EFFECTS OF GEOMETRY ON MECHANICAL BEHAVIOR OF DOVETAIL CONNECTION

EFFECTS OF GEOMETRY ON MECHANICAL BEHAVIOR OF DOVETAIL CONNECTION Gi Young Jeong 1, Moon-Jae Park 2, KweonHwan Hwang 3, Joo-Saeng Park 2 ABSTRACT: The goal of this study is to analyze the effects of geometric variations of mortise and tenon on mechanical behavior of dovetail connections. Different tenon angles (θ), tenon neck widths (w 1 ), tenon head widths (w 2 ), and tenon heights (h) were used to analyze the stress distribution around critical area in dovetail connection using deterministic finite element method (FEM) models. The strength of dovetail connection from the FEM models was validated from the results of experimental tests. Although stress values were changed by geometric factors, critical shear stress occurred along the side of tenon. Critical normal stress occurred at the reentrant corner of mortise. Critical compression stress occurred at the tenon head. Critical tension perpendicular to the grain stress occurred around the mortise area. Different failure modes were observed associated with stress values given geometric factors. Optimizing geometrical variables to maximize strength of dovetail connection were found to be θ for 57 degree, w 1 for 7 mm, w 2 for 50 mm, and h for 33 mm. KEYWORDS: dovetail connection, stress, stochastic finite element method 1 INTRODUCTION 123 Dovetail connection have been commonly used for traditional wood frame buildings in Korea. The design of dovetail connection used to be entirely dependent upon skilled workers. With invent of advance cutting machinery, various geometries of dovetail connections are currently available. However, there is lack of guidelines for designing dovetail connection. Hierarchical structure and direction dependent property of wood materials are hard to be considered fully in the simulation to optimize geometry and predict strength of wood connection. It is important to use practical methodology and intuitive modelling to design wood connection. The stress distribution associated with 1 Gi Young Jeong, Dept. of Wood Science and Engineering, Chonnam National University, 77 Youngbongro Bukgu Gwangju, South Korea. Email: gjeong1@jnu.ac.kr 2 Moon-Jae Park, Div. of Wood Engineering, Korea Forest Research Institute, 57 Hoegiro dongdaemungu, Seoul, South Korea. Email: mjpark@forest.go.kr. 3 KweonHwan Hwang, Korea Forestry Promotion Institute, 1653 Sangamdong, Mapogu, Seoul, South Korea. Email: khwang@kofpi.or.kr 2 Joo-Saeng Park, Div. of Wood Engineering, Korea Forest Research Institute, 57 Hoegiro dongdaemungu, Seoul, South Korea. Email: jusang@forest.go.kr connection structure under various loading conditions could lead to quantify failure modes of materials. With known stress distribution associated with failure modes, critical factors could be identified and used in predicting strength and optimizing geometry of dovetail connection. Simplified approach and controllable assumption are key aspects to simulate dovetail connection. The dovetail connection can be largely divided into tenon and mortise. The geometry of tenon and mortise influenced the stress distribution in dovetail connection (Tannert 2010). If main variables influencing failure of dovetail connection are found, optimized geometry to maximize load carrying capacity for dovetail connection could be established. Based on the design equation, optimum geometry of dovetail connection could be created for different materials. Also allowable load carrying capacity for dovetail connection member could be estimated. Park et al. (2010) investigated the effects of tenon neck width, tenon head width, tenon length, and tenon angle on dovetail connection. Four different tenon neck widths of 15, 20, 35, and 50 mm and two different tenon lengths of 30 and 45 mm, and four different tenon angles of 15, 20, 25, and 30 degrees were used to investigate the effects of geometry on tensile strength of dovetail connection. Based on experimental test, tenon neck

width was recommended for 20 mm and tenon angle was recommended from 15 to 30 degree. Tenon neck length was recommended for 30 mm. However, it seems insufficient to provide the optimized geometry of dovetail connection based on limited experimental tests. Jeong and Hindman (2010a) measured orthotropic properties of loblolly pine strands. Wood as a natural material its material property is not quantified as one number. Orthotropic properties of wood can be quantified as specific distributions. Due to the different material properties in the longitudinal, radial, and tangential directions of wood, the failure type was different associated with different stress distributions. Jeong and Hindman (2010b) investigated mechanical behaviour of differently oriented strands using stochastic finite element methods. Although all wood specimens showed brittle failure behaviour, differently oriented strands showed different stress distribution. Strength of differently oriented strands was predicted using Tsai-hill failure criteria. Sensitivity analysis showed that earlywood and latewood from differently oriented strands participated in different proportion in terms of load carrying capacity. Pang et al. (2011) investigated effects of crossing beam shoulder on moment carrying capacity of dovetail connection. With increment of beam shoulder width, maximum moment of dovetail connection increased. Failure behaviour