Structural response of timber-concrete composite beams predicted by finite element models and manual calculations

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1 Sruural repone of imber-onree ompoie beam predied by finie elemen model and manual alulaion *Nima Khorandnia 1), Hamid R. Valipour ) and Keih Crew 3) 1), 3) Cenre for Buil Infraruure Reearh (CBIR), Shool of Civil and Environmenal Engineering, Univeriy of Tehnology, Sydney, P.O.Box13 Broadway, NSW, Auralia ) Cenre for Infraruure Engineering and Safey (CIES), Shool of Civil and Environmenal Engineering, The Univeriy of New Souh Wale, Sydney, Auralia 1) Nima.Khorandnia@u.edu.au ABSTRACT Thi paper preen a omparaive udy of he ruural repone of imberonree ompoie (TCC) beam predied by finie elemen model (i.e. oninuumbaed and 1D frame) and manual alulaion. Deail of oniuive law adoped for modelling imber and onree are provided and appliaion of he Hahin damage model in onjunion wih oninuum-baed FE for apuring failure of imber under biaxial re ae i diued. A novel raegy for modelling he TCC onneion i propoed in whih he onneion i modelled by a nonlinear pring and he full loadlip behaviour of eah TCC onneion i expreed wih a formula ha an be direly implemened in he general purpoe FE ode and ued for nonlinear analyi of TCC beam. The developed FE model are verified by example aen from he lieraure. Furhermore, he load-diplaemen repone and ulimae loading apaiy of he TCC beam are deermined aording o Euroode 5 mehod and ompared wih FE model prediion. 1 INTRODUCTION Timber onree ompoie (TCC) beam have higher iffne, ulimae loading apaiy and fire raing ompared o imber beam. Furhermore, under ervie load TCC floor have le defleion and vibraion and an provide more effeive diaphragm aion ompared o floor made olely from imber. Aordingly, TCC member have found inreaed uage over he la weny year and exenive reearh ha been devoed o experimenal, numerial and analyial udie a well a developmen of implified mehod and deign proviion for TCC beam (Ahmadi & Saa 1993; Ceoi 1995; Ceoi e al. 6; Clouon e al. 5; Lope e al. 1). The experimenal udie underaen by differen reearh group over variou 1) PhD Candidae ) Senior Leurer 3) Profeor Noe: Copied from he manurip ubmied o Sruural Engineering and Mehani, An Inernaional Journal for preenaion a ASEM13 Congre 51

2 loal and global ape of TCC yem. A loal (join or onneion) level, behaviour of differen ype of onneion (Brano e al. 9; Deam e al. 8; Guowi e al. 4; Seinberg e al. 3) and developing new onneion wih higher level of ompoie aion (Clouon e al. 4; Fragiaomo e al. 7; Yeoh e al. 11a) have been inveigaed and a global level appliaion of differen imber produ (i.e. LVL, awn imber and glulam) (Balogh e al. 8; Clouon e al. 5; Guowi e al. 8; Yeoh e al. 11b), uing differen lae of onree or developing new onruion mehod for he lab (Brunner e al. 7; Jorge e al. 11; LeBorgne & Guowi 1; Luazewa e al. 8), ulimae loading apaiy of he TCC beam under hor-erm load and long-erm behaviour of TCC yem (Ceoi e al. 6; Fragiaomo 5, 1) have been udied by differen reearher. The numerial udie fou on appliaion of FE model for apuring he loal repone of TCC join (Dia e al. 7a; Shäfer & Seim 11) and global repone of he TCC beam (Guowi e al. 1; Lope e al. 1). Timber-onree ompoie beam an be analyed uing eiher oninuum-baed finie elemen model or 1D diree frame elemen. Typially, in he 1D frame model he eion i deriized ino fibre (filamen) and only behaviour of maerial under a uniaxial re ae an be apured (Luazewa e al. 1; Valipour & Bradford 9). Aordingly, he frame FE model are mainly appliable for apuring he global repone of TCC beam wherea he oninuum-baed FE model an apure he global and loal repone of TCC beam and join wih good auray (Dia e al. 7b; Guowi e al. 1). The implified analyial model are ypially derived from he oluion of governing differenial equaion of he imply uppored TCC beam by auming a linear elai behaviour for imber, onree and onneion (CEN 8; Clouon e al. 5). In addiion, ome aemp have been made o formulae he behaviour of mehanial faener uing beam on elai foundaion heory (Gelfi e al. ). For nonlinear analyi of TCC beam uing oninuum-baed FE model, he imber beam and onree lab are divided o mall bri or membrane elemen and he bond beween onree and imber i uually modelled by a ona elemen (Dia e al. 7b; Shäfer & Seim 11). However, he normal and angenial iffne of exiing ona elemen are ypially linear and herefore anno uffiienly repreen he nonlinear behaviour of diree mehanial faener (uh a nail & rew) in TCC yem. Furhermore, he loading apaiy of he ypial inerfae elemen are formulaed baed on elai/rigid-perfe plai behaviour aording o Columb or modified Columb friion model (ABAQUS 11; ANSYS 11) ha warran a prior alibraion of he inpu parameer (i.e. oheion and oeffiien of friion) wihou having dire relevane o he real behaviour of diree mehanial faener. In hi paper he nonlinear hor-erm ruural repone of TCC beam i apured by hree differen model (viz. oninuum-baed FE, 1D frame fibre elemen and manual alulaion aording o Euroode 5 proviion). Furher, a novel raegy for modelling TCC onneion i propoed in whih he faener i modelled by a nonlinear pring. In he propoed approah, he full load-lip repone of he onneor an be direly inorporaed ino he FE model o predi he load-diplaemen repone of TCC beam inluding heir ulimae loading apaiy. A omparaive udy i underaen o verify he auray and demonrae he meri of eah model. 511

