Timber Beams with Holes: Fracture Mechanics Approach
Publication: Journal of Structural Engineering
Volume 121, Issue 2
Abstract
Timber beams with holes have been analyzed with linear elastic fracture mechanics. The energy release rate corresponding to the beginning of the crack growth is set equal to the external work done by the loading of the beam. Further, this fracture energy is partitioned into a mode I and a mode II component. Stress intensities at the hole corner are calculated from the strain energy release rates, and the orthotropicity of the material is taken into account. If the hole is near to the support or the point load, a correction term is given for the basic solution. The equations are derived for a rectangular hole, but a circular hole can be modeled with a rectangular one. Solutions for special cases as beam with cracks are given. The method can be extended to other load and support conditions, crack sources, and other orthotropic materials. The analytical solution was experimentally evaluated. Wu's fracture criterion was found to be applicable for beams with known material properties. For small clear beams, the measured capacity was 0.97 times the predicted one. For glulam beams, the measured capacity was 1.04 times the predicted one.
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References
1.
Carling, O., and Johannesson, B. (1988). Limträhandboken [glulam handbook] . Svenskt Limträ, Stockholm, Sweden (in Swedish).
2.
Fonselius, M. (1992). “Fracture mechanics testing of wood.”Rep. No. 92-15, Royal Institute of Technology, Stockholm, Sweden.
3.
Fonselius, M. (1993). “Long-term experiments with end-cracked wooden beams.”Wood Sci. and Technol., Vol. 27, 137–150.
4.
Fonselius, M., and Riipola, K.(1992). “Determination of fracture toughness for wood.”J. Struct. Engrg., ASCE, 118(7), 1727–1740.
5.
Gustafsson, P. J., and Enquist, B. (1988). “Träbalks hållfasthet vid rätvinklig urtagning [the strength of a wooden beam with a rectangular notch].”Rep. TVSM-7042, Tekniska högskolan i Lund, avdelningen för byggnadsmekanik, Lund, Sweden (in Swedish).
6.
Johannesson, B. (1983). Design problems for glulam beams with holes . Chalmers University of Technology, Division of Steel and Timber Structures, Doktorsavhandlingar vid Chalmers Tekniska Högskola, Ny serie Nr 458, Göteborg, Sweden.
7.
Kolb, H., and Frech, P. (1977). “Untersuchungen an durchbrochenen Bindern aus Brettschichtholz [a study concerning glulam beams with holes].”Holz als Roh- und Werkstoff, Munich, Germany, Vol. 35, 125–134 (in German).
8.
Leicester, R. H. (1971). “Some aspects of stress fields at sharp notches in orthotropic materials. I: plane stress.”Paper No. 57, CSIRO Aust. Div. For. Prod. Technol., Melbourne, Australia.
9.
Mall, S., Murphy, J. F., and Shottafer, J. E.(1983). “Criterion for the mixed mode fracture in wood.”J. Engrg. Mech., ASCE, 109(3), 680–690.
10.
Murphy, J. K.(1988). “Mode II wood test specimen: beam with central slit.”J. Testing and Evaluation, 16(4), 364–368.
11.
Penttala, V. (1980). “Reiällinen liimapuupalkki [glulam beam with hole].”Publ. 33, Helsinki University of Technology, Division of Structural Engineering, Espoo, Finland (in Finnish).
12.
Pizio, S. (1991). “Die Anwendung der Bruchmechanik zur Bemessung von Holzbauteilen, untersucht am durcbrochenen und am ausgeklinkten Träger [the use of fracture mechanics for the design of wooden construction elements, studied with beams with holes and notches].”Publ. Nr. 91-1, Baustatik und Stahlbau, Eidg. Techn. Hochschule, Zürich, Switzerland (in German).
13.
Pook, L. P. (1979). “Approximate stress intensity factors obtained from simple plate bending theory.”Engrg. Fract. Mech., Vol. 12, 505–522.
14.
Williams, J. G.(1988). “On the calculation of energy release rates for cracked laminates.”Int. J. Fract., 36, 101–119.
15.
Wu, E. M. (1967). “Application of fracture mechanics to anisotropic plates.”J. Appl. Mech., E 34(4), 967–974.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 121 • Issue 2 • February 1995
Pages: 225 - 239
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Feb 1, 1995
Published in print: Feb 1995
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