of dovetail connection was also varied associated with crossing beam shoulder width. When the crossing shoulder width was less than 50% of the crossing beam width, failure occurred at mortise area of the post. When the crossing shoulder width was larger than 50% of the crossing beam width, a tension perpendicular to the grain failure occurred at the crossing beam shoulder. Moses and Prion (2004) used finite element method to predict mechanical properties of single bolt connection. Different combination of panel type, end, edge distance, bolt diameter, and direction of loading were used to analyze ultimate load, ultimate displacement and failure mode of single bolt connection. Weibull weakest link theory and the maximum stress theory were used to count stress concentration area, probability of failure, material variability. The results were reasonably accurate. applied to predict the strength of rounded dovetail connection. Sangree and Schafer (2009) used finite element method to predict load carrying capacity of traditional timber scarf joint. Two specific failure modes including shear parallel to grain and tension perpendicular to the grain were identified. Hankinson s formula was used to predict strength of scarf joint subjected to combined bending and tension forces. Although previous studies showed that structure of material and failure behaviours are critical to predict strength of material, the effects of variation of material properties and geometry of structure on the design of dovetail connection were not considered. The goal of this study is to analyze the effect of geometry on tensile strength of dovetail connection using stochastic finite element method (SFEM). Different geometries of tenon and mortise were evaluated to maximize strength of dovetail connection. Based on the results, allowable load for dovetail connection made of glulam associated with geometry variables was established. 2 MATERIALS AND METHODS 2.1 DEVELOPMENT OF DOVETAIL CONNECTION USING FINITE ELEMENT METHOD Figure 1 shows the dovetail connection including mortise and tenon. Different geometry of dovetail connection was constructed using finite element method. Four node quad elements with plane strain assumption were applied to simulate mechanical behaviour of dovetail connection under tension. Width of member was 150 mm and total length of member was 1000 mm. As it can be seen from Equation 1, the geometry of mortise and tenon could be defined by the relation of four factors, tenon head width (w 2 ), tenon neck width (w 1 ), tenon height (h), and tenon angle (θ). Thomas et al. (2010a and 2010b) investigated mechanical behaviour of rounded dovetail connections by experiment and FEM. Bending load applied dovetail connection. Experimental test results showed that the failure behaviour of dovetail connection was brittle. The failure location within the rounded dovetail connection joist member predicted from linear elastic finite element method was matched with the location observed from the experimental test. The modified Hashin criterion was

Figure 1: Geometry variables for dovetail connection Different friction coefficients from 0.3 to 0.6 for wood to wood connection were investigated. With increment of friction coefficient from 0.3 to 0.6, tension stress in y- direction decreased 4.1% and shear stress decreased 2.7%, and compression stress decreased 13.9%. Although friction coefficient influenced stress distribution of wood to wood connection, friction coefficient of 0.3 was applied to check the most critical case. sin w 2 h w1 2 2 h 2 (1) where θ = tenon angle, h = tenon height, w 1 = tenon neck width, w 2 = tenon head width 2.2 INPUT VARIABLES FOR DOVETAIL CONNECTION MODELS Table 1 shows the different material properties and fitted distributions used for dovetail connection models. Transverse isotropic assumption including 11.3 GPa for longitudinal elastic modulus (E Y ), 0.44 GPa for transverse elastic modulus (E X ), 0.7 GPa for shear modulus (G XY ), and 0.038 for Poisson s ratio (ν XY ) was applied to represent material property of glulam. E Y and E X were determined from tension test and shear modulus and Poisson s ratio were assumed based on elastic ratios (Bodig and Goodman 1973). Shear and transverse strength were determined from shear block and tension test, respectively. Table 1: Specific distributions of material properties Material Fitted property distribution scale shape Theta Longitudinal elastic Weibull 12.69 3.05 0 modulus Transverse elastic Weibull 0.48 2.48 0 modulus Shear strength Weibull 12.98 5.47 0 Radial strength Weibull 4.69 3.90 0 Tangential strength Weibull 2.98 7.70 0 Based on the experimental and simulation results, most critical failures of dovetail connection were govern by shear and tension perpendicular to the grain. The failure criterion for the material should reflect failure behaviour of materials (Jeong and Hindman 2010). Therefore, practical failure criteria could be defined as below tpe T S pe xy 1 0 (2) Where σ tpe is the tension perpendicular to the grain and τ xy is shear stress values from finite element method. T pe is the tension perpendicular to the grain strength and S is the shear strength. Stress components (σ tpe, τ xy ) associated with geometry factors were evaluated from FEM models and strength indexes (T pe, S) were obtained from experimental test. Based on specific distributions for each