BEHAVIOR OF A REINFORCED CONCRETE BEAM UNDER IMPACT LOADING: A SIMPLIFIED APPROACH

摘要

The motion of a reinforced concrete beam or one-way plate during and after dynamic loading is modeled by the classical partial differential equation and by the elastoplastic bilinear bending moment / curvature law for elastic and beyond elastic deformation. A resolution method is proposed by using the finite difference approximation. The progression of the beam deformation vs. time is stabilized by introducing some retroaction according to the implicit scheme. Beam spatial discretization concentrates the kinematics features (displacement, rotation, curvature, velocity and acceleration) and the mechanical properties (loading, bending moment and shear force) in nodes. The method consists of gathering each preceding beam characteristic or property in two vectors whose size is the total number of nodes. These vectors are node velocity and node bending moment. Computation of these vectors is made by iteration from preceding time step by using matrix products. Such a method of resolution can be easily programmed on spreadsheets. Comparison of the computed mid-span displacements with experimental results shows good accuracy and is used to choose the mechanical properties to be introduced for any predicting purpose.