Effect of the dowel length, dowel diameter, and adhesive consumption on bending moment capacity of heat-treated wood dowel joints

Georgescu, S., Varodi, A. M., Racasan, S., and Bedelean, B. (2019). "Effect of the dowel length, dowel diameter, and adhesive consumption on bending moment capacity of heat-treated wood dowel joints," BioRes. 14(3), 6619-6632.

Abstract

This study applied response surface methodology for modeling and optimizing heat-treated wood dowel joints, the most used joint in furniture construction. The factors examined were dowel length, dowel diameter, and adhesive consumption. The bending moment capacity of the joints loaded in compression or tension were the responses. The load was applied at a constant speed until a major separation between the two parts occurred. To figure out the bending moment capacity, the ultimate failure loads and the moment arms were obtained during testing the joints. The joints were tested by using a universal testing machine. A two-factor interaction model was established to describe the relationship between the factors and the responses. An analysis of variance was employed to test the significance of the developed mathematical model. The dowel length, dowel diameter, and adhesive consumption had significant effects on the bending moment capacity of the heat-treated dowel joints. The dowel length was the main factor that affected the bending moment capacity of the heat-treated dowel joints.

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Effect of the Dowel Length, Dowel Diameter, and Adhesive Consumption on Bending Moment Capacity of Heat-treated Wood Dowel Joints

Sergiu Georgescu, Anca Maria Varodi, Sergiu Răcășan, and Bogdan Bedelean*

Keywords: Heat-treated wood; Wood joints; Tension and compression loading; Bending moment capacity Response surface methodology; Optimization

Contact information: Transilvania University of Brasov, Faculty of Wood Engineering, Universității Str. 1, 500036 Brasov, Romania; *Corresponding author: bedelean@unitbv.ro

INTRODUCTION

Heat treatment is an effective method to enhance wood dimensional stability. It has been developed to enhance wood properties and make wood competitive against other materials (Dilik and Hiziroglu 2012; Sandberg et al. 2013). Outdoor furniture is one potential application of heat-treated wood (Sandberg et al. 2013; Kuzman et al. 2015).

The furniture structural system can be classified as frame- or case-type construction (Smardzewski 2015). When a combination of these solutions are observed in the same product, the designed furniture has a composite structure (Eckelman 2003). However, the designed structure must resist to the loads that are going to act on the furniture.

The most used joint in furniture construction is the dowel joint (Fig. 1) because it has favorable cost and production characteristics (Eckelman 2003; Diler et al. 2017). Various factors can affect the strength of dowel joints, including wood species, dowel length, depth of dowel embedment, dowel type, hole diameter, distance between holes, number of dowels, adhesive type and consumption, tightness of fit, boring speed, and feed rate (Eckelman 2003).

Dowel joint sizing (e.g., dowel length, dowel diameter, and adhesive consumption) is based on the studies that have been developed for untreated wood (Curtu et al. 1988; Eckelman 2003; Cismaru 2009; Smardzewski 2015). Because heat-treated wood has inferior mechanical properties compared to untreated wood, an optimization tool could be used in the designing phase of the furniture for appropriate sizing of joints made of heat-treated wood (Tankut et al. 2014).

Fig. 1. The aspect and main characteristics of the analyzed L-shaped dowel joint (dimensions in mm) (Craftsmanspace 2019)

Moreover, there is limited information on the influence of various factors on the strength of heat-treated wood dowel joints. Kuzman et al. (2015) studied the effect of heat treatment on the mechanical properties of dowel joints produced from untreated and heat-treated beech (Fagus sylvatica L.) and spruce (Picea abies L.). Diler et al. (2017) determined that wood species, heat treatment, adhesive, and joint type have significant effects on the withdrawal force capacity of dowel joints. Georgescu and Bedelean (2017) analyzed the effect of heat treatment, dowel length, dowel spacing, and depth of dowel embedment on the mechanical strength of dowel joints made of ash (Fraxinus excelsior). Their results matched Kuzman et al. (2015): The joints of heat-treated wood had lower compressive and tensile failure loads than the joints of untreated wood. Additionally, Georgescu and Bedelean (2017) reported that the compressive and tensile strengths of heat-treated dowel joints increases when the dowel length increases, the distance between holes increases, and the ratio of dowel embedment in the rail of the joint decreases. However, the analyzed factors could not fully describe the behavior of heat-treated wood dowel joints, and other factors must be considered.

