A study on the formula of fundamental period of high-rise shear wall structures based on ambient vibration testing

The dynamic performance test was conducted on 50 high-rise shear wall structures with heights ranging from 30 to 80 m in the high-risk seismic region of Northern China. The test data were fitted and analyzed. The fitting equations and the corresponding sample coefficients of determination (R2) were obtained by considering the heights (H), as well as the heights (H) and the structural dimensions (D) in the perpendicular (T) direction. These equations and coefficients were used to evaluate the degree of fit between the calculated values and the sample values. The residual plots are used to assess whether the fitted equations satisfy the relevant assumptions of the regression model. The sum of squares of the residuals is calculated to measure the discrepancy between the fitted values and the actual measured values. Additionally, the relationship between the fundamental natural vibration period of the longitudinal direction and the transverse direction was investigated. The results indicated that the fundamental natural vibration period of the long situdinal axis is smaller than that of the transverse axis, and both axes have the same period in the range of 30 m to 50 m. The ratio of the fundamental natural vibration period in the longitudinal direction to that in the transverse direction ranges from 0.8 to 1.0 between 30 m and 50 m, and from 0.6 to 1 between 50 m and 80 m. This indirectly indicates that considering only the height (H) as the influencing factor for calculating the fundamental natural vibration period insufficient. Both the height (H) and the structural dimensions (D) in the perpendicular (T) directions should be considered simultaneously.