3 FINITE ELEMENT MODELLING OF TCC BEAMS.1 Coninuum-baed finie elemen model Appliaion of Hahin failure rieria for modelling imber From he mehanial poin of view, imber i anioropi maerial wih differen behaviour along he grain and perpendiular o he grain direion (Maenzie- Helnwein e al. 3). In he developed D oninuum-baed FE model, he nonlinear behaviour of imber i apured by Hahin damage rieria (Hahin 198; Hahin & Roem 1973). The Hahin damage model ae aoun of ineraion beween hear and normal re omponen o evaluae differen failure mode. The Hahin damage model wa originally developed for unidireional polymeri ompoie (Hahin 198; Hahin & Roem 1973), and hene, appliaion o oher laminae ype or nonpolymeri ompoie repreen a ignifian approximaion. In hi udy, however, i i hown ha Hahin model an adequaely apure he failure mode of imber under bi-axial re ae, pariularly wihin he imber and imber-onree ompoie beam. The auray of Hahin model ha been verified by experimenal reul inluding imber beam wih and wihou nohe and hole ubje o hree and fourpoin bending e (Khorandnia e al. 13). The D Hahin failure rieria adoped in hi udy are ued o predi he one of damage, and he damage evoluion law i baed on he energy diipaed during he damage proe and linear maerial ofening (ABAQUS 11). The D Hahin rieria onider four differen damage iniiaion mehanim expreed in erm of effeive re omponen ˆ ( i, j 1,), a follow ij ˆ 11 ˆ F 1 f T L X S ˆ F 11 f C X ˆ ˆ F 1 m T L Y S ˆ C Y F m T T S S ˆ 1 Y C ˆ S 1 L : Tenile failure of fiber : Compreion failure of fiber : Tenile failure of marix : Compreion failure of marix (1) where X T and Y T are he enile rengh of imber along he grain and perpendiular o grain, repeively, X C and Y C are he ompreive rengh of imber along he grain and perpendiular o grain, repeively, S L and S T denoe he hear rengh along he grain and perpendiular o grain, repeively, and α i a oeffiien ha deermine he onribuion of he hear re o he fibre enile iniiaion rierion. The effeive re veor σ ˆ ˆ ˆ T, i relaed o re veor 11 ˆ1 51

4 σ 11 1 T by σˆ ωσ () in whih, ω i a damage marix defined a follow 1/(1 f ) ω 1/(1 m) (3) 1/(1 ) where ω f and ω m are alar damage variable for fibre and marix, repeively, and ω i hear damage variable expreed a a funion of ω f and ω m (ABAQUS 11). Modelling onree uing a plai-damage oniuive law In he developed FE model, a plai-damage oniuive law i adoped for onree (Lubliner e al. 1989). The inremenal re-rain relaionhip of he adoped model i a in he formwor of ioropi damage and governed by el el pl ε σ (1 ) D ( ε ) (4) pl where D i he iniial (undamaged) elai iffne of he maerial, ε i plai rain and i he alar damage variable ha apure he iffne degradaion of maerial. I hould be noed ha damage aoiaed wih he failure mehanim of he onree (raing and ruhing) lead o a reduion in he elai iffne of maerial. Furher deail on yield urfae, flow rule and hardening law of he adoped plai-damage model an be found in Lee and Fenve (1998). The modulu of elaiiy of onree i a funion of ompreive rengh and ypially varie beween 5 f and 1 fp (MPa) in differen andard and herefore, an average value i adoped in hi mehod. p Modelling he TCC onneion In he finie elemen modelling of TCC beam, he onneion beween imber beam and onree lab i uually modelled by ona elemen (Dia e al. 7b; Maia & Soriano 4; Shäfer & Seim 11). The available ona elemen are ypially haraeried by five parameer inluding normal iffne of inerfae K nn, angenial iffne of inerfae K, oheion, oeffiien of friion and enile rengh f of he inerfae. The normal and angenial iffne of ona elemen are linear elai up o failure poin and herefore he exiing inerfae elemen an only apure he linear elai-brile failure behaviour (Fig. 1), whih i no onien wih he real behaviour of TCC onneion (normal rew, SFS, e) oberved during eing. Wih regard o he lumped naure of mehanial faener ued in TCC onneion, in hi udy a imple modelling ehnique i propoed ha an adequaely apure he 513

