钢筋混凝土梁承载力分析的打靶法及其应用

Shooting method and its application for bearing capacity analysis of reinforced concrete beam

根据钢筋混凝土(RC)梁静力学分析的虚功原理,导出了考虑钢筋和混凝土非线性材料特性及梁身剪切变形的RC梁静力分析控制微分方程与边界条件。将得到的控制方程转化为由6个一阶常微分方程构成的非线性微分方程组边值问题,从而采用非线性打靶法研究RC梁的静力学行为,得到了RC梁的位移与弯矩响应。对比RC梁Timoshenko模型与Euler-Bernoulli模型分析结果,验证了所展开分析的正确性、参数研究了RC梁的剪切效应,以及通过RC梁的弯矩分析,得到非线性RC梁弯矩调幅系数;通过RC梁的正应力分析,得到了RC梁的裂纹分布区域。

According to the virtual work principle for the static analysis of the reinforced concrete（RC） beam, the differential equations and their boundary conditions governing the static response are derived, taking into account the nonlinear properties of the rebar and concrete and the shearing deformation of the beam body. Subsequently, a nonlinear boundary value problem composed of 6 first order ordinary differential equations is obtained, thus, the static behavior of the RC beam is studied using the nonlinear shooting method, and the responses of displacements and bending moment of the RC beam are obtained. At the end, via the comparisons of results generated by Timoshenko and Euler-Bernoulli beam models, the correctness of the analysis is verified, and the shear effect of the RC beam is parametrically studied.Besides, the bending moment modulation coefficient of the nonlinear RC beam is gained, and the crack zone of the RC beam are obtained through the normal stress analysis.