组合梁徐变和收缩应力重分布的代数本构方程求解

摘要

To calculate the creep and shrinkage effects of steel⁃concrete composite beams, we adopted an algebraic constitutive equation based on the age⁃adjusted effective modulus method. We established and solved equations for the composite beams based on the graphic method for internal force distribution. Then, using example analysis, we obtained the change in mechanical characteristics with time, with respect to the internal forces, stresses, and strains due to creep and shrinkage in the composite beam sections. We verified the accuracy of our results by per⁃forming a self⁃equilibrium of the redistributed internal forces. The results show that the redistribution of internal forces caused by creep and shrinkage increases ith time, and the changing rate decreases with time. We also found that the redistribution bending moments of the steel beams are significant, while those of the concrete slab are very small. If we ignore the effects of the bending moments, we can solve the equations independently, further simplify⁃ing the calculations. The redistribution of the internal forces caused by creep and shrinkage can result in self⁃equi⁃librium, which can be used to test the accuracy of the results. These results can be directly applied in practical en⁃gineering calculations.%针对钢－混凝土组合梁徐变和收缩效应的计算问题，采用龄期调整有效模量法的代数本构方程，并用内力分配的图解方式推导和求解了组合梁弯矩和轴力重分布的代数方程组。通过算例分析，获得了受徐变和收缩影响的组合梁截面内力、应力和应变随时间变化的力学特征，并利用重分布内力自相平衡的特点验证了结果的正确性。计算结果表明：由徐变和收缩引起的重分布内力均随时间增长而增大，变化速度随时间增加而递减；钢梁重分布弯矩显著，而混凝土板的重分布弯矩很小，若忽略该弯矩的影响可以使方程组独立求解，进一步简化计算；徐变和收缩引起的重分布内力都是自平衡内力，由此可检验计算结果的正确与否。此方法得到的解可直接应用于工程的实用计算。