THE EFFECT OF DOWEL SPACING ON THE STRESS AND STRAIN OF CASE-TYPE FURNITURE CORNER JOINT

THE EFFECT OF DOWEL SPACING ON THE STRESS AND STRAIN OF CASE-TYPE FURNITURE CORNER JOINT Seid Hjdrević, Sndr Mrtinović Astrct University of Srjevo, Mechnicl Engineering Fculty, Vilsonovo setliste 9, Srjevo 71000, Bosni nd Herzegovin This pper presents stress nd strin nlysis of doule-dowel cse-type furniture corner joint. Numericl clcultions re crried out with liner elstic model for orthotropic mteril. The mthemticl model is solved y finite element method. The von Mises stress nd displcement re clculted for the simple stte of lod of MDF ord structure. Three dowel spcing re used in order to evlute the effect of the distnce etween the centers of dowel holes. The results show tht the dowel spcing nd the distnce etween the dowel nd the ord edge hve considerle impct on the stress stte of the fce nd edge memer. Stress ptterns otined in plnes of ords show tht stress is incresed in the res of frcture zones tht occur during the frcture moment tests of dowel joints. Results of the displcement clcultion indicte tht joint ecomes stiffer when the distnces etween the dowels nd the dowel nd the ord edge re rtionlly defined. Keyword: cse-type furniture; dowel spcing; MDF; numericl nlysis; stress nd strin This Puliction hs to e referred s: Hjdrevic, S[eid] & Mrtinovic, S[ndr] (2016). The Effect of Dowel Spcing on the Stress nd Strin of Cse-Type Furniture Corner Joint, Proceedings of the 26th DAAAM Interntionl Symposium, pp.0391-0399, B. Ktlinic (Ed.), Pulished y DAAAM Interntionl, ISBN 978-3-902734-07-5, ISSN 1726-9679, Vienn, Austri DOI:10.2507/26th.dm.proceedings.053-0391 -

1. Introduction Cse-type constructions re one of the most common products of the furniture industry. The strength nd the stiffness structures of this type re predominntly determined y properties of joints. In order to find solution tht would improve the properties of the dowel joints, nd indirectly, to improve the resistnce of structure during service, mny ffecting fctors re nlyzed [1, 2, 3, 4, 5]. Due to efficient technology, utiliztion of dowel joints is the most often wy used to ssemle wood pnels or wood-sed pnels. The experimentl investigtions focus on the fctors tht ffect the moment cpcity [6, 7, 8]. Zhng nd Eckelmn hve developed the expressions for estimting the ending strength s function of numer of dowels used, dowel dimeter, nd depth of insertion [8]. Although the expressions re limited to multi-dowel corner joints within the tested rnge, the uthors hve stted tht depth of insertion hs much more effect then dowel dimeter. The study [9] crried out using doule-dowel corner joints with vrious configurtions indicte tht the strength of dowel joints ecomes higher when the memer s thicknesses nd/or dimeter of dowels re incresed. It ws determined tht gretest prt of joints, ~ 98 %, fils due to frcture of fce memer [9]. The investigtion of joints produced y vrious wood sed mterils shows tht the higher vlues of strength nd stiffness re otined for MDF joints thn for PB joints nd the highest vlues re otined for PLY joints [10]. Filure lod nd optimum dowel spcing of joints, which re reinforced with glss-fire fric, re investigted y Yerliky [11, 12]. Filure lods of reinforced joints re significntly higher thn filure lods of unreinforced joints. The highest strength is otined for 96 mm dowel spcing in LMDF joints, nd for 128 mm dowel spcing in LPB joints. The studies [13, 14, 15, 16] provide descriptions of the numericl pproches to nlyse properties of the furniture corner joints. The study [17] provides lterntive methods of numericl rigidity modelling of dowel joints using nodes of sustitute liner elsticity modulus tht should e determined empiriclly. The stiffness vlues otined y numericl nlysis re compred with the experimentl results in the study [10]. The difference revels tht the numericl results provide more rigid ehviour of joints. The norml stress ptterns to contct plnes on the edge one of the ords hve een nlyzed y the uthors [18]. The stress vlue reched only the hlf-point of mximum vlues in the middle of the distnce etween fsteners. 2. Reserch ojective nd methodology Some of the literture provides informtion on the influence dowel spce on the corner joint strength. Generlly, the mximum strength of joints (drilling module m=32 mm) is otined when the distnce etween the centers of dowel holes is not less thn 96 mm [9, 19]. The criticl distnce of dowel to the edge of ord is 50 60 mm. The filure mode nlysis found tht the wekest prt of dowel joint is the fce memer. Three types of joint filure tht cn occur re consequence of the position nd the length of the frcture zone [9]. When the dowel spcing is less thn 96 mm, the frctures zones re overlpping, cusing the reduction of joint strength, s opposed to instnces where the zones re not overlpping. The expnded frcture zone reches the edge of the fce memer when the distnce etween dowel nd the ord edge is less thn criticl. Also, the joint resistnce depends on the joint loding scheme [8]. In the cse of compression loding, the joint strength is predominntly relted to the internl ond strength of the ord. In the cse of tension loding, the joint strength is predominntly relted to the tensile strength of the ord. In contrst with the experimentl studies, there re shorter rticles ville regrding the numericl nlysis of the effect of dowel spcing on the joint properties. The im of this study is to investigte the pplicility of numericl pproch in cse of determining the influence of dowel spcing on the mechnicl properties of cse-type furniture corner joints. Since the numericl clcultion ws limited to liner elstic model for orthotropic mteril, the study presents the nlysis of the qulittive spect of stress nd strin. The ojective is to evlute the effect of the distnce etween the centers of dowel holes, nd the distnce of dowel to the edge of ord, on the distriution of the von Mises stress, nd the distriution of trnsltion displcement. Three significnt dowel spcing were used in order to ssess the differences etween stress ptterns, s well s displcement ptterns, nd the stiffness of the doule-dowel corner joint sujected to compression or tension lods. Clcultions were performed using the Cti softwre pckge. 2.1. Mthemticl model The stress nd strin of loded solid ody in sttic equilirium re descried y the eqution of momentum lnce, expressed in the Crtesin tensor nottion [20], S n ds ij j V f dv 0 i (1) nd the constitutive reltion for elstic mteril 1 u u k l C C ij ijkl kl ijkl (2) 2 x x l k - 0392 -