Therefore, the objective of this study was to examine the influence of dowel diameter, adhesive consumption, and dowel length on the bending moment capacity of heat-treated wood dowel joints using response surface methodology (RSM). Design and analysis with RSM consist of designing and executing an experiment to generate response data, fitting the data to a series of polynomial models, conducting an analysis of variance to assess factors’ statistical significance, comparing models, selecting the simplest model that best predicts the analyzed response, and using the selected model to determine the influence of the factors and to reveal the optimal configuration (Anderson and Whitcomb 2005; Yuan et al. 2015).

EXPERIMENTAL

Materials

The wood used in this study, heat-treated ash (Fraxinus excelsior) boards, was obtained from a local sawmill located in Brasov, Romania. Some basic technological steps (namely, straightening, planing, ripping, and crosscutting at final dimensions) were followed to obtain the parts of the dowel joint (parts A (200 x 70 x 30 mm) and B (130 x 70 x 30 mm)) (Fig. 1). Prior to boring, the parts were visually sorted based on several criteria, namely, lack of structural and technological defects and presence of radial annual ring orientation, to maximize the joint reliability (Záborský et al. 2017).

The sorted parts (682 pieces for part A and 703 pieces for part B) were weighed using a digital scale and grouped (based on their weight) into classes using frequency analysis techniques. Parts of the joints were randomly selected from each class, to assure that all groups were similar in terms of material characteristics.

Polyvinyl acetate adhesive (Kleiberit 303 (D4); Kleiberit, Weingarten, Germany) was uniformly dosed and applied in each hole of the joints using a syringe and a glass rod. The quantity of adhesive was calculated by multiplying the adhesive consumption rate by the area of each hole. The possible influence of excess adhesive on the strength of the joints was limited using wax paper (Fig. 1) to separate the parts of the joints (Dalvand et al. 2014).

Multi-grove dowel pins (Fig. 1) made of beech wood (Fagus sylvatica) was used to assemble the parts of the joints. The depth of dowel penetrations in the rail (part B of the joint) was 0.55 from its length (Fig. 1).

The steps to assemble one joint were: applying the adhesive on each wall of the hole; inserting the dowels in the rail; applying the wax paper; mounting the other part of joint; and pressing the joint in a wood clamp until 24 h.

Methods

To obtain the configurations of dowel joints, a central composite design (CCD) was generated with the statistical package Design-Expert^® (version 9, Stat-Ease Inc., Minneapolis, MN, USA). In this experimental design, the factors were dowel length (X₁), dowel diameter (X₂), and adhesive consumption (X₃). The responses were bending moment capacities of joints loaded in compression (Ŷ_MC) or tension (Ŷ_MT). The CCD was built up from the following (Anderson and Whitcomb 2005; Ariaee et al. 2014):

Two-level factorial design points (Fig. 2b) (estimating first-order and two-factor interactions). These points take into account all possible combination of the low (-1) and high (+1) levels of analyzed factors. In this study, there were three factors and each analyzed at two levels (-1, +1). Therefore, there were eight possible combinations (+1, +1, +1), (+1, +1, -1), (+1, -1, -1), (-1,-1,-1), (-1, +1,+1), (-1, -1, +1), (-1, +1, -1) and (+1, -1, +1). Based on these combinations, the configurations #1, 2, 4, 5, 6,11, 12 and 14 of the joints were constructed (Table 1);
Axial points (estimating pure quadratic effects). Two factors were analyzed at the center value (0) and the third one has the value of alpha (α) (Fig. 2c). Therefore, in this study, there were six possible combinations, namely, (-α, 0, 0), (+α, 0, 0), (0, 0, + α), (0, 0, – α), (0, + α, 0) and (0, – α, 0). Based on these combinations the configurations #3, 7, 8, 9, 10 and 15 of the joints were constructed (Table 1);
Center points (estimating the experimental error). Each factor was analyzed at the center value (Fig.2b), namely, the configuration #13 (Table 1) of analyzed joints was constructed.

