Consistent matrices for steel framed structures with semi-rigid connections accounting for shear deformation and rotary inertia effects

Estimation of vibration characteristics and thus the seismic loads acted on steel framed structures are influenced by the presence of semi-rigid connections and accurate modeling of shear deformations and rotary inertia effects. This paper presents a finite element model that takes into account all these effects in order to calculate consistent stiffness and mass matrices. The formulation of the element utilizes three-fields Hu-Washizu-Barr principle, where the need for displacement shape function approximation is eliminated through the use of force-based approach. The proposed model does not require extra discretization to capture localized connection response. An accurate shear correction coefficient for I-shaped steel sections is implemented to represent shear deformation and rotary inertia along steel beams and columns. Numerical examples on single member, portal frame and multi-story steel framed structures verify the accuracy and robustness of the proposed element with and without semi-rigid connections.