在将钢结构锚固到混凝土时，施工项目中通常使用锚栓或化学锚栓以确保结构稳定性和承载能力。该模型在 IDEA StatiCa Detail 软件中进行分析。
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"value": "<p>CSFM（协调应力场法）在混凝土中考虑连续应力场（二维有限单元），并辅以离散\"杆\"单元表示钢筋（一维有限单元）。因此，钢筋并非弥散地嵌入混凝土二维有限单元中，而是被显式建模并与之连接。计算模型中采用平面应力状态。</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:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3f70008c-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=\"\"></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>既可以对整体<a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">墙体</a>和梁进行建模，也可以对梁的局部（部分）（即孤立的非连续区，又称截断端）进行建模。对于墙体和整体梁，支座的定义方式须使结构形成（外部）静定或超静定体系。梁截断端处的荷载传递通过特殊的圣维南传递区引入，从而确保被分析局部区域内的应力分布符合实际。</p>"
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"value": "<p>非线性（非弹性）有限单元法分析模型由多种有限元类型组成，用于模拟混凝土、钢筋及其之间的粘结。混凝土和钢筋单元首先分别划分网格，然后通过多点约束（MPC 单元）相互连接。这使得钢筋可以相对于混凝土处于任意位置。若需计算锚固长度验证，则在钢筋与 MPC 单元之间插入粘结单元和锚固端弹簧单元。</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:443/66e7a155-be94-0096-73e6-c55dfc7e5788/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></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>混凝土</h3>\n<p>混凝土采用四边形和三角形壳单元（CQUAD4 和 CTRIA3）进行模拟，分别由四个或三个节点定义。这些单元仅考虑平面应力状态，即不考虑 z 方向的应力或应变。</p>\n<p>每个单元有四个或三个积分点，位于单元尺寸约 1/4 处。在每个单元的每个积分点处，计算主应变方向 α<sub>1</sub>、α<sub>2</sub>。在这两个方向上，根据图 2 所示的混凝土应力-应变图，分别计算主应力 σ<em><sub>c</sub></em><sub>1</sub>、σ<em><sub>c</sub></em><sub>2</sub> 及刚度 <em>E</em><sub>1</sub>、<em>E</em><sub>2</sub>。需要注意的是，压力软化效应将主压缩方向的行为与另一主方向的实际状态相耦合。</p>\n<h3>钢筋</h3>\n<p>钢筋采用两节点一维\"杆\"单元（CROD）模拟，仅具有轴向刚度。这些单元与专门开发的\"粘结\"单元相连，用于模拟钢筋与周围混凝土之间的滑移行为。粘结单元随后通过 MPC（多点约束）单元与混凝土网格相连。该方法允许钢筋与混凝土独立划分网格，同时在后续确保二者的相互连接。</p>\n<h3>粘结单元</h3>\n<p>通过在有限单元法模型中引入混凝土单元（2D）与钢筋单元（1D）之间的粘结剪应力，对锚固长度进行验证。为此，专门开发了\"粘结\"有限元类型。</p>\n<p>粘结单元的定义与壳单元（CQUAD4）类似，同样由 4 个节点定义，但与壳单元不同的是，它仅在上下两对节点之间的剪切方向具有非零刚度。在模型中，上部节点与钢筋单元相连，下部节点与混凝土单元相连。该单元的行为由粘结应力 τ<em><sub>b</sub></em> 描述，其为上下节点相对滑移量 δ<em><sub>u</sub></em> 的双线性函数，见图 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:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></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>粘结-滑移关系的弹性刚度模量 <em>G</em><em><sub>b</sub></em> 定义如下：</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>其中：</p>\n<p><em>k</em><em><sub>g</sub></em> 取决于钢筋表面的系数（默认值 <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2）</p>\n<p><em>E</em><em><sub>c</sub></em> 混凝土弹性模量（按 EN 规范取 <em>E</em><em><sub>cm</sub></em>）</p>\n<p>Ø 钢筋直径</p>\n<p>采用相应设计规范 EN 1992-1-1 或 ACI 318-19 中规定的极限粘结剪应力设计值（分项系数值）<em>f</em><em><sub>bd</sub></em> 验证锚固长度。塑性段的硬化默认计算为 <em>G</em><em><sub>b</sub></em>/10<sup>5</sup>。</p>\n<h3>锚固弹簧</h3>\n<p>为钢筋端部设置锚固端（即弯折、弯钩、环形锚固等），满足设计规范的规定，可将钢筋的基本锚固长度（<em>l</em><em><sub>b,net</sub></em>）减小一定系数 β（以下称为\"锚固系数\"）。锚固长度的设计值（<em>l</em><em><sub>b</sub></em>）计算如下：</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p><em>l</em><em><sub>b,net</sub></em> 的预期折减等效于钢筋端部以锚固折减系数所对应的最大承载力百分比被激活，如图 15a 所示。</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:443/66e7a155-be94-0096-73e6-c55dfc7e5788/748b5346-4251-4154-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=\"\"></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>锚固长度的折减通过在钢筋端部设置弹簧单元（图 15）引入有限单元法模型，该弹簧单元由图 15b 所示的本构模型定义。弹簧传递的最大力（<em>F</em><em><sub>au</sub></em>）为：</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>其中：</p>\n<p><em>β</em> 基于锚固类型的锚固系数，</p>\n<p><em>A</em><em><sub>s</sub></em> 钢筋截面面积，</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em> 钢筋屈服强度的设计值（分项系数值）。</p>"
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"value": "<p><strong>CSFM（协调应力场法）考虑混凝土受压时的最大主应力（σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>2</sub></strong><em><strong><sub>r</sub></strong></em><strong>）以及裂缝处的钢筋应力（σ</strong><em><strong><sub>sr</sub></strong></em><strong>），同时忽略混凝土抗拉强度（σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>1</sub></strong><em><strong><sub>r</sub></strong></em><strong> = 0），但保留其对钢筋的刚化效应。</strong> 考虑拉力刚化效应可模拟钢筋的平均应变（ε<em><sub>m</sub></em>）。模型中考虑了虚拟旋转无应力裂缝（无滑移开展，见图 2a），同时兼顾裂缝处的平衡条件与钢筋的平均应变。 </p>\n<figure data-asset-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" data-image-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/70d687dc-a209-4d67-aeb9-c0bdabacd5c1/Fig.%202%20-%20Basic%20assumptions%20of%20CSFM.png\" data-asset-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" data-image-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 2\\qquad Basic assumptions of the CSFM: (a) principal stresses in concrete; (b) stresses in the reinforcement direction;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(c) stress-strain diagram of concrete in terms of maximum stresses with consideration of compression softening;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) stress-strain diagram of reinforcement in terms of stresses at cracks and average strains; (e) compression softening}}}\\) \\( \\textsf{\\textit{\\footnotesize{law; (f) bond shear stress-slip relationship for anchorage length verifications.}}}\\)</em></p>\n<p><br></p>\n<p>尽管上述假设较为简单，但已有研究表明，对于承受平面内荷载的配筋构件，只要所配钢筋能避免开裂时发生脆性破坏，类似假设可给出精确的预测结果（Kaufmann 1998；Kaufmann and Marti 1998）。此外，不考虑混凝土抗拉强度对极限荷载的贡献，与现代设计规范（大多基于塑性理论）的原则一致。</p>\n<p>然而，<strong>CSFM（协调应力场法）不适用于无横向钢筋的细长构件</strong>，因为此类构件的关键受力机制——骨料咬合、裂缝尖端残余拉应力及销栓作用——均直接或间接依赖混凝土抗拉强度，而该方法对此不予考虑。尽管部分设计规范允许基于半经验公式对此类构件进行设计，但 CSFM（协调应力场法）并不适用于这类潜在脆性结构。</p>\n<h4>混凝土</h4>\n<p>CSFM（协调应力场法）中采用的混凝土模型基于设计规范针对截面设计所规定的单轴受压本构关系，该关系仅取决于抗压强度。CSFM（协调应力场法）默认采用抛物线-矩形图（图 2c），设计人员也可选择更简化的弹性理想塑性关系。按 ACI 规范进行评估时，只能使用抛物线-矩形应力-应变图。如前所述，与经典钢筋混凝土设计一样，抗拉强度被忽略。</p>\n<p>对于开裂混凝土，有效抗压强度通过 <em>k</em><em><sub>c</sub></em><sub>2</sub> 折减系数根据主拉应变（ε<sub>1</sub>）自动计算，如图 2c 和图 2e 所示。所采用的折减关系（图 2e）是对 <em>fib</em> Model Code 2010 中剪力验算建议的推广，该建议规定有效混凝土强度与混凝土抗压强度之比的最大值限制为 0.65，但该限值不适用于其他荷载工况。</p>\n<p><a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\"><em>IDEA StatiCa Detail</em></a> 中的 CSFM（协调应力场法）对受压混凝土不考虑以应变表示的显式破坏准则（即认为达到峰值应力后存在无限塑性分支）。这一简化处理无法验证压缩破坏结构的变形能力。然而，当在（图 2e）所定义的开裂混凝土折减系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>）基础上，通过 <em>fib</em> Model Code 2010 中定义的 <em>\\( \\eta_{fc} \\)</em> 折减系数考虑混凝土强度提高导致脆性增加的影响时，可正确预测其极限承载力，公式如下：</p>\n<p>\\[f_{c,red} = k_c \\cdot f_{c} = \\eta _{fc} \\cdot k_{c2} \\cdot f_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>k</em><em><sub>c </sub></em>为抗压强度的综合折减系数</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为横向开裂引起的折减系数</p>\n<p><em>f</em><em><sub>c</sub></em> 为混凝土圆柱体特征强度（在定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<p>为保证计算稳定性，<em>k</em><em><sub>c</sub></em><sub>2</sub> 系数也有所折减。该折减不影响构件的总体承载力。以 <em>f</em><em><sub>cd</sub></em> 作为混凝土的折减强度（设计值），<em>k</em><em><sub>c</sub></em><sub>2</sub> 值按以下规则折减。</p>\n<p>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> < 0.11f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em>=1.0<br>0.11f</em><em><sub>cd</sub></em><em> < </em>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> < 0.37f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em> </em>在 1.0 与图 2f 中取值之间进行线性插值<br> <em><br></em>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> > 0.37f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em> </em>直接从图 2f 的图表中取值</p>\n<h4>钢筋</h4>\n<p>模型采用设计规范通常规定的裸钢筋理想化双线性应力-应变图（图 2d）。该图的定义仅需在设计阶段掌握钢筋的基本性能（强度和延性等级）。用户也可自定义应力-应变关系。</p>\n<p>通过修改裸钢筋的输入应力-应变关系来考虑拉力刚化效应，以反映埋置于混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<h4>粘结模型</h4>\n<p>在有限单元法模型中，通过采用图 2f 所示的简化刚性-完全塑性本构关系来引入钢筋与混凝土之间的粘结滑移，其中 <em>f</em><em><sub>bd</sub></em> 为设计规范针对特定粘结条件规定的极限粘结应力设计值（折减值）。</p>\n<p>该简化模型的唯一目的是按设计规范验算粘结要求（即钢筋的锚固）。采用弯钩、环形及类似弯折形式时锚固长度的折减，可通过在钢筋端部定义一定承载力来考虑，详见后续说明。 </p>"
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"value": "<h3>混凝土 - 承载能力极限状态</h3>\n<p>CSFM（协调应力场法）中采用的混凝土模型基于 EN 1992-1-1 针对截面设计所规定的单轴受压本构关系，该关系仅取决于抗压强度。CSFM（协调应力场法）默认采用 EN 1992-1-1 第 3.1.7 (1) 条规定的抛物线-矩形图（图 24a），但设计人员也可根据 EN 1992-1-1 第 3.1.7 (2) 条选择更为简化的弹性理想塑性关系（图 24b）。与经典钢筋混凝土设计一样，抗拉强度忽略不计。</p>\n<figure data-asset-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" data-image-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e72b03ac-c1db-4c39-bbc2-f4d87b7522f2/Concrete%20stress-strain%20diagram%20CSFM.PNG\" data-asset-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" data-image-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 24\\qquad The stress-strain diagrams of concrete for ULS: a) parabola-rectangle diagram; b) bilinear diagram.}}}\\]</em></p>\n<p><em>IDEA StatiCa Detail</em> 中 CSFM（协调应力场法）的实现未对受压混凝土的应变设置显式破坏准则（即达到峰值应力后，考虑塑性分支，ε<em><sub>cu</sub></em><sub>2</sub>（ε<em><sub>cu</sub></em><sub>3</sub>）取值为 5%，而 EN 1992-1-1 假定极限应变小于 0.35%）。这一简化使得无法验证受压破坏结构的变形能力。然而，当在开裂混凝土系数（图 25 中定义的 <em>k</em><em><sub>c</sub></em><sub>2</sub>）的基础上，通过 <em>fib</em> Model Code 2010 中定义的 <em>\\(\\eta_{fc}\\)</em> 折减系数考虑混凝土强度提高时脆性增大的影响，其极限承载力 <em>f</em><em><sub>cd</sub></em> 可按 EN 1992-1-1 第 3.1.3 条正确预测，公式如下：</p>\n<p>\\[f_{cd}={\\alpha_{cc}} \\cdot \\frac{f_{ck,red}}{γ_c} = {\\alpha_{cc}} \\cdot \\frac{k_c \\cdot f_{ck}}{γ_c} = {\\alpha_{cc}} \\cdot \\frac{\\eta _{fc} \\cdot k_{c2} \\cdot f_{ck}}{γ_c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{ck}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p>α<em><sub>cc</sub></em> 为考虑抗压强度长期效应及荷载施加方式不利影响的系数，依据 EN 1992-1-1 第 3.1.6 (1) 条确定，默认值为 1.0。</p>\n<p><em>k</em><em><sub>c </sub></em>为抗压强度的综合折减系数</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为横向开裂引起的折减系数</p>\n<p><em>f</em><em><sub>ck</sub></em> 为混凝土圆柱体特征强度（定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 25\\qquad The compression softening law.}}}\\]</em></p>\n<h3>混凝土 - 正常使用极限状态</h3>\n<p>正常使用极限状态分析对承载能力极限状态分析所用的本构模型进行了一定简化。受压混凝土应力-应变曲线的塑性分支被忽略，弹性分支为线性且无限延伸，不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，只要正常使用阶段的材料应力结果明显低于屈服点（如欧洲规范所要求），则不影响解的普遍性。因此，正常使用阶段所采用的简化模型仅在满足所有验算要求时方为有效。</p>\n<figure data-asset-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" data-image-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bca48b51-2839-4b96-8dac-078574e47c12/Fig.%2011%20-%20Concrete%20stress-strain%20for%20serviceability%20.png\" data-asset-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" data-image-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 26\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>在正常使用极限状态分析中，混凝土的长期效应采用有效无限徐变系数（\\(\\varphi\\)，默认取值为 2.5）加以考虑，该系数按 EN 1992-1-1 第 3.1.4 (3) 条及第 7.4.3 (5) 条对混凝土割线弹性模量（<em>E</em><em><sub>cm</sub></em>）进行修正，公式如下：</p>\n<p>\\[E_{c,eff} = \\frac{E_{cm}}{1+\\varphi}\\]</p>\n<p>考虑长期效应时，首先采用徐变系数（即混凝土有效弹性模量 <em>E</em><em><sub>c,eff</sub></em>）计算包含所有永久荷载的荷载步，然后不采用徐变系数（即使用 <em>E</em><em><sub>cm</sub></em>）计算附加荷载。此外，为进行短期验算，另行进行一次计算，所有荷载均不采用徐变系数。长期和短期验算的两种计算均如图 26 所示。</p>\n<p>徐变系数由用户在材料属性中定义，应按 EN 1992-1-1 图 3.1 计算。</p>\n<h3>钢筋</h3>\n<p>默认采用 EN 1992-1-1 第 3.2.7 条（图 27）中针对裸钢筋定义的理想化双线性应力-应变图。该图的定义仅需在设计阶段掌握钢筋的基本性能（强度和延性等级）。在已知的情况下，可考虑钢筋的实际应力-应变关系（热轧、冷加工、淬火及自回火等）。钢筋应力-应变图可由用户自定义，但在此情况下无法考虑拉力刚化效应（即无法计算裂缝宽度）。采用水平顶部分支的应力-应变图不允许对结构耐久性进行验算，因此需手动验算标准延性要求。</p>\n<figure data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/47fb26f0-9509-403c-ac42-7d68821d59d1/Steel%20stress-strain%20diagram%20CSFM.PNG\" data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 27 \\qquad Stress-strain diagram of reinforcement: a) bilinear diagram with an inclined top branch; b) bilinear diagram}}}\\) \\( \\textsf{\\textit{\\footnotesize{with a horizontal top branch.}}}\\)</em></p>\n<p><br></p>\n<p>拉力刚化（图 28） 通过修正裸钢筋的输入应力-应变关系自动加以考虑，以反映埋入混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/111ff130-8480-486a-adca-4c0068bcf66e/Tension%20stiffening%20CSFM.PNG\" data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 28\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
