Damping Ratios of the First Mode for the Seismic Analysis of Buildings
Publication: Journal of Structural Engineering
Volume 147, Issue 1
Abstract
This paper analyzed damping ratios inferred from 1,335 seismic responses recorded in 154 instrumented buildings in California. These values were inferred using a parametric system identification technique in the time domain, and subjected to a series of reliability screening tests to retain only high-quality data. The resulting damping ratios conformed a data set of 1,037 high-quality values inferred exclusively from the seismic response of buildings, a database several times larger than previous studies of damping inferred from seismic response. The data set was analyzed using a linear mixed-effects statistical model to account for the fact that many of the data points were clustered, because they came from damping ratios in the same building shaken by various earthquakes. It was shown that damping decreases with increasing building height, which is the factor that best explained the relatively large variance observed in the data. Contrary to some previous recommendations, it was found that once the variation with height is taken into account, the primary structural building material is not statistically significant in the damping ratio of buildings subjected to earthquakes. However, when including the combined material and lateral resistant system as a factor in the statistical model, an additional 6% of the variance was explained. Results showed that steel buildings with moment-resistant frames have, on average, a slightly higher damping ratio than those with steel braced frames. The amplitude dependency of damping showed that there was no significant correlation between damping ratio and the overall lateral deformation demand in the building as measured by the peak roof drift ratio for amplitudes typically observed during moderate earthquake motions once a minimum level of amplitude is exceeded.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request. All ground and structural motion records employed in this investigation are available at the Center for Engineering Strong Motion Data website (USGS, CGS, and ANSS 2015). Identified damping ratios are available upon request.
Acknowledgments
The authors acknowledge the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT)—Becas Chile, the Blume Earthquake Engineering Center at Stanford University, and the Shaw Family Fund for the financial aid provided for this investigation. Ground and structural motions used in this investigation were obtained from the California Strong Motion Instrumentation Program of the California Geological Survey and from the United States Geological Survey. Efforts to install, operate, and maintain seismic instrumentation in buildings as well as to process and disseminate earthquake records by these organizations are gratefully acknowledged.
References
AEC (Atomic Energy Commission). 1963. Nuclear reactors and earthquakes. Washington, DC: AEC.
AEC (Atomic Energy Commission). 1973. Damping values for seismic design of nuclear power plants. Washington, DC: AEC.
Alford, J. L., and G. W. Housner. 1953. “A dynamic test of a four-story reinforced concrete building.” Bull. Seismol. Soc. Am. 43 (4): 7–16.
Alford, J. L., G. W. Housner, and R. R. Martel. 1951. Spectrum analysis of strong-motion earthquakes. Pasadena, CA: California Institute of Technology.
Anderson, J., E. Miranda, and V. Bertero. 1991. Evaluation of the seismic performance of a thirty-story RC building. Berkeley, CA: Univ. of California.
Aquino, R. E. R., and Y. Tamura. 2013. “On stick-slip phenomenon as primary mechanism behind structural damping in wind-resistant design applications.” J. Wind Eng. Ind. Aerodyn. 115 (Apr): 121–136. https://doi.org/10.1016/j.jweia.2012.12.017.
ASCE. 2016. Minimum design loads for buildings and other structures. ASCE/SEI 7-16. Reston, VA: ASCE.
Bates, D., M. Mächler, B. M. Bolker, and S. C. Walker. 2014. “Fitting linear mixed-effects models using lme4.” J. Stat. Software 67 (1): 1–48. https://doi.org/10.18637/jss.v067.i01.
Beck, J. L., and P. C. Jennings. 1980. “Structural identification using linear models and earthquake records.” Earthquake Eng. Struct. Dyn. 8 (2): 145–160. https://doi.org/10.1002/eqe.4290080205.
Bentz, A., and T. Kijewski-Correa. 2008. “Predictive models for damping in buildings: The role of structural system characteristics.” In Proc., 18th Analysis and Computation Specialty Conf. Reston, VA: ASCE.
