The differences of empirical formulas of China, the United States, Japan, and Europe for estimating the fundamental periods of frame structures are investigated. Summing up paradigms of the empirical formulas from the above representation countries, the paradigm formulas expressed as single-variable exponential type, single-variable linear type, and multi-variable non-linear type. Using statistical data of 36 groups of the measured fundamental period for least-squares regression analysis, and the effect of fitting regression formula is judged by the norm of relative error ‖δ‖2, the norm of root mean square error ‖RMSE‖2, the norm of residual mass‖CRM‖2. The results show that: the single-variable exponential type has wide application and gets closer with measured fundamental period; the single-variable linear type is brief, and the single-variable based on structural height has a smaller error with measured fundamental period, the single-variable based on the stories of structures has a larger error with measured fundamental period; the multi-variable non-linear type is very complex and larger error compared with the measured fundamental period. Considering the formula in the form of simple, practical and consistent with the codes, this paper gives single-variable exponential type as recommended empirical formula for estimating the fundamental periods of frame structures .The proposed empirical formula can serve as a reference for revision of the seismic design code, frame structure seismic design and related studies.
Estimate and asymptotic of the solution for the p-Laplacian parabolic equation double non-linear type with damping