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"value": "<p>CSFM（协调应力场法）符合现代设计规范的要求。由于计算模型仅使用标准材料属性，设计规范规定的分项安全系数格式可直接应用，无需任何调整。这样，输入荷载经过系数放大，材料特征值通过设计规范规定的相应安全系数进行折减，与常规混凝土分析完全一致。EN 1992-1-1 第 2.4.2.4 条规定的材料安全系数值为默认设置，但用户可在规范与计算设置中修改安全系数（图 29）。</p>\n<figure data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4cadae4a-9a8a-4f9b-935c-51395116ed4e/Material%20factors.png\" data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 29\\qquad The setting of material safety factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>荷载安全系数须由用户在组合规则中针对每个非线性荷载工况组合进行定义（图 30）。对于 <a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\">Idea StatiCa Detail</a> 中已实现的所有模板，分项安全系数均已预先定义。</p>\n<figure data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d2607d1-29e9-4dfd-80ef-db2ba7d172bf/Combination%20factors.png\" data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 30\\qquad The setting of load partial factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>通过使用用户自定义的分项安全系数组合，用户也可采用整体抗力系数法（Navrátil 等，2017）进行 CSFM（协调应力场法）计算，但该方法在设计实践中极少使用。部分指南建议在非线性分析中采用整体抗力系数法。然而，对于简化非线性分析（如 CSFM（协调应力场法）），其仅需常规手算中所用的材料属性，采用分项安全系数格式仍更为适宜。</p>"
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8.4.2 条规定的极限粘结强度 <em>f</em><em><sub>bd</sub></em><sub>,</sub> 之比：</p>\n<p>\\[\\frac{τ_{b}}{f_{bd}}\\]</p>\n<p>\\[f_{bd} = 2.25 \\cdot η_1\\cdot η_2\\cdot f_{ctd}\\]</p>\n<p>其中：</p>\n<p><em>f</em><em><sub>ctd</sub></em><sub> </sub> 为根据 EN 1992-1-1 第 3.1.6 (2) 条规定的混凝土抗拉强度设计值。由于高强混凝土脆性随强度增大而增加，根据 EN 1992-1-1 第 8.4.2 (2) 条，<em>f</em><em><sub>ctk,0.05</sub></em><sub> </sub>限制为 C60/75 对应的值</p>\n<p>η<sub>1</sub> 为与浇筑混凝土时钢筋的粘结条件质量及位置相关的系数（图 31）。</p>\n<p>η<sub>1</sub> = 1.0 适用于\"良好\"粘结条件，</p>\n<p>η<sub>1</sub> = 0.7 适用于其他所有情况，以及采用滑模施工的结构构件中的钢筋，除非能证明存在\"良好\"粘结条件</p>\n<p>η<sub>2</sub> 与钢筋直径相关：</p>\n<p> η<sub>2</sub> = 1.0，当 Ø ≤ 32 mm 时</p>\n<p> η<sub>2</sub> = (132 - Ø)/100，当 Ø > 32 mm 时</p>\n<figure data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aa307dc-3cd6-4d42-8dd8-d0ff97994677/Bond%20conditions.PNG\" data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 31\\qquad EN 1992-1-1 Figure 8.2 - Description of bond conditions.}}}\\]</em></p>\n<p>在 IDEA StatiCa Detail 中，粘结条件按图 31 c) 和 d) 考虑。浇筑方向可在软件中针对每个项目构件进行设置，如下所示。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p>上述验算针对结构各部分的相应限值进行（即尽管混凝土和钢筋材料各自只有单一等级，但由于拉力刚化和压力软化效应，结构各部分的最终应力-应变图仍会有所不同）。</p>\n<p>此外，还可以模拟<strong>光圆钢筋</strong>。更多信息请参见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 为有限单元法分析的结果，可通过以下两种方式定义。</p>\n<p>\\[F_{tot}=A_{s}\\cdot \\sigma_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>σ</em><em><sub>s</sub></em> 为钢筋中的应力。</p>\n<p>或表示为锚固力 <em>F</em><em><sub>a </sub></em>与粘结力 <em>F</em><em><sub>bond</sub></em><em> </em>之和。</p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可通过沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分求得。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 为钢筋单元中考虑钢筋<strong>极限强度</strong>及<strong>锚固条件</strong>（混凝土与钢筋之间的粘结以及锚固弯钩、环形锚固等）的最大力。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=k\\cdot f_{yd}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot k\\cdot f_{yd}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bd}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到计算截面的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 32\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元夹角大小计算的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括：直筋（即无锚固端折减）、弯折、弯钩、环形锚固、焊接横向钢筋、完全粘结及连续钢筋。所有这些类型及其对应的锚固系数 β 均在图 32（纵向钢筋）和图 33（箍筋）中示出。所采用的锚固系数值符合 EN 1992-1-1 第 8.4.4 条表 8.2 的规定。需要指出的是，尽管有多种可选方案，CSFM（协调应力场法）仅区分三种锚固端类型：(i) 锚固长度无折减；(ii) 标准锚固情况下锚固长度折减 30%；(iii) 完全粘结。</p>\n<figure data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b16975dc-aeea-4e7e-bfc7-23a8f8b28c7e/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 33\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in the CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) bend; (c) hook; (d) loop; (e) welded transverse bar; (f) perfect bond; (g) continuous bar.}}}\\]</em></p>\n<p><br></p>\n<figure data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86ffb525-5912-4a7f-9576-fff17481b7a1/Available%20anchorage%20types%20for%20stirrups.png\" data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 33\\qquad Available anchorage types and respective anchorage coefficients for stirrups.}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Closed stirrups: (a) hook; (b) bend; (c) overlap. Open stirrups: (d) hook; (e) continuous bar.}}}\\]</em></p>\n<p>为符合 EN 1992-1-1 的要求，计算中应使用锚固弹簧，锚固弹簧通过 β 系数进行修正，因此用户在定义钢筋起始和终止条件时必须选用其中一种可用的锚固类型。 </p>"
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"value": "<p>在设计混凝土结构时，我们会遇到两大类局部受压区（PLA）——第一类包括支座，另一类包括锚固区。根据现行有效的钢筋混凝土结构设计标准 EN 1992-1-1 第 6.7 条（<em>图 34</em>），对于局部受压区，应考虑混凝土的局部压碎和横向拉力。对于作用在面积 <em>A</em><em><sub>c0</sub></em> 上的均布荷载，混凝土的受压承载力可根据设计分布面积 <em>A</em><em><sub>c1</sub></em> 提高至三倍。</p>\n<figure data-asset-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" data-image-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/94ecb791-703a-44b7-8665-2f1526a20c1e/Partially%20loaded%20areas%20EC.PNG\" data-asset-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" data-image-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 34\\qquad Partially loaded areas according to EN 1992-1-1.}}}\\]</em></p>\n<p>局部受压区必须配置足够的横向钢筋，以传递该区域产生的劈裂力。对于局部受压区横向钢筋的设计，根据欧洲规范采用拉压杆方法。若未配置所需的横向钢筋，则不能考虑提高混凝土的受压承载力。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部受压区</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 35\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>利用 CSFM（协调应力场法），可以在设计和评估钢筋混凝土结构时考虑局部受压区混凝土受压承载力提高的影响。由于 CSFM（协调应力场法）是平面（2D）模型，而局部受压区是空间（3D）问题，因此有必要找到一种将这两种不同类型问题相结合的解决方案（<em>图 35</em>）。若激活\"局部受压区\"功能，则根据欧洲规范生成允许的锥体几何形状（<em>图 34</em>）。对于指定的混凝土构件几何形状及每个 PLA 的尺寸，所有几何碰撞均在三维空间中完整求解。随后，建立局部受压区的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 36\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>材料模型修正的方法被证明是不合适的，主要原因在于将属性映射到有限单元法网格存在困难。研究表明，独立于有限单元法网格的方法是更为合适的解决方案。对于已知的压力锥几何形状，建立完全协调的虚拟压杆（<em>图 35</em> <em>和图 37</em>）。这些压杆与模型中所用混凝土具有相同的材料属性，包括应力-应变图。锥体形状决定了压杆的方向，从而将荷载从 PLA 逐渐分布至设计分布面积。虚拟压杆的面积密度在锥体各部分是变化的，并在荷载方向上增加了虚拟混凝土面积。在受压面积（<em>A</em><em><sub>c0</sub></em>）处，根据比值 \\(\\sqrt{A_{c0} \\cdot A_{c1}} - A_{real}\\) （其中 <em>A</em><em><sub>real</sub></em> 为二维计算模型中假定的支座面积）增加虚拟混凝土面积，该面积向设计分布面积（<em>A</em><em><sub>c1</sub></em>）方向线性减小至零。该方案确保混凝土中的压应力在整个锥体体积内保持恒定。</p>\n<figure data-asset-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" data-image-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c4ff37a9-9d49-493b-946e-f048713b05cf/Partially%20loaded%20areas.PNG\" data-asset-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" data-image-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{c1}}{A_{c0}}} - \\frac{A_{real}}{A_{c0}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 37\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压区的承载力根据 EN 1992-1-1 第 (6.7) 条规定的设计分布面积与受压面积之比进行提高。应注意，这是一种设计模型，无法精确描述局部受压区的应力状态，其实际分布要复杂得多。然而，该方案能够在考虑局部受压区承载力提高的同时，正确地将荷载分布至整个模型。此外，它还能正确引入该区域的横向应力。</p>\n<p>在使用局部受压区功能模拟混凝土受压承载力提高时，需根据 EN 1992-1-1 第 6.7 条第 (2) 款单独进行规范校核。由钢筋承担的横向拉力（劈裂力）将自动进行验算。</p>"
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"value": "<p>正常使用极限状态（SLS）评估针对应力限制、裂缝宽度和挠度限值进行。混凝土和钢筋单元中的应力按照 EN 1992-1-1 进行校核，方式与承载能力极限状态（ULS）规定的方式类似。</p>\n<h3>应力限制</h3>\n<p>混凝土中的压应力应加以限制，以避免纵向裂缝的产生。根据 EN 1992-1-1 第 7.2 条第 (2) 款，若在荷载标准组合下应力水平超过 <em>k</em><sub>1</sub><em>f</em><em><sub>ck</sub></em>，则可能出现纵向裂缝。混凝土压应力的评估方式为：由有限单元法分析得到的正常使用极限状态下最大主压应力 σ<em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与限值 σ<em><sub>c,lim</sub></em> 之比。则：</p>\n<p>\\[\\frac{σ_{c}}{σ_{c,lim}}\\]</p>\n<p>\\[σ_{c,lim} = k_1\\cdot f_{ck}\\]</p>\n<p>其中：</p>\n<p><em>f</em><em><sub>ck</sub></em> 混凝土圆柱体抗压强度标准值，</p>\n<p><em>k</em><sub>1</sub> =0.6。</p>\n<p>根据 EN 1992-1-1 第 7.2 条第 (3) 款，若在准永久荷载作用下混凝土应力小于 <em>k</em><sub>2</sub><em>f</em><em><sub>ck</sub></em>，则可假定为线性徐变。若混凝土应力超过 <em>k</em><sub>2</sub><em>f</em><em><sub>ck</sub></em>，则应考虑非线性徐变（见 EN 1992-1-1 第 3.1.4 条）。在 IDEA StatiCa Detail 中，仅可假定按 EN 1992-1-1 第 3.1.4 条第 (3) 款的线性徐变（见材料模型（EN））。</p>\n<p>若在荷载标准组合下，钢筋中的拉应力不超过 <em>k</em><sub>3</sub><em>f</em><em><sub>yk</sub></em>（EN 1992-1-1 第 7.2 条第 (5) 款），则可假定不会出现不可接受的裂缝或变形。钢筋强度的评估方式为：裂缝处钢筋应力 σ<em><sub>s</sub></em> <em>= </em>σ<em><sub>sr</sub></em> 与规定限值 σ<em><sub>s,lim</sub></em> 之比：</p>\n<p>\\[\\frac{σ_{s}}{σ_{s,lim}}\\]</p>\n<p>\\[σ_{s,lim} = k_3\\cdot f_{yk}\\]</p>\n<p>其中：</p>\n<p><em>f</em><em><sub>yk</sub></em> 钢筋屈服强度，</p>\n<p><em>k</em><sub>3</sub> =0.8。</p>\n<h3>挠度</h3>\n<p>挠度仅可针对墙体、静定梁或超静定梁进行评估。在这些情况下，挠度取绝对值（相对于加载前的初始状态），最大允许挠度值须由用户设定。截断端处的挠度无法进行校核，因为这类结构本质上是不稳定结构，其平衡通过施加端部力来满足，因此挠度值不具有实际意义。可计算短期挠度 <em>u</em><em><sub>z,st</sub></em> 或长期挠度 <em>u</em><em><sub>z,lt</sub></em>，并与用户定义的限值进行校核：</p>\n<p>\\[\\frac{u_ z}{u_{z,lim}}\\]</p>\n<p>其中：</p>\n<p><em>u</em><em><sub>z</sub></em> 由有限单元法分析计算得到的短期或长期挠度，</p>\n<p><em>u</em><em><sub>z,lim</sub></em> 用户定义的挠度限值。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和方向仅针对长期效应（采用 <em>E</em><em><sub>c,eff</sub></em>）在启用裂缝宽度评估的荷载组合下进行计算。按照欧洲规范，基于用户指定限值的验算结果如下所示：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<p><em>w</em> 由有限单元法分析计算得到的裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p><br></p>\n<p>裂缝宽度的计算有两种方式（稳定开裂和非稳定开裂）。在一般情况下（稳定开裂），裂缝宽度通过对钢筋一维单元上的应变进行积分来计算。裂缝方向则由距给定钢筋一维有限单元中心最近的三个二维混凝土单元积分点计算得出。虽然这种计算裂缝方向的方法与裂缝的实际位置并不完全对应，但仍能提供具有代表性的数值，所得裂缝宽度结果可与规范要求的钢筋位置处裂缝宽度限值进行比较。</p>"
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"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM（协调应力场法）中用于强度计算的混凝土模型，基于抛物线-塑性应力-应变曲线，该曲线源自波特兰水泥协会（PCA）的抛物线应力-应变曲线，详见PCA《ACI 318-99结构混凝土建筑规范要求注释》图6-8。与经典钢筋混凝土设计一致，忽略混凝土抗拉强度。</p>\n<figure data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 38\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p>IDEA StatiCa Detail 中CSFM（协调应力场法）的实现，对受压混凝土未设置以应变表示的显式破坏准则（即达到峰值应力后，考虑最大值为5%的ε<em><sub>c</sub></em><sub>0</sub>塑性分支，而ACI 318-19第22.2.2.1条假定极限应变小于0.3%）。这一简化使得无法验证受压破坏结构的变形能力。然而，当在开裂混凝土折减系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，定义见图39）的基础上，通过<em>fib</em>模型规范2010中定义的<em>\\(\\eta_{fc}\\)</em> 折减系数考虑混凝土随强度提高而增大的脆性时，可正确预测强度，具体如下：</p>\n<p>\\[f'_{c,lim}=\\alpha_{1}\\cdot\\phi_{c}\\cdot k_{c}\\cdot f'_{c}\\]</p>\n<p>\\[k_{c}=\\eta_{fc}\\cdot k_{c2}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>1</sub> 为ACI 318-19第22.2.2.4.1条定义的混凝土抗压强度折减系数。采用抛物线-矩形应力-应变图时，需将最大压应力乘以该系数进行折减。此举对受压区应力分布取平均，使所得抗压强度不超过采用具有下降塑性分支的应力-应变图所计算的抗压强度<em>。</em></p>\n<p><em>Φ</em><em><sub>c </sub></em>为混凝土强度折减系数，默认值按ACI 318-19表24.2.1 (b)(f)设定。</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为横向开裂存在时的折减系数。</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体强度（在定义<em>\\( \\eta_{fc} \\)</em>时单位为MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 39\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 是基于与ACI 318-19表23.9.2中节点区系数<em>β</em><em><sub>n</sub></em>相同假设的折减系数，区别在于CSFM（协调应力场法）中对每个有限单元均检验垂直于主压应力方向的主拉应力是否存在（而非仅针对拉压杆模型的节点）。</p>\n<h3>混凝土 – 正常使用性</h3>\n<p>正常使用性分析对强度分析所用的本构模型进行了若干简化：忽略受压混凝土应力-应变曲线的塑性分支，弹性分支取线性且无限延伸，不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，且只要正常使用极限状态下的材料应力结果明显低于屈服点（如ACI所要求），不会降低解的普遍性。因此，正常使用性简化模型仅在所有验算要求均满足时方为有效。</p>\n<figure data-asset-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" data-image-id=\"0d015331-6ce6-4a70-b087-58766f33e248\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/07b977ad-1511-48d6-b96e-12b3c67bb3b9/Concrete%20stress-strain%20for%20serviceability%20-%20ACI.png\" data-asset-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" data-image-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 40\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>结构的长期行为，如长期挠度或持续荷载引起的裂缝宽度计算，受混凝土徐变影响。ACI 318-19第24.2.4.1.3条定义了持续荷载的时间相关系数ξ，用于表示指定持续荷载持续时间的徐变效应。</p>\n<p>在Detail 软件中，通过系数ξ对弹性模量<em>E</em><em><sub>c</sub></em>进行调整，以确定结构的长期行为。调整后的弹性模量记为<em>E</em><em><sub>c,eff</sub></em>，见图40。</p>\n<p>假设构件变形以应变表示，可写出：</p>\n<p>\\[\\epsilon_{tot} = \\epsilon_{0} + \\epsilon_{creep} = \\epsilon_{0} \\cdot (1+\\xi)\\]</p>\n<p>其中：</p>\n<p><em>ε</em><em><sub>0</sub></em> 为短期应变（不含徐变影响），<em>ε</em><em><sub>creep</sub></em> 为徐变引起的应变。</p>\n<p>利用胡克定律，可写出：</p>\n<p>\\[E_{c,eff} = \\frac{f_{c}}{\\epsilon_{tot}}\\]</p>\n<p>将\\(\\epsilon_{tot} = \\epsilon_{0} \\cdot (1+\\xi)\\)及\\(\\epsilon_{0} = f_{c} / E_{c}\\)代入，得：</p>\n<p>\\[E_{c,eff} = \\frac{E_{c}}{1+\\xi}\\]</p>\n<p>用于确定系数ξ的持续荷载持续时间，可针对每个正常使用长期组合单独设定。</p>\n<figure data-asset-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" data-image-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1bb4b6d8-065d-4c52-a7e0-66ed3c01281f/Sustained%20load%20duration%20-%20ACI.png\" data-asset-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" data-image-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 41\\qquad Sustained load duration}}}\\]</em></p>\n<p>时间相关的挠度、应力及裂缝宽度随后采用修正后的材料模型计算，其中受压细化效应由有限单元法分析的性质自动考虑，因此无需再乘以第24.2.4.1.1条所定义的系数。</p>\n<p><strong>短期效应</strong></p>\n<p>为进行短期验算，另行执行一次计算，其中所有荷载均不计持续荷载的时间相关系数。长期与短期验算的两次计算均示于图40。</p>\n<h3>钢筋</h3>\n<p>对非预应力钢筋采用具有明确屈服点的理想弹塑性应力-应变图，见ACI 319-19第20.2.1条。该图的定义仅需已知钢筋的基本性能——强度和弹性模量。</p>\n<p>钢筋应力-应变图也可由用户自定义，但在此情况下，无法考虑拉力刚化效应（即无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 42 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋强度折减系数，默认值按ACI 318-19表24.2.1设定。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋弹性模量</p>\n<p>10%被选为计算终止的极限应变，依据ASTM A955/A955M-20c第7条，此值被认为是安全的。</p>\n<p>拉力刚化（图43） 通过修正裸钢筋的输入应力-应变关系自动考虑，以反映埋入混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 43\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