5 nonlinear behaviour of onneion. In hi modelling raegy, he onree lab and imber beam are generaed and mehed a wo eparae obje and ome eleed node from imber beam are horizonally onrained o node wihin he onree lab by equivalen nonlinear pring whih repreen he mehanial faener (Fig. ). In he verial direion, he inerfaial node from onree lab and imber beam are fully onrained o preven poible peneraion of onaing obje (ee Fig. ). The propoed modelling raegy ha wo advanage. Fir, he nonlinear hear-lip repone of he onneion an be direly inorporaed ino he FE formulaion, whih i more onien wih he real behaviour of TCC onneion and improve he auray of FE model. Seond, he propoed modelling raegy doe no need a prior alibraion of inpu parameer a oppoed o normal ona elemen. (a) (b) Fig. 1 Typial inerfae model behaviour under (a) angenial (b) normal (enion/ Compreion) ree. Fig. Shemai ouline of he oninuum-baed FE meh and inerfae beween RC lab and imber beam. 514

6 The hear-lip behaviour of equivalen pring repreening TCC onneion an be haraeried uing a urve fiing or nonlinear regreion ehnique. Depending on he onneion ype (e.g. normal rew, SFS, nohe e) and he funion adoped for regreion, differen model an be developed (Khorandnia e al. 1; Yeoh e al. 11a). For example, he pre-pea repone (aending par) of he hear-lip (P veru ) diagram for normal rew onneion an be adequaely repreened by he Rihard-Abbo model (Khorandnia e al. 1; Valipour & Bradford 13) P P p n n p p 1 1 (5) where i he iniial iffne, p i he rain-hardening iffne, P i a referene hear fore and n i a parameer whih onrol he urvaure of he diagram (Fig. 3a). In addiion, he aending par of he hear-lip behaviour for SFS and noh onneion an be repeively modelled by he exponenial funion (Khorandnia e al. 1) and Ollgard model (Ollgard e al. 1971) a follow (a) (b) () (d) Fig. 3 Shemai ouline of he (a) Rihard-Abbo model (b) Exponenial model () Ollgard model (d) Pre-pea and Po-pea repone for TCC onneion. f u u P P P P p n n p p 1 1 e e P e P P 1 max b P f 515

7 e e e max (7) P (6) P P 1 where P max repreen he maximum hear rengh of he onneion and α, β, γ are parameer whih onrol he urvaure of funion (Fig. 3b,). Regarding he po-pea (ofening) par of he hear-lip diagram, ypially a linear funion (ee Fig. 3d) i adequae (Khorandnia e al. 1; Yeoh e al. 11a). In hi udy, even differen onneion inluding normal rew, SFS, noh and rew have been hoen from lieraure and heir pre-pea and po-pea repone are aegorized and repored in Table 1. The NS i a normal wood rew wih a lengh of 1 mm and 5 mm diameer. The SFS omprie wo inlined rew wih a lengh of mm peifially deigned for appliaion in TCC beam. The BM and T are bird mouh onneion wih a riangular noh reinfored wih 16 mm diameer oah rew. Furher, he R15 and R3 onneion repreen riangular noh wih 15 and 3 mm lengh, repeively, reinfored wih 16 mm diameer lag rew. Seel Meh i a oninuou onneion wih one half glued ino a lo in imber and he oher half embedded in onree. Table 1. Pre-pea, po-pea and emi-ompoie iffne of TCC onneion ued in FE model and manual analyi. Conneion Type NS (Khorandnia e al. 1) SFS (Khorandnia e al. 1) BM (Khorandnia e al. 1) R15 (Yeoh e al. 11a) R3 (Yeoh e al. 11a) T (Yeoh e al. 11a) Seel Meh (Clouon e al. 5) Pre-pea Repone Po-pea Repone K for emi- Model Parameer Model Parameer omp. (N/mm) P p n f b K,.6 Rihard- Linear Abbo Exponenial Ollgard α β γ f b K,.4 Linear P max α β f b K, Linear

8 . 1D frame fibre elemen In he 1D frame elemen model, reinfored onree (RC) lab and imber beam are modelled by wo eparae frame elemen whih are oupled by diree nodal pring in he longiudinal direion (ee Fig. 4) and he iffne (viz. forediplaemen relaionhip) of hee longiudinal pring an be direly exraed from he hear-lip repone of TCC onneion a deribed in previou eion. In he ranvere direion, RC lab and imber beam are rigidly onrained auming ha eparaion beween lab and beam i negligible. Moreover, he eion of RC lab a well a imber beam i ub-divided ino fibre (layer in D) ha allow for monioring he behaviour of maerial poin over he eion deph (Valipour & Bradford 1). Fig. 4 Coupling of reinfored onree (RC) lab and imber beam uing longiudinal nodal pring (q and Q are generalied nodal diplaemen and fore, repeively). Coniuive law for imber In he ypial fibre elemen model, effe of hear on he nonlinear repone of maerial i negleed; aordingly a uniaxial maerial law an adequaely model he nonlinear behaviour of imber properie parallel o grain (along he beam axi). Among he variou available uniaxial oniuive law for imber in ompreion (Conner 1989), he re-rain law preened by Glo (1981), whih originally ha been developed for mall lear imber peimen, i adoped in hi udy (Fig. 5a), n 1 n 3 4 for for u u (8) 1 f 1 ( n 1) E 1, E 3 y ( n1) 1 1 f u f y / f n ( n 1) E u,, f y 1 4 f y f u 1(MPa) (9) 517

