Inelastic second-order analysis of steel columns under minor-axis bending

Abstract The inelastic second-order behavior of steel structural columns under minor-axis bending is presented in this article. To study this behavior, a nonlinear frame element formulation is adopted in which the steel's plasticity process is accompanied at the nodal points of each finite element through the refined plastic-hinge method (RPHM). A tangent modulus approach is employed in order to consider the stiffness degradation in function of the internal forces' variation, and the second-order effects, residual stresses and geometric imperfections are considered in the modeling of column behavior. As a criterium for defining the ultimate limit state of the column cross-section, strength surfaces are adopted. These surfaces describe the interaction between the axial force and bending moment (N-M interaction diagrams). To solve the nonlinear equilibrium equation for the structural system, the Newton-Raphson method is used, coupled with continuation strategies. Columns with different slenderness, boundary and loading conditions are analyzed, and the results obtained are comparable to those found by other researchers. The results lead to the conclusion that the numerical approach adopted in this study can be used for a better behavioral understanding of the steel column under weak-axis bending.摘要 本文阐述了钢结构柱在弱轴弯曲（minor-axis bending）下的非弹性二阶力学行为。为研究该力学特性，本文采用非线性框架单元理论公式，其中通过精细化塑性铰法（refined plastic-hinge method, RPHM）在各有限元的节点处模拟钢材的塑性发展过程。为考虑内力变化引发的刚度退化，本文采用切线模量法（tangent modulus approach）；同时在柱行为建模过程中，纳入了二阶效应、残余应力与几何初始缺陷。作为确定柱截面极限状态（ultimate limit state）的判据，本文采用强度曲面（strength surfaces），此类曲面可描述轴力与弯矩间的交互作用关系，即轴力-弯矩交互作用图（N-M interaction diagrams）。为求解结构系统的非线性平衡方程，本文采用结合延续策略（continuation strategies）的牛顿-拉夫逊法（Newton-Raphson method）。本文对不同长细比、边界条件与荷载工况的钢柱开展了分析，所得结果与其他研究者的成果具有良好一致性。研究结果表明，本文所采用的数值方法可用于更深入地理解钢结构柱在弱轴弯曲下的力学行为。