变截面波形腹板组合梁悬臂施工约束扭转分析

Analysis on restrained torsion of composite girder with corrugated steel webs during cantilever construction

为明确变截面波形腹板组合梁在悬臂施工状态偏载作用下的抗扭性能,将波形腹板组合梁等效为混凝土箱梁,通过乌式第二理论推导竖向偏载作用下的约束扭转微分方程,采用有限差分法建立方程组并引入悬臂边界条件求解变截面波形腹板悬臂梁的约束扭转翘曲正应力和剪应力;通过实际工程算例,建立有限元模型研究不同施工工法、横隔板浇筑顺序等对扭转效应的影响,并将有限元分析结果与理论解对比,验证计算公式的适用性。结果表明:基于乌式定理并考虑波形腹板褶皱效应的计算理论可以有效评估变截面悬臂梁的扭转效应;偏载作用下约束扭转产生的应力不可忽略,底板翘曲正应力占弯曲正应力比例可达26%、顶板为18%,腹板的扭转剪应力占弯曲剪应力约22%;采用不同悬臂施工方法的结构抗扭性能具有明显差异,异步浇筑法的自由端节段扭转翘曲应力较大且变化显著,应当避免该工法下悬臂自由端的集中偏载作用;横隔板的浇筑可使翘曲程度沿桥梁固定端至自由端相当范围内趋于均匀分布,宜及时浇筑已施工节段对应的横隔板。

In order to understand restrained torsion of composite girder with Corrugated Steel Webs(CSWs)during cantilever construction,the composite girder with CSWs is converted to the PC box girder.Based on the second theory of the restrained torsion of box girder,the differential equations under eccentric load are derived,the finite-difference method is used to establish a system of equations,and the restrained torsion induced warping positive stress and shear stress are solved by substituting the cantilever boundary conditions.Based on a case study of an actual project,FEM are established to investigate the effects of different construction methods and the pouring sequence of diaphragms on the torsion behavior,also the FEM analytical results are compared with theoretical values to verify the applicability of the calculation equations.The results indicate that the calculation theory considering CSWs’accordion effect can effectively evaluate the torsional behavior of composite girder with variable cross-section.The stress caused by the restrained torsion under eccentric load cannot be negligible.The proportion of warping stress at the bottom slab to the bending stress can reach 26%,while the ratio at top slab is 18%,and the torsion induced shear stress at the CSWs accounts for about 22%of the bending induced shear stress.The torsional resistance of the structure using different cantilever construction methods has obvious differences.The torsional warping stress at the cantilever end segment is large and varies significantly when using asynchronous-pouring-construction method,thus,the eccentric loading should be avoided.The diaphragm can make the warping evenly distributed along the fixed to the cantilever end;therefore,it is better to timely pour the diaphragm for the constructed segments.