除双曲线应力状态(n<sub>1,low(upp)</sub> > 0 且 n<sub>1,low(upp)</sub> < 0)外,所有应力状态下压杆方向可按以下公式计算:</p>\n<p> α<sub>3</sub> = 0,5(α<sub>1</sub> + α<sub>2</sub>)</p>\n<p>二维单元两个表面及所有校核方向(包括压杆方向)的换算内力显示在<strong>换算力</strong>表格中。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>将换算内力转换至截面重心</h4>\n<p>为校核二维单元,需将特定方向的表面力换算至截面重心。结果为作用于二维单元截面重心处的法向力 n<sub>d,i</sub> 和弯矩 m<sub>d,I</sub>。</p>\n<p> 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> </sub> 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>说明</strong></td></tr>\n <tr><td>n<sub>lower,i</sub></td><td>第 i 个校核方向下表面的换算表面力,其中 n<sub>lower,i</sub> = n<sub>surface,low,i</sub>。</td></tr>\n <tr><td>n<sub>upper,i</sub></td><td>第 i 个校核方向上表面的换算内力,其中 n<sub>upper,i</sub> = n<sub>surface,upp,i</sub>。</td></tr>\n <tr><td>z<sub>s,low (upp)</sub></td><td>受压混凝土重心或下(上)表面钢筋重心的距离,其中 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>备注:</strong></td></tr>\n <tr><td>若下表面与上表面的压杆方向不同,则在将力换算至重心时,需计算下表面沿上表面压杆方向的虚拟力,反之亦然。</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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8b4256d5-68ca-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>将剪力换算至定义的校核方向</h4>\n<p>剪力采用以下公式换算至校核方向:</p>\n<p>\\[{{v}_{d,i}}={{v}_{x}}\\cdot \\cos ({{\\alpha }_{i}})+{{v}_{y}}\\cdot \\sin ({{\\alpha }_{i}})\\]</p>\n<p>最大剪力为:</p>\n<p>\\[{{v}_{d,max~}}=\\sqrt{{{v}_{x}}^{2}+{{v}_{y}}^{2}}\\]</p>\n<p>其作用方向为</p>\n<p>\\[\\beta ={{\\tan }^{-1}}\\left( \\frac{{{v}_{y}}}{{{v}_{x}}} \\right)\\]</p>\n<table><tbody>\n <tr><td><br></td><td>说明</td></tr>\n <tr><td>α<sub>i</sub></td><td>第 i 个方向的校核角度</td></tr>\n</tbody></table>\n<p><br></p>\n<table><tbody>\n <tr><td><strong>备注:</strong></td></tr>\n <tr><td>当校核剪力较大的二维单元时,宜沿最大剪力方向进行校核,即定义的校核方向对应角度 β。</td></tr>\n</tbody></table>\n<p><br></p>\n<h2>各方法内力换算结果比较</h2>\n<h4>按 EN 1992-1-1 进行力的换算</h4>\n<p>EN 1992-1-1 中描述的方法被多个程序及工程实践用于计算设计内力。EN 1992-1-1 仅考虑垂直钢筋方向。考虑扭矩影响的设计力计算流程如下图所示,其中 m<sub>y</sub>³ m<sub>x</sub>。对于 m<sub>y</sub> < m<sub>x</sub> 的情况,可建立类似图表。</p>\n<figure data-asset-id=\"aad2766e-2051-417c-b519-2289649459fc\" data-image-id=\"aad2766e-2051-417c-b519-2289649459fc\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>说明</strong></td></tr>\n <tr><td>m<sub>xd+, </sub>m<sub>xd-</sub></td><td>x 轴方向的设计弯矩,用于下(-)或上(+)表面钢筋的设计与校核</td></tr>\n <tr><td><p>m<sub>yd+</sub></p>\n<p>m<sub>yd-</sub></p>\n</td><td>y 轴方向的设计弯矩,用于下(-)或上(+)表面钢筋的设计与校核</td></tr>\n <tr><td>m<sub>cd+, </sub>m<sub>cd-</sub></td><td>下(-)或上(+)表面混凝土压杆中的设计弯矩,须由混凝土承担</td></tr>\n</tbody></table>\n<p><br></p>\n<p>以下表格显示了构件类型为板时,按 EN 方法计算的换算设计力值:</p>\n<figure data-asset-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\" data-image-id=\"5a811994-5c4e-4cfc-8333-53dde9cf4789\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7b530370-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>在 IDEA StatiCa RCS 中,不显示上、下表面的弯矩值,而显示两个表面的法向力值以及换算至截面重心的弯矩值。