Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Abstract

Based on the method of reverberation ray matrix (MRRM), a reverberation matrix for planar framed structures composed of anisotropic Timoshenko (T) beam members containing completely hinged joints is developed for static analysis of such structures. In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method (FEM) results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli (EB) beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.