AN ANALYTICAL TOOL TO PREDICT LOAD DISTRIBUTION OF MULTI-BOLT SINGLE-LAP THICK LAMINATE JOINTS

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1 8 TH INTERNATIONAL CONERENCE ON COMOITE MATERIAL AN ANALYTICAL TOOL TO REDICT LOAD DITRIBUTION O MULTI-BOLT INGLE-LA THIC LAMINATE JOINT Longqun Liu*, Ying Mo, Rn Wei chool of Aeronuics nd Asronuics, hnghi Jio Tong Universiy, hnghi, Chin * Corresponding uhor(liulongqun76@sju.edu.cn eywords: hick lmine, nlyicl ool, lod disriuion, single-lp Inroducion Wih he incresing demnd of energy nd environmenl proecion, composie merils hve een exensively used in eronuic srucures, especilly in he primry lod componens, due o is weigh-sving poenil. Therefore, he secion of some composie srucures could e much hicker hn efore. Thick-secion composies re ones where he effec of geomery, meril consiuens, lminion scheme, processing nd service loding exhii hree dimensionl ses of sress. In order o join hick-secion composies, i sill requires onding, fsening or hyrid wys, mong which he oled join is populr mehod ecuse of is high reliiliy, lod-crrying cpciy nd convenience o disssemle []. However, sress concenrion, composie rileness nd nisoropy re sources of wekness in mechniclly fsened joins, wh is more, he single-lp join is more dngerous ecuse of he secondry ending effec induced, nd hese disdvnges could e more serious when hick-secion lmines ke pr in he join. Thus, precise predicion of he lod disriuion in oled join composie srucures is in d need for he indusry engineers nd reserchers. Trdiionlly, here re mehods o sudy he lod disriuion in muli-ol composie joins: experimenl es mehods, nlyicl mehod nd finie elemen nlysis mehod. ATM commiee hs developed es procedure ATM D78 o ssess he lod disriuion of -fsener polymer mrix composie lmines. The lod disriuion cn lso e mesured y insrumened ol wih rosee srin guges []. However, he es mehod is expensive nd ime-consuming, so i s no esy for ircrf designer o dop. inie elemen nlysis, which usully requires D nonliner finie elemen model since he lod is no uniform hrough he lmine hickness [,], ofen coss dozens of hours o yield he resuls. This pper, considering he chnges of fseners flexiiliy nd ples flexiiliy inroduced in hick lmine single-lp join, will inroduce new nlyicl ool, which mkes he designer in he comfor of predicing he lod disriuion in muliol single-lp hick lmine join. sener lexiiliy in Composie Join The flexiiliy of he mechnicl composie join is composed of he flexiiliies of he ples nd fseners, nd he co-operions of hose flexiiliies will influence he lod rnsfer over he fseners. In ddiion, he flexiiliies of he ples re smller in hick lmine join compring wih h in hin lmine join, which mens he fsener flexiiliy will ke more effor in lod shring hn h in hin ples join. uhermore, he lod crried y fsener will no e uniform long he ple hickness in single-lp join, which will influence he fsener s displcemen, h is o sy he flexiiliy of fsener needed o e verified ccording o he lod condiion. To e precise, he flexiiliies of he fseners in he hick lmine single-lp join needs o e more ccurely esimed ccording o he cul.. Lod Condiion of ingle-lp Boled Join The lod condiion of single-lp oled composie join is shown in ig.. i hs shown h he fseners undergo he ering force (he fsener exer ering force o he ple inverselyfrom ples, shering force nd ending momen inroduced y eccenric lod from he wo ples, hus he deformion in he join includes 6 prs: he shering deformion of he fsener, he ending deformion of he fsener, he fsener s ering deformion y ple, he fsener s ering deformion y ple, he ple ering

