Determination of Fundamental Time Period of Bare-Frame Building Incorporating Number of Bays and Storey

Abstract

The fundamental time period of a building plays a crucial role in determining the base shear during the seismic design of earthquake-resistant structures and is a vital parameter in modal analysis. For structural engineers, the basic knowledge of the fundamental time period is key for efficient and safe design of structures. There are various codes that give an empirical relationship to calculate the fundamental time period of buildings. All these relations are a function of height of the building. However, another influential parameter often overlooked is the number of bays, which directly affects both mass and stiffness, and consequently, the time period. In this study, the fundamental time period of buildings was analyzed incorporating height of building and number of storeys in x and y direction, and an empirical relationship incorporating these factors was created. Modal analysis was carried out in ETABS V17 where 81 models were created by varying storey from 1 to 9 and the number of bays from 2 to 4 in both directions. The storey height and bay spacing were taken as 3.5 m. A regular bare-frame building was analyzed without infill walls to isolate the effect of geometric parameters. Regression analysis was carried out for the time period obtained from the models to propose an empirical relation incorporating height of building and number of bays in both x and y direction using MATLAB code. The model yielded a coefficient of determination (R²) of 0.9902 and RMSE of 0.048 s, showing a strong correlation between predicted and analytical results. The obtained values were compared with empirical code-based expressions (NBC, Euro, IS) and showed deviations upto ±35\%. This indicates that while height remains the dominant factor, inclusion of bay numbers improves accuracy, particularly for bare-frame structures. The study therefore provides empirical expression for fundamental time period of RC bare-frame buildings with number of bay and storey.