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Beams with notches or slits - Extensions of the Gustafsson approach

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The conditions necessary for the application of fracture mechanics to anisotropic materials were examined and verified experimentally on orthotropic plates. It was observed that crack extension, by opening and forward sliding, occurred independently and the associated stress-intensity factors at the state of incipient fracture are material constants. An empirical relation (k1 /k1 c ) + (k2 /k2 c )2 = 1 was found to be a fracture criterion for both balsa wood and fiber-glass-reinforced plastic plates, inferring the existence of a general law of fracture for orthotropic materials.
Experimental results and theoretical predictions for failure of timber beams with end notches, or cuts on the tension face, are discussed. The validity of Gustafsson's formula and the underlying assumptions are examined in the context of structural design codes. Attention is drawn to the arbitrary dependence of theoretical predictions on the load and geometric arrangement of specimens, and the method by which fracture energy is estimated. It is not intended at this stage to give a complete solution for the problem, but it is concluded to be premature to incorporate the proposed Eurocode 5 failure criterion for notched beams into the Canadian Standard CAN/CSA 086.1. Key words: timber, fracture, notched beam, design criterion.
Traditional timber engineering design approaches use for simple geometries stress- or strain-based criteria for strength analyses. For more complex cases purely empirical methods are also used. Although practical, purely empirical methods are not general, and could lead to estimations on the unsafe side, if extrapolated outside their original scope. It is furthermore known that stress- or strain-based methods are not useful in situations where large stress or strain concentrations arise, such as close to holes or notches, in dowel joints or in glued joints. Furthermore, such phenomena like size effects cannot be predicted, unless stochastic methods are introduced. The paper discusses some fracture mechanics strength analysis methods that in recent years have been proposed in relation to timber engineering strength design. The methods discussed range from simple hand calculations based on linear elastic fracture mechanics and useful for simple geometries to finite element analyses for general cases taking into account non-linear performance of the material during fracture. Fracture mechanics results in rational strength design, which is based on mechanics, as opposed to purely empirical methods, and with parameters with a clear physical meaning. In order to obtain material characteristics needed for this approach examples of test methods are discussed. Application examples include structural components, dowel joints and adhesive joints. Design formulae for beams with notches at the support and for the pull out strength of glued-in rods are presented.
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Notches in wood at arbitrary beam location -numerical modelling and challenges
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J. Kunecký, G. Hochreiner. Notches in wood at arbitrary beam location -numerical modelling and challenges. CompWood, Växjö, Sweden, 2019.