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"value": "<p>协调应力场法符合现代设计规范的要求。由于计算模型仅使用标准材料属性，设计规范规定的分项安全系数格式可直接应用，无需任何调整。输入荷载经过系数放大，材料特征值通过相应的强度折减系数进行折减，与常规混凝土分析方法完全一致。</p>\n<p><strong>强度折减系数</strong>的取值规定于 ACI 318-19 第 21.2 条。混凝土和钢筋的默认值基于以下假定：软件中求解的典型算例为剪力控制型（依据表 21.2.1 (b)、(f)、(g)）。然而，软件可对任意类型的构件进行建模。因此，若评估的是受压控制或受拉控制构件，用户可在\"首选项\"中修改强度折减系数的取值。</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 44\\qquad The setting of strength reduction factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>强度组合的<strong>荷载系数</strong>应按 ACI 318-19 表 5.3.1 的规定确定。</p>\n<p>除第 34 章另有规定外，ACI 318-19 未定义正常使用荷载组合。建议采用 ASCE/SEI 7-16 附录 C 中的组合规则。所有模板的荷载系数均已预先设定。</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 45\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>"
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为钢筋截面面积。</p>\n<p>由上式可方便地推导出粘结强度的计算公式：</p>\n<p>\\[f_{bu}=\\frac{f_{y}\\cdot A_{s}}{\\pi\\cdot d_{b} \\cdot l_{d} }\\]</p>\n<p>锚固长度 <em>l</em><em><sub>d</sub></em> 按 ACI 318-19 表 25.4.2.3 确定如下：</p>\n<p>\\[l_{d}=\\left( \\frac{f_{y}\\cdot\\psi_{t}\\cdot\\psi_{e}\\cdot\\psi_{g}}{C\\cdot\\lambda\\sqrt{f'_{c}}} \\right)\\cdot d_{b}\\]</p>\n<p>其中：</p>\n<p>对于 6 号及以下钢筋和变形钢丝，<em>C = 25</em>（公制为 2.1）；对于 7 号及以上钢筋，<em>C = 20</em>（公制为 1.7）；普通重量混凝土取 λ = 1.0；<em>ψ</em><em><sub>t</sub></em>、<em>ψ</em><em><sub>e</sub></em><sub>、</sub><em>ψ</em><em><sub>g</sub></em> 按 ACI 318-19 表 25.4.2.3 确定。 </p>\n<p>本软件仅支持无涂层或镀锌（热镀锌）钢筋，因此 <em>ψ</em><em><sub>e</sub></em><em> = 1.0</em>。<em>ψ</em><em><sub>g</sub></em> 根据钢筋等级自动确定，<em>ψ</em><em><sub>t</sub></em> 则根据模型中钢筋的位置及浇筑方向自动推导，浇筑方向可在软件中针对每个项目单独设置，如下所示。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 46\\qquad Direction of concreting}}}\\]</em></p>\n<p>上述验证针对结构各部分的相应限值进行（即尽管混凝土和钢筋材料均采用单一等级，但由于拉力刚化和压力软化效应，结构各部分的最终应力-应变图将有所不同）。</p>\n<p>软件还提供<strong>光圆钢筋</strong>建模选项。更多信息请参见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 为有限元分析的结果，可通过以下两种方式定义。</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>f</em><em><sub>s</sub></em> 为钢筋中的应力。</p>\n<p>或表示为锚固力 <em>F</em><em><sub>a </sub></em>与粘结力 <em>F</em><em><sub>bond</sub></em><em> </em>之和。</p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可通过沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分求得。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中综合考虑钢筋<strong>强度</strong>及<strong>锚固条件</strong>（混凝土与钢筋之间的粘结以及锚固弯钩、环等）的最大力。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到计算点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 47\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元夹角大小计算的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括：直钢筋（即无锚固端折减）、90° 弯钩、180° 弯钩、完全粘结以及连续钢筋。所有这些类型及其对应的锚固系数 β 均在图 48 中针对纵向钢筋进行了展示。所采用锚固系数的取值由 ACI 318-19 第 25.4.3.1 节公式与第 25.4.2.3 节公式的对比推导得出。需要指出的是，尽管提供了多种选项，CSFM（协调应力场法）实际上区分三种锚固端类型：（i）锚固长度无折减；（ii）标准锚固情况下锚固长度折减 30%；（iii）完全粘结。</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 48\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) 90-degree hook; (c) 180-degree hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>箍筋的锚固系数始终取 β = 1.0。</p>\n<p>为符合 ACI 规范要求，计算中应使用锚固弹簧，锚固弹簧通过 β 系数进行修正，因此用户在定义钢筋起始和终止条件时必须选择一种可用的锚固类型。 </p>"
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"value": "<p>在设计混凝土结构时，我们会遇到两大类局部受压区域（PLA）——第一类为<strong>支承区</strong>，第二类为<strong>锚固区</strong>。 </p>\n<p>根据现行钢筋混凝土结构设计标准 ACI 318-19 第 22.8 章，对于<strong>支承区</strong>，应考虑混凝土局部压碎及横向拉力。对于作用在面积 <em>A</em><em><sub>c1</sub></em> 上的均布荷载，混凝土的受压承载力可根据设计分布面积 <em>A</em><em><sub>c2</sub></em> 提高至最多两倍。详见 ACI 318-19 表 22.8.3.2。</p>\n<figure data-asset-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" data-image-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d1db553-b91c-4327-8c20-396cc2144140/Partially%20loaded%20areas%20Bearings.png\" data-asset-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" data-image-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 49\\qquad Partially loaded areas for bearings according to ACI 318-19}}}\\]</em></p>\n<p>对于后张<strong>锚固区</strong>，应遵循 ACI 318-19 第 25.9 章的相关规定。</p>\n<p>局部受压区域必须配置足够的横向钢筋，以传递该区域产生的劈裂力。若未配置所需的横向钢筋，则不能考虑提高混凝土的受压承载力。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部受压区域</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 50\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>采用 CSFM（协调应力场法），可在考虑局部受压区域混凝土受压承载力提高影响的同时，对钢筋混凝土结构进行设计和验算。由于 CSFM（协调应力场法）为平面（2D）模型，而局部受压区域属于空间（3D）问题，因此需要找到一种能将这两种不同类型问题相结合的解决方案（<em>图 50</em>）。若激活\"局部受压区域\"功能，则根据 ACI 规范（<em>图 49</em>）创建允许的锥体几何形状。对于指定的混凝土构件几何形状及各 PLA 的尺寸，所有几何碰撞均在三维空间中完整求解。随后，建立局部受压区域的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 51\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>修改材料模型的方法被证明是不适合的，主要原因在于将属性映射到有限单元法网格存在困难。研究表明，与有限单元法网格无关的方法是更为合适的解决方案。对于已知的压力锥几何形状（<em>图 51</em> <em>和图 52</em>），创建完全协调的虚拟压杆。这些压杆与模型中所用混凝土具有相同的材料属性，包括应力-应变图。锥体形状决定了压杆的方向，从而将荷载从 PLA 逐渐分布至设计分布面积。虚拟压杆的面积密度在锥体各部分是变化的，并在荷载方向上增加了虚拟混凝土面积。在受荷面积（<em>A</em><em><sub>c1</sub></em>）处，根据比值 \\(\\sqrt{A_{c1} \\cdot A_{c2}} - A_{real}\\) （其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支承面积）增加虚拟混凝土面积，该面积向设计分布面积（<em>A</em><em><sub>c2</sub></em>）方向线性减小至零。该方案确保混凝土中的压应力在整个锥体体积内保持恒定。</p>\n<figure data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png\" data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{c2}}{A_{c1}}} - \\frac{A_{real}}{A_{c1}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 52\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压区域的承载力根据 ACI 318-19 第 22.8 章规定的设计分布面积与受荷面积之比进行提高。需要注意的是，这是一种设计模型，无法精确描述局部受压区域的应力状态，实际应力分布要复杂得多。然而，该方案能够在考虑局部受压区域承载力提高的同时，正确地将荷载分配至整体模型。此外，它还能在该区域正确引入横向应力，从而正确设计抵抗劈裂力的钢筋。</p>\n<p>表 22.8.3.2 中列出了允许的<strong>支承</strong>应力 <em>0.85f</em><em><sub>c</sub></em><em>'</em>。密度受到限制，以确保不超过表 22.8.3.2(b) 公式中给出的最大双倍承载力。 </p>\n<p>对于<strong>锚固区</strong>，软件中 PLA 的使用方式与支承区相同。因此，ACI 318-19 第 25.9 章中定义的局部区域必须按照 ACI 318-19 第 25.9.3 条手动进行验算。PLA 的使用仅为避免局部区域超过应变准则而导致计算提前终止。另一方面，根据 ACI 318-19 第 25.9.4.3.1(b) 条，抵抗平面内劈裂应力和剥落应力的钢筋可在软件中直接且有效地进行验算。</p>"
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"value": "<p>正常使用极限状态评估包括应力限制、裂缝宽度和挠度限值的验算。根据 ACI 318-19，混凝土和钢筋单元中的应力校核方式与承载能力极限状态的校核方式类似。</p>\n<h3>应力限制</h3>\n<p>对于预应力构件 U 类和 T 类，应验算正常使用荷载下混凝土的允许压应力。根据表 R24.5.2.1，对于假定已开裂的混凝土，无需进行应力限制校核。用户需在设计构件设置中指定预应力构件的类别。</p>\n<figure data-asset-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" data-image-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5dff4f86-fd02-432a-812c-cf520aabe92b/Prestressed%20member%20class.png\" data-asset-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" data-image-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 53\\qquad Prestressed flexural member class selection}}}\\]</em></p>\n<p>ACI 318-19 第 24.5.4.1 条规定，承受瞬时荷载构件的允许压应力为 <em>0.6f</em><em><sub>c</sub></em><em>'。</em>压应力限值 <em>0.45f</em><em><sub>c</sub></em><em>'</em> 的设定是为了降低预应力混凝土构件在重复荷载作用下的破坏概率。该限值同时也被认为是防止过度徐变变形的合理取值。当应力较高时，随着施加应力的增大，徐变应变往往会更快速地增加。</p>\n<p>混凝土受压应力以正常使用极限状态有限元分析所得最大主压应力 <em>f</em><em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与基于表 24.5.4.1 确定的限值之比来评估。</p>\n<figure data-asset-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" data-image-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/26aa9ff8-a409-41a2-b69b-b28fc2841ec0/Concrete%20compressive%20stress%20limits%20at%20service%20loads%20-%20ACI.png\" data-asset-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" data-image-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 54\\qquad Concrete compressive stress limits at service loads}}}\\]</em></p>\n<p>在软件中，<em>预应力加持续荷载</em>作为长期组合处理，<em>预应力加总荷载</em>作为短期组合处理。</p>\n<h3>挠度</h3>\n<p>根据所选组合类型（长期或短期），分别计算长期或短期挠度。最大允许挠度值应由用户确定，并应按照 ACI 138-19 第 24.2 条的规定考虑。 </p>\n<figure data-asset-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" data-image-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/35ae9de1-6a34-4952-a6e7-ffc528e1e5aa/Deflection%20limit%20value%20selection.png\" data-asset-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" data-image-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 55\\qquad Maximum allowable deflection value}}}\\]</em></p>\n<p>在软件中，可以分别显示恒载挠度 <em>Δ</em><em><sub>DL</sub></em> 和活载挠度 <em>Δ</em><em><sub>LL</sub></em>，以及总挠度 <em>Δ</em><em><sub>Tot</sub></em><sub> </sub>（恒载+活载），同时显示变形形状。</p>\n<p>截断端处的挠度无法进行校核。</p>\n<h3>裂缝宽度</h3>\n<p><br></p>\n<p>裂缝宽度和裂缝方向按正常使用极限状态短期或长期组合计算。由于 ACI 规范未直接规定裂缝宽度限值，用户须自行指定裂缝宽度限值 <em>w</em><em><sub>lim</sub></em>。</p>\n<p>验算结果表示如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<p><em>w</em> 由有限元分析计算所得的短期或长期裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p>软件中采用的裂缝宽度计算方法符合 ACI 224R-01 的规定，本文档中亦有更详细的说明。因此，可参照 ACI 224R-01 表 4.1 确定裂缝宽度限值。</p>\n<figure data-asset-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" data-image-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4af498a4-6b3b-4043-be8f-f10522f5b188/Reasonable%20crack%20widths%20-%20ACI.png\" data-asset-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" data-image-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 56\\qquad Reasonable crack widths for reinforced concrete under service load}}}\\]</em></p>\n<p>裂缝宽度有两种计算方式（稳定开裂和非稳定开裂）。在一般情况下（稳定开裂），裂缝宽度通过对钢筋一维单元的应变进行积分来计算。裂缝方向则由距给定钢筋一维有限单元中心最近的三个二维混凝土单元积分点计算得出。虽然这种裂缝方向计算方法与实际裂缝位置并不完全对应，但其结果仍具有代表性，所得裂缝宽度结果可与规范要求的钢筋位置处裂缝宽度限值进行比较。</p>"
