Deep Evaluation of Structural Time Period Formulae Using Finite Element Modelling

The accurate estimation of the fundamental period is critical for seismic design using the Equivalent Lateral Force method. This study evaluates widely used empirical period formulae from international seismic codes and previous research by comparing them with detailed finite element method (FEM) analyses. A total of 93 reinforced concrete building models were assessed. The results show that most empirical formulae, notably the American Society of Civil Engineers Standard (ASCE 7-10), the Eurocode, the National Building Code of Canada (NBCC), and the Saudi Building Code (SBC 301), systematically underestimate the fundamental period in low- and mid-rise buildings often by more than 40% under cracked conditions, while discrepancies reduce under uncracked assumptions. Equations such as those proposed by the Building Standard Law of Japan (BSLJ) and Australian Standard (AS 11407.2) show comparatively closer agreements with FEM predictions, whereas formulae developed by Goel and Chopra and by Alguhane et al. have distinct differences, especially at greater heights. Statistical parameters, including the arithmetic mean difference and the standard deviation, were employed to enhance the comparison and assess the accuracy and dispersion of the estimated fundamental periods. The results indicate that empirical formulae, although beneficial in first-design stages, are likely to yield conservative results and suggest the use of advanced numerical computation or revised models and coefficients for RC high-rise and irregular buildings.