A shift approach for the dynamic response of rigid-plastic systems. - Voyagaki, Elia (Earthquake engineering & structural dynamics.)
A shift approach is presented for evaluating and interpreting the response of rigid-perfectly plastic single-degree of freedom systems to dynamic loading. Scaling laws for such systems are, as the term suggests, multiplicative in nature, relating peak dynamic response to products of key problem parameters such as linear spectral coordinates, force reduction coefficient and peak values of the excitation and its time derivatives. Contrary to classical laws, the proposed approach is additive, imposing a shift in the ordinates and the abscissa of the excitation function by means of a set of parameters uniquely related to the yielding resistance of the system. The dynamic response is then obtained by integrating the modified excitation function in a linear-like manner within a particular yielding branch, for the nonlinearity is incorporated into the forcing term. The mathematical validity of the approach is demonstrated analytically and its importance is highlighted for systems with symmetric yielding resistance subjected to near-fault earthquake motions. The modified excitation function may be discontinuous between different yielding brances and relates uniquely to the development of plastic deformation. It is thereby referred to as Plastic Input Motion (PIM). It is shown that the ordinates and the duration of this function may be significantly (yet not necessarily) smaller than those of the original ground motion depending on yield strength. The relationship of the proposed approach to the existing methods and parameters of earthquake engineering such as Newmark's sliding block and relative ground acceleration, is discussed.