箱梁剪力滞效应一维有限元模型及评价方法

One-dimensional finite element model and evaluation methodfor shear lag effect of box girder

文章针对相关研究中剪力滞翘曲位移函数物理意义不明确的问题,分析了剪力滞效应引起的箱梁附加挠度以研究箱梁剪力滞效应;将箱梁挠度分为按初等梁计算的挠度与附加挠度2个部分,利用新的箱梁纵向位移函数,通过箱梁的总势能泛函,推导出关于附加挠度和初等梁挠度的微分方程;在将初等梁挠度与附加挠度分离的基础上,建立箱梁的一维离散有限元模型,对比研究了不同剪力滞翘曲位移函数和不同附加挠度形函数对计算结果的影响;提出用总挠度二阶导数和初等梁挠度二阶导数的比值作为剪力滞效应的评价指标,该指标能较真实地反映箱梁的剪力滞效应,且与实体模型截面应力不均匀程度变化规律一致;最后,为了反映在移动荷载下箱梁的应力分布,提出用箱梁的应力包络来评价箱梁的剪力滞效应,这种方法更直观,且容易被工程师所接受。

In view of the unclear physical meaning of the shear lag warping displacement function in the traditional research on shear lag,the additional deflection of box girder is proposed to analyze the shear lag effects.The deflection of box girder is divided into the deflection calculated according to the elementary beam theory and the additional deflection.Using the new box girder longitudinal displacement function,the differential equations of additional deflection and deflection of elementary beam are derived by using the total potential energy functional of the box girder.On the basis of separating the deflection of elementary beam from the additional deflection,a one-dimensional discrete finite element model of box girder is established,and the effects of different shear lag warping displacement functions and different additional deflection functions on the calculated results are compared.The ratio of the second derivative of the total deflection and the second derivative of deflection of elementary beam is used as the evaluation index for evaluating the shear lag effect,which is more in line with reality.Finally,in order to reflect the stress distribution of the box girder under the moving load,stress envelope of the box girder is proposed to evaluate the shear lag effect of the box girder,which is more intuitive and easily accepted by engineers.