Analysis of second-order shear-deformable beams with semi-rigid connections

In this paper a new beam finite element is proposed for the solution of framed structures with semi-rigid connections. The element uses the second order Timoshenko's beam model. Power series expansion of kinematic relations is employed to improve solution stability. Effect of flexible and eccentric connections is considered by means of rotational and linear springs plus rigid end-offset. The proposed approach has the same computational cost of a standard beam element since additional degrees of freedom are condensed out. The resulting element stiffness matrix expression is given as the summation of the second order Timohenko's beam stiffness matrix and corrective matrices. The proposed element is readily implementable in existing finite element codes. Some benchmark problems are used to test the efficiency of the proposed procedure.