Vibrations of rotationally restrained Timoshenko beam at hinged supports during an earthquake

Abstract

Abstract The present paper describes an analytic solution procedure for flexural vibration of a rotationally restrained hinged-hinged Timoshenko beam at the supports during an earthquake. Focusing on maximal magnitudes of internal loads such as bending moment and shearing force under wide variations of two parameters, k L / E I and κ G A L 2 / E I , various beams under synchronous and asynchronous support motions are simulated. The simulations under asynchronous support motions show the following facts. The variations of the maximal magnitudes of internal loads of stocky beams due to the variation of k L / E I from zero to infinity show much wider variations than those of slender beams as κ G A L 2 / E I decrease s . The maximal magnitudes of internal loads of a beam tend to be governed by their static components as k L / E I increases and κ G A L 2 / E I decreases. When the internal loads are governed by their static components, maximal magnitudes of internal loads of the stocky tend to increase monotonically as the value of k L / E I increases. However, the simulations under synchronous support motions show the static components of the internal loads vanish and the internal loads are governed by dynamic components irrespective of the two parameters.