Direct plastic analysis of steel structures by flexibility-based element with initial imperfection

Second-order direct analysis has been used in some regions for reliable analysis and design of steel structures. Currently, the stiffness-based element is widely used with accuracy improved by enforcing equilibrium along mid-span or “stations” along the member length in order to achieve equilibrium which is not guaranteed along an element. In this paper, a flexibility-based beam-column element considering member imperfection based on Hellinger-Reissner functional is developed and used for practical second-order direct analysis. This new element is a flexibility-based element with member initial bowing at the element level for direct analysis of three-dimensional frame analysis whereas previous flexibility-based elements assumed perfectly straight geometry for the element. The fiber plastic hinge approach is adopted to account for the distributed plasticity of a section. The new flexibility-based element performs excellently for modeling of members under high stress with material yielded as the conventional stiffness-based element has less accuracy when few elements are used in modeling a plastic member. This will significantly enhance accuracy and computational efficiency for direct plastic analysis which can then be more widely used in practical design. Several examples are employed to validate the accuracy and efficiency of the proposed element along this line of thought.