预应力在 Detail 中的应用 - 模型描述

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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://preview-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://preview-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。&nbsp;</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。&nbsp;</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>&nbsp;-&nbsp;预应力引起的初始应变<br><em>σ</em><em><sub>pm0</sub></em>&nbsp;- 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://preview-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://preview-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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