Analytical Model of Nonlinear Semi-rigid Frames Using Finite Element Method

Performance-based design for a constructional steel frame in nonlinear-plastic region requires an improvement in order to achieve a reliable structural analysis. The need to explicitly consider the nonlinear behaviour of structures makes the numerical modelling approach much more favourable than expensive and potentially dangerous experimental work. The parameters considered in the analysis are not limited to the linear change of geometry and material yielding, but also include the effect of large deformations, geometrical imperfections, load eccentricities, residual stresses, strain-unloading, and the nonlinear boundary conditions. Such analysis requires the use of accurate mathematical modelling and effective numerical procedures for solving equations of equilibrium. With that in mind, this paper presents the mathematical formulations and finite element procedures of nonlinear inelastic steel frame analysis with quasi-static semi-rigid connections. It is an approach that enables the structural behaviour of constructional steel frames to be traced throughout the entire range of loading until failure. It also provides information on the derivation of the structural analysis by using finite element method. Verification of the developed analytical procedures is conducted with theoretical pin-ended perfect and imperfect columns. A good agreement is achieved between theoretical and developed analytical models. Furthermore, validation of the analytical model with load and unloading behaviour of the material properties for a semi-rigid steel frame was also conducted