2 deformion y he fsener, he ple ering deformion y he fsener. ig.. Lod condiion in single-lp join. sener lexiiliy over Uniform Bering Lod orce nlysis The sener lod model over uniform ering lod is shown in ig. (, which is siclly indeermine sysem h cn e divided ino ig. ( nd ig.(c. ( le le ( (c ig.. sener over uniform ering lod The ngle of roion of he em θ under w, θ under w nd θ under he momen M [5], θ w ( w ( L θ ( ML θ EI ( While he roion ngle of he em on he righ equls zero, Equilirium equion, θ θ θ θ ( w (5 w usiuing θ, θ, θ from Equion (- o Equion (, Thus, lexiiliy w w ( L ML EI (6 w ( M (7 6L As shown in ig., pr from underking deformion cused y sher sress nd ending momen, he cominion of fsener nd ple lso endure he ering deformion eween he wo ojecs. Hence, he deformion eween oin nd oin of he ol is he resul of he co-operion of he six differen consiuens menioned ove. The displcemens of oin cused y w w M, w ( δ 6 ( (8 EI w ( δ L (9 EI M ( δ ( EI δ δ δ δ ( Displcemens of oin cused y w w M, w δ ( EI ( w δ [( ( ( EI 6( ( ( ] (

AER TITLE M ( δ ( EI δ δ δ δ (5 The ending flexiiliy of he ol, δ δ δ C (6 9 57 96 57 9 8LEI The sher flexiiliy, ering flexiiliy of he ol nd he ple flexiiliy, ( Cs (7 9G A Cr Er Er (8 C pr E E (9 x

sener lexiiliy in ingle-lp Boled Join The conc force is non-uniform long he ple hickness in he single-lp joins shown in ig., herefore he iems in Equion ( needed o e correced ccordingly.

3 AER TITLE M ( δ ( EI δ δ δ δ (5 The ending flexiiliy of he ol, δ δ δ C ( LEI The sher flexiiliy, ering flexiiliy of he ol nd he ple flexiiliy, ( Cs (7 9G A Cr Er Er (8 C pr E E (9 x Thus he fsener s flexiiliy over uniform ering lods hrough susiuion nd clculion, ( G A 8EI( ( E E E E r r x x x. sener lexiiliy in ingle-lp Boled Join The conc force is non-uniform long he ple hickness in he single-lp joins shown in ig., herefore he iems in Equion ( needed o e correced ccordingly. Though hey cn e oined hrough fiing he experimenl resuls, here is no physicl mening on every fcor, esides he fcors my chnge wih differen experimenl resuls, nd he experimenl cos is high. everl single-join D finie elemen models, whose modeling mehod is vlide y he es resuls crried ou ccording o ATM D 596 es sndrd[6], employed he 6 correcion fcors seprely. The D finie elemen model of single lp oled composie join nd conc re seing re shown in ig.. le ( Bol ( ig.. D E model of single-lp oled join nd conc odies Compring he ering deformion of he ples, nd he ering deformion, he sher deformion nd ending deformion of he ol seprely, correcion fcors of he single-lp hick lmine oled join could e consruced respecively. The fsener s flexiiliy in single-lp oled hick composie join (nmed s Liu-Mo in his pper is shown s: 6G A EI( x E E E E r r x 57 9 ( Anlyicl Tool of Lod Disriuion in Muliol Join In ircrf srucure design, excep for sel res where he fseners re sggered, join eween wo srucures cn e divided ino severl muli-row single-column susrucures. Usully, rows is umos. ollowing conens focus on consrucing he row nd row fseners join nlyicl model.. pring Model of ingle-lp Join le The spring model of single lp -ol join model is shown in ig.5. ig.5. pring model of single-lp wo-ol join nd re he siffness of he ple secions eween he wo ols, nd 6 re he siffness of he ple secions from he ols o he ends of he EA ples, which cn e clculed y. nd 5 l

