Nonlinear analysis of damped semi-rigid frames considering moment–shear interaction of connections

• This paper presents a solution method for nonlinear vibration analysis of damped semi-rigid frames.
• A novel method is proposed to consider connection moment–rotation and shear interaction.
• A parametric study is performed to examine the effects of connection damper and mechanical response on semi-rigid frame dynamic response.

Nonlinear vibration analysis of semi-rigid frames, considering moment and shear interaction (MVI) for the joint, is performed in this article. The numerical model of the semi-rigid frames is created using the nonlinear finite element (FE) formulation. In the numerical model, the beams and the columns are formulated based on the Euler–Bernoulli beam theory and the Partially Restrained (PR) connections are simulated as a discrete rotational springs and a parallel rotational damper. The previously formulated three-parameter model is modified and the nonlinear moment–rotation relation of the connection is tied to its shear force to assess the interaction effects of the moment and shear of the connections. An analysis algorithm is proposed to solve the eigenvalue problem of the semi-rigid frames subjected to pre-loading conditions, taking into account the MVI effects. The method is verified through comparison with analytical examples.