FLEXURAL PERFORMANCE OF CIRCULAR CONCRETE FILLED CFRP-STEEL TUBES

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1 Advaned Seel Conrion Vol. 11, No. 2, pp (215) 127 FLEXURAL PERFORMANCE OF CIRCULAR CONCRETE FILLED CFRP-STEEL TUBES Q. L. Wang 1, * and Y. B. Shao 2 1 Profeor, Shool of Civil Engineering, Shenyang Jianzh Univeriy, Shenyang, P. R. China 2 Profeor, Shool of Civil Engineering, Yanai Univeriy, Yanai, P. R. China *(Correponding ahor: eqlwang@jz.ed.n) Reeived: 26 Sepember 212; Revied: 15 Janary 214; Aeped: 26 Febrary 214 ABSTRACT: Sixeen irlar onree filled CFRP-eel blar (C-CF-CFRP-ST) flexral member were eed. The e rel indiae ha he momen ver rvare rve a mid-pan of C-CF-CFRP-ST member wiho longidinal CFRP reinforemen i imilar o h relaionhip of orreponding n-reinfored irlar onree filled eel blar (C-CFST) flexral member. The momen ver rvare rve a mid-pan for member wih longidinal CFRP reinforemen an be divided ino following age: elai age, elao-plai age and ofening age. The longidinal CFRP an enhane he iffne of he peimen ignifianly. The eel be and he CFRP be old ooperae boh in he ranvere and in he longidinal direion. The eel be in he region nder longidinal enion ha no onfinemen effe on he ore onree in he ame enile region beae he onree i in a ae of onraion in ranvere direion. The longidinal rain diribion over deph of he peimen ro-eion aifie he plane eion ampion approximaely. Finie elemen model i bil and ABAQUS i ed o analyze boh he momen ver rvare rve a mid-pan and he deformaion of he C-CF-CFRP-ST flexral member. The finie elemen rel are fond o agree well wih experimenal rel. Ineraion fore exi boh in he enile region and in he ompreive region beween he oer be and he onree. However, here i eenial differene beween he ineraion fore in he enile region and in he ompreive region repeively. Finally, flexral load arrying apaiy of he C-CF-CFRP-ST i defined, and parameri eqaion for allaing i are preened. The aray and he reliabiliy of he propoed eqaion are verified. Keyword: Cirlar CFRP-eel be, In-filled onree, Beam, Flexral performane, Ineraion fore, Flexral load arrying apaiy 1. INTRODUCTION Conree Filled Tblar rre (denoed by CFT rre, a hown in Figre 1) ha aroed wide appliaion and deep die all over he world for i advanage of high rengh of ri-axially ompreed onree. Conree Filled Seel Tblar rre (denoed by CFST rre, a hown in Figre 1 (a)) i a very ypial CFT rre and i i ed widely in ivil engineering. The reearh work in hi field ha been died yemaially in he lierare, h a he inveigaion on he ai behavior (Han [1]; Tao e al. [2]; Georgio and Lam [3]; Uy [4]), he hyerei behavior (Han and Yang [5]; Han and Li [6]) of he omponen and he onneion, and fire and orroion reiane (Han, Wang and Y [7]; Han, Ho and Wang [8]). Neverhele, Carbon Fiber Reinfored Polymer (denoed by CFRP) ha been ed in more and more engineering rre de o i advanage of high rengh/weigh raio, good orroion reiane, eae of inallaion, heaper o and o on. Conree Filled CFRP Tblar rre (denoed by CF-CFRP-T rre, a hown in Figre 1 (b)) i a ypial example of CFRP rre (Wang and Rerepo [9]; Teng e al. [1]). However, he failre mode of CF-CFRP-T rre ha brile haraerii in mo ae, and he load arrying apaiy in he ranvere direion for hi rre i weak. There i alo a new ype of CFT rre, i.e., Conree Filled CFRP-Seel Tblar rre (denoed by CF-CFRP-ST rre, a hown in Figre 1 ()). CFRP an enhane load arrying apaiy of he CFST rre and rede loal bkling of he eel be. I an alo improve he rral drabiliy. Comparing wih CF-CFRP-T, CF-CFRP-ST ha beer diliy and hearing load arrying apaiy. Addiionally, CF-CFRP-ST an alo provide a new approah o

