Nonlinear inelastic time-history analysis of three-dimensional semi-rigid steel frames

• An efficient analysis procedure of 3-D semi-rigid steel frames is developed.
• Plastic hinges and stability functions are employed for modeling nonlinear effects.
• Semi-rigid connections are modeled by nonlinear rotational springs.
• A nonlinear solution procedure for differential equations of motion is proposed.
• Proposed procedure proves to be a reliable tool for daily use in practical design.

This paper presents a simple, effective numerical procedure based on the beam–column method by using the based-displacement finite element method for nonlinear inelastic time-history analysis of three-dimensional semi-rigid steel frames. The nonlinear geometry effects are considered by using stability functions and the geometric stiffness matrix. The inelasticity of material is considered by the gradual yielding of plastic hinges. A space zero-length multi-spring element is proposed to simulate the nonlinear cyclic behavior of steel connections through the independent hardening model. The Hilber–Hughes–Taylor method combined with the Newton–Raphson balance iterative algorithm is adopted to solve the nonlinear equations of motion. The results of nonlinear responses for steel frames with fully rigid and linear semi-rigid connections compare well with those of previous studies and commercial SAP2000 software. Moreover, the results of steel frames with semi-rigid connections shown in this paper can be used to calibrate similar frames in future studies.