Analysis of Elastic-Plastic Grid Systems

An incremental load method for analyzing the piecewise linear behavior of elastic-plastic grid systems with various support conditions is presented. The assumption is made that the torsional rigidity of the members is negligible. The equilibrium and compatibility equations are written in terms of bending moments, plastic hinge rotations, load parameters and an elastic-plastic transition function. The use of this transition function allows the formulation to be applicable to every regime as well as facilitates the treatment of the reversal of plastic hinge rotations. A technique of linear scaling is employed to determine the points of transition including the state of incipient plastic collapse. The collapse mechanism is verified by means of the solution of a system of hinge rotation equations. The analysis provides the complete load-deflection history of the grid systems from the elastic regime, through all the intermediate regimes, up to and including the collapse regime. Numerical examples are given to illustrate the method of analysis.