扭转荷载作用下考虑横隔板刚度影响的一种新型箱梁单元

A NOVEL BOX GIRDER BEAM-ELEMENT CONSIDERING DIAPHRAGM STIFFNESS EFFECTS UNDER TORSIONAL LOADING

  • 摘要: 为研究扭转荷载作用下内置横隔板的薄壁箱梁力学性能,该文提出了一种考虑横隔板刚度影响的新型箱梁单元(BnCTD)。根据荷载分解法,将薄壁箱梁的扭转分解为刚性扭转和畸变,分别在刚性扭转分析中考虑圣维南扭转和二次扭转剪切变形的影响,在畸变分析中考虑二次畸变剪切变形的影响。基于广义坐标法,统一了扭转荷载作用下约束扭转效应和畸变效应的位移形式。利用变形协调关系和内力平衡条件,建立了不同类型横隔板与主梁变形之间的几何关系,提出了横隔板应变分析方法以及应变能表达式。通过最小势能原理,推导出考虑剪切变形影响的薄壁箱梁扭转控制微分方程,选用齐次解构造了广义位移(扭转角θ、畸变角χ、主扭转角率η和主畸变角率Θ)的插值函数。基于能量变分原理,开发了考虑横隔板刚度影响的两节点八自由度新型箱梁单元,并推导了单元刚度矩阵和结点荷载向量。通过算例分析,验证了BnCTD梁单元的计算精度与广泛适用性。计算结果表明,BnCTD梁单元能够有效考虑不同类型横隔板对主梁内力和变形的影响,准确反映主梁应力分布的差异,与实体有限元模型相比,使用较少单元即可达到较高计算精度,显著提升了计算效率。分析结果表明,在扭转荷载作用下,横隔板主要为畸变变形提供刚度支撑,且随着横隔板数量的增加,主梁扭转翘曲应力在横隔板附近逐渐减小。

     

    Abstract: To investigate the mechanical behavior of thin-walled box girders with internal diaphragms under torsional loads, a novel box girder beam element (BnCTD) considering the effect of diaphragm stiffness is proposed. Based on the force decomposition method, the torsion of the thin-walled box girder can be divided into rigid torsion and distortion. In the rigid torsion analysis, shearing deformation induced by Saint-Venant torsion and the secondary torsional moment deformation effect are considered, while in the distortion analysis, the effect of secondary distortional moment deformations is incorporated. Using the generalized coordinate method, displacement expressions for the constrained torsion and distortion under torsional loads are unified. The geometric relationship between different types of diaphragms and the main girder deformation is established through deformation compatibility conditions and internal force equilibrium ones. Additionally, a strain analysis method for different diaphragms and the corresponding strain energy expressions are proposed. The governing differential equation for torsion of the thin-walled box girder, accounting for shearing deformations, is derived using the principle of minimum potential energy. The homogeneous solution is employed to construct interpolation functions for the generalized displacements (torsion angle θ, distortion angle χ, main torsional rate η, and main distortional rate Θ). A new box girder beam element that accounts for the effect of diaphragm stiffness is developed upon the energy variational principle, and the element stiffness matrix and nodal load vector are derived. Numerical examples are provided to validate the computational accuracy and broad applicability of the BnCTD element. The results demonstrate that the BnCTD element can effectively consider the impact of different diaphragm types on the internal forces and deformations of the box girder, accurately reflecting variations in stress distribution, while achieving high computational accuracy with fewer elements compared to solid finite element models, thereby significantly improving computational efficiency. The analysis further reveals that under torsional loads, diaphragms mainly provide stiffness support for distortion deformations. Moreover, as the number of diaphragms increases, the torsional warping stress of the main girder gradually decreases in the vicinity of the diaphragms.

     

/

返回文章
返回