In the equtions ove, x j re Crtesin sptil coordintes, V is the volume of solution domin ounded y the surfce S, ij is the stress tensor, n j is the outwrd unit norml to the surfce S,f i is the volume force, C ijkl is the elstic constnt of tensor components, kl is the strin tensor, nd u k represents the point displcement. Twelve non-zero orthotropic elstic constnts A ij re relted to the Young's modulus E i, the Poisson's rtio ij, nd the sher modulus G ij. The mthemticl model is complete when the oundry conditions re specified. Surfce trction f Si nd/or displcement u S t the domin oundries re known, i.e. ijn j f S nd ui us. (3) i Governing equtions (1) comined with the constitutive reltions (2) re solved with numericl method sed on the finite element. Generl form of the von Mises stress cn e expressed in terms of stress invrints I 1nd I 2 (4) VM 2 I 1 3I 2 2.2. Physicl model Doule-dowel cse-type furniture corner joint ws selected for investigtion. Geometries nd mesurements of the joint re shown in the Fig. 1.(). The fce memer nd the edge memer of 18 mm in thickness were joined y two 50 mm long dowels with 10 mm dimeter, Fig. 1.(). A symmetric hlf of the joint ws tken for the solution domin, Fig. 1.(c). The dowel ws fstened to the ords without glue line. The ords were contct-connected together s were the ords nd the dowel ends. The fce memer ws fixed t the lower end. Bending moment M ws pplied to the end of the edge memer. The imposed ending moment ws -10 Nm (compression loding) nd 10 Nm (tension loding). c Fig. 1. () Dowel joint geometries; () configurtion of the dowel; (c) joint loding scheme Clcultion ws crried out for MDF ords. Its elstic properties, for ord thickness of 18 mm, density =0.787 g/cm 3 nd internl ond strength of 0.55 MP, re presented in T. 1 [18]. The dowel mteril ws mple. Elstic properties of the mple wood, for wood density of =0.57 g/cm 3 nd moisture content of 12%, re presented in T. 1 [21]. Glol nd locl coordinte systems were pplied, nd numericl clcultions re crried out with model for orthotropic mteril. MDF ord Modulus of elsticity (GP) Rigidity modulus (GP) Poisson s rtio E x E y E z G xy G xz G yz xy xz yz 3.2 3.4 0.05 0.068 0.058 0.068 0.45 0.50 0.50 Mple (Acer scchrum Mrsh.). Modulus of elsticity (GP) Rigidity modulus (GP) Poisson s rtio E L E R E T G LR G LT G RT LR LT RT TR RL L 13.810 1.311 0.678 1.013 0.753 0.255 0.46 0.50 0.82 0.42 0.044 0.025 Tle 1. Elstic properties of MDF ord nd mple dowel - 0393 -

