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Analytical cracking load estimation of Laminated Veneer Lumber (LVL) beams with holes

Analytische Bestimmung der Risslast von Furnierschichtholzbalken mit Durchbrüchen

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Abstract

Predicting the load-carrying capacity of timber beams with holes cannot be performed by usual analysis methods if the failure of the beam is governed by the crack initiation and propagation around the hole at low load levels. Predicting the cracking load is an important design issue because it corresponds to the load-carrying capacity of the timber beam before the crack propagation. One of the models that can be used for the fracture formulation is that of a beam on elastic foundation. In this model a part of the beam is assumed to follow the conditions of beam with elastic foundation which has spring stiffness equal to the fracture properties of the material in the crack surface. Based on beam on elastic foundation model, the cracking load prediction is the target of the paper. Some closed form solutions for the beam with hole are presented. The formulation has been derived for two cases of pure shear and pure bending moment. Finally a semi-empirical formulation for combination of shear and bending moment in the section is presented. The model predictions are compared with the results of an experimental program showing good correlation. The analytical model can therefore be proposed for future revisions of codes of practice such as the Eurocode 5.

Zusammenfassung

Die Tragfähigkeit von Holzbalken mit Durchbrüchen kann nicht mit herkömmlichen Methoden bestimmt werden, wenn der Bruch darauf zurückzuführen ist, dass am Durchbruch ein Riss bei einer geringen Belastung entsteht und sich fortpflanzt. Die Bestimmung der Risslast, d.h. der Last bei der Entstehung des Risses, ist ein wichtiger Bemessungsaspekt, da sie die Tragfähigkeit des Holzbalkens vor der Rissfortpflanzung angibt. Eines der Modelle, das für die Bruchformulierung verwendet werden kann, ist das des elastisch gebetteten Balkens. In diesem Modell wird davon ausgegangen, dass ein Teil des Balkens einem elastisch gebetteten Balken entspricht, wobei die Federsteifigkeit den Brucheigenschaften des Materials in der Rissfläche entspricht. Ziel dieser Arbeit ist die Bestimmung der Risslast unter Verwendung des Modells des elastisch gebetteten Balkens. Es werden einige geschlossene Lösungen für einen Balken mit Durchbruch vorgestellt. Die Formulierung wird für die zwei Fälle reiner Schub- und reiner Biegebeanspruchung hergeleitet. Weiterhin wird eine halbempirische Formulierung für eine Kombination von Schub- und Biegebeanspruchung dargestellt. Die Modellvorhersagen werden mit den Ergebnissen eines Versuchsprogramms verglichen und zeigen eine gute Korrelation. Aus diesem Grund kann das analytische Modell zur Verwendung für zukünftige Revisionen anerkannter technischer Regeln wie zum Beispiel dem Eurocode 5 vorgeschlagen werden.

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Acknowledgments

The authors would like to extend their gratitude to Dr. Jørgen Jensen from the University of Auckland, New Zealand, for the useful ideas and suggestions provided on the topic of this paper. The scholarship provided by the University of Canterbury for the first author, and funding for the experimental work through the Structural Timber Innovation Company (STIC) are also highly appreciated. The authors would also like to extend their appreciation to Mr. John Maley for experimental program support and technical advice. Review and comments of the paper by two anonymous reviewers is also acknowledged.

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Authors and Affiliations

  1. University of Canterbury, Private Bag 4800, Christchurch, 8041, New Zealand

    Manoochehr Ardalany

  2. Department of Architecture, Design and Urban Planning, University of Sassari, Sassari, Italy

    Massimo Fragiacomo

  3. University of Canterbury, Christchurch, 8041, New Zealand

    Bruce Deam

  4. University of Technology of Sydney (UTS), Sydney, Australia

    Keith Crews

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  1. Manoochehr Ardalany
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  2. Massimo Fragiacomo
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  3. Bruce Deam
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  4. Keith Crews
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Correspondence to Manoochehr Ardalany.

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Ardalany, M., Fragiacomo, M., Deam, B. et al. Analytical cracking load estimation of Laminated Veneer Lumber (LVL) beams with holes. Eur. J. Wood Prod. 71, 37–48 (2013). https://doi.org/10.1007/s00107-012-0646-3

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  • DOI: https://doi.org/10.1007/s00107-012-0646-3

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