Technical Papers
Jul 16, 2019

Generalized Wind Loading Chain: Time-Frequency Modeling Framework for Nonstationary Wind Effects on Structures

Publication: Journal of Structural Engineering
Volume 145, Issue 10

Abstract

This study proposes a generalized wind loading chain to describe a complete relationship among wind, force, and response induced by nonstationary wind events such as tropical storms or downbursts to complement the Davenport wind loading chain. In the proposed chain, nonstationary winds are represented as a nonstationary model in terms of the time-varying mean and nonstationary fluctuating wind components similar to a stationary model involving the mean and stationary fluctuating wind components in the Davenport’s stationary wind loading chain. Specifically, the five chain components of the fluctuating wind in the Davenport’s chain such as gustiness of wind, aerodynamic transfer/admittance, aerodynamic force, structural transfer/admittance, and response statistics are recast as time-dependent counterparts in the time-frequency domain to capture nonstationary winds effects on structures. These components are formulated using the evolutionary power spectral density (EPSD) as a form of time-frequency representation that captures salient features of nonstationary tropical storm and downburst winds. As an alternative, a wavelet-based representation is also offered. A numerical example demonstrates the estimation of nonstationary response using the proposed generalized chain. For possible codification of nonstationary wind effects on structures, a preliminary examination suggests that the extreme nonstationary response computed by the generalized chain may be conveniently meshed with the gust front factor or its generalized version frameworks. This may facilitate a rapid shift in the current design approach from stationary to nonstationary winds.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors wish to acknowledge the financial supports from the US National Science Foundation (CMMI 1462076), and the National Natural Science Foundation of China (No. 51308244). Any opinions and concluding remarks presented in this paper are entirely those of the authors.

References

Abd-Elaal, E. S., J. E. Mills, and X. Ma. 2014. “Empirical models for predicting unsteady-state downburst wind speeds.” J. Wind Eng. Ind. Aerodyn. 129 (Jun): 49–63. https://doi.org/10.1016/j.jweia.2014.03.011.
Aboshosha, H., A. Elawady, A. El Ansary, and A. El Damatty. 2016. “Review on dynamic and quasi-static buffeting response of transmission lines under synoptic and non-synoptic winds.” Eng. Struct. 112 (Apr): 23–46. https://doi.org/10.1016/j.engstruct.2016.01.003.
Aboshosha, H., T. Mara, and P. Case. 2017. “New framework for estimating thunderstorm design speed.” In Proc., 13th Americas Conf. on Wind Engineering (13ACWE). Gainesville, FL: Univ. of Florida.
ASCE. 2016. Minimum design loads for buildings and other structures. ASCE 7. Reston, VA: ASCE.
Bendat, J. S., and A. G. Piersol. 2010. Random data: Analysis and measurement procedures. New York: Wiley.
Benowitz, B. A., M. D. Shields, and G. Deodatis. 2015. “Determining evolutionary spectra from non-stationary autocorrelation functions.” Probab. Eng. Mech. 41 (Jul): 73–88. https://doi.org/10.1016/j.probengmech.2015.06.004.
Butler, K., S. Cao, A. Kareem, Y. Tamura, and S. Ozono. 2010. “Surface pressure and wind load characteristics on prisms immersed in a simulated transient gust front flow field.” J. Wind Eng. Ind. Aerodyn. 98 (6–7): 299–316. https://doi.org/10.1016/j.jweia.2009.11.003.
Canor, T., L. Caracoglia, and V. Denoël. 2016. “Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization.” Probab. Eng. Mech. 46 (Oct): 1–17. https://doi.org/10.1016/j.probengmech.2016.07.001.
Cao, S., A. Nishi, H. Kikugawa, and Y. Matsuda. 2002. “Reproduction of wind velocity history in a multiple fan wind tunnel.” J. Wind Eng. Ind. Aerodyn. 90 (12): 1719–1729. https://doi.org/10.1016/S0167-6105(02)00282-9.
Chay, M. T., F. Albermani, and R. Wilson. 2006. “Numerical and analytical simulation of downburst wind loads.” Eng. Struct. 28 (2): 240–254. https://doi.org/10.1016/j.engstruct.2005.07.007.
