Second-order spread-of-plasticity approach for nonlinear time-history analysis of space semi-rigid steel frames

• Second-order spread-of-plasticity response of 3D semi-rigid steel frames is studied.
• Second-order effects are considered by stability functions, save computational time.
• Geometric, material and connection nonlinearities are taken into account.
• Three major sources of damping of steel frames are considered simultaneously.
• A solution procedure for nonlinear differential equations of motion is developed.

In this paper, a nonlinear inelastic time-history analysis procedure for space semi-rigid steel frames subjected to dynamic loadings is presented. Geometric nonlinearities are taken into account by using stability functions and the geometric stiffness matrix. The spread of plasticity over the cross section and along the member length is captured by monitoring the uniaxial stress–strain relation of each fiber on selected sections. The nonlinear semi-rigid beam-to-column connection is simulated by a multi-spring space element. Three main sources of inelastic hysteretic, nonlinear connecting, and structural viscous damping are considered. The differential equation of motion is solved by the Hilber–Hughes–Taylor method combined with the Newton–Raphson method for the equilibrium iterative procedure. Using only one element per member in the structure modeling, the nonlinear time-history responses which are predicted by the proposed program compare well with those given by commercial finite element packages and other available results. Numerical examples are presented to verify the accuracy and efficiency of the proposed method.