Influence of diaphragm stiffness on distortional behavior of composite box girder with corrugated steel webs
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摘要:
为研究横隔板刚度和横隔板数量对波形钢腹板组合箱梁畸变效应的影响，提出了一种可同时考虑横隔板刚度和剪切变形影响的畸变梁单元(B2D-CSW)；基于广义坐标法，建立了波形钢腹板组合箱形截面畸变翘曲位移表达式，修正了畸变剪力对畸变剪切变形的影响，理论推导了畸变剪力与畸变双力矩的物理关系；利用横隔板与箱形截面之间的位移协调条件，建立了不同类型横隔板的变形表达式及其与畸变角的几何关系，揭示了其抵抗畸变变形的工作机理；基于能量变分法，推导了考虑畸变剪切变形影响的波形钢腹板组合箱梁控制微分方程，选用齐次解构造了广义位移的插值函数；结合有限单元法，开发了考虑畸变剪切变形影响的两节点四自由度畸变梁单元，并推导了考虑横隔板刚度影响的单元的刚度矩阵和等效结点荷载向量；通过算例分析，验证了B2D-CSW梁单元的计算精度与广泛适用性。研究结果表明：与实体有限元模型相比，B2D-CSW梁单元模型仅需少量单元即可准确预测不同横隔板刚度和数量条件下波形钢腹板组合箱梁的畸变响应，显著提升了建模与计算效率；分析表明，横隔板的抗畸变刚度对波形钢腹板组合箱梁的畸变变形具有显著的弹性约束作用，随着横隔板刚度或数量达到临界阈值，其对主梁畸变变形的抑制作用趋于稳定。提出的B2D-CSW梁单元为波形钢腹板PC组合连续箱梁桥横隔板的设计与分析提供了可靠的计算方法。
Abstract:To investigate the influence of diaphragm stiffness and number on the distortional behavior of composite box girders with corrugated steel webs (CSWs), a distortional beam element (B2D-CSW) that incorporates both diaphragm stiffness and shear deformation effects was developed. Based on the generalized coordinate method, expressions for distortional warping displacement in composite box sections with CSWs were formulated, incorporating the influence of distortional shear force on shear deformation. The physical relationship between distortional shear force and distortional bimoment was derived theoretically. By enforcing displacement compatibility between diaphragms and the composite box section, deformation expressions for different diaphragm types and their geometric relationships with the distortion angle were established, thus revealing their mechanism for resisting distortional deformation. Using the energy variational method, governing differential equations for composite box girders with CSWs that account for distortional shear deformation were derived, and interpolation functions for generalized displacements were constructed based on homogeneous solutions. Based on the finite element method, a two-node, four-degree-of-freedom distortional beam element considering distortional shear deformation was developed, and the stiffness matrix and equivalent nodal load vector considering diaphragm stiffness were derived. Through numerical examples, the computational accuracy and wide applicability of the proposed B2D-CSW beam element were verified. The results indicate that, compared with solid finite element models, the B2D-CSW beam element can accurately predict the distortional response of composite box girders with CSWs under varying diaphragm stiffness and number of diaphragms, using only a small number of elements and thus significantly improving modeling and computational efficiency. The analysis shows that the anti-distortional stiffness of diaphragms provides significant elastic restraint on the distortional deformation of composite box girders with CSWs. As the diaphragm stiffness or number reaches a critical threshold, the restraining effect on the distortional deformation of the main girder tends to stabilize. The proposed B2D-CSW beam element provides a reliable computational method for the design and analysis of diaphragms in continuous prestressed concrete (PC) composite box girder bridges with CSWs.
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图 4 波形钢腹板组合箱形截面荷载分解示意
Figure 4. Schematic of load decomposition for composite box section with CSWs
图 10 简支波形钢腹板组合箱梁(单位：cm)
Figure 10. Simply supported composite box girder with CSWs (unit: cm)
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图 11 简支波形钢腹板组合箱梁的有限元模型
Figure 11. Finite element model of simply supported box girder with CSWs
图 14 横隔板刚度对波形钢腹板组合箱梁畸变翘曲应力的影响
Figure 14. Influence of diaphragm stiffness on distortional warping stress in composite box girders with CSWs
图 16 横隔板数量对波形钢腹板组合箱梁畸变翘曲应力的影响
Figure 16. Influence of diaphragm quantity on distortional warping stress in composite box girders with CSWs
图 17 某变截面波形钢腹板PC组合连续箱梁桥(单位：m)
Figure 17. Non-prismatic PC continuous composite box girder bridge with CSWs (unit: m)
表 1 横隔板刚度对跨中截面畸变翘曲应力的影响
Table 1. Influence of diaphragm stiffness on distortional warping stress at mid-span section
MPa 测点 不同横隔板厚度(mm)的翘曲应力 0 1 2 5 8 14 20 B 1.01 0.84 0.77 0.69 0.66 0.64 0.63 D 0.22 0.18 0.17 0.15 0.14 0.14 0.14 
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表 2 横隔板数量对跨中截面畸变翘曲应力的影响
Table 2. Influence of diaphragm quantity on distortional warping stress at mid-span section
MPa 测点 不同横隔板数量的翘曲应力 0 1 2 4 B 1.01 0.61 0.53 0.51 D 0.22 0.13 0.12 0.11
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