The explicit expression of internal forces in prismatic membered structures

Analytic expressions for member forces in linear elastic redundant trusses have recently been given by the author. It was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures that can be derived from the original structure. It was shown that coefficients of the polynomials can be computed through the equilibrium equations and by enforcing global compatibility of deformations. This paper generalizes these results to the case of linear elastic structures, composed of uniform prismatic elements that have extensional, flexural, and toisional stiffness.