Dynamic instability of laterally-restrained zed-purlin beams under uplift loading

Abstract

This paper presents an analytical investigation on the free vibration, static buckling and dynamic instability of laterally-restrained zed-section purlin beams when subjected to uplift wind loading. The analysis is carried out by using the classical principle of minimum potential energy. By assuming the instability modes, the kinetic energy and strain energy of the beam and the loss of the potential energy of the applied load are evaluated, from which the mass, stiffness and geometric stiffness matrices of the system are derived. These matrices are then used to carry out the analyses of free vibration, static buckling and dynamic instability of the beams. Theoretical formulae are derived for the free vibration frequency, critical buckling moment, and excitation frequency of the beam. The effects of the section size of the beam and the static part of the applied load on the change of dynamic instability zone are also discussed.