9 where, f u and are he ulimae ompreive rengh and orreponding rain, repeively, f y i he reidual re, E i he iniial elai modulu of imber in ompreion and n i a hape parameer whih onrol he urvaure (ee Fig. 5a). The ypial value adoped for he inpu parameer in he Glo model (1981) are: fy. 8 f u,.8. 1 and u 3. Tenion behaviour of imber follow a linear elai par up o enile rengh f u, and afer ha he maerial ofen linearly (ee Fig. 5a). The lope of he ofening branh i haraeried and adjued by auming a onan fraure energy deniy G f, ha erve a a loaliaion limier. Coniuive law for onree In 1D frame fibre elemen model, a uniaxial re-rain relaionhip baed on he CEB-FIP model ode 199 (CEB-FIP 1993) i ued for onree under ompreion and enile onree follow a linear elai-quai brile failure model wih an exponenial ofening urve (Fig. 5b). The rain orreponding wih maximum re for ompreive onree i. and ulimae rain of onree i u. 1 (Fig. 5b). Furher, for unloading/reloading regime a damage model wih no plai rain i adoped in hi udy (Fig. 5b). ( / o ) ( / ) 1 ( ) ( / o ) o f (a) (b) Fig. 5 Shemai ouline of he adoped re-rain relaionhip for (a) imber (b) onree. 3 MANUAL ANALYSIS ACCORDING TO EUROCODE 5 PROVISIONS Thi mehod i baed on dire fulfilmen of rain-diplaemen ompaibiliy and ai equilibrium equaion of ompoie eion. Uing manual alulaion he fullompoie, emi-ompoie and no-ompoie aion a well a behaviour of imber beam alone an be apured. In he full-ompoie ae, i i aumed ha no lip beween imber and onree 518

10 our and flexural iffne EI f for he full-ompoie T-eion an be obained from E I f 1 E I E A a E I E A a (1) where ubrip and repreen onree and imber, repeively, E denoe maerial modulu of elaiiy and A and I denoe he ro-eional area and he eond momen of he area for eah eion, repeively (i.e. onree and imber) abou heir referene axi (ee Fig. 6). h and h denoe hine of onree lab and deph of imber beam a hown in Fig. 6 and a E ( ) h h A h h, a1 a (11) ( E A E A ) Fig. 6 TCC ro-eion and hemai diribuion of bending ree in differen ae. The emi-ompoie ae i baed on he parial ineraion beween imber beam and onree lab whih are oupled by onneion (e.g. hemial bond, mehanial faener or ombinaion of boh). In manual alulaion he faener are haraeried by heir lip modulu K (auming a linear repone) and paing S beween hem (equally paed). Mo of he aforemenioned onneion how almo linear behaviour before failure and herefore, he linear iffne (K) in hi mehod an be aumed o be he ame a ervieabiliy lip modulu (K,.4 ) aording o European Sandard (CEN 1991). Sine here i a ignifian nonlineariy in hear-lip repone of NS onneion, he ulimae lip modulu (K,.6 ) eem o be more appropriae for apuring he global repone of he TCC beam. The magniude and ype of iffne adoped for manual analyi of eah and every one of he onneion onidered in hi udy are given in Table 1. Furher, he faener paing, S, i alo alulaed baed on he equally paed diribuion of he onneion over he beam lengh. The defleion of a imply uppored emi-ompoie TCC beam wih pan lengh L an be alulaed by uing an effeive flexural iffne EI ef given in Euroode 5, Annex B (CEN 8) a follow Where E I e f 1 E A a1 E I E A a E I (1) 519

11 a 1 E A ( h h ), ( E A E A ) E A S 1 K L, a 1 h h a (13) In he no-ompoie ae, he horizonal hear i no ranferred on he inerfae beween imber and onree lab and he oal bending iffne of he member EI n in uh a ae i obained from E I n E I E I (14) Finally, in he imber-only ae i i aumed ha here i no onree lab on op of he imber beam and herefore he oal bending iffne equal o only imber beam iffne, EI o = E I. The hemai diribuion of bending ree in all of he ae i diplayed in Fig. 6. The failure of he TCC beam in bending e i uually riggered by enile failure of fibre loaed on he boom of he eion (LeBorgne & Guowi 1; Yeoh e al. 11b) and he re-rain relaionhip of imber in enion i eenially linear up o he failure poin. Aordingly, he ulimae loading apaiy (P u ) and orreponding ulimae defleion (δ u ) of he imply uppored beam for differen ae under fourpoin bending e an be alulaed, repeively from P P u u 8 EI f f E (a h )(1 ) L 8 EIef f E (a h )(1 ) L 8 EI n f Pu Eh (1 ) L 8 EIo f Pu E h (1 ) L u u u u ( ) f L 1E (a h ) ( ) f L 1E (a h ) ( ) f L 1Eh ( ) f L 1E h : Full ompoie :Semi ompoie : No ompoie : Timber only (15) where f, L and α are he maximum enile re of imber (modulu of rupure), beam pan and proporion of applied ouple load diane o oal beam pan, repeively. 5

