Vibration of x-braced portal frames

Abstract Both free and forced vibrations of elastic X-braced portal frames are investigated. Solutions of the Euler-Bernoulli equation for the transverse vibration coupled with the axial vibration are used. The first five natural frequencies, with the angle of inclination, α, of the bracing bars ranging from 15° to 75°, with different slenderness ratios, R, of the columns, and different stiffness of the floor beam and crossing bars, are presented along with two sets of the natural modes of the frames with α = 45°. For the forced vibration, the dynamic responses of the frames with a concentrated horizontal time dependent force acting at a top joint are studied. The responses of the frames with α = 45° are analyzed in detail.