Dynamic Motion of RC Beams and One-Way Slabs Impacted by a Missile at Medium Velocity: Models for Spreadsheet Application

This paper deals with the simulation of the motion of a one-span slender rectilinear RC beam or a thin one-way RC rectangular slab when impacted by a missile, within and beyond the elastic domain, up to a maximal displacement equal to the height of the section. The loading is variable in time and in space and the supporting conditions at each extremity are either of simply resting type or of clamping type. The equation of motion for each beam segment is expressed, through finite differences method, by relations between velocity and flexural moment that are decomposed on the basis of the first N modes of beam deformation. The plastic deformations are taken into account by constraining the flexural moment to follow elastic/perfectly plastic flexural moment–curvature law. The algorithms are well adapted to a spreadsheet application that allows easily: i) presizing such a structure against this type of loading, ii) the sensitivity studies regarding the mechanical parameters, iii) checking the order of magnitude of the results of big FEM models by using highly sophisticated codes. Simulations by this method show good agreement with experimental results and give access to some mechanical properties of the structure when damaged.