12 4 COMPARATIVE STUDIES 4.1 Servieabiliy range Four TCC beam eed by Khorandnia e al. (1) wihin ervieabiliy range are analyed uing developed FE model and manual alulaion. The maximum ize of elemen in he 1D frame and oninuum-baed FE model i limied o 4 mm and 4 mm, repeively. The beam were ubjeed o 4-poin bending and deail of he beam inluding pan, RC lab and imber beam dimenion, number and ype of onneion, applied load diane and he maerial properie (inluding ompreive rengh of onree, moduli of elaiiy and rupure of imber) are repored in The geomery and maerial properie of he beam are wihin he ame range, however, he number and ype of onneion are oally differen. Therefore, he ineraion behaviour beween onree and imber i differen from ample o ample and ha affe he global behaviour of TCC beam. Table. The geomery and maerial properie of he beam are wihin he ame range, however, he number and ype of onneion are oally differen. Therefore, he ineraion behaviour beween onree and imber i differen from ample o ample and ha affe he global behaviour of TCC beam. Table. TCC beam deail and maerial properie ued in FE model and manual analyi in ervieabiliy range. Beam B-NS (Khorandnia e al. 1) B-SFS (Khorandnia e al. 1) B-4BM (Khorandnia e al. 1) B-6BM (Khorandnia e al. 1) Span (m) Dimenion (mm) RC Slab Timber Beam Conneion No. Type Load Di. (m) Maerial Properie MOE Tim. (GPa) f p Con. (MPa) MOR Tim. (MPa) NS SFS BM BM The reul of oninuum-baed and frame elemen FE model, repeively are denoed a FEM-CON and FEM-FR and hown in Fig. 7. Furher, he reul of manual alulaion baed on Full-ompoie, Semi-ompoie, No-ompoie and Timber-only behaviour are provided in Fig. 7. Baed on he obained reul, he load-diplaemen behaviour of all TCC beam remain ignifianly linear wihin ervieabiliy range whih i in good agreemen wih analyial ouome. Regarding he overall performane of he FE model wihin he ervieabiliy range, i hould be noed ha 51

13 he iffne of B-SFS, B-4BM and B-6BM beam have been undereimaed ompared o he experimenal reul, wherea for B-NS beam he iffne ha been overeimaed by FE model. All TCC beam how emi-ompoie behaviour onidering ha he loading and unloading repone are beween Full-ompoie and No-ompoie behaviour. Furher, he omparion beween experimenal and analyial reul indiae he uffiien auray of he developed FE model. In Table 3, he load orreponding o 1 mm defleion and predied ulimae loading apaiy of eah TCC beam are repored and ompared wih FE prediion and manual alulaion. Baed on he predied reul by FE model, B-NS ha he minimum error (FEM-CON = %, FEM-FR = 6% and Semi-omp. = 3%) ompared o experimenal reul, wherea B-4BM ha he greae error (FEM-CON = 31%, FEM- FR = 5% and Semi-omp. = 1%). Overall, he reul of B-4BM and B-6BM beam are abou 15-3% le han he experimenal value. Thi may parly be due o he fa ha friion beween imber and onree in he middle of he beam i ignored where here i no onneion. I may alo be a reul of undereimaing he load apaiy of bird mouh onneion. However, furher inveigaion are reommended o underand he underlying reaon for hi direpany. Moreover, for he B-NS beam he ulimae loading apaiy predied by FE model i dramaially differen han manual alulaion, whih i believed o be he reul of allowing for he nonlinear behaviour of he onneion in he FE model. 5

14 Load (N) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only Load (N) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. 4 4 Load (N) Defleion (mm) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only (a) Load (N) Defleion (mm) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. (b) Defleion (mm) () Defleion (mm) (d) Fig. 7 Load veru defleion of (a) B-NS, (b) B-SFS, () B-4BM and (d) B-6BM beam for Khorandnia e al. (1) e in ervieabiliy range. The average, andard deviaion and oeffiien of variaion of differen analyial model in ervieabiliy range are repored in Table 4. Baed on he reul, all he model ued for analyi of TCC beam under SLS load have uffiien auray and hey an adequaely repreen he global behaviour of he beam wihin hi range. Among he differen mehod, manual alulaion ha he minimum error (9%) a well a he lea variaion (1.6%). Aordingly, in he ae onidered in hi udy, uing linear repone baed on Euroode 5 proviion an be uffiien for analyi of TCC beam wihin he ervieabiliy range. 53

15 Table 3. Load orreponding o 1 mm defleion and predied ulimae loading apaiy obained from experimenal and analyial reul in ervieabiliy range. Beam B-NS (Khorandnia e al. 1) B-SFS (Khorandnia e al. 1) B-4BM (Khorandnia e al. 1) B-6BM (Khorandnia e al. 1) Mehod Load orr. o 1 mm def. P u P (N) P/P(e) (N) Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Table 4. Average, andard deviaion and oeffiien of variaion of FE and manual analye in ervieabiliy range. Mehod Ave. San. Dev. Coef. of Var. FEM-CON % FEM-FR % Semi-omp % 4. Ulimae range Five TCC beam from wo differen experimenal program (Clouon e al. 5; Yeoh e al. 11b) have been hoen from he lieraure o verify he auray of he developed FE model for apuring he full load-defleion and ulimae loading apaiy. The geomerial deail and adoped maerial properie for he TCC beam are ummarized in Table 5. The pan of he beam i wihin he range of 8-1 m. The 54

