Energy Evaluation for Ramberg–Osgood Hysteretic Model

Response of structures to static and dynamic loads may be assessed in terms of energy. The energy evaluation depends on hysteretic models used to describe inelastic behavior of structures and their elements. One of the hysteretic models often employed in structural analysis is the Ramberg–Osgood model. In the paper a physically motivated model, which leads to the Ramberg–Osgood force–displacement relationship under monotonic loading and exhibits Masing type of behavior for unloading/reloading, is described. Based on the model formulas to calculate recoverable elastic strain energy and irrecoverable hysteretic energy for systems/elements under monotonic loading are derived. It is also shown how recoverable elastic strain energy and irrecoverable hysteretic energy can be evaluated at any point of unloading/reloading curves for a system/element of Masing type. The application of the derived formulas is illustrated by evaluating the energy of a single-degree-of-freedom system subjected to impulse and seismic loading.