Dynamic Analysis of Inelastic Multi-Degree Systems

A method is developed whereby the dynamic response of statically determinate and indeterminate elastic-plastic beams may be computed with a maximum degree of accuracy and with a minimum of computational difficulty. The development is applied to a mathematical model of the actual beam consisting of a system of concentrated masses connected by massless segments whose stiffnesses are identical to the stiffnesses of the corresponding parts of the original beam. The equations of motion are written in the usual manner, in which the structural resistance to deformation is expressed explicitly in terms of the deflections for any elastic-plastic phase of deformation. These equations of motion are solved by means of a single step forward numerical integration procedure. A method of determining the points of elastic-plastic and plastic-elastic transitions is described that, in conjunction with the numerical integration procedure, is suitable for programming on a high-speed digital computer. Several examples are given to show the versatility of the method, including the response of a continuous beam subjected to a moving load.