变截面梁柱刚度方程的近似解

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 .

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

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 I 0 (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 P cr (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.