Monitoring-Based Fatigue Reliability Assessment of Steel Bridges: Analytical Model and Application
Publication: Journal of Structural Engineering
Volume 136, Issue 12
Abstract
A fatigue reliability model which integrates the probability distribution of hot spot stress range with a continuous probabilistic formulation of Miner’s damage cumulative rule is developed for fatigue life and reliability evaluation of steel bridges with long-term monitoring data. By considering both the nominal stress obtained by measurements and the corresponding stress concentration factor (SCF) as random variables, a probabilistic model of the hot spot stress is formulated with the use of the curve and the Miner’s rule, which is then used to evaluate the fatigue life and failure probability with the aid of structural reliability theory. The proposed method is illustrated using the long-term strain monitoring data from the instrumented Tsing Ma Bridge. A standard daily stress spectrum accounting for highway traffic, railway traffic, and typhoon effects is derived by use of the monitoring data. Then global and local finite element models (FEMs) of the bridge are developed for numerically calculating the SCFs at fatigue-susceptible locations, while the stochastic characteristics of SCF for a typical welded T-joint are obtained by full-scale model experiments of a railway beam section of the bridge. A multimodal probability density function (PDF) of the stress range is derived from the monitoring data using the finite mixed Weibull distributions in conjunction with a hybrid parameter estimation algorithm. The failure probability and reliability index versus fatigue life are achieved from the obtained joint PDF of the hot spot stress in terms of the nominal stress and SCF random variables.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work described in this paper was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. UNSPECIFIEDPolyU 5241/05E), and partially by a grant from The Hong Kong Polytechnic University through the Development of Niche Areas Program (Project No. UNSPECIFIEDNo. 1-BB68). The writers also wish to thank the engineers at the Highways Department of the Hong Kong SAR Government for their support throughout the work.
References
AISC. (1986). Load and resistance factor design specifications for structural steel buildings, American Institute of Steel Construction, Chicago.
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, 19(6), 716–723.
Albrecht, P., and Lenwari, A. (2009). “Variable-amplitude fatigue strength of structural steel bridge details: Review and simplified model.” J. Bridge Eng., 14(4), 226–237.
American Welding Society (AWS). (1998). “Structural welding code-steel.” ANSI/AWS D1.1-98, Miami.
Basquin, O. H. (1910). “Exponential law of endurance tests.” Proc., ASTM, Vol. 10, ASTM, West Conshohocken, Pa., 625–630.
British Standards Institution (BSI). (1980). “Steel, concrete and composite bridges. Part 10: Code of practice for fatigue.” BS5400, London.
Brownjohn, J. M. W. (2007). “Structural health monitoring of civil infrastructure.” Philos. Trans. R. Soc. London, Ser. A, 365(1851), 589–622.
Byers, W. G., Marley, M. J., Mohammadi, J., Nielsen, R. J., and Sarkani, S. (1997a). “Fatigue reliability reassessment procedures: State-of-the-art paper.” J. Struct. Eng., 123(3), 271–276.
Byers, W. G., Marley, M. J., Mohammadi, J., Nielsen, R. J., and Sarkani, S. (1997b). “Fatigue reliability reassessment applications: State-of-the-art paper.” J. Struct. Eng., 123(3), 277–285.
Chan, T. H. T., Zhou, T. Q., Li, Z. X., and Guo, L. (2005). “Hot spot stress approach for Tsing Ma Bridge fatigue evaluation under traffic using finite element method.” Struct. Eng. Mech., 19(3), 261–279.
Chiew, S. P., Lie, S. T., Lee, C. K., and Huang, Z. W. (2004). “Fatigue performance of cracked tubular T joints under combined loads. I: Experimental.” J. Struct. Eng., 130(4), 562–571.
Cho, H. N., Lim, J. K., and Choi, H. H. (2001). “Reliability-based fatigue failure analysis for causes assessment of a collapsed steel truss bridge.” Eng. Failure Anal., 8(4), 311–324.
Connor, R. J., and Fisher, J. W. (2006). “Consistent approach to calculating stresses for fatigue design of welded rib-to-web connections in steel orthotropic bridge decks.” J. Bridge Eng., 11(5), 517–525.
Crespo-Minguillon, C., and Casas, J. R. (1998). “Fatigue reliability analysis of prestressed concrete bridges.” J. Struct. Eng., 124(12), 1458–1466.
DeWolf, J. T., Lauzon, R. G., and Culmo, M. P. (2002). “Monitoring bridge performance.” Struct. Health Monit., 1(2), 129–138.
