Innovative displacement-based beam-column element with shear deformation and imperfection

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.