2 Q.L. Wang and Y.B. Shao 128 repair exiing CFST wih ome ligh damage (fire or orroion) or wih reqiremen o ain more addiional load. Conree Conree Conree Seel be Seel be CFRP CFRP (a) CFST Srre (b) CF-CFRP-T Srre () CF-CFRP-ST Srre Figre 1. CFT Srre I i poined o here ha mo rein a he marix of CFRP ompoie ha a poor fire-reian apaiy, and how o reolve he fire reiane of CFRP in engineering praie i ill he primary onern. I i beer o e CF-CFRP-ST in an environmen wih le fire b wih evere orroion, h a bridge engineering, offhore and oean engineering and o on. From repored experimen nder fire ondiion in he lierare (Han, Tao and Wang [11]), i eem ha CF-CFRP-ST ha demonraed aifaory fire endrane nder exernal loading when pplemenal inlaion o he CFRP ompoie ha been ed. Aally, he ompoie CFRP-meal ank or be have been ed in many field, for example, ga ank ed in moor vehile, pipeline yem for ranporing high prere ga or liqid ed in mniipal engineering or hemial engineering. Someime, eel perolem pipeline yem afer orroion i alo reinfored wih CFRP, whih an ave mh o ompared o he meare of replaing he orroded be wih new one. Baed on he above inrodion, i i believed ha he e of CF-CFRP-ST in ivil engineering i qie reaonable and poenial. Some reearh die in hi field have been repored in he lierare. Reearh work of ing CFRP o repair CFST b olmn inlding irlar peimen and qare peimen afer expoed o fire wa onded (Tao, Han and Wang [12]). A new CFST olmn yem wih irlar ro-eion, where CFRP maerial were ed a addiional onfinemen o he poenial plai hinge region of he ompoie olmn, wa propoed (Xiao, He and Choi [13]), and a implified analyial olion in aoiaion wih a nmerial omper program of he CF-CFRP-ST olmn wa developed (Choi and Xiao [14]). Addiionally, a yemai dy on Cirlar CF-CFRP-ST (denoed by C-CF-CFRP-ST) b olmn ha been arried o (Che, Wang and Shao [15]). The oniive relaionhip of onree onfined by irlar CFRP-eel be nder ompreion a well a he index of load arrying apaiy of he axially ompreed C-CF-CFRP-ST b olmn wa preened. However, he performane of he C-CF-CFRP-ST flexral member or beam-olmn i arely repored, alhogh ing CFRP wrapped in ranvere direion o repair irlar CFST (denoed by C-CFST) flexral member afer expoed o fire wa inveigaed (Tao, Han and Wang [12]). For he member arrying large bending

3 129 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe momen, i i fond ha CFRP wrapped in ranvere direion doe no have remarkable effiieny, and in hi iaion CFRP i only neeary o be wrapped mainly in longidinal direion. Frhermore, heoreial analyi on C-CF-CFRP-ST flexral member i alo are. In order o do ome frher die and o nderand he reinforing effiieny of longidinal CFRP, 16 C-CF-CFRP-ST flexral member wih boh ranvere and longidinal CFRP are eed. Momen ( M ) ver rvare ( ) rve a mid-pan, ooperaion beween he eel be and he CFRP, plane eion ampion and iffne of he ompoie member are all analyzed and died. Frhermore, he finie elemen ofware ABAQUS i ed o imlae he deforming hape and he M - rve of he C-CF-CFRP-ST flexral member. The diribion of longidinal re and rain on he ro-eion a mid-pan, effe of he renghening faor of he longidinal CFRP (), and ineraion fore ( p ) beween ore onree and oer be are alo analyzed. Finally, he flexral load arrying apaiy i defined, and a orreponding heoreial eqaion i preened. 2. EXPERIMENTAL PROGRAM 2.1 Speimen Geomery In overall, ixeen C-CF-CFRP-ST flexral peimen were onded, and he parameer inlde he nmber of longidinal CFRP layer() ( m ') and he oer diameer of he eel be ( D ) repeively. Speimen deail are provided in Table 1. Table 1. Speimen Label and Member Capaiie No. m ' Speimen D L L m M K ie K e lr' (layer label (mm) (mm) (mm) (mm) (layer) 2 2 ()) ( kn m ) ( kn m ) ( kn m ) ( με ) 1 CB A CB A CB A CB A CB B CB B CB B CB B CB C CB C CB C CB C CB D CB D CB D CB D In Table 1, CB in he peimen label refer o Cirlar Beam, and he hird leer an be anyone among leer A, B, C or D whih denoe differen D wih i vale eqal o 89 mm, 18mm, 133mm or 159 mm repeively. The nmber in he peimen label wih, 1, 2 or 3 refer o he vale of m '. For oher parameer, i wall hikne of he eel be, L i lengh of he peimen, L i ne pan of he peimen, and m i nmber of he ranvere CFRP layer.

4 Q.L. Wang and Y.B. Shao Speimen Preparaion Fabriaion of C-CFST peimen an be fond in repored referene (Han [1]). Carbon fiber hee are applied ing a hand lay-p mehod. The longidinal CFRP i gled firly, and he ranvere CFRP i hen plaed eqenially. The final end of a hee i overlapped he iniial end by 15 mm. Some peimen before eing are hown in Figre 2. (a) D 89mm Speimen (b) D 159mm Speimen 2.3 Maerial Properie Figre 2. Several Speimen before Teing Tenile e on eel opon from he original eamle eel be are onded o meare he maerial properie. The eed rel are given in Table 2, where E, f y, v and f are elai modl, yield re, Poion raio and limae re of he eel be repeively. D (mm) Table 2. Maerial Properie of Seel Tbe E (GPa) f (MPa) v y f (MPa) All he peimen were a wih ame onree. In he onree mixre, Porland emen wa ed, and fine aggregae wa ilia-baed and. The ore aggregae wa limeone wih he large ize of 2mm, and 1% (in weigh) waer reding agen wa added. The mixre proporion of he onree i mmarized in Table 3. 3 Table 3. Mixre Proporion of Conree ( kg m ) Cemen Waer Fine aggregae Core aggregae To deermine he ompreive rengh of he onree, ix 15mm bi peimen were a and red in ondiion imilar o ha of he eed peimen. The average bi rengh ( f ) a 28 day wa 48.8 MPa. A he ime of e (ix monh laer de o he delay of he e program), he bi rengh of 6.7 MPa wa ahieved and hi rengh i ed in following FE imlaion and

