考虑剪切剪滞双重效应波形钢腹板组合箱梁的矩阵分析

Matrix Analysis of Composite Box Girder with Corrugated Steel Webs Considering Shear Deformation and Shear Lag Effect

为了更精确地研究考虑剪切剪滞双重效应波形钢腹板组合箱梁的力学性能,首先运用有限元分析方法,在综合考虑剪力滞与剪切变形双重效应影响的基础上,通过能量变分原理导出了波形钢腹板组合箱梁的控制微分方程并给出了解析解;之后在该解析解的基础上进一步推导了单元刚度矩阵及结点荷载列阵,还根据相关方程编制了FORTRAN有限元程序;最后将室内模型试验梁对波形钢腹板简支梁和连续梁的实测结果与所提理论的计算结果、ANSYS实体单元模型的计算结果进行对比分析。结果表明:所提理论和模型试验、有限元模拟3种方法所得剪力滞系数和挠度值吻合良好,且理论计算值与模型试验实测值所得跨中剪力滞系数、挠度值更接近;简支梁在承受集中荷载作用比承受均布荷载作用同一截面处的剪力滞效应影响大,连续梁在承受集中载荷作用时,在支座附近处截面的剪力滞效应的影响比跨中要大,并在靠近弯矩零点的一部分区域内表现出负剪力滞现象;波形钢腹板简支梁、连续梁的剪力滞系数随跨宽比的增大而呈曲线减小。研究成果可将波形钢腹板考虑双重效应的复杂计算问题,方便地纳入普通杆系结构矩阵位移结构体系中,可直接得到用于结构设计的剪力、弯矩,从而避免建立复杂的ANSYS有限元模型。

In order to accurately investigate the mechanical properties of the composite box girder with corrugated steel web plates,based on the consideration of the effect of shear lag and shear deformation,the governing differential equation of the composite box girder with corrugated steel web plates was derived by dint of the energy variation principle,whilst the analytic solution was given.On the basis of the analytical solution,the element stiffness matrix and node load array were obtained,and then finite element programs of FORTRAN were written on the basis of the corresponding equations.Taking a simply supported beam and a continuous beam with corrugated steel web plates for examples,measured results,calculated results based on the theory of the derived equations and calculated results of the ANSYS solid element model were analyzed andcompared.The results show that deflection values are identical with coefficients of shear lag and deformation obtained by dint of the proposed theory,the model test and finite element simulation.Moreover,the theoretical values of the coefficient of shear lag and deflection are closer to tested results of the model experiment.The shear lag effect of simply supported beams is largely affected by concentrated load,rather than uniformly distributed load in the identical section.Under the condition of concentrated load,the shear lag effect of continuous beams has a greater influence on the section near the support than the mid-span section.In addition,the negative shear lag of continuous beams in the area close to zero bending moment is manifested.The coefficients of shear lag of simply supported girder or continuous beam with corrugated steel web plates decrease with the increase of span-to-width ratios.The complicated problem of corrugated steel web plates considering double effect can be conveniently included into ordinary truss structure matrix displacement system.The shear and bending moment for structure design can be gained directly,so as to avoid the establishment of complicated ANSYS finite element model.