STATIC BEHAVIOR OF AXIALLY COMPRESSED CIRCULAR CONCRETE FILLED CFRP-STEEL TUBULAR (C-CF-CFRP-ST) COLUMNS WITH MODERATE SLENDERNESS RATIO

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1 Advanced Seel Conrucion Vol. 12, No. 3, pp (216) 263 STATIC BEHAVIOR OF AXIALLY COMPRESSED CIRCULAR CONCRETE FILLED CFRP-STEEL TUBULAR (C-CF-CFRP-ST) COLUMNS WITH MODERATE SLENDERNESS RATIO Q.L. Wang 1, *, S.E. Qu 2, Y.B. Shao 3 and L.M. Feng 4 1 Profeor, School of Civil Engineering, Shenyang Jianzhu Univeriy, Shenyang, P. R. China 2 Graduae Suden, School of Civil Engineering, Shenyang Jianzhu Univeriy, Shenyang, P. R. China 3 Profeor, School of Mecharonic Engineering, Souhwe Peroleu Univeriy, Chengdu, P. R. China 4 Graduae Suden, School of Civil Engineering, Shenyang Jianzhu Univeriy, Shenyang, P. R. China *(Correponding auhor: E-ail: ceqlwang@jzu.edu.cn) Received: 19 January 215; Revied: 7 Ocober 215; Acceped: 5 January 216 ABSTRACT: Thiry-wo pecien are experienally eed in hi paper o udy he aic perforance of axially copreed circular concree filled CFRP-eel ubular (C-CF-CFRP-ST) colun. The eed reul indicae ha, for colun wih relaive all lenderne raio, failure i doinaed by he rengh lo of he aerial. However, for colun wih relaive large lenderne raio, failure i conrolled by inabiliy. The load veru deflecion curve a he id-heigh of he copoie colun can be divided ino hree age, i.e., elaic, elao-plaic and ofening age. Analye of he eed reul how ha diribuion of longiudinal rain in he eel ube over deph on he cro-ecion i approxiaely linear, and he eel ube and i ouer CFRP aerial can cooperae boh longiudinally and ranverely. The longiudinal rain and he ranvere rain a a poin have oppoie ign, and he eel ube under longiudinal enion ha no ranvere confineen effec on i concree. The Defored ode of he colun, he axial load vere deflecion curve a he id-heigh, he axial load vere axial horening curve and he ree in he eel ube are iulaed by uing finie eleen ehod. The calculaed reul agree well wih he experienal reul o prove he accuracy of he finie eleen odel. Sree in he concree, he eel ube and he CFRP are analyzed by uing finie eleen ehod. The nuerical reul how ha he ineracion force beween he eel ube and he concree decreae gradually fro copreive region o enile region. The adheive rengh beween he concree and he eel ube ha lile effec on he criical buckling load and on he elaic iffne of he colun. Equaion for calculaing he criical buckling load of he copoie colun i preened, and he eiaed reul agree well wih he experienal reul. Keyword: Circular CFRP-eel ube, In-filled concree, Axially copreed colun wih oderae lenderne raio, Saic perforance, Criical buckling load DOI:1.1857/IJASC INTRODUCTION Fiber Reinforced Plaic (FRP) ha been ued in any engineering rucure due o i advanage of high rengh/weigh raio, good corroion reiance, eae of inallaion, ore and ore cheaper co and o on, in which Concree Filled FRP Tubular (CF-FRP-T) rucure or FRP renghened concree rucure i a ypical exaple. There are any reearch repor on CF-FRP-T (Wang and Rerepo [1]; Fa and Rizkalla [2]; Teng e al. [3]; Karabini e al. [4]; Rouaki e al. [5]; Yu. e al. [6]; Yu. e al. [7]; Jiang and Wu [8]). CF-FRP-T rucure have beer corroion reiance. However, he failure ode of CF-FRP-T rucure ha brile characeriic in o cae, and he load carrying capaciy in he ranvere direcion for hi rucure i weak. A one ypical yle of he eel-concree copoie rucure, Concree Filled Seel Tubular (CFST) rucure are widely ued in civil engineering, and hey how good conrucional efficiency. The reearch work in hi field ha been udied yeaically in he lieraure. Beide he yeaic inveigaion on he aic and he hyereic behavior of he coponen and he connecion (Han [9]; Han e al. [1]; Han e al. [11]; Han e al. [12]; Han and Li [13]), fire reiance (Han [14]), orion perforance (Han e al. [15]) and local copreion (Han e al. [16])

