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Torsion element and its applications of box girder based on a new generalized displacement

DOI：10.7511/jslx20220508003

 作者 单位 梁永永 兰州交通大学 土木工程学院, 兰州 730070 张元海 兰州交通大学 土木工程学院, 兰州 730070

为了改进变截面连续箱梁桥的扭转分析理论，将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角，选取自由翘曲转角扭率作为广义位移，提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发，推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数，以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析，结果表明，双力矩影响线与弯矩影响线较为类似，按双力矩影响线进行最不利荷载加载时最大应力值偏小；应力增大系数在集中荷载作用截面出现极值，均发生在腹板与顶板交点处；利用偏载放大系数来考虑扭转附加效应时，不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。

In order to improve the torsion analysis theory of variable-section box girder bridges, the total section rotation is decomposed into free warping rotation and constrained shear rotation.The free warping torsion rate is selected as the generalized displacement, and a torsional beam segment element with 2 nodes and 8 DOFs is proposed.Starting from the constrained differential equation torsion, the stiffness matrix and the equivalent nodal load array of the element are established.A stress increase coefficient is introduced to reflect the increasing effect of constrained torsion on elementary beam stresses.Numerical examples verify the reliability of the beam element in this paper.Finally, a three-span variable cross-section continuous box girder bridge is analyzed.The results show that the bimoment influence line is similar to the bending moment influence line, and the maximum stress is smaller when the most unfavorable load is loaded according to the bimoment influence line.The extreme value of the stress increase coefficient in the concentrated load action section occurs at the intersection of the web and the top plate.When using the offset load amplification coefficient to consider the additional effect of torsion, it is not appropriate to consider the beam section area where the bending normal stress is small and the warping normal stress has an extreme value.