Empirical formula for fundamental period of frame-shear wall structures based on structural strong motion records

To improve the seismic design of reinforced concrete frame-shear wall structures, the empirical formula for estimation of the fundamental periods were investigated, and a new formula was presented. A total of 40 reinforced concrete frame-shear wall buildings were selected for the statistical analysis, and all the buildings maintained strong motion records during past earthquakes. The on-line adaptive system identification method was employed to detect if the structural response was nonlinear and time-varying, then the fundamental periods of all the buildings were identified by using the ARX system identification model. The empirical formula for fundamental periods of frame-shear wall buildings was obtained through nonlinear least square regression. The availability, reliability and accuracy of the formula were verified by using two examples. The study shows that the fundamental period from the proposed formula is larger than that from the formula of present load code for the design of building structures of China, and the difference increases with the increase of structure height. The proposed empirical formula can serve as a reference for revision of the seismic design code, frame-shear wall building seismic design and related studies.