A critical study on empirical period - height relationship for reinforced concrete moment resisting frame buildings

Transcription

1 A critical study on empirical period - height relationship for reinforced concrete moment resisting frame buildings Shilpa P. Kewate and M.M. Murudi Most of the building codes provide the empirical equations to estimate period of vibration of the building. It is shown that, even though the code formulas provide periods that are generally shorter than measured periods, these formulas can be improved to provide better correlation with the measured data. The present study makes an attempt to gather the possible empirical period - height relationships for RC buildings. It points out the new trends that have become apparent, reflects on the gaps that have been missing in our knowledge and speculates on probable future studies that will allow to enlarge knowledge of this relationship. 1. INTRODUCTION The Fundamental natural period is an important parameter in earthquake-resistant design. Design horizontal acceleration A h or design horizontal base shear coefficient V B / W of a building is a function of its translational natural periods in the considered direction of design lateral force. In case of seismic design of building the fundamental natural period of the structure helps in finding out the base shear to be resisted by the structure and mode shape gives the distribution of base shear at every storey. An improved understanding of the global demands on a structure under a known seismic input can be obtained from this single characteristic. A reasonably accurate estimation of the fundamental period is necessary in earthquake analysis of structures. Fundamental period of vibration is dependent on the mass, strength and stiffness of the structure At initial stage in design of building, when the exact size of a structural member is not known, the fundamental time period can be calculated by the empirical expression suggested by the seismic code of a country. Simple equations are employed in the seismic design codes to relate the fundamental period to the height of the building. These equations have conventionally been obtained by regression analysis on the periods of vibration measured throughout earthquakes. Most of the building codes provide the empirical equations to estimate period of vibration from height or number of floors of the building. Many researchers have attempted to propose these code specified formulae. These formulae were evaluated using available periods measured during past earthquakes. Empirical equations were obtained from the regression analysis. Generally, the code formulae were calibrated to give shorter periods than that measured to produce conservative design seismic forces. However, some times the degree of conservatism may be excessive, while at the other times the period may be overestimated due to the omission of non structural elements in period calculations, leading to non-conservative design forces. Although The Indian Concrete Journal July

2 some improvements have been introduced over the years, these equations still need to be verified and improved, as new data become available after earthquakes. that context, buildings are said to have shorter natural periods with increase in column size. Stiffer buildings have smaller natural period. The present study makes an attempt to gather the possible empirical period-height relationships for RC buildings available in the literature. It points out the progress made and the new trends that have become apparent, reflects on the gaps that have been missing in knowledge and speculates on probable future studies that will allow to enlarge knowledge of this relationship. 2. FUNDAMENTAL NATURAL PERIOD OF BUILDING Each building has a number of natural frequencies, at which it offers minimum resistance to shaking induced by external effects and internal effects. All of these natural frequencies and the associated deformation shape of a building constitute a natural mode of oscillation. The mode of oscillation with the smallest natural frequency and largest natural period is called the Fundamental Mode; the associated natural period is called the Fundamental Natural Period. The period of vibration (T) of a single degree of freedom oscillator can be obtained from equation 1. T = 2π m/k...(1) Where m is the mass of the oscillator and k is the stiffness.the stiffness of the oscillator can be found from the base shear (V) divided by the lateral displacement (Δ). 2.1 Factors Influencing Natural Period (a) Effect of Stiffness Increasing the column size increases both stiffness and mass of buildings. But, when the percentage increase in stiffness as a result of increase in column size is larger than the percentage increase in mass, the natural period reduces. Hence, the usual discussion that increase in column size reduces the natural period of buildings, does not consider the simultaneous increase in mass; in Factors affecting stiffness 1. Length : It is inversely proportional to stiffness. 2. Material Properties: Material properties like modulus of elasticity are directly proportional to stiffness. 3. Moment of Inertia :It is directly proportional to stiffness (b) Effect of Mass Mass of a building that is useful in lateral oscillation during earthquake shaking is called the seismic mass of the building. It is the addition of its seismic masses at different floor levels. Seismic mass at every floor level is equal to full dead load plus suitable fraction of live load. The fraction of live load depends on the intensity of the live load and connection with the floor slab. Seismic design codes of each country/region provide portion of live loads to be considered for design of buildings to be built in that country/region. Heavier buildings have larger natural period (c) Effect of Building Height As the height of building increases, its mass increases but its in general stiffness decreases. Thus, the natural period of a building increases with increase in height. Taller buildings have larger natural period (d) Effect of Column Orientation Orientation of rectangular columns influences lateral stiffness of buildings along two horizontal directions. Hence, changing the orientation of columns changes the translational natural period of buildings. Hence, natural period of buildings along the longer direction of column cross-section is smaller than that along the shorter direction. Buildings with bigger column dimension oriented in the direction reduces the translational natural period of oscillation in that direction. 90 The Indian Concrete Journal July 2018