All mesurements except dowel spcing l were held constnt. According to the furniture 32 mm system (m x 32mm), investigtions were conducted on the corner joints with three different significnt distnces etween dowels of 160 mm, 96 mm nd 32mm, Fig. 2. 3. Results Fig. 2. Three distnces etween dowels The effect of dowel spcing on the von Mises stress ptterns in the width directions of ords t the ord surfce plnes ws ssessed. Positions of the selected width directions re shown in Fig. 3. Fig. 3. Width directions: () fce memer, () edge memer The von Mises stresses long the ord width on the plne thickness of fce nd edge memers, nd for compression nd tension lodings, re presented in Fig. 4. nd 5. Stress ptterns vry significntly nd indicte tht the stress increses in the res of the dowel. For the compression loding, the von Mises stress t the plne thickness of the fce memer is dominntly relted to the tensile stress perpendiculr to ord plne.the dowel insertion ffects the position of the stress tht cuse locl ord delmintion. Fig 4.() showsthe res where stress vlues re higher thn the internl ond strength of the ord (0.55 MP). The stress ptternsof three dowel spcing correspond to frcture zones tht occur during the frcture moment tests of dowel joints [9].For the tension loding, the edge of the fce memer is less significnt due to the occurrence compression stress perpendiculr to ord plne, Fig. 4 ().The high stress vlues in the edge memer re the consequence of the locl geometric nd mteril discontinuity of the edge ord wekened y the dowel holes.at the distnce etween dowels, nd distnce etween dowels nd the edges of the ords, stress vlues re lowerfor oth cses of lodings, Fig 5. Fig. 4. The von Mises stress fce memer (direction: x = -9 mm, z = 0): () compression loding; () tension loding - 0394 -

Fig. 5. The von Mises stress edge memer (direction: x = 0, z = -9 mm): () compression loding; () tension loding The vlues of the von Mises stress long the other width directions, shown in Fig. 3., re higher nd dominntly relted to tensile nd compression stress in the ord plnes. The stresses long the ord width t the inner surfce of fce memer, nd for compression nd tension lodings, re presented in Fig. 6. nd 7. The von Mises stress long the ord width, t the inner nd outer surfces of fce memer, nd for compression nd tension lodings, re presented in Fig. 8. nd 9. Fig. 6. The von Mises stress fce memer (direction: x = 0, z = -9 mm): () compression loding; () tension loding Fig. 7. The von Mises stress fce memer (direction: x = 0, z = -15.5 mm): () compression loding; () tension loding - 0395 -

Fig. 8. The von Mises stress edge memer (direction: x = 15mm, z = 0): () compression loding; () tension loding Fig. 9. The von Mises stress edge memer (direction: x = 15 mm, z = -18 mm): () compression loding; () tension loding The stress ptterns clerly indicte tht dowel spcing ffects the position nd size of the high stress res. The mximum vlues of the von Mises stress re otined t the positions where dowels re inserted. The mximum vlues of stress re close to the MDF ending strength (MOR > 20 MP) t the selected directions of the fce memer. For selected directions of the edge memer, the mximum stresses re much lower. The effect of dowel spcing on the trnsition of the lower stress re etween dowels is noticele t llselected directions.when dowel spcing is 32 mm, the lower stress re etween dowels is miniml. The re of lower stress stretches nd the length of the re re lrgest when dowel spcing is t 160 mm. The effect of the dowel distnce to the ord edge on the von Mises stress is noticele when the distnce of dowel to the ord edge is 20 mm, nd dowel spcing is t 160 mm. In tht cse, the res of incresed stress rech the ord edges. The minimum stress vlues t the ord edges re otined when dowel spcing is t 32 mm nd 96 mm. The res of lower stress etween dowels nd etween the dowel nd the ord edge re otined when distnce etween the centres of dowel holes is 96 mm. For compression loding, the results show tht the mximum von Mises stress t the plne thickness of the fce memer is much higher thn the internl ond strength of the ord while the von Mises stress, dominntly relted to the compression, t the inner surfce of the fce memer is close to the surfce strength of the ord, Fig. 4.() nd 7.(). The inner surfce of the fce memer is more significnt in the cse of tension loding, Fig. 6.() nd 7.(). The von Mises stress t the surfce is dominntly relted to the tensile stress, the mximum vlues of stress re higher, nd the vlues of stress re incresed t the edges of the fce memer, compred to the cse of compressing loding. In tht cse, the mximum vlues of compression stress perpendiculr to the fce ord re low, Fig 4.(). As opposed to the fce memer, the vlues of stress t the surfces of the edge memer increse if the von Mises stress is dominntly relted to the compression stress, Fig. 8. nd 9. Fig. 10. Totl trnsltionl displcement of the free end of the edge memer: () compression loding; () tension loding - 0396 -

