Fundamental period equations for plan irregular moment-resisting frame buildings

The fundamental natural period of oscillation is a critical parameter in evaluating the design base shear of buildings. Worldwide seismic design codes typically employ height -based empirical formulas to estimate this period for various building categories, without distinguishing between regular and irregular buildings. This study proposes a formula specifically for reinforced concrete (RC) moment -resisting frame (MRF) buildings with dominant re-entrant corner type plan irregularity. A total of 190 re-entrant corner dominant building models with different shapes (C-, L-, T-, and PLUS -type), heights, and floor configurations were prepared, and eigenvalue analysis (EVA) was conducted. The fundamental natural period of oscillation for each model was evaluated and compared with the height -based formulas from seismic design codes and the period- height relationship proposed in existing literature. A nonlinear regression model, using a multi -variable power function, is proposed to estimate the fundamental natural period for these re-entrant corner dominant building models. This model considers the A/L ratio in both directions of the building, along with its height. Both unconstrained and constrained regression analyses were performed to derive a formula that best fits the fundamental natural period data. The study recommends that the unconstrained best -fit minus one standard deviation curve can conservatively define the fundamental natural period of oscillation for re-entrant corner dominant RC building models. The equation defining this curve has the potential to replace the existing seismic design code -based period -height formula.