矩形箱梁力学性能分析的修正计算方法

本文对矩形箱梁翼板设置了不同的剪滞翘曲位移差函数，继而综合考虑剪力滞效应、剪切变形以及剪滞翘曲应力和弯矩自平衡条件等因素，且以能量变分原理为基础建立了矩形箱梁的弹性控制微分方程和自然边界条件，基于此修正了现行薄壁结构分析方法。与传统剪滞理论相比，本文方法深刻反映了矩形箱梁的力学特性。研究表明，(1)由于剪滞翘曲应力和弯矩自平衡条件的引入，矩形箱梁力学性能分解为独立的初等梁理论和剪滞理论体系，且箱梁力学性能为两者的叠加效应；(2)矩形箱梁断面尺寸确定，剪滞效应对其正应力的影响值不变，即剪滞效应的竖向力学行为与箱梁跨径无关；(3)尽管矩形箱梁的梁高对箱形梁剪滞翘曲应力和初等梁理论的应力值皆有一定影响，但其剪力滞系数不变，因此剪力滞效应与梁高无关；(4)剪力滞效应不仅影响箱梁翼板力学性能，而且对其腹板力学行为的影响不可忽视。因而，与传统剪滞理论相比，本文修正法不仅计算精度明显提高，而且更能真实反映矩形箱梁的力学性能。

Modified analysis method on mechanical properties of rectangular box girders

Firstly, different shear lag warping displacement functions are set for a rectangular box girder, then factors such as shear lag effect, shear deformation, self-equilibrium conditions for shear lag warping stress and moment are considered.Based on the energy-variation principle, the differential equations and natural boundary conditions of the rectangular box girder are established, and the existing analytical method of thin-walled structures is modified.Compared with the traditional shear lag theory, a deeper understanding of the mechanical properties of the rectangular box girder is obtained.This research shows that:(1) Due to the introduction of self-equilibrium conditions, the mechanical properties of the box girders can be decomposed into independent elementary beam theory and shear lag theory.Therefore, the mechanical properties of the rectangular box girder are represented by the superposition of two theories. (2) After the section size of the box girder is determined, the shear lag effect on the normal stress remains unchanged, the vertical mechanical behavior of shear lag effect is independent of the span of the box girder. (3) Although the height of rectangular box girder has some influence on the shear warping stress of the box girder and the theoretical stress value of an elementary beam, its shear lag coefficient remains unchanged;so the shear lag effect is independent of the height of the rectangular box girder.(4) The shear lag effect not only affects the mechanical properties of the box girder''s flanges, but also can not be ignored on the mechanical properties of the box girder''s webs.Therefore, the modified method in this paper not only improves the calculation accuracy significantly, but also better reflects the mechanical characteristics of the rectangular box girder.