Chay, M. T., and C. W. Letchford. 2002. “Pressure distributions on a cube in a simulated thunderstorm downburst. Part A: Stationary downburst observations.” J. Wind Eng. Ind. Aerodyn. 90 (7): 711–732. https://doi.org/10.1016/S0167-6105(02)00158-7.
Chen, J., M. C. H. Hui, and Y. L. Xu. 2007. “A comparative study of stationary and non-stationary wind models using field measurements.” Boundary Layer Meteorol. 122 (1): 105–121. https://doi.org/10.1007/s10546-006-9085-1.
Chen, L. 2006. “Vector time-varying autoregressive (TVAR) models and their application to downburst wind speeds.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Texas Tech Univ.
Chen, L., and C. W. Letchford. 2004a. “A deterministic-stochastic hybrid model of downbursts and its impact on a cantilevered structure.” Eng. Struct. 26 (5): 619–629. https://doi.org/10.1016/j.engstruct.2003.12.009.
Chen, L., and C. W. Letchford. 2004b. “Parametric study on the along-wind response of the CAARC building to downbursts in the time domain.” J. Wind Eng. Ind. Aerodyn. 92 (9): 703–724. https://doi.org/10.1016/j.jweia.2004.03.001.
Chen, L., and C. W. Letchford. 2005. “Proper orthogonal decomposition of two vertical profiles of full-scale nonstationary downburst wind speeds [lzcl].” J. Wind Eng. Ind. Aerodyn. 93 (3): 187–216. https://doi.org/10.1016/j.jweia.2004.11.004.
Chen, L., and C. W. Letchford. 2006. “Multi-scale correlation analyses of two lateral profiles of full-scale downburst wind speeds.” J. Wind Eng. Ind. Aerodyn. 94 (9): 675–696. https://doi.org/10.1016/j.jweia.2006.01.021.
Chen, L., and C. W. Letchford. 2007. “Numerical simulation of extreme winds from thunderstorm downbursts.” J. Wind Eng. Ind. Aerodyn. 95 (9–11): 977–990. https://doi.org/10.1016/j.jweia.2007.01.021.
Chen, X. 2008. “Analysis of alongwind tall building response to transient nonstationary winds.” J. Struct. Eng. 134 (5): 782–791. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:5(782).
Chen, X. 2015. “Analysis of multimode coupled buffeting response of long-span bridges to nonstationary winds with force parameters from stationary wind.” J. Struct. Eng. 141 (4): 04014131. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001078.
Chen, X., and A. Kareem. 2002. “Advances in modeling of aerodynamic forces on bridge decks.” J. Eng. Mech. 128 (11): 1193–1205. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1193).
Cheng, J., J. J. Jiang, R. C. Xiao, and H. F. Xiang. 2002. “Nonlinear aerostatic stability analysis of Jiang Yin suspension bridge.” Eng. Struct. 24 (6): 773–781. https://doi.org/10.1016/S0141-0296(02)00006-8.
Choi, E. C. C. 2000. “Wind characteristics of tropical thunderstorms.” J. Wind Eng. Ind. Aerodyn. 84 (2): 215–226. https://doi.org/10.1016/S0167-6105(99)00054-9.
Conte, J. P., and B. F. Peng. 1996. “An explicit closed-form solution for linear systems subjected to nonstationary random excitation.” Probab. Eng. Mech. 11 (1): 37–50. https://doi.org/10.1016/0266-8920(95)00026-7.
Corotis, R. B., and E. H. Vanmarcke. 1975. “Time-dependent spectral content of system response.” J. Eng. Mech. Div. 101 (5): 623–636.
Corotis, R. B., E. H. Vanmarcke, and C. A. Cornell. 1972. “First passage of nonstationary random processes.” J. Eng. Mech. Div. 98 (2): 401–414.
Davenport, A. G. 1967. “Gust loading factors.” J. Struct. Eng. 93 (3): 11–34.
Deodatis, G. 1996. “Non-stationary stochastic vector processes: Seismic ground motion applications.” Probab. Eng. Mech. 11 (3): 149–167. https://doi.org/10.1016/0266-8920(96)00007-0.
Emanuel, K., S. Ravela, E. Vivant, and C. Risi. 2006. “A statistical deterministic approach to hurricane risk assessment.” Bull. Am. Meteorol. Soc. 87 (3): 299–314. https://doi.org/10.1175/BAMS-87-3-299.