strength index, random strength indexes were generated using Monte-Carlo simulation. Regardless of different dovetail geometry, brittle failure occurred (Park et al. 2010). From the load-stress relationship, extrapolation of slope would meet the strength, which can be calculated from the experimental results (Hwang et al. 2009 and Park et al. 2010). The maximum stress can be considered as a function of load due to the lack of nonlinear deformation. From the slope of stress and load relationship, the stress components could be summarized as a function of load and values of slope for the stress components (Jeong and Hindman 2010). To validate the FEM models, failure loads determined from experimental test and predicted from the FEM models were compared. Deterministic FEM was used to analyze the effects of geometry factors on mechanical behaviour of dovetail connection. The average elastic modulus and strength values from Table 1 were used for the FEM. Different combinations of four geometry variables associated with Equation 1 were used to investigate the geometry effects on stress values. It should be noted that the variables in Table 2 were not used as a combination. To analyze the effect of tenon angle on mechanical behaviour of dovetail connection, fixed tenon height of 30 mm and tenon neck width of 20 mm and different tenon angles from Table 2 associated tenon head width were used. To analyze the tenon neck width, fixed tenon angle of 57 degree, tenon height of 30 mm, and different tenon neck width from Table 2 associated with tenon head width were used. To analyze the tenon head width, fixed tenon angle of 57 degree, tenon neck width of 11 mm and different tenon head width from Table 2 associated with tenon height were used. To analyze the tenon height, fixed tenon angle of 57 degree, tenon head width of 50 mm and different tenon height from Table 2 associated with tenon neck width were used. With the stress components from FEM and strength indexes from experimental tests, failure loads of different geometry

dovetail connections were predicted using Equation 2. From the results, dovetail connection with a combination of four geometry variables carrying the highest load was defined. Table 2: Different geometry factors for tenon and mortise in dovetail connection Angle ( ) Tenon neck Tenon head Tenon width (mm) width (mm) height (mm) 80.57 88.16 32.55 41.22 71.60 78.16 36.19 39.84 63.46 68.16 39.83 38.47 56.33 58.16 43.47 37.10 50.21 48.16 47.11 35.72 45.02 38.16 50.74 34.35 40.62 28.16 54.38 27.48 36.88 18.16 58.02 20.61 33.70 8.16 61.66 13.74 30.97 65.30 28.62 68.94 26.57 72.58 76.22 3. RESULTS AND DISCUSSION Table 3 shows the difference of failure load of dovetail connection from experimental (Park et al. 2010) and FEM. The results showed that the difference between experimental and FEM ranged from 3.4% to 20.8%. Considering the variability of materials, FEM predicted the failure load of dovetail connection very well. With validated FEM model, more systematic analysis of geometry variable effects on stress distribution and load carrying capacity of dovetail connection could be achieved. Figure 2a shows stress x distribution. Although absolute compression stress value in x direction occurred at the head of tenon, positive tension stress occurred at the mortise. Since tension strength perpendicular to the grain was a brittle failure mode, failure occurred at the mortise area observed from experimental test. Figure 2b shows stress y distribution. The highest stress occurred at the re-entrant corner. When the tension force applied, tension force occurred along the grain at the reentrant corner of mortise, whereas compression stress occurred at the beneath of the re-entrant corner of mortise. These stress distribution created shear between fibers in lengthwise. Figure 2c shows the shear stress distribution. Maximum shear stress occurred along the side of tenon. Experimental test results showed that the side of tenon failed along the shear plane. This failure mode occurred due to the fact that wood is weak in shear parallel to the grain. Shear in the longitudinal direction between fiber and fiber occurred. The shear strength of glulam was varied from 9.6 MPa to 13.0 MPa (Hwang et al. 2009). The lowest shear strength was observed when shear block specimen contained a pith in shear section area whereas the highest shear strength was observed when shear block specimen had no pith (Hwang et al. 2009). Keean (1974) found that shear strength of Douglas-fir glued-laminated beams depended on the sheared area. Considering the fact that strength ratios in glulam from Table 1 and stress distributions in Figure 2, most failure modes of dovetail connection were dominated by either tension perpendicular to the grain stress or shear stress. Table 3: Difference between failure load from experimental test and failure load from FEM Geometry variables Failure load from Experimental, kn (COV) Failure load from FEM,kN Diff. (%) 60 18.3 (15.8) 20.4 11.4% 75 14.4 (13.5) 11.4 20.8% 65 20.2 (18.9) 16.8 16.8% 75 11.7 (14.6) 11.3 3.4% 3.1 COMPARISON BETWEEN STRESS DISTRIBUTIONS AND FAILURE MODES FROM DOVETAIL CONNECTION Figure 3 shows the different stress distributions from simulation and typical failure behaviours of dovetail connection from experimental test. Stress distributions from simulation captured different failure modes of dovetail connection.