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"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM（协调应力场法）中用于强度计算的混凝土模型，基于 AASHTO LRFD 强度设计中的平衡条件与应变协调假定。根据 AASHTO LRFD（2024）第 5.6.2.1 条，忽略混凝土的抗拉强度。</p>\n<figure data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 57\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p>CSFM（协调应力场法）在 <em>IDEA StatiCa Detail</em> 中的实现，未对受压混凝土采用以应变表达的显式破坏准则（即在达到峰值应力后，采用塑性分支，ε<em><sub>c</sub></em><sub>0</sub> 最大值取 5%，而 AASHTO LRFD（2024）第 5.6.2.1 条假定极限应变小于 0.3%）。这一简化使得无法验证受压破坏结构的变形能力。然而，当在开裂混凝土折减系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，定义见图 57）的基础上，通过 <em>fib</em> Model Code 2010 中定义的 <em>\\(\\eta_{fc}\\)</em> 折减系数考虑混凝土强度提高时脆性增大的影响，可以正确预测强度，具体如下：</p>\n<p>\\[f'_{c,lim}=\\alpha_{1}\\cdot\\phi_{c}\\cdot k_{c}\\cdot f'_{c}\\]</p>\n<p>\\[k_{c}=\\eta_{fc}\\cdot k_{c2}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>1</sub> 为混凝土抗压强度折减系数，定义见 AASHTO LRFD（2024）第 5.6.2.2 条。采用抛物线-矩形应力-应变图时，需将最大压应力乘以该系数进行折减。该系数对受压区应力分布取平均，使得所得抗压强度不超过采用带下降塑性分支的应力-应变图所计算的抗压强度<em>。</em></p>\n<p><em>Φ</em><em><sub>c </sub></em>为混凝土抗力系数，默认值按 AASHTO LRFD（2024）第 5.5.4.2 条取用。</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为横向开裂引起的折减系数。</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体抗压强度（在定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 58\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为折减系数，其假定与 AASHTO LRFD（2024）第 5.8.2.5.3a 条及表 5.8.2.5.3a-1 中给出的混凝土效率系数 <em>ν</em> 相同，区别在于：在 CSFM（协调应力场法）中，对每个有限单元均检验垂直于主压应力方向的主拉应力是否存在（而非仅在拉压杆模型的节点处检验）。</p>\n<h3>混凝土 – 正常使用</h3>\n<p>正常使用极限状态分析对强度分析所用的本构模型进行了一定简化。受压混凝土应力-应变曲线的塑性分支被忽略，弹性分支取为线性且无限延伸，压力软化规律不予考虑。这些简化提高了数值稳定性和计算速度，只要正常使用极限状态下的材料应力结果明显低于屈服点，即不影响解的普遍性（与 AASHTO LRFD 正常使用极限状态方法一致）。因此，正常使用分析所采用的简化模型仅在所有验算要求均满足时方为有效。</p>\n<figure data-asset-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" data-image-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/be2c4149-9e8e-4595-b5a5-7e9fa87c20f3/Concrete%20stress-strain%20for%20serviceability%20-%20AASHTO.png\" data-asset-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" data-image-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 59\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>长期本构关系（图 59 中红色曲线）用于裂缝宽度计算、总挠度计算以及预应力构件在顶部功能区选择长期效应时的应力限值验算。在 IDEA StatiCa Detail 软件中，长期效应验算采用有效弹性模量，如 AASHTO LRFD（2024）C5.12.5.3.6-1 所述。</p>\n<p>\\[E_{eff} = \\frac{E_{c}}{1+\\psi}\\]</p>\n<p>其中：<br><em>E</em><em><sub>c</sub></em> 为弹性模量，定义见 AASHTO LRFD（2024）第 5.4.2.4 条<br><em>ψ</em> 为徐变系数，定义见 AASHTO LRFD（2024）第 5.4.2.3.2 条</p>\n<p>徐变系数由用户在材料属性中定义。</p>\n<p><strong>短期效应</strong></p>\n<p>短期验算需另行进行计算，所有荷载均不计徐变系数。长期与短期验算的两次计算均如图 59 所示。</p>\n<h3>钢筋</h3>\n<p>非预应力钢筋采用具有明确屈服点的理想弹塑性应力-应变图，见 AASHTO LRFD（2024）第 5.4.3 条。该图的定义仅需已知钢筋的基本参数——强度和弹性模量。</p>\n<p>钢筋的应力-应变图也可由用户自定义，但在此情况下，无法考虑拉力刚化效应（即无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 60 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋抗力系数，默认值按 AASHTO LRFD（2024）第 5.5.4.2 条取用。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋弹性模量</p>\n<p>计算终止的极限应变取为 10%，该取值基于 ASTM A955/A955M-20c 第 7 条，被认为是安全的。</p>\n<p>拉力刚化（图 61） 通过修正裸钢筋的输入应力-应变关系自动加以考虑，以反映埋入混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 61\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
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"value": "<p>协调应力场法符合现代设计规范的要求。由于计算模型仅使用标准材料属性，设计规范规定的分项安全系数格式可直接应用，无需任何调整。这样，输入荷载经过分项系数处理，材料特征值通过相应的抗力系数进行折减，与常规混凝土分析方法完全一致。</p>\n<p><strong>抗力系数</strong>的取值规定于 AASHTO LRFD（2024）第 5.5.4 条。混凝土和钢筋的默认值采用偏保守的取值，基于典型算例为 D 区的假设——这是拉压杆方法的典型应用场景。然而，该方法可对任意类型的构件进行建模。因此，若评估的是受压控制或受拉控制构件，用户可在\"首选项\"中修改强度折减系数的取值。</p>\n<figure data-asset-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" data-image-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/22c831e5-30cb-49da-9661-edf4748ca6aa/Resistance%20factors%20-%20AASHTO.png\" data-asset-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" data-image-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 62\\qquad The setting of resistance factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>荷载分项系数和荷载组合应按照 AASHTO LRFD 桥梁设计规范（2024）第 3.4.1 条及表 3.4.1-1 至 3.4.1-6 的规定确定。AASHTO LRFD 明确规定了承载能力极限状态荷载组合（Strength I 至 Strength V）以及正常使用极限状态荷载组合（Service I 至 Service IV），并给出了各工况对应的荷载分项系数。</p>\n<p>对于每个模板，程序均包含预定义的基本组合，需根据所处理的构件情况进行补充完善。</p>\n<figure data-asset-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" data-image-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b3a557f2-2e6a-4b2c-8ba8-bfd210e04c3f/Load%20factors%20AASHTO.png\" data-asset-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" data-image-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 63\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>"
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"value": "<p>AASHTO 要求的各项验算基于模型直接输出的结果进行评估。验算内容包括混凝土强度、钢筋强度以及锚固（粘结剪应力）。</p>\n<p><strong>混凝土抗压强度</strong>通过有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em>（辅助结果中也称为 σ<sub>2</sub>）与限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>在受拉和受压状态下均通过裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定限值 <em>f</em><em><sub>y,lim</sub></em> 之比进行评估。</p>\n<p><strong>粘结剪应力</strong>单独通过有限元分析计算得到的粘结应力 τ<em><sub>b</sub></em> 与粘结强度 <em>f</em><em><sub>bu</sub></em> 之比进行评估。</p>\n<p>然而，由于 AASHTO 中未明确定义粘结强度，其值须通过确定锚固长度的公式推导得出。粘结强度实际上是确定锚固长度的主要输入参数；参见 AASHTO LRFD (2024) 第 C5.10.8.2 条或 NCHRP Report 733 附录 E 第 E-9 页。</p>\n<p>AASHTO LRFD (2024) 第 5.10.8.2.1 条和第 5.10.8.2.2 条所述的计算方法，需要了解 <em>l</em><em><sub>d</sub></em> 范围内横向钢筋的最大中心间距、沿劈裂面展开的钢筋根数、所有横向钢筋的总截面面积以及其他几何量，而这些参数在 Detail 软件模型中对于一般输入无法可靠确定，因此采用了 AASHTO LRFD (2014) 第 5.11.2.1.1 条的方法，具体如下：</p>\n<p>假设将钢筋锚入混凝土块中，锚固长度达到 <em>l</em><em><sub>d</sub></em> 或更大时，拔出钢筋将导致钢筋断裂而非混凝土拔出破坏。可用以下公式表达：</p>\n<p>\\[\\pi\\cdot d_{b} \\cdot l_{d} \\cdot f_{bu}=f_{y}\\cdot A_{b}\\]</p>\n<p>其中：</p>\n<ul>\n <li><em>d</em><em><sub>b</sub></em> 为钢筋直径</li>\n <li><em>l</em><em><sub>d</sub></em> 为锚固长度</li>\n <li><em>f</em><em><sub>bu</sub></em> 为粘结强度</li>\n <li><em>f</em><em><sub>y</sub></em> 为钢筋屈服强度</li>\n <li><em>A</em><em><sub>b</sub></em> 为钢筋截面面积</li>\n</ul>\n<p>由上式可方便地推导出粘结强度的计算公式：</p>\n<p> \\[f_{bu}=\\frac{f_{y}\\cdot A_{b}}{\\pi\\cdot d_{b} \\cdot l_{d} }\\]</p>\n<p><br></p>\n<p>基本受拉锚固长度 <em>l</em><em><sub>db</sub></em> 按 AASHTO LRFD (2014) 第 5.11.2.1.1 条确定如下：</p>\n<p>对于 11 号及以下钢筋： \\(l_{bd}=\\max\\left(1.25\\cdot\\dfrac{A_{b}\\cdot f_{y}}{\\sqrt{f'_{c}}},\\ 0.4\\cdot d_{b}\\cdot f_{y}\\right)\\)</p>\n<p>对于 14 号钢筋： \\(l_{bd}=\\dfrac{2.70\\cdot f_{y}}{\\sqrt{f'_{c}}}\\)</p>\n<p>对于 18 号钢筋： \\(l_{bd}=\\dfrac{3.5\\cdot f_{y}}{\\sqrt{f'_{c}}}\\)</p>\n<p>其中：</p>\n<ul>\n <li><em>A</em><em><sub>b</sub></em> 为钢筋截面面积（in<sup>2</sup>）</li>\n <li><em>f</em><em><sub>y</sub></em> 为钢筋规定屈服强度（ksi）</li>\n <li><em>f'</em><em><sub>c</sub></em> 为混凝土 28 天规定抗压强度，除非另有规定龄期（ksi）</li>\n <li><em>d</em><em><sub>b</sub></em> 为钢筋直径（in）</li>\n</ul>\n<p>然后，将基本锚固长度 <em>l</em><em><sub>db</sub></em> 乘以 AASHTO LRFD (2014) 第 5.11.2.1.2 条和第 5.11.2.1.3 条所述的修正系数，即可确定作为输入的锚固长度 <em>l</em><em><sub>d</sub></em>。</p>\n<p>来自第 5.11.2.1.3 条的减小锚固长度的修正系数在软件中始终取 1.0。根据下图，对于\"不良\"粘结条件，顶部水平或近水平钢筋的修正系数取 1.4：</p>\n<figure data-asset-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" data-image-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9daaedd3-8368-4677-b72f-1dbc0933690e/Bond%20conditions%20-%20AASHTO.png\" data-asset-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" data-image-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 64\\qquad Description of bond conditions; a) b) 'good' bond conditions for all bars; c) d) unhatched zone – 'good' bond conditions, hatched zone – 'poor' bond conditions}}}\\]</em></p>\n<p>浇筑方向可在软件中设置。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 65\\qquad Direction of concreting}}}\\]</em></p>\n<p>第 5.11.2.1.2 条中确定的所有其他系数均取 1.0，因为软件仅支持普通重量混凝土，且仅支持无涂层钢筋。</p>\n<p>受压钢筋的粘结剪应力和粘结强度的计算方法与受拉钢筋类似，但采用 AASHTO LRFD (2014) 第 5.11.2.2 条的公式。</p>\n<p>软件还提供<strong>光圆钢筋</strong>的建模选项。更多信息请参见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><br></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可通过以下两种方式定义。</p>\n<p>\\[F_{tot}=A_{b} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>b</sub></em> 为钢筋截面面积，<em>f</em><em><sub>s</sub></em> 为钢筋中的应力。</p>\n<p>或表示为锚固力 <em>F</em><em><sub>a </sub></em>与粘结力 <em>F</em><em><sub>bond</sub></em> 之和<em>。</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可通过沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到<em>。</em></p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中考虑钢筋<strong>强度</strong>以及<strong>锚固条件</strong>（混凝土与钢筋之间的粘结及锚固弯钩、环等）的最大力。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{b}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{b}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋的周长，<em>l</em> 为从钢筋起点到所关注点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 66\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为由相邻单元夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括：直钢筋（即无锚固端折减）、90° 弯钩、180° 弯钩、完全粘结以及连续钢筋。图 67 展示了纵向钢筋的所有这些类型及相应的锚固系数 β。所采用锚固系数的取值来源于 AASHTO LRFD (2014) 第 5.11.2.1 节公式与第 5.11.2.4.1 节公式的对比。需要指出的是，尽管有多种可用选项，CSFM（协调应力场法）仅区分三种锚固端类型：(i) 锚固长度无折减；(ii) 标准锚固情况下锚固长度折减 30%；(iii) 完全粘结。</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 67\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; 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"value": "<p>在设计混凝土结构时，我们会遇到两大类局部受压区（PLA）——第一类为<strong>支座</strong>，第二类为<strong>锚固区</strong>。 </p>\n<p>根据现行钢筋混凝土结构设计规范，对于<strong>支座</strong>，应考虑混凝土局部压碎和横向拉力。对于作用在面积 <em>A</em><em><sub>1</sub></em> 上的均布荷载，混凝土的受压承载力可根据设计分布面积 <em>A</em><em><sub>2</sub></em> 提高至最多两倍。详见 AASHTO LRFD (2024) 第 5.6.5 条。<br></p>\n<figure data-asset-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" data-image-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e777285d-ac56-4c61-801e-d2edd9ae0318/PLA%20AASHTO.png\" data-asset-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" data-image-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 68\\qquad Partially loaded areas for bearings according to AASHTO LRFD (2024) Article 5.6.5}}}\\]</em></p>\n<p>对于后张<strong>锚固区</strong>，应遵循 AASHTO LRFD (2024) 第 5.8.4.4 条的规定。</p>\n<p>局部受压区必须配置足够的横向钢筋，以承受该区域产生的劈裂力。若未配置所需的横向钢筋，则不能考虑提高混凝土的受压承载力。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部受压区</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 69\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>利用 CSFM（协调应力场法），可以在设计和评估钢筋混凝土结构时考虑局部受压区混凝土受压承载力提高的影响。由于 CSFM（协调应力场法）是平面（2D）模型，而局部受压区是空间（3D）问题，因此需要找到一种将这两种不同类型问题相结合的解决方案（<em>图 69</em>）。若激活\"局部受压区\"功能，则根据 ACI 规定创建允许的锥体几何形状（<em>图 68</em>）。对于指定的混凝土构件几何形状及每个 PLA 的尺寸，所有几何碰撞均在三维空间中完整求解。随后，建立局部受压区的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 70\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>实践证明，修改材料模型的方法并不适用，主要原因在于将属性映射到有限单元法网格存在困难。研究表明，独立于有限单元法网格的方法是更为合适的解决方案。对于已知的压力锥几何形状，建立完全协调的虚拟压杆（<em>图 70</em> <em>和图 71</em>）。这些压杆与模型中所用混凝土具有相同的材料属性，包括应力-应变图。锥体形状决定了压杆的方向，从而将荷载从 PLA 逐渐分布至设计分布面积。虚拟压杆的面积密度在锥体各部分是变化的，并在荷载方向上增加了虚拟混凝土面积。在受荷面积（<em>A</em><em><sub>1</sub></em>）处，根据比值 \\(\\sqrt{A_{1} \\cdot A_{2}} - A_{real}\\) （其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支承面积）增加虚拟混凝土面积，该面积向设计分布面积（<em>A</em><em><sub>2</sub></em>）方向线性减小至零。该方案确保混凝土中的压应力在整个锥体体积内保持恒定。</p>\n<figure data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png\" data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{2}}{A_{1}}} - \\frac{A_{real}}{A_{1}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 71\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压区的抗力根据 AASHTO LRFD (2024) 第 5.6.5 条规定的设计分布面积与受荷面积之比进行提高。需要注意的是，这是一种设计模型，无法精确描述局部受压区的应力状态，实际应力分布要复杂得多。然而，该方案能够在考虑局部受压区承载力提高的同时，正确地将荷载分布至整个模型。此外，它还能在该区域正确引入横向应力，从而合理设计抵抗劈裂力的钢筋。</p>\n<p>AASHTO LRFD (2024) 第 5.8.4.4 条规定了允许的<strong>支座</strong>承压应力为 <em>0.85f</em><em><sub>c</sub></em><em>'</em>。密度受到限制，以确保不超过公式 5.6.5-3 中规定的最大两倍承载力。 </p>\n<p>对于<strong>锚固区</strong>，PLA 在软件中的使用方式与支座相同。因此，第 5.8.4.4 条和第 5.8.4.5 条中定义的局部区域和整体区域的压应力必须手动校核。PLA 的使用仅为避免局部区域的应变准则被超越，从而导致计算过早终止。另一方面，抵抗整体区域（第 5.8.4.5 条定义）中劈裂、剥落面内及边缘拉应力的钢筋，可在软件中直接且便捷地进行验算。</p>"
