考虑滑移效应的组合梁的附加挠度计算研究

Study on calculation of additional deflection of composite beams considering slip effect

对于两端简支组合梁,根据其控制微分方程推导了关于相对滑移的微分方程以及相对滑移与挠度的关系转换公式,结合边界条件得到相对滑移,然后计算弯曲曲率和挠度,得到了附加挠度的理论精确解计算公式。附加曲率法先通过滑移应变除以组合梁高度得到附加曲率,然后计算附加挠度,与其理论精确解对比发现,两者并不一致。根据组合梁的跨中弯曲曲率,得到了弯曲曲率系数的理论计算公式并提出了简化公式。理论分析和算例结果表明,滑移效应产生的附加挠度不可忽略,应用附加曲率法计算组合梁的附加挠度并不可行,其计算值小于理论值,偏于不安全。

For the simply supported composite beams at both ends,the differential equations for relative slip and the relational transformation formula of relative slip and deflection were derived according to the governing differential equations.The relative slip was obtained by combining the boundary conditions,and then the bending curvature and deflection were calculated.The theoretical exact solution formula for the additional deflection was obtained.The additional curvature method obtains the additional curvature by dividing the slip strain by the height of the composite beams,and then calculates the additional deflection,which is inconsistent with the theoretical exact solution.According to the mid-section bending curvature of the composite beam,the theoretical calculation formula of the bending curvature coefficient was obtained,and a simplified formula was proposed.Theoretical analysis and numerical results show that the additional deflection generated by the slip effect is not negligible.It is not feasible to apply the additional curvature method to calculate the additional deflection of composite beams.The calculation result is less than the theoretical value and is not safe.