基于势能驻值原理的薄壁箱梁畸变效应分析

Analysis on distortion effect of thin-walled box girders based on principle of stationary potential energy

在对梯形截面箱梁的畸变角给出一般定义的基础上,提出一种与薄壁箱梁约束扭转分析相似的薄壁箱梁畸变效应分析方法,推导梯形箱梁畸变效应分析的一般公式。应用基于势能驻值原理的能量变分法,建立以所定义的畸变角为未知量的控制微分方程,并给出其初参数解。对1个简支箱梁模型的畸变翘曲应力计算值与相关文献中的有限梁段单元计算值吻合良好,验证分析方法和所推导公式的正确性。研究结果表明:按本文方法揭示的梯形箱梁畸变内力及位移的分布规律与相关文献中的一致,但本文畸变双力矩和畸变矩均大于相关文献中的相应内力,而畸变角和畸变翘曲均小于相关文献中的相应位移。在跨中畸变矩荷载作用下,梯形箱梁腹板与顶板交点处的畸变翘曲应力和横向弯矩绝对值都小于腹板与底板交点处的对应值。

Based on the definition of the distortion angle presented for trapezoidal box girder, a method for analyzing distortion effect of thin-walled box girders was proposed which is similar to that of the restraint torsion analysis of thin-walled box girders. The general formulas for the distortion effect analysis of trapezoidal box girders were derived. The governing differential equation on the distortion angle defined was established by applying the energy variation calculus based on the principle of stationary potential energy and the initial parameter solutions to the equation were achieved. A simply supported box girder model was analyzed and the calculated values of the distortion warping stress are in a good agreement with those in the related literatures obtained by using finite beam segment element, validating the analytical method presented and the formulas derived. The results show that the distribution regularities of the distortion force and displacement of the trapezoidal box girders revealed in this paper are identical to those in the related literatures. However, the distortion bi-moment and moment are greater than those in the related literatures, while the distortion angle and warping displacement are smaller than those in the related literatures. The distortion warping stress and transverse bending moment at the intersection of the web and top slabs of trapezoidal box girder subjected to mid-span distortion moment are smaller in absolute values than those at the intersection of the web and bottom slabs.