Pressure–impulse diagram of a beam developing non-linear membrane action under blast loading

•An analytical model to predict the response of a frame beam subjected to blast loading is proposed.•The lateral restraint may significantly reduce the required ductility at the beam level.•The M–N interaction developing in the yielded zone increases the required ductility at the beam level.•The asymptotic solutions provide a good level of accuracy, with a maximum error of 6%.

The p–I diagram of a frame beam subjected to blast loading is established, including the elastic lateral restraint and inertia offered by the rest of the structure, the development of nonlinear membrane action and also, the bending-tension (M−N) interaction that develops in the plastic hinges. The analytical procedures to compute the asymptotes in the p–I diagram as well as a parametric study on the p–I diagram are provided. A dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the required ductility of the beam. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the mechanical properties of the investigated beam (i.e. the ratio of the bending to axial resistance). The last parameter incorporates scales of the geometry and of the deformed configuration at the onset of the plastic mechanism.