基于细长梁单元的悬索桥主缆线形分析Study on main cable shape of suspension bridge based on slender beam element

悬索桥主缆线形的精细化计算需要同时考虑弯曲刚度及初始弯曲的影响，为此将主缆离散为小挠度的细长梁单元，推导包含自重项的细长梁单元的刚度矩阵，其中考虑了轴力对弯曲刚度的影响及弯矩引起的轴向刚度修正系数。基于细长梁单元编制主缆线形计算的有限元程序，采用改进的迭代法求解几何非线性结构的平衡状态，并考虑鞍座处主缆线形的修正。利用程序计算了两座悬索桥主缆在恒载作用下的变形，结果表明，主缆弯曲刚度对跨中和桥塔附近主缆线形的影响较大，且矢跨比越大，主缆线形的计算误差就越大。由弯曲刚度引起的主缆线形计算误差将会带来吊索下料长度计算不准确、索夹放样坐标不准确、成桥桥面线形达不到设计线形以及成桥吊索力分布不均匀等问题，尤其是对矢跨比较大的自锚式悬索桥，需要在设计和施工中引起足够的重视。

Study on main cable shape of suspension bridge based on slender beam element

Refined analysis for main cable shape of suspension bridge needs to consider the impact of bending stiffness and original curve simultaneously.For the reason the main cable is discretized into the slender beam element with small deflection.Stiffness matrix of the slender beam element is derived,which contains the dead weight items,and takes into account the influence of axial force on the bending stiffness and the axial stiffness correction factor caused by the bending moment.Finite element program for shape calculation of main cable is compiled based on the slender beam element.An improved iteration method for solving nonlinear equilibrium geometry of the structure is adopted in the program,and the modification method for main cable shape at the saddle is also considered.Deformation of main cable under dead load is calculated by the program for two suspension bridge.The results show that there is a greater impact on the deformation of the bending stiffness of main cable in the mid span and in the vicinity of cable pylon.And the greater sag to span ratio,the greater deformation calculation error.Deformation calculation error of main cable caused by the bending stiffness will bring some problems,such as cutting length of hanger inaccurate,lofting coordinate of cable clamp inaccurate,bridge deck shape not up to the design requirements and uneven distribution of hanger axial force in the finished bridge state.These problems need to be taken seriously enough in the design and construction,especially for the self-anchored suspension bridge with a larger sag to span ratio.