Transverse natural vibration of a beam with an internal joint carrying in-plane flexibilities

Existing research on semirigid jointed frame includes only the rotational flexibility of the joint without consideration of the flexibility in the direction of the transverse shear force. This omission would lead to inaccuracies in the dynamic response of structures, especially in the nonlinear analysis. This paper investigates the dynamic behavior of a bolted joint which has flexibility in both the tangential and rotational directions. The joint is prestressed with axial tension in the bolt shank. It is represented as a virtual connection spring element at the intersection between the beam and the supporting member. The formulation of the hybrid beam-column element including the end springs is presented, and the dynamic behavior of a cantilever beam with this nonlinear semirigid joint is studied. The natural frequencies and mode shapes remain relatively unchanged only for a limited range of the joint stiffnesses, and the eigenpair is influenced by the instantaneous stiffness of the joint defined at a point on the hysteretic loop, particularly when the initial moment stiffness is small.