5 131 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe allaion of flexral load arrying apaiy. Elai modl of he onree ( E ) wa 35.9GPa. The ed arbon fiber hee i made in EPO Company, Germany, whih i a kind of one-way hee. The maerial properie of he CFRP in enion, deermined from enile e of ix fla opon (a hown in Figre 3), are given in Table 4, where f ', E, and w are enile rengh, elai modl, elongaion perenage and deniy of he arbon fiber hee repeively, and i hikne of one layer arbon fiber hee. Figre 3. Typial Failed CFRP Copon Table 4. Main Tehnial Properie of Carbon Fiber Shee Model nmber f ' (GPa) E (GPa) (%) w (g m -2 ) (mm) C3/ JGN-C, a kind of epoxy rein ed for bilding rre proded by Bilding Siene Reearh Inie of Liaoning Provine, P. R. China, wa ed for adhering he CFRP o he eel be. Anoher epoxy rein, JGN-P, wa alo ed for gling CFRP ogeher. 2.4 Te Sep and Inrmenaion Rpre The experimenal e wa arried o in he Srral Engineering Laboraory of Shenyang Jianzh Univeriy, P. R. China. A hown in Figre 4, he peimen i imply ppored a boh end. A jak whih i loaed a he mid-pan of he peimen i ed o apply laeral load ( P ), and he load i ranferred by a pread beam wih enogh iffne o he wo ri-pan poin of he peimen. The load i applied in everal ep. In he elai age, eah loading ep i 5. kn. When he applied load i abo 6% of he eimaed flexral load arrying apaiy, he magnide of he loading ep rede. The eimaed flexral load arrying apaiy i obained by he following mehod: he ranvere and he longidinal CFRP are ranferred o eqivalen eel be, and hen he flexral load arrying apaiy an be allaed by ing orreponding eqaion of C-CFST flexral member (Han [16]). However, he eqivalen eel be beide longidinal CFRP i no onidered in allaing he onfinemen faor of he eel be ( ) (Han [17]). Afer he defleion a he mid-pan exeed L 5, diplaemen onrol i ed ill failre. A fore rander wih a apaiy of 6kN wa ed o meare he loading magnide. Three Linear Variable Differenial Tranformer (LVDT) were plaed o meare he defleion of he peimen. A he wo pporing poin, wo LVDT were alo ed o meare he elemen. Overall 11 rain gage were gled on he rfae of eah eel be and he CFRP arond ro-eion a mid-pan of he peimen repeively, a hown in Figre 5, where poin 1-7 were he loaion for mearing longidinal rain and poin 1, 3, 5 and 8 were he loaion for mearing ranvere rain.

6 Q.L. Wang and Y.B. Shao 132 P LVDT Spread beam Speimen LVDT Sppor Sppor LVDT (a) General Plaemen (in mm) LVDT Fore rander Spread beam Speimen LVDT Sppor Sppor LVDT (b) Te Figre Figre 4. Te Arrangemen 1 P Conree CFRP 3 D /6 D 6 4 Seel be Figre 5. The Loaion of Srain Gage The daa wa apred and aved by daa aqiiion yem U-CAM-7A, and he load ( P ) ver defleion ( m ) a mid-pan rve wa obained imlaneoly. 2.5 Te Obervaion and Failre Mode 5 For he peimen only reinfored wih ranvere CFRP, he failre proe i gradal. Dring he iniial loading age, in general, he bending load preen an approximaely proporional relaionhip o m. There are no obvio damage in he appearane of he peimen. New rak beween arbon fiber and exenion of exiing rak are oberved dring frher loading. A he end of he e, hrogh-rak are oberved on he CFRP jake in he pre-bending region and large deformaion of he peimen appear. Finally, he ranvere CFRP loaed a longidinally ompreed region begin o rpre a hown in Figre 6 (a).

7 133 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe Rpre Rpre (a) Tranvere CFRP (b) Longidinal CFRP Figre 6. Rpre of CFRP For hoe peimen reinfored wih longidinal CFRP, longidinal CFRP begin o rpre when he rain a he exreme fiber of he enile region reahe abo 1 με whih an be een in Figre 6 (b). A hi ime, he flexral load arrying apaiy of he beam dereae ddenly. The ranvere CFRP loaed a longidinally ompreive region begin o rpre when he deformaion of he peimen beome larger in he laer loading age. The final failre mode of everal peimen are hown in Fig. 7. (a) D 89mm Speimen (b) D 159mm Speimen Figre 7. Typial Deformaion of Several Speimen The peimen are ino wo halve afer he e, a hown in Figre 8, o find ha he onree an be divided ino boh enile and ompreive region. I an be een ha he onree in longidinally enile region ha ome rak while i i rhed in he region nder longidinal ompreion. Crak Crhed onree (a) Longidinally Tenioned Conree (b) Longidinally Compreed Conree Figre 8. Failre Mode of Conree

