Elastic-Plastic Model of Pinned Beams Subjected to Impulsive Loading

An elastic-plastic dynamic analysis of simply supported beams with end membrane restraints subjected to impulsive loading is developed. The beam is elastically curved. The model takes into account elastic and plastic deformations and their effect on the stretch force and the distribution of inertia forces. Instantaneous plastification of the midspan zone due to bending and axial actions is considered. The effect of the length of the plastic zone is discussed. Equations of motion are derived by virtual work. Using the yield condition, the number of these equations is reduced by relating the variations of the displacement variables. This analysis is compared to the standard form of Lagrangeʹs equation of motion showing that the latter is not energy conservative for this case where the deflection shape is nonlinearly dependent on the generalized displacements. Test results using a spring-powered apparatus are presented. Strain rate sensitivity is accounted for as plastic damping. The modelʹs results are compared to test and rigidsegment model results. The comparison shows that the tests are sensitive to the curvature of the axis.