Loading Capacity Determination of the Wooden Scarf Joint

Loading capacity determination of the wooden scarf joint

D. Herák1, M. Müller2, R. Chotěborský2, O. Dajbych1

1Department of Mechanical Engineering, Faculty of Engineering, Czech University of Life Sciences Prague, Prague, Czech Republic 2Department of Material Science and Manufacturing Technology, Faculty of Engineering, Czech University of Life Sciences Prague, Prague, Czech Republic

Abstract: The paper describes the complete derivation of the theoretical bonded scarf joint loading capacity and the construction of the Mohr’s circle for linear state of stress. Then the method of the experimental determination of the bonded joint loading capacity is explained in detail. A part of this paper deals also with the bonded joint real loading capacity determination.

Keywords: Mohr’s circles; linear state of stress; bonding; scarf joint; wooden joint

Bonding is much more than art, it is science and rupture of the body tissue occurs. The ruptured part it is exploited ever more. The choice and the use of of a higher strength wood is fibriform, of a minor a suitable adhesive is very important in productive strength wood it is stairform or almost smooth. With and repair industry. A suitable choice saves costs and the increasing moisture content the tensile strength enhances the quality (Franklin International 1998). across the fibres decreases up to the limit of the cell Wood is one of raw materials which renews all walls saturation (Lorenz 2002). the time. In contrast to metals it is a porous, non- By the compressive force acting along the fibres homogenous, water-absorbing and volume labile deformation appears – the body shortens. The material, whose base is cellulose and, according to deformation character depends on the quality and the wood type, certain additional substances, as well. structure of the wood. The density and the moisture Wood possesses a number of excellent properties: content are important factors. elasticity, strength, toughness, mach inability etc. Anisotropy is one of the most important proper- The selection of the correct wood type makes the ties of wood (the mechanical properties are different use of wood possible in a great spectrum of human in different directions). activities, from building industry to medicinal ap- Wood is a fibriform material and therefore it is plications (Němec et al. 2005). much tougher in the longitudinal axis (in the fibres Generally, wood possesses positive mechanical direction) than in the normal (transversal) direction. properties. Mechanical properties of wood can be But the anisotropy of wood is three-dimensional. characterised as the ability to defy the deformation Therefore, we distinguish the longitudinal, radial, caused by outer forces. These properties are utilised and tangential directions. when wood is used as the construction material. The values of individual mechanical properties of wood are different in various directions. The tensile Basic stress of wood strength of green wood is about five times lower than that of the same dry wood. Mechanical properties of According to the stress type, we can distinguish wood, namely strength, are influenced by a number the strength in the fibres direction – deformation of factors, e.g. density, moisture content, knots, appears as the body elongation. In the last stage, the wood defects etc. (Pizzi 1994).

Supported by the Internal Grant Agency of Faculty of Engineering, Czech University of Life Science in Prague, Project No. 31140/1312/313104, CZU v Praze.

