哈密顿力学下双箱单室波形钢腹板组合箱梁剪力滞效应分析  

Shear lag effect of double-box single-cell corrugated steel web with box girder based on Hamiltonian mechanics

作　　者：胡启平[1] 岳朝峰 HU Qiping;YUE Chaofeng(College of Civil Engineering,Hebei University of Engineering,Handan,Hebei 056038,China;The Second Construction Limited Company of China Construction Eighth Engineering Division,Jinan 250014,China)

机构地区：[1]河北工程大学土木工程学院,河北邯郸056038 [2]中建八局第二建设有限公司,济南250014

出　　处：《中国科技论文》2023年第10期1070-1076,1104,共8页China Sciencepaper

基　　金：河北省自然科学基金资助项目(E2016402110)。

摘　　要：针对双箱单室波形钢腹板组合箱梁这一新型结构,结合波形钢腹板的结构特点,在哈密顿(Hamilton)力学体系下进行箱梁剪力滞效应研究。考虑箱梁弯曲时的剪切变形及纵向翘曲位移,对箱梁悬臂板、底板、顶板和内侧顶板分别假定不同的纵向位移差函数,选用二次抛物线描述翼板的剪滞翘曲位移,建立结构的总势能及对应的拉格朗日(Lagrange)函数。与传统变分法不同,所提方法基于哈密顿力学体系,根据勒让德(Legendre)变换引入对偶变量,推导得出结构弯曲问题的哈密顿正则方程,利用两端边值问题的精细积分法进行求解,计算箱梁上下翼板应力与变形,并与文献算例结果及有限元数值结果进行比较验证。结果表明,所提方法能简单、正确地描述双箱单室波形钢腹板组合箱梁的剪力滞后现象,可在初步设计阶段对结构稳定性进行评估。For the new structure of double-box single-cell waveform steel web composite box girder,the shear lag effect of box girder was studied under Hamiltonian mechanics system by combining the structural characteristics of waveform steel webs.Different longitudinal displacement difference functions were assumed for the cantilever plate,bottom plate,top plate,and inner top plate of the box girder,considering the shear deformation and longitudinal warpage displacement of the box girder in bending.Moreover,the quadratic parabola was chosen to describe the shear lag warpage displacement of the wing plate,and the total potential energy of the structure and the corresponding Lagrange function were established.Unlike the traditional variation method,this method was based on the Hamiltonian mechanics system and introduced the pairwise variables according to the Legendre transformation to derive the Hamiltonian canonical equations for the structural bending problem.The solving process was carried out by using the fine integration method for the two-end edge value problem to calculate the stresses and deformations of the upper and lower wing plates of the box girder,and was compared with the results of literature examples and finite element numerical results for verification.The results show that the method proposed herein can simply and correctly describe the shear lag effect of double-box single-cell waveform steel web composite box girder,and can be used to evaluate the structural stability at the preliminary design stage.

关 键 词：波形钢腹板 剪力滞后 弯曲变形 哈密顿对偶体系 精细积分法 

分 类 号：TU311[建筑科学—结构工程]