a) Transverse stress x distribution from FEM and tension perpendicular to the grain failure at mortise in dovetail connection c) Shear stress distribution from FEM and shear failure of dovetail connection Figure 2: Different failure behaviours of dovetail connection. a) Transverse stress x distribution from FEM and tension perpendicular to the grain failure at mortise in dovetail connection, b) Longitudinal stress y distribution from FEM and shear failure at mortise in dovetail connection, c) Shear stress distribution from FEM and shear failure of dovetail connection 3.2 CHANGES OF TENSION PERPENDICULAR TO THE GRAIN STRESS AND SHEAR STRESS ASSOCIATED WITH GEOMETRY OF TENON AND MORTISE IN DOVETAIL CONNECTION Different tenon angle, tenon head width, tenon neck width, and tenon length derived from the geometry equation 1 to analyze the effects of those variables on stress values of dovetail connection. b) Longitudinal stress y distribution from FEM and shear failure at mortise in dovetail connection Figure 3a shows the change of tension perpendicular to the grain stress and shear stress values around tenon and mortise area when the tenon angle increases at tenon height of 30 mm and tenon neck width of 20 mm. With change of tenon angle, tension stress x and shear stress

xy showed a parabolic curve. Minimum shear stress occurred at tenon angle of 63 degree. Minimum tension stress x occurred at tenon angle of 56 degree. Considering the fact that failure of dovetail connection controlled by two mixed stress values, optimum angle for maximizing load capacity could range from 56 degree to 63 degree. Figure 3b shows the change of stress values around tenon and mortise area when the neck width increases at tenon angle of 57 degree and tenon height of 30 mm. With change of tenon neck width, tension perpendicular to the grain stress and shear stress showed a different trend. While shear stress at the tenon area showed a parabolic curve with increment of tenon neck width, tension perpendicular to the grain stress increased. The minimum shear stress occurred when the tenon neck width was 41 mm. Tension perpendicular to the grain stress increased as the tenon neck width increased. The minimum tension perpendicular to the grain stress occurred when tenon neck width was 11.04 mm. Figure 3c shows the change of stress values associated with the tenon head width (w 2 ) given angle of 57 degree and tenon neck width of 11 mm. While shear stress showed a parabolic curve with increment of tenon head width (w 2 ), tension perpendicular to the grain stress increased gradually. The minimum tension perpendicular to the grain stress was found to be when w 2 was 49.95 mm. The minimum shear stress occurred when w 2 was 69.43 mm. Considering consistent tenon angle and tenon neck width, tension perpendicular to the grain stress increased associated with increment of tenon head width and tenon length. Due to the geometry relation from Equation 1, with increment of tenon head width, tenon length also increased at consistent tenon angle and tenon neck width. Therefore, the optimum tenon head width should be ranged from 49.95 mm to 69.43 mm. Considering the fact that tension perpendicular to the grain strength was the most critical stress that control the strength of dovetail connection, w 2 should be close to 49.95 mm to minimize the stress value. Figure 3d shows the change of stress values associated with tenon height (h) given tenon angle of 57 degree and tenon head width of 50 mm. Tension perpendicular to the grain stress and shear stress showed different trends with increment of h. When h increased, shear stress decreased until the tenon height of 33mm and sharply increased after 33 mm, whereas tension perpendicular to the grain stress was almost not changed. The minimum shear stress 43.87 MPa occurred at h of 33.11 mm. Since tension perpendicular to the grain stress was not varied with increment of tenon height, shear stress value associated with tenon height could be used to maximize load carrying capacity. Considering the ratio of shear stress to tension perpendicular to the grain stress, the h of 33.11 mm appeared to be maximizing the load carrying capacity of dovetail connection associated with tenon angle of 57 degree, tenon head width of 50 mm, and tenon neck width of 7 mm. The determined combination of four different geometry variables from deterministic FEM was used to maximize load carrying capacity for dovetail connection. The average load carrying capacity for dovetail connection was calculated to be 21.4 kn. a) Change of tension perpendicular to the grain stress and shear stress in dovetail connection with increment of tenon angle b) Change of tension perpendicular to the grain stress and shear stress in dovetail connection with increment of tenon neck width c) Change of tension perpendicular to the grain stress and shear stress in dovetail connection with increment of tenon head width

