Capacity Spectrum Method for Buildings with Viscoelastic Dampers Using Developed Equivalent Damping Ratio Formula

A proposed formula based on the square root of the sum of the squares was derived in this research to combine the hysteresis and viscous damping in structures equipped with viscoelastic dampers (VEDs). To validate the accuracy of the proposed formula, a comparative study was conducted with the Kasai integral formula, as well as the formulas specified in the Japanese building code and in ASCE standards. The results indicate that the proposed formula yields damping ratio values closer to those of Kasai’s formula than the Japanese Building Code and ASCE formulas. This formula is utilized to propose a design procedure based on the capacity spectrum method (CSM) for designing structures with VEDs; the core of this design method is to calculate the required damping to reduce the performance displacement of the main structure to the target displacement based on the CSM, thereby determining the design parameters of VEDs. This method was verified on four-story and 10-story steel frames, and its accuracy was evaluated through a comparison with time history analysis (THA). The story drift and shear force obtained from THA were compared with the responses at the target displacement using CSM, revealing a high correlation between both methods, indicating good accuracy for the proposed design method.