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The Use of Natural Period of Vibration as a Simplified Indicator of Second-Order Effects for RC Frames

Rodrigo G. Mamone, Gustavo H. Siqueira, and Luiz C. M. Vieira Jr.
Department of Structural Engineering, University of Campinas, Campinas, Brazil
Abstract—In this study, the derivation of a simplified parameter ( Xt), based on the modal analysis of reinforced concrete frames, is presented. This simplified parameter can be used as an indicator of the susceptibility to global second-order effects as well as an amplifier to multiply first-order results in order to satisfactorily obtain the results of second-order analysis. The simplified amplification factor formulation is based on the Rayleigh's method, virtual work principles and the use of generalized coordinates to represent the behavior of flexible structures. The main advantage of a formulation based on a simple modal analysis is that natural period of vibration can be easily obtained using a finite element software. The simplified factor X is developed for an equivalent cantilever beam-column and the results compared with the values of the overturning moment amplification ratio obtained from first- and second-order analyzes performed using a finite element software. The results obtained demonstrate a satisfactory agreement between the simplified amplification factor and the amplification overturning moment amplification ratio. 

Index Terms—Second-Order Effects, Modal Analysis, Structural Stability

Cite: Rodrigo G. Mamone, Gustavo H. Siqueira, and Luiz C. M. Vieira Jr., "The Use of Natural Period of Vibration as a Simplified Indicator of Second-Order Effects for RC Frames," International Journal of Structural and Civil Engineering Research, Vol. 7, No. 1, pp. 15-21, February 2018. doi: 10.18178/ijscer.7.1.15-21
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