考虑界面滑移和掀起的组合梁弯曲变形解析解

Analytic solutions of bending deformation of composite beams with interfacial slip and lift

考虑组合梁连接面的纵向滑移与竖向掀起效应,在组合梁子梁满足Euler-Bernoulli梁弯曲理论的假定下,以组合梁纵向滑移和子梁竖向挠度为基本未知量,建立了组合梁弯曲变形的控制方程.利用Laplace变换及其Laplace逆变换,得到了均布载荷作用下简支组合梁弯曲挠度、滑移位移、轴力和弯矩的解析解.假定组合梁两子梁材料和几何参数相同,重点分析了加载方式和连接面纵向滑移与竖向掀起刚度对简支组合梁弯曲变形的影响.研究结果表明:随着界面纵向刚度的增大,组合梁挠度、滑移位移、弯矩均先减小后趋于不变,而组合梁的轴力先增大后不变;随着界面竖向刚度的增大,当上部加载时,上部子梁的挠度与弯矩先减小后趋于不变,下部子梁的挠度与弯矩先增大后趋于不变;当下部加载时,与上部加载情况相反;当两梁所受载荷一致时,组合梁的变形及内力与竖向刚度无关.

To consider the effects of the longitudinal slip and vertical uplift of composite beam connection surface,the governing equations of composite beam bending deformation were established with fundamental unknowns of the longitudinal slip and vertical deflec-tions of sub beams under the assumption that sub-beams satisfied Euler-Bernoulli bending theory.Through Laplace transform and inverse Laplace transform,analytical solutions of deflection,slip displacement,axial force and bending moment of simply-supported compos-ite beams under uniform loads were obtained.Based on the assumption that the material and geometric parameters of the two sub-beams were the same,the effects of the loading mode and longitudinal slip and vertical uplift stiffnesses of the connection surface on the bending deformation and internal forces of a simply supported composite beam were an-alyzed.The results showed that with an increase in interface longitudinal stiffness,the deflection,slip displacement and bending moment of the composite beams first decreased and then tended to be constant,whereas the axial force of the composite beams first in-creased and then remained constant.When a composite beam was loaded from the top sub-beam,with the increase the vertical stiffness of the interface,the deflection and bend-ing moment of the upper beam first decreased and then tended to be constant,whereas the deflection and bending moment of the lower beam first increased and then tended to be constant.When a composite beam was loaded at the bottom sub-beam,it acted in a manner opposite to that at the top.The deformation and internal force of composite beams had nothing to do with the vertical stiffness when the upper and lower loads were the same.