Shear Strength of Beam Splice Joints with Glued-In Rods
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J Wood Sci (2004) 50:123–129 © The Japan Wood Research Society 2004 DOI 10.1007/s10086-003-0538-6 ORIGINAL ARTICLE Jørgen Lauritzen Jensen · Per-Johan Gustafsson Shear strength of beam splice joints with glued-in rods Received: November 11, 2002 / Accepted: March 7, 2003 Abstract Splitting failure in beam splice joints with glued- Although glued-in rods are very efficient for making in rods parallel to grain in endwood subjected to pure shear joints with high bending moment capacity, the shear capac- is considered. A simple theoretical expression based on ity is low unless special actions are taken. In Fig. 1 is shown beam-on-elastic-foundation theory and quasi-non-linear a shear failure mode in a beam with glued-in rods. Failure fracture mechanics is presented for calculation of the joint occurs as splitting of the beam due to stresses perpendicular strength. Tests were conducted on jointed beams in a four- to the grain. To make a joint with high moment capacity, the point bending test setup in which the joints were located at most efficient use of the rods is obtained if they are placed the point of pure shear force. Hardwood dowels with a as close as possible to the top and bottom of the beam, i.e., diameter of 12mm and a glued-in length of 120mm were using as small effective edge distance, he (as shown in Fig. used as rods, and various beam cross sections and dowel 1), as possible. However, the shear capacity obviously in- configurations were tested. The theory presented is found creases with increasing he. to agree well with test results in all cases in which the edge A simple expression is proposed for calculation of the distance of the glued-in rods is relatively small. Some test strength of a joint with glued-in rods subjected to pure results indicate that the theory may be conservative in case shear. The expression is derived using beam-on-elastic- of large edge distances. foundation theory and quasi nonlinear fracture mechanics. Joints in beams with cross-sectional dimensions of 100 ϫ Key words Shear strength · Splice joint · Glued-in rods · 200mm, 50 ϫ 300mm, and 120 ϫ 420mm and various dowel Quasi-non-linear fracture mechanics · Beam-on-elastic- configurations were tested in pure shear. foundation Theory Introduction Introduction Much research on timber joints has recently been dedicated to pull-out of glued-in rods and to the performance of A symmetrical joint as shown in Fig. 1 is considered. Failure 1 moment-resisting joints with glued-in rods. Hardwood occurs as a splitting failure in the beam (mode I fracture of dowels have also been investigated as an alternative to steel the wood due to tensile stress perpendicular to grain) at the 2–5 rods. Beam splice joints subjected to pure bending have rods located closest to the beam axis as shown in Fig. 1. The previously been tested and simple theoretical expressions part above the crack of the beam to the right of the joint is for calculation of their strength and stiffness have been considered and treated as a beam on elastic foundation. 6–9 presented. However, the shear strength of joints with This is a simplifying assumption used in the present theory glued-in rods seems not to have been investigated so far. and may be regarded as a compromise between the strive for simplicity and that of accuracy. J.L. Jensen (*) The properties of the elastic foundation are chosen so Institute of Wood Technology, Akita Prefectural University, Noshiro that the perpendicular-to-grain tensile strength and fracture 016-0876, Japan energy properties of the wood are correctly represented. Tel. ϩ81-185-52-6985; Fax ϩ81-185-52-6976 e-mail: [email protected] The analysis is linear elastic, but because strength, fracture energy, and a nonzero size of the fracture process region are P.