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钢-混凝土组合梁(以下简称组合梁)的界面滑移总是存在的,滑移的存在会降低组合梁的组合作用和刚度,增大挠度,要计算组合梁界面的滑移及挠度,对于简支梁在简单荷载情况下,还可得到解析解,但对于连续梁要得到解析解是十分困难的,另外简支梁的解析解十分冗长,实际运用十分不便。用有限元法计算组合梁的滑移和挠度将是很有效的,不受荷载及支撑条件限制,而有限元法的关键是单元刚度矩阵,该文用虚功原理推导了组合梁的单元刚度矩阵,并用自编的有限元程序对组合梁的滑移和挠度进行了计算,在简支情况下与解析解进行了对比和验证,误差很小,在1%以内。该文推导的单元刚度矩阵可用于小型的自编有限元软件,为快速经济地解决相关的大量实际工程问题奠定了基础。
The interface slip always exists in the steel-concrete composite beam (hereinafter referred to as the composite beam). The existence of slip will reduce the combined action and rigidity of the composite beam and increase the deflection. To calculate the slip and deflection of the composite beam interface, Simply supported beams can be analytically solved under simple loading conditions. However, it is very difficult to obtain analytical solutions for continuous beams. In addition, the analytical solution of simply supported beams is very long and very inconvenient in practical application. Finite element method to calculate the slip and deflection of the composite beam will be very effective, not subject to load and support conditions, and finite element method is the key to the unit stiffness matrix. This paper deduces the unit stiffness of the composite beam with virtual work principle Matrix. The slip and deflection of the composite beams are calculated by using the self-programmed finite element program. Compared with the analytical solution under simple support, the error is very small, less than 1%. The element stiffness matrix deduced in this paper can be used in small self-made finite element software, which lays the foundation for solving a large number of practical engineering problems in a fast and economic way.