8 Q.L. Wang and Y.B. Shao Te Rel and Analyi Teed M- rve Figre 9 how he defleion ( ) rve of peimen CB D-3, where M i eed vale of he flexral load arrying apaiy ( M ). All vale of M are lied in Table 1. From Figre 9, i i fond ha he defleion of eah peimen i very loe o half inoidal rve. Therefore, an be allaed from m approximaely aording o he following eqaion (Han, Yao and Zhao [18]) 2 2 π m L (1) (mm) M.52M.71M.93M 1.9M Sine rve L (mm) (a) Before Rpre of Longidinal CFRP (mm) M.96M 1.2M 1.9M 1.14M Sine rve L (mm) (b) Afer Rpre of Longidinal CFRP Figre 9. Defleion Crve of Speimen CB D-3 Figre 1 how he M - rve a mid-pan of he peimen, where M PL 6 (2) M (knm) M CB A- CB B- CB C- CB D- M (knm) M CB A-1 CB B-1 CB C-1 CB D-1 M (knm) M (m -1 ) (a) m'= CB A-2 CB B-2 CB C-2 CB D-2 M (knm) M (m -1 ) (b) m'=1 CB A-3 CB B-3 CB C-3 CB D (m -1 ) () m'= (m -1 ) (d) m'=3 Figre 1. Teed M - Crve

9 135 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe I i fond ha parameer m ' ha a remarkable effe on he rve hape of he C-CF-CFRP-ST flexral member. For peimen wih m'=, heir rve are imilar o hoe of he orreponding C-CFST flexral member (Han [16]). While for peimen wih m ', boh he load and he defleion are maller dring he iniial loading age, and he relaionhip beween hem i approximaely linear. Thi age belong o elai age. A load inreae oninoly, he defleion inreae mh more rapidly han before, and hi age belong o elao-plai age. The rve fall in ofening age afer he longidinal CFRP i rpred, and he re of he rve are imilar o hoe of he orreponding C-CFST flexral member. For he peimen wih m ', heir failre eem o be brile. However, de o he exiene of he eel be, he peimen old ill keep high flexral load arrying apaiy even hey are ffered from a large deformaion Siffne Aording o he M - rve hown in Figre 1, he iniial flexral iffne ( K ie ) and he ervie flexral iffne ( K e ) (Verma e al. [19]) are defined. The relaionhip of Kie - m ' and Ke - m ' i illraed in Figre 11. K ie and K e are alo lied in Table 1. A how in Figre 11, K ie and K e are boh enhaned by he inreae of m '. I i lear ha he longidinal CFRP an enhane he iffne of he peimen ignifianly. 24 K ie (knm 2 ) K e (knm 2 ) m' (layer()) (a) Hiogram of m' (layer()) (b) Hiogram of K - m ' ie Ke - m ' D = 89mm Speimen D =18mm Speimen D =133mm Speimen D =159mm Speimen D = 89mm Speimen D =18mm Speimen D =133mm Speimen D =159mm Speimen Figre 11. Siffne ver m ' Relaionhip Cooperaion beween Seel Tbe and CFRP Figre 12 how he omparion of rain beween he eel be and he CFRP, where l and are longidinal and ranvere rain repeively. Similarly, l and l are longidinal rain of he eel be and he CFRP repeively, and and are ranvere rain of he eel be and he CFRP repeively. A hown in Figre 12, l and l are baially he ame, and

10 Q.L. Wang and Y.B. Shao 136 o i he relaionhip beween and. Addiionally, from he obervaion of he CFRP-eel be afer he experimen, i i fond ha he adherene beween he CFRP and he eel be i ill ina exep in he region where CFRP i rpred. All above rel indiae ha eel be and CFRP an ooperae well in boh longidinal and ranvere direion. Oherwie, a hown in Figre 12 (b), he diribion of ranvere rain arond he ro-eion i no niform: large ranverely enile and ompreive rain are loaed a poin 5 and a poin 1 repeively. Aally, he oer be an be divided ino a enile region and a ompreive region in ranvere direion. Sh laifiaion depend on he fa ha he oer be i nder enion or nder ompreion in longidinal direion. A he peimen i bjeed o bending momen, par of he ro-eion of he oer be i nder ompreion in longidinal direion, whih ae hi par of he ro-eion nder enion in ranvere direion. Aordingly, he oher par of he ro-eion of he oer be i nder enion in longidinal direion, whih ae hi par of he ro-eion nder ompreion in ranvere direion. Thi phenomenon ha been proved from experimenal mearemen. De o he above reaon, he oer be ompreed ranverely doe no provide onfinemen effe for he onree. 6 3 M (knm) 4 l for poin 1 l for poin 5 2 l for poin 1 l for poin l () (a) M - l Crve of Speimen CB C-3 M (knm) 2 1 for poin 1 for poin 5 for poin 1 for poin () (b) M - Crve of Speimen CB B-1 Figre 12. Comparion of Srain beween Seel Tbe and CFRP Plane Seion Ampion Figre 13 how he diribion of l over deph of he ro-eion of he peimen wih D 133mm, where Δ n i he diane meared from he neral axi o he enroid axi. The diribion of l i baially in aordane wih he plane eion ampion. The neral axi move oward he ompeion region gradally a he momen inreae. D (mm) Cenroid axi l ().M ( n =mm).25m ( n =7.5mm).5M ( n =12.5mm).65M ( n =12.5mm).76M ( n =21.5mm).87M ( n =28.5mm) (a) Speimen CB D-