-J. Gustafsson Division of Structural Mechanics, Lund Institute of Technology/Lund considered in the analysis, the analysis may be called a University, Lund S-221 00, Sweden quasi-non-linear fracture mechanics analysis. Results of 124 Fig. 1. Splitting failure in a beam with glued-in rods subjected to shear loading Fig. 2. Semi-infinite beam on elastic foundation Fig. 3. Beam on elastic foundation after development of a crack of linear elastic fracture mechanics are obtained as a special length a case by allowing the tensile strength of the wood approach an infinitely large value. P 6Kb Stress and energy release rate σλ(04) 0 2 (4) b 5GA Figure 2 shows a beam on elastic foundation subjected ϭ The crack propagation energy release rate is denoted by G to a shear force, P0, and a moment, M0, at x 0. If the beam is supposed to be infinitely long, and if shear deformations and is by definition the release of elastic strain energy and ϭ potential energy of loads per unit area of crack extension. are taken into account, the deflection at x 0, w0, is given 10,11 For a linear elastic body loaded by a single load, P , G is by 0 given by12 2 λ 2 2 ww00(0) ( PM0 ) P0 dC Kb G (5) 2b da 3Kb Kb (1) λ 24 , λ 10GA 4EI where a is the crack length and C is the compliance given by where b is the beam width, E is the modulus of elasticity δ C (MOE) in the grain direction of the beam, G is the shear P (6) modulus of the beam, K is the stiffness of the elastic founda- 0 3 tion (units: N/m ), I is the moment of inertia, and A is the δ being the deflection at the loading point. cross-sectional area of the beam (rectangular cross section A cantilever beam on elastic foundation, as shown in is assumed). Fig. 3 (only the beam axis is shown), is considered. The θ ϭ The rotation, 0, of the beam end at x 0 is given by projecting length, a, models the crack in the fracture me- chanics analysis. The total deflection, δ, of the loading point Ê λ 2 ˆ θθ P0 M0 6 1 may be given as 0 ()0 2 Á ˜ (2) 2EIλË 5GA EI ¯ δδ δ δ awθ (7) The foundation stress acting on the beam (σ), σ Ͼ 0 cor- δ responding to tensile perpendicular-to-grain stress in the where a is the contribution from the projecting cantilever wood, is given by 3 σ δ Ê a 6a ˆ ()xKwx () (3) a Á ˜P0 (8) Ë 3EI 5GA¯ ϭ Pure shear load, i.e., M0 0, is assumed. In this case, maxi- ϭ δ ϩ δ mum deformation and stress occur at x 0. Eqs. 1 and 3 and w θ is the contribution from the beam on elastic ϭ give foundation using M0 P0a in Eqs. 1 and 2 125 G G where the critical energy release rate, c, is the value of δδ θ wa θ w 00 when a crack is about to start to propagate. Assuming static Ê α22λ ˆ or quasi-static conditions and no energy dissipation outside Ê 6 12ˆ a (9) Á Á ˜ 2 ˜P0 G Ë 5GA EI ¯ EIλ Kb the fracture region, c is equal to the material property Ë ¯ G parameter f: From Eqs. 6–9, the increase in compliance due to an infini- GG cf (18) tesimal crack extension is found to be From Eq. 18, it follows from Eqs. 11 and 17 that 22λ dC a 26a Ê 116ˆ Á ˜ λ2 (10) G da EI Ë 5GA EI¯ EI5 GA bK2 f Pc 2 6 Kb (19) Inserting Eq. 10 in Eq. 5, and utilizing the fact that maxi- 4λ 5 GA mum failure load is obtained for a Æ 0, leads to The value of P by the energy release analysis is the same as 2 c P0 Ê 16ˆ the value obtained by the stress analysis because, from Eq. G Á ˜ (11) 2bEIË λ2 5 GA¯ G 14, 2Kff t . The present strength analysis of mode I failure using Comparison of this equation with Eq. 4 shows a simple beam on elastic foundation and Eq. 14 is a complete anal- relation between the maximum stress, σ(0), and the energy ogy to the fracture mechanics application of the Volkersen release rate, G: model to strength analysis of mode II failure in lap joints13 1,5 2 and pull-out of glued-in rods. σ(0) G ( ) (12) 2K Equations for the shear failure load Foundation properties and failure criteria ϭ The shear failure load, Vc,L 2Pc, of the symmetrical joint The foundation of the beam is intended to model the shown in Fig. 1 may, by means of Eq. 16 or 19 together with strength and fracture performance of the wood perpendicu- Eqs. 1 and 14, be written lar to the grain. The damage and fracture performance of wood is nonlinear. This nonlinear response is represented in h h f 2 Vblfl 2 ,, eetω the present analysis by a linear response that is equivalent c,L e t e G 6 E E 2 f 43ωω 2 in terms of peak stress, ft, and fracture energy dissipation, G 5 G f. The two parameters determine the fracture stress, ft, and the foundation stiffness, K. Since the energy dissipation in (20) the case of linear performance is The length le may be interpreted as the equivalent length on both sides of the joint, over which the beam with depth he is G 1 Ê ft ˆ able to distribute the stresses perpendicular to the grain ftf Á ˜ (13) 2 Ë K ¯ uniformly.