Abstract
In the structural design of tall buildings, peak factors have been widely used to predict mean extreme responses of tall buildings under wind excitations. Vanmarcke’s peak factor is directly related to an explicit measure of structural reliability against a Gaussian response process. We review the use of this factor for time-variant reliability design by comparing it to the conventional Davenport’s peak factor. Based on the asymptotic theory of statistical extremes, a new closed-form peak factor, the so-called Gamma peak factor, can be obtained for a non-Gaussian resultant response characterized by a Rayleigh distribution process. Using the Gamma peak factor, a combined peak factor method was developed for predicting the expected maximum resultant responses of a building undergoing lateral-torsional vibration. The effects of the standard deviation ratio of two sway components and the inter-component correlation on the evaluation of peak resultant response were also investigated. Utilizing wind tunnel data derived from synchronous multi-pressure measurements, we carried out a wind-induced time history response analysis of the Commonwealth Advisory Aeronautical Research Council (CAARC) standard tall building to validate the applicability of the Gamma peak factor to the prediction of the peak resultant acceleration. Results from the building example indicated that the use of the Gamma peak factor enables accurate predictions to be made of the mean extreme resultant acceleration responses for dynamic serviceability performance design of modern tall buildings.
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References
Cermak, J.E., 2003. Wind-tunnel development and trends in applications to civil engineering. Journal of Wind Engineering and Industrial Aerodynamics, 91:355–370. [doi:10.1016/S0167-6105(02)00396-3]
Chen, X., Huang, G., 2009. Evaluation of peak resultant response for wind-excited tall buildings. Engineering Structures, 31:858–868. [doi:10.1016/j.engstruct.2008.11.021]
Cheng, P.W., van Bussel, G.J.W., van Kuik, G.A.M., Vugts, J.H., 2003. Reliability-based design methods to determine the extreme response distribution of offshore wind turbines. Wind Energy, 6:1–22. [doi:10.1002/we.80]
Clauset, A., Shalizi, C.R.,, Newman, M.E.J., 2009. Power-law distributions in empirical data. SIAM Review, 51(4): 661–703. [doi:10.1137/070710111]
Davenport, A.G., 1964. Note on the Distribution of the Largest Value of a Random Function with Application to Gust Loading. Proceedings, Institution of Civil Engineering, 28(2):187–196.
Fujimura, K., Der Kiureghian, A., 2007. Tail-equivalent linearization method for nonlinear random vibration. Probabilistic Engineering Mechanics, 22:63–76. [doi:10.1016/j.probengmech.2006.08.001]
Grigoriu, M., 1984. Crossing of non-Gaussian translation process. Journal of Engineering Mechanics, ASCE, 110(4):610–620.
Gurley, K.R., Tognarelli, M.A., Kareem, A., 1997. Analysis and simulation tools for wind engineering. Probabilistic Engineering Mechanics, 12(1):9–31. [doi:10.1016/S0266-8920(96)00010-0]
Holmes, J.D., Cochran, L.S., 2003. Probability distribution of extreme pressure coefficients. Journal of Wind Engineering and Industrial Aerodynamics, 91:893–901. [doi:10.1016/S0167-6105(03)00019-9]
Hong Kong Code of Practice, 2004. Code of Practice on Wind Effects in Hong Kong. Buildings Department, Hong Kong.
Huang, M.F., Chan, C.M., Kwok, K.C.S., Hitchcock, P.A., 2009a. Cross correlation of modal responses of tall buildings in wind-induced lateral-torsional motion. Journal of Engineering Mechanics, ASCE, 135(8):802–812. [doi:10.1061/(ASCE)0733-9399(2009)135:8(802)]
Huang, M.F., Chan, C.M., Kwok, K.C.S., Lou, W.J., 2009b. A Peak Factor for Predicting Non-Gaussian Peak Resultant Response of Wind-Excited Tall Buildings. Proc. the Seventh Asia-Pacific Conference on Wind Engineering, Taipei, Taiwan.
Isyumov, N., Fediw, A.A., Colaco, J., Banavalkar, P.V., 1992. Performance of a tall building under wind action. Journal of Wind Engineering and Industrial Aerodynamics, 41–44: 1053–1064. [doi:10.1016/0167-6105(92)90112-N]
Kareem, A., 1987. Wind effects on structures: a probabilistic viewpoint. Probabilistic Engineering Mechanics, 2:166–200.
Li, Q.S., Zhi, C.H., Duan, Y.D., Kao, C.S., Su, S.C., 2010. Full-scale measurements and analysis of wind-induced response of Taipei 101 Tower. Journal of Building Structures, 31(3):24–31 (in Chinese).
Melbourne, W.H., 1980. Comparison of measurements of the CAARC standard tall building model in simulated model wind flows. Journal of Wind Engineering and Industrial Aerodynamics, 6:78–88. [doi:10.1016/0167-6105(80)90023-9]
Melbourne, W.H., Palmer, T.R., 1992. Accelerations and comfort criteria for buildings undergoing complex motions. Journal of Wind Engineering and Industrial Aerodynamics, 41–44:105–116. [doi:10.1016/0167-6105(92)90398-T]
Ochi, M.K., 1998. Probability distribution of peaks and troughs of non-Gaussian random process. Probabilistic Engineering Mechanics, 13(4):291–298. [doi:10.1016/0266-8920(94)90017-5]
Sadek, F., Simiu, E., 2002. Peak non-Gaussian wind effects for database-assisted low-rise building design. Journal of Engineering Mechanics, ASCE, 128(5):530–539. [doi:10.1061/(ASCE)0733-9399(2002)128:5(530)]
Sun, B.N., Chen, S.F., 2000. Wind-induced stochastic response of controlled tall buildings by complex-mode. Journal of Zhejiang University SCIENCE, 1(4):421–426.
Tieleman, H.W., Ge, Z., Hajj, M.R., 2007. Theoretically estimated peak wind loads. Journal of Wind Engineering and Industrial Aerodynamics, 95:113–132. [doi:10.1016/j.jweia.2006.05.004]
Vanmarcke, E.H., 1972. Properties of spectral moments with applications to random vibration. Journal of Engineering Mechanics, 98(EM2):425–446.
Vanmarcke, E.H., 1975. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics, 42:215–220.
Wardlaw, R.L., Moss, G.F., 1970. A Standard Tall Building Model for the Comparison of Simulated Natural Winds in Wind Tunnels. Report CC-662 Tech. 25, Commonwealth Advisory Aeronautical Research Council, UK.
Winterstein, S.R., 1988. Nonlinear vibration models for extremes and fatigue. Journal of Engineering Mechanics, ASCE, 114(10):1772–1790.
Xie, J.M., Haskett, T., Kala, S., Irwin, P., 2007. Review of Rigid Building Model Studies and Their Further Improvements. Proc. 12th International Conference on Wind Engineering, Cairns, Australia, p.1175–1182.
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Project supported by the National Natural Science Foundation of China (No. 51008275), and the China Postdoctoral Science Foundation (No. 201104736)
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Huang, Mf., Chan, Cm., Lou, Wj. et al. Statistical extremes and peak factors in wind-induced vibration of tall buildings. J. Zhejiang Univ. Sci. A 13, 18–32 (2012). https://doi.org/10.1631/jzus.A1100136
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DOI: https://doi.org/10.1631/jzus.A1100136
Key words
- Level-crossing rate (LCR)
- Wind-induced vibration
- Mean extreme response
- Combined resultant process
- Peak factor method