A DYNAMIC-MODEL FOR A TIMOSHENKO BEAM IN AN ELASTIC-PLASTIC STATE

In this paper, equations which describe the propagation of elastic-plastic waves of combined stress resultants in a Timoshenko beam under symmetrical bending and tension or compression are derived. It is assumed that the beam material exhibits a weak work-hardening and strain-rate independent behaviour. The normality rule is postulated for the plastic strain rates of an infinitesimal volume element. The wave propagation is described by a hyperbolic system of differential equations, the state variables of which are the stress resultants and the strain rates of an infinitesimal beam element. It is shown that the actual distribution of shear stress in the plastic range need not be taken into account by means of a plastic shear correction factor.