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Various technologies (i.e. seismic isolation, fluid viscous dampers, tuned masses, etc.) have been developed and implemented on diverse typologies of structures in order to increase their seismic performance [1]. These devices modify the seismic response of the structure through the beneficial reduction of the inter-story drifts and hence, a reduction in inelastic actions, which also reduce the losses related to structural damage. However, few studies have investigated the impact of the implementation of such technologies on the acceleration demand on non-structural elements which, as it has been observed in the last decade [2], can govern the losses caused during a strong seismic event. This research studies the impact of the different parameters that rule the design of fluid viscous dampers (added supplemental damping, velocity exponent, damping constant distribution and brace stiffness) on the acceleration demand on non-structural elements on three steel moment-resisting frame buildings retrofitted with fluid viscous dampers [1, 3-5]. Six different velocity exponents were used, three targeted supplemental damping ratios and two different distribution approaches of the damping constants were applied: a uniform distribution approach and an equivalent lateral stiffness distribution approach [1]. An incremental dynamic analysis was carried out with the FEMA P-695 far-field ground motions set [6] scaled to 10 different intensities and the seismic performance was assessed in terms of probability of collapse, median peak inter-story drifts, median peak floor accelerations and median floor spectral accelerations.
The implementation of fluid viscous dampers to provide supplemental damping has demonstrated to have a positive impact on the seismic performance of a structure. The basic constitutive model that represents the force developed by fluid viscous dampers is given by:
Where C is the damping constant, sgn is the sign function, ẋ(𝑡) is the relative velocity between the two ends of the viscous damper at a time t, and α is the velocity exponent of viscous dampers that rules the force-velocity relationship and consequently the shape of its hysteresis loop. When α is equal to unity, the viscous damper is linear, therefore the force in the damper is linearly proportional to the velocity. If α is smaller than unity, the damper is nonlinear and the force-velocity relationship exhibits a reduction on the slope at high velocities [1] (Fig. 1).
Fig. 1 Force - velocity and force - displacement hysteresis comparison for fluid viscous dampers [after 1].
As it was expected, the implementation of the different configurations of fluid viscous dampers improves the seismic performance of the structure in terms of reduction of the probability of collapse and the median peak inter-story drifts (Fig. 2). Nevertheless, the results related to the acceleration demand show that some configurations of fluid viscous dampers can increase the acceleration demand in terms of peak floor acceleration or floor spectral acceleration (Fig. 3).
Fig. 2 (Left) Probability of collapse at the maximum credible earthquake and (Right) median peak inter-story drifts at the design earthquake with 20% of supplemental damping of the six-story archetype buildings.
Fig. 3(Left) Peak floor acceleration and (Right) Top floor absolute acceleration response spectra at the design earthquake with 35% of supplemental damping of the six-story archetype buildings.
The addition of supplemental damping through the implementation of fluid viscous dampers can improve the seismic performance of a structure in terms of reducing inter-story drifts and probability of collapse. However, what is beneficial for the structure could be deleterious for the acceleration sensitive non-structural elements since an increment of the acceleration demand is noticeable for some configurations of viscous dampers, especially those involving low velocity exponents (i.e. α lower than 0.5) and high targeted added supplemental damping ratios (i.e. 20% and 35% of critical damping). These results highlight the need of including the assessment of the non-structural seismic performance at the moment of evaluating potential retrofitting technics due to the significant impact of the acceleration sensitive non-structural elements on the total building’s cost and on the expected annual losses [5]. Additionally, the limitations of using the peak floor acceleration (PFA) as engineering demand parameter for the evaluation or design of non-structural elements are highlighted since PFA completely neglects the dynamic interaction between the structure and non-structural elements, which can lead to unconservative assessments as it is demonstrated in the comparison of the floor absolute response acceleration spectrum (Fig. 3b) where, for certain range of non-structural periods, there is an amplification of the spectral acceleration compare to that of the non-retrofitted buildings. This amplification can be even much larger than the amplification factors recommended in some codes to design flexible non-structural elements.
References:
[1] Christopoulos C., Filiatrault A. (2006): Principles of Passive Supplemental Damping and Seismic Isolation. IUSS Press, Pavia, Italy.
[2] Bevere. L., Ewald. M., Wunderlich S. (2019): A Decade of Major Earthquakes: Lesson for Business. Swiss Re Institute, Zurich, Switzerland.
[3] Chalarca B., Filiatrault. A., Perrone. D. (2019): Floor Acceleration Demand on Steel Moment Resisting Frame Buildings Retrofitted with Linear and Nonlinear Viscous Dampers, Proceedings of the 4th International Workshop on the Seismic Performance of Non-Structural Elements SPONSE, Pavia, Italy.
[4] Chalarca B., Filiatrault. A., Perrone. D. (2019): Seismic Performance of Steel Moment-Resisting Frame Retrofitted with Linear and Nonlinear Viscous Dampers, Proceedings of the 16th World Conference on Seismic Isolation, Energy Dissipation and Active Control of Structures, Saint Petersburg, Russia.
[5] Chalarca B., Filiatrault. A., Perrone. D. (2020): Earthquake Economic Losses in Moment-Resisting Steel Frames Equipped with Fluid Viscous Dampers. Proceedings of the 17th World Conference on Earthquake Engineering, Sendai, Japan.
[6] FEMA. (2009): Quantification of Building Seismic Performance Factors FEMA P-695, Federal Emergency Management, Washington D.C., USA.
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