Fig. 2. Face centered experimental design (a), two level factorial design and center points (b) and axial points (c) (Anderson and Whitcomb 2005)

Table 1. Factors and Corresponding Levels for the Applied Experimental Design

The analyzed configurations are presented in Table 2. Each configuration was replicated 15 times. Therefore, a total of 450 joints were assembled and tested. Following assembly, the joints were conditioned for at least one month in the same area where the compressive and tensile tests were performed (Kasal et al. 2015). The equilibrium moisture content of heat-treated wood joints was about 5%, and the average density was equal to 618 kg/m³. Half of the joints were subjected to compression tests, and the other half were subjected to tension tests.

The mechanical testing of joints was performed on a universal testing machine (Zwick Roell Z10; Zwick GmbH & Co. KG, Ulm, Germany). The load was applied at a constant speed of 3 mm/min until a notable separation between the two parts occurred (Kuzman et al. 2015). The ultimate failure load was recorded for each analyzed dowel joint. The compression and tension tests simulated two possible situations, which could be observed when a force is applied to a typical frame structure. In the first situation, the corner joint was subjected to a compression load (Fig. 3a). In the other, the corner joint was subjected to a tension force (Fig. 3b) causing a moment tending to open the joint (Negreanu 2003; Yerlikaya and Aktaş 2012; Kasal et al. 2015).

Table 2. Configuration of Joints According to the Experimental Plan and the Mean Experimental Values with Coefficient of Variation

Fig. 3. The loading forms of dowel joints subjected to compression (a) and tension (b) (dimensions in mm)

The bending moment capacity of the analyzed joints was calculated by means of Eq.1 for compression test and Eq. 2 for tension test (Derikvand and Eckelman 2015),

where M_c is the bending moment of joints subjected to compression (Nm), M_t is the bending moment of joints loaded in tension, F is the ultimate failure load (N), L_c is compression moment arm (42 mm), and L_t is the tension moment arm (92 mm).

RESULTS AND DISCUSSION

The bending moment capacities of joints that were under a diagonal tension load were, on average, about 45% higher than those of the joints loaded in compression (Table 2). The coefficient of variation was between 9 and 23% for compression sets and between 11 and 26% for the joints loaded in tension. Therefore, the bending moment capacity in tension was more variable than that in compression.

In general, the failure modes of joints included glue-line fracture, dowel deformation, and dowel and material fracture (Fig. 4). Displacement and deformation of the dowels was also observed. Also, a separation of the parts of the joints was frequently observed when the dowel length, dowel diameter and adhesive consumption were tested at the minimum value (30 mm, 6 mm and 250 g/m²). On the other hand, when the dowel length, dowel diameter and adhesive consumption were analyzed at maximum value (70 mm, 10 mm and 450 g/m²), either material fracture or dowel fracture was observed. These failures occurred both during compression and tension testing.

Two-factor interaction (2FI) empirical models were suggested by the statistical software to predict the bending moment capacity under diagonal compression and tension loading of heat-treated wood dowel joints. The models were significant at the 1% level. The mathematical models that could predict the bending moment capacity of the joints loaded in compression (Ŷ_Mc) or tension (Ŷ_Mt) are presented in terms of both coded and actual factors (Eqs. 3 to 6):

The coded equations (Eqs. 3 and 5) are useful for identifying the relative impacts of the factors (Sova et al. 2016). Meanwhile, the equations in terms of actual factors (Eqs.4 and 6) can be used to make predictions about the bending moment capacity of the heat-treated dowel joints. The relation between the coded and actual values is described by the Eq. 7 (Zhu et al. 2015),

(7)

where X_i is the coded value of the analyzed factor, A_iis the actual value of the analyzed factor, A₀ is the actual value at the center point of the factor (Table 1), ΔA is the step change.

