Constant-Strength Inelastic Displacement Ratio and Orientation for Simple Systems Under Multiaxial Earthquakes

Displacement is crucial in performance-based seismic design and assessment of civil constructions. A simple estimate of the peak displacement demand uses the inelastic displacement ratio. Importantly, relevant research is limited to uniaxial motion, despite seismic action being multiaxial. Herein, a definition and parametric analysis of the constant-strength inelastic displacement ratio under multiaxial earthquakes is presented as a first attempt to characterize this ratio as opposed to the uniaxial ratio. Displacement is examined in terms of the modulus and phase angle in the horizontal plane. Means and standard deviations over 22 far-field records are calculated by time-history simulation with a biaxial hysteresis model, and several structural parameters considered in previous uniaxial analyses are varied. In addition, three parameters specific to multiaxial analysis are varied: the number of earthquake components, the natural period of vertical oscillation, and the degree of strength interaction. The findings show that, of the variables examined, the strength interaction is the most important, while concurrent components are of intermediate importance, and the vertical period is the least important. Notably, the increase in the standard deviation of the displacement ratio is larger than that in its mean. In contrast, the mean of displacement orientation is more affected than its standard deviation, indicating extreme randomness in this variable. In conclusion, the multiaxial approach is recommended. The development necessary for its practical application is outlined.