4 re he siffness of he fseners in he single-lp join, he reciprocl of he fseners flexiiliies which cn e clculed hrough equion(. nd 6 jus influence he siffness of he whole join sysem nd hve lile impc on he fseners lod shring, herefore, when u 5 is reed s zero, he lnce equions cn e wrien s elow: ( u u ( u u ( u u 5u ( ( u u u Clcule u, u nd u : ( u ( 5 ( u ( 5( 5 (5 u ( ( 5 The lods crried y ol nd ol re: ( u 5 (6 5 u u u ( (7 The displcemen of he whole join under lod, (8 u 6 ( The lod disriuion of -ol single-lp join cn e oin hrough he sme mehod wih h of -ol join.. Model Vlidion Lod disriuion ess following ATM D 78 sndrd (shown in ig.7 were used o vlide he lod disriuion clculion mehod sed on he spring model menioned ove. There re groups of specimens, whose geomery configurion of he joins re shown in le., where,, W, e, p, D snd for he wo ple hicknesses, widhs, edge disnce, row disnce nd hole dimeer respecively. Tle. lised he equivlen engineering consns of he lmine ple. The deil es mehod, prmeers nd resuls cn lso refer o reference 7. 5 ig.7 Lod disriuion es Tle. geomery configurion Tes No. W (mm e (mm (mm (mm (mm D (mm Tle. mechnicl properies Tes No. E (G E (G G (G υ Tle. Ly-ups nd equivlen consns No. ly-up E x (G E y (G G xy (G υ xy [5//- 5/9/] s [5//-5//9 //5//-5/] s [5//-5//9 //5//-5/] s The lod disriuion of differen ols is clculed using fsener flexiiliy equion from ATM D 78 [8] (Equion 9, Hr-mih [9] (Equion nd his pper (Equion. The fsener flexiiliy equions re shown s elow. The resuls of he lod disriuion re shown in Tle., from which i shows h he resul clculed hrough equion presened in his pper is more ccure hn he oher wo. C 8( E ( E πe E ( ν d x 6 (8 6 9 πe E x ( E E ( E E d ( β (9 δ ( G A ( r L T L T

AER TITLE Tle. lod disriuion resuls (in percenge Tes No. ATM D 78 Hrsmih Liu-Mo Tes 5.7 5.76 5.65 56. Error (% 6...8 5.9 5.6 56.9 57. Error (%. 5..5 5.5 5. 56.68 57.8 Error (%. 7.6.. Lod Disriuion Anlyicl Tool in Excel The nlyicl ools, compiled in Excel, re shown in igure.

Upon enering ll he prmeers, he clculion will e ccomplished uomiclly.

5 AER TITLE Tle. lod disriuion resuls (in percenge Tes No. ATM D 78 Hrsmih Liu-Mo Tes Error (% Error (% Error (% Lod Disriuion Anlyicl Tool in Excel The nlyicl ools, compiled in Excel, re shown in igure.8 nd igure.9, in which he prmeers re hickness of ple ( nd ple (, disnces from he ols o he ple ends (L nd L, elsic modulus of he ples nd ols (E, E, E nd E, ple widh (W, row disnce (p, nd he ol lod (. Upon enering ll he prmeers, he clculion will e ccomplished uomiclly. Moreover, he nlyicl ools could e used in he clculion wih ols h hve differen dimeers nd elsic modulus, hence gre convenience for he engineers he eginning of srucure design. ig.8 he nlyicl ool for fseners ig.9 he nlyicl ool for fseners Influences of Differen cors on Lod Disriuion. Rio of Bol Dimeer o le Thickness or he single-lp join, one of he ple is lmine, wih scking sequence eing [ /±5 /9 ]6, ply hickness eing.5mm, nd he meril properies is shown in Tle.5; he oher is 8mm hick CrMni ple(e96g,υ.. Tle.5 Meril properies of T/QY89 E (G E (G G (Gp υ The hole dimeers disinguished y D6mm, 8mm, mm nd mm.the lod disriuion go from he nlyicl ool is ploed in ig.. Lod Disriuion(% Lod Disriuion(% Bol Bol 6 8 Bol Dimeer(mm ( ols Bol Bol Bol 6 8 Bol Dimeer(mm ( ols ig. Influence of /d Boh he digrms ( nd ( indice h he mos loded ol endures much more lod, wih he incresing of he ol dimeer. The chnge of ol dimeer cuses he proporion of he siffness eween ol nd ples which resul in he uneven lod disriuion should e he explnion.. Rio of Row Disnce o le Thickness Use he sme ples depiced in secion., u he row disnce is, 5 nd 7, respecively. Lod Disriuion(% Lod Disriuion(% Bol Bol 8 8 Row Disnce(mm ( ols Bol Bol Bol 8 8 Row Disnce(mm ( ols ig. Influence of p/ 5

