Withdrawal of lag screws in end-grain

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1 Wihrawal of lag crew in en-grain Jørgen L. Jenen 1, ierre Quenneille, Makoo Nakaani 3 ABSTRACT: Glue-in ro hae in recen year gaine populariy a a mean of making iff an rong momenreiing connecion in imber rucure. For ome applicaion, lag crew may be a compeiie alernaie. A imple fracure mechanic moel preiouly eelope for wihrawal of glue-in ro i ue on lag crew in a lighly moifie erion. Though he moel oe no explicily ake ino accoun pecial feaure of he crew uch a he effec of he crew hrea, i may be brough o goo agreemen wih e reul, an i may be eirable for eign coe o hae a unifie approach for imilar connecion meho. The crew moel inrouce he concep of hear ree caue by he hrea of he crew when riing he crew ino he woo. The re i ue a a fiing parameer, an experimen inicae ha a ingle alue of he hear re can be ue for ifferen embemen lengh an ifferen crew iameer if he hrea geomery i conan. KEYWORDS: Lag crew, en grain, wihrawal rengh, fracure mechanic, hear re 1 NTRODUCTON 13 Glue-in ro hae uring he la ecae gaine wie populariy a an efficien mean of making rong connecion in imber rucure. Numerou paper hae been preene paricularly on wihrawal of ingle ro, bu only few aemp eem o hae been mae a eeloping analyical moel. Johanon e al. [1] fir preene a ery imple moel bae on Guafon moel for glue lap-join []. The moel, which i characerize a a quai-non-linear fracure mechanic moel an i bae on he Volkeren moel, ha proen inee ery ueful [3]. Guafon an Serrano [4] laer aempe o improe he moel by coniering hear eformaion in he aheren, bu he gain in accuracy eem no o be able o juify he increae in complexiy. A an alernaie o glue-in ro, aemp hae recenly been mae o ue lag crew, which are crewe ino he en-grain of imber beam, an goo wihrawal rengh hae been obaine experimenally [5]. Nakaani an Komau [5] applie he glue-in ro moel for 1 Jørgen L. Jenen, Deparmen of Ciil an Enironmenal Engineering, The Unieriy of Aucklan, 0 Symon Sree, Aucklan Ciy, New Zealan. jl.jenen@aucklan.ac.nz ierre Quenneille, Deparmen of Ciil an Enironmenal Engineering, The Unieriy of Aucklan, 0 Symon Sree, Aucklan Ciy, New Zealan. p.quenneille@aucklan.ac.nz 3 Makoo Nakaani, SCON Reearch niue, Te apa Tipu nnoaion ark, 49 Sala Sree, Roorua, New Zealan. Makoo.Nakaani@cionreearch.com calculaion of he wihrawal rengh of he lag crew an obaine excellen agreemen beween heory an e by uing he hear rengh an fracure energy a fiing parameer. n cae of crew, i may be argue ha ince he failure occur a a hear failure in he woo, he uual alue of hear rengh an moe fracure energy of woo houl be applie raher han ome fie alue. The moel preene in hi paper applie he uual alue of hear rengh an moe fracure energy for woo an conier amage caue o he woo by he crew hrea when inalling he crew. The amage i accoune for by auming an hear re, which i eermine experimenally an may be coniere a fiing parameer. THEORY.1 STRESS ANALYSS A crew embee in woo i chemaically hown in Figure 1. Two ifferen loaing coniion may be of inere, pull-pull or pull-puh. For he pull-pull loaing coniion, he maximum hear re may occur a eiher en of he embee crew. For he pull-puh loaing coniion, he maximum hear re will alway occur a he enrance. Figure how he geomery of he crew. The hank iameer i enoe, he hrea eph i enoe, he lengh of he reae area i enoe l, an he hrea pich i enoe. Wihrawal failure occur a hear failure a he ip of he crew hrea, i.e. in he urface beween par 1 an in Figure. n realiy, he crew hrea iie he hear failure urface ino ecion of lengh, beween which

