An Investigation of the Fundamental Period of Vibration for Moment Resisting Concrete Frames

Abstract

The determination of fundamental period of vibration for structures is essential to earthquake design. The current codes provide empirical formulas to estimate the approximated fundamental period and these formulas are dependent on building material, height of structure or number of stories. Such a formulation is excessively conservative and unable to account for other parameters such as: length to width ratios, vertical element size and floors area. This study investigated the fundamental periods of mid-rise reinforced concrete moment resisting frames. A total of 13 moment resisting frames were analyzed by ETABS 15.2.2, for gross and cracked eigenvalue analysis and Extreme Loading for Structures Software® or ELS, for non-linear dynamic analysis. The estimated periods of vibration were compared with empirical equations, including current code equations. As expected, the results show that building periods estimated based on simple equations provided by earthquake design codes in Europe (EC8) and America (UBC97 and ASCE 7-10) are significantly smaller than the periods computed using nonlinear dynamic analysis. Based on the results obtained from the analyzed models, equations for calculating period of vibration are proposed. These proposed equations will allow design engineers to quickly and accurately estimate the fundamental period of moment resisting frames with taking different length to width ratios, vertical element size, floors area and building height into account. The interaction between reduction factor and the reduced period of vibration is studied, and it is found that values of maximum period of vibration can be used as an alternative method to calculate the inelastic base shear value without taking reduction factors in consideration.

Fundamental Period Prediction of Infill Reinforced Concrete Structures using an Ensemble of Regressors

“…The period is increased by 9 percent to 71% when the opening ratio in the walls is increased [7]. Some in ll wall apertures, such as windows and doorways, alter the in ll wall stiffness and extend the fundamental time period [11].…”

“…Ahmed 2019 [11]conducted a study by considering varied length-to-width ratios, vertical element size, oor area, and building height, the suggested equation is utilized to predict the time period of momentresisting frames.…”

A simplified formula for the determination of the fundamental period of mixed structures with vertical combination of different seismic resisting systems

“…Kwon and Kim (2010) investigated the ASCE/SEI 7-05 building period formulae for known resisting systems and concluded that these formulae, in general, predict accurately the lower bound of the fundamental period for low-to medium-rise braced frames and overestimate the fundamental natural period of shear wall buildings. Ahmed et al (2019) determined the fundamental period of mid-rise reinforced concrete moment resisting frames by nonlinear dynamic analysis and compared the results with the period formulae in Eurocode 8, UBC 1997 and ASCE/SEI 7-16. They proposed some equations for calculating the period of vibration by regression analysis of the results.…”

Estimating vibration period of reinforced concrete moment resisting frame buildings

“…Multiple fundamental period to building height relations for different seismic intensities were developed by Verderame et al [31] based on modal analyses results. Mohamed et al [32] used applied element method in modeling reinforced concrete buildings and conducted nonlinear dynamic analysis in which the fundamental period was extracted from the time history curve. An equation relates fundamental vibration period to building height, building width to length ratio and column size was developed.…”