Dynamic instability of simple structural systems

Lateral strengths required to avoid dynamic instability of single-degree-of-freedom systems are examined. Oscillators with a bilinear hysteretic behavior with negative postyield stiffness are considered. Mean lateral strengths normalized by the lateral strength required to maintain the system elastic are computed for systems with periods ranging from 0.2 to 3.0 s when subjected to 72 earthquake ground motions recorded on firm soil. The effect of the period of vibration and postyield stiffness are investigated. Results indicate that mean normalized lateral strengths required to avoid dynamic instability decrease as negative postyield stiffness increases and that the reductions are much larger for small negative postyield stiffness than for severe negative postyield stiffnesses. It is concluded that there is a significant influence of the period of vibration for short-period systems and for systems with mildly negative postyield stiffnesses. Dispersion of normalized lateral strengths required to avoid dynamic instability are found to increase as the negative postyield stiffness decreases and as the period of vibration increases. Simple equations that capture the effects of period and postyield stiffness to aid in the evaluation of existing structures are obtained through nonliner regression analyses.