Advanced flexibility-based beam-column element allowing for shear deformation and initial imperfection for direct analysis

In this paper, a new flexibility-based beam-column element allowing the interaction of shear deformation and initial imperfections is proposed. The element is based on Hellinger-Reissner functional with exact force interpolation functions. An extended displacement interpolation based on the curvature and shear strain is adopted to account for shear effects. The member initial imperfection is considered in the derivation of elemental formulation while the distributed plasticity is taken into account by fiber section approach. Three-dimensional inelastic materials are adopted to consider the coupling effect of axial force, bending moments and shear forces. A special element state determination method is adopted to incorporate the proposed element to the conventional finite element programs. The proposed work provides one-element per member model for practical direct analysis with consideration of shear deformation, initial imperfection and material yielding, which is limited in literature. Several numerical examples are demonstrated the accuracy and efficiency of the proposed element in second-order direct analysis of frame structures.