The effect of dowel spcing on the totl trnsltionl displcements of the free end of the edge memer ws ssessed. Trnsltionl displcement nd deformtions of jointin cses of compression nd tension lodings re shown in Fig. 10. nd 11. When the distnce etween the centers of dowel holes is 96 mm, the joint stiffness is t mximum. By incresing the dowel spcing to 160 mm, joint stiffness decreses y ~ 8.5 % for oth cses of lodings. When the distnce is 32 mm, joint stiffness is decresed y ~ 12 %for cse of compression loding nd ~ 4 %for cse of tension loding. Differences etween displcement otined for the compression nd tension lodings rnge from ~ 5 % (distnces: 160mm nd 96 mm) to ~ 14 % (distnce: 32mm). c d e f Fig. 11. Trnsltionl displcement nd deformtions of joint (scle 5:1). Compression loding dowel spcing: () 32mm; () 96 mm; (c) 160 mm. Tension loding dowel spcing: (d) 32mm; (e) 96 mm; (f) 160 mm The effect of dowel spcing on displcement of the ords contct zone ws otined. The components of displcement long the ord width t the outer surfce edge (Fig. 3.(); x = 0, z = 0) of the edge memer, nd for compression nd tension lodings, re presented in Fig. 12. nd 13. Compression loding of the joint cused lck of contct etween memers on the selected edge. In the cse of tension loding, contct stress occurred on the edge nd reduced the displcement. Displcement differences due to pplied cses of loding cn e noticed t the u component displcement ptterns. The influence of dowel distnce on the displcement is more noticele t the w component displcement ptterns. When the distnce etween the centers of dowel holes is 96 mm, the differences etween displcements t the points long the width direction of the ord re miniml nd displcements re more uniform. Generlly, the numericl results indicte tht the dowel spcing nd the loding schemes influence the qulittive stress stte nd the strin in similr wy to the effect on the joint strength nd stiffness otined y experimentl investigtions [8, 9]. - 0397 -

Fig. 12. Component displcement u edge memer (direction: x = 0, z = 0): () compression loding; () tension loding Fig. 13. Component displcement w edge memer (direction: x = 0, z = 0): () compression loding; () tension loding 4. Conclusion The study ws crried out in order to otin informtion concerning the influence of three dowel positions of the loded doule-dowel corner joints on the qulittive fetures of the von Mises stress nd strin. The results indicte tht dowel spcing hs n effect on the stress ptterns tht correspond to the frcture zones of filure mode nlysis. The joint with 96 mm dowel spcing hs lover vlue of stress nd/or the lrger length of lower stress res etween the dowels, nd etween the dowels nd the ord edges thn those with 32 nd 160 mm dowel spcing. For joints with dowel spcing other thn optiml, the results show incresed stress etween the dowels (dowel spcing: 32mm), or etween the dowels nd the ord edges (dowel spcing: 160mm). The joint loding schemes influence the stress stte t the nlyzed directions. Prticulrly noticele is the significnce of the free edge of the fce memer of the compression loded joint. For oth loding schemes, the highest joint stiffness is otined with 96 mm dowel spcing. Future work will include considertion of the reinforced doule-dowel corner joints. In ddition, numericl nlysis for elstic-plstic model is needed to ssess the influence of dowel spcing on the stress nd strin stte of the corner joint. 5. References [1] S. Prekrt, N. Špnić, Scientific methods for determintion of wooden corner joint designs, Drvn industrij, Vol. 60, No. 4 (2009) 245-251. [2] K. Sr, J. Kers, Ü. Lug, A. Reisk, Detchle connecting fittings filure lods on plywood furniture, Proceedings of the Estonin Acdemy of Sciences, 64, 1S (2015) 113-117. [3] J. Smrdzewski, R. Klos, B. Fisik, Determintion of the impct of creeping of furniture joints on their rigidity, Turkish Journl of Agriculture nd Forestry, (2013) 37: 802 811. [4] M. Yuksel, N. Yildirim, A. Ksl, Y.Z. Erdil, S. Demirci, Effect of the pnel type nd pnel thickness on mement resistnce of screw-jointed corner joints nd stiffness of four-memer cinets, BioResources, 9(4), (2014) 6340-6349. - 0398 -

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