Doerk, O., Fricke, W., and Weissenborn, C. (2003). “Comparison of different calculation methods for structural stresses at welded joints.” Int. J. Fatigue, 25(5), 359–369.
Downing, S. D., and Socie, D. F. (1982). “Simple rainflow counting algorithms.” Int. J. Fatigue, 4(1), 31–40.
Duda, R. O., and Hart, P. E. (1973). Pattern classification and scene analysis, Wiley, New York.
European Committee for Standardization (CEN). (1992). “Design of steel structures, part 1.1.” Eurocode 3, Brussels, Belgium.
Fisher, J. W. (1984). Fatigue and fracture in steel bridges: Case studies, Wiley, New York.
Gandhi, P., and Berge, S. (1998). “Fatigue behavior of T-joints: Square chords and circular braces.” J. Struct. Eng., 124(4), 399–404.
Gurney, T. R. (1979). Fatigue of welded structures, 2nd Ed., Cambridge University Press, Cambridge, England.
Imai, K., and Frangopol, D. M. (2002). “System reliability of suspension bridges.” Struct. Safety, 24(2–4), 219–259.
International Institute of Welding (IIW). (2000). “Fatigue design procedures for welded hollow section joints.” IIW Doc. XIII-1804-99/XV-1035-99. Recommendations for IIW subcommision XV-E, Abington Publishing, Cambridge, England.
Kim, S. H., Lee, S. W., and Mha, H. S. (2001). “Fatigue reliability assessment of an existing steel railroad bridge.” Eng. Struct., 23(10), 1203–1211.
Ko, J. M., and Ni, Y. Q. (2005). “Technology developments in structural health monitoring of large-scale bridges.” Eng. Struct., 27(12), 1715–1725.
Lie, S. T., Chiew, S. P., Lee, C. K., and Huang, Z. W. (2004). “Fatigue performance of cracked tubular T joints under combined loads. II: Numerical.” J. Struct. Eng., 130(4), 572–581.
McLachlan, G. J., and Peel, D. (2000). Finite mixture models, Wiley, New York.
Miner, M. A. (1945). “Cumulative damage in fatigue.” J. Appl. Mech. 12(3), 159–164.
Mohammadi, J. (2001). “Input data requirements for fatigue reliability analysis of aging structures.” Proc., Structures Congress and Exposition 2001 (CD-ROM), P. C. Chang, ed., ASCE, Reston, Va.
Mohammadi, J., Guralnick, S. A., and Polepeddi, R. (1998). “Bridge fatigue life estimation from field data.” Pract. Period. Struct. Des. Constr., 3(3), 128–133.
Morgan, M. R., and Lee, M. M. K. (1998a). “Parametric equations for distributions of stress concentration factors in tubular K-joints under out-of-plane moment loading.” Int. J. Fatigue, 20(6), 449–461.
Morgan, M. R., and Lee, M. M. K. (1998b). “Stress concentration factors in tubular K-joints under in-plane moment loading.” J. Struct. Eng., 124(4), 382–390.
Moses, F., Schilling, C. G., and Raju, K. S. (1987). “Fatigue evaluation procedures for steel bridges.” NCHRP Rep. No. 299, Transportation Research Board, Washington, D.C.
Nagode, M., and Fajdiga, M. (1998). “On a new method for prediction of the scatter of loading spectra.” Int. J. Fatigue, 20(4), 271–277.
Nagode, M., and Fajdiga, M. (2006). “An alternative perspective on the mixture estimation problem.” Reliab. Eng. Syst. Saf., 91(4), 388–397.
Ni, Y. Q., Ye, X. W., and Ko, J. M. (2006). “Fatigue reliability analysis of a suspension bridge using long-term monitoring data.” Key Eng. Mater., 321–323, 223–229.
Niemi, E., Fricke, W., and Maddox, S. J. (2006). Fatigue analysis of welded components: Designer’s guide to the structural hot-spot stress approach, CRC, Boca Raton, Fla.
Pines, D. J., and Aktan, A. E. (2002). “Status of structural health monitoring of long-span bridges in the United States.” Prog. Struct. Eng. Mater., 4(4), 372–380.
Pourzeynali, S., and Datta, T. K. (2005). “Reliability analysis of suspension bridges against fatigue failure from the gusting of wind.” J. Bridge Eng., 10(3), 262–271.
Poutiainen, I., Tanskanen, P., and Marquis, G. (2004). “Finite element methods for structural hot spot stress determination—A comparison of procedures.” Int. J. Fatigue, 26(11), 1147–1157.