16 beam eed by Yeoh e al. (11b) have T-hape eion, wherea he beam in Clouon e al. (5) e i reangular. The onidered beam have variou number and ype of onneion and he hear-lip behaviour of onneion are deribed in he previou eion. Table 5. TCC beam deail and maerial properie ued in FE model and manual analyi in ulimae range. Beam A1-R15 (Yeoh e al. 11b) B1-R15 (Yeoh e al. 11b) C1-T (Yeoh e al. 11b) E1-R3 (Yeoh e al. 11b) Clouon e al. (5) Span (m) Dimenion (mm) RC Slab Timber Beam Conneion No. Type Load Di. (m) Maerial Properie MOE Tim. (GPa) f p Con. (MPa) MOR Tim. (MPa) R R T R Seel Meh The experimenal load-defleion of Yeoh e al. (11b) and Clouon e al. (5) e a well a he repone apured by FE model and manual analye are diplayed in Fig. 8 and 9, repeively. In he developed FE model, he ulimae loading apaiy of he TCC beam i governed by he enile failure of he imber in he boom layer whih i ypial failure mode in TCC beam a oberved in he benhmar experimenal reul onidered in hi udy (Clouon e al. 5; Yeoh e al. 11b). Mo of he repone remain almo linear up o he failure poin, however, ome nonlineariie near he ollape load i obervable (ee Fig. 8 and 9) whih hould be aen ino aoun when he aurae analyi of he beam required. The omparion beween full-ompoie model, model wih no-ompoie aion and he e reul how ha he beam have high ompoie effiieny ha dereae near he failure load. The model baed on FE and manual analyi an adequaely repreen he global behaviour (inluding iffne and ulimae apaiy) of TCC beam up o failure. The ulimae loading apaiy and he orreponding defleion a ulimae load obained from experimenal daa and analyial reul are given in Table 6. Baed on he reul, all hree analyial mehod (oninuum-baed FE, frame elemen FE and manual analyi) an apure he ulimae loading apaiy wih reaonable auray. For apuring he ulimae defleion, however, he FE model have beer auray han manual analyi and i wa oberved ha uing he ervieabiliy iffne (K,.4 ) for onneion i an appropriae value o ar wih when he ulimae loading apaiy of he TCC beam i being predied. 55

17 Load (N) Load (N) Defleion (mm) (a) () Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only Defleion (mm) Load (N) Load (N) Defleion (mm) (b) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only (d) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only Defleion (mm) Fig. 8 Load veru defleion of (a) A1-R15, (b) B1-R15, () C1-T and (d) E1- R3 beam for Yeoh e al. (1) e in ulimae range. The average, andard deviaion and oeffiien of variaion for ulimae loading apaiy and he orreponding defleion are alulaed and provided in Table 7. The developed oninuum-baed model an auraely apure boh he ulimae loading apaiy and i orreponding defleion (1% error) wih maximum 6.8% variaion, while he developed frame elemen model alo offer good orrelaion wih he experimenal reul (maximum 6% error wih 8.6% variaion). The auray in he manual analyi i no a good a for he FE model, pariularly when he ulimae 56

18 defleion i onerned. I i alo onluded ha when he TCC beam have high ompoie effiieny, he global behaviour i almo linear up o failure and he nonlinear behaviour of imber and onree doe no have a ignifian influene on he repone. Load (N) Te FEM-CON FEM-FR Full-omp. Semi-omp. No-omp. Timber-only Defleion (mm) Fig. 9 Load veru defleion of Clouon e al. (5) e in ulimae range. 5 CONCLUSIONS Thi paper preen he ho-erm analyial repone of imber-onree ompoie ruure wih differen mehod. Two differen ype of finie elemen model, i.e. oninuum-baed and 1D frame fibre elemen, a well a proedure for manual alulaion baed on Euroode 5 proviion are developed and heir deail are diued. Deail of he FE model and he adoped oniuive law for imber and onree are provided and diued. For modelling onneion, appliaion of nonlinear pring i inrodued, whih allow for he full load-lip behaviour of onneion o be direly onidered in he developed FE model. Furhermore, deail of manual alulaion aording o Euroode 5 are provided ha apure four differen ype of behaviour inluding full-ompoie (no lip beween imber and onree), emi-ompoie (parial ineraion beween imber and onree), noompoie (free lip beween imber and onree) and imber-only (wihou onree lab). For verifiaion of he developed model, hree differen experimenal program in ervieabiliy and ulimae range wih variou TCC onneion are hoen and he load-mid pan defleion of he beam under four-poin bending e i ompared o analyial reul. Furher, he load orreponding o 1 mm defleion in ervieabiliy range and he ulimae loading apaiy and i orreponding defleion in ulimae range are repored and he error of eah wih repe o e reul are alulaed and repored. The developed FE model, inluding oninuum-baed and 1D frame, an apure he hor-erm global behaviour of TCC beam under ervieabiliy and ulimae load 57

