Prediction of fundamental period of regular frame buildings
The most important structural parameter in the estimation of the seismic demand on a building is the natural period of the building’s fundamental/first mode of vibration. There are several existing empirical, analytical, and experimental methods which can be used to estimate the fundamental period of a building. The empirical equations prescribed in the building codes are simple, but they do not consider actual building properties, and are very approximate. On the other hand, analytical methods like Eigenvalue analysis and Rayleigh method are able to consider most of the structural parameters that are known to affect the period of a building. Nevertheless, the analytical methods require considerable effort and expertise; often requiring structural analysis software’s to estimate the fundamental period of a building.
In this paper, a generic method is developed to estimate the fundamental period of regular frame buildings and a simple yet reliable equation is proposed. The equation is derived using the basic concept of MacLeod’s method for estimation of roof/top deflection of a frame building, which is modified to more accurately predict the lateral stiffness of moment resisting frames under triangular lateral force distribution typically used in seismic design and analysis of frame buildings. To verify the reliability and versatility of the developed equation, the fundamental periods predicted are compared with the periods obtained from Eigenvalue analysis for a large number of low to medium rise RC frame buildings. The fundamental period predicted using the proposed equation is also verified using the period obtained using the Rayleigh method and measured in experimental tests. Since the proposed equation was found to closely predict the fundamental period, the results are used to study the limitations of the empirical equations prescribed in building codes. The applicability of the proposed equation to predict the fundamental period of low to medium rise frame buildings with minor irregularity is also investigated, and it was found that the proposed equation can be used for slightly irregular frame buildings without inducing any additional error. The proposed equation is simple enough to be implemented into building design codes and can be readily used by practicing engineers in design of new buildings as well as assessment of existing buildings.
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