2 hear ree canno be ranferre irecly in he cylinrical hear failure urface only. Howeer, in a bol que for impliciy, i i here aume ha he hear failure urface i coninuou in he enire lengh, l, of he crew. Moel hae been coniere aking ino accoun he iconinuou hear urface for crew, bu he gain in accuracy eem o be limie. ull-puh 1 ω ( x 0) (3) π l anhω ull-pull 0 ( x 0) 1 1 ω α cohω π l α anh ω cohω (4) pull - pull l x pull - puh 1 1 ω α + cohω ( x l) (5) π l α anh ω cohω Figure 1: Loaing coniion 0 l x A w A A Figure : Screw geomery 1. FRACTURE ENERGY The fracure performance of woo i in realiy non-linear a inicae in Figure 3, bu in he preen reamen, a linear performance ha i equialen in erm of hear rengh, f, an fracure energy iipaion, G f, i aume (Serrano an Guafon 006). The hear failure urface i in he preen analyi moelle a an infiniely hin hear layer wih finie iffne. i aume ha all hear eformaion an fracure amage occur in hi hear layer. The following coniuie relaion i ue for he hear layer: ( x) Γδ ( x) (1) where i he hear re, Г i he iffne of he hear layer, an δ i he relaie iplacemen beween he woo an he crew. The crew an he woo are aume o be in ae of pure axial re. The following imenionle parameer are efine: E w Aw l Γ α α, λ, ω λ () E A E α where A w an A are cro ecion area of he woo an he crew hank, repeciely, an E w an E are mouli of elaiciy (MOE) of he woo an he crew hank, repeciely. Following he eriaion a gien in e.g. [3], he maximum hear ree become: Figure 3: Linearize coniuie relaion for fracure layer From Figure 3 follow:.3 FALURE CRTERON f Γ (6) G f may be reaonable o aume ha he proce of riing a crew ino a hole amage he woo aroun he hrea of he crew. Here i will be aume ha hi amage can be expree in erm of an hear re,, he ize of which ha o be eermine by experimen. Wihrawal failure of a crew i aume o occur when he oal maximum hear re in he hear layer reache he maerial hear rengh, f, i.e. (for he pull-puh loaing coniion < ) oal max ; { } + f (7)

3 A mean re failure crierion [6] may be inrouce inea of he maximum re failure crierion ue in he preen paper. Howeer, ince he mean re lengh oer which he hear ree hae o be aerage ypically i 0-30 mm, an herefore ery hor a compare wih he embee lengh of he lag crew coniere here, he mean re an he maximum re failure crieria lea o pracically he ame reul..4 DESGN EQUATONS From Equaion (), (3), (4), (5), (6) an (7), he following expreion for he wihrawal failure loa, u, may be erie: ull-puh ull-pull π l π l anhω 1 + ( f ) ω u ( f ) u 1 + anh ω ω ( α ) coh ω min + 1 coh α coh ω ω α + cohω where α an ω are gien by Equaion () an (6). Equaion (8) an (9) are he ame oluion a preiouly foun by Nakaani an Komau (004) for lag-crewbol ( 0) an by Jenen e al. (001) ( 0 an 0) for glue-in ro. 3 EXERMENTS 3.1 MATERALS AND METHODS Wihrawal e were conuce on lag-crew-bol () embee parallel o grain in glulam. Deail on he geomery of he are gien in Table 1 an in Figure 4. The were mae of eel a moulu of elaiciy, E 10 Ga. The imber member were mae of Dougla-fir (euouga menzieii) glulam wih an MOE of 10.5 Ga. The mean moiure conen wa 1% an he mean eniy a he gien moiure conen wa 55 kg/m 3. The alue of he hear rengh, f 9 Ma, an he moe fracure energy, G f 0.7 N/mm, were aken from (Serrano an Guafon 006). (8) (9) Table 1: Geomery of (uni in mm) h L L L : Shank iameer : Threa eph : ich h : Hole iameer Figure 5: Wihrawal e e-up The e program i eaile in Table, an Figure 5 how he e e-up for wo ifferen loaing coniion. n he pull-puh loaing cae, pecimen were hooke ino a eel box, in which he hole for he bol ha a iameer of 35 mm. 10 pecimen of ype L1, L, an L3 an 16 pecimen of ype SL were ee. Table : Te program Specimen ull-pull Loaing coniion ull-puh Glulam imenion [mm 3 ] Embemen lengh, l [mm] L1 pull-pull L L pull-pull L L3 pull-pull L SL pull-puh L [mm] Female hrea (inie) ich () Threa eph () Shank iameer () Threae lengh (l) Figure 4: Geomery of lag-crew-bol

