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A probabilistic fracture mechanics method and strength analysis of glulam beams with holes

Probabilistische Bruchmechanik und Festigkeitsanalyse von Brettschichtholzträgern mit Durchbrüchen

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Abstract

A probabilistic fracture mechanics method is presented and applied to glulam beams with holes. The method is based on a combination of Weibull weakest link theory and a mean stress method which is a generalization of linear elastic fracture mechanics. Combining these two methods means that the global strength will be governed by both fracture energy and material strength and also that the stochastic nature of the material properties are taken into account. The probabilistic fracture mechanics method is evaluated by comparison to experimental test results. The method shows good ability to predict strength, with the exception of very small beams where the capacity is overestimated. The comparison to experimental tests deals also with other methods for strength analysis including code design methods.

Zusammenfassung

Ein probabilistisches Bruchmechanikverfahren wird vorgestellt und auf Brettschichtholzträgern mit Durchbrüchen angewandt. Grundlage dieser Methode ist eine Kombination der Weibull Theorie des schwächsten Gliedes und der Methode der mittleren Spannung, einer Verallgemeinerung der linear-elastischen Bruchmechanik. Die Kombination dieser beiden Methoden bedeutet, dass die globale Festigkeit sowohl von der Bruchenergie als auch der Materialfestigkeit bestimmt wird und dass die stochastische Natur der Materialeigenschaften berücksichtigt wird. Das probabilistische Bruchmechanikverfahren wird durch Vergleich mit Versuchsergebnissen überprüft. Das Verfahren erweist sich als gut geeignet zur Vorhersage der Festigkeit mit Ausnahme von sehr kleinen Trägern, deren Tragfähigkeit überschätzt wird. Mit den Versuchsergebnissen werden auch andere Methoden der Festigkeitsanalyse einschließlich normierter Bemessungsverfahren verglichen.

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Acknowledgements

The financial support from Formas through grant 24.3/2003-0711 is greatly appreciated. In relation to the experimental tests carried out at Lund University, the financial support through collaboration with Ulf Arne Girhammar at Umeå University within the project Multi-story timber frame buildings (The European Union’s Structural Funds – Regional Fund: Goal 1) is acknowledged. We would also like to thank Svenskt Limträ AB for assisting the project by supplying all glulam beams.

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  1. Division of Structural Mechanics, Lund University, P.O. Box 118, 221 00, Lund, Sweden

    Henrik Danielsson & Per Johan Gustafsson

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  1. Henrik Danielsson
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  2. Per Johan Gustafsson
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Correspondence to Henrik Danielsson.

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Danielsson, H., Gustafsson, P.J. A probabilistic fracture mechanics method and strength analysis of glulam beams with holes. Eur. J. Wood Prod. 69, 407–419 (2011). https://doi.org/10.1007/s00107-010-0475-1

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