Abstract
Manuscript Reference: Rakesh K. Goel, Earthquake Spectra, vol. 27, no. 3 (August 2011): 939–946.
This writer would like to congratulate the author for his study on estimation of base shears of buildings, a topic of recognized importance in seismic assessment of buildings, and for recalling the attention of the scientific and engineering community to the pertinent effect that damping forces have on the results of nonlinear structural analysis.
The paper focuses on the comparison between base shears computed from floor accelerations (inertial) and column shears (structural), which have been found in disagreement, according to observations from buildings strongly shaken during past earthquakes. Such discrepancy between inertial and structural base shear is attributed by the author to (i) the error in interpolation when obtaining accelerations at non-instrumented floors, (ii) the error associated to modeling and analytical assumptions when estimating peak structural base shear capacity from pushover analysis, and (iii) the contribution of damping forces.
Results from an analytical comparative study carried out by the author, comprising two buildings and 30 recorded ground motions, showed that median inertial base shear exceeded structural base shear by 10% to 20%, a percentage that became significantly higher when considering particular individual earthquake ground motions. The author isolated equivalent viscous damping as the only possible source of differences in such base shear estimates; as such, this writer feels that readers could benefit from a clarification on the equivalent viscous damping assumptions that have been made in the nonlinear dynamic analyses carried out by the author.
The use of equivalent viscous damping in nonlinear dynamic analysis, in particular mass-and stiffness-proportional Rayleigh damping (suggested, e.g., in Clough and Penzien 1993 or Chopra 1995), has been recently shown to have the potential of introducing unrealistically large damping forces. Some authors (e.g., Wilson 2011) strongly suggest for such equivalent modeling to be avoided altogether, whereas others (Hall 2006, Priestley and Grant 2005) believe that the mass-proportional damping component should not be used, since, as discussed by Pegon (1996), Wilson (2011), Abbasi et al. (2004), and Hall (2006), among others, if a given structure is “insensitive” to rigid body motion, mass-proportional damping will generate spurious (i.e., unrealistic) energy dissipation.
The stiffness-proportional damping modeling approach may then be further subdivided in initial stiffness-proportional damping and tangent stiffness-proportional damping, the latter having been shown by Priestley and Grant (2005) as the possibly soundest option for common structures featuring an important hysteretic dissipation component. Hall (2006), in turn, suggests bounding the stiffness-proportional damping contribution in Rayleigh's approach.
This writer thus reiterates that, the above considered, it would be very useful for readers in general, and practitioners in particular, to be informed of the damping assumptions made by the author in his interesting parametric study, so that a deeper insight can be gained on the importance/impact that the introduction of equivalent viscous damping may have in nonlinear dynamic analysis of building frames and in the estimation of the corresponding structural base shear forces.