On the correction of spectra by a displacement reduction factor in direct displacement-based seismic design and assessment

The application of some design and assessment approaches, such as the direct displacement-based design (DDBD) and the capacity spectrum methods, requires the modification of elastic design spectra by some displacement reduction factor, to account for the appropriate energy dissipation capacity of different structures. While several equations to correlate dissipation and hysteresis cycles are available, once the displacement reduction factor has been obtained, the correction of the spectra is operated reducing the displacement demand accordingly and conserving the period of vibration at each point. This procedure is here discussed and proved to be conceptually inappropriate, because the spectral acceleration rather than the period should be kept at each point. The application of this alternative procedure may result in increased shear strength demand in design and in larger required displacement capacity for the same level of strength in assessment, if all other factors are not modified. However, the calibration of the reduction factors applied in DDBD has been extensive, and the method has proved to be effective in predicting displacement demands consistent with those resulting from refined nonlinear time history analysis; therefore, a possible introduction of the proposed correction will require equally extensive studies and possibly compensating corrections in the calculation of the equivalent damping. On the contrary, an appropriate calibration of the factors to be used in the application of the "capacity spectrum" method is still being developed, and the consideration of a constant acceleration may facilitate the derivation of effective equations.