考虑Resal效应影响的变截面波形钢腹板PC组合梁桥的力学性能研究

The mechanical properties of non-prismatic box girders with corrugated steel webs (CSWs) are quite different from prismatic members because of Resal effect. This project is mostly concentrated on the shear behavior, restrained torsion and distortion effect and non-linear shear buckling of the large-span non-prismatic prestressed concrete (PC) box girders with CSWs. First of all, shearing stress formula of a large-span non-prismatic PC box girder with CSWs is put forward by considering the effect of variable cross section and prestressing force, and the distribution of shearing stress and shear transmission mechanism in composite cross-section can be investigated using the proposed formula. Then warping stresses arisen by constrained torsion and distortion in a non-prismatic box girder with CSWs under eccentric loads is derived from energy variation principle, and these formulas are programmed by Visual C++ to improve the efficiency of design. In addition, a fine three dimensional finite element model is established to investigate the influence of concrete cracking on stress distribution and predict the buckling modes, buckling location and bucking loads when the structure undergo non-linear shear buckling. On this basis, two types of test beams, namely two non-prismatic restrained scale test beams and a non-prismatic double cantilever scale test beam, are carried out to verify the correctness of the above theoretical formulas and calculation programs. The goal for this research is to provide theoretical references for the design of shear buckling and arrangement of encased concrete in a long-span non-prismatic PC box girders with CSWs.

由于Resal效应的影响，变截面波形钢腹板PC组合梁的力学性能与等截面情形差异显著。本课题结合变截面波形钢腹板PC组合梁的结构特点，紧紧围绕其受剪性能、约束扭转和畸变效应及非线性剪切屈曲等问题展开理论与试验研究。首先，推导考虑Resal效应和预应力作用的变截面PC组合梁剪应力解析计算公式，揭示截面剪应力的分布规律和剪力传递机理。其次，提出组合截面约束扭转及畸变应力的计算方法并基于Visual C++编程平台研发求解扭转及畸变应力的分析程序。最后，构建精细化有限元分析模型揭示混凝土开裂对组合截面应力重分布的影响，以期准确预测结构发生非线性剪切屈曲时的几何模态、破坏位置及临界载荷。在此基础上，开展变截面约束梁缩尺模型试验和变截面双悬臂梁缩尺模型试验以验证上述理论公式及分析程序的正确性。本项目的研究成果将为大跨径变截面波形钢腹板PC组合梁桥的抗剪设计和内衬混凝土的合理设置提供理论参考依据。

课题研究首次发现了变截面波形钢腹板PC组合梁中存在Resal效应，这是导致等截面和变截面波形钢腹板组合梁受剪性能差异的主要因素。既有国内外设计规范中基于等截面梁提出的计算假定不可直接应用于变截面梁情形，因此需对变截面波形钢腹板PC组合梁的基本受力性能进行研究。课题基于弹性微元体平衡条件和剪应力互等定理，利用铁木辛柯高等材料力学理论推导了弯矩-剪力-轴力共同作用下任意变截面波形钢腹板组合梁剪应力解析计算公式，并基于数学积分严格证明了弯矩和轴力产生的附加剪应力为自平衡应力。根据乌氏第二理论，利用差分法推导了变截面波形钢腹板组合箱梁约束扭转变系数微分方程，得到约束扭转正应力和剪应力计算公式。根据箱梁理论，忽略波形钢腹板平面内纵向刚度，利用等代梁法分析变截面波形钢腹板组合箱梁的畸变效应，并采用集中框架刚度原理结合力法实现等代梁变系数挠曲微分方程的求解。并基于ABAQUS非线性分析程序，对变截面波形钢腹板PC组合梁剪切屈曲破坏全过程进行仿真模拟，仿真计算破坏形态和破坏荷载与试验结果相近，发现由于Resal效应的存在变截面波形钢腹板组合梁最不利受剪截面位置并非在支座截面处，且混凝土翼缘板的损伤破坏对结构承载力有较大的影响。