悬索桥主缆线形静力解析解

Static Analytical Solution of the Main Cable Curve of a Suspension Bridge

假设悬索桥主缆自重沿弧长均匀分布,加劲梁、桥面等其余恒载沿水平均匀分布,根据索微元的力学平衡关系,通过引入一个参变量,导出了悬索桥主缆成桥线形的解析参数方程。由边界条件,将定解问题转化为一组非线性方程组,以抛物线理论值为求解初始值,采用拟牛顿法求解未知参数和水平张力,然后由积分法确定主缆索有应力长和无应力长,算例结果表明该法收敛速度较快,计算精度较高。

With the hypotheses that the weight per unit length of the main cable of a suspension bridge is uniform along its curve length and the weight per unit length of the other dead load such as the stiffened girders and decks is uniform along the horizon length, according to the mechanical equilibrium conditions of the element of the main cable, by using a parameter variable, the analytical parameter equations of the cable curve of the suspension bridge after completion are derived. A group of nonlinear equations are set up according to the boundary conditions. Taking the values determined through the parabolic theory as the initial iteration values and with the quasi-Newton method, the unknown parameter and horizontal component of the tensile force of the main cable are obtained. Then, the formula is derived for the main cable length of the suspension bridge in stressed and non-stressed states with the integration method. The calculation result shows that the calculation method presented in this paper has the advantages of quick convergence and high precision.