箱型梁附加挠度与剪力滞效应的一维有限元分析

One-dimensional finite element analysis on additional deflection and shear-lag effect of box-girders

当前箱型梁剪力滞效应分析的一维离散有限元法对剪力滞函数的处理存在局限性,而且剪力滞系数难以准确反映翼缘截面剪力滞效应及其变化规律。为此,利用箱梁附加挠度代替剪力滞函数建立箱梁翼缘的纵向位移函数,并根据能量变分原理建立控制微分方程并识别了其中的待定参数。以箱梁挠度、附加挠度及其一阶导数作为单元节点位移参数,提出了箱型梁剪力滞效应分析的一维离散有限元法,给出了箱梁的自然边界条件和强迫边界条件。基于箱梁挠度和附加挠度定义了新的剪力滞系数,分析了不同支撑条件对箱型梁剪力滞效应的影响。算例分析证明了该方法的有效性,且具有较高的计算精度;与传统的基于应力的剪力滞系数相比,基于挠度的剪力滞系数能够更加准确地反映箱型梁截面的剪力滞效应及其分布规律。

The shear-lag function in one-dimensional finite element method for box-girders has no definite physical interpretation, and moreover the shear-lag coefficient can not reflect correctly the shear-lag effect and its variation along the axis of box girder. In order to circumvent these problems, the additional deflection function instead of the shear-lag function is incorporated in the longitudinal displacement of the flange of the box girder. The variational principle is employed to identify the undetermined constants in the longitudinal displacement function. Furthermore, the deflection, additional deflection and their first derivatives are adopted as nodal displacement parameters in the discreted finite elements of box-girder, leading to one-dimensional finite element method for the shear-lag effect of box girders. A new shear-lag coefficient is defined in terms of the deflection of the box-girder, based on which the shear-lag effect on box girders is analysed with different boundary conditions considered. Examples show that the shear-lag coefficient based on the additional deflection can reflect much more accurately the shear-lag effect and its variation on the box girder than the conventional shear-lag coefficient based on the stress.