Fig. 4. Failure modes of the analyzed dowel joints, including glue-line fracture (a, b, and e), material fracture (f, g, k, and l), dowel fracture (c and h), and deformation and displacement (d, j, and i)

Table 3. Analysis of Variance Results for the 2FI Equation of the Statistical Software for the Bending Moment Capacity of the Joints Loaded in Compression

Table 4. Analysis of Variance Results for the 2FI Equation of the Statistical Software for the Bending Moment Capacity of the Joints Loaded in Tension

The selected models obtained greater adjusted and predicted R² (Tables 3 and 4) values in comparison with other models (linear, quadratic, and cubic). The predicted R² was in reasonable agreement with the adjusted R². Moreover, the lack of fit was not significant. Therefore, the models adequately described the analyzed responses (Anderson and Whitcomb 2005). According to the ANOVA results (Tables 3 and 4), all main factors (X₁, X₂, and X₃) and their interactions (X₁X₂, X₁X₃, and X₂X₃,) were statistically significant at the 5% level.

Based on the obtained models (Eqs. 3 and 5) the main factor that affected the bending moment capacity of heat-treated wood dowel joints loaded in compression or tension was the dowel length (X₁), followed by dowel diameter (X₂) and adhesive consumption (X₃). All three factors had synergetic (interaction) effects in increasing the bending moment capacity under diagonal compression and tension loading of the heat-treated wood dowel joints. The relative magnitudes of these interactions were in the order of X₁X₃ > X₁X₂ > X₂X₃ for the diagonal compression loading and X₁X₃ > X₂X₃ > X₁X₂ for the diagonal tension loading of the heat-treated wood dowel joints.

Fig. 5. 3D plot showing the interaction effects of dowel length and dowel diameter on the bending moment capacity of joints loaded in compression when the adhesive consumption was set at 250 g/m²

Fig. 6. 3D plot showing interaction effects of dowel length and diameter on bending moment capacity of joints loaded in compression when adhesive consumption was set at 350 g/m²

The interaction effects of dowel length and dowel diameter on the bending moment capacity of joints loaded in compression or tension are shown in Figs. 5 through 10. The greatest bending moment capacity can be achieved by increasing the dowel length, dowel diameter, and adhesive consumption (Figs. 7 and 10).

Fig. 7. 3D plot showing interaction effects of dowel length and diameter on the bending moment capacity of joints loaded in compression when the adhesive consumption was set at 450 g/m²

Fig. 8. 3D plot showing the interaction effects of dowel length and dowel diameter on the bending moment capacity of joints loaded in tension when the adhesive consumption was set at 250 g/m²

Fig. 9. 3D plot showing the interaction effects of dowel length and dowel diameter on the bending moment capacity of joints loaded in tension when the adhesive consumption was set at 350 g/m²

Fig. 10. 3D plot showing the interaction effects of dowel length and diameter on the bending moment capacity of joints loaded in tension when the adhesive consumption was set at 450 g/m²

The analyzed factors were optimized based on three scenarios. In the first optimization scenario, it was supposed that in the design phase of the product, one wants to achieve the maximum bending moment capacity of the heat-treated wood dowel joints. The second optimization scenario took into account the target value of 2225 N, which is the upper level of the vertical seat loads that can be transferred on the structure of a chair (Eckelman 2003). The third optimization scenario sought to achieve the target value of 1780 N, which is the upper level of the vertical loads that can be transferred on the arms of a chair (Eckelman 2003).

