为了分析剪切效应对曲线箱梁的影响,基于薄壁箱梁弯曲理论,用一个剪切翘曲参数来综合表达翼板和腹板的剪切变形,运用能量变分法导出考虑剪切效应及约束扭转时曲线箱梁弯扭挠曲控制微分方程组.通过分析边界条件,采用伽辽金数值法求解上述微分方程,从而得出曲线箱梁的弯扭挠曲应力表达式.数值算例结果表明,按本文公式计算出的曲线箱梁弯扭挠曲应力与实测值吻合良好,验证了本文方法的正确性;腹板的剪切变形对箱梁剪切翘曲应力影响较小,可忽略.通过分析曲线箱梁在竖向均布荷载下的整体正应力可知,剪切翘曲应力占比为15%-20%,而扭转翘曲应力相对较小,占比约为6%.
In order to analyze the influence of shear effect on curved box girder,the shear deformation of flange plates and web plates is expressed by using only one shear warping parameter based on the bending theory of thin-walled box girder.By using energy variation principle,the bending-torsion deflection governing differential equations are deduced considering the shear effect and restrained torsion.By analyzing the boundary conditions and using Galerkin method,the differential equations are solved and the stress expression of bending-torsion deflection of curved box girder is obtained.The numerical example results show that the bending-torsion stress of curved box girder calculated from the calculation formula is in good agreement with the measured value,and the shear deformation of web has less influence on shear-warping stress of box girder which can be ignored.By analyzing the component of the whole stress of simply supported box girders under the vertical uniform loading,it shows that the shear-warping stress accounts for 15%-20% of the whole stress,and the torsion-warping stress accounts for about 6%,which is relatively small.