Fujita, T. T. 1981. “Tornadoes and downbursts in the context of generalized planetary scales.” J. Atmos. Sci. 38 (8): 1511–1534. https://doi.org/10.1175/1520-0469(1981)038%3C1511:TADITC%3E2.0.CO;2.
Gunter, W. S., and J. L. Schroeder. 2015. “High-resolution full-scale measurements of thunderstorm outflow winds.” J. Wind Eng. Ind. Aerodyn. 138 (Mar): 13–26. https://doi.org/10.1016/j.jweia.2014.12.005.
Gurley, K., and A. Kareem. 1999. “Applications of wavelet transforms in earthquake, wind and ocean engineering.” Eng. Struct. 21 (2): 149–167. https://doi.org/10.1016/S0141-0296(97)00139-9.
Hammond, J. K. 1973. “Evolutionary spectra in random vibrations.” J. R. Stat. Soc. Ser. B (Methodol.) 35 (2): 167–188. https://doi.org/10.1111/j.2517-6161.1973.tb00950.x.
Hao, J., and T. Wu. 2017. “Nonsynoptic wind-induced transient effects on linear bridge aerodynamics.” J. Eng. Mech. 143 (9): 04017092. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001313.
Hjelmfelt, M. R. 1988. “Structure and life cycle of microburst outflows observed in Colorado.” J. Appl. Meteorol. 27 (8): 900–927. https://doi.org/10.1175/1520-0450(1988)027%3C0900:SALCOM%3E2.0.CO;2.
Holmes, J. D., and S. E. Oliver. 2000. “An empirical model of a downburst.” Eng. Struct. 22 (9): 1167–1172. https://doi.org/10.1016/S0141-0296(99)00058-9.
Howell, L. J., and Y. K. Lin. 1971. “Response of flight vehicles to nonstationary atmospheric turbulence.” AIAA J. 9 (11): 2201–2207. https://doi.org/10.2514/3.50026.
Hu, L., and Y. L. Xu. 2014. “Extreme value of typhoon-induced non-stationary buffeting response of long-span bridges.” Probab. Eng. Mech. 36 (Apr): 19–27. https://doi.org/10.1016/j.probengmech.2014.02.002.
Hu, L., Y. L. Xu, and W. F. Huang. 2013. “Typhoon-induced non-stationary buffeting response of long-span bridges in complex terrain.” Eng. Struct. 57 (Dec): 406–415. https://doi.org/10.1016/j.engstruct.2013.09.044.
Hu, L., Y. L. Xu, Q. Zhu, A. Guo, and A. Kareem. 2017a. “Tropical storm-induced buffeting response of long-span bridges: Enhanced nonstationary buffeting force model.” J. Struct. Eng. 143 (6): 04017027. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001745.
Hu, L., Z. Xu, Y. L. Xu, L. Li, and A. Kareem. 2017b. “Error analysis of spatially varying seismic ground motion simulation by spectral representation method.” J. Eng. Mech. 143 (9): 04017083. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001282.
Huang, G., and X. Chen. 2009. “Wavelets-based estimation of multivariate evolutionary spectra and its application to nonstationary downburst winds.” Eng. Struct. 31 (4): 976–989. https://doi.org/10.1016/j.engstruct.2008.12.010.
Huang, G., Y. Su, A. Kareem, and H. Liao. 2016. “Time-frequency analysis of nonstationary process based on multivariate empirical mode decomposition.” J. Eng. Mech. 142 (1): 04015065. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000975.
Huang, G., H. Zheng, Y. Xu, and Y. Li. 2015. “Spectrum models for nonstationary extreme winds.” J. Struct. Eng. 141 (10): 04015010. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001257.
Huang, W. F., and Y. L. Xu. 2013. “Prediction of typhoon design wind speed and profile over complex terrain.” Struct. Eng. Mech. 45 (1): 1–18. https://doi.org/10.12989/sem.2013.45.1.001.
Igusa, T. 1989. “Characteristics of response to nonstationary white noise: Theory.” J. Eng. Mech. 115 (9): 1904–1918. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:9(1904).
Isyumov, N. 2012. “Alan G. Davenport’s mark on wind engineering.” J. Wind Eng. Ind. Aerodyn. 104–106 (May–Jul): 12–24. https://doi.org/10.1016/j.jweia.2012.02.007.
