Evaluating Accuracy of FEMA-356 Proposed Equation for Effective Damping Ratio for Viscous and Visco-elastic Dampers

The use of dampers for retroftting and reducing seismic induced vibrations of structures is rising. Among all types of dampers, viscous and visco-elastic dampers are extensively used for buildings. Adding dampers increases equivalent damping ratio of structure which decreases displacement and member stresses. FEMA-356 has proposed an equation for calculating equivalent damping ratio of shear buildings with added dampers, based on the frst mode of vibration. In the present research, the goal was to study the accuracy of FEMA-356 formula for evaluating equivalent damping ratio with
dampers as compared with the theoretical one. For the latter, the calculation is based on the hysteresis force-displacement response of the dampers. For obtaining hysteresis response, dynamic equation of motion of 2 to 12 stories 2D shear buildings equipped with viscous and visco-elastic dampers subjected to harmonic base excitation were solved. Both regular and mass distributed in height irregular structures with added dampers at all levels were considered. In addition to that, dampers were considered at random stories of the buildings and accuracy of equivalent damping ratios of FEMA-356 were evaluated. This study has shown that for viscous dampers, error of FEMA-356 formula in comparison with theoretical
formula for viscous dampers would be in the range of 1 to 3 percent and for visco-elastic ones in which stiffness ratio of visco-elastic dampers to story shear stiffness is 10 percent, would be in the range of 1 to 17 percent. When the stiffness ratio is decreased to 5 percent, the error would decrease to 2, in the worst case. Also, it has been shown that mass irregularity in the height of the buildings increases the maximum error from 17% to 58% for viscoelastic dampers; no signifcant effect for viscous dampers. Moreover, addition of dampers in random stories of buildings up to six stories would increase error of FEMA-356 formula about 42 and 50 percent, respectively, for viscous and visco-elastic dampers.