</p>\n<figure data-asset-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\" data-image-id=\"8f13acb8-917b-43aa-90ac-03e4e6fc8451\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86dc5414-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>下、上表面的弯矩可利用数值输出中显示的表面力,按以下公式计算:</p>\n<p>\\[{{m}_{surface,i,dlow\\left( upp \\right)}}={{n}_{surface,i,low\\left( upp \\right)}}\\cdot z\\]</p>\n<p>表面力及换算弯矩的值显示在以下表格中:</p>\n<figure data-asset-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\" data-image-id=\"8aaa727b-210d-4c62-b970-5b3997c5cd60\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/16817eac-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://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>表格显示,IDEA Concrete 计算的板表面弯矩与按 EN 方法计算的结果仅在一个表面吻合。这一差异源于混凝土压杆优化方式的不同。IDEA StatiCa RCS 采用的方法以压杆中力最小为目标搜索压杆角度,而 EN 方法则以所有方向负力之和最小为目标进行搜索。</p>\n<h4>与 RFEM 和 SCIA Engineer 程序内力计算结果的比较</h4>\n<p>为比较 IDEA Concrete、RFEM 和 SCIA Engineer(SEN)程序中换算内力的计算结果,建立了一个尺寸为 6 m × 4 m、厚度为 200 mm 的简单板模型。板四边采用线支座支承,并施加 10 kN/m<sup>2</sup> 的均布荷载。</p>\n<p>为简化展示,仅显示一个纵向截面的换算内力值。该截面距板边缘 1.5 m。RFEM 程序计算的内力作为 IDEA Concrete 的输入值。</p>\n<figure data-asset-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\" data-image-id=\"e5794ff4-42a8-40d2-8b0f-c11e6abae0bf\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>表格显示,各程序计算的力具有良好的一致性。</p>"
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Name: Theoretical background RCS - 2D - Check
ID: 925950f1-b3b0-4cad-a609-72301fdfb968
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"value": "<p>如<a data-item-id=\"08114e5b-38b9-4a22-8909-df5524080155\" href=\"\"><strong>内力</strong></a><strong> </strong>章节中<strong>将重新计算的内力转换至截面形心</strong>所述,面配筋力被转换至二维单元截面的形心处。该转换的结果为作用于矩形截面形心处的弯矩和轴力,其中边长为1 m,高度对应于板的厚度。</p>\n<p>二维单元的规范校核在所有已定义方向上同时进行。程序自动使用以下公式将钢筋换算至校核方向:</p>\n<p>\\[{{A}_{Si,\\alpha }}={{A}_{S}}\\cdot {{\\cos }^{2}}({{\\alpha }_{i}})\\]</p>\n<table><tbody>\n <tr><td><br></td><td><strong>说明</strong></td></tr>\n <tr><td>As<sub>i,a</sub></td><td>第i层钢筋换算至方向a的面积</td></tr>\n <tr><td>As</td><td>二维单元第i层钢筋的面积</td></tr>\n <tr><td>α<sub>i</sub></td><td>第i层钢筋与校核方向之间的夹角</td></tr>\n</tbody></table>\n<table><tbody>\n <tr><td><strong>备注:</strong></td></tr>\n <tr><td>板和壳-板类型二维单元中的<strong>分布钢筋</strong>仅在构造规定校核中予以考虑,不用于其他二维单元的规范校核。</td></tr>\n</tbody></table>\n<h3>各定义方向的规范校核结果</h3>\n<p>所有启用的规范校核均在所有所需方向上自动执行。结果的呈现方式与一维单元结果的呈现方式类似。二维单元的结果呈现可设置所需显示的方向。二维单元的结果以校核方向呈现。所有已计算规范校核的方向均在图形显示中绘出。</p>\n<p>图中箭头表示校核方向,其中橙色为最大校核值方向,红色为当前校核方向。如需更改当前方向,可单击箭头或单击功能区中的相应按钮。</p>\n<figure data-asset-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\" data-image-id=\"6c5f48f5-2f2b-49ce-802d-3425d0bf5c2a\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/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>备注:</strong></td></tr>\n <tr><td>计算完成后,所有规范校核中的校核方向均设置为截面最大承载比方向。