Capacity-based inelastic displacement spectra for reinforced concrete bridge columns

Capacity-based inelastic displacement spectra that comprise an inelastic displacement ratio (C-R) spectrum and the corresponding damage index (DI) spectrum are proposed in this study to aid seismic design and evaluation of reinforced concrete (RC) bridges. Nonlinear time history analyses of single-degree-of-freedom (SDOF) systems are conducted using a versatile smooth hysteretic model when subjected to far-field and near-fault ground motions. It is demonstrated that the Park and Ang damage index can be a good indicator for assessing the actual visible damage condition of columns regardless of its loading history, providing a better insight into the seismic performance of bridges. The computed spectra for near-fault (NF) ground motions show that as the magnitude of pulse period ranges increases from NF1 (0.5-2.5 seconds) to NF2 (2.5-5.5 seconds), the spectral ordinates of the C-R and DI spectra increase moderately. In contrast, the computed spectra do not show much difference between NF2 and NF3 (5.5-10.5 seconds) when the period of vibration T-n <= 1.5 seconds, after which the spectral ordinates of NF3 tend to increase obviously, whereas those of NF2 decrease with increasing T-n. Moreover, when relative strength ratio R = 5.0, nearly all of the practical design scenarios could not survive NF3. On the basis of the computed spectra, C-R and DI formulae are presented as a function of T-n, R, and various design parameters for far-field and near-fault ground motions. Finally, an application of the proposed spectra to the performance-based seismic design of RC bridges is presented using DI as the performance objective.