Theoretical study on dynamic response stability of reinforced concrete structures with a negative skeleton curve gradient under steady-state oscillation

Abstract

The dynamic stability of reinforced concrete structures in regions of reduced restoring force was theoretically investigated according to the ductility and negative gradient in the skeleton curve of their restoring force - displacement relationship, using the frequency response function derived by Caughey (1960). This method derives the frequency response function, which is a relational expression between input and response, for a single-degree-of-freedom system subjected to a harmonic external force in the form of a cosine wave; it also derives two conditions that make the response solution of a nonlinear one-degree-of-freedom system unstable. The results of the investigation showed that the behavioral range in which the structure was stable in the region of reduced restoring force could be determined using the ductility and negative stiffness indicated by the skeleton curve of the restoring force - displacement relationship. Parametric studies varying the ductility and negative stiffness also suggested the possibility that dynamic stability cannot be ensured in the region of reduced restoring force when the ductility is excessive.