Reed, R. P., Smith, J. H., and Christ, B. W. (1983). “The economic effects of fracture in the United States.” Special publication 647-1, National Bureau of Standards, U.S. Department of Commerce, Washington, D.C.
Schijve, J. (2001). Fatigue of structures and materials, Kluwer, Dordrecht, The Netherlands.
Schilling, C. G., Klippstein, K. H., Barson, J. M., and Blake, G. T. (1978). “Fatigue of welded steel bridge members under variable-amplitude loadings.” NCHRP Rep. No. 188, Transportation Research Board, Washington, D.C.
Steiner, P. M., and Hudec, M. (2007). “Classification of large data sets with mixture models via sufficient EM.” Computational Statistics & Data Analysis, 51(11), 5416–5428.
Stephens, R. I., Fatemi, A., Stephens, R. R., and Fuchs, H. O. (2001). Metal fatigue in engineering, 2nd Ed., Wiley, New York.
Sturges, H. A. (1926). “The choice of a class interval.” J. Am. Stat. Assoc., 21(153), 65–66.
Szerszen, M. M., Nowak, A. S., and Laman, J. A. (1999). “Fatigue reliability of steel bridges.” J. Constr. Steel Res., 52(1), 83–92.
Titterington, D., Smith, A., and Makov, U. (1985). Statistical analysis of finite mixture distributions, Wiley, New York.
Traffic and Transport Survey Division of the Transport Department (TTSD) of Hong Kong SAR Government. (2004). The Annual Traffic Census 2003, Publication No. 04CAB1, Hong Kong.
Wang, J. Y., Ko, J. M., and Ni, Y. Q. (2000). “Participation of local modes in seismic response of Tsing Ma Suspension Bridge.” Advances in structural dynamics, Vol. 2, J. M. Ko and Y. L. Xu, eds., Elsevier Science, Oxford, U.K., 963–970.
Wirsching, P. H., and Chen, Y. N. (1987). “Fatigue design criteria for TLP tendons.” J. Struct. Eng., 113(7), 1398–1414.
Wirsching, P. H., and Chen, Y. N. (1988). “Considerations of probability-based fatigue design for marine structures.” Mar. Struct., 1(1), 23–45.
Wong, K. Y. (2004). “Instrumentation and health monitoring of cable-supported bridges.” Struct. Control Health Monit., 11(2), 91–124.
Wong, K. Y. (2007). “Structural health monitoring of Tsing Ma Bridge.” Proc., 5th Workshop on Nondestructive Evaluation of Civil Infrastructural System, Society of Nondestructive Testing, Taipei, Taiwan, 33–56.
Wong, K. Y., and Ni, Y. Q. (2009). “Modular architecture of structural health monitoring system for cable-supported bridges.” Encyclopedia of structural health monitoring, C. Boller, F. -K. Chang, and Y. Fujino, eds., Vol. 5, Wiley, Chichester, U.K., 2089–2105.
Wong, M. P. (2005). “Validation of Tsing Ma Bridge influence coefficients using measurement data.” Project Rep. Prepared for Dept. of Civil and Structural Engineering, The Hong Kong Polytechnic Univ., Kowloon, Hong Kong.
Ye, X. W. (2010). “Fatigue reliability assessment of steel bridges instrumented with structural health monitoring system.” Ph.D. thesis, Dept. of Civil and Structural Engineering, The Hong Kong Polytechnic Univ., Kowloon, Hong Kong.
Ye, X. W., Ni, Y. Q., and Ko, J. M. (2007a). “Hot spot stress approach for fatigue life assessment in welded bridge connections using monitoring data and FEM analysis.” Proc., 3rd Int. Conf. on Structural Health Monitoring and Intelligent Infrastructure (CD-ROM), Vancouver, Canada.
Ye, X. W., Ni, Y. Q., and Ko, J. M. (2007b). “Monitoring-based fatigue life assessment of a suspension bridge accounting for both traffic and typhoon effects.” Proc., 4th Cross-Strait Conf. on Structural and Geotechnical Engineering, Zhejiang University Press, Hangzhou, China, 832–843.
Zhao, Y. G., and Ang, A. H. S. (2003). “System reliability assessment by method of moments.” J. Struct. Eng., 129(10), 1341–1349.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 136 • Issue 12 • December 2010
Pages: 1563 - 1573
Copyright
© 2010 ASCE.
History
Received: Aug 26, 2009
Accepted: May 3, 2010
Published online: May 28, 2010
Published in print: Dec 2010
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.