彎矩分配法例題

彎矩分配法計(jì)算：由對稱性，該題計(jì)算模型可簡化為一個(gè)全跨加一個(gè)半跨，半跨端部為滑動支座。一．頂層彎矩計(jì)算1：計(jì)算分配系數(shù)iEI；遠(yuǎn)端固定S=4i；遠(yuǎn)端滑動S=i；l遠(yuǎn)端固定非底層柱：S10.94EI0.94E5.21035.943103El3.15遠(yuǎn)端固定全跨梁：S24EI4E8.111034.864103El6.67遠(yuǎn)端滑動半跨梁：S3EIE8.111032.432103El6.67/2對頂部全跨的端點(diǎn)A：ADS15.9430.550S1S25.9434.864ABS24.8640.450S1S25.9434.864對節(jié)點(diǎn)B:BAS24.8640.367S1S2S35.9434.8642.432BCS32.4320.184S1S2S35.9434.8642.432BES15.9430.449S1S2S35.9434.8642.4322：各桿的固端彎矩為MAB1ql21105.666.72391.50KNM1212MBC1q(l)21105.666.72391.50KNM3234MCF1q(l)21105.666.72195.75KNM62643：頂層彎矩分配法計(jì)算過程如下圖所示0.5500.4500.3670.4490.184ADABBABEBCCFA-391.50391.50B-391.50-195.75C215.32176.181/288.09-16.171/2-32.33-39.55-16.21-116.218.897.281/23.64-0.671/2-1.34-1.63-0.67-10.670.370.301/20.15-0.05-0.07-0.03-10.03224.58-224.58449.66-41.25-408.41-178.84柱子傳遞系數(shù)取1/3：224.58×1/3=74.86-41.25×1/3=-13.75二．標(biāo)準(zhǔn)層彎矩計(jì)算1，計(jì)算彎矩分配系數(shù)對節(jié)點(diǎn)DDADGS15.9430.355S1S25.9435.9434.864S1DES24.8640.290S1S1S25.9435.9434.864對節(jié)點(diǎn)EEBEHS15.9430.3102S1S2S325.9434.8642.432EDS24.8640.2542S1S2S325.9434.8642.432EFS32.4320.1262S1S2S325.9434.8642.4322,各桿固端彎矩與頂層相同3，中間層彎矩分配計(jì)算過程如下圖所示0.3550.3550.2900.2540.3100.3100.126DADGDEEDEBEHEFFED-391.50391.50E-391.50-195.75138.98138.94113.541/256.77-7.211/2-14.42-17.60-17.60-7.15-17.152.562.562.091/21.05-0.141/2-0.28-0.32-0.32-0.13-10.130.050.050.041/20.020-0.01-0.010-10141.59 141.59 -283.18 434.64 -17.93 -17.93 -398.78 -188.47柱子傳遞系數(shù)取 1/3: 141.59×1/3=47.20-17.93 ×1/3=-5.98三，底層彎矩計(jì)算1.計(jì)算彎矩分配系數(shù)對節(jié)點(diǎn)G:SGDSHE0.94EI0.94E5.21033El3.155.94310SGJSHK4EI4E5.21033.947103El5.27SGHSHG4EI4E8.111034.864103El6.67SHIEIE8.111032.432103El6.67/2GDSGD5.9430.403SGDSGJSGH5.9433.9474.864GJSGJ3.9470.267SGDSGJSGH5.9433.9474.864GHSGH4.8640.330SGDSGJSGH5.9433.9474.864對節(jié)點(diǎn)H:HGSHG4.8640.283SHGSHESHISHK4.8645.9432.4323.947HESHE5.9430.346SHGSHESHISHK4.8645.9432.4323.947HISHI2.4320.141SHGSHESHISHK4.8645.9432.4323.947HKSHK3.9470.230SHGSHESHISHK4.8645.9432.4323.9472.各桿固端彎矩與頂層相同底層彎矩分配計(jì)算過程如下0.4030.2670.3300.2830.3460.2300.141GDGJGHHGHEHKHIIHG-391.50391.50H-391.50-195.75157.77104.53129.201/264.60-9.141/2-18.28-22.35-14.86-9.11-19.113.682.443.021/21.51-0.221/2-0.43-0.52-0.35-0.