弯矩二次分配法

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,4.3.2,竖向荷载作用下框架分析的近似计算方法,-,弯矩二次分配法,1.,弯矩二次分配法的思路：,由分层法得知，某一节点的不平衡弯矩只对邻近节点的杆件影响较大，对较远节点影响较小，为简化计算，可假定某一节点的不平衡弯矩只对与该节点相交的杆件近端及远端有影响，而对其余杆件的影响忽略不计。,竖向荷载下框架内力计算，要考虑所有节点不平衡弯矩对所有杆件的影响，故计算量很大。,弯矩二次分配法的思路,:.,近端对节点不平衡弯矩进行一次分配。,节点相交各杆件远端传来弯矩进行迭加,然后对不平衡弯矩进行二次分配，整个弯矩分配与传递过程即告结束。,注意,:,远端传递弯矩系数为,1/2.,先求梁的固端弯矩，,在节点进行不平衡弯矩的分配与传递。弯矩分配是按节点各杆弯矩分配系数进行弯矩反号分配一次，并按,1/2,传递系数进行传递。,然后，各节点把梁远端，柱远端传来弯矩求代数和后再在节点分配一次。最终的杆端弯矩应为固端弯矩与分配弯矩之代数和。因总共只进行了两次弯矩分配，所以称为“弯矩的二次分配法”。,弯矩二次分配法计算时，柱的线刚度不必折减。,梁内力对相邻层无影响；,柱内力对相邻层有影响，柱的远端弯矩按,1/2,传递系数传来后与梁传来弯矩求和后进行了第二次的分配。,2.,弯矩二次分配法的要点：,弯矩二次分配法计算的框架内力，梁与柱的内力对相邻层有何影响？,3.,弯矩二次分配法的计算过程与示例讲解,g1=40.2kN/m,g1=40.2kN/m,g2=32.8kN/m,3600,3800,3600,i=0.471,i=0.471,i=0.498,i=0.498,i=0.498,i=0.498,1,1.24,6000,6000,2700,g1=40.2kN/m,g1=40.2kN/m,g2=32.8kN/m,3600,3800,3600,i=0.471,i=0.471,i=0.498,i=0.498,i=0.498,i=0.498,1,0.62,6000,1350,框架对称，荷载对称，可仅按半跨分析,注意：,（,1,）中间跨中切开后用滑动支座取代；,（,2,）中间跨梁相对线刚度除以,2,。,右梁,左梁,上柱,下柱,1,）节点弯矩分配系数,i=0.471,i=0.471,i=0.498,i=0.498,i=0.498,i=0.498,1,0.62,0.332 0.668,0.472 0 0.235 0.290,0.250,0.250,0.500,0.383 0.19,0.19,0.237,0.253 0.239 0.508,0.386 0.192 0.182 0.240,右梁,左梁,上柱,下柱,2,）求节点固端弯矩,g1=40.2kN/m,g1=40.2kN/m,g2=32.8kN/m,i=0.471,i=0.498,i=0.498,0.332 0.668,0.472 0 0.235 0.290,0.250,0.250,0.500,0.383 0.19,0.19,0.237,0.253 0.239 0.508,0.386 0.192 0.182 0.240,-98.4,98.4,-19.9,-120.6,120.6,-24.4,-120.6,120.6,-24.4,右梁,左梁,上柱,下柱,3,）“节点不平衡弯矩”进行第一次分配,0.332 0.668,0.472 0 0.235 0.293,0.250,0.250,0.500,0.383 0.19,0.19,0.237,0.253 0.239 0.508,0.386 0.192 0.182 0.240,-98.4,98.4,-19.9,-120.6,120.6,-24.4,-120.6,120.6,-24.4,4,）“传递弯矩”的第二次分配,32.7 65.7,-37.1 -18.4 -23.0,30.1,30.1,60.3,-36.8 -18.3,-18.3,-22.8,-37.1 -18.5 -17.5 -23.1,30.5 28.8 61.3,-18.6,15.1,2.34,1.2,49.0,-49.0,32.85,-9.2,-11.16,-5.56,-6.93,82.99,-33.16,-49.83,-18.4,15.25,16.35,30.15,-9.2,-9.25,-6.63,-3.31,-3.31,-2.22,-2.22,-4.48,-2.77,-85.33,42.04,43.14,-29.72,109.5,-50.0,-29.72,-18.55,15.05,-9.15,30.65,1.78,0.83,0.89,-4.13,-8.30,-5.16,-3.91,-76.07,29.63,46.44,-31.8,105.9,-52.66,-21.41,14.8,-10.7,-over!,