3 (e) Effect of Unreinforced Masonry Infill Walls in RC Frames In many countries, the space among the beams and columns of building are filled with unreinforced masonry infills. These infills take part in the lateral response of buildings and as a consequence alter the lateral stiffness of buildings. Therefore, natural periods of the building are affected in the presence of URM. Natural Period of building is lower when the stiffness contribution of URM infill is considered. 3. FUNDAMENTAL NATURAL PERIOD OF RC MOMENT RESISTING FRAMES (MRF) BUILDINGS IN DESIGN CODES Different empirical formulas used in different design codes for the estimation of fundamental period of RC buildings are explained in this section. The first empirical formula in seismic design codes was presented in the USA building code ATC3-06 (1978)[1] and had the form of Equation 2. T= H 0.9 (H in meters)...(3) In the European code EC8 (2004) [4] the period height expression for moment resisting frames adopted the same values by SEAOC-96 (1996) [2] as given in equation 4. T= 0.075H (4) In this C t coefficient has simply been altered considering that the height is measured in metres (0.03x = 0.073and has also been rounded up for simplicity), leading to C t = The approximate fundamental natural period of vibration (Ta) in seconds of a moment resisting frame building without brick infill panels may be estimated by the empirical expression given in equation 7 as per IS 1893 (Part 1):2016 [7]. T a =0.075h (7) T = C t H (2) where C t is a regression coefficient calibrated in order to achieve the best fit to experimental data and H represented the height of the building in feet. The form of Equation (2) has derived from the Rayleigh s method by assuming that the equivalent static lateral forces are linearly distributed over the height of the building and the base shear force is assumed to be proportional to 1/ T 2/3. In ATC3-06 (1978) [1], the value for the coefficient C t in Equation (2) was proposed equal to as a lower limit for evaluating the period of vibration of RC MRF buildings. In SEAOC88 (1996) [2] it was found that a value of C t = 0.03 was more appropriate for reinforced concrete buildings and has been adopted in many design codes (UBC-97 (1997) [3], SEAOC-96 (1996) [2] and EC8 (2004) [4].Other values or 0.04 in feet or and 0.097, respectively in meters for the coefficient C t have also been recommended. ASCE 7-05 (2006) [5] adopted the period height formula proposed by Goel and Chopra [6] who found that the best fit lower bound for reinforced concrete frames was given by the following expression STUDIES FOR ESTIMATION OF FUNDAMENTAL PERIOD OF VIBRATION Goel and Chopra [6] studied RC moment-resisting frames. They carried out the regression analysis of measured data to develop formulas to estimate fundamental periods of the buildings. Database contained a total of 106 Californian buildings including 21 of them with peak ground acceleration (PGA) higher than 0.15g. Results are shown in Figure 1. It was noticed that the calculated Figure 1. Results of RC MRF using regression analysis (Source: Goel and Chopra 1997[6] ) The Indian Concrete Journal July