11 137 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe D (mm) D (mm) D (mm) Cenroid axi l () (b) Speimen CB D-1 Cenroid axi l () () Speimen CB D-2 Cenroid axi l () (d) Speimen CB D-3.M ( n =mm).27m ( n =4.5mm).54M ( n =8.5mm).63M ( n =9.5mm).74M ( n =12.5mm).88M ( n =2.5mm).M ( n =mm).24m ( n =2.5mm).52M ( n =7.5mm).77M ( n =8.5mm).89M ( n =9.5mm) 1.2M ( n =14.5mm).M ( n =mm).25m ( n =.5mm).46M ( n =5.5mm).69M ( n =8.5mm).81M ( n =12.5mm).92M ( n =17.5mm) Figre 13. Diribion of l over Deph on Cro-Seion of Speimen wih D 133mm 3. FE SIMULATION 3.1 Sre-Srain Relaionhip of Maerial A 5-age re-rain relaionhip of eel maerial (Han, Yao and Tao [2]) i ed here. Thi re-rain rve inlde 5 egmen: linear and elai age, nonlinear b elai age, plai flowing age, hardening age and ofening age. The oniive relaionhip of onree onfined by CFRP-eel be nder ompreion a well a nder enion (Che, Wang and Shao [15]) i adoped. CFRP i amed o be only able o ain enion. Before frare, he re-rain relaionhip of CFRP i in aordane wih Hooke Law a follow E (3) where and are he re and rain of CFRP repeively.

12 Q.L. Wang and Y.B. Shao 138 When longidinal CFRP reahe i rpre rain ( lr, =1 με. Rpre rain of he longidinal CFRP for eah peimen meared from experimenal e ( lr ') i ablaed in Table 1. The vale of lr i deermined from he average vale of all meared lr ' ), i loe longidinal renghening effe o he member. However, when ranvere CFRP reahe i rpre rain ( r, =55 με ) (Che, Wang and Shao [15]), i loe ranvere onfinemen o he eel be. An inereing poin i reed here ha CFRP ha hree rpre rain, i. e., for he ranvere 1 CFRP, r 55με, m ; for he longidinal CFRP, lr 1με, 1.1.2m ; while for he CFRP opon, 2.1% 21με,. Thi mean he rpre rain may dereae wih a bigger rvare. Similar onlion an be fond from he repored reearh work (Y e al. [21]). The above defined rpre rain of he CFRP in longidinal and in ranvere direion are ed in finie elemen imlaion. In he reearh work on CFST (Han [17]), he onfinemen of eel be o onree i repreened by a onfinemen faor of he eel be ( ). Similarly, he onfinemen of he ranvere CFRP an be alo repreened by a onfinemen faor of he ranvere CFRP ( ) (Che, Wang and Shao [15]), and he renghening effiieny of longidinal CFRP may be repreened by a renghening faor of he longidinal CFRP (). The definiion of all he onfinemen or renghening faor are lied a follow: y k A f A f (4) f f (5) k. 67 k A f A f (6) f E l l r 126MPa y A f A f (8) f E 23MPa (9) l lr where A i ro-eional area of he eel be; A and haraerii axial ompreive rengh of he onree repeively; ro-eional area and limae enile rengh of he ranvere CFRP repeively; (7) f k are ro-eional area and A and f are f are ro-eional area and limae enile rengh of he longidinal CFRP repeively. l 3.2 FE Model Elemen ype eleion A l and Shell elemen S4 wih fll inegraion i eleed for direizing he eel be in finie elemen model. Simpon inegraion wih 9 inegraing poin in he hell hikne direion i ed. For he ore onree, 3-D brik elemen C3D8R wih reded inegraion are ed. Membrane elemen

13 139 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe M3D4 wih 4-node i ed for modelling CFRP Meh diriizaion The onvergen analyi i arried o by ing refined meh in finie elemen analyi, and he deail an be referred o relaive reearh (Che, Wang and Shao [15]). Figre 14 how he FE meh of a ypial model. (a) Tranvere Elemen (b) Longidinal Elemen Figre 14. Meh Diriizaion Inerfae model Hard ona i ed for defining ona inerfae beween eel be and onree, i.e., he prere perpendilar o he ona rfae ( p ) an be ranferred ompleely beween he wo rfae (Han, Li and Yang [22]). The angenial fore beween he eel be and he onree rfae i imlaed by ing Colmb model, i.e., hear fore an be ranferred beween rfae (Han, Li and Yang [22]). In he experimenal e, CFRP i bond o he eel be, and i i amed ha no lip exi beween CFRP and he eel be. Same nodal freedom are ed for he ona elemen beween CFRP and he eel be. In he angenial direion of he ona rfae beween he end plae and he onree, here i alo no lipping, and hard ona ampion i ed in normal direion of he ona rfae Bondary ondiion Bondary ondiion are hown in Figre15, whih are in aordane wih experimenal proe. Aording o he ymmery of boh he geomery and he bondary ondiion, 1/4 model i eleed for FE analyi. On he ymmerial plane of he model, ymmerial onrain are applied. The diplaemen in y-direion a he pporing poin i onrained. End plae Conrain are applied ymmerially abo y-z plane Loading poiion of 1/3 poin Mid-pan ro-eion, onrain are applied ymmerially abo x-y plane y z x Sppor poiion, diplae in y-axi direion i onrained Figre 15. Bondary Condiion

