Empirical Expression for the Fundamental Natural Period of Buildings on Slopes

Abstract

Seismic codes worldwideprovide empirical formulas for estimating the fundamental natural period of vibrations (Ta), preferably suitable for regular buildings. As per IS 1893:2016, the fundamental natural period is an inherent building property which is a function of height and base dimensions of the building. However, the formula specified in the existing code is not suitable for a building that is irregular both in plan and elevation. One such case of irregular buildings is building structures on slopes, which are supported on foundations at different horizontal levels leading to non-uniform column heights, where the present period formula is not suitable for estimation of Ta. In the present study, an attempt is made to develop an empirical expression for estimating Ta for buildings on slopes, by performing a regression analysis of numerically obtained natural periods. A total of 180 RC moment-resisting frame structures with varying floor heights and slope angles have been modelled and analyzed using SAP 2000 for the study and an empirical expression has been presented.