Bernal, D., M. Dohler, S. M. Kojidi, K. Kwan, and Y. Liu. 2015. “First mode damping ratios for buildings.” Earthquake Spectra 31 (1): 367–381. https://doi.org/10.1193/101812EQS311M.
Biot, M. 1932. “Vibrations of buildings during earthquakes.” Ph.D. thesis, Aeronautics Dept., California Institute of Technology.
Celebi, M. 1992. “Highlights of Loma Prieta responses for four tall buildings.” In Proc., 10th World Conf. on Earthquake Engineering, 4039–4044. Rotterdam, Netherlands: A.A. Balkema.
Celebi, M. 1993. “Seismic responses of two adjacent buildings. I: Data and analyses.” J. Struct. Eng. 119 (8): 2461–2476.
Celebi, M. 1994. “Response study of a flexible building using three earthquake records.” In Proc., ASCE Structures Congress XII, 1220–1225. Reston, VA: ASCE.
Celebi, M. 1996. “Comparison of damping in buildings under low-amplitude and strong motions.” J. Wind Eng. Ind. Aerodyn. 59 (2): 309–323.
Celebi, M., L. Phan, and R. Marshall. 1993. “Dynamic characteristics of five tall buildings during strong and low-amplitude motions.” Struct. Des. Tall Build. 2 (1): 1–15.
Center for Engineering Strong Motion Data. 2015. “Center for engineering strong motion data.” Accessed August 01, 2015. http://strongmotioncenter.org.
Chopra, A. K. 2012. Dynamics of structures: Theory and applications to earthquake engineering. 4th ed. Upper Saddle River, NJ: Pearson Education.
Cruz, C., and E. Miranda. 2017a. “Evaluation of damping ratios for the seismic analysis of tall buildings.” J. Struct. Eng. 143 (1): 04016144. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001628.
Cruz, C., and E. Miranda. 2017b. Evaluation of damping ratios from the seismic response of buildings. Stanford, CA: John A. Blume Earthquake Engineering Center, Stanford Univ.
Cruz, C., and E. Miranda. 2019. “Reliability of damping ratios inferred from the seismic response of buildings.” Eng. Struct. 184 (Apr): 355–368. https://doi.org/10.1016/j.engstruct.2019.01.056.
Erwin, S., T. Kijewski-Correa, and S.-W. Yoon. 2007. “Full-scale verification of dynamic properties from short duration records.” In Proc., 2007 Structures Congress: New Horizons and Better Practices. Reston, VA: ASCE.
Fritz, W. P., N. P. Jones, and T. Igusa. 2009. “Predictive models for the median and variability of building period and damping.” J. Struct. Eng. 135 (5): 576–586. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:5(576).
Fukuwa, N., R. Nishizaka, S. Yagi, K. Tanaka, and Y. Tamura. 1996. “Field measurement of damping and natural frequency of an actual steel-framed building over a wide range of amplitudes.” J. Wind Eng. Ind. Aerodyn. 59 (2–3): 325–347. https://doi.org/10.1016/0167-6105(96)00015-3.
Ghahari, S. F., and E. Taciroglu. 2016. “Identification of dynamic foundation stiffnesses and input motions from strong motion data recorded at CSMIP instrumented buildings.” In Proc., SMIP16 Seminar. Sacramento, CA: California Strong Motion Instrumentation Program.
Goel, R. K., and A. K. Chopra. 1997. Vibration properties of buildings determined from recorded earthquake motions. Berkeley, CA: Univ. of California.
Harris, A., Y. Xiang, F. Naeim, and F. Zareian. 2015. “Identification and validation of natural periods and modal damping ratios for steel and reinforced concrete buildings in California.” In Proc., SMIP15 Seminar on Utilization of Strong-Motion Data, 121–134. Sacramento, CA: California Strong Motion Instrumentation Program.