Jangid, R. S. 2004. “Response of SDOF system to non-stationary earthquake excitation.” Earthquake Eng. Struct. Dyn. 33 (15): 1417–1428. https://doi.org/10.1002/eqe.409.
Jesson, M., M. Sterling, C. Letchford, and M. Haines. 2015. “Aerodynamic forces on generic buildings subject to transient, downburst-type winds.” J. Wind Eng. Ind. Aerodyn. 137 (Feb): 58–68. https://doi.org/10.1016/j.jweia.2014.12.003.
Kareem, A. 2009. “The changing dynamics of aerodynamics: New frontiers.” In Proc., 7th Asia–Pacific Conf. on Wind Engineering (APCWQ-VII). Taiwan, Republic of China: Tamkang Univ.
Kareem, A., and T. Kijewski. 2002. “Time-frequency analysis of wind effects on structures.” J. Wind Eng. Ind. Aerodyn. 90 (12–15): 1435–1452. https://doi.org/10.1016/S0167-6105(02)00263-5.
Kareem, A., T. Kijewski, and C. E. Smith. 1999. “Analysis and performance of offshore platforms in hurricanes.” Wind Struct. Int. J. 2 (1): 1–23. https://doi.org/10.12989/was.1999.2.1.001.
Kareem, A., and T. Wu. 2013. “Wind-induced effects on bluff bodies in turbulent flows: Nonstationary, non-Gaussian and nonlinear features.” J. Wind Eng. Ind. Aerodyn. 122 (Nov): 21–37. https://doi.org/10.1016/j.jweia.2013.06.002.
Kawai, H. 2000. “Response of structure during a typhoonwind.” In Proc., 8th ASCE Specialty Conf. on Probabilistic Mechanics and Structural Reliability. Reston, VA: ASCE.
Kijewski-Correa, T., and A. Kareem. 2003. “Wavelet transforms for system identification in civil engineering.” Comput. Aided Civ. Infrastruct. Eng. 18 (5): 339–355. https://doi.org/10.1111/1467-8667.t01-1-00312.
Kim, J., and H. Hangan. 2007. “Numerical simulations of impinging jets with application to downbursts.” J. Wind Eng. Ind. Aerodyn. 95 (4): 279–298. https://doi.org/10.1016/j.jweia.2006.07.002.
Kong, F., and J. Li. 2015. “Wavelet-expansion-based stochastic response of chain-like MDOF structures.” J. Sound Vib. 359 (Dec): 136–153. https://doi.org/10.1016/j.jsv.2015.09.011.
Kwon, D. K., and A. Kareem. 2009. “Gust-front factor: A new framework for wind load effects on structures.” J. Struct. Eng. 135 (6): 717–732. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:6(717).
Kwon, D. K., and A. Kareem. 2013. “Generalized gust-front factor: A computational framework for wind load effects.” Eng. Struct. 48 (Mar): 635–644. https://doi.org/10.1016/j.engstruct.2012.12.024.
Langley, R. S. 1987. “On quasi-stationary approximations to non-stationary random vibration.” J. Sound. Vib. 113 (2): 365–375. https://doi.org/10.1016/S0022-460X(87)80222-5.
Letchford, C. W., and M. T. Chay. 2002. “Pressure distributions on a cube in a simulated thunderstorm downburst. Part B: Moving downburst observations.” J. Wind Eng. Ind. Aerodyn. 90 (7): 733–753. https://doi.org/10.1016/S0167-6105(02)00163-0.
Li, C., Q. S. Li, Y. Q. Xiao, and J. P. Ou. 2012. “A revised empirical model and CFD simulations for 3D axisymmetric steady-state flows of downbursts and impinging jets.” J. Wind Eng. Ind. Aerodyn. 102 (Mar): 48–60. https://doi.org/10.1016/j.jweia.2011.12.004.
Li, J., and J. Chen. 2009. Stochastic dynamics of structures. Singapore: Wiley.
Li, L., A. Kareem, J. Hunt, Y. Xiao, C. Zhou, and L. Song. 2015. “Turbulence spectra for boundary-layer winds in tropical cyclones: A conceptual framework and field measurements at coastlines.” Boundary Layer Meteorol. 154 (2): 243–263. https://doi.org/10.1007/s10546-014-9974-7.