76 RES. AGR. ENG., 55, 2009 (2): 76–83 Bonding of wood state of equilibrium depends on the air humid- ity and the temperature (Mukam & Mouongue The bonding technology, which is very prospective 2003). even at present, can be used for the wood joining. It The contemporary offer of adhesives suitable for is used for bonding various materials. This technol- wood bonding enables a large selection of these ogy can be used for solving otherwise difficult prob- products. It is necessary to choose the suitable prod- lems. For wood bonding, it is necessary to use quality uct for the pertinent application. The comparison of and above all dry semi-products (ASTM 1994). prices is also important. The price often depends on The advantages of the bonded wooden joints are: the knowledge of the respective product. – they do not reduce the bonded woods The bonded wooden surfaces are conventionally – they are relatively strong larger. At bonding larger surfaces, the disperse types In wood bonding, the wood properties must be of adhesives are suitable. The advantage of these taken into account, namely the wood hardness and adhesive types is a simple use. The usable life of a the structure of the bonded parts. The flushing of majority of adhesives is sufficient for the easy and hard woods must be more thorough than of soft correct assembly of the bonded surfaces. The suit- woods. Minute surface unevenness of soft wood can able moment of the bonded surfaces connection can be suppressed by elevated clamping pressure of the be recognised according to the adhesive colour. After assembled joint. On the contrary, using this practice being applied on the bonded surface, the adhesive on hard wood can lead to the adhesive being pressed is non-transparent. After a certain time, it begins out from the bonded joint (Morlier 1994). to lose slowly its coloring. In this phase, additional The size of the bonded surface is the substantial corrections are not recommended, because by now factor affecting the bonded joint strength. When the coupling forms between the adhesive and the designing a bonded joint, the size of the bonded sur- bonded parts. face transmitting the load should be as large as possible. Therefore, various shapes of contact surfaces Disperse solvent-type adhesives are used (scarf joints, indented joints). In bonding wood, four basic positions of the wood structure The film-forming substance of the disperse adhe- come into consideration. The optimum strength of sives is a very fine dispersion of polymers dispersed a wooden joint is reached at parallel arrangement of in water. After the water imbibition and evaporation, annual shoots of the bonded surfaces. The butt joint the sintering of polymeric particles in a coherent is suitable for the wooden parts bonding, especially film occurs. The minimal film-forming temperature when a sufficient bonded surface is at disposal. In ranges to about 10°C–12°C. Compared with solvent- using butt joints, the scarf joints are advantageous type adhesives, some advantages of the polymers (Müller 2006). dispersed in water are: Before bonding the wood surface preparation is – low viscosity even at high dry basis contents of necessary: 50%–60% – evenness preparation – the smoothly worked – very low contents of inflammable and health- surface is the most suitable (the unevenness damaging organic solvents should be max. ± 0.2 mm). It can be reached e.g. – thinning ability by water and water washable aids by planing, milling, or grinding. After grinding, – workability at room temperature as well as one- the dust removal is necessary. The working of component adhesives and the use without curing hard wood must be more precise than that of soft additives (Pizzi & Mitta 2003). wood. When bonding rough surfaces, it is necessary to spread the adhesive with a filler (Herák Material and methods et al. 2005) – resins, wax, and impregnation removal – me- Theoretical loading capacity of the wooden bon- chanical, e.g. using brushes ded scarf joints – improvement of water content – we practice the temperature treatment of bonded parts For the determination of the loading capacity of Every wood contains a specific quantity of water. the wooden bonded scarf joints, must be derived We must eliminate the majority of water before which describe the shear and normal stress distri- the correct use of the wood. Wood loses or ac- bution. cumulates water to reach the state of equilibrium If we consider the section according to Figure 1, we according to the storage and use conditions. This determine the principal component of stress as

RES. AGR. ENG., 55, 2009 (2): 76–83 77 α

N F α T α

F So Figure 2. Forces diagram of the bonded scarf joint

Figure 1. Diagram of the bonded scarf joint coverer, this circle is also called the Mohr’s circle of linear state of stress or uniaxial state of stress.

F Each adhesive has its failure strength in the normal σ = ––– (1) o S direction (tensile strength) and in the tangential di- o rection (shear strength). These data are determined where: from mechanical tests of the bonded joint (Ševčík S – cross section of the sample 0 2005) described further. If we resolve the force F into the normal and If we plot the theoretical limiting tensile strength tangential components, we receive the following in the circle of stress, we can simply determine equations, which describe the individual force com- the minimal angle which defines the surface of the ponents (Figure 2). bonded joint optimum applicability.

N = F × cosα (2) σ –––o σmez = × (1 + cos2αmin) (7) T = F × sinα (3) 2 We express the bonded surface according to the σ –––––mez following Eq. αmin = 2 × arccos 2 × – 1 (8) ( σo )

So s = –––––– (4) If we plot the theoretical limiting shear strength cosα in the circle of stress, we can simply determine the If we introduce (3) and (4) into the basic Eq. of maximal angle which defines the surface of the the shear stress, we obtain the Eq. which describes bonded joint optimum applicability. the relation between the shear stress and the cross section angle α (5) (Figure 3).

T F × sinα F σo τ = –– = ––––––– = –– × sinα × cosα = –– × sin2α (5) α S S S 2 o o cosα If we introduce (2), (4) into the basic Eq. of the tensile stress, we obtain the Eq. which describes the relation between the normal stress and the cross section angle α (6) (Figure 3).

