Problem 27

Abstract

Consider the simple beam structure shown in Figure 27.1. The properties of the beam are as follows: E=3x10⁶ psi, v =.3333, and p (mass per unit of volume) = 7x10^-4 llb-s² /in⁴. The beam is excited by a base acceleration f(t) in the y-direction given in units of in/s² by

$$ {\rm{f(t) = - }}{e^{{\rm{ - t}}}}\cos (2\pi {\rm{t}}) $$

((27.1))

Determine the forces in the structure and the displacement at the top (relative to the base) produced by this excitation. This is a typical baseexcitation problem, also called an enforced acceleration problem. This class of problems is of considerable interest in earthquake engineering.