Reduced analysis of pin-supported beams under blast loading

An elastic-plastic formulation of simply supported beams with end membrane restraints subjected to uniformly distributed loading is developed. Flexibility and mass are distributed along the beam axis. Instantaneous plastification of the section at midspan due to bending and axial actions is considered. The deflected shape of the beam satisfies the boundary conditions at the supports and midspan. The equations of motion are derived by virtual work. These equations are reduced by relating the variations of the elastic and plastic deformations. The analysis using Lagrange equation of motion is compared with this analysis showing that the standard form of the Lagrange equation is energy dissipative for displacement dependent shape functions. This model is better suited for this analysis than earlier models as it takes into account elastic deformations and their effect on the stretch force and the distribution of inertia forces.