Numerical formulation for advanced non-linear static analysis of semi-rigid planar steel frames

Abstract

This paper presents a displacement-based numerical methodology to analyze the non-linear behavior of semi-rigid multi-story planar steel frames. The formulation uses the plastic hinge principles to simulate the material’s plasticity at the co-rotational finite element nodes. To present a more realistic simulation of the cross-sectional axial and flexural stiffness reduction, the strain compatibility method (SCM) is applied using the material constitutive relationships explicitly. The SCM is also applied to determine the structural elements’ bearing capacity. The residual stress model is addressed and introduced explicitly in the sub-areas of the steel sections generated by a two-dimensional cross-sectional discretization. Geometrical non-linearity is introduced by a simplified approach using the linear terms of the geometrical stiffness matrix. The semi-rigid connections are simulated using rotational zero-length pseudo-springs at the ends of the finite elements, while the connections behavior is given by the moment–rotation relationship. Three models for beam-to-column connections are considered here: exponential, three power parameter and multi-linear. The proposed approach is tested in five planar steel frames with both experimental and numerical analysis available in the literature. The numerical responses obtained here presented befitting stiffness reduction and critical loads. In the tested examples, the simplification in the evaluation of geometrical non-linearity is not harmful to numerical analyses since other effects are dominant.