4 code periods were shorter than the measured periods from the recorded motions. For buildings up to 36 meters high, the code formulas produced lower-bound values compared to measured period data, on the other hand, the same formulas resulted in 20% to 30% shorter periods compared to the measured ones for buildings taller than 36 meters. For many buildings, measured period values were greater than 1.4T, where T was described as the fundamental period obtained from the empirical equation. This implied that the code limits on the period are too conservative. It was stated that the database must had been expanded to include the results from the new earthquake data[6]. Hong and Hwang [8] experimentally determined the fundamental time period of 21 RC moment resisting frames located in Taiwan through vibration measuring instruments. Based on the experimental results, the 118 empirical relationship between building period and height was derived. However, the obtained relation was different from that of U.S. building code formula. On comparing the numerical values of fundamental time period it was observed that the formula based on data pertinent to Taiwanse buildings under predicted the period value as compared to U.S. Code proposed formulae. This implies that Taiwanese buildings are stiffer than the Californian buildings. RC moment-resisting frames from ambient vibrations and compared results with code-specified period formulae. Depending on the results of the experimental and numerical studies, a following simple relationship between height and fundamental period of vibration for the buildings was derived as given in equation 9. T a = H (9) Pinho et al. [11] took a critical look at the way in which seismic design codes around the world have endorsed the designer to estimate the period of vibration for use in both linear static and dynamic analysis. Based on this review, some preliminary proposals are made for updating the clauses related to the estimation of the periods of vibration in Eurocode 8. Chiauzzi et al. [12] focused on twelve RC framed buildings, located in the cities of Victoria and Vancouver (British Columbia, Canada) and carried out a field campaign to estimate their fundamental periods using in-situ ambient vibration measurements. They concluded that building periods estimated based on simple equations provided by earthquake design codes in Europe EC8(2004) [4] and North America (UBC-97 (1997)[3]) are significantly greater than the periods computed using ambient vibration records on the monitored buildings. Helen Crowley [9] studied existing buildings from five different European countries exposed to earthquake forces. The majority of the existing buildings were designed and built between 1930 and The study led to a simplified period versus height equation in the assessment of existing RC Framed buildings taking due account of the presence of infill panels. Analytical yield period-height relationship for cracked infilled RC buildings compared with the EC8 empirical equation are shown in Figure 2. The following equation (8) was proposed in this study. Ditommaso et al [13] investigated 68 RC MRF buildings in Italy with different characteristics, such as age, height T y =0.055H...(8) Kadir Guler et al.[10] examined the relationship between the height and fundamental period of vibration of Turkish Figure 2. Analytical yield period-height relationship for cracked infilled RC buildings compared with the EC8 empirical equation (Source- Helen Crowley 2006 [9] ) 92 The Indian Concrete Journal July 2018

5 and damage level, by performing ambient vibration measurements that provided their fundamental translational periods. Four different damage levels (DL 0,DL 1, DL 2, DL 3 ) were considered according to the definitions in EMS 98 (European Macro seismic Scale), trying to regroup the estimated fundamental periods versus building heights using damage level as a key parameter. The two suggested experimental period height relationships were obtained. The first one for undamaged buildings considering it as a lower limit in elastic forcebased design (DL 1 and DL 0 ) is provided in the following equation (10): T = H...(10) and the second one related to buildings with DL 2 and DL 3 is given equation (11) : T = H...(11) The second one represents the higher limit value for the assessment and retrofitting of existing RC buildings, in particular when the post-elastic behaviour of the structure was taken into account. Elgohary [14] has carried out a parametric study using finite element analysis to study the effect of the major parameters influencing in the fundamental period. He concluded that the code s formulae, in most cases, underestimate the fundamental period with a large deviation from finite element results. This large deviation is a result of considering only the effect of frame height and neglecting of remaining major parameters in the codes formulae. He has suggested following formula mentioned in equation (12) by considering frame height. T = 0.28 H (12) Magdy [15] converse about enhanced formulas for estimating the fundamental period of vibration of reinforced concrete moment-resisting frame buildings by taking the effect of both building height (H) and number of stories together (N). The enhanced formula is derived from regression analysis of the existing data for the fundamental vibration period of reinforced concrete moment resisting frame buildings measured from their motions recorded during eight California earthquakes. The obtained formula is mentioned in equation (13): T = N 0.17 H (13) Sangamnerkar et al.[16] predicted the fundamental period of vibration of reinforced concrete buildings with moment resisting frames by considering the effect of base width and stiffness of the structure. A few examples of dynamic analysis are presented in this study in order to show that the base width should also be incorporated in the formula to evaluate period of vibration. In view of the results obtained in the analysis, values of the time period of vibration differ substantially, and the variation comes out to be on higher side, which results in reduction in base shear and makes the structure economical. Further conclusions can be drawn for the changes made in column dimensions i.e. reduction in column sizes raises in the value of time period. Therefore period formulae mentioned in seismic codes need to be reviewed with respect to base width and stiffness of the structure. 5. CONCLUSIONS The fundamental time period is an primary parameter in seismic design methodologies Hence, accurate estimation of this parameter is very necessary as it affects the seismic design of structural members. The review of previous literature shows that the code proposed expressions were based on regression analysis performed on the data set consisting of experimentally determined period of few buildings located in a certain region. Extensive literature review suggested that code limits on the period are too conservative. The database has to be expanded to include the results from the new earthquake data. Therefore, there is a need of improved empirical expressions to estimate the fundamental time period for buildings. References 1. Applied Technology Council (ATC), Tentative provisions for the development of seismic regulations for buildings, Report No. ATC306,Palo Alto, The Indian Concrete Journal July