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"value": "<p>正常使用极限状态的评估包括应力限制、裂缝宽度和挠度限值。根据 AASHTO LRFD，以与承载能力极限状态类似的方式对混凝土和钢筋单元中的应力进行校核。</p>\n<h3>应力限制</h3>\n<p>混凝土压应力仅对预应力构件（当模型中存在预应力荷载工况时）进行评估，评估方式为：将正常使用极限状态有限元分析所得最大主压应力 <em>f</em><em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与基于 AASHTO LRFD 表 5.9.2.3.2a-1 设定的限值之比进行计算。</p>\n<figure data-asset-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" data-image-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aacf656a-eb2c-4aae-a8b2-6b1c16cdc864/Compressive%20Stress%20Limits%20in%20Prestressed%20Concrete%20at%20Service%20Limit%20State%20-%20AASHTO.png\" data-asset-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" data-image-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 72\\qquad Concrete compressive stress limits at service loads}}}\\]</em></p>\n<p>在软件中，<em>预应力加永久荷载</em>视为持续荷载，<em>预应力、永久荷载和瞬时荷载</em>视为总荷载。</p>\n<figure data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bf637c0b-a972-4836-a119-45f59df9ed58/Combination%20types%20-%20AASHTO.png\" data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 73\\qquad Serviceability combination types}}}\\]</em></p>\n<p>此外，始终可以使用考虑或不考虑徐变系数的材料模型，分别对短期效应和长期效应进行分析——详见\"材料模型（AASHTO）\"章节。</p>\n<figure data-asset-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" data-image-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/74bf96e4-46c2-4bb5-9b9f-2ab9ebf8f58b/Stress%20limitation%20model%20type%20-%20AASHTO.png\" data-asset-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" data-image-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 74\\qquad Serviceability material models}}}\\]</em></p>\n<h3>挠度</h3>\n<p>对每个启用挠度评估的组合，分别计算瞬时挠度和总挠度。 </p>\n<ul>\n <li>对于瞬时挠度，采用 AASHTO LRFD（2024）第 5.4.2.4 条规定的弹性模量 <em>E</em><em><sub>c</sub></em>。 </li>\n <li>对于总挠度，采用 AASHTO LRFD（2024）第 C5.12.5.3.6 条规定的有效弹性模量 <em>E</em><em><sub>c,eff</sub></em>。 </li>\n</ul>\n<p>详见本文档\"<em>材料模型（AASHTO）- 混凝土 – 正常使用极限状态</em>\"章节。</p>\n<p>挠度校核功能在顶部功能区中启用。用户根据 AASHTO LRFD（2024）第 2.5.2.6.2 条，依据所分析构件的类型设定挠度限值。</p>\n<figure data-asset-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" data-image-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b95113f5-c76d-4a13-8962-99fd504ce2f2/Deflection%20check%20AASHTO.png\" data-asset-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" data-image-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 75\\qquad Maximum allowable deflection value}}}\\]</em></p>\n<p>截断端处的挠度无法进行校核。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和方向仅针对长期效应（采用 AASHTO LRFD（2024）第 C5.12.5.3.6 条规定的 <em>E</em><em><sub>c,eff</sub></em>）在启用裂缝宽度评估的组合中进行计算。基于用户指定限值的验证如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<p><em>w</em> 有限元分析计算所得裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p>限值 <em>w</em><em><sub>lim</sub></em> 应根据构件类型和暴露类别，依据 AASHTO LRFD（2024）第 5.6.7 条及其注释确定。 </p>\n<p>裂缝宽度的计算有两种方式（稳定裂缝和非稳定裂缝）。在一般情况下（稳定裂缝），裂缝宽度通过对钢筋一维单元的应变进行积分来计算。裂缝方向则由距给定钢筋一维有限单元中心最近的三个二维混凝土单元积分点计算得出。尽管这种计算裂缝方向的方法与裂缝的实际位置并不完全对应，但其仍能提供具有代表性的数值，所得裂缝宽度结果可与规范要求的钢筋位置处裂缝宽度限值进行比较。</p>"
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"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM（协调应力场法）中用于强度计算的混凝土模型基于抛物线-塑性应力-应变曲线。与经典钢筋混凝土设计一样，忽略抗拉强度。</p>\n<figure data-asset-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" data-image-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc47139c-3c53-4397-bfa6-71fe09d5c24b/Concrete%20stress-strain%20diagram%20CSFM%20-%20AUS.png\" data-asset-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" data-image-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 76\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p>CSFM（协调应力场法）在 <em>IDEA StatiCa Detail</em> 中的实现，对受压混凝土未考虑以应变表示的显式破坏准则（即，在达到峰值应力后，考虑最大值为 5% 的 ε<em><sub>c</sub></em><sub>0</sub> 塑性分支，而 AS 3600 第 8.3.1 条假定极限应变小于 0.3%）。这一简化不允许验证受压破坏结构的变形能力。然而，当在考虑开裂混凝土系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，定义见图 77）的基础上，同时通过 <em>fib</em> 模型规范 2010 中定义的 <em>\\(\\eta_{fc}\\)</em> 折减系数考虑混凝土随强度提高而增加的脆性时，可以正确预测强度，具体如下：</p>\n<p>\\[f'_{c,lim}=\\alpha_{2}\\cdot\\phi_{s}\\cdot \\beta \\cdot \\eta_{fc}\\cdot f'_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>2</sub> 为 AS 3600 第 8.3.1 条定义的混凝土抗压强度折减系数<br>采用抛物线-矩形应力-应变图时，需将最大压应力乘以该系数进行折减。这样对压缩区应力分布取平均，使得所得抗压强度不超过采用具有下降塑性分支的应力-应变图计算所得的抗压强度<em>。</em>第 8.1.3 章对矩形应力块定义了类似方法。</p>\n<p><em>Φ</em><em><sub>s </sub></em>为混凝土的应力折减系数。默认值按 AS 3600 表 2.2.3 设定。</p>\n<p><em>β</em> 为横向开裂引起的折减系数（本文中亦称为 <em>k</em><em><sub>c</sub></em><sub>2</sub>）</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体强度（在定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 77\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>β</em> 是基于与第 2.2.3 章定义的有效抗压强度系数相同原则的折减系数。确定该系数所依据的文献（包括 AS3600 标准的相关背景）可在 AS3600:2018 Sup 1:2022 第 C2.2.3 条中查阅。</p>\n<h3>混凝土 – 正常使用极限状态</h3>\n<p>正常使用极限状态分析对强度分析所用的本构模型进行了一定简化。忽略混凝土受压应力-应变曲线的塑性分支，弹性分支为线性且无限延伸。不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，只要正常使用极限状态下的材料应力结果明显低于屈服点（如 AS3600 所要求），则不会降低解的普遍性。因此，正常使用极限状态所用的简化模型仅在满足所有验证要求时有效。</p>\n<figure data-asset-id=\"1a187098-8984-42f2-b203-d261cab0f727\" data-image-id=\"1a187098-8984-42f2-b203-d261cab0f727\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5b3dc17b-2a5b-4258-8495-b5d436e4885b/Concrete%20stress-strain%20for%20serviceability%20-%20AUS.png\" data-asset-id=\"1a187098-8984-42f2-b203-d261cab0f727\" data-image-id=\"1a187098-8984-42f2-b203-d261cab0f727\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 78\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>在正常使用极限状态分析中，混凝土的长期效应采用按 AS 3600 第 3.1.8 条确定的设计徐变系数（<em>φ</em><em><sub>cc</sub></em>，默认取值为 2.5）来考虑，该系数对混凝土割线弹性模量（<em>E</em><em><sub>c</sub></em>）进行如下修正：</p>\n<p>\\[E_{c,eff} = \\frac{E_{c}}{1+\\varphi_{cc}}\\]</p>\n<p>荷载增量按以下顺序依次计算：预应力 - 永久荷载 - 可变荷载，每个增量采用如图 78 所示的相应有效弹性模量。徐变系数由用户在材料属性中定义，并应按 AS 3600 第 3.1.8.3 条计算。</p>\n<figure data-asset-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" data-image-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f9c75c70-4a16-4077-963e-7ccbed22202a/Desgn%20creep%20factor%20-%20AUS.png\" data-asset-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" data-image-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 79\\qquad Definition of the design creep factor}}}\\]</em></p>\n<p><strong>短期效应</strong></p>\n<p>为进行短期验证，另行进行一次计算，其中所有荷载均不考虑持续荷载的时间相关系数。长期和短期验证的两次计算均如图 78 所示。</p>\n<h3>钢筋</h3>\n<p>对于非预应力钢筋，采用具有明确屈服点的理想弹塑性应力-应变图，见 AS 3600 第 3.2 节。该图的定义仅需了解钢筋的基本属性——强度和弹性模量。</p>\n<p>钢筋的应力-应变图也可由用户自定义，但在此情况下，无法考虑拉力刚化效应（无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4e33b934-9d0f-4ba7-9764-4f31801c752b/Steel%20stress-strain%20diagram%20CSFM%20-%20AUS.png\" data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 80 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋的强度折减系数。默认值按 AS 3600 表 2.2.3 设定。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋弹性模量</p>\n<p>拉力刚化（图 81） 通过修正裸钢筋的输入应力-应变关系自动加以考虑，以反映埋入混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b27b5ab6-24ea-410b-901a-fccbd7e4005f/Tension%20stiffening%20CSFM%20-%20AUS.png\" data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 81\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
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"value": "<p>AS 3600 要求的各项验证基于模型直接输出的结果进行评估。验证内容包括混凝土强度、钢筋强度及锚固（粘结剪应力）。</p>\n<p><strong>混凝土强度</strong>（受压）以有限元分析所得最大主压应力 <em>f</em><em><sub>c</sub></em>（辅助结果中亦记为 σ<sub>2</sub>）与限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>在受拉和受压状态下均以裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定限值 <em>f</em><em><sub>sy,lim</sub></em> 之比进行评估。</p>\n<p><strong>粘结剪应力</strong>单独以有限元分析计算所得粘结应力 τ<em><sub>b</sub></em> 与极限设计粘结应力 <em>f</em><em><sub>bu</sub></em> 之比进行评估。</p>\n<p>极限设计粘结应力 <em>f</em><em><sub>bu</sub></em> 的确定采用 AS3600:2018 Sup 1:2022 中公式 C13.1.2.2：</p>\n<p>\\[f_{bu}=\\frac{k_{2}}{k_{1} \\cdot k_{3}} \\cdot (0.5 \\cdot \\sqrt{f'_{c}})\\]</p>\n<p>其中 <em>f'</em><em><sub>c</sub></em><em> ≤ 65 MPa</em>（公式中单位为 MPa），<em>k</em> 系数按 AS 3600 第 13.1.2.2 条确定如下：</p>\n<p><em>k</em><em><sub>3</sub></em><em> = 0.7</em> （所有钢筋的保守取值）<br><em>k</em><em><sub>2</sub></em><em> = (132 - d</em><em><sub>b</sub></em><em>) / 100</em> （<em>d</em><em><sub>b</sub></em> 为钢筋直径，单位毫米）<br>= 1.3（适用于水平钢筋，其下方浇筑混凝土厚度超过 300 mm），否则取 1.0</p>\n<p><em>k</em><em><sub>1</sub></em> 由模型中钢筋的位置及浇筑方向自动推导，浇筑方向可在软件中针对每个项目条目进行设置，如下所示。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 84\\qquad Direction of concreting}}}\\]</em></p>\n<p>基本锚固长度 <em>L</em><em><sub>sy,tb</sub></em> 按 AS 3600 公式 13.1.2.2 计算如下：</p>\n<p>\\[L_{sy,tb}=\\frac{0.5\\cdot k_{1}\\cdot k_{3}\\cdot f_{sy}\\cdot d_{b}}{k_{2}\\cdot \\sqrt{f'_{c}}}\\ge 29 \\cdot k_{1}\\cdot d_{b}\\]</p>\n<p>由公式可见，基本锚固长度 <em>L</em><em><sub>sy,tb</sub></em> 存在下限，因此软件中极限设计粘结应力 <em>f</em><em><sub>bu</sub></em> 也须相应加以限制，即：</p>\n<p>\\[f_{bu}\\le \\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p>其中 <em>f</em><em><sub>sy</sub></em> 单位为 MPa。</p>\n<p><em>f</em><em><sub>bu</sub></em> 限值的推导过程如下：</p>\n<p>\\[f_{bu}= \\frac{f_{sy}\\cdot A_{s}}{ \\pi \\cdot d_{b} \\cdot L_{sy,tb}}=\\frac{f_{sy}\\cdot \\pi \\cdot d_{b}^{2}}{4 \\cdot \\pi \\cdot d_{b} \\cdot 29 \\cdot k{1} \\cdot d_{b}} =\\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p>软件中还提供<strong>光圆钢筋</strong>的建模选项。更多信息请参阅：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><br></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与限制力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 为有限元分析的结果，可通过以下两种方式定义。</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>f</em><em><sub>s</sub></em> 为钢筋中的应力。</p>\n<p>或表示为锚固力 <em>F</em><em><sub>a </sub></em>与粘结力 <em>F</em><em><sub>bond</sub></em> 之和<em>。</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可通过沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分求得。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>限制力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是综合考虑钢筋<strong>强度</strong>及<strong>锚固条件</strong>（混凝土与钢筋之间的粘结以及锚固弯钩、环等）后，钢筋单元所能承受的最大力。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到计算截面的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 85\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为由相邻单元夹角大小计算所得的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括：直钢筋（即无锚固端折减）、标准弯折、标准弯钩、完全粘结及连续钢筋。图 86 展示了纵向钢筋的所有锚固类型及相应锚固系数 β。所采用锚固系数的取值依据 AS 3600 第 13.1.2 条。需要注意的是，CSFM（协调应力场法）区分三种锚固端类型：（i）锚固长度不折减；（ii）标准锚固情况下锚固长度折减 50%；（iii）完全粘结。</p>\n<figure data-asset-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" data-image-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\"><img 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"value": "<p>正常使用极限状态评估针对裂缝宽度和挠度限值进行。 </p>\n<h3>挠度</h3>\n<p>根据所选组合类型（长期或短期），分别计算长期或短期挠度。最大允许挠度值应由用户确定，并应按照 AS 3600 第 2.3.2 条的规定考虑。 </p>\n<figure data-asset-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" data-image-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b1e12226-ebe6-4ecf-be42-0f9857c02cf9/Maximum%20allowable%20deflections.png\" data-asset-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" data-image-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 87\\qquad Maximum allowable deflection values}}}\\]</em></p>\n<p>在软件中，可以分别显示永久荷载产生的挠度 <em>Δ</em><em><sub>PL</sub></em> 和可变荷载产生的挠度 <em>Δ</em><em><sub>IL</sub></em>，以及总挠度 <em>Δ</em><em><sub>Tot</sub></em><sub> </sub>（永久 + 可变），同时显示变形形状。</p>\n<p>截断端处的挠度无法进行验算。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和裂缝方向按正常使用短期或长期组合进行计算。软件中直接计算裂缝宽度的方法依据 AS 3600 第 8.6.2.3 条规定的方法。 </p>\n<p>验算结果表示如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<p><em>w</em> 由有限单元法分析计算得到的短期或长期裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 由用户定义的裂缝宽度限值。</p>\n<p>推荐的最大裂缝宽度可参见 AS3600:2018 Sup 1:2022 表 C2.3.3.1。</p>\n<figure data-asset-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" data-image-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/34472a7f-e0a5-4d30-b990-361d7cd59f2b/REcommended%20final%20design%20crack%20widths%20-%20AUS.png\" data-asset-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" data-image-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 88\\qquad Recommended final design crack widths}}}\\]</em></p>\n<p>另外，根据 AS3600:2018 Sup 1:2022 第 C8.6.1 条——对于承受长期使用荷载的结构，<em>w</em><em><sub>lim</sub></em> 的推荐值如下：</p>\n<figure data-asset-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" data-image-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e16caacd-4f7b-4ba4-a7d1-48dd71a47890/Reccomended%20max%20cracks%20widths%20values%20for%20long-term%20loads.png\" data-asset-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" data-image-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 89\\qquad Recommended values for the limit value of the crack width for beams based on exposure classes}}}\\]</em></p>\n<p>裂缝宽度的计算有两种方式（稳定裂缝和非稳定裂缝）。在一般情况下（稳定裂缝），裂缝宽度通过对钢筋一维单元上的应变进行积分来计算。裂缝方向则由距给定钢筋一维有限单元中心最近的三个二维混凝土单元积分点计算得出。虽然这种计算裂缝方向的方法与裂缝的实际位置并不完全对应，但仍能提供具有代表性的数值，所得裂缝宽度结果可与规范要求的钢筋位置处裂缝宽度限值进行比较。</p>"