Hart, G., and R. Vasudevan. 1975. “Earthquake design of buildings: Damping.” J. Struct. Div. 101 (1): 11–30.
Hill-Carroll, P. E. B. 1985. “The prediction of mean structural damping values and their coefficients of variation.” Master’s thesis, Faculty of Engineering Science, Univ. of Western Ontario.
Housner, G. W., R. R. Martel, and J. L. Alford. 1953. “Spectrum analysis of strong-motion earthquakes.” Bull. Seismol. Soc. Am. 43 (2): 97–119.
INN (Instituto Nacional de Normalización). 2012. NCh 433.Of1996 Mod.2012: Earthquake resistant design of buildings. Santiago, Chile: INN.
Jacobsen, L. S. 1930. “Steady force vibration as influenced by damping.” Trans. Am. Soc. Mech. Eng. 52 (15): 169–181.
Jacobsen, L. S. 1959. Frictional effects in composite structures subjected to earthquake vibrations. Stanford, CA: Dept. of Mechanical Engineering, Stanford Univ.
Jacobsen, L. S. 1960. “Damping in composite structures.” In Proc., 2nd World Conf. on Earthquake Engineering, 1029–1044. Tokyo: Science Council of Japan.
Jeary, A. P. 1986. “Damping in tall buildings—A mechanism and a predictor.” Earthquake Eng. Struct. Dyn. 14 (5): 733–750. https://doi.org/10.1002/eqe.4290140505.
Kijewski-Correa, T., and J. D. Pirnia. 2007. “Dynamic behavior of tall buildings under wind: insights from full-scale monitoring.” Struct. Des. Tall Special Build. 16 (4): 471–486. https://doi.org/10.1002/tal.415.
LATBSDC (Los Angeles Tall Buildings and Structural Design Council). 2017. An alternative procedure for seismic analysis and design of tall buildings located in the Los Angeles region. Los Angeles: LATBSDC.
Li, Q. S., D. K. Liu, J. Q. Fang, A. P. Jeary, and C. K. Wong. 2000. “Damping in buildings: Its neural network model and AR model.” Eng. Struct. 22 (9): 1216–1223. https://doi.org/10.1016/S0141-0296(99)00050-4.
Li, Y., and S. T. Mau. 1991. “A case study of MIMO system identification applied to building seismic records.” Earthquake Eng. Struct. Dyn. 20 (11): 1045–1064. https://doi.org/10.1002/eqe.4290201106.
Lin, B., and A. Papageorgiou. 1989. “Demonstration of torsional coupling caused by closely spaced periods—1984 Morgan Hill earthquake response of the Santa Clara County building.” Earthquake Spectra 5 (3): 539–556. https://doi.org/10.1193/1.1585539.
Malley, J. O., G. Deierlein, H. Krawinkler, J. R. Maffei, M. Pourzanjani, J. Wallace, and J. A. Heintz. 2010. Modeling and acceptance criteria for seismic design and analysis of tall buildings. Richmond, CA: Applied Technology Council.
Marshall, R. D., L. T. Phan, and M. Celebi. 1994. “Full-scale measurement of building response to ambient vibration and the Loma Prieta earthquake.” In Proc., 5th US National Conf. on Earthquake Engineering, 661–770. Oakland, CA: Earthquake Engineering Research Institute.
McVerry, G. 1979. Frequency domain identification of structural models from earthquake records. Pasadena, CA: California Institute of Technology.
Miranda, E. 1991. “Seismic evaluation and upgrading of existing buildings.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of California.
Miranda, E., and S. Taghavi. 2005. “Approximate floor acceleration demands in multistory buildings. I: Formulation.” J. Struct. Eng. 131 (2): 203–211. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:2(203).
Nakagawa, S., and H. Schielzeth. 2013. “A general and simple method for obtaining from generalized linear mixed-effects models.” Methods Ecol. Evol. 4 (2): 133–142. https://doi.org/10.1111/j.2041-210x.2012.00261.x.
