A unified linear bending/shear beam (spar) theory: From deterministic da Vinci–Euler–Bernoulli elastic beams

Abstract

A unified bending/shear beam (spar) theory has been formulated by merging a number of previously completed theoretical segments into a comprehensive analytical treatment of linear non-homogenous viscoelastic Timoshenko beams (spars) with stochastic properties and random dynamic loads including shear center and neutral axis spatial and temporal motions due to bending, and including realistic physical starting load transients.  These inverse problem analyses are framed entirely in terms of relaxation moduli or creep compliances, excluding any dependence on Poisson's ratios. The deterministic and stochastic effects of unequal tension and compression relaxation moduli/compliances on normal and shear bending stresses are derived and evaluated. The influences of all these phenomena on combined bending and shear stress distributions, structural instabilities, material failures and structural survival times also are formulated and discussed.