变截面梁柱刚度方程的近似解  

Approximate solution of stiffness equation of a non-uniform beam-column

作　　者：宋启根[1] 庄和星 吕令毅[1] 

机构地区：[1]东南大学土木工程学院,南京210096 [2]厦门市建筑设计院,厦门361012

出　　处：《东南大学学报（自然科学版）》2003年第5期553-556,共4页Journal of Southeast University：Natural Science Edition

摘　　要：取变截面梁柱单元的挠度函数w为五次多项式 ,用最小势能原理解w及梁柱的刚度系数 .通过对截面按幂函数变化的梁柱的计算与由Bessel函数的准确解的比较 ,检验了近似解的适用性 .计算结果表明 ,当I0 /i<1 0及P/Pcr<2 (Pcr为杆件的临界荷载 )时近似解有较高的精度 .对可视为拟变截面梁柱的弹塑性梁柱 ,可以推断本近似解也适用 .Taking a fifth-order polynomial as the deflection function w of a non-uniform beam-column, the stiffness coefficient and w can be determined by the principle of minimum potential energy. Through the comparison of the calculation results for the beam-columns with varying cross sections according to a power function and the correct results by the Bessel function, the validity of the approximate solution is examined. It is shown that the accuracy of the approximate solution is satisfactory when the ration of I0 (the maximum moment of inertia of the cross section of the member) to i (the minimum moment of inertia of the cross section of the member) is less than 10 and the ratio of P (the applied axial load) to Pcr (the critical load of the member) is less than 2. It is expected that the method would also be valid for the elasto-plastic beam-column, which can be regarded as an analogical non-uniform member.

关 键 词：变截面梁柱 弹塑性杆件 最小势能法 

分 类 号：TU375.4[建筑科学—结构工程]