A simplified model for inelastic second order analysis of planar frames

A simplified model for predicting second order inelastic behavior of steel frames is developed. New empirical formulae are developed to describe the tangent stiffness of steel sections subjected to an axial compression force and bending moment. The tangent stiffness formula is extended to evaluate the secant stiffness that is used for the internal force recovery. The formulae are derived for steel sections considering the residual stresses as recommended by the European Convention for Construction Steelwork (ECCS). The tangent stiffness for steel sections is also evaluated for the case where residual stresses are neglected. A finite element program is prepared to predict the inelastic second order behavior of plane steel frames using the derived formulae for the steel cross sections. The updated Lagrange coordinates are used to include the second order effect. The Newton–Raphson scheme combined with the minimum residual displacement method is employed to satisfy the equilibrium between external and internal forces. Comparisons with fiber model indicate good agreement with the present model. The analysis results indicate that the new model is accurate and has a faster rate of convergence for problems involving inelastic behavior.