2 264 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio of hi rucure are alo repored. Coparing wih he CF-FRP-T, CFST ha higher hearing load carrying capaciy. However, he ouer urface corroion of he eel ube canno be ignored when CFST i ued in a corroive environen, and oe correponding reearch udie in hi field have been repored in recen year (Han e al. [17]; Han e al. [18]). In any engineering field, he FRP-eal copoie ank or ube have been ued widely, uch a ga ank ued in oor vehicle (a hown in Figure 1, where GFRP refer o Gla Fiber Reinforced Plaic) and pipeline ye for ranporing high preure ga or liquid ued in unicipal engineering or cheical engineering. Soeie, peroleu pipeline ye afer corroion i alo reinforced wih CFRP (Carbon Fiber Reinforced Plaic), which can ave uch co copared o he eaure of replacing he corroded ube wih a new one. CFRP-eal ube can alo be ued in civil engineering, for exaple, by infilling concree ino CFRP-eel copoie ube (Che e al. [19]), or by uing CFRP o renghen daaged CFST (Tao e al. [2]). Boh of he above ehod can for he o-called Concree Filled CFRP-Seel Tubular (CF-CFRP-ST) rucure. CF-CFRP-ST rucure have he advanage of boh he CFST and he CF-FRP-T rucure, and he CF-CFRP-ST rucure can alo avoid he repecive deficiency of he CFST and he CF-FRP-T rucure o oe degree. Recen udy how ha CF-CFRP-ST ha aifacory fire endurance ie when adequae fire reian eaure have been aken (Tao e al [21]). Figure 1. Ga Tank Ued in Moor Vehicle Figure 2. An Engineering Pracice of C-CF-CFRP-ST Colun Ued in Nanjing Ciy, Jiangu Province, P. R. China There are any reearch udie abou CF-CFRP-ST rucure in he lieraure, and hee udie oly focu on Circular CF-CFRP-ST (C-CF-CFRP-ST) ub colun (Xiao e al. [22]; Choi and Xiao [23]; Park e al. [24]; Hu e al. [25]; Li e al. [26]; Teng e al. [27]), C-CF-CFRP-ST flexural eber (Wang and Shao [28]), Square CF-CFRP-ST (S-CF-CFRP-ST) ub colun (Tao e al

3 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 265 [29]; Park e al. [3]; Sundarraja and Ganeh [31]; Sundarraja and Ganeh [32]; Sundarraja and Ganeh [33]; Wang and Shao [34]) and S-CF-CFRP-ST flexural eber (Sundarraja and Ganeh [35]; Wang e al. [36]). More applicaion in pracical engineering are colun wih large lenderne raio (a hown in Figure 2) alhough correponding reearch i quie carce. For axially copreed ub colun (lenderne raio 3), copreive buckling doe no occur in general, and i load carrying capaciy i deerined by he aerial properie and he cobinaion effec, while for axially copreed colun wih oderae lenderne raio, i. e., >3, i criical buckling load i generally deerined by abiliy, which i neceary o be udied pecially. To underand he aic perforance of he axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio, 32 copoie pecien wih boh ranvere CFRP and longiudinal CFRP are eed and he deail are inroduced in hi paper. Axial load (N) veru deflecion a he id-heigh ( u ) curve, cooperaion beween he eel ube and he CFRP and plane ecion aupion of he copoie pecien are analyzed. Furherore, he finie eleen ofware ABAQUS i ued o iulae he defored ode and he N- u curve of he copoie colun. The diribuion of he re and he rain, he effec of adheive rengh beween he eel ube and he concree, and he ineracion force (p) beween he concree and he eel ube are alo analyzed. Finally, he equaion for calculaing he criical buckling load of he axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio i given. 2. EXPERIMENTAL PROGRAM 2.1 General In overall, e on 32 axially copreed C-CF-CFRP-ST colun are conduced, and he baic paraeer conidered for hee pecien include and renghening facor of he longiudinal CFRP ( ) (Wang and Shao [28]), repecively, where 4L D (1) l l y A f A f (2) f E 23MPa (3) l lr where L i he lengh of he colun; D i he ouer diaeer of he eel ube. A l and f l are he cro-ecional area and he uliae enile rengh of he longiudinal CFRP, repecively. A and f y are he cro-ecional area and he yield rengh of he eel ube, repecively. E and lr are he elaiciy odulu of CFRP and he rupure rain of he longiudinal CFRP, repecively. In hi udy, lr=1 με, and he deerinaion of lr can be referred o he correponding reference (Wang and Shao [28]). The pecien' deail are provided in Table 1. In he noenclaure of he pecien a lied in Table 1, CC ean Circular Colun. Leer A, B, C, D, E, F, G and H denoe he differen lengh of he colun: 4, 53, 6, 8, 12, 18, 24 and 3, repecively. Nuber, 1, 2 or 3 refer o he nuber of he longiudinal CFRP layer() ( '). i

