EFFECT OF DISTANCES, SPACING AND NUMBER OF DOWELS IN A ROW ON THE LOAD CARRYING CAPACITY OF CONNECTIONS WITH DOWELS FAILING BY SPLITTING
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1 CIB-W8/5-7-7 INTERNATIONAL COUNCIL FOR RESEARCH AND INNOVATION IN BUILDIN AND CONSTRUCTION WORKIN COMMISSION W8 - TIMBER STRUCTURES EFFECT OF DISTANCES, SPACIN AND NUMBER OF DOWELS IN A ROW ON THE LOAD CARRYIN CAPACITY OF CONNECTIONS WITH DOWELS FAILIN BY SPLITTIN M Scmd H J Blß Unvers o Krlsrue ERMANY R P M Frsson Federl Unvers o Espro Sno BRAZIL MEETIN THIRTY-FIVE KYOTO JAPAN SEPTEMBER 00
2 Eec o Dsnces, Spcng nd Number o Dowels n Row on e Lod Crrng Cpc o Connecons w Dowels Flng b Splng M. Scmd, H.J. Blß Unvers o Krlsrue, ermn R.P.M. Frsson Federl Unvers o Espro Sno, Brzl. Inroducon Jons n mber srucures oen l n one o e wo brle modes sown n gure. Fg. : plug ser lure splng lure
3 In order o vod ese brle lure modes, mos mber desgn codes conn rules bsed on e experence o crsmen nd resuls o connecon ess n lborores. Tese rules mosl conss o prescrbed mnmum dmensons, suc s sener end nd edge dsnces, sener spcng, or mber ckness. Regrdng ese mnmum dmensons, no dsncon s mde beween deren mber sowood speces n mn codes. Recen reserc resuls e. g. b Jorssen (998) sowed brle lure modes lso n cses were e mnmum dmensons were respeced. In order o sud e nluence o e mber speces on e splng endenc, reserc projec ws crred ou Krlsrue Unvers. As or economcl resons s no possble o es ll pes o sener usng deren speces nd deren jon geomer, mecncl model bsed on rcure mecncs ws developed. In s pper e model or splng, ws requenl observed n e ess perormed bo, b Blß nd Scmd (00) nd Msud (998), s presened. In erms o rcure mecncs s mode I crck exenson.. Mecncl Model Sble crck grow n e close negbourood o e dowels s oen observed (g. ), beore one o e lure modes sown n gure evenull kes plce, ledng o n lmos complee loss o e jon s sreng,. Fg. : crck close o e dowel Te jon re ncludng e sble crck propgon s modelled s bem on elsc oundon (g. ). Ts model seems o be que crude, e lernve could be wo- or ree-dmensonl ne elemen model. Bu e lrge vron o locl mber properes s ken no ccoun, s well s e non-lner sress-srn relon n e re close o e sener nd e ororopc bevour, s resonble o coose s smple model. Jorssen (998) rs used smlr jon re model. Conrr o e model presened ere, Jorssen ncluded no crck exenson, e nsed compred e ensle sresses perpendculr o e grn e dowel surce w e ensle sreng o e merl. Smlr o e pproc used b Jorssen (998) e bem s loded b rnsverse orce V F / 7 () nd momen
4 F/ F/ M () / /,c dependng on e embeddng bevour nd e dowel lod F prllel o e grn. z, w σ z (x) σ z (x) neurl xs / x0 x x x00 F crck dowel neurl xs x E I, A M w(x) K Fg. : modellng e crcked jon s bem on elsc oundon V Assumng sress dsrbuon perpendculr o e grn σ z (x,z) s sown n gure (Tmosenko nd ooder (970)), e modulus o oundon K, cng on e neurl xs o e delsed bem, s clculed: σ z (x,0) ( / + z) ( / + z) σ z ( x,z) σ z (x,0) (), w( / ) z / 90 z 0 z / ε (z) dz σ z (x,z) σ z (x,0) dz E E z () eldng σz( x, 0) K w( / ) E90 (5). As e ro beween e dep o e bem nd e leng s smll, ser deormon s ken no ccoun. Equon (6) ollows rom equlbrum condons: d w κ K d w K w (x) + 0 dx A dx² E I A dsplcemen spe uncon ssng equon (6) s w α x α x (x) e (C cos( β x) + C sn( β x)) + e (C cos( β x) + C sn( β x)) (6) (7)