The analyzed factors were kept within the range of the data as given by the CCD experimental plan (Table 2). Equal importance was assigned to all of the analyzed factors (Table 5). The numerical optimization algorithm included in the statistical software was run to evaluate the optimal values as presented in Table 5. The solution with the highest desirability coefficient (D) was selected for each analyzed scenario. The relative error was computed using Eq. 8,

(8)

where E_R represents the relative error (%), Y is the experimental value (N), and Ŷ is the predicted value (N).

Table 5. Criteria for Different Factors and Responses in Optimization of Heat-treated Wood Dowel Joints

Table 6. Experimental Summary of Optimization of Heat-treated Wood Dowel Joints

One can observe that the relative error (E_R) was between 5% and 29% in predicting the bending moment capacity of heat-treated wood dowel joints (Table 6). In the case of the first scenario, namely, when the maximum bending moment capacity was planned to be achieved, the relative error was 25% in case of joints loaded in compression and 29% for the joints loaded in tension. For the second analyzed scenario, when the target value of 2225 N was imposed during optimization study, the relative error was 24% for compression and 5% for tension models. On the other hand, when the target value was 1780 N, the relative error was 19% for the compression test and 8% for the tension test. The obtained errors could be considered reasonable. Therefore, the proposed methodology could represent a tool for predicting and optimizing the bending moment capacity of heat-treated wood dowel joints loaded in compression or tension.

CONCLUSIONS

The effect of dowel length, dowel diameter, and adhesive consumption on the bending moment capacity of heat-treated wood dowel joints loaded in compression or tension was analyzed in this study. Moreover, two regression equations were developed to predict the bending moment capacity of heat-treated wood dowel joints based on the analyzed factors.

Dowel length, dowel diameter, and adhesive consumption had significant effects on the bending moment capacity of heat-treated wood dowel joints.
The dowel length was the main factor affecting the bending moment capacity under diagonal tension and compression loading of the heat-treated dowel joints.
The bending moment capacity of joints loaded in tension was, on average, about 45% higher than that of the joints loaded in compression.
The optimum dowel length, dowel diameter, and adhesive consumption were revealed for the analyzed scenarios using response surface methodology.

ACKNOWLEDGMENTS

The authors are grateful for the support of the Transilvania University of Brasov, Romania, Grant No. 8019/14.07.2017.

REFERENCES CITED

Anderson, M. J., and Whitcomb, P. J. (2005). RSM Simplified: Optimizing Processes Using Response Surface Methods for Design of Experiments, CRC Press, Taylor & Francis Group, Boca Raton, FL, USA.

Ariaee, S., Tutunchi, A., Kianvash, A., and Entezami, A. A. (2014). “Modeling and optimization of mechanical behavior of bonded composite–steel single lap joints by response surface methodology,” International Journal of Adhesion and Adhesives 54, 30-39. DOI: 10.1016/j.ijadhadh.2014.05.002

Cismaru, M. (2009). Structuri Tehnice Pentru Produse din Lemn [Wood Structures for Wood Products], Transilvania University Publishing House, Brasov, Romania.

Craftsmanspace (2019). “Dimensioning woodworking and carpentry joints,” (http://www.craftsmanspace.com/knowledge/dimensioning-woodworking-and-carpentry-joints.html), Accessed 15 March 2019.

Curtu, I., Nastase, V., Mihai, D., Mihailescu, T., and Stoian, O. (1988). Îmbinări în Lemn. Structură, Tehnologie și Fiabilitate [Joints in Wood: Structure, Technology and Reliability], Technical Publishing House, Bucharest, Romania.