4 266 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio nuber of he ranvere CFRP layer. i he wall hickne of he eel ube, and N u,cr i he eed value of he criical buckling load of he C-CF-CFRP-ST colun. i he confineen facor of he eel ube (Han [9]). i he confineen facor of he ranvere CFRP ube (Che e al. [19]), where y c ck A f A f (4) c ck A f A f (5) f f (6) ck. 67 cu f E 1265MPa (7) r where A c and f ck are he cro-ecional area and he characeriic axial copreive rengh of he concree, repecively. A and f are he cro-ecional area and he uliae enile rengh of he ranvere CFRP, repecively. f cu i he cubic rengh of he concree pecien. r i he rupure rain of he ranvere CFRP ( r =55με and he deerinaion of r can be referred o he correponding reference (Che e al. [19]). 2.2 Specien Preparaion Fabricaion of Circular CFST (C-CFST) pecien can be found in relaive reference (Han [9]). Carbon fiber hee are applied uing a hand lay-up ehod. The longiudinal CFRP i glued firly, and hen he ranvere CFRP i glued. The finihing end of a hee i overlapped o he aring end of he oher hee wih an overlapped lengh of 15. Table 1. Specien Label and Capaciie No. Specien label L ' (layer()) (layer) 1 CC A CC A CC A CC A CC B CC B CC B CC B CC C CC C CC C CC C CC D D N u,cr (kn)

5 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng CC D CC D CC D CC E CC E CC E CC E CC F CC F CC F CC F CC G CC G CC G CC G CC H CC H CC H CC H Maerial Properie Seale eel ube i in he colun. Tenile e on eel coupon cu fro he original eel ube are conduced. The eaured properie of he eel ube obained fro hee e are given in Table 2, where E and v are he elaiciy odulu and he Poion raio of he eel ube, repecively. Table 2. Maerial Properie of Seel Tube E (GPa) f (MPa) y v The in-filled concree of all he pecien ha ae aerial propery. In he concree ixure, Porland ceen i ued, and he fine aggregae i ilica-baed and. The coure aggregae i lieone wih a large ize of 2, and 1% (in weigh) waer reducing agen i added. The ixure proporion of he concree are uarized in Table 3. Table 3. Mixure Proporion of Concree (kg -3 ) Ceen Waer Sand Coure aggregae To deerine he copreive rengh of he in-filled concree, ix cube wih a ide lengh of 15 are ca and cured in condiion iilar o hoe of he relaed pecien. The averaged cubic