19 wih uffiien auray. The ulimae apaiy of all beam onidered in hi udy i governed by enile failure of imber in he boom layer whih i in good agreemen Table 6. Ulimae loading apaiy and orreponding defleion obained from experimenal and analyial reul in ulimae range. Beam A1-R15 (Yeoh e al. 11b) B1-R15 (Yeoh e al. 11b) C1-T (Yeoh e al. 11b) E1-R3 (Yeoh e al. 11b) Clouon e al. (5) Mehod Ulimae Load Ulimae Def. P u (N) P u /P u (e) δ u (mm) δ u /δ u (e) Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only Te FEM-CON FEM-FR Full-omp Semi-omp No-omp Timber-only

20 Table 7. Average, andard deviaion and oeffiien of variaion of FE and manual analye in ulimae range. Mehod Ulimae Load Ulimae Defleion Ave. San. Dev. Coef. of Var. Ave. San. Dev. Coef. of Var. FEM-CON % % FEM-FR % % Semi-omp % % wih he experimenal daa. Typially, he load-defleion repone of TCC beam i almo linear line up o failure and hi i due o high iffne and rengh of he onneion uilied in hi reearh program. Furhermore, uing manual alulaion baed on Euroode 5 in onjunion wih enile failure of imber an apure he ervieabiliy and ulimae repone of TCC beam wih reaonable auray, provided he lip modulu of he onneion i eleed arefully (baed on experimenal daa). For high iffne onneion, uing ervieabiliy lip modulu (haraeried by a onan iffne) i i poible o ahieve aurae reul pariularly for he ulimae loading apaiy. However, for onneion wih rongly nonlinear load-lip behaviour (e.g. normal rew), appliaion of more advaned mehod uh a nonlinear FE i warraned. ACKNOWLEDGEMENTS The auhor would lie o graefully anowledge he finanial uppor of he Sruural Timber Innovaion Company (STIC) Reearh Conorium ha ha enabled hi wor o be underaen. REFERENCES ABAQUS (11), Ver Doumenaion edn, Daaul Syème. Ahmadi, B.H. and Saa, M.P. (1993), "Behavior of Compoie Timber-Conree Floor" Journal of Sruural Engineering, Vol. 119(11), ANSYS (11), Releae 14. UP1114 edn, SAS IP, In. Balogh, J., Fragiaomo, M., Guowi, R.M. and Fa, R.S. (8), "Influene of Repeaed and Suained Loading on he Performane of Layered Wood-Conree Compoie Beam" Journal of Sruural Engineering, Vol. 134(3), Brano, J.M., Cruz, P.J.S. and Piazza, M. (9), "Experimenal analyi of laerally loaded nailed imber-o-onree onneion" Conruion and Building Maerial, Vol. 3(1), 4-1. Brunner, M., Romer, M. and Shnüriger, M. (7), "Timber-onree-ompoie wih an adheive onneor (we on we proe)" Maerial and Sruure, Vol. 4(1), 59

21 CEB-FIP (1993), CEB-FIP model ode 199: Deign ode, Thoma Telford, London. Ceoi, A. (1995), Timber-Conree Compoie Sruure, Timber Engineering, Sep, 1 Edn. (Cenrum Hou, The Neherland) E13/1-E13/1. Ceoi, A., Fragiaomo, M. and Giordano, S. (6), "Long-erm and ollape e on a imber-onree ompoie beam wih glued-in onneion" Maerial and Sruure, Vol. 4(1), CEN (1991), Timber Sruure - Join made wih mehanial faener - General priniple for he deerminaion of rengh and deformaion haraerii. EN 6891, BSI, European Commiee for Sandardizaion, Bruel, Belgium. CEN (8), Euroode 5: Deign of imber ruure - Par 1-1: General - Common rule and rule for building. EN :4+A1, BSI, European Commiee for Sandardizaion, Bruel, Belgium. Clouon, P., Bahon, L.A. and Shreyer, A. (5), "Shear and Bending Performane of a Novel Wood-Conree Compoie Syem" Journal of Sruural Engineering, Vol. 131(9), Clouon, P., Civjan, S. and Bahon, L. (4), "Experimenal behavior of a oninuou meal onneor for a wood-onree ompoie yem" Fore Produ Journal, Vol. 54(6), Conner, T.E. (1989), "Segmened model for re-rain diagram" Wood Siene and Tehnology, Vol. 3(1), Deam, B.L., Fragiaomo, M. and Buhanan, A.H. (8), "Conneion for ompoie onree lab and LVL flooring yem" Maerial and Sruure, Vol. 41(3), Dia, A.M.P.G., Lope, S.M.R., Van de Kuilen, J.W.G. and Cruz, H.M.P. (7a), "Load-Carrying Capaiy of Timber-Conree Join wih Dowel-Type Faener" Journal of Sruural Engineering, Vol. 133(5), 7-7. Dia, A.M.P.G., Van de Kuilen, J.W., Lope, S. and Cruz, H. (7b), "A non-linear 3D FEM model o imulae imber-onree join" Advane in Engineering Sofware, Vol. 38(8-9), 5-3. Fragiaomo, M. (5), "A finie elemen model for long-erm analyi of imberonree ompoie beam" Sruural Engineering and Mehani, Vol. (), Fragiaomo, M. (1), "Experimenal behaviour of a full-ale imber-onree ompoie floor wih mehanial onneor" Maerial and Sruure, Fragiaomo, M., Amadio, C. and Maorini, L. (7), "Shor- and long-erm performane of he Tenaria ud onneor for imber-onree ompoie beam" Maerial and Sruure, Vol. 4(1), Gelfi, P., Giuriani, E. and Marini, A. (), "Sud Shear Conneion Deign for Compoie Conree Slab and Wood Beam" Journal of Sruural Engineering, Vol. 18(1), Glo, P. (1981), Zur modellierung de feigeiverhalen von bauholz bei dru-, Zug- und biegebeanpruhung, Berihe zur zuverlaigeiheorie der bauwere, SFB 96, Munih, Germany. Guowi, R., Brown, K., Shigidi, A. and Naerer, J. (8), "Laboraory e of ompoie wood-onree beam" Conruion and Building Maerial, Vol. (6), Guowi, R.M., Balogh, J. and To, L.G. (1), "Finie-Elemen Modeling of Shor- Term Field Repone of Compoie Wood-Conree Floor/De" Journal of Sruural Engineering, Vol. 136(6), Guowi, R.M., Brown, K., Shigidi, A. and Naerer, J. (4), "Inveigaion of Nohed Compoie Wood-Conree Conneion" Journal of Sruural Engineering, Vol. 13(1),