Newmark, N. M. 1967. Design criteria for nuclear reactors subjected to earthquake hazards. Urbana, IL: Univ. of Illinois at Urbana Champaigne.
Newmark, N. M. 1972. “Earthquake response analysis of reactor structures.” Nucl. Eng. Des. 20 (2): 303–322. https://doi.org/10.1016/0029-5493(72)90117-3.
Newmark, N. M., and J. F. Hall. 1969. “Seismic design criteria for nuclear reactor facilities.” In Proc., 4th World Conf. on Earthquake Engineering, 37–50. Santiago, Chile: Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas.
NIST. 2012. Soil-structure-interaction for building structures. Gaithersburg, MD: NIST.
PEER (Pacific Earthquake Engineering Center). 2017. Guidelines for performance-based seismic design of tall buildings. Richmond, CA: PEER.
Pinheiro, J., and D. Bates. 2000. Mixed-effects models in S and S-PLUS. New York: Springer.
Satake, N., K. Suda, T. Arakawa, A. Sasaki, and Y. Tamura. 2003. “Damping evaluation using full-scale data of buildings in Japan.” J. Struct. Eng. 129 (4): 470–477. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:4(470).
Smith, R., R. Merello, and M. Willford. 2010. “Intrinsic and supplementary damping in tall buildings.” Proc. Inst. Civ. Eng. Struct. Build. 163 (2): 111–118. https://doi.org/10.1680/stbu.2010.163.2.111.
Spence, S. M. J., and A. Kareem. 2014. “Tall buildings and damping: A concept-based data-driven model.” J. Struct. Eng. 140 (5): 04014005. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000890.
Stagner, J. R., and G. Hart. 1971. Damping estimation and digital filtering applied to structural motion studies. Los Angeles: Univ. of California.
Stevenson, J. D. 1980. “Structural damping values as a function of dynamic response stress and deformation levels.” Nucl. Eng. Des. 60 (2): 211–237. https://doi.org/10.1016/0029-5493(80)90238-1.
Tamura, Y. 2012. “Amplitude dependency of damping in buildings and critical tip drift ratio.” Int. J. High-Rise Build. 1 (1): 1–13.
Tamura, Y. 2013. “Damping in buildings and estimation techniques.” In Chap. 13 in Advanced structural wind engineering, 347–376. Tokyo: Springer.
Tamura, Y., K. Suda, and A. Sasaki. 2000. “Damping in buildings for wind resistant design.” In Proc., Int. Symp. on Wind and Structures for the 21st Century, 115–130. Daejeon, South Korea: Techno Press.
Tamura, Y., and S. Suganuma. 1996. “Evaluation of amplitude-dependent damping and natural frequency of buildings during strong winds.” J. Wind Eng. Ind. Aerodyn. 59 (2–3): 115–130. https://doi.org/10.1016/0167-6105(96)00003-7.
Tanaka, T., S. Yoshizawa, and Y. Osawa. 1969. “Period and damping of vibration in actual buildings during earthquakes.” Bull. Earthquake Res. Institute 47 (6): 1073–1092.
Veletsos, A. S. 1977. “Dynamics of structure-foundation systems.” In Structural and geotechnical mechanics, 333–361. Upper Saddle River, NJ: Prentice-Hall.
Veletsos, A. S., and J. Meek. 1974. “Dynamic behaviour of building-foundation systems.” Earthquake Eng. Struct. Dyn. 3 (2): 121–138. https://doi.org/10.1002/eqe.4290030203.
Werner, S. D., A. Nisar, and J. L. Beck. 1992. “Assessment of UBC seismic design provisions using recorded building motions.” In Proc., 10th World Conf. on Earthquake Engineering, 5723–5726. Rotterdam, Netherlands: A.A. Balkema.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 147 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 7, 2019
Accepted: Aug 10, 2020
Published online: Oct 24, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 24, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.