Dalvand, M., Ebrahimi, G., Tajvidi, M., and Layeghi, M. (2014). “Bending moment resistance of dowel corner joints in case-type furniture under diagonal compression load,” Journal of Forestry Research 25(4), 981-984. DOI:10.1007/s11676-014-0481-y

Derikvand, M., and Eckelman, C. A. (2015). “Bending moment capacity of l-shaped mitered frame joints constructed of MDF and particleboard,” BioResources 10(3), 5677-5690. DOI: 10.15376/biores.10.3.5677-5690

Diler, H., Acar, M., Balıkçı, E., Demirci, S., and Erdil, Y. Z. (2017). “Withdrawal force capacity of T-type furniture joints constructed from various heat-treated wood species,” BioResources 12(4), 7466-7478. DOI: 10.15376/biores.12.4.7466-7478

Dilik, T., and Hiziroglu, S. (2012). “Bonding strength of heat treated compressed Eastern redcedar wood,” Materials & Design 42, 317-320. DOI: 10.1016/j.matdes.2012.05.050

Eckelman, C. A. (2003). Textbook of Product Engineering and Strength Design of Furniture, Purdue University Press, West Lafayette, IN, USA.

Georgescu, S., and Bedelean, B. (2017). “Effect of heat treatment on compressive and tensile strength of end to edge butt joint,” Pro Ligno 13(4), 500-507.

Kasal, A., Eckelman, C. A., Haviarova, E., Erdil, Y. Z., and Yalcin, I. (2015). “Bending moment capacities of L-shaped mortise and tenon joints under compression and tension loadings,” BioResources 10(4), 7009-7020. DOI: 10.15376/biores.10.4.7009-7020

Kuzman, M. K., Kutnar, A., Ayrilmis, N., and Kariz, M. (2015). “Effect of heat treatment on mechanical properties of selected wood joints,” European Journal of Wood and Wood Products 73(5), 689-691. DOI: 10.1007/s00107-015-0931-z

Negreanu, C. (2003). Contributii la Studiul Imbinarilor cu Cepuri Cilindrice din Structura Mobilei din Lemn Masiv [Contributions to the Study of Dowel Joints That Are Used in the Structure of Furniture Made of Solid Wood], Ph.D. Dissertation, Transilvania University of Brasov, Brasov, Romania.

Sandberg, D., Haller, P., and Navi, P. (2013). “Thermo-hydro and thermo-hydro-mechanical wood processing: An opportunity for future environmentally friendly wood products,” Wood Material Science & Engineering 8(1), 64-88. DOI: 10.1080/17480272.2012.751935

Smardzewski, J. (2015). Furniture Design, Springer International Publishing, Cham, Switzerland. DOI: 10.1007/978-3-319-19533-9

Sova, D., Bedelean, B., and Sandu, V. (2016). “Application of response surface methodology to optimization of wood drying conditions in a pilot-scale kiln,” Baltic Forestry 22(2), 348-356.

Tankut, N., Tankut, A. N., and Zor, M. (2014). “Mechanical properties of heat-treated wooden material utilized in the construction of outdoor sitting furniture,” Turkish Journal of Agriculture and Forestry 38, 148-158. DOI: 10.3906/tar-1211-9

Yerlikaya, N. Ç., and Aktaş, A. (2012). “Enhancement of load-carrying capacity of corner joints in case-type furniture,” Materials & Design 37, 393-401. DOI: 10.1016/j.matdes.2012.01.010

Yuan, Z., Yang, J., Zhang, Y., and Zhang, X. (2015). “The optimization of air-breathing micro direct methanol fuel cell using response surface method,” Energy 80, 340-349. DOI: 10.1016/j.energy.2014.11.076

Záborský, V., Borůvka, V., Kašičková, V., and Ruman, D. (2017). “Effect of wood species, adhesive type, and annual ring directions on the stiffness of rail to leg mortise and tenon furniture joints,” BioResources 12(4), 7016-7031. DOI: 10.15376/biores.12.4.7016-7031

Zhu, C., Zhai, X., Li, L., Wu, X., and Li, B. (2015). “Response surface optimization of ultrasound-assisted polysaccharides extraction from pomegranate peel,” Food Chemistry 177, 139-146. DOI: 10.1016/j.foodchem.2015.01.022

Article submitted: March 15, 2019; Peer review completed: May 14, 2019; Revised version received and accepted: June 18, 2019; Published: June 28, 2019.

DOI: 10.15376/biores.14.3.6619-6632