Torsional instability in structures

Abstract

Abstract Torsional instability under harmonic excitation was detected in structures with cubic softening member stiffness. A variational procedure was introduced to perform the analysis for the general problem formulation. Single‐storey structures with zero eccentricity were studied first; previous findings were checked and corrected, and the behaviour was examined in greater detail. Two‐storey structures with large eccentricity were also examined, and further regions of torsional instability were detected. Time history analysis was then employed to quantify the behaviour of various typical structures. An unbounded growth in rotation or column displacement was not observed. Rather, the instability appeared to be related to the jump in response which exists in single degree‐of‐freedom softening oscillators subjected to harmonic excitation. The practical significance of torsional instability is therefore rather weak, although prudent practice would recommend its avoidance.