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"value": "<p>协调应力场法（CSFM）是一种基于二维平面应力的计算方法，其中混凝土采用二维有限单元模拟，钢筋单元以一维单元通过约束与之连接。模型中还可加入代表有粘结预应力钢筋的特殊一维单元，可模拟为先张和后张形式。</p>\n<p>预应力钢筋的模拟方式与普通钢筋类似，采用传递轴力的线性单元。每根预应力钢筋单元由其截面面积和材料属性表征，这些属性由所用规范（EN 1992-1-1、ACI 318-19 等）规定的特征材料曲线给出。</p>\n<p><strong>欧洲规范</strong></p>\n<p>预应力钢筋的应力-应变图：a) EN 1992-1-1 中定义的应力-应变图；b) 先张钢筋的初始应变</p>\n<figure data-asset-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" data-image-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aa25e678-c691-4887-9f8f-b5ae0c4a4fb2/prestressing%20model_Detail_01.png\" data-asset-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" data-image-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" alt=\"\"></figure>\n<p><strong>ACI</strong></p>\n<p>预应力钢筋的应力-应变图：a) 应力-应变图；b) 先张钢筋的初始应变</p>\n<figure data-asset-id=\"7b26f280-9951-4255-98c4-90f558de030f\" data-image-id=\"7b26f280-9951-4255-98c4-90f558de030f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c112ef0-c06a-4141-9d09-1e3cfa42d079/prestressing%20model_Detail__ACI.png\" data-asset-id=\"7b26f280-9951-4255-98c4-90f558de030f\" data-image-id=\"7b26f280-9951-4255-98c4-90f558de030f\" alt=\"\"></figure>\n<p><br></p>\n<p>钢筋单元通过粘结模型与混凝土模型的二维单元连接，方式与普通混凝土钢筋相同。 </p>\n<ul>\n <li>阅读 <a data-item-id=\"85424e98-41cd-4bdd-a978-e4b540a10be5\" href=\"\">有限单元类型</a></li>\n</ul>\n<p>粘结模型单元允许预应力钢筋与混凝土之间发生相对变形，并具有适当的非线性特性。这能正确模拟钢筋与混凝土之间的粘结力，以及先张钢筋的锚固模型。后张钢筋端部的构造（如锚板）通过刚度对应于预应力钢筋端部锚具的单元来模拟，端部预应力以面荷载的形式施加到混凝土模型中，作用面积为锚板尺寸。该模型无法正确描述锚下区域的局部三轴应力，该区域须单独考虑。 </p>\n<p>由于预应力钢筋附近的混凝土假定处于受压状态，因此预应力钢筋不考虑混凝土相互作用引起的拉力刚化效应。</p>\n<h2>先张钢筋</h2>\n<p>先张钢筋在构件浇筑前完成张拉，预应力钢筋几乎始终沿直线布置，因此不产生摩擦预应力损失。当混凝土达到所需强度后，钢筋从锚固块上释放，从而激活预应力钢筋，将力从钢筋传递至混凝土。这一效应在物理上等效于钢筋的降温，通过类似热荷载的初始应变来模拟。由此得到预应力钢筋的应力-应变图，如上图 b) 所示。计算模型自动计算结构对所施加预应力的变形响应，从而直接确定构件弹性应变引起的预应力损失。</p>\n<p>由于预应力已知，因此预应力应力 <em>σ</em><em><sub>pmo</sub></em> 也已知，钢筋的材料图用于描述应力对变形的依赖关系，可写为：</p>\n<p><em>\\[{{σ}_{p}}=~{{f}}({{ε}}-{{ε}_{0}})\\]</em></p>\n<p>假设钢筋中的预应力低于屈服强度（即满足 EN 1992-1-1 第 5.10.3 条规定的条件），初始变形也可计算为：</p>\n<p><em>\\[{{ε}_{0}}=\\frac{{{σ}_{pm0}}}{{{E}_{p}}}\\]</em></p>\n<p><em>ε</em><em><sub>0</sub></em> - 预应力引起的初始应变<br><em>σ</em><em><sub>pm0</sub></em> - 放张前的应力<br><em>E</em><em><sub>p</sub></em> - 预应力钢筋的弹性模量</p>\n<p>先张钢筋的特殊性在于其端部锚固通过多种不同机制实现——钢筋与混凝土在分子层面的粘附力、钢筋表面与混凝土界面产生的摩擦力、螺旋钢筋对混凝土的机械挤压，以及预应力钢筋直径增大所产生的楔形机制（即 Hoyer 效应）。上述效应通过修改先张钢筋端部区域锚固模型的属性，纳入 CSFM（协调应力场法）计算模型中。</p>\n<p>先张钢筋与混凝土的相互作用：a) 螺旋钢筋挤入混凝土；b) Hoyer 效应</p>\n<figure data-asset-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" data-image-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/035bbeed-4b37-4477-b848-8ee98b174f72/prestressing%20model_Detail_02.png\" data-asset-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" data-image-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" alt=\"\"></figure>\n<h2>后张钢筋</h2>\n<p>后张钢筋在结构浇筑完成后进行张拉。张拉设备直接支承于结构上，从而消除了结构因预应力弹性应变引起的损失。达到所需预应力后，钢筋被锚固，随后对管道进行灌浆，使钢筋与结构形成粘结。在模拟后张钢筋时，计算因此分为若干加载步骤——张拉、施加其他永久荷载以及施加可变荷载。</p>\n<p>附有一维预应力钢筋单元的混凝土有限单元网格：</p>\n<figure data-asset-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" data-image-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a028db63-b458-44e7-945b-bedabb1a6785/prestressing%20model_Detail_03.png\" data-asset-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" data-image-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" alt=\"\"></figure>\n<h4>加载步骤\"张拉\"</h4>\n<p>在对钢筋进行张拉时，钢筋的刚度不计入结构刚度。在此加载步骤中，线性单元的刚度不在模型中考虑，钢筋单元由与预应力应力和钢筋面积对应的等效荷载代替，如上图所示。在达到预应力全部荷载并收敛后，读取特定线性单元的变形，根据变形确定各预应力钢筋线性单元的初始应变 <em>ε</em><em><sub>0</sub></em>。</p>\n<p>预应力应力可沿钢筋长度手动定义，也可根据钢筋几何形状自动计算。若选择自动计算损失，则考虑摩擦损失（依据 EN 1992-1-1 第 5.10.5.2 条或 ACI 318-19 第 20.3.2 条）以及锚固时的钢筋滑移（锚楔压入）。由于所有预应力钢筋在一个步骤中施加，因此不考虑逐根张拉引起的损失。</p>\n<h4>预应力钢筋参与工作的后续加载步骤</h4>\n<p>在后续加载步骤（施加其他永久荷载和可变荷载）中，采用与先张钢筋相同的处理方式。考虑预应力钢筋的全部刚度，考虑钢筋与周围混凝土之间的粘结，并通过初始应变 <em>ε</em><em><sub>0</sub></em> 修正预应力钢筋的应力-应变图。该应变对每个单元各不相同，由前一加载步骤\"张拉\"获得。由于钢筋与混凝土之间存在粘结，外部荷载引起的结构弹性变形所导致的预应力变化在模型中得到正确考虑。</p>"
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"value": "<p><br></p>\n<p>理论背景基于《结构混凝土协调应力场设计》<br>（Kaufmann 等，2020）</p>\n<h1>IDEA StatiCa Detail 中混凝土非连续区域的结构设计</h1>\n<h2>1 CSFM（协调应力场法）方法简介</h2>\n<p><a href=\"#general-introduction\">1.1 混凝土细部结构设计概述</a><br><a href=\"#main-assumptions-and-limitations\">1.2 主要假设与限制条件</a><br><a href=\"#design-tools-for-reinforcement\">1.3 钢筋设计工具</a></p>\n<h2>2 IDEA StatiCa Detail 分析模型</h2>\n<p><a href=\"#introduction-to-finite-element-implementation\">2.1 有限单元法实现简介</a><br><a href=\"#supports-and-load-transmitting-components\">2.2 支座与荷载传递构件</a><br><a href=\"#load-transfer-at-trimmed-ends-of-beams\">2.3 梁截断端部的荷载传递</a><br><a href=\"#geometric-modification-of-cross-sections\">2.4 截面几何修正</a><br><a href=\"#finite-element-types\">2.5 有限单元类型</a><br><a href=\"#meshing\">2.6 网格划分</a><br><a href=\"#solution-method-and-load-control-algorithm\">2.7 求解方法与荷载控制算法</a><br><a href=\"#presentation-of-results\">2.8 结果展示</a></p>\n<h2>3 模型验证</h2>\n<p><a href=\"#limit-states-and-crack-width-calculation\">3.1 极限状态、裂缝宽度计算与拉力刚化</a></p>\n<h2>4 按欧洲规范进行结构验算</h2>\n<p><a href=\"#material-models-en\">4.1 材料模型（EN）</a><br><a href=\"#safety-factors\">4.2 安全系数</a><br><a href=\"#ultimate-limit-state-analysis\">4.3 承载能力极限状态分析</a><br><a href=\"#partially-loaded-areas\">4.4 局部受压区（PLA）<br></a><a href=\"#serviceability-limit-state-analysis\">4.5 正常使用极限状态分析</a></p>\n<h2>5 按 ACI 318-19 进行结构验算</h2>\n<p><a href=\"#material-models-aci\">5.1 材料模型（ACI）</a><br><a href=\"#strength-reduction-and-load-factors\">5.2 强度折减系数与荷载系数</a><br><a href=\"#strength-verifications\">5.3 强度验算</a><br><a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">5.4 承压区与锚固区——局部受压区<br></a><a href=\"#serviceability-verifications\">5.5 正常使用极限状态验算</a></p>\n<h2>6 按 AASHTO 进行结构验算</h2>\n<p><a href=\"#material-models-aahsto\">6.1 材料模型（AASHTO）</a><br><a href=\"#resistance-and-load-factors\">6.2 抗力系数与荷载系数</a><br><a href=\"#strength-limit-state\">6.3 强度极限状态</a><br><a href=\"#bearing-and-anchorage-zones-resistance-partially-loaded-areas\">6.4 承压区与锚固区抗力——局部受压区</a><br><a href=\"#service-limit-state\">6.5 正常使用极限状态</a></p>\n<h2>7 按 AS 3600 进行结构验算</h2>\n<p><a href=\"#material-models-aus\">7.1 材料模型（AUS）</a><br><a href=\"#stress-reduction-and-load-factors\">7.2 应力折减系数与荷载系数</a><br><a href=\"#strength-and-anchorage-verifications\">7.3 强度与锚固验算</a><a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\"><br></a><a href=\"#serviceability-checks\">7.4 正常使用极限状态验算</a></p>\n<h2><a href=\"#prestressing-in-detail-model-description\">8 Detail 中的预应力——模型描述</a></h2>\n<p><br></p>\n<p><br></p>\n<h1>1 CSFM（协调应力场法）方法简介</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n02b04ae1_9ac2_0186_8a2e_afbfaac3c39e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" 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type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___presentation_of_re\"></object>\n<h1><br></h1>\n<h1>3 模型验证</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n805f2d39_5e1d_0196_07ec_d526e6056d4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___verifica\"></object>\n<h1><br></h1>\n<h1>4 按欧洲规范进行结构验算</h1>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用极限状态荷载组合，另一种针对承载能力极限状态荷载组合。正常使用极限状态分析假定构件在极限状态下的受力性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。该方法允许在正常使用极限状态分析中采用简化本构模型（混凝土应力-应变曲线取线性段），以提高数值稳定性和计算速度。</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n34484ce7_0966_01b0_4e4e_ced1381a2b83\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n87402a88_f6a7_01e2_3c54_6a74bb42f492\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___safety_factors\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"fc5356e8_ad66_019d_500e_56112b2c54e1\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___ultimate_limit_sta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4ffa73af_7903_018b_f050_5cb47586f489\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___partially_loaded_a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c0faeafd_fe53_0187_955b_d143d9265810\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_lim\"></object>\n<h1><br></h1>\n<h1>5 按 ACI 318-19 进行结构验算</h1>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用极限状态，另一种针对强度荷载组合。正常使用极限状态分析假定构件在系数荷载作用下的受力性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。该方法允许在正常使用极限状态分析中采用简化本构模型（混凝土应力-应变曲线取线性段），以提高数值稳定性和计算速度。</p>\n<p>CSFM（协调应力场法）符合 ACI 318-19 第 6.8.1.1 条的规定。为使 CSFM（协调应力场法）满足 ACI 318-19 第 6.8.1.2 条的要求，各高校开展了大量验证试验。汇总验证与确认结果的相关论文可通过以下链接获取。</p>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">验证案例：Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" 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type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___bearing_and_anchor\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ca9b6d78_562b_01cd_b7c1_e9e14bcade98\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_ver\"></object>\n<h1><br></h1>\n<h1>6 按 AASHTO 进行结构验算</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n718b61d6_ca9a_01c4_c411_608ecc9bfe42\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__a_0b99d24\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1e0b8118_0346_01fc_5843_6a60b409c862\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___resistance_and_loa\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n835a26bd_d5f1_0140_4fe1_9ae73d901010\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___strength_limit_sta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"a29abd54_d307_013b_44ed_56d973e7aacc\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___bearing_and_anchor_69cbe39\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d19c5c7a_4da5_01be_7a24_1918c7d60c76\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___service_limit_stat\"></object>\n<h1><br></h1>\n<h1>7 按澳大利亚标准 AS 3600（2018）进行结构验算</h1>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用极限状态，另一种针对强度荷载组合。正常使用极限状态分析假定构件在系数荷载作用下的受力性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。该方法允许在正常使用极限状态分析中采用简化本构模型（混凝土应力-应变曲线取线性段），以提高数值稳定性和计算速度。</p>\n<p>CSFM（协调应力场法）是一种满足第 6.1.1 条和第 6.1.2 条一般规定的结构分析方法，在第 6.1.3 条中被定义为 (f) 非线性应力分析——详见第 6.6 条。 </p>\n<p>CSFM（协调应力场法）分析考虑了第 6.6.3 条所规定的所有相关非线性和非弹性效应（收缩除外）。 </p>\n<p>为满足第 6.6.4 条和第 6.6.5 条的要求——详见 AS3600:2018 Sup 1:2022 第 C6.6 条——各高校对该方法进行了验证与确认。汇总验证与确认结果的相关论文可通过以下链接获取。</p>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">验证案例：Detail 2D</a></li>\n</ul>\n<p>由于 IDEA StatiCa Detail 是一款实用设计程序，计算中采用经系数折减的28天特征抗压圆柱体强度 <em>f'</em><em><sub>c</sub></em>，具体说明见下一章。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n83eff71e_cb6d_0152_d7f9_4621fe4095f0\"></object>\n<object 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data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_ver_77b5f2c\"></object>\n<h1><br></h1>\n<h1>8 预应力——模型描述</h1>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1ecc3d2d_b87a_01f1_a493_9161e2eae77d\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"prestressing_in_detail___model_description__body_\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"aec1d9ba_c119_0122_d551_4e09e764c5f9\"></object>\n<h1><br></h1>\n<h1>参考文献</h1>\n<p>ACI Committee 318. 2019. <em>Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary</em>. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. <em>Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton</em>. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. \"The Prediction of Crack Widths in Hardened Concrete.\" <em>The Structural Engineer</em> 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. \"Crack Width and Crack Spacing In Reinforced Concrete Members.\" <em>ACI Journal Proceedings</em> 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. \"Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.\" IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. <em>Non-Linear Finite Element Analysis of Solids and Structures</em>. Wiley.