Predictions of the anticipated stress demands and their effect on load carrying capacity were evaluated using finite element method. ACKNOWLEDGEMENT The current work was supported by Korea Forest Research Institute (KFRI). d) Change of tension perpendicular to the grain stress and shear stress in dovetail connection with increment of tenon height Figure 3: Change of tension perpendicular to the grain stress and shear stress in dovetail connection with increment of geometry variables a) tenon angle ( ), b) tenon neck width (w 1), c) tenon head width (w 2), d) tenon height (h) 4. CONCLUSIONS The current study was to investigate the effects of geometry variables on mechanical behaviour of dovetail connection. Different stress distribution associated with geometry of dovetail connection was observed. Three representative failure modes were observed. Based on the results, geometry of maximizing load carrying capacity was found to be tenon angle for 57 degree, w 1 for 7 mm, w 2 for 50 mm, and h for 33 mm. Although stress values were changed by geometry factors, critical shear stress occurred along the side of tenon. Critical normal stress occurred at the re-entrant corner of mortise. Critical compression stress occurred at the tenon head. Critical tension perpendicular to the grain stress occurred around the mortise area. Different failure modes were observed associated with stress values given geometry factors. Experimental test and simulation results identified two limit states including shear failure parallel to grain and tension perpendicular to the grain stress for dovetail connection. Average allowable load for dovetail connection was estimated to be 21.4kN. Failure modes of dovetail connection were dominated by tension perpendicular to the grain stress and shear stress. The proposed failure criteria associated with the critical stress were effective in prediction of load carrying capacity from dovetail connection. REFERENCES [1] American Forest and Paper Association (AF&PA). Standard for load and resistance factor design for engineered wood construction. AF&PA/ASCE, Washington DC, 1996 [2] American Forest and Paper Association (AF&PA). National design specification (NDS) for wood construction. Washington DC, 2005. [3] Park J. S., Hwang K. H., Park M. J., Shim K. B. Tensile performance of machine-cut dovetail joint with Larch glulam. Mokchae Konghak, 38(3):1-6, 2010. [4] Jeong G. Y., Hindman D. P., Zink-Sharp A.: Orthotropic properties of loblolly pine (Pinus taeda) strands. J Mater Sci, 45(21):5820-5830, 2010. [5] Jeong G. Y., Hindman, D. P.: Ultimate tensile strength of loblolly pine strands using stochastic finite element method. J mater Sci, 44(14):3824-3832, 2009. [6] Tannert T., Lam F., Vallée T.: Structural performance of rounded dovetail connections: experimental and numerical investigations. Eur J Wood Prod, 69(3):471-482, 2010a. [7] Tannert T., Lam F., Vallée T.: Strength prediction for rounded dovetail connections considering size effects. J Engineering Mechanics, 136(3):358-366, 2010b. [8] Pang S. J., Oh J. K., Park J. S., Park C.Y., Lee J. J.: Moment-carrying capacity of dovetailed mortise and tenon joints with or without beam shoulder. J Struct Eng ASCE, 137(7):785-789, 2010. [9] Mose D. M., Prion H. G. L.: Stress and failure analysis of wood composites: a new model. Compostes: Part B, 35(3):251-261, 2004. [10]Sangree R. H., Schafer B.W.: Experimental and numerical analysis of a halved and tabled traditional timber scarf joint. Construction and Building Materials, 23(2):615-624, 2009. [11]Hwang K. H., Park J. S.: Estimation of moment resisting property for pin connection using shear strength of small glulam specimens. Mokchae Konghak, 36(4):58-65, 2010. [12]Keenan, F. J.: Shear strength of wood beams. Forest Prod J, 24(9):63-70, 1974. [13]ASTM D 5457 Standard specification for computing the reference resistance of wood-based materials and structural connections for load and resistance factor design. American Society for Testing and Materials, West Conshohocken, PA. [14]ASTM D 245 Standard practice for establishing structural grades and related allowable properties for

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