Li, Y., J. P. Conte, and M. Barbato. 2016. “Influence of time-varying frequency content in earthquake ground motions on seismic response of linear elastic systems.” Earthquake Eng. Struct. Dyn. 45 (8): 1271–1291. https://doi.org/10.1002/eqe.2707.
Li, Y. S., and A. Kareem. 1991. “Simulation of multivariate nonstationary random-processes by FFT.” J. Eng. Mech. 117 (5): 1037–1058. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:5(1037).
Li, Y. S., and A. Kareem. 1995. “Stochastic decomposition and application to probabilistic dynamics.” J. Eng. Mech. 121 (1): 162–174. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:1(162).
Liang, J., S. R. Chaudhuri, and M. Shinozuka. 2007. “Simulation of nonstationary stochastic processes by spectral representation.” J. Eng. Mech. 133 (6): 616–627. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:6(616).
Lin, J. H. 2004. Pseudo excitation method in random vibration. Beijing: Science Press.
Lombardo, F. T., D. A. Smith, J. L. Schroeder, and K. C. Mehta. 2014. “Thunderstorm characteristics of importance to wind engineering.” J. Wind Eng. Ind. Aerodyn. 125 (Feb): 121–132. https://doi.org/10.1016/j.jweia.2013.12.004.
McCullough, M., D. K. Kwon, A. Kareem, and L. Wang. 2014. “Efficacy of averaging interval for nonstationary winds.” J. Eng. Mech. 140 (1): 1–19. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000641.
Mélard, G., and A. H. D. Schutter. 1989. “Contributions to evolutionary spectral theory.” J. Time Ser. Anal. 10 (1): 41–63. https://doi.org/10.1111/j.1467-9892.1989.tb00014.x.
Michaelov, G., L. D. Lutes, and S. Sarkani. 2001. “Extreme value of response to nonstationary excitation.” J. Eng. Mech. 127 (4): 352–363. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(352).
NatHaz Modeling Laboratory. 2007. “NatHaz gust-front factor.” Accessed August 14, 2018. http://gff.ce.nd.edu.
Peng, L., G. Huang, X. Chen, and Q. Yang. 2018. “Evolutionary spectra-based time-varying coherence function and application in structural response analysis to downburst winds.” J. Struct. Eng. 144 (7): 04018078. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002066.
Priestley, M. B. 1965. “Evolutionary spectra and non-stationary processes.” J. R. Stat. Soc. Ser. B Stat. (Methodol.) 27 (2): 204–237. https://doi.org/10.1111/j.2517-6161.1965.tb01488.x.
Priestley, M. B. 1966. “Design relations for non-stationary processes.” J. R. Stat. Soc. Ser. B Stat. (Methodol.) 28 (1): 228–240.
Solari, G., and P. De Gaetano. 2018. “Dynamic response of structures to thunderstorm outflows: Response spectrum technique vs time-domain analysis.” Eng. Struct. 176 (Dec): 188–207. https://doi.org/10.1016/j.engstruct.2018.08.062.
Solari, G., P. De Gaetano, and M. P. Repetto. 2015. “Thunderstorm response spectrum: Fundamentals and case study.” J. Wind Eng. Ind. Aerodyn. 143 (Aug): 62–77. https://doi.org/10.1016/j.jweia.2015.04.009.
Song, L. L., W. C. Chen, B. L. Wang, S. Q. Zhi, and A. J. Liu. 2016. “Characteristics of wind profiles in the landfalling typhoon boundary layer.” J. Wind Eng. Ind. Aerodyn. 149 (Feb): 77–88. https://doi.org/10.1016/j.jweia.2015.11.008.
Spanos, P. D., and G. Failla. 2004. “Evolutionary spectra estimation using wavelets.” J. Eng. Mech. 130 (8): 952–960. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:8(952).
Spanos, P. D., and G. Failla. 2005. “Wavelets: Theoretical concepts and vibrations related applications.” Shock Vib. Digest 37 (5): 359–375. https://doi.org/10.1177/0583102405055441.
Spanos, P. D., F. Kong, J. Li, and I. A. Kougioumtzoglou. 2016. “Harmonic wavelets based excitation-response relationships for linear systems: A critical perspective.” Probab. Eng. Mech. 44 (Apr): 163–173. https://doi.org/10.1016/j.probengmech.2015.09.021.