</td></tr>\n</tbody></table>\n<p>各规范校核的结果以当前方向呈现。校核角度显示在规范校核汇总表的上方。</p>\n<p>极值方向的结果将打印在报告中。</p>\n<h3>承载能力极限状态</h3>\n<p>承载能力极限状态规范校核的原理在一维单元的<a data-item-id=\"08dd67a9-0d8a-4013-a59a-b02f8feafceb\" href=\"\"><strong>理论背景</strong></a>手册中有所描述。以下章节仅描述二维单元与一维单元的差异。</p>\n<h4>承载力校核</h4>\n<p>承载力校核与一维单元的规范校核无差异。荷载仅作用于一个平面内,因此校核类型为 N + M。</p>\n<h4>响应校核</h4>\n<p>各校核方向的响应校核采用与一维单元规范校核相同的算法。</p>\n<h4>相互作用校核</h4>\n<p>与一维单元不同,相互作用校核仅用于评估 V + M 的利用率,即剪力与弯矩的相互作用。V<sub>Rd,c </sub>和 V<sub>Rd,max </sub>的值可在相互作用校核的汇总表中查看。</p>\n<h4>IDEA Concrete、RFEM 与 SCIA Engineer 之间的承载力校核对比</h4>\n<p>为将承载力校核结果与 RFEM 和 SCIA Engineer 进行对比,采用了与<a data-item-id=\"08114e5b-38b9-4a22-8909-df5524080155\" href=\"\"><strong>内力</strong></a><strong> </strong>章节中<strong>与 RFEM 和 SCIA Engineer 程序的内力计算对比</strong>所述相同的数据。对比在板的两个点处进行。</p>\n<p>由于 RFEM 和 SEN 程序不对板中的实际钢筋进行规范校核,而仅设计所需钢筋面积,因此采用两种方法进行计算对比。第一种方法对比在 RFEM 和 SEN 中设计的所需钢筋的截面承载比,假设当使用计算所得所需钢筋面积时,截面承载比恰好为100%。</p>\n<p>IDEA Concrete 中配筋截面的承载比可相对表示如下。</p>\n<p>相对承载比 = A<sub>s, req</sub> / A<sub>s, RCS</sub> × 100 [%]</p>\n<table><tbody>\n <tr><td><br></td><td><strong>说明</strong></td></tr>\n <tr><td>A<sub>s, req</sub></td><td>在 RFEM 或 SEN 中计算的所需钢筋面积</td></tr>\n <tr><td>A<sub>s, RCS</sub></td><td>IDEA Concrete 中的钢筋面积</td></tr>\n <tr><td>100 [%]</td><td>百分比</td></tr>\n</tbody></table>\n<p>IDEA Concrete 中的截面在下表面配置了钢筋,直径 d=10 mm,间距 200 mm,双向布置,两个方向的钢筋面积均为 314 mm<sup>2</sup>。</p>\n<figure data-asset-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\" data-image-id=\"2428d5cb-30e4-4ee6-9e45-3b5fa872f6d6\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/733f88e0-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>表格显示所有程序的承载比吻合良好。</p>\n<p>第二种方法在 IDEA Concrete 中定义了与 RFEM 和 SEN 计算所得所需钢筋面积大致相同的钢筋,随后对截面承载比进行对比。结果显示在下表中:</p>\n<figure data-asset-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\" data-image-id=\"d91f78fb-c409-40c9-b6ae-66641d2a71da\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7d869414-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>此处结果同样吻合良好。</p>\n<h3>正常使用极限状态</h3>\n<h4>应力限制</h4>\n<p>应力限制校核与一维单元的规范校核无差异。</p>\n<h4>裂缝宽度校核</h4>\n<p>在一维单元规范校核的基础上,还可校核裂缝方向,该方向可在二维单元中绘出。</p>\n<h3>构造规定</h3>\n<p>二维单元的构造规定校核可分为两个基本组: </p>\n<ul>\n <li>配筋率校核</li>\n <li>钢筋间距校核</li>\n</ul>\n<p>构造规定校核也取决于二维单元的类型。对于壳-板和板单元,分别对主钢筋和分布钢筋进行单独校核。对于墙单元,则区分竖向钢筋和水平钢筋。</p>\n<p>配筋率校核沿主应力方向进行。二维单元截面中定义的钢筋(分布钢筋除外)被转换至主应力方向。</p>\n<p>钢筋间距校核垂直于已定义钢筋的方向进行。该校核对所有已定义钢筋层执行,限值取决于被校核单元的类型和已定义钢筋的类型。</p>\n<figure data-asset-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\" data-image-id=\"946b5557-37f2-468f-8b01-54a90e1dc921\"><img src=\"https://preview-assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5219c67f-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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