N F × cosα F σo σ = –– = ––––––– = –– × cos2α = –– × (1 + sin2α) (6) α S S S 2 o o cosα By graphical representation of the foregoing Eqs., we obtain the representation by means of the circle Figure 3. Mohr’s circle of the linear state of stress of the of the linear state of stress (3). According to its dis- bonded joint

78 RES. AGR. ENG., 55, 2009 (2): 76–83 If we express graphically (Figure 5) the relation between both limiting forces and the cross section

F F angle, we find that up to the angle α1 the joint must be dimensioned according to the limiting tensile

force, over the angle α1 according to the limiting shear force.

We determine the limiting angle α1 from the limiting stresses equality.

σmez ––––– = 1 (13) τmez If we introduce Eqs. (5), (6) into the foregoing one, F So F we get after modification the stress ratio. F 2 cos αI σmez So cosαI 1 ––––– = –––––––––––––––– = ––––– = –––– (14) τ sinα tgα Figure 4. Diagrams of the bonded butt joint and the lap mez F I I S × sinα × cosα joint o I I From Eq. (14), we express the limiting angle sought. σ ––––o τmez = × sin2αmax (9) τmez 2 α = arctg –––– (15) I σ mez τ ––––mez αmax = 2 × arcsin σ (10) o Results and discusion Theoretically we can say (evidently if it is possible) that the most suitable adherent utilisation is in the Real load capacity determination cross section angle position in the range from αmin of the wooden bonded scarf joint to αmax.

2So Laboratory tests were carried out according to the F = τ × –––––– (11) mezτ mez standard CSN 66 8508 (1995) (Method of test for sin2α strength properties of adhesives in shear by tension From Eq. (6), we can determine the limiting tensile loading (wood to wood)) using the recommended force for the individual cross section angles. size of test specimens. The cross section surface 2 2So was S = 300 mm . The shape and dimensions of the F = σ × ––––––––– (12) 0 mezσ mez specimen are evident from Figures 6 and 7. 1 + cos2α For the bonding of specimens from the spruce, the disperse solvent-type adhesive Herkules was used. Tests were carried out for the determination of the tensile strength and shear strength, (Figure 4). The scarf influence on the bonded joint strength was also tested, (Figure 8). The bonded surfaces were prepared according to CSN 66 8508 (1995).

Fmezτ(α) Characteristics of the chosen adhesive Fmezσ(α) αmez Herkules pertains to significant disperse adhesives. In the Czech Republic it is commonly available. Poly- vinyl acetate (PVAC) is the film-forming component. Polyvinyl acetate adhesives contain 50%–60% of α solids. At a long-term storage or at bonded joints Figure 5. Graphical representation of the bonded joint limit- ageing a small amount of acetic acid is separated. ing angle This conduces to the chalk addition. Chalk removes

RES. AGR. ENG., 55, 2009 (2): 76–83 79 Figure 6. Shape and dimensions of the specimen for the tensile test

Figure 7. Shape and dimensions of the specimen for the shear test

Figure 8. Shape and dimensions of the scarf spruce specimen

the acid trace amounts and above all it concentraces rate of the jaw was 6 mm/min. After the failure, the the mixture. maximal force was read and recorded. In the end, the data were evaluated. Methodical procedure of laboratory tests Tests using 30 specimens were carried out for each of 6 scarf angles, thus total of 180 specimens were Bonded spruce specimens were tested using used. The calculated average force needed for the the disperse solvent-type adhesive Herkules. The bonded joint failure at each scarf is presented in Ta- tensile tests and the shear tests were carried out. ble 1. The following limiting allowable stresses were Then the relation between the scarf (15°, 30°, 45°, determined: Pure tensile stress σmez = 3.85 MPa, 60°, and 75°), (Figure 8), and the load capacity pure shear stress τmez = 10.4 MPa. Table 1 presents were tested. The bonded surfaces were prepared the shear and normal stresses at the joint failure, according to the recommendations presented in calculated using Eqs. (5) and (6). special literature. According to the foregoing table, the relation The bonded specimens were homogenous, with- between shear/normal stresses and scarf angle is out defects and knots. The surface for the adhesive graphically represented in Figure 9. By interlay of application in sufficient amount was clean, dry, individual points we get the Eqs. and even. The adhesive was evenly spread. Then τ(α) = 10–6 α4 – 4 × 10–5α3 – 0.0007α2 + 0.1061α – 0.025 (16) the second bonded piece was joined to the first one 2 and fixed. R = 0.9997 The specimens were cured for 48 hours at labora- σ(α) = 0.0006α2 + 0.0156α + 3.9565 (17) tory temperature. After curing, the bonded speci- R2 = 0.8914 mens were clamped symmetrically in the jaws of the universal tensile-strength testing machine ZDM 5 Using the measured values, we can get the rela- and the breakdown test was carried out. The feed tion between the failure force and the scarf angle

