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PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
A Reappraisal of Time Period Formulas of Design Codes for Framed Reinforced Concrete Buildings
K.M. Amanat and E. Hoque
Department of Civil Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
K.M. Amanat, E. Hoque, "A Reappraisal of Time Period Formulas of Design Codes for Framed Reinforced Concrete Buildings", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 45, 2002. doi:10.4203/ccp.75.45
Keywords: period, earthquake, design codes, infill, concrete, frame.
An acceptable finite element modeling and analysis procedure has been shown in this paper that may be used to determine the period of vibration of typical RC frame buildings. Seismic design of buildings by equivalent force method requires the fundamental period of vibration to estimate the base shear. Generally the codes like Uniform Building Code (UBC) , Bangladesh National Building Code (BNBC)  or the Building Standard Law of Japan (BSLJ)  and many other codes around the world provide empirical equations to estimate the period. These formulas are developed on the basis of the measured periods of real buildings subjected to ground motion during earthquakes and are generally accepted to give good results. Codes also permit the use of rational methods like modal analysis (eigenvalue analysis) or Rayleigh's method to determine the fundamental period. However, codes also puts a maximum limit on the period determined by such rational analysis. This is because of the fact that conventional rational analysis based on computer modeling generally renders the structure too flexible resulting in an unreasonably high value of period. The limit put by the code on period is thus aimed at safeguarding the structure from underestimating the base shear due to too long period.
While sophisticated computer packages are being developed and used around the world by engineers to model and analyze building structures in a comprehensive way, code specifications still advocate the use of empirical equations for estimating the fundamental period of buildings. The approximations made in idealization of the structure during the generation of computer based FE model is basically the source of error in predicting the period though the same idealization is generally thought to be comprehensive enough for strength design under static design loads. The accuracy of the rational methods like modal analysis (eigenvalue analysis) or Rayleigh's method are limited by the error introduced as a result of approximation of the real structure. In this paper it has been shown by various sensitivity study that when the effect of infill is considered in the FE modeling, rational analysis do give reliable results and agree reasonably well with the code equations.
In this paper computational investigation has been carried out with different three-dimensional FE models of framed RC structures to study fundamental period of vibration. The effects of infill were included by modeling it as diagonal struts [4,5]. The study has been carried out with models of different numbers of floors, spans, bays etc. The periods were determined by eigenvalue analysis and compared with the same predicted by code formulas. It has been found that the when the models do not include the infills, the period given by the analysis is significantly longer than the period predicted by the code equations. However, when the effect of the infills are included in the model, the time period determined from eigenvalue analysis were remarkably close to those predicted by the code formulas.
The study has revealed the relative importance of these parameters in influencing the fundamental period of buildings. Among these parameters, panel size, number of bays, number of spans and percentage of infill have been found to be most important. Any further attempt to improve the code equations should include the effect of these parameters so that the predicted period of building is more representative of the real situation.
Since conventional frame modeling and FE analysis does not produce correct period, it can be said that such conventional modeling is also not suitable for dynamic load-history analysis or response spectrum analysis of tall RC framed buildings where higher modes of vibrations are also important. In such situations, adding the infills as diagonal struts in the FE model may improve the acceptability and reliability of analysis of RC frames.
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