6 2. SEAOC.[1996], Recommended lateral force requirements,6 th Edition, Seismology Committee, Structural Engineers Association of California, Sacramento, Uniform Building Code (UBC97), Structural engineering design provisions, International Conference of Building Officials, Whittier, p CEN (2004), Eurocode 8: Design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings, European Standard EN :2004, Comité Européende Normalisation, Brussels, Belgium, ASCE (2006), Minimum design loads for buildings and other structures, ASCE 7-05,Structural Engineering Institute of the American Society of Civil Engineers, Goel R. & Chopra A., Period formulas for moment-resisting frame buildings. Journal of Structural Engineering,1997 Vol. 123(11), pp IS 1893(Part I): 2016,Criteria for earthquake resistant design of structures: part I general provisions and buildings, (sixth revision), Bureau of Indian Standards, New Delhi, December Hong L. and Hwang, Empirical formula for fundamental periods of vibration for Reinforced concrete buildings in Taiwan, Earthquake Engineering and Structural Dynamics 2000,Vol. 29, pp Helen C. and Rui P., Simplified equations for estimating the period of vibration of existing buildings, First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, Paper Number: 1122, September 2006, pp Kadir G., Ercan Y., and Ali K., Estimation of the fundamental vibration period of existing RC buildings in Turkey utilizing ambient vibration records, Journal of Earthquake Engineering,2008 Vol.12(S2) pp R. Pinho and H. Crowley, Revisiting Eurocode 8 formulae for periods of vibration and their employment in linear seismic analysis, Earthquake Engineering &Structural Dynamics, 2010, Vol. 39, No. 2, pp Chiauzzi,L., Masi, A. and Mucciarelli, M., Estimate of fundamental period of reinforced concrete buildings: code provisions vs. experimental measures in Victoria and Vancouver (BC, Canada), Proceeding of the 15th World Conference on Earthquake Engineering, Lisbon, September Ditommaso R.,Vona M., Gallipoli M.R., and Mucciarelli, Evaluation and considerations about fundamental periods of damaged reinforced concrete buildings, Natural Hazards Earth System Science, 2013,pp Elgohary H., Empirical formula for the fundamental period of vibration of multi-storey RC framed buildings, Earthquake Engineering and Structural Dynamics, 2013pp , Vienna, Austria Paper No Magdy I. Salama, Estimation of period of vibration for concrete moment-resisting frame buildings, Housing and Building National Research Centre, 2015 Vol.11, pp Sangamnerkar, P. and Dubey, S.K., Effect of base width and stiffness of the structure on period of vibration of RC framed buildings in seismic analysis, Open Journal of Earthquake Research, 2015, Vol.4, pp Shilpa Kewate holds an M.Tech in Structural Engineering from Shri Ramdeobaba Kamla Nehru College of Engineering, Nagpur; pursuing her PhD in Civil Engineering from Mumbai University. She is at present Associate Professor and PG Coordinator in Civil Engineering Department at Saraswati College of Engineering, Navi Mumbai, Maharashtra. She has 14 years of teaching experience. She has guided more than 12 M.Tech. students. She has more than 20 papers to her credit in various national and international conferences and journals. Her area of interest is concrete technology, structural dynamics, Earthquake Engineering. Dr. M.M. Murudi holds a PhD in Civil Engineering. He is presently Professor and Vice Principal at Sardar Patel College of Engineering, Maharashtra. He has 28 years of Teaching experience. He has guided 45 M.Tech. students and is currently guiding four PhD students. He has published more than 21 papers credit in various national and international conferences and journals. He has undertaken various consultancy projects. He is a member of ISTE, ISET, Indian society for non destructive testing, Indian association for structural engineering, Indian association of structural rehabilitation. His area of research is structural dynamics, earthquake engineering, concrete technology, repairs and rehabilitation. 94 The Indian Concrete Journal July 2018