Applying the Weibull and Stüssi Methods that Derive Reliable Wöhler Curves to Historical German Bridges
Publication: Practice Periodical on Structural Design and Construction
Volume 25, Issue 4
Abstract
Preserving the structural integrity of historical bridges made of wrought iron is a mandatory technical requirement in several countries in Europe. A reliable fatigue lifetime estimation of theses bridges allows for proposal of adequate maintenance policies to keep these historical structures as part of the historical legacy for the next generations. In this paper, fatigue data of German bridges built between 1850 and 1900 are considered. The Weibull model of Castilllo and the model of Stüssi to depict the Wöhler curves and estimate the fatigue limit are applied. Their results are compared with those from the linear model of Basquin, which is used in international standards.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The fatigue experimental data of the historical bridges considered in this paper are available from the corresponding author upon reasonable request.
References
Ashton, T. S. 1998. The industrial revolution, 1760–1830. Oxford, UK: Oxford University Press.
ASTM. 2015. Standard practice for statistical analysis of linear or linearized stress-life (S-N) and strain-life (ε-N) fatigue data. ASTM E739-10. West Conshohocken, PA: ASTM.
Bähre, R., and D. Kosteas. 1979. Einfluß der Vorbelastung auf die Restnutzungsdauer schweiß eisener Brücken. Karlsruhe, Germany: Karlsruher Institut für Technologie.
Basquin, O. H. 1910. “The exponential law of endurance tests.” Am. Soc. Test. Mater. Proc. 10: 625–630.
Castillo, E., and A. Fernández-Canteli. 2009. A unified statistical methodology for modeling fatigue damage. New York: Springer.
Castillo, E., A. Fernández-Canteli, H. Pinto, and M. López-Aenlle. 2008. “A general regression model for statistical analysis of strain-life fatigue data.” Mater. Lett. 62 (21–22): 3639–3642. https://doi.org/10.1016/j.matlet.2008.04.015.
CMC (CEN Management Centre). 2010. Eurocode 3: Design of steel structures, Part 1-9: Fatigue. Brussels, Belgium: CMC.
Greiner, R., A. Taras, and H. Brunner. 2007. “Statistisch begründete Festigkeitskennwerte genieteter Bauteile—statische Festigkeit und Wöhlerlinienkatalog.” Stahlbau 76 (8): 537–552. https://doi.org/10.1002/stab.200710056.
Gupta, V. G., and R. C. Panchang. 1989. “On the determination of three-parameter Weibull MLE’s.” Comm. Stat. Simul. Comput. 18 (3): 1037–1057. https://doi.org/10.1080/03610918908812805.
Helmerich, R. 2005. Alte Stähle und Stahlkonstruktionen. Materialuntersuchungen, Ermüdungsversuche an originalen Brückenträgern und Messungen von 1990 bis 2003. Berlin: Bundesanstalt für Materialforschung und -prüfung.
Hobbacher, A. F. 2009. “The new IIW recommendations for fatigue assessment of welded joints and components—A comprehensive code recently updated.” Int. J. Fatigue 31 (1): 50–58. https://doi.org/10.1016/j.ijfatigue.2008.04.002.
Hobbacher, A. F. 2010. “New developments at the recent update of the IIW recommendations for fatigue of welded joints and components.” Steel Constr. 3 (4): 231–242. https://doi.org/10.1002/stco.201010030.
Hobsbawm, E. 1999. Industry and empire: The birth of the industrial revolution. New York: The New Press.
ISO. 2008. Metallic materials—Fatigue testing—Statistical planning and analysis of data. ISO 12107:2012. Washington, DC: ISO.
Mang, F., and O. Bucak. 1991. “Remaining fatigue life of old steel bridges—Theoretical and experimental investigations on railway bridges.” In Proc., Int. Symp. on Fatigue and Fracture in Steel and Concrete Structures, Madras, India, 971–991. Oxford, UK: Structural Engineering Research Centre, IBH Publishing.
Mang, F., and O. Bucak. 1993. “Application of the S-N line concept for the assessment of the remaining fatigue life of old bridge structures.” Chap. 85 in Bridge management 2, 821–832. London: Thomas Telford Publishing.
Mayorga, L. G., S. Sire, J. A. Correia, A. M. D. Jesus, C. Rebelo, A. Fernández-Canteli, M. Ragueneau, and B. Plu. 2017. “Statistical evaluation of fatigue strength of double shear riveted connections and crack growth rates of materials from old bridges.” Eng. Fract. Mech. 185 (Nov): 241–257. https://doi.org/10.1016/j.engfracmech.2017.05.039.
Pedrosa, B., J. A. Correia, C. Rebelo, G. Lesiuk, A. M. D. Jesus, A. A. Fernández-Canteli, M. Duda, R. Calçada, and M. Veljkovic. 2019. “Fatigue resistance curves for single and double shear riveted joints from old Portuguese metallic bridges.” Eng. Fail. Anal. 96 (Feb): 255–273. https://doi.org/10.1016/j.engfailanal.2018.10.009.
Schijve, J. 2009. Fatigue of structures and materials. New York: Springer.
Sedlacek, G., A. Hobbacher, A. Nussbaumer, and J. Stötzel. 2005. “1st draft of the background document prEN 1993-1-9.” Eurocode 3: Design of steel structures. Brussels, Belgium: European Committee for Standardization.
Spindel, J., and E. Haibach. 1979. “The method of maximum likelihood applied to the statistical analysis of fatigue data.” Int. J. Fatigue 1 (2): 81–88. https://doi.org/10.1016/0142-1123(79)90012-4.
Stüssi, F. 1955. Tragwerke aus Aluminium. New York: Springer.
Toasa Caiza, P. D. 2008a. Ermüdungsversuche an alten Stahlkonstruktionen. Karlsruhe, Germany: Karlsruher Institut für Technologie.
Toasa Caiza, P. D. 2008b. Linear regression analysis for fatigue results and its implementation in the program “Wöhler”. Karlsruhe, Germany: Universität Karlsruhe.
Toasa Caiza, P. D. 2018. “Consideration of runouts in the evaluation of fatigue experiments.” Ph.D. thesis, Karlsruhe Institute of Technology.
Toasa Caiza, P. D., and T. Ummenhofer. 2011. “General probability weighted moments for the three-parameter Weibull distribution and their application in S-N curves modelling.” Int. J. Fatigue 33 (12): 1533–1538. https://doi.org/10.1016/j.ijfatigue.2011.06.009.
Toasa Caiza, P. D., and T. Ummenhofer. 2018a. “A probabilistic Stüssi function for modelling the S-N curves and its application on specimens made of steel S355J2+N.” Int. J. Fatigue 117 (Dec): 121–134. https://doi.org/10.1016/j.ijfatigue.2018.07.041.
Toasa Caiza, P. D., and T. Ummenhofer. 2018b. “Consideration of the runouts and their subsequent retests into S-N curves modelling based on a three-parameter Weibull distribution.” Supplement, Int. J. Fatigue 106 (SC): 70–80. https://doi.org/10.1016/j.ijfatigue.2017.09.010.
Wöhler, A. 1870. “Über die Festigkeitsversuche mit Eisen and Stahl.” Zeitschrift für Bauwesen 20: 73–106.
Information & Authors
Information
Published In
Practice Periodical on Structural Design and Construction
Volume 25 • Issue 4 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Dec 23, 2019
Accepted: Mar 19, 2020
Published online: Jul 13, 2020
Published in print: Nov 1, 2020
Discussion open until: Dec 13, 2020
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.