P-Δ effect on inelastic displacement ratio spectra for inelastic structures

For the evaluation of structures with known ductility demands, the constant-ductility displacement ratio spectra (CDDRS) are particularly useful for providing inelastic displacement ratios to estimate maximum lateral inelastic displacement demands from maximum elastic displacement demands. The CDDRS are computed for single-degree-of-freedom systems (SDOF) by considering or ignoring P-Δ effect for different ductility levels when subjected to 344 earthquake ground motions recorded in four site classes. The modified expressions of CDDRS for P-Δ effect are proposed. It is concluded that the P-Δ effect on CDDRS is significant, and the effect increases with the increase of ductility level. In the long-period region, the CDDRS ignoring P-Δ effect almost conforms to the equal-displacement rule. But in the case of higher ductility level, the CDDRS considering P-Δ effect are much higher than 1.0, which do not conform to the equal-displacement rule.