问题描述:
如下所示,SAP2000 在反应谱分析是如何考虑偶然偏心的呢?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ4AAAEgCAIAAADKdQq0AAAReElEQVR4nO2dv24TWRuH5y64gK+hXCmScaqvQYELIKB1E4sod5AtKFAkKCxtCi6A4ktvtlpBBLsNUkrkLk34ik1JBLLrSMRb2J45c/68887/sf08+gmNj8/8STjPvGdsjxPNAUBBNAMABagCoAJVAFSgCoCKTqgSRacNrAJQhtyqRNFpKJqeVofQQmgLcR9UgYYpVVW84zU07oUWYfSHdEIVaJjqVZmFR7M53OV4V5E3DlArtagSejZXVQkphCrQCh5V/u/Dv3I5VTKvVYQ+Zk/vAQOUxB6K7hB3O+llsJ7VzKyEbQr9qSpQK42qYvbJW3/kVbwvuAFUSHOqyFfh+st6zb4AKqchVYSLEPnK3n1K7xJAhTShiteKUKPwULMvgJooq0qB90PcdWeiFVYfCgu0QsVVBWBTQRUAFagCoAJVAFRUpsofsGVUMwDXhypVuYatIValbWErAFWgRv4wVGn7WEqBKlAvqIIqoAJVUAVUFFAliiJzOSazc6ilElAF6qVYVYmHu7sgdM7sWYa2Vfl8smOeNwZndfyQxTkbVHRoZ4Odk88VHdR6UXICplEltEq1dECVZAydDaIuDajPJzuxIJ9PdsocW+rH3C5QpQ5Vrs8Gq7EZn86Xj5Pqs+z++WRnZzDYSZ3w405Jn8FgIG/Hsy//sRmN9n49W0j2MziLH+ycfE5WH5wl218tGRvfOTk72UkfZ/f4888/MxvzqmJembgzK2/L1kzA3KpiNC7lSTk0OLs2T/Ork39SBIztJC2Ds+vAdqx9GZylPbsO7dfeQlIel53iPmZ18qoSOQtddeXy8vLp06dv3741G9++ffv06dPLy8u4peS1ir5z5EO/kUw6oIrxgy1HhXGFsGyMu5mnbWvIGSN9uegfi4GCYJWaFItOtlrJft2jtTZkqhI/5a8q6W4dVuXascX15LqcKsqhv21VxbhQcU/vced4nBdTxd1OaF++nVsauPt1fiinxa+KU07XRJVrwxavJ9fVvQJ2HXZg21Qx5kvOJMe8wF4OK+UELK2KajsxZwPr4mO1F3e/1hbS2i8vUXyqWD/vGqpyvbLF68l1FRMw73WL29lrV4V0SZXF4Fw8dC6Uk2lOMoaCl/XJNbxTVezt+PZlHp09NytyWb/qYTpjrrczGKznBCzm8vLS68l1CVU09UTX2TgJOleRetpWpTBtjaE1GbvdobGqEnpYFaiyJvtdW8q8r+KWC40GqAJrCR+XRBVQgSqoAipQBVVABaqUUgW2io35f29aFYDNBlUAVKAKgApUAVCBKgAqUAVABaoAqNCqAgDZqgCAC6oAqEAVABWoAqCiuCqaP4ct98n1B7X569vQLqWqSkkT4g6Zf5A+/kv2RY8UoCz5VLHGtBtln1l63IeWNc8CNEPBqiIMWU2psYQRZJDNAWiM1lSxKoy37IQ2JTwFUBPad+vt1RQzK/28S64qoR3JBwxQEpUqHqccVUItSiv01yoAzdMVVeRXAsy15NcGAGqiGlWE13O9C6FG7wY1FQZVoG6aViXzWkV+BQxVoC0qUCVz+OpfAfNukwkYdIGyqngvUYRxL/e02uUSJB8GQLVUdlkPsNmgCoAKVAFQgSoAKlAFQAWqAKioXZWLi4vj4+NHjx71+/1Hjx4dHx9fXFwU3hpAW9Soyo8fP169enV4eHh+fv7t27fb29tv376dn58fHh6+evXq+/fvRY4XoCVqVOXly5e///773d3dPM3d3d3p6enLly+LHC9AS9SlysXFxfPnzxdufPr0aX9/v9/v7+/vf/r0adH4/Pnz4ExsPIxWDMez2Ww2m4x6kcGy1dcz1AhQjrpU+e233z58+DCfz//++++dNAtbPnz4cHx87FlzMurFI3wy6kW90WQ2m4x6vdFk2WM8jBu9Pd1GgNLUpcrDhw9//Pgxn8/39/ctVfb39+fz+c3Nzd7enmfNlBX+xvEwGo5VPQGqoi5VdnZ2FhOtfr9vqdLv9+fz+e3tbb/f9667mkAZsydvVfH2DDQClKR7VSVhMeaH45l9reKUDaNnRiNAQepS5fj4+Pz8fD6f//XXX5YqHz9+nM/n5+fn/muVNMtyklSVpKT4eyoaAQpQ4ytgh4eHP3/+nM/nHz9+fPLkyYMHD548ebLw5OfPn4eHh/5XwMZDoxSsLtLNIR9fuHt7ehsBSlPj+yqvX78+PT0Nva/y+vXr0IrmbGspiHNZn7zc5czKvI0AJalRle/fv8fv1t/c3Nze3t7c3PBuPawpDX0GbG9vr9/v7+3t8RkwWFP4ZDGAClQBUIEqACpQBUAFqgCoQBUAFagCoIJ76wFUcG89gArurQdQ0cS99V6ke+uNTzyanwtO7plPfVrY0znuyceKoSpqv7c+RPDe+tQd8ekbHlcD31j2dV7eTzwzlwBKUvtdkCGU99ZPJuPJZOYM+tVDf2enG0Bpar+3PkTw3nrv8LbvZlw9DruwmJYhClRF96pKRaoIGwMoQO331ocI3lvvvx0+HvOT8XgSmoBpNwaQnyburXeR7q23r9SXy/Gl/OLVrVUHX2ejlFBVoCq6eG+9+bKwWROSl4BHo16UMsTqHDdRUqAquLceQAX31gOo4JPFACpQBUAFqgCoQBUAFagCoAJVAFSgCoAKVAFQwddQAKjo6NdQRFHkXc7E6pxrO3GHUM9cRwIbRke/hsIa4jGZO/WqEvnI3Kl7AJl7hw2mi19DIQzZeCE06IUy4o51r0KZW85UDjaSzn0NhTUi3XZvf+/wDQ1ueVMh3M1mrgKbROduGHaHuzzK5XO/3Mdd1miGKttJ976GYnEQ6SEbejjTaSD75trlFYCqsuV0rqrMfGPRe7IX2oVG92HcKHvi7YAq20PnvobCOveHCkJo1BaoKta6mc+iynbSwa+hSB9NeCx6a0WBqpK3NKHKdtLNr6EIToeEqmJ1mCmqilAihC3LBQo2lc59DYU8w5HP8bNCVSVzX8LWUGV7WIOvoXDP4nLpsJ5yS4q3GmSWCKzYcvhkMYAKVAFQgSoAKlBlE/iyxTT2S0aVTeDLly/yx4g2FVSBfCxUafsomgZVIDeo0gCosgmgSgOsmSpnZ2fCwzLtMcIqodVbB1UaYGNV8Y7+eDnUwd24+28HQZUG2BxVTA1Cz8pFI3OPqNIpUEUipIrszCygiiyeW3kyC1FboEoDrJ8q1tid+Ya41VnoKY9+a2vWQndAlQZYP1Wsh6E5lTWyhYsNwZOZzxZU6QioIiHPoMxGjSquJKEakulbu6BKA2ymKqHx7c7NvMi7Q5WOgCoSmrmQd6wr+5s9XXlQpVOgioR3cmUtZ5aFUP/MyZjbpyOgSgOsnyqhgat5qSpz9MsXM1SVToEqEt7Rr5kmmX2s0S9MwEIb7JotqNIAa6YKeEGVBkCVTYBbuxoAVTaBem/J7TaN/ZJRBUAFqgCoQBUAFagCoEKrCgBkqwIALhWoEkWni7gtbuIOcs/yRwVQLblV0QxrSxthOfQsQNcooorwUO7jdhaeAugUFVQVq8LIHbwWMfuC7lN7VfEuWwtMw6D7aF8sTlYIlw6zT2ZJMSURqkrDrw8CLNCqIrnl1AGzXb8c2hpVBVqnFlW81+XKC5WZoqoANE9zqrj95a1pegI0RvWquP/GffJeq3i3A9AKFaiivwiRnzJrkb5AATRDNVVluZr4ZqLyfRW3EGl+DIC6qVIVgA0GVQBUoAqAClQBUFGlKvJ3ywN0k7nuqwYrVkWzS4BOgSoAKlAFQEXbqkxGvcigN5poDidhPIyG43yrhJmMhqPJ4pBSBzIexg3m8cY71jZaP6yva/oXYPx042Hu3w1USgdUMYZA+lHDTEa94Xh5EMNhLzFwPOz1FseVOr7Vg1yNyVbjHuNhIshk1FvJMR46PlV3UoD8dFGVyajX6/UWo2Q5YFan2+TculwxOe/GPZcNxtBarrXq4R9xcf/JqNcbjeO1J6PhaJyMdbfw5Wp0VAmcHSaj0dhdAVdapAOqOBOw5NRqTECWA2XVsho3q8epqUo0HHtUiTWbTHyFK3l65etyR8OFvKvxnCgZmYVH0+ibgIkCpJ/ElVbpgCq+k++izefRQoTYDNeL1aB3q8pqc9453sQoI71k/fjyxbOSOXNSNSb7MK48rIuQyXicPEKVDtFpVbzXspNRbziM28WqEm/FHL2h6yGrqix2NBoNzSuP9JaWO9I3mmM9NXNMXaukj9WQo9KXMCAv3VYlNYkxX0cynw9cqyQ1aWlW3EFzrTJJ7Sg5IrPQpQa4ptEZ+e5G078MrlU6RNuqdIiOD8WOH97mgyoGiwuTbsL7Km2DKgAqUAVABaoAqEAVABWoAqACVQBUoAqAClQBUNGCKnOA9aRpVQA2GFQBUOFXZerw9etXtxFge3AVQBUAD7IqB3G+fn1mPiRk25JWAFUICQRVCFFFqwohxEghVaLowSLmshmzZ2j1UB/vKoS0naKqTHVjOu7jFcnamqCctTVCGk8Vqgjj2+wjbMrbIVSR2v6Vke1MRapYT02dMqJRJbOquLsjpKmUuFaxHmZWFbeb2T9TAH1PQmqI+GKxm8VTwinfjFtV3OGuryqZMzTvARNSMipVBAfMf0ND3K0esiref92Hsj+EVJiKVcn8N9Q4TfumWdd7JITUlOpV8S64jV5VNNVpiiqkjVSgijuOvS92ySK57Zm1xV2RkPpSTVWxloWqItQHzbWKu1n3ISF1pEZVrFeuQi8Ha6qN9yWv0OtjhNSRsqoQsiVBFUJUQRVCVEEVQlRBFUJUQRVCVEEVQlRBFUJUQRVCVEEVcjCdHrx48cvWRvkrQhVyMJ0evHjxy93d0RYGVUi+oEpmUIUcTFFFkYZUiaJIeFhJ6tjm9gRVMtOoKpEPeRV5mzKtj781CqpkpglV4lHrDl95QOuHO2KUTEqV9/cX55qj987Ycp56fxSfmu6/b3vcb5Qqec/9GpfMPm4L0cRQ5fFRdO/N1dHd1e6uPfrdp5692b335qr9Eb8Jqpg+FKgSeadhufZC4iSqXO3u7u5eeTVwn/LotGbpkCrTQlUl71RN04EISVR5fz86erxYfn+UnoO5T72/H+3e213OyR63Pu43ShXvv25n77gXGuVtkswUVOXu6O7q2dXd0d3d0dWbe55rm86ni6pYE6RKVDG3zBysTApOwIwxd/Xm3u6bZ60P/bVXxTumvROwvFVF+SyRU/Cy3qgzVBWrU5HoJ2Chq/mQOTKtj781ivhi8eOj2Jnwi8XrWFLWWBV3Fe9DzSokV3gLMjNtvgUpn/vzlghUKRNUyQwflyQHU1RRBFXIwRRVFEEVcjBFFUVQhRxMuWFYEVQhRBVUIUQVVCFEFVQhRBVUIUQVVCFEFVQhRBVUIUQVVCFEFVQhRBVUIcu8e/dwC6P//aAKWebdu4f//PPrVgVVSJGgipyGvjIv1x3woe+myLuX1gffegVV5DRaVUJ3Dgs9hc5eJTCkcKpSJYoi73KuFbdUlVxVpUz9wZMyqUmVGLeb9RSqeIqJsrzoiw8TsPKpRJVQSRE0QJUkDVQV73ZaH3zrlQpVMUe/t6SEVBGq0FaoMg2MaX3R0G9WWa+Im/KqxEPcHe7C6Lfs+qfB8tI5VaL0d+QVKymh/pkLRJk6qoow9N0aEjU+E+uWKqYn05xVRblxeYEoU5MqcjHxtmypKlPnrxEJVcLtoOk8RZUqUrkqcbmQxRA02y5VImf2ZT3l7T8Vy5HcgiTFUl9VCU3AXGea9KRzqixiGRKqEtM8qsi7aH3krV1qrSquBqGpWrrbf3+N/vM//8JGq+JWFWtMC7Mv2S5NzSFyKn9fxWz0TrdCIjVWW7qoCul+qlXFPMFlSqW5kkEV0pXwcUk5qEKWQRU5qEKWaf2GRO6CJGQTgiqEqIIqhKiCKoSogiqEqIIqhKiCKoSogiqEqIIqhKiCKoSogiqEqIIqhKiCKoSogiqEqKJVhRCSrQohxMhSlX8BefkWYaay1H8AAAAASUVORK5CYIIA)
解答:
偶然偏心在反应谱分析中的实现方法类似于自动地震荷载(底部剪力法),也就是在不考虑偶然偏心的基础上对各个节点附加一个绕 Z 轴的集中力矩。集中力矩的大小等于沿地震作用方向的地震力(节点集中力)与偏心距的乘积。但与自动地震荷载不同的是,此处的地震力并非单一振型中的地震力,而是各个振型中的地震力的组合值(如 CQC 或 SRSS)。
事实上,SAP2000 针对考虑偶然偏心的反应谱工况(如 RS+0.05)会自动生成一个附加的线性静力工况(如 ~TorsionRS+0.05),用于施加上述提及的作用于各个节点上的附加集中力矩。注意,该附加工况为线性静力工况(类似于恒载或活载工况)而非反应谱工况,故无需进行振型组合。因此,结构不同位置处的结构响应值有正有负,如以下中图所示。
常规反应谱工况(如 RS)中的结构响应值与附加工况中结构响应值的绝对值之和即考虑偶然偏心的结构响应值,故反应谱工况中偏心率或偏心距的正负号对分析结果无影响。注意,在反应谱分析中考虑偶然偏心的前提同样是刚性或准刚性隔板的定义,否则程序无法计算偏心距。关于这一点,读者可参阅筑信达知识库文档《自动地震荷载与偶然偏心》,此处不再赘述。
那么,我们如何才能验证上述实现方法呢?换言之,对于考虑和不考虑偶然偏心的反应谱分析,如何查看或输出作用于各个节点上的地震力和附加力矩并对『附加力矩 = 地震力 X 偏心距』的计算公式加以验证呢?反应谱分析不同于自动地震荷载,后者可以对作用于各个节点上的集中力或集中力矩进行图形显示甚至表格输出,详见《自动地震荷载的表格输出》。
对于反应谱分析,我们可以通过定义截面切割输出作用于节点上的地震荷载。如下所示,基于 #120 节点及与之相连的三个框架对象定义截面切割,分别输出 RS 和 RS+0.1 工况下的截面内力。对于 X 向地震作用,在不考虑偶然偏心的情况下,X 向地震力 F1=0.0222;在考虑偶然偏心的情况下,在 F1 的基础上附加力矩 M3 = 0.0266 = F1 x e x L = 0.0222 x 12 x 0.1。 由此即可验证 SAP2000 在反应谱分析中以『附加力矩 = 地震力 X 偏心距』的方式考虑地震作用的偶然偏心。