80 RES. AGR. ENG., 55, 2009 (2): 76–83 Table 1. Individual stress values at different scarf angles Table 2. Values of coefficientk in the dependence on the scarf angle α (°) F (N) τ (MPa) σ (MPa) α (°) k (–) 0.00 1348.57 0.00 3.85 0.00 1.00 15.00 1617.14 1.19 4.31 15.00 1.20 30.00 1834.29 2.62 3.93 30.00 1.36 45.00 2157.14 4.35 3.08 45.00 1.60 60.00 4542.86 11.23 3.24 60.00 3.37 75.00 9614.29 26.51 1.84 75.00 7.13 α – scarf angle; F –loading force; τ– shear stress; σ – tensile stress α – scarf angle; k – coefficient of the influence of the scarf angle

(Figure 10) at a bonded rectangular surface S0 of From the measured values, we can also determine 300 mm2. the Eq. of the relation between the coefficientk value 3 2 and the scarf angle (Figure 11). F(α) = 0.0537α – 3.4418α + 66.8α + 1319.5 (18) 6 2 α R = 0.9991 k(α) = (–––––––– + 1 × (–2.489 × 10–4α2 + 0.017α + 1) (21) 2.5 × 1010 ) For the practice, it is better to determine the coef- 2 ficient k which indicates the influence of the scarf R = 0.9824 angle on the tensile stress. Then we can define the CONCLUSIONS following relation: Based on the tests described, the characteristics σ = σ × k (19) red d were determined of the bonded scarf joint load where: capacity. For the design of the bonded joint load σ – reduced tensile stress red capacity, the above mentioned characteristics can σ – allowed normal stress for the given bonded joint d be used (Figures 9, 10, 11). The coefficientk can be defined as the quotient of With a detailed view on the relation between the the failure force at the given scarf angle divided by shear and normal stresses and the scarf angle, we the failure force at the scarf angle equal to zero. can say that up to the value of the so-called limiting angle (15) is it necessary to determine the load Fα k = –––– (20) capacity according to the normal stress allowed, F 0 and over the limiting angle according to the allowed The values of the coefficient k are presented in shear stress. Our tests confirmed the validity of the Table 2. theoretical relations of the limiting angle derived

30 shear stress normal stress

15 t (MPa) s s (MPa) σ (MPa) τ (MPa) 10

0 0 20 40 60 80 -5 Figure 9. Relations between shear/nor- α (°) mal stresses and scarf angle a (°)

RES. AGR. ENG., 55, 2009 (2): 76–83 81 8 Figure 10. Relation between failure force and scarf angle at the bonded 2 7 rectangular surface S0 = 300 mm 6

4 (kN) F 3

0 0 10 20 30 40 50 60 70 80

α (°)a (°) from the Mohr’s circle of stress. If we determine the plastic deformation decreases. The classical the limiting angle using these tests (Figures 5, 8) Mohr’s relations are not valid either. These rela- (it means the point where the curves of the normal tions were derived for the materials with covalent stress and of the shear stress intersect), we find out bonding. The stress distribution is not constant but the limiting angle value α1 = 41°. But if we calculate is influenced by the intermolecular bonds between the limiting angle value using Eq. (15) derived from the bonded material and the adhesive line. Mohr’s theory, we find out that the theoretical angle For practical calculation of the spruce bonded is joints loading capacity, we can read the experimen- tally determined values of the allowable stress in τmez 10.4 α = arctg –––– = arctg ––––– = 69.9° the dependence on the scarf angle (Figure 9). For a σ mez 3.85 simple calculation, the method using the coefficients The difference between the theoretical and experi- of the scarf angle value can be used. These data are mental values verified tests consists in several basic presented in the diagram (Figure 11). factors. In fact, the point is not the linear state of When bonding wooden semi-products, it is nec- stress but the triaxial state of stress. The adhesive essary to accept the mechanical properties of wood line behaves as a block of plastic material with non- which are very different in various directions. One covalent bonding. At loading, the deformation of the of the most important properties of wood is its molecular chains occurs, and at the correctly chosen anisotropy (the properties of wood are different in adhesive line thickness the adhesive line strength various directions). Wood is a fibrous material and increases with regard to this deformation. Of course, therefore it is much stronger in the longitudinal axis