14 Q.L. Wang and Y.B. Shao FE Rel Failre mode To verify he reliabiliy of he above preened FE mehod, overall 16 C-CF-CFRP-ST flexral peimen are analyzed by ing ABAQUS ofware. Figre 16 how he deformaion obained from experimenal e and FE imlaion. From Figre 16, i an be fond ha he FE predied deformaion of he peimen i qie imilar o he experimenal obervaion. (a) Experimenal Rel M- rve (b) Simlaed Rel Figre 16. Comparion of Deformaion The FE M - rve ogeher wih he experimenally meared rel are ploed in Figre 17. In he FE imlaion, he defleion of he peimen an be obained from FE analyi, and he rvare i hen allaed from Eq. (1). I an be fond from Figre 17 ha he FE rel are reaonable ompared wih he experimenal rel alhogh he FE prediion eem o be a lile lower. M (knm) M (knm) (m -1 ) (a) (m -1 ) (b) m ' = m ' =1 FE rel of peimen CB A- FE rel of peimen CB B- FE rel of peimen CB C- FE rel of peimen CB D- Te rel of peimen CB A- Te rel of peimen CB B- Te rel of peimen CB C- Te rel of peimen CB D- FE rel of peimen CB A-1 FE rel of peimen CB B-1 FE rel of peimen CB C-1 FE rel of peimen CB D-1 Te rel of peimen CB A-1 Te rel of peimen CB B-1 Te rel of peimen CB C-1 Te rel of peimen CB D-1

15 141 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe M (knm) M (knm) (m -1 ) () (m -1 ) (d) m ' =2 m ' =3 FE rel of peimen CB A-2 FE rel of peimen CB B-2 FE rel of peimen CB C-2 FE rel of peimen CB D-2 Te rel of peimen CB A-2 Te rel of peimen CB B-2 Te rel of peimen CB C-2 Te rel of peimen CB D-2 FE rel of peimen CB A-3 FE rel of peimen CB B-3 FE rel of peimen CB C-3 FE rel of peimen CB D-3 Te rel of peimen CB A-3 Te rel of peimen CB B-3 Te rel of peimen CB C-3 Te rel of peimen CB D-3 Figre 17. Comparion of M - Crve beween FE Rel and Experimenal Rel 4. THEORETICAL ANALYSIS Three ypial poin, a hown in Figre 18, are eleed for diion: a poin 1, he enile exreme fiber of he eel be reahe i proporional limi; a poin 2, longidinal CFRP i frared; and a poin 3, he defleion a he mid-pan i abo L M 3 Poin 1 Poin 2 Poin Figre 18. Typial Poin in M - Crve 4.1 Longidinal Sre and Srain of Conree on Cro-Seion a Mid-Span Figre 19 and 2 how he diribion of he longidinal rain and he longidinal re of onree on he ro-eion a mid-pan repeively ( D 4mm, 9.31mm, L 4mm, f 345 y MPa, f MPa 6,. 115,. 13, E 26GPa, v. 3, E 47 f'mpa, (where f ' i rengh of he ylinder onree peimen, and Poion raio of he onree ( v ) wa.2). '. 8 f f ),

16 Q.L. Wang and Y.B. Shao 142 (a) Poin 1 (b) Poin 2 () Poin 3 Figre 19. Longidinal Sre Diribion of Conree on Cro-Seion a Mid-pan Neral axi Neral axi Neral axi (a) Poin 1 (b) Poin 2 () Poin 3 Figre 2. Longidinal Srain Diribion of Conree on Cro-Seion a Mid-Span I i fond ha he neral axi move oward he ompreive region gradally wih he inreae of he rvare a he mid-pan, and hi i in aordane wih experimenal rel a hown in Figre 13. In elai age (before poin 1), he neral axi i very loe o he enroid of he ro-eion, and he eel be and CFRP are boh in elai age and he maximm longidinal re of he ompreive onree i le han ' f. In he elao-plai age (beween poin 1 and poin 2), plai region form. In hi age, he longidinal CFRP i no frared, and i an ill reri he deformaion of he flexral member. A poin 2, rain of he longidinal CFRP reahe

17 143 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe abo 1 με and he longidinal CFRP begin o frare. The maximm longidinal re of he onree in he ompreive region i loe o f '. In he age beween poin 2 and poin 3, he longidinal re of he eel be inreae oninoly wih he developmen of he defleion. The area of he enile onree region inreae. A poin 3, he maximm longidinal re of he ompreive onree exeed f. ' The longidinal re diribion of he onree in axial direion i hown in Figre 21. The longidinal re in pre-bending egmen of he member diribe niformly in axial direion. The maximm longidinal re i loaed a he exreme fiber of he peimen. Compreive region a mid-pan Compreive region a mid-pan Compreive region a mid-pan (a) Poin 1 (b) Poin 2 () Poin 3 Figre 21. Diribion of Longidinal Sre of Conree along Axial Direion 4.2 Inflene of Figre 22 how he inflene of on he poiion of he neral axi on he ro-eion a mid-pan dring elao-plai age ( D 16mm, 4.5mm, f 345 y MPa, f MPa 6, L 14mm,. 1, -. 4, E 26GPa, v. 3, E 47 f' MPa, and v.2 ). The neral axi ha a lile offe oward he enile region of he onree. Neral axi Neral axi Neral axi Neral axi (a) (b). 14 (). 27 (d). 4 Figre 22. Inflene of on Poiion of Neral Axi Figre 23 how he effe of on he longidinal re diribion on he ro-eion a mid-pan. I i lear ha he longidinal ompreive re of he onree inreae a lile a inreae.

