考虑剪切变形效应下波形钢腹板组合箱梁的矩阵分析方法

Matrix analysis method considering shear deformation effect for composite box girder with corrugated steel webs

为精确分析钢腹板剪切变形效应对波形钢腹板组合箱梁位移的影响,基于势能驻值原理以波形钢腹板组合箱梁截面的竖向位移、弯曲角位移及剪切角位移为未知位移函数,推导出波形钢腹板组合箱梁在考虑钢腹板剪切变形效应下的单元刚度矩阵和结点荷载列阵。根据推导所得的单元刚度矩阵和结点荷载列阵,采用MATLAB软件编制考虑钢腹板剪切效应影响的波形钢腹板组合箱梁位移计算的求解程序。MATLAB求解程序计算所得挠度值的正确性,得到实测值和三维有限元值的验证。研究成果将考虑剪切变形效应下波形钢腹板组合箱梁力学性能复杂计算的问题,方便地纳入到普通杆系结构矩阵位移结构体系中,避免了ANSYS有限元模型建立和求解的复杂性,可为今后波形钢腹板组合箱梁桥的设计计算提供参考。

In order to accurately analyze the effect of shear deformation of steel web on displacement of corrugated steel web composite box girder,the vertical displacement,bending angular displacement and shear angular displacement of corrugated steel web composite box girder were considered as unknown displacement functions based on the potential energy standing value principle.The element stiffness matrix and the node load array of the corrugated steel web composite box girder under the shear deformation effect of the steel web were derived.According to the derived element stiffness matrix and node load array,the solution program for calculating the displacement of corrugated steel web composite box girder considering the influence of steel web shearing effect was compiled by MATLAB software.The correctness of the deflection calculated by the MATLAB program was verified by the measured values and the three-dimensional finite element values.The research results will consider the complex calculation of the mechanical properties of corrugated steel web composite box girder under shear deformation effect,which is conveniently incorporated into the matrix displacement structure system of ordinary bar system structure,avoiding the complexity of establishing ANSYS finite element model and solving it and can provide reference for design and calculation of composite box girder bridge with corrugated steel webs in the future.