考虑收缩徐变影响的新旧混凝土叠合梁单元刚度矩阵改进

摘要

混凝土自身的收缩徐变会在新旧混凝土叠合梁中使应力重分布。为了计算重分布应力，首先推导以挠度表达的叠合梁非线性微分方程，然后通过求解该微分方程，引入位移形函数、刚度形函数和等效节点载荷形函数，最后得出新混凝土梁、旧混凝土梁和 Goodman 弹性夹层三合一的叠合梁改进型单元刚度矩阵和等效节点载荷，从而为收缩徐变影响下的混凝土的内力计算提供了一种有效的新方法。文中还进行了实例验证分析，并从中得出了一些有益的结论。%The shrinkage and the creep of concrete will lead to a stress redistribution in new-old composite concrete beams. The nonlinear differential equation for the composite beam is derived in terms of the deflection. By solving the differential equation, the displacement shape function, the stiffness shape function and the equivalent nodal load shape function are introduced. Finally, the improved element stiffness matrix and the equivalent nodal loads with the combination of the new concrete beams, the old concrete beam and the Goodman elastic intermediate layer, are obtained, which may serve as an effective way to calculate the internal force of the concrete under the influence of shrinkage and creep. An example is given to verify the analysis.