18 Q.L. Wang and Y.B. Shao f '.75f '.61f '.47f '.34f '.2f '.7f '.95f '.81f '.66f '.52f '.37f '.22f '.8f ' 1.2f '.87f '.71f '.56f '.4f '.24f '.9f ' 1.3f '.88f '.72f '.56f '.4f '.25f '.9f ' (a) (b). 14 (). 27 (d). 4 Figre 23. Inflene of on Diribion of Longidinal Sre of Conree 4.3 Ineraion Fore beween Conree and Seel Tbe Figre 24 how he ineraion fore ( p ) beween he onree and he oer be on he ro-eion a mid-pan ( D 16mm, 4.5mm, f 345 y MPa, f MPa 6, L 14mm,. 976,. 169, E 26GPa, v. 3, E 47 f' MPa, and v.2 ). Ineraion fore wih a large magnide alo exi beween he enile eel be and he onree. However, i i differen in eene for he ineraion fore in he ompreive region and in he enile region of he onree. In he ompreive region, eel be reri he expanion of onree, whih prode onfinemen fore. While in he enile region, he eel be i nder enion in longidinal direion b nder onraion in ranvere direion. Conree alo onra in ranvere direion. However, he ranvere deformaion of he onree i mh maller han ha of he eel be (epeially afer he raking of he onree). Th, he ranvere deformaion of he eel be i rerained by he onree, and he reaion fore beween eel be and onree hen iniiae. However, hi ineraion fore i no he onfinemen fore. p (MPa) Poin 1 Poin 2 Poin 3 Compreive region Tenile region (m -1 ) Figre 24. Ineraion Fore beween Oer Tbe and Conree on Cro-Seion a Mid-Span 5. FLEXURAL LOAD CARRYING CAPACITY 5.1 Definiion of Flexral Load Carrying Capaiy The allaed rel of he FE model ( f MPa, f 3 12MPa,.2 4, y.6,. 9, E 26GPa, v. 3, E 47 f' MPa, and v. 2 ) how ha he bending momen orreponding o he enile rain a he exreme fiber reahing max i he flexral load arrying apaiy ( M ), and max i defined in hi dy a follow:

19 145 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe max D (1) where D i in mm. Eq. (1) i obained ing regreion analyi baed on a parameri dy on he allaed FE model. In Eq. (1), he bending momen a hi ime ( max ) i larger han he elai limi vale b le han he plai limae momen. Parial eion of he eel be i already in yielding ae, and he defleion a hi ime i abo L 1. I i larified here ha M hown in Figre 1 i aally deermined by max. In Eq. (1), max of eah peimen an be firly allaed. The bending momen orreponding o max i hen defined a M. 5.2 Parameri Eqaion of Load Carrying Capaiy The flexral load arrying apaiy of he member wih only ranvere CFRP ( M ) i deermined 3 firly. M i mainly relaed o he flexral modl ( W m, π D 32 ), he oal onfinemen oeffiien ( ) (Che, Wang and Shao [15]) and he index of axial ompreive load arrying apaiy ( f y ) (Che, Wang and Shao [15]) of C-CF-CFRP-ST b olmn. Baed on a parameri dy on amon of FE model, he relaionhip beween M W m fy and i obained, and i i hown in Figre 25 (a) = ln(+.36) f.7 y =235MPa f y =345MPa f y =39MPa M (knm) M =M D =89mm D =18mm D =133mm D =159mm M (knm) (a) - Relaionhip (b) Comparion beween M and M Figre 25. Flexral Load Carrying Capaiy The relaionhip beween and an alo be preened a well and i i lied a follow: ln.36 (11) (12) Hene M W (13) m fy