5 w κ K α λ² +, A κ K β λ², A K λ (8). E I Fg. sows e dsrbuon o sresses perpendculr o e grn ccordng o FEclculon. Te ollowng properes were ssumed: E 0 N / mm² coecen o rcon µ 0,9 dep d E 990 d 6 mm N / mm² 7 N / mm², 7 ν,c 0,07 Te Posson coecen ν nd e coecen o rcon µ re no ncluded n e model ccordng o Fgure. S VALUE -.6E+00 +.E E E E+00 x 0 F RESTART FILE dubel oro_rebung STEP INCREMENT TIME COMPLETED IN THIS STEP.00 TOTAL ACCUMULATED TIME.00 ABAQUS VERSION: 5.8- DATE: -JUN-00 TIME: 09:8:59 Fg. : Sresses perpendculr o e grn ccordng o FE-clculon, coecen o rcon µ 0,9 Fg. 5 sows e sress dsrbuon perpendculr o e grn long e smmer xs ccordng o bo models. Close o e dowel ere s sgncn derence beween e resuls. Elsewere e sresses concde well. As or e FE-clculon lner-elsc bevour ws ssumed, wc s no rue close o e dowel, nd e Posson coecen ν s no ver well known eer, e precson o e FE-clculon s o be consdered w cre. Usng e model ccordng o g. crck propgon s modelled b prolongon o e non embedded pr nd n equvlen sorenng o e embedded bem prs. Consequenl e ssem becomes weker resulng n delecons nd roons o e pons o cons o M nd V.
6 ,5 σz(x,0) [N/mm²] 0,75 0,5 0, x [mm] 0 sz(x,0) [N/mm²] bem on elsc oundon sz(x,0) [N/mm²] FE-model Fg. 5: sresses perpendculr o e grn ccordng o e model nd e FE-clculon Te elsc poenl s reduced w ncresng crck leng nd e energ relese re s clculed s: Π Π + Π V w(x ) / + M ϕ(x ) / (9). n V M I Te cor n equon (9) resuls rom e smmer o e jon re, snce wo bems on elsc oundons orm e end o e mber member. For more n one row o seners, e model ccordng o gure s onl pplcble or e ouer prs close e member edges, e mber prs beween dowel rows re loded rom bo sdes nd bscll remn srg. Consequenl e energ relese re o mode I or connecon w more n one row s onl e l o e vlue ccordng o equon (9) crck exenson onl one o e ouer rows occurs. For s pe o jon more oen group er ou or ser lure s mxed mode crck exenson (mode I nd II) s observed (Quennevlle (998), Mommd nd Quennevlle (999)). A model or clculng e energ relese re II or s ser lure mode s presened n Blß nd Scmd (00), bu due o lck o knowledge regrdng crcl vlues n mode II nd especll or e mxed mode crck exenson ccordng o modes I nd II comprson beween model nd ess remns dcul. V, M Π + w(x ), w'(x ) Fg. 6: clculng e energ relese re rom e cnge o e poenl Π 5
7 Te model sown n gure m esl be exended o mulple sener connecon. Fnll e energ relese re s creron or crck propgon cn be clculed or deren geomer, numbers o seners nd mecncl properes. Fg. 7 sows e energ relese res o model w ree dowels nd crck exenson srng lernvel e rs, e second nd e rd sener rom e end grn, respecvel. I [Nmm/mm²] 0,6 0,5 0, 0, 0, 0, crck exenson srng e. dowel crck exenson srng e. dowel crck exenson srng e. dowel Abs(crck leng) [mm] Fg. 7: Energ relese res Usng crcl energ relese re o c 0, Nmm/mm² e correspondng lod F c per sener per ser plne nd crck exenson srng rom e rs sener dependng on e crck leng s clculed or mber ckness o mm (g. 8) F c [Nmm/mm²] crck exenson srng e. dowel Abs(crck leng) [mm] Fg. 8: crcl lod F c Te dmeer used or e resuls presened n g. 7 nd 8 ws d mm. Obvousl sble crck grow occurs unl crck leng o s reced. Ts ws lso observed n ess. 6
