A New Formula to Calculate the Fundamental Frequency of a Multistory Building by Approximate Numerical Method

Abstract

A new formula has been developed in this study, to calculate the fundamental frequency of a multistory building. This formula is derived from Dunkerley’s estimate, complies with the requirements of Uniform Building Code (UBC) and the Building Officials Code Administrators (BOCA) Code, and accounts for multistory building frames of different type and size. A coefficient Γ, function of moments of inertia and lengths of column/girder was introduced in the formula, in order to obtain a relative simple algebraic equation. To verify the validity of the new formula a thorough investigation has been conducted. Fundamental frequencies and periods have been calculated for different building frames using the new formula (Formula 1). A formula for buildings with rigid floors, Formula 2, has been derived from Formula 1. Formula 2 has been used to calculate the fundamental frequency for the same type and size of buildings used in the calculations with Formula 1, considered with rigid floors. In addition, three different empirical formulas have been used to calculate the fundamental period for the same buildings. Two of these formulas are recommended in different versions of the codes. For the same type and size of buildings the fundamental frequencies and periods have been determined by computer. Comparing with the computer values, formulas 1 and 2 give the best results and can be used in preliminary design, in vibration problems or to determine seismic lateral loads for buildings with a maximum height of 160/65 ft. The empirical formulas show large differences and have to be used with caution, only in the limited range imposed by UBC and BOCA.