基于辛普森公式的变截面波形钢腹板组合箱梁弯曲和剪切变形计算

Calculation of Bending and Shear Deformations of Non-Prismatic Corrugated Steel Web Composite Box Girders Based on Simpson Formula

摘要: 为研究变截面波形钢腹板组合箱梁弯曲和剪切变形计算问题，本文基于辛普森积分公式，推导了计算变截面波形钢腹板组合箱梁在集中荷载和自重荷载作用下弯曲和剪切变形的等效惯性矩法。以一实际单箱单室变截面波形钢腹板组合箱梁为算例，考虑施工过程中的最大悬臂80 m时的工况，利用所提方法计算了其受集中荷载和自重荷载作用下的弯曲和剪切变形。为对比分析，通过建立悬臂梁的梁单元模型和实体–壳单元模型，分别计算了悬臂梁在集中荷载和自重荷载作用下的弯曲和剪切变形。与实体–壳单元模型计算的弯曲和剪切变形相比，集中荷载作用下等效惯性矩法计算的弯曲和剪切变形误差分别为1.3%和13.4%，梁单元模型计算结果误差分别为4.6%和34.1%；自重荷载作用下等效惯性矩计算的弯曲和剪切变形误差分别为2.8%和15.8%，梁单元模型计算结果的误差分别为5.5%和29.7%。同时基于顶底板混凝土对剪切变形影响的定量分析表明，由于考虑了顶底板混凝土的抗剪效应，利用等效惯性矩方法计算的剪切变形更接近实体–壳单元模型计算结果。结果表明，提出的变截面波形钢腹板组合箱梁弯曲和剪切变形计算方法结果吻合良好，计算效率较高，适合波形钢腹板组合箱梁在施工过程中的变形分析计算。

Abstract: To study the non-prismatic corrugated steel web composite box girder bending and shear deforma-tions, this paper derived the Simpson formula based equivalent moment of inertia method to calcu-late the bending and shear deformations of non-prismatic corrugated steel web composite box gird-ers subjected to concentrated and distributed loads. A non-prismatic corrugated steel web composite box girder with considering the cantilever length of 80 m, is simulated as an example. The bending and shear deformations of the girder subjected to concentrated and distributed loads are obtained based on the proposed methods. For comparison, the finite element models of the girder established by using beam elements, solid-shell elements are also created to calculate the bending and shear deformations. To compare with the deformations calculated by the solid-shell element model, the errors of the calculated bending and shear deformations under the concentrated load based on the proposed methods are 1.3% and 13.4%, respectively, and the errors of the calculated bending and shear deformations under the concentrated load based on the beam element model are 4.6% and 34.1%, respectively. The bending and shear deformations are also obtained for the box girder under distrusted loads. To compare with the bending and shear deformations calculated by the solid-shell element model, the errors of the bending and shear deformations based on the proposed methods are 2.8% and 15.8%, respectively, and the errors of the bending and shear deformations based on the beam element model are 5.5% and 29.7%, respectively. In this paper, the shear contribution of the top and bottom concreted flanges is also quantitatively studied. Since the proposed method considered the shear effect of the top and bottom flanges, the calculated deformation is more consistent with the result calculated from the solid-shell element model. The results of this paper show that the calculated bending and shear deformations based on the proposed method are in a good agreement with the results obtained from the entity-shell element model, and the proposed method can be applied into the bending and shear deformations calculation of the non-prismatic corrugated steel web composite box girder with relatively high efficiency and resolution.