Coupled Tilt and Translational Ground Motion Response Spectra

Abstract

Dynamic response of structures subjected to earthquake-induced base excitations are often simplified by ignoring the tilt components of ground motion. However, close to the earthquake source, tilting of the ground surface may become significant. Based on strong-motion records at the Pacoima Dam–upper left abutment obtained during the 1994 Northridge Earthquake, residual tilt reached 3.1° in the N45°E direction while the dynamic tilt remained higher. This study investigates the consequences of neglecting the effects of the tilt component in ground motions on elastic and inelastic spectral ordinates. A complete equation of motion for a single-degree-of-freedom (SDOF) oscillator is developed which includes the effects of tilt (as the secondary P–Δ effect) in addition to inertial force effects due to angular and translation accelerations. The expected values of the largest response peaks are computed for the translational and tilting excitations to investigate the relative contribution of each forcing function. The coupled tilt and translational ground motion response spectrum (CTT spectrum) is generated considering elastic and inelastic response of SDOF oscillator. The CTT spectrum reflects kinematic characteristics of the ground motion that are not identifiable by the translational ground motion response spectrum alone and therefore emerges as a distinct intensity measure of translational ground motion when it is coupled with dynamic tilting of the ground surface on the order of few degrees.