8 . Resuls W models, s e.g. sown or jon w one sener n gure, clculons o e energ relese re were perormed ssumng crck exenson srng rom e rs sener. An equl lod dsrbuon beween e seners or mulple sener jons ws ssumed. For solvng e ssem o equons resulng rom e boundr condons o e model e progrm memc ws used. As e boundr condons led o que dcul expressons due o e used spe uncon (7), e progrm ws onl ble o solve e ssem o equons or gven vlues o e suded vrbles. Conrr o FE-clculon ese soluons re nlcl nd no numercl. Te nluence o e geomer on e energ relese re I or crck exenson rom x -d unl x -,5 d ( d / ) ws en suded b ng non-lner regresson o e numerous resuls (equon (0)): 0,70 0,0 0, ,69,00 I,75 0 n ρ [N / mm] (0). d d d For equon (0) onl models w more n one sener n row were used (n ). In e suded models mode b ccordng o Jonsen ws ssumed. Equon (0) m conservvel lso ppled or mber members, were e sener remns srg nd s nclned. For mber members, were plsc nge occurs n e sener, equon (0) cn esl be exended: 0,70 0,0 0, ,69,00 I,75 0 n ρ d d d [N / mm] (), were F / F / 0,08 ( 0,0) ρ (), Jonsen ( ) ( ) Jonsen F Jonsen lod-crrng cpc per dowel per ser plne ccordng o Jonsen mber ckness, n number o seners n row, d sener dmeer, ρ dens, dsnce beween seners n row, sener end dsnce, sener edge dsnce. Te creron or crck exenson resulng rom (), () s 0,70 0, ,69 FJonsen,75 0 n d d d c I ( 0,08 ( 0,0) ) w e crcl energ relese re c s proper o ressnce. 0,07 [N / mm] () 7
9 I equon () s no ullled e ressnce per sener per ser plne s o be lmed ccordng o equon (): w n.,75 0 n ( 0,08 ( 0,0) ) F c Jo _ red _ 0,70 0,0 0, ,69 d d d A smlr equon ws ed kng lso no ccoun models w one sener (n ), e dsnce beween e seners s en obvousl no ncluded: w n. 0, 0 ( 0,08 ( 0,0) ) c FJo _ red _ 0,90 0, ,6 n d d Equons () nd (5) re compred o e emprcll ound resul o Jorssen (998) wc ws rnsormed resulng n e lod per sener per ser plne ssumng equl lod dsrbuon wn e seners n row : 0,0 0, 0,0 FJorssen _ 0,7 n () λ FJonsen (6) d w m d m : ckness o e mddle member λ mn (7) s d s : ckness o e sde member nd F Jonsen e lod crrng cpc per sener nd ser plne ccordng o Jonsen. As e equon ccordng o Jorssen s bsed on ess ncludng jons w one sener, e eec o numbers o sener n n row s ken no ccoun usng equon (5) nd (6). Te resulng exponen o n ccordng o equon (5) s: 0,8 0, n n wc s n good greemen o Jorssen s exponen o -0,. Usng e vrbles o equon (9) nd ssumng equl lod dsrbuon wn e seners e dgrm n g. 9 sows e eec o e number o seners n per row. Te spe o e curves ccordng o (), (5) nd (6) s que smlr. Te derence n e vlues mg be cused b e ssumpon o equl lod dsrbuon wn e row, n eec wc s ncluded n Jorssen s emprcll bsed equon. Furermore e vron o e embeddng sreng s ncluded n (6) bu no n () nd (5) usng equon (). / [ N] [N] () (5) (8) 8
