箱型梁剪力滞效应的解耦求解

Decoupling Solution to Shear Lag Effect on Box Girder

针对运用能量变分理论分析箱型梁剪力滞效应时存在的问题,用箱型梁的附加挠度函数代替剪力滞函数建立箱型梁翼缘截面的纵向位移表达式,用外荷载代替内力建立箱型梁的总势能泛函,根据变分原理推导箱型梁在剪力滞效应下的4阶控制微分方程及各类边界条件,提出剪力滞效应下箱型梁挠度、附加挠度和经典梁挠度的解耦求解方法,首次得到箱型梁在剪力滞效应下自由端的边界条件和固定—简支箱型梁响应量的封闭解。算例分析验证了该求解方法的有效性和计算精度,同时也表明,箱梁挠度和附加挠度具有完全相同的边界条件,但在自由端二者的边界条件与Euler梁理论不同。

In order to solve the problems in energy variational theory for analyzing the shear lag effect on box girder,the longitudinal displacement expression of the flange section of box girder was established by the additional deflection function instead of the shear lag function of box girder.The total potential energy functional of box girder was developed using external load instead of inner force.Fourth-order governing differential equations and various boundary conditions under shear lag effect were derived according to variational principle.The decoupling solution method was presented for the deflection and the additional deflection of box girder as well as the deflection of classical beam under shear lag effect.The boundary conditions at the free end of box girder under shear lag effect and closed-form solution to the response of the box girder clamped at one end and simply supported at another end were obtained for the first time.Example analysis has demonstrated the effectiveness and calculation accuracy of the proposed method.Meanwhile,the boundary conditions are quite same for both the deflection and additional deflection of box girder,but are different from those of Euler beam at the free end.