Distributed plasticity approach for time-history analysis of steel frames including nonlinear connections

• Second-order spread-of-plasticity response of plane steel frames is performed.
• Deriving a nonlinear beam-column stiffness matrix with connection flexibility.
• Geometric, material and connection nonlinearities are simultaneously considered.
• Three major sources of damping of steel frames are considered at the same time.
• A nonlinear solution procedure for differential equations of motion is proposed.

This paper presents a displacement-based finite element procedure for second-order spread-of-plasticity analysis of plane steel frames with nonlinear beam-to-column connections under dynamic and seismic loadings. A partially strain-hardening elastic–plastic beam-column element, which directly takes into account geometric nonlinearity, gradual yielding of material, and flexibility of nonlinear connections, is proposed. Three major sources of damping are considered at the same time. They are structural viscous damping, hysteretic damping due to inelastic material, and hysteretic damping due to nonlinear connections. A nonlinear solution procedure based on the combination of the Hilber–Hughes–Taylor method and the well-known Newton–Raphson equilibrium iterative algorithm is proposed for solving differential equations of motion. The dynamic behavior predicted by the proposed program compares well with those given by the commercial finite element software ABAQUS and previous studies. Coupling effects of three primary sources of nonlinearity, the bowing effect, geometric imperfections, and residual stress are investigated and discussed in this paper.