Dynamic Response of Softening Structures

Abstract

Computation of the full response of concrete frame structures to severe dynamic loads requires consideration of softening in addition to plasticity and hysteresis. Critical softening parameters and ground frequencies are determined for simple flexural structures. For unidirectional loads, the critical softening parameter depends on the severity of the applied load as represented by the ratio of maximum applied force to maximum resistance (or by energy of impulse to maximum elastic strain energy), on the plastic plateau length (ductility) on any limit to the softening region, and on the duration of load in the case of a rectangular load function. Conversely, for a given softening slope, a critical severity of load, critical plateau length, or critical duration of load may be identified. For the response to reversible loads, a stiffness matrix for flexural elements with finite softening lengths is used in the analysis. The softening of individual hinges is reflected in the overall hysteresis loop of a structure. Elastic‐softening structures perform well in absorbing energy at relatively high frequencies.