22 Hahin, Z. (198), "Failure Crieria for Unidireional Fiber Compoie" Journal of Applied Mehani, Vol. 47(), Hahin, Z. and Roem, A. (1973), "A Faigue Failure Crierion for Fiber Reinfored Maerial" Journal of Compoie Maerial, Vol. 7(4), Jorge, L.F., Lope, S. and Cruz, H. (11), "Inerlayer influene on imber-lwac ompoie ruure wih rew onneion" Journal of Sruural Engineering, Vol. 137(5), 7. Khorandnia, N., Valipour, H.R. and Crew, K. (1), "Experimenal and analyial inveigaion of hor-erm behaviour of LVL-onree ompoie onneion and beam" Conruion and Building Maerial, Vol. 37(9-38. Khorandnia, N., Valipour, H.R. and Crew, K. (13), "Nonlinear finie elemen analyi of imber beam and join uing he layered approah and hypoelai oniuive law" Engineering Sruure, Vol. 46( LeBorgne, M.R. and Guowi, R.M. (1), "Effe of variou admixure and hear ey in wood-onree ompoie beam" Conruion and Building Maerial, Vol. 4(9), Lee, J. and Fenve, G.L. (1998), "Plai-damage model for yli loading of onree ruure" Journal of Engineering Mehani, Vol. 14(8), 89. Lope, S., Jorge, L. and Cruz, H. (1), "Evaluaion of non-linear behavior of imberonree ompoie ruure uing FE model" Maerial and Sruure, Vol. 45(5), Lubliner, J., Oliver, J., Oller, S. and Oñae, E. (1989), "A plai-damage model for onree" Inernaional Journal of Solid and Sruure, Vol. 5(3), Luazewa, E., Fragiaomo, M. and Johnon, H. (1), "Laboraory Te and Numerial Analye of Prefabriaed Timber-Conree Compoie Floor" Journal of Sruural Engineering, Vol. 136(1), Luazewa, E., Johnon, H. and Fragiaomo, M. (8), "Performane of onneion for prefabriaed imber onree ompoie floor" Maerial and Sruure, Vol. 41(9), Maenzie-Helnwein, P., Eberhardeiner, J. and Mang, H.A. (3), "A muli-urfae plaiiy model for lear wood and i appliaion o he finie elemen analyi of ruural deail" Compuaional Mehani, Vol. 31(1- SPEC.), Maia, N. and Soriano, J. (4), "Benefi of imber-onree ompoie aion in rural bridge" Maerial and Sruure, Vol. 37(), 1-8. Ollgard, G., Sluer, G. and Fiher, W. (1971), "Shear rengh of ud onneor in lighweigh and normal weigh onree" AISC Engineering Journal, Vol. 8( Shäfer, M. and Seim, W. (11), "Inveigaion on bonding beween imber and ulrahigh performane onree (UHPC)" Conruion and Building Maerial, Vol. 5(7), Seinberg, E., Selle, R. and Fau, T. (3), "Conneor for Timber-Lighweigh Conree Compoie Sruure" Journal of Sruural Engineering, Vol. 19(11), Valipour, H.R. and Bradford, M. (1), "An effiien ompound-elemen for poenial progreive ollape analyi of eel frame wih emi-rigid onneion" Finie Elemen in Analyi and Deign, Vol. 6( Valipour, H.R. and Bradford, M.A. (9), "A eel-onree ompoie beam elemen wih maerial nonlineariie and parial hear ineraion" Finie Elemen in Analyi and Deign, Vol. 45(1), Valipour, H.R. and Bradford, M.A. (13), "Nonlinear P-Δ analyi of eel frame wih emi-rigid onneion" Seel and Compoie Sruure, Vol. 14(1), 1-. Yeoh, D., Fragiaomo, M., De Franehi, M. and Buhanan, A.H. (11a), "Experimenal e of nohed and plae onneor for LVL-onree ompoie beam" Journal of Sruural Engineering, Vol. 137(),

23 Yeoh, D., Fragiaomo, M. and Deam, B. (11b), "Experimenal behaviour of LVLonree ompoie floor beam a rengh limi ae" Engineering Sruure, Vol. 33(9),