考虑缆-梁联合作用的自锚式悬索桥恒载状态计算方法研究

摘要

In most calculation methods for the reasonable finished bridge state of self-anchored suspension bridge, the combined action of cable-stiffening girder can not be considered in a single model, so repeated manual iteration or model boundary condition modification are usually adopted. For this reason, an analytical calculation method considering the combined action of cable-stiffening girder is proposed. Based on the stiffening girder deflection theory, the differential equilibrium equations, geometric equations, and the physical equations of the stiffening girder are used to derive the analytic relationship between the stiffening girder alignment and the suspender force. The end reaction force of the main cable is calculated from the suspender force using the segmental catenary theory. The solutions that meet the compatibility condition of the suspender force and the end reaction of the main cable is obtained by the iteration method. The calculation results by the proposed method agree well with the theoretical reasonable finished bridge state satisfying the principle of minimum potential energy of stiffening girder. The proposed method has the advantage of fast convergence speed and high precision that needed in practical engineering.%自锚式悬索桥合理成桥状态的已有算法中，很难在一个模型中同时考虑缆-梁的联合作用，需要通过反复手动迭代或是修改模型边界条件进行求解，较为繁琐。对此，笔者提出一种考虑缆-梁联合作用的恒载状态计算方法。该方法基于加劲梁的挠度理论，通过梁段的平衡微分方程、几何方程、物理方程推导出加劲梁的线形和索力的解析关系；主缆基于分段悬链线理论，通过已知吊索索力计算主缆端部反力；再用迭代方法得出满足以主缆端部反力和吊索索力为相容条件的解。计算结果表明，该方法能够考虑缆-梁联合作用，得到满足加劲梁最小应变能原理的合理成桥状态，且收敛速度快，精度高，能够满足实际工程的需求。