10 ρ M 6 50 kg / m³ 7, β, d 6 d 0 N / mm² 7 c 0, Nmm/ mm² λ d (9) lod crrng cpc per sener [N] F_Jonsen [N] F_Jorssen_ [N] F_Jo_red_ [N] F_Jo_red_ [N] 5 numbers o seners n row n Fg. 9: eec o e number o seners per row Fg. 0 nd g. sow e nluence o e dmeer on e lod crrng cpc wc s no ncluded n Jorssen s nvesgons s onl 0 rom 958 ess d dmeer deren rom mm. Vlues used or g. 0 ρ 50 kg / m³ c 0 N / mm² n 0, Nmm/ mm² M 6 7, β, d 6 7 λ d (0) Vlues used or g. : 9
11 ρ 50 kg / m³ + 6 c 0 N / mm² 0, Nmm/ mm² M 7 β 6 n 7 λ d (),5 F_Jorssen_ / F_Jonsen F_Jo_red_ / F_Jonsen relon 0,75 0, dmeer o sener [mm] Fg. 0: eec o dmeer w consn slenderness ledng o lure mode b, properes ccordng o (0),5 relon,5 0, dmeer o sener [mm] F_Jorssen_ / F_Jonsen F_Jo_red_ / F_Jonsen Fg. : eec o dmeer w consn slenderness ledng o lure mode, properes ccordng o () 0
12 Accordng o g. splng would rdl occur Jonsen s lure mode s governng. Fg. o sow e eec o e jon geomer ccordng o equons () nd (5). Te properes were ose o (0) excep or e vrbles. Te dmeer ws d 6 mm. F_Jo_red_ [N] n n n , / d Fg. : eec o end dsnce, 9500 F_Jo_red_ [N] n n n /d Fg. : eec o spcng Te mos vourble nluence s ereore n ncrese o e sener spcng. Incresng e edge dsnce ncreses e lod crrng cpc o sngle sener jon (g. ). Fgures o re bsed on e ed equons bsed on numerous clculons o e energ relese re. I gures o would drecl be bsed on e clculon o energ relese res or e congurons consdered, e nluence o e prmeers would be even more pronounced.
13 0000 F_Jo_red_ [N] d d d 5 number o seners per row n Fg. : eec o edge dsnce,c. Conclusons Te nluence o geomer nd merl properes on e splng endenc n e connecon re o mber members ws suded usng rcure mecncs pproc. Bsed on e resuls o s pproc, e model developed b Jorssen (998) ws moded. Te predcons o e lod-crrng cpc o mulple sener jons sow good greemen w e es resuls o Jorssen. Te eec o jon geomer ws lso suded usng e model. Te mjor nluencng prmeer on e splng endenc o mber n e connecon re s e sener spcng prllel o e grn, wle, nd,c re o mnor nluence or jons w more n one sener. For smlr geomer nd e sme sener slenderness e bsolue dmeer s sgncn nluence s well. Jons, were lure mode ccordng o Jonsen s eld eor governs e desgn sould rdl l b mber splng. Furer reserc s necessr or e group er lure or plug ser lure. Tese lure modes re combnon o mode I nd II crck exenson. I mode I domnes, owever, e resuls sould be smlr ose presened ere. Lerure Blß, H.J.; Scmd, M. (00). Splger von Ndelölzern. Versucsnsl ür Sl, Holz und Sene, Abelung Ingeneurolzbu, Unversä Krlsrue (TH). In ermn. Msud, M. (998). Frcure nlss o boled jons usng e ne smll re creron. F World Conerence on Tmber Engneerng. Monreux. Volume I, S. -8 Jorssen, A.J.M. (998). Double Ser Tmber Connecons w Dowel Tpe Fseners. Del Unvers Press, Del, 998. Tmosenko, S.P. und ooder, J.N. (970). Teor o Elsc.. Edon, Mcrw-Hll Book Compn, Sngpore. Quennevlle, P. (998)Predcng e lure modes nd sreng o brle boled connecons. 5 World conerence on mber engneerng, Monreux, Swzerlnd. Mommd, M.; Quennevlle, P. (999). Bevour o wood-seel-wood boled glulm connecons. CIB-W8, pper -7-, rz, Ausr.
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