Stiffness Matrix For A Battened Beam Including Shear Effects

Abstract

A battened beam is composed of chords and battens. The model of a structure composed by this type of beams is done, generally, by modeling each batten and chord sectors between battens using beam finite elements, and this implies models with a large number of degrees of freedom. In the previous stages of design or to do simple verifications is convenient to have a simplified analytical solution to assimilate the lattice beam to an equivalent solid beam. To do this we consider a pattern of bars that repeats many times along the beam and using variational techniques it is possible to find an approximated continuous formulation for the displacements of the beam. The shear effects must be taken into account to reproduce adequately the case of very stiff battens where the influence of the shear effect is important. The purpose of this work is to obtain a simplified stiffness matrix for a finite element of a battened beam. These finite elements can be incorporated into a finite element program to obtain approximate solutions in frames. Comparisons are made with the complete finite element solution that show a very good approximation.