4 3. RESULTS n Figure 6 are he heoreical preicion compare wih he experimenal reul for all he ee pecimen. Figure 6: Theoreical. experimenal failure loa Figure 7 how he wihrawal failure loa a a funcion of he embemen lengh accoring o Equaion (8) an (9) an experimen. Figure 7(a) how he heoreical preicion for he L1-pecimen obaine by uing mean, 1.0 Ma,.0 Ma, an 3.0 Ma. Figure 7(b)- () for pecimen L, L3, an SL are bae on.0 Ma. Two L an one L3 pecimen faile in pliing an hae been icare from he analyi. i worh noing ha all he ee crew ha he ame hrea geomery. For he concep of auming an hear re o be preen ue o he amage caue o he woo by riing he crew ino a prerille hole o be conincing, a conan alue of he re houl lea o goo agreemen beween heory an experimen if uing he ame hrea geomery in all experimen. Figure 6 an 7 how hi neceary coniion o be fulfille. Figure 7: Theoreical an experimenal failure loa a funcion of he embemen lengh

5 4 CONCLUSON A imple analyical moel for preicion of he wihrawal rengh of lag crew embee in en grain of woo wa eelope bae on quai-non-linear fracure mechanic. Expreion were erie for pullpull a well a pull-puh loaing coniion. The oluion for glue-in ro appear a pecial cae of he heory for crew. Comparion of he heoreical expreion wih experimenal reul of e on lag crew in en-grain how ha goo agreemen beween heory an experimen can be obaine by he uggee approach uing an experimenally eermine alue of he hear re, which i aume o accoun for amage o he woo caue by he hrea when riing a crew ino he woo. A conan alue of he hear re eem o prouce workable oupu for lag crew wih ifferen hank iameer. A compare wih preiou approache, he preen approach ha he aanage of uing he uual alue of hear rengh an fracure energy of woo raher han uing fie alue of hee maerial properie. Furher, he expreion for he wihrawal rengh of lag crew a preene here conain he expreion for glue-in ro a a pecial cae, an a uniform approach for wo imilar connecion can be ue, making eign eaier for praciioner. REFERENCES [1] Johanon C.-J., Serrano E., Guafon.J., Enqui B.: Axial rengh of glue-in bol. Calculaion moel bae on non-linear fracure mechanic A preliminary uy. CB W18A, Meeing weny eigh, [] Guafon.J.: Analyi of generalize Volkerenjoin in erm of non-linear fracure mechanic. Mechanical Behaiour of Aheie Join, Eiion lurali, ari, pp33-338, [3] Jenen J.L., Koizumi A., Saaki T., Tamura Y., ijima Y.: Axially loae glue-in harwoo owel. Woo Sci Technol 35: 73-83, 001. [4] Guafon.J., Serrano E.: Glue-in ro for imber rucure Deelopmen of a calculaion moel. Repor TVSM 01/3056, Lun Unieriy, Sween, 001. [5] Nakaani M., Komau K.: Deelopmen an erificaion of heory on pull-ou properie of lagcrewbole imber join. roceeing of he 8 h Worl Conference on Timber Engineering, Lahi, Finlan, pp95-99, 004. [6] Serrano E., Guafon.J.: Fracure mechanic in imber engineering Srengh analyi of componen an join. Maerial an Srucure 40: 87-96, 006.