部分共同作用框架组合梁有限元分析模型

本文提出了一种新的适用框架整体分析的组合梁有限元模型。在分析了相互作用程度对组合梁刚度影响的基础上,根据Newmark等人的一维部分相互作用理论,建立起部分共同作用组合梁平衡微分方程;结合框架组合梁受力特点引入合理的边界条件,推导出了能够考虑滑移的组合梁单元弹性刚度方程;还给出了常见非节点荷载的等效荷载公式。该组合梁单元节点自由度少,每个构件只需一个单元来模拟,方便了带组合梁钢框架的结构分析。本文的研究还为进一步地考虑混凝土开裂、压碎,钢材屈服等非线性因素,建立组合梁单元弹塑性刚度矩阵提供了理论基础。

A Finite Element Model of Partial Composite Girders

A new finite element model of composite beams was presented,which is applicable to the analysis of steel frames.After the analysis of the impact of interaction degree on bending stiffness of composite beams,the equilibrium differential equation of partial composite beams was established on the basis of Newmark's one dimensional partial interaction theory.By considering the characters of composite girders and introducing the rational boundary conditions,the elastic stiffness equation of composite beam element was deduced,which takes account of the influence of interface slips.Furthermore,the formulas of calculating the equivalent nodal loads of common non-nodal loads were also given.The composite beam element has less nodal degrees of freedom,and only one element is needed for one component which brings efficiency to the analysis of structural steel frames with composite beams.The study also provides a theoretical basis for establishing the elasto-plastic element stiffness matrices of composite beam,which takes the nonlinear factors such as cracks and crushes in concrete and yield in steel into consideration.