单箱多室波形钢腹板组合箱梁剪力分配的高阶梁单元法

HIGH-ORDER BEAM ELEMENT METHOD FOR SHEAR FORCE DISTRIBUTION IN SINGLE-BOX MULTI-CELL COMPOSITE BOX GIRDERS WITH CORRUGATED STEEL WEBS

  • 摘要: 为研究单箱多室波形钢腹板组合箱梁的剪力分配,提出了一种包含波形钢腹板等效剪切变形自由度的新型高阶箱梁单元(CSW-ESD)。通过引入上、下翼缘板的剪应力分布系数,建立了弯矩作用下混凝土翼缘板剪力与波形钢腹板等效剪应变之间的数学关系,实现了翼缘板与波形钢腹板剪力的有效分离。进一步对比统一了等截面与变截面组合箱梁微元体的内力平衡方程,揭示了变截面效应对剪力分配的影响机理,修正了附加弯矩效应下各组成部分剪力分配的计算表达式,构建了单箱多室波形钢腹板组合箱梁的剪力分配理论模型。在此基础上,基于有限单元理论,以竖向位移、等效剪应变和等效弯曲转角作为节点自由度,建立了可考虑横隔板约束影响的CSW-ESD梁单元,并利用平衡微分方程的齐次通解构造其广义位移模式。结果表明,CSW-ESD梁单元能够准确预测等截面与变截面单箱多室波形钢腹板组合箱梁的剪力分配特征。在等截面组合箱梁中,各组成部分的承剪比例相对稳定,仅在集中荷载和横隔板附近发生急剧变化;而在变截面组合箱梁中,其承剪比例受下翼缘板剪力分量的反向作用以及水平轴力附加弯矩效应的影响,波形钢腹板承担的剪力可能出现明显增大或减小,甚至发生“剪力超分配”现象,传统“剪力主要由波形钢腹板承担”的假设已不再适用。此外,由于单箱多室波形钢腹板组合箱形截面弯曲剪力流非均匀分布,中腹板承担的剪力普遍高于边腹板,因此,建议以CSW-ESD梁单元模型计算得到的中腹板剪力作为设计参考值。

     

    Abstract: To investigate the shear force distribution in composite single-box multi-cell girders with corrugated steel webs (CSWs), a novel high-order beam element (CSW-ESD) incorporating an equivalent shear deformation degree of freedom (DOF) was developed. By introducing shear stress distribution coefficients for top and bottom flanges, a quantitative relationship between the shear forces in concrete flanges and the equivalent shear strains of CSWs under bending was established, enabling effective separation of shear force contributions between concrete flanges and CSWs. Furthermore, the equilibrium equations of the micro-segment for both prismatic and non-prismatic composite box girders were unified. The influence mechanism of non-prismatic effects on shear force distribution was clarified, and the expressions for shear force distribution among different components under additional bending effects were refined, leading to the establishment of a theoretical model for shear force distribution in composite box girders with CSWs. Based on the finite element formulation, a CSW-ESD beam element was developed by adopting vertical displacement, equivalent shear strain, and equivalent bending rotation as nodal DOFs. The influence of diaphragms was incorporated through generalized displacement modes derived from the homogeneous solutions of the governing differential equations. Numerical results demonstrate that the CSW-ESD element can accurately predict the shear force distribution in both prismatic and non-prismatic composite box girders with CSWs. For prismatic girders, the shear force ratios among different components remain relatively stable, except in the vicinity of concentrated loads and diaphragms. In contrast, for non-prismatic girders, the shear force distribution is significantly affected by the reverse shear contribution of the bottom flange and the additional bending moment induced by axial force. This may lead to notable increases or decreases in the shear force carried by CSWs, and even to a “shear force over-distribution” phenomenon, indicating that the conventional assumption that “shear force is mainly resisted by CSWs” is no longer applicable. Moreover, due to the non-uniform distribution of flexural shear flow, the shear force in interior webs is consistently higher than those in the side webs. Therefore, it is recommended that the shear force of interior webs predicted by the CSW-ESD beam element be adopted as a rational and conservative design reference value.

     

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