TABLE OF CONTENTS The basic relations required for any calculation for a member is the stress-strain properties of the material. In the elastic range, this presents no difficulties. The relationship is assumed to be linear governed by Hooke's law and analytical solution for a member subjected to loads may be obtained in most cases. As long as the stress-strain relation for the material remains linear, a single theory, based on either the strength of materials approach or the theory of elasticity approach, is valid for a given member made of any material, concrete or metal. Once in the plastic range, there are problems because the stress-strain relationship in this range is not linear but varies according to the current state of stress and the strain history which the material has experienced before. Further, the nonlinear stress-strain relationship is not unique but differs for every material. For these reasons, an idealization of stress-strain relationship in the plastic range is inevitable in order to develop a reasonably simple plastic theory. A different plastic theory results from each different shape of stress-strain diagram, based on either the strength of materials approach or the theory of plasticity.
Initial yield state at which the material loses its elastic characteristic for the first time must be known first. This defines the initial yield function which gives the limit of elasticity of the material. Further, the rule of stress-strain relationship in plastic loading and unloading states or in reloading state must also be prescribed for the plastic analysis...
