自重荷载作用下悬索静力解析解

从悬索微元体平衡出发,分别推导以悬索张力分量、索长等为参变量,考虑和不考虑悬索自重集度变化的两种悬索解析式。通过比较发现,去掉悬索伸长影响项,就可直接由考虑悬索自重集度变化的解析式缩减到不考虑其变化的解析式。在用索长表达的解析式中,考虑悬索自重集度变化时对应无应力索长,不考虑悬索自重集度变化时对应有应力索长。算例假定斜拉索梁端张力的竖向分量为已知,按以上两种情况,分别建立以悬索张力的水平分量和塔端张力的竖向分量为未知数的非线性方程组,用拟牛顿法求解,得到悬索未知参数的精确解析解。

Static Solution of Suspension Cables under Tare Load

From the static equilibrium condition of the cable element, the analytical solutions of suspension cables are derived, both when the influence of its elongation on its weight per unit length is consider and not considered. By comparison, it is found that if the cable elongation is not considered, the formula of considering the influence can be reduced to that of not considering the influence. In the solution expressed with cable length, the case that considers the influence corresponds to the unstressed cable length; the case that does not consider the influence corresponds to the stressed cable length. Provided that the vertical component of cable tension at the attachment of deck is given, according to the above two cases, with the unknown quantities of the horizontal component of the cable tension and the vertical component at the tower attachment, two groups of nonlinear equations are established respectively. The quasi-Newton method is used to solve the solution.