Su, Y., G. Huang, and Y.-l. Xu. 2015. “Derivation of time-varying mean for non-stationary downburst winds.” J. Wind Eng. Ind. Aerodyn. 141 (Jun): 39–48. https://doi.org/10.1016/j.jweia.2015.02.008.
Vickery, P. J., F. J. Masters, M. D. Powell, and D. Wadhera. 2009a. “Hurricane hazard modeling: The past, present, and future.” J. Wind Eng. Ind. Aerodyn. 97 (7–8): 392–405. https://doi.org/10.1016/j.jweia.2009.05.005.
Vickery, P. J., D. Wadhera, M. D. Powell, and Y. Chen. 2009b. “A hurricane boundary layer and wind field model for use in engineering applications.” J. Appl. Meteorol. Climatol. 48 (2): 381–405. https://doi.org/10.1175/2008JAMC1841.1.
Vicroy, D. D. 1992. “Assessment of microburst models for downdraft estimation.” J. Aircr. 29 (6): 1043–1048. https://doi.org/10.2514/3.46282.
Wang, H., T. Wu, T. Tao, A. Li, and A. Kareem. 2016. “Measurements and analysis of non-stationary wind characteristics at Sutong bridge in Typhoon Damrey.” J. Wind Eng. Ind. Aerodyn. 151 (Apr): 100–106. https://doi.org/10.1016/j.jweia.2016.02.001.
Wang, J., L. Fan, S. Qian, and J. Zhou. 2002. “Simulations of non-stationary frequency content and its importance to seismic assessment of structures.” Earthquake Eng. Struct. Dyn. 31 (4): 993–1005. https://doi.org/10.1002/eqe.134.
Wang, L., and A. Kareem. 2004. “Modeling of non-stationary winds in gust-fronts.” In Proc., 9th ASCE Joint Specialty Conf. on Probabilistic Mechanics and Structural Reliability. CD-ROM. Reston, VA: ASCE.
Wang, L., M. McCullough, and A. Kareem. 2014. “Modeling and simulation of nonstationary processes utilizing wavelet and Hilbert transforms.” J. Eng. Mech. 140 (2): 345–360. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000666.
Wood, G. S., K. C. S. Kwok, N. A. Motteram, and D. F. Fletcher. 2001. “Physical and numerical modelling of thunderstorm downbursts.” J. Wind Eng. Ind. Aerodyn. 89 (6): 535–552. https://doi.org/10.1016/S0167-6105(00)00090-8.
Xu, Y. L., and J. Chen. 2004. “Characterizing nonstationary wind speed using empirical mode decomposition.” J. Struct. Eng. 130 (6): 912–920. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:6(912).
Yeh, C. H., and Y. K. Wen. 1990. “Modeling of nonstationary ground motion and analysis of inelastic structural response.” Struct. Saf. 8 (1–4): 281–298. https://doi.org/10.1016/0167-4730(90)90046-R.
Zhang, Z. C., J. H. Lin, Y. H. Zhang, Y. Zhao, W. P. Howson, and F. W. Williams. 2010. “Non-stationary random vibration analysis for train-bridge systems subjected to horizontal earthquakes.” Eng. Struct. 32 (11): 3571–3582. https://doi.org/10.1016/j.engstruct.2010.08.001.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 145Issue 10October 2019

History

Received: Jun 19, 2018
Accepted: Jan 15, 2019
Published online: Jul 16, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 16, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Ahsan Kareem, Dist.M.ASCE [email protected]
Robert M. Moran Professor, NatHaz Modeling Laboratory, Dept. of Civil and Environmental Engineering and Earth Sciences, Univ. of Notre Dame, Notre Dame, IN 46556. Email: [email protected]
Ph.D. Student, NatHaz Modeling Laboratory, Dept. of Civil and Environmental Engineering and Earth Sciences, Univ. of Notre Dame, Notre Dame, IN 46556 (corresponding author). Email: [email protected]
Yanlin Guo, A.M.ASCE [email protected]
Assistant Professor, Dept. of Civil and Environmental Engineering, Colorado State Univ., Fort Collins, CO 80523. Email: [email protected]
Dae-Kun Kwon, M.ASCE [email protected]
Research Assistant Professor, NatHaz Modeling Laboratory, Dept. of Civil and Environmental Engineering and Earth Sciences, Univ. of Notre Dame, Notre Dame, IN 46556. Email: [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share