Dynamic analysis of spatial beam-like lattice girders

Abstract

A structural simplification method that can save computer time and space and achieve reasonable accuracy for solving the dynamic problem of spatial beam-like lattice girders was studied. Incorporated with the simplification method, a lumped-mass model for arriving at better accuracy in natural frequencies was presented. The recovery expressions for determining the nodal displacements and nodal forces of each member of the original spatial lattice girder from the simplified equivalent beam were derived. Numerical results show that the simplification method is suitable for the dynamic analysis of the X-braced, Warren or Pratt spatial (or planar) beam-like lattice girders. For a 20-bay spatial X-braced lattice girder with rigid joints, the simplification method needs computer time less than 0.2% of that required by the conventional finite element method and achieves an average accuracy higher than 95% in natural frequencies. To demonstrate the application of the present method in structural design, the dynamic responses of a 10-bay X-braced lattice girder subjected to 1940 El Centre NS earthquake acceleration were solved and the maximum nodal displacements and forces of each constituent member in the lowermost and topmost bays were determined.