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. <em>1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings</em>. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. \"On Development of Suitable Stress Fields for Structural Concrete.\" <em>ACI Structural Journal</em> 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova. 2020. \"<em>Compatible Stress Field Design Of Structural Concrete</em>. Berlin, Germany.\"AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. \"Structural Concrete: Cracked Membrane Model.\" <em>Journal of Structural Engineering</em> 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. \"Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.\" Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. <em>Use of Topology Optimization in Concrete Reinforcement Design</em>. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. \"Truss Models in Detailing.\" <em>Concrete International</em> 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. <em>Theory of Structures: Fundamentals, Framed Structures, Plates and Shells</em>. First edition. Berlin, Germany: Wiley Ernst & Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&genre=book&isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. \"Tension Chord Model for Structural Concrete.\" <em>Structural Engineering International</em> 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. \"Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).\" PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. \"Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.\" Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. <em>A Solution for Walls and Details of Concrete Structures</em>. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. \"Toward a Consistent Design of Structural Concrete.\" <em>PCI Journal</em> 32 (3): 74–150.</p>\n<p><br></p>\n<p>Standards Australia. 2018. <em>Concrete Structures (AS 3600:2018)</em>. Sydney, NSW: Standards Australia.</p>\n<p><br></p>\n<p>Standards Australia. 2022. <em>Concrete Structures – Commentary (Supplement 1 to AS 3600:2018)</em>. Sydney, NSW: Standards Australia.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. \"The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.\" <em>ACI Journal</em> 83 (2): 219–31. </p>"
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"value": "<p>在实践中，<strong>拉压杆（S&T）</strong>和<strong>应力场法</strong>是设计钢筋混凝土及预应力混凝土结构不连续区域的标准方法。<strong>协调应力场法（CSFM）</strong>是在这些经典理论基础上扩展发展而来的，具有高度自动化的特点，并与设计规范保持一致。尽管方法简洁，但它能够非常真实地描述混凝土结构在承载能力极限状态（ULS）和正常使用极限状态（SLS）下的响应。CSFM（协调应力场法）已在<a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\">IDEA StatiCa Detail</a>中实现。 </p>\n<figure data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7fd8d041-20d1-40a8-9a71-eb9cdce27155/7.png\" data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" alt=\"\"></figure>\n<p><em>图1 a) 带开洞墙体 b) 剪力墙 c) 带企口端和开洞的梁 d) 桥墩 e) 桥梁横隔板 </em></p>\n<p>混凝土结构截面设计的标准方法适用于满足Bernoulli-Navier平截面假定的区域（B区）。不满足该假定的区域称为<strong>不连续区域（D 区）</strong>。这些区域包括集中荷载作用处或截面突变处，如企口端（图1c）、深梁、带开洞墙体（图1a、1b）、牛腿及桩承台等。在桥梁工程领域，典型示例包括墩帽（图1d）、横隔板（图1e）、转向块等。</p>\n<h2>1. 拉压杆模型</h2>\n<p>建立拉压杆（S&T）模型的基本假定是忽略混凝土的抗拉强度。简单桁架模型由受压和受拉构件组成，代表承载能力极限状态下的行为。总体而言，这并非复杂问题，对于有经验的工程师来说，建立基本的拉压杆模型（图2a）应不成问题。然而，即便是这一基本任务，按照设计规范对模型进行正确评估也可能是一个繁琐、手动且反复迭代的过程。</p>\n<figure data-asset-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" data-image-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aecb55f-dac0-47db-a25c-48082e5e70c4/Untitled%20design.png\" data-asset-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" data-image-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" alt=\"\"></figure>\n<p><em>图2 a) 拉压杆模型方案1 b) 拉压杆模型方案2 c) 拉压杆模型方案 </em></p>\n<p>需要对拉杆、节点区域及压杆中的横向拉应变进行评估。若模型未通过规范校核，则需调整拉压杆几何形状，或选择不同的拉压杆模型（图2b、2c）。这往往导致结构工程师仅建立一次拉压杆模型几何形状，而只对钢筋进行评估，从而可能引入较大误差。模型的选择始终取决于工程经验。对于更复杂的结构细节，选择能充分反映结构实际行为的拉压杆模型并不像上述情况那样简单。此外，拉压杆法仅适用于承载能力极限状态的设计，无法用于<strong>正常使用极限状态（变形、裂缝）</strong>的设计，而这些对于重要结构而言是关键控制指标，直接影响结构的使用寿命。</p>\n<h2>2. 协调应力场法 - CSFM</h2>\n<p>CSFM（协调应力场法）是一种用于分析 D 区及可简化为平面应力状态（即二维模型）构件的现代<strong>非线性方法</strong>。然而，它仍基于规范的基本安全假定：<strong>混凝土不承受拉力</strong>，所有拉力均由钢筋承担。协调应力场法（CSFM）是拉压杆法和应力场法的发展演进，消除了上述主要缺点：模型选择的不确定性、自动化困难以及无法评估正常使用极限状态等问题。</p>\n<figure data-asset-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" data-image-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9e760312-8401-44c8-aae1-020b514876fb/2.png\" data-asset-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" data-image-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" alt=\"\"></figure>\n<p><em>图3 a) 平面应变 b) 主应力 c) CSFM（协调应力场法）</em></p>\n<p>CSFM（协调应力场法）的原理可通过钢筋混凝土结构基本平面单元的<strong>平面应力</strong>状态加以说明。图3a展示了弹性力学和材料力学教材中常见的平面应力基本二维单元。这是结构中某一点的应力状态，例如可通过有限单元法（FEM）线弹性分析获得。该单元承受水平法向应力σ<sub>x</sub>、竖向法向应力σ<sub>z</sub>及剪应力τ<sub>xz</sub>。由这些应力可确定所谓的<strong>主应力</strong>及其由角度θ定义的方向（图3b）。该单元随即承受主拉应力σ<sub>1</sub>和主压应力σ<sub>2</sub>。</p>\n<p>经CSFM（协调应力场法）分析的同一单元的应变状态如何？应变如图3c所示。混凝土沿主压应力σ<sub>2</sub>方向受压，并产生应力为σ<sub>c2</sub>的应力场。如前所述，基本假定是混凝土不承受拉力。因此，横向主拉应力σ<sub>1</sub>不由混凝土承担，裂缝将垂直于该方向形成。应力σ<sub>c1r</sub>必须为零。为避免二维单元破坏，所有拉应力必须由钢筋承担（图3c中以蓝色表示），钢筋必须作为计算模型的组成部分。 </p>\n<p>若在待求解的<strong>整个二维区域内连续</strong>进行上述应力分析，结果将得到混凝土中的连续压力场以及钢筋中的拉应力和压应力。图4给出了CSFM（协调应力场法）应力场的简化图形表示。除混凝土和钢筋的承载比外，图中还标示了各区域内计算应力σ<sub>c2</sub>方向的变化情况。</p>\n<figure data-asset-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" data-image-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc56c80f-67f3-481d-a2c8-26dacc258bb2/csfm%20explained%20%281%29.png\" data-asset-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" data-image-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" alt=\"\"></figure>\n<p><em>图4 IDEA StatiCa Detail 整体计算结果 </em></p>\n<p>采用<strong>CSFM（协调应力场法）对细部或结构进行分析，以有限单元法为基础</strong>。混凝土采用二维壁单元建模，钢筋采用一维构件单元建模（图7）。由于属于非线性问题，分析不在单一步骤中完成。计算过程中荷载分级施加，非线性方程组的求解采用<strong>Newton-Raphson法</strong>。 </p>\n<p>虚拟弥散裂缝（ε<sub>1</sub>为平均值）\"形成\"于垂直于主应力方向，该方向可能随非线性计算过程中单元在每级荷载增量下\"逐步开裂\"而发生变化。综上所述，计算中考虑虚拟无应力旋转裂缝。 </p>\n<p>采用CSFM（协调应力场法）进行有限单元法求解的结果是协调应力场（即模型中混凝土不会分裂为各自独立作用的压杆）以及在整个求解二维域内连续分布的应变状态。这是相较于经典拉压杆方法的重要优势，使计算模型能够实现自动化和精细化，详见以下各段。</p>\n<figure data-asset-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" data-image-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/40e41bf7-4a81-4245-bd1b-843963c104e8/3.png\" data-asset-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" data-image-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" alt=\"\"></figure>\n<p><em>图5 混凝土压力软化原理</em></p>\n<p>CSFM（协调应力场法）的简洁表达形式允许直接采用设计规范规定的混凝土受压标准单轴抛物线-矩形应力-应变图。众所周知，当混凝土因横向裂缝而受损时，其抗压强度会降低（图5）。该方法通过自动考虑混凝土有效抗压强度，将这一所谓的<strong>压力软化</strong>效应纳入计算。 </p>\n<p>根据横向拉应变ε<sub>1</sub>的水平，确定折减系数k<sub>c</sub>，并相应调整混凝土的应力-应变图（图5）。由于结构中各处的应变场已知，可根据各截面局部横向拉应变ε<sub>1</sub>的水平，自动计算混凝土的有效抗压强度。</p>\n<figure data-asset-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" data-image-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/51628156-5014-4501-8f28-9f3b93783840/1.png\" data-asset-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" data-image-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" alt=\"\"></figure>\n<p><em>图6 拉力刚化原理</em></p>\n<p>此外，CSFM（协调应力场法）还考虑了裂缝间受拉混凝土对钢筋的<strong>刚化效应</strong>，即所谓的拉力刚化。在计算模型中，采用平均钢筋应变ε<sub>m</sub>，并相应修正钢筋的应力-应变图（图6）。这使得对裂缝损伤钢筋混凝土结构刚度的模拟更加真实。然而，混凝土抗拉强度不计入极限承载力这一原则仍然成立。裂缝处钢筋的最大应力σ<sub>sr</sub>是设计的控制指标（图6）。</p>\n<p>CSFM（协调应力场法）采用<strong>设计规范</strong>中规定的常用单轴材料模型（应力-应变图）。随后采用标准方法——分项安全系数法——对承载能力极限状态进行评估。该方法的简洁性使其适合工程实践，并与设计规范保持一致。 </p>\n<p>尽管属于非线性有限元分析，结构工程师无需在计算中输入设计阶段可能尚不具备的额外材料属性和混凝土特性，而这些参数在基于断裂力学的非线性有限元分析中是必需的。如前所述，CSFM（协调应力场法）分析的主要优势除承载能力极限状态外，还在于能够评估<strong>正常使用极限状态：挠度、应力限值，尤其是裂缝宽度</strong>。</p>\n<figure data-asset-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" data-image-id=\"6c090b06-f906-4e6e-9016-d73de172f321\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8fd3f66a-63b9-4aba-bb10-9e12889ed7d4/Finite%20element%20model.png\" data-asset-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" data-image-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" alt=\"\"></figure>\n<p><em>图7 IDEA StatiCa Detail 中有限元模型表示示例</em></p>\n<p>（图7）CSFM（协调应力场法）中的有限元模型由以下几类有限单元组成：</p>\n<ul>\n <li>用于钢筋的具有轴向刚度的一维单元</li>\n <li>用于混凝土的二维等参单元</li>\n <li>用于带端部处理的钢筋锚固模型的端部弹簧</li>\n <li>用于模拟钢筋与混凝土之间粘结的特殊二维单元</li>\n <li>粘结单元与混凝土之间的刚性约束和插值约束（多点约束，MPC）</li>\n</ul>\n<p>若所设计的钢筋能防止构件发生脆性破坏，则CSFM（协调应力场法）已被证明能够以简洁的公式对结构响应和极限承载力给出非常准确的预测。换言之，该方法不适用于例如无横向抗剪钢筋、可能表现出脆性行为的梁的设计。包含试验验证在内的方法<a data-item-id=\"1e879886-9e36-49e1-acb1-e6001361531f\" href=\"\">验证</a>详见文献[1]。方法的详细描述超出本文范围，亦可参阅<a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">理论背景</a>。</p>\n<p>显然，CSFM（协调应力场法）的原理具有普遍性，其应用不限于 D 区，还可用于对整体构件（如预制梁）进行建模，以及可简化为平面二维模型的情形。该方法及其在软件（IDEA StatiCa Detail）中的实现也已得到扩展，支持指定<strong>预应力和后张预应力钢筋</strong>。</p>\n<h2>3. 桥墩墩帽设计示例</h2>\n<p>CSFM（协调应力场法）的实际应用通过图8所示的桥墩墩帽设计加以说明。该桥墩为一座三跨连续桥梁的第二个桥墩，三跨跨径分别为30.0 m、42.0 m和30.0 m。钢筋混凝土桥墩墩帽采用C40/50混凝土，其厚度（沿桥梁纵向）为2.0 m。</p>\n<figure data-asset-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" data-image-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7bd9ebbf-5d30-448a-93e2-c89641d05677/4.png\" data-asset-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" data-image-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" alt=\"\"></figure>\n<p><em>图8 墩帽：a) 综合设计；b) 承载能力极限状态下混凝土压应力；c) 承载能力极限状态下钢筋拉应力；d) 正常使用极限状态下裂缝宽度</em></p>\n<p>首先在墩帽顶部设计了横梁B500钢筋20xϕ28+20xϕ25——顶部四层。图8a展示了承载能力极限状态下的综合设计结果，显示了混凝土中的压应力、压应力方向及钢筋中的应力。混凝土和钢筋中更详细的应力分布分别记录于图8b和图8c。横向钢筋应力略低于屈服强度，混凝土中的应力（及相对应变）在承载能力极限状态下亦满足要求。然而，裂缝宽度计算结果（图8d）表明，设计不满足<strong>正常使用极限状态</strong>要求：w<sub>max</sub> = 0.36 mm > w<sub>lim</sub> = 0.3 mm。<strong>为满足裂缝宽度限值，需将横梁钢筋增加至20xϕ32+20xϕ28。</strong>若w<sub>lim</sub> = 0.2 mm（例如，位于产生盐雾道路附近的桥墩，环境影响等级XF2），横梁钢筋甚至需增加至24xϕ32+24xϕ28。</p>\n<h2>结论</h2>\n<p>CSFM（协调应力场法）采用<strong>设计规范中规定的简单材料模型</strong>，适合工程实践。除承载能力极限状态外，它还支持正常使用极限状态的设计，而后者在采用拉压杆模型时此前难以实现。通过在<strong>IDEA StatiCa Detail</strong>中实现该方法，可以真实捕捉结构响应，并高效、安全地设计和评估不连续区域及较大的结构组合体。</p>\n<p>CSFM（协调应力场法）主要由瑞士联邦理工学院（ETH）苏黎世分校结构工程讲席教授Walter Kaufmann主导开发。他及其团队还对<a data-item-id=\"0dd36e25-63b2-4d63-a33e-6043644fda4f\" href=\"\">该方法及其软件实现进行了验证</a>。</p>\n<h2>参考文献</h2>\n<p>[1] KAUFMANN, Walter, et al.: Compatible stress field design of structural concrete, ETH Zurich, 2020, ISBN 978-3-906916-95-8,</p>\n<p>[2] KAUFMANN, W., MARTI, P.: Structural Concrete: Cracked Membrane Model. Journal of Structural Engineering 124 (12): 1467-75, 1998 https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467)</p>\n<p>[3] KRAUS, M., M. WEBER, W. KAUFMANN, W, BOBEK, L.: Numerical analysis of experimentally tested frame corners with opening moments using the Compatible Stress Field Method (CSFM). In: Computational Modelling of Concrete and Concrete Structures, pp. 694-03. CRC Press, 2022 <a href=\"https://doi.org/10.1201/9781003316404\">https://doi.org/10.1201/9781003316404</a></p>\n<h2>作者</h2>\n<p>Ing. Pavel Kaláb, Ph.D.</p>\n<p>IDEA StatiCa s.r.o.</p>\n<p><br></p>"
