考虑畸变影响的箱梁横向弯矩计算方法

Calculation methods of transverse bending moment of box girder considering the distortional influence

为研究偏心垂向荷载作用下梯形截面单室箱梁的横向弯矩,对框架分析法计算箱梁横向弯矩的方程进行优化,并在刚性支承法的基础上提出一种更加简单的横向弯矩计算方法;与框架分析法不同,横向弯矩可采用能量变分法求解,建立以箱梁顶板剪力差为未知量的四阶控制微分方程,采用比拟的弹性地基梁解法解出剪力差,得出梯形截面单室箱梁横向弯矩的能量变分法解。对几种箱梁横向弯矩计算方法用两个算例进行验证,结果表明,能量变分法解将箱梁底板上的弯矩误差绝对值由15.41%降到了9.68%;本文方法得出的横向弯矩结果和有限元结果吻合较好,弯矩误差绝对值最大不超过6.01%;本文方法和能量变分法可有效降低箱梁底板上的弯矩误差,计算精度得到提高。

In order to investigate the transverse bending moment of a trapezoidal cross-section single-cell box girder under eccentric vertical load,the process of calculating the transverse bending moment of the box girder by a frame analysis method was optimized.On the basis of the rigid support method,a simple method for calculating the transverse bending moment was proposed.Unlike the frame analysis method,the transverse bending moment can be determined by a variational energy principle.The shear increment of the top slab was taken as the unknown variable,and the fourth-order governing differential equation was established.The shear increment was acquired by the Beam on Elastic Foundation analogy,and the transverse bending moment of the trapezoidal single-cell box girder was obtained.The several methods of calculating transverse bending moment were verified by two examples.The results show that the variational energy method reduces the absolute error of the bending moment on the bottom slab of the box girder from 15.41%to 9.68%.The results of transverse bending moment obtained by the proposed method are in good agreement with the finite element method,and the absolute error is no more than 6.01%.The proposed method and variational energy method can reduce the bending moment error of the bottom slab effectively and improve the accuracy.