9 8 7 6 5 k (–) 4 3 2 1 0 10 20 30 40 50 60 70 80 Figure 11. Values of the coefficientk in the α (°) dependence on the scarf angle

82 RES. AGR. ENG., 55, 2009 (2): 76–83 (in the fibres direction) than in the perpendicular Franklin International (1998): Gluing and Furniture Design. (transversal) direction. Commonly, the strength of Wood Adhesives Division, Industrial Product Group, wood is sufficient especially at the tension in the Columbus. fibres direction. The very strength of wood is influ- Herák D., Chotěborský R., Müller M., Hrabě P. (2005): enced by a row of further significant factors (density, Bonded wooden balks. Research in Agricultural Engineer- matter content, knots, wood defects etc.). ing, 51: 145–151. The tests carried out confirmed a great influence of Lorenz K. (2002): Supporting Structure II. ČVUT, Praha. the bonded surface size and of the stress type. It is use- (in Czech) ful to provide the butt joints with a scarf. In this way, Morlier P. (1994): Creep in Timber Structures. [RILEM the bonded surface increases. By the laboratory tests Report.] E & FN Spon, London. evaluation it was found that the scarfs of 60° and 75° are Müller M. (2006): Adhesive bonding of metallic and non- most useful for the bonded joint strength increase. metallic materials, [Ph.D. Thesis.] CULS, Prague. (in Using the disperse adhesive Herkules, the labo- Czech) ratory tests of spruce wood bonding were carried Mukam F.J.A., Mouongue A. (2003): Strength of some out. The presumption of the suitability of using the wood adhesives used in Cameroo. International Journal scarf joints was confirmed. By the tests, the scarfs of Adhesion and Adhesives, 23: 287–291. of angles 60° and 75° were found as suitable for a Němec J., Janáček V., Hurda B. (2005): Wood – Historical substantial bonded joint strength increase. Lexicon. Grada publishing, Praha. (in Czech) Pizzi A. (1994): Advanced Wood Adhesives Technology. References Dekker Inc., New York. Pizzi A., Mitta K.L. (2003): Handbook of Adhesive Technol- ASTM (1994): ASTM D905-94 Standard Test Method ogy. Dekker Inc., New York. for Strength Properties of Adhesive Bonds in Shear by Ševčík L. (2005): New methods of optimization machine Compression Loading. ASTM International, West Con- details. Vědecká pojednání, Wissenenshaftliche Abhand- shohocken. lungen, Práce naukowe, 11: 357–360. CSN 66 8508 (1995): Test Methods for Wood Adhesives for Non-structural Parts. Determination of the Strength of Received for publication August 31, 2008 Glued Connections in a Tensile Stress. UNMZ, Praha. Accepted after corrections February 25, 2009 (in Czech)

Abstrakt

Herák D., Müller M., Chotěborský R., Dajbych O. (2009): Stanovení únosnosti dřevěných lepených spojů s úkosem. Res. Agr. Eng., 55: 76–83.

V článku je popsáno kompletní odvození teoretické únosnosti lepeného spoje s úkosem a sestrojení Mohrovy kruž- nice napjatosti pro jednoosou napjatost. Dále je v článku detailně vysvětlena metodika experimentálního stanovení únosnosti lepeného spoje. Součástí této práce je také stanovení skutečné únosnosti lepeného spoje s úkosem. Klíčová slova: Mohrovy kružnice; jednoosá napjatost; lepení; úkosový spoj; dřevěný spoj

Corresponding author:

Ing. David Herák, Ph.D., Česká zemědělská univerzita v Praze, Technická fakulta, katedra mechaniky a strojírenství, Kamýcká 129, 165 21 Praha, Česká republika tel.: + 420 224 383 186, fax: + 420 220 921 361, e-mail: [email protected]

RES. AGR. ENG., 55, 2009 (2): 76–83 83