高强钢焊接箱形柱力学性能研究(Ⅱ)：二阶非弹性分析

高强钢的焊接残余应力分布和普通钢材的有较大差异，现有的切线模量和刚度退化函数不适合用于高强钢焊接箱形截面的二阶非弹性分析。而精炼塑性铰模型通过切线模量和刚度退化函数可合理考虑残余应力的影响和塑性渐进发展，达到与塑性区模型相近的精度。基于此，提出适合高强钢焊接箱形截面的二阶非弹性分析方法。通过稳定函数考虑单元二阶效应，基于杆端部转动引起的构件弯曲及其导致的轴向应变，考虑弯曲效应。在精炼塑性铰模型中，采用高强钢焊接箱形截面的残余应力统一分布模型，通过截面分析法构建不同强度等级的焊接箱形截面切线模量计算公式。同时，分析轴力和弯矩共同作用下的渐进屈服对箱形截面刚度退化的影响，从而建立可模拟截面塑性发展的刚度退化函数。结合塑性铰的产生与发展对平衡微分方程解的影响，建立梁柱单元的弹塑性刚度矩阵。结果表明，所提出的二阶非弹性分析方法可准确分析高强钢焊接箱形截面轴压构件的力学性能，可应用于高强钢框架结构设计，为二阶非弹性分析方法的工程应用提供参考。

Research on mechanical properties of high strength steel welded box columns (Ⅱ): second-order inelastic analysis

The residual stress distribution of high-strength steel is quite different from that of ordinary steel. The existing tangent modulus and stiffness degradation function are not suitable for the second-order inelastic analysis of welded high-strength steel box sections. While the refined plastic hinge model can reasonably consider the residual stress and the gradual development of plasticity through the tangent modulus and stiffness degradation function, and thus achieve similar accuracy to the plastic zone model. Therefore, a second-order inelastic analysis method suitable for welded high-strength steel box sections was proposed. The second-order effect of the element was considered through the stability function, and the bending effect was obtained based on the bending of the member caused by the rotation of the rod end and the resulting axial strain. In the refined plastic hinge model, the uniform distribution model of residual stress of welded high-strength steel box sections was adopted, and the calculation formulas for the tangent modulus of the welded box sections of different strength grades were constructed through the section analysis method. At the same time, the common axial force and bending were analyzed. By considering the effect of gradual yielding on the stiffness degradation of the box section, a stiffness degradation function that could simulate the plastic development of the section was established. Then, combined with the influence of the initiation and development of plastic hinges on the solution of the equilibrium differential equation, the elastic-plastic stiffness matrix of the beam-column element was established. It indicates that the second-order inelastic analysis method proposed in this study can estimate the mechanical properties of high-strength steel box sections and be employed into design of high-strength steel frame structures, providing a reference for the engineering application of the second-order inelastic analysis method.