20 Q.L. Wang and Y.B. Shao 146 where f y k 1 f (14) When he member ha boh ranvere and longidinal CFRP, he relaionhip beween M W f and an be obained a follow m m y.3. 2 (15) m Th, he flexral load arrying apaiy of he C-CF-CFRP-ST member ( M ) i given a follow: M W f (16) m m y 5.3 Validaion of Eqaion Figre 25 (b) diplay omparion beween he allaed flexral load arrying apaiy M and he eed vale M. The average vale of M M i.96, and he mean qare error i.7. Tha mean he wo rel agree well. 6. CONCLUSIONS Baed on he experimenal dy, he finie elemen imlaion, and he heoreial analyi, he following onlion an be drawn: (1) The M- rve a mid-pan of irlar onree filled CFRP-eel blar flexral peimen wiho longidinal CFRP reinforemen are imilar o hoe of he orreponding irlar onree filled eel blar flexral member, while M- rve a mid-pan of C-CF-CFRP-ST flexral peimen wih longidinal CFRP reinforemen an be defined a elai age, elao-plai age and ofening age. Thereafer, he re of he rve are imilar o hoe of he orreponding C-CFST flexral member. The iffne of he peimen an be enhaned by he longidinal CFRP. (2) The eel be and he CFRP be an ooperae well boh in ranvere and in longidinal direion. The diribion of he longidinal rain of he peimen over he deph of he ro-eion mee he plane eion ampion approximaely. The hape of he defleion-rve i baially imilar o half inoidal rve. (3) The finie elemen imlaion rel of he deformaion and M- rve of C-CF-CFRP-ST flexral member agree well wih experimenal rel. (4) Ineraion fore beween he oer be and he ore onree exi no only in he ompreive region b alo in he enile region. However, he mehanim of he ineraion fore in he wo region are eenially differen. (5) The flexral load arrying apaiy of C-CF-CFRP-ST i defined, and he allaing eqaion of he flexral load arrying apaiy i given. ACKNOWLEDGEMENTS The reearh repored in he paper i par of he Proje ppored by Naral Siene Fondaion of China (NSFC) and he Proje ppored by Pbli Welfare Fondaion of Liaoning Provine, P R China. Their finanial ppor are highly appreiaed.

21 147 Flexral Performanne of Cirlar Conre Filled CFRP-Seel Tbe NOMENCLATURE A : Cro-eional area of onree A l : Cro-eional area of longidinal CFRP A : Cro-eional area of ranvere CFRP A : Cro-eional area of eel be C-CF-CFRP-ST : Cirlar onree filled CFRP-eel be C-CFST : Cirlar onree filled eel be CF-CFRP-ST : Conree filled CFRP eel be CF-CFRP-T : Conree filled CFRP be CFRP : Carbon fiber reinfored polymer CFST : Conree-filled eel be CFT : Conree-filled be D : Oer diameer of eel be E : Elai modl of onree E : Elai modl of arbon fiber hee E : Elai modl of eel be f : Load arrying apaiy index of axial ompreive rengh of irlar onree y filled CFRP-eel blar (C-CF-CFRP-ST) b olmn : Ulimae enile rengh of longidinal CFRP f l f : Ulimae enile rengh of ranvere CFRP f f f f k y : Charaerii axial ompreive rengh of onree : Cbi rengh of onree : Ulimae rengh of eel be : Yield rengh of eel be f ' f : Tenion rengh of arbon fiber hee ' K ie : Compreive rengh of ylinder onree peimen : Iniial flexral iffne K e : Servie flexral iffne L : Lengh of peimen L : Ne pan of peimen M : Momen a mid-pan M : Flexral load arrying apaiy of irlar onree filled CFRP-eel blar (C-CF-CFRP-ST) member wih only ranvere CFRP M : Flexral load arrying apaiy of irlar onree filled CFRP-eel blar (C-CF-CFRP-ST) member wih boh ranvere CFRP and longidinal CFRP M : Teed vale of M m : Nmber of ranvere CFRP layer m' : Nmber of longidinal CFRP layer() P : Laeral load p : Ineraion fore beween onree and oer be : Thikne of one layer arbon fiber hee : Wall hikne of eel be

22 Q.L. Wang and Y.B. Shao 148 : Defleion m : Defleion a mid-pan v : Poion raio of onree v m : Poion raio of eel be W : Flexral modl w : Deniy of arbon fiber hee : Elongaion perenage of arbon fiber hee Δ n : Srain of CFRP l : Diane meared from neral axi o enroid axi : Srain of longidinal CFRP : Srain of ranvere CFRP : Rpre rain of longidinal CFRP : Rpre rain of longidinal CFRP for eah peimen meared from e lr lr ' r : Rpre rain of ranvere CFRP l : Longidinal rain : Tenile rain a exreme fiber of peimen orreponding o max M l : Longidinal rain of eel be : Tranvere rain of eel be : Tranvere rain : Crvare a mid-pan M W : Coeffiien, m fy : Coeffiien, M W f m m : Srenghening faor of longidinal CFRP : Sre of CFRP : Toal onfinemen faor : Confinemen faor of CFRP y : Confinemen faor of eel be REFERENCES [1] Han, L. H., Te on Conree Filled Seel Tblar Colmn wih High Slenderne Raio, Advane in Srral Engineering, 2, Vol. 3, No. 4, pp [2] Tao, Z., Uy, B., Han, L. H. and Wang, Z. B., Analyi and Deign of Conree-filled Siffened Thin-walled Seel Tblar Colmn nder Axial Compreion, Thin-Walled Srre, 29, Vol. 47, No. 12, pp [3] Georgio, G. and Lam, D., Axial Capaiy of Cirlar Conree-filled Tbe Colmn, Jornal of Conrional Seel Reearh, 24, Vol. 6, No. 7, pp [4] Uy, B., Srengh of Shor Conree Filled High Srengh Seel Box Colmn, Jornal of Conrional Seel Reearh, 21, Vol. 57, No. 2, pp [5] Han, L. H. and Yang, Y. F., Cyli Performane of Conree-filled Seel CHS Colmn nder Flexral Loading, Jornal of Conrional Seel Reearh, 25, Vol. 61, No. 4, pp

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