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"value": "<h2>简介 </h2>\n<p>本文讨论了使用 <a data-item-id=\"eaab962d-ba44-4ee0-8fa7-45193c9f52b5\" href=\"\">CSFM（协调应力场法）</a> 分析低箍筋用量梁剪切破坏的方法。为此，对 Huber（2016）、Piyamahant（2002）以及 Vecchio 和 Shim（2004）在简支钢筋混凝土梁上进行的一系列试验进行了分析。这些试验涵盖了大量参数，包括不同尺寸、剪跨比以及剪切和纵向钢筋用量。本节描述了使用 CSFM（协调应力场法）对这些试验系列中 17 个试验的分析，探讨了 CSFM（协调应力场法）正确模拟各种不同破坏模式的能力，这些破坏模式涵盖有无箍筋断裂的剪切破坏、弯曲破坏以及剪弯混合破坏。 </p>\n<p>试验装置 图 6.17 展示了所分析试验的几何形状、试验装置和钢筋布置。剪切钢筋（直径（<em>Ø</em><em><sub>t</sub></em>）、间距（<em>s</em><em><sub>t</sub></em>）和几何配筋率（<em>ρ</em><em><sub>t,geo</sub></em>））、纵向钢筋（根数（<em>n</em><em><sub>l</sub></em>）和直径（<em>Ø</em><em><sub>l</sub></em>））以及几何参数（有效高度（<em>d</em>）、剪跨比（<em>a/d</em>）和梁宽（<em>b</em>））的信息列于表 6.10 中。Huber（2016）进行的试验 R1000m60 和 R500m351 采用单肢弯钩，而其他所有试验均采用双肢封闭箍筋。在 Piyamahant（2002）的分析试验中，几何形状和纵向钢筋保持不变，而在其他两项研究中则有所变化。 </p>\n<figure data-asset-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" data-image-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b04ab1b6-8164-42a4-8153-b0bca529109d/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.17.png\" data-asset-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" data-image-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" alt=\"\"></figure>\n<figure data-asset-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" data-image-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f016576c-b58f-4934-8a91-92a8f02ada8b/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010.png\" data-asset-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" data-image-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" alt=\"\"></figure>\n<figure data-asset-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" data-image-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c39493d-2611-4b20-8595-b15bd109181c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010-2.png\" data-asset-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" data-image-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"four_point_bending_tests_on_t_beams__definition_of\"></object>\n<h2>材料属性</h2>\n<p>CSFM（协调应力场法）分析中使用的剪切钢筋、纵向钢筋和混凝土的材料属性汇总于表 6.11 中。<a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">CSFM（协调应力场法）</a>分析所需的大多数材料属性可从相应的试验报告中获取。需要假定的数值在表 6.11 中注明。 </p>\n<figure data-asset-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" data-image-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d40a91ae-9e7a-4cbe-9980-8bc295693359/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11.png\" data-asset-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" data-image-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" alt=\"\"></figure>\n<figure data-asset-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" data-image-id=\"b38d80f8-07f0-4992-b707-36da923011d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/037428f1-0d3f-4404-9321-db2a2a0f0c8c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-2.png\" data-asset-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" data-image-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" alt=\"\"></figure>\n<figure data-asset-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" data-image-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6388402c-7243-4c35-9936-241e9bbc86e5/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-3.png\" data-asset-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" data-image-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" alt=\"\"></figure>\n<h2>使用 CSFM（协调应力场法）建模</h2>\n<p>根据试验装置，在 CSFM（协调应力场法）中对几何形状、钢筋、<a data-item-id=\"50ed723b-9b87-4870-a69f-e05b5a8a8150\" href=\"\">支座和加载</a>条件进行了建模。图 6.18 以 Vecchio 和 Shim（2004）的试验 A3 为例，展示了建模过程。</p>\n<figure data-asset-id=\"be95afab-6efa-4ca2-af2d-187495214492\" data-image-id=\"be95afab-6efa-4ca2-af2d-187495214492\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ee8f6a35-2573-4491-a59a-c75249bae2ec/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.18.png\" data-asset-id=\"be95afab-6efa-4ca2-af2d-187495214492\" data-image-id=\"be95afab-6efa-4ca2-af2d-187495214492\" alt=\"\"></figure>\n<p>对于每个试验，使用以下参数进行了四次数值计算：</p>\n<ul>\n <li>网格尺寸，在梁高方向上从 5 个有限单元（这些特定示例的默认值）变化至 10 个，再到 20 个有限单元。由于默认网格已经非常粗糙，本研究仅分析更细的网格，除 M0 外均使用 10 个单元的网格。 </li>\n <li> 是否考虑拉力刚化效应。默认情况下，CSFM（协调应力场法）中考虑拉力刚化。 </li>\n <li>是否考虑箍筋中潜在的非稳定裂缝。当考虑时（默认），拔出模型（POM）定义箍筋中的拉力刚化（所有梁的几何配筋率均低于（<em>ρ</em><em><sub>cr</sub></em>），因此从不使用拉力弦模型）。当停用时，模型通过 TCM 考虑拉力刚化。</li>\n</ul>\n<p><em>\\[ρ_{\\text{cr}} = \\frac{f_{\\text{ct}}}{f_{\\text{y}} - (n-1)f_{\\text{ct}}}\\]</em></p>\n<p>其中<em>：</em></p>\n<ul>\n <li>\\(f_y\\)<em> - </em>钢筋屈服强度</li>\n <li>\\(f_{ct}\\) - 混凝土抗拉强度</li>\n <li>\\(n = \\frac{E_s}{E_c}\\) - 弹性模量比</li>\n</ul>\n<p>表 6.12 列出了每次数值计算中使用的参数。M0 对应于 CSFM（协调应力场法）中使用默认设置的模型。</p>\n<figure data-asset-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" data-image-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/654a5eaa-78a1-4ba4-aa24-c24a2bb360bd/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.12.png\" data-asset-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" data-image-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" alt=\"\"></figure>\n<h2>与试验结果的对比</h2>\n<p>本节包含 <a data-item-id=\"8b9399db-b927-491a-a50f-c66ad97560af\" href=\"\">CSFM（协调应力场法）</a>给出的极限荷载和破坏模式与试验结果的对比。为了同时验证 CSFM（协调应力场法）在正常使用极限状态行为和变形能力方面的表现，对所选梁的模型荷载-变形响应与试验结果进行了对比。</p>\n<h4>破坏模式与极限荷载</h4>\n<p>表 6.13 汇总了试验中测得的极限剪力（<em>V</em><em><sub>u,exp</sub></em>）、CSFM（协调应力场法）预测的极限剪力（<em>V</em><em><sub>u,calc</sub></em>）以及相应的破坏模式。该表还给出了每个数值模型中实测极限荷载与计算极限荷载之比的均值和变异系数（CoV）。在所有分析中（忽略拉力刚化的 M3 除外），CSFM（协调应力场法）均预测到箍筋处发生剪切破坏。这与 Huber（2016）和 Piyamahant（2002）试验中观察到的破坏机制吻合良好，但与 Vecchio 和 Shim（2004）中观察到的破坏机制不符。未能准确捕捉破坏模式导致在此情况下对极限荷载的估计略偏保守。总体而言，默认参数提供了良好的承载力估计，但略偏不安全（平均偏差约 6%）。</p>\n<p>图 6.19 通过试验与计算极限剪力之比（<em>V</em><em><sub>u,exp</sub></em><em>/V</em><em><sub>u,calc</sub></em>）展示了 CSFM（协调应力场法）承载力预测对不同数值参数的敏感性。极限荷载对所选有限单元尺寸明显敏感（见图 6.19 a）。最粗网格与最细网格（M0 和 M2）之间的最大差异达 36%（Piyamahant（2002）的试验 4），平均差异约为 15%。使用默认参数（模型 M0 中梁高方向 5 个有限单元）时，对试验承载力略有高估（约 5%）。当将网格细化至梁高方向 10 或 20 个有限单元（分别为模型 M1 和 M2）时，可获得略偏安全的极限荷载预测，精度优良。在改变有限单元网格尺寸时，未观察到破坏模式的变化。即使使用默认网格尺寸，结果也非常令人满意，考虑到多个试验呈现脆性剪切破坏，这类破坏采用设计方法预测具有相当难度。</p>\n<p>拉力刚化的考虑方式对承载力预测具有高度相关的影响，如图 6.19 b-c 所示。通过 POM（CSFM（协调应力场法）中的默认设置）考虑箍筋中的拉力刚化，平均而言与试验结果吻合优良（见图 6.19 b）。然而，忽略拉力刚化会导致极限荷载平均高估约 22%（见表 6.12）。当忽略拉力刚化时，破坏模式转变为弯曲破坏（见表 6.12），与观察到的剪切破坏模式不符。结果对所考虑的压力软化关系也非常敏感。如图 6.19 c 所示，在箍筋中使用拉力弦模型（模型 M4）代替拔出模型（模型 M1），比忽略拉力刚化（模型 M3）的结果略好，但仍对极限荷载高估约 15%（见表 6.12）。因此，可以得出结论：在这些示例中，使用拔出模型对于正确模拟承载行为至关重要。 </p>\n<figure data-asset-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" data-image-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4c6d49ee-719b-4472-9a67-06b062b2df81/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13.png\" data-asset-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" data-image-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" alt=\"\"></figure>\n<figure data-asset-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" data-image-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f3c49504-d203-4f82-a25e-0ab44da27aaa/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-2.png\" data-asset-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" data-image-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" alt=\"\"></figure>\n<figure data-asset-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" data-image-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6fcfdbf1-9666-447a-988f-40df2e112587/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-3.png\" data-asset-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" data-image-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" alt=\"\"></figure>\n<figure data-asset-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" data-image-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/23242854-167d-40ac-8182-edd05e68f870/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19.png\" data-asset-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" data-image-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" alt=\"\"></figure>\n<figure data-asset-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" data-image-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a1037f6e-2499-4ade-bb10-681d8ea41e54/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-2.png\" data-asset-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" data-image-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" alt=\"\"></figure>\n<figure data-asset-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" data-image-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2391dda1-eba7-4458-8142-a7ff352da592/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-3.png\" data-asset-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" data-image-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" alt=\"\"></figure>\n<p>图 6.20 展示了连续应力场结果（主压应力（<em>σ</em><em><sub>c</sub></em>）和钢筋应力（<em>σ</em><em><sub>sr</sub></em>）（裂缝处）对 Vecchio 和 Shim（2004）试件 A1 和 A3 的计算结果，其中预测的剪切破坏已被标注。这些结果使用数值参数 M1（默认参数，但网格尺寸为默认值的一半）计算得出。从应力场可以看出，弯曲引起的受压区压应力处于塑性阶段（99.5%）。然而，由于所采用的混凝土压碎判据，箍筋断裂发生在混凝土压碎之前。 </p>\n<figure data-asset-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" data-image-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86e2648e-f52e-4162-8ad8-a9615fc572c6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20.png\" data-asset-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" data-image-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" alt=\"\"></figure>\n<figure data-asset-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" data-image-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/65718f07-1206-42f2-990a-97e7e18d0547/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20-2.png\" data-asset-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" data-image-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" alt=\"\"></figure>\n<h2>荷载-变形响应</h2>\n<p>图 6.21 将使用数值参数 M1（对纵向钢筋采用 TCM，对箍筋采用 POM）和 M3（忽略任何拉力刚化效应）计算得到的荷载-变形响应与试验 R500m352、T1、A1 和 A3 的实测荷载-变形响应进行了对比。荷载 <em>V</em> 对应施加的剪力，<em>u</em> 对应跨中挠度（见图 6.20a）。</p>\n<figure data-asset-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" data-image-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b2a3cfdf-9892-4c29-b6b0-a26d1f47bb22/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21.png\" data-asset-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" data-image-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" alt=\"\"></figure>\n<figure data-asset-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" data-image-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e90b12fb-ba6f-4ce8-97c3-ebca7c6212f6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-2.png\" data-asset-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" data-image-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" alt=\"\"></figure>\n<figure data-asset-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" data-image-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ba5f9efa-97c3-461f-b6fc-5e3fdd4f0ff9/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-3.png\" data-asset-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" data-image-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" alt=\"\"></figure>\n<p>考虑拉力刚化效应后，整个加载历程中的试验挠度可以得到较好的预测，但峰值荷载处的挠度略有低估。特别是在 Vecchio 和 Shim（2004）的试验 A3 中，由于数值分析首先预测到箍筋断裂，因此无法在数值分析中准确捕捉试验中因纵向钢筋屈服而出现的平台段。忽略拉力刚化效应会导致极限荷载和变形的高估。上述关于不考虑拉力刚化分析的结论在使用 M4 参数（箍筋和纵向钢筋均采用 TCM）时同样适用。</p>\n<h2>结论</h2>\n<p>关于 CSFM（协调应力场法）结果与低箍筋用量简支梁分析试验中观察到的行为的对比，可得出以下结论： </p>\n<ul>\n <li>CSFM（协调应力场法）对极限荷载给出了良好的估计，使用默认数值参数时略有高估（平均约 5%）。由于剪切和弯曲混凝土压碎的组合破坏模式难以捕捉，CSFM（协调应力场法）预测的破坏为箍筋断裂，这导致承载力预测偏于保守。 </li>\n <li>极限荷载预测对有限单元网格尺寸的变化具有一定敏感性。对默认有限单元网格进行细化时可获得最佳预测结果。因此，在进行最终验算时，始终建议研究有限单元尺寸对结果的影响。 </li>\n <li>忽略拉力刚化会导致极限荷载和变形能力的严重高估。即使通过拉力弦模型对箍筋中的拉力刚化进行建模，预测的极限荷载也明显偏于不安全。当通过拔出模型考虑低配筋率箍筋中非稳定裂缝的影响时，可获得最佳结果。这是 CSFM（协调应力场法）中默认实现的拉力刚化模型。 </li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"take_idea_statica_24_0_for_a_test_drive_today\"></object>"
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"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Never translated</li>\n <li>de-DE: Never translated</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Never translated</li>\n <li>fr-FR: Never translated</li>\n <li>hu-HU: Never translated</li>\n <li>it-IT: Never translated</li>\n <li>ko-KR: Never translated</li>\n <li>nl-NL: Never translated</li>\n <li>pl-PL: Never translated</li>\n <li>pt-PT: Never translated</li>\n <li>ro-RO: Never translated</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Never translated</li>\n <li>tr-TR: Never translated</li>\n <li>vi-VN: Never translated</li>\n <li>zh-CN: Translated on 26.6.2026 21:21</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
}
}