6 The resuls in ig. ( imply he disriuion ecomes more uneven mong fseners wih he increse of row disnce.. Rio of le Widh o le Thickness Wih ll he oher prmeers idenicl wih secion., he vrile s, column disnce vries from D o 5D. Resuls in he wo-fsener nd hree- fsener siuions re ploed in ig.. Lod Disriuion(% Lod Disriuion(% Bol Bol 8 Column Disnce(mm ( ols Bol Bol Bol 8 Column disnce(mm ( ols ig. Influence of W/ As shown in ig., he lod disriuions in differen ols remin nerly he sme wih he vriion of column disnce. These indice h he column disnce is no s significn s oher prmeers discussed ove in he influence over lod disriuion. Conclusions (The clculion ool geing lod disriuions of hick-lmine muli-ol single-lp join ws vlided o e ccure nd efficien, especilly when deling wih he hick ples. (Considering h in mos of he siuions, he join re shll e divided ino severl regions conining he originl numer of rows u only one column of fseners, ccurcy of he soluion could e gurneed. Thus, i is very useful ool for he designers o commence he evluion of prmeers he very eginning. (The incresing of ol dimeers nd row disnces hs impc on he lod disriuion, which develops more uneven mong fseners. Due o he simplified mehod which divides he muli-row, muli-column join re ino muli-row, singlecolumn su res, he influence of column disnce over lod disriuion is equivlen of he influence of ple widh of he su re over lod disriuion, which hs lile effec on he lod disriuion. ( The siffness rio hs gre influence on he lod disriuion, which differs more seriously eween fseners when rising he siffness rio. Besides, he disriuion ecomes more uneven when he rio of fseners disnce o he ple hickness comes lrger. References [] M.A. McCrhy, C.T. McCrhy, G.. dhi A simple mehod for deermining he effecs of ol hole clernce on lod disriuion in single-column muli-ol composie joins. Composie rucures, Vol. 7, pp 78-87, 6. [] Romn rikov igue ehviour of mechniclly fsened luminium joins esed in specrum loding. Inernionl Journl of igue, Vol. 6, pp 5-7,. [] John Ekh, Jokin chon inie elemen modeling nd opimizion of lod rnsfer in muli-fsener joins using rucurl elemens. Composie rucures, Vol. 8, pp 5-56, 8. [] B. Andersson Opimizion nd sisicl nlysis of oled joins-r A: Theory nd sysem verificion. Composie cience nd Technology, Vol. 66, pp , 6. [5] Timoshenko,., Gere,J. Mechnics of Merils, cience ress, Beijing, 99 [6] D596/D596M-8. ndrd Tes Mehod for Bering Response of olymer Mrix Composie Lmines. Composie Merils. ATM Inernionl. Wes Conshohocken,. [7] Y.Mo udy of lod disriuion in muli-ol hick lmine joins, Thesis of hnghi Jio Tong Universiy, [8] D 78/D78M 8. ndrd Tes Mehod for Bering/Bypss Inercion Response of olymer Mrix Composie Lmines Using - sener pecimens. Composie Merils. ATM Inernionl. Wes Conshohocken,. [9] Hsien-Yng Yeh, Johnhn J. Lee,Dniel Y. T. Yng udy of mulirow highly loded ol joins in composie wing srucure.journl of Aircrf,Vol.(,pp 8-85,

M r. d 2. R t a M. Structural Mechanics Section. Exam CT5141 Theory of Elasticity Friday 31 October 2003, 9:00 12:00 hours. Problem 1 (3 points)

M r. d 2. R t a M. Structural Mechanics Section. Exam CT5141 Theory of Elasticity Friday 31 October 2003, 9:00 12:00 hours. Problem 1 (3 points) Delf Universiy of Technology Fculy of Civil Engineering nd Geosciences Srucurl echnics Secion Wrie your nme nd sudy numer he op righ-hnd of your work. Exm CT5 Theory of Elsiciy Fridy Ocoer 00, 9:00 :00