6 268 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio rengh ( f cu ) a 28 day i 48.8 MPa. A he eing ie (ix onh laer due o he delay of he e progra), he cubic rengh of 57.4 MPa i achieved and i adoped in laer FE iulaion and calculaion. Elaiciy odulu of he concree ( E ) i 35.9GPa. c Carbon fiber hee ued in he pecien i a kind of one-way hee, and he properie of he CFRP deerined fro enile e of ix fla coupon are given in Table 4, in which f ', and w are he enile rengh, he elongaion percenage and he deniy of he carbon fiber hee, and i he hickne of one-layer carbon fiber hee. Model nuber Table 4. Main Technical Properie of Carbon Fiber Shee f ' (GPa) E (GPa) (%) w (g -2 ) C2/ I hould be poined ou ha he rupure rain of he coupon CFRP i 21με while he rupure rain of he longiudinal CFRP lr=1με and ha of he ranvere CFRP r =55με. Such difference i poibly caued by differen curvaure a CFPR poiion, and he relaive reearch (Yu e al. [37]) provided iilar concluion. JGN-C, a ypical kind of epoxy rein, which i produced by Building Science Reearch Iniue of Liaoning Province of China and i ued for building rucure, i eleced for adhering he CFRP o he eel ube. Anoher kind of epoxy rein, JGN-P, i ued for gluing CFRP ogeher. 2.4 Te Seup and Inruenaion The experienal e i carried ou in he Srucural Laboraory of Shenyang Jianzhu Univeriy, P. R. China. The criical buckling load of he pecien i prediced before he pecien i loaded: he ranvere and he longiudinal CFRP are iplified o equivalen eel ube, and hen he criical buckling load can be calculaed by uing correponding equaion of C-CFST colun (Han e al. [11]). However, he equivalen eel ube beide longiudinal CFRP i no conidered in calculaing he confineen facor of he eel ube. The e eup i hown in Figure 3. The pecien i pinned a boh end. A inruen wih a loading capaciy of 5,kN i ued o apply axial copreive load N. The load i applied in any loading ep. In he elaic age, each loading ep i 1/1 of he eiaed criical buckling load. When he applied load i abou 6% of he eiaed criical buckling load, he agniude of he loading ep i reduced o 1/15-1/2 of he eiaed criical buckling load. Afer he deflecion a he id-heigh exceed L 5, diplaceen conrol i ued ill he deflecion a he id-heigh reache abou L 25. The inerval beween wo coninuou loading ep i ainained for abou 2 o 3 in. A hown in Figure 3, 3-5 Linear Variable Differenial Tranforer (LVDT) are placed in he bending plane wih equal diance in he heigh direcion according o differen heigh of he pecien o eaure he laeral deflecion. Siulaneouly, wo LVDT are ued o eaure he longiudinal copreion of he pecien. Overall, 11 rain gauge are glued on he urface of each eel ube and on he CFRP a he id-heigh of he pecien repecively, a hown in Figure 4, where poin 1-7 are he locaion for eauring he longiudinal rain and poin 1, 3, 5 and 8 are he locaion for eauring he ranvere rain.

7 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 269 The daa i capured by Daa Acquiiion Sye U-CAM-7A, and he N- u curve i achieved iulaneouly. Figure 3. Te Arrangeen (Specien CC H-1) CFRP Concree Seel ube D /6 D Figure 4. Locaion of Srain Gauge 2.5 Te Obervaion and Failure Mode The failure of he pecien i ainly deerined by he lenderne raio ( ). For pecien wih all, ranvere CFRP locaed in longiudinal copreive region a he id-heigh begin o fracure a a loading abou.85 N u,cr. Wih he increae of he applied load, he aoun of fracured ranvere CFFP becoe bigger (a hown in Figure 5 (a)) ill he applied load reache N u,cr. Longiudinal CFRP locaed in longiudinal enile region a he id-heigh i no fracured in general, and he pecien have local ouward buckling (a hown in Figure 5 (a)) which indicae a ybol of rengh failure. For pecien wih large, ranvere CFRP locaed in longiudinal copreive region a he id-heigh begin o fracure afer N. Wih he increae of he deflecion, he longiudinal CFRP locaed in longiudinal enile region a he id-heigh begin o fracure (a hown in Figure 5 (b)). Finally, he pecien fail and he eel ube doe no buckle ouward and for an inabiliy failure. All pecien afer failure are hown in Figure 6. The CFRP-eel copoie ube are cu off afer e. A hown in Figure 7, i i found ha he concree could be divided ino boh enile and copreive region. For pecien wih all, u,cr

8 27 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio he failure of he concree i evere, and he concree in he copreive region i cruhed (a hown in Figure 7 (a)). In he enile region, he concree crack ha a big widh, and he diance beween any wo adjacen crack i all (a hown in Figure 7 (b)). For pecien wih large, he concree failure i no evere, and hu he concree in copreive region i alo no daaged (a hown in Figure 7 (c)). The crack in enile region ha a narrow widh, and he diance beween any wo adjacen crack i bigger (a hown in Figure 7 (d)). Ouward buckling Rupure Rupure (a) Tranvere CFRP (b) Longiudinal CFRP Figure 5. Rupure of CFRP and Local Buckling (a) ' Specien (b) '1 Specien (c) ' 2 pecien (d) ' 3 Specien Figure 6. All Specien afer Teing Cruhed concree Crack (a) Copreed Concree of Specien CC C-1 (b) Tenioned Concree of Specien CC C-1 Crack (c) Copreed Concree of Specien CC H-2 (d) Tenioned Concree of Specien CC H-2 Figure 7. Failure Mode of Concree 2.6 Te Reul and Analyi Teed N- curve Figure 8 how he N- curve of he pecien, and i can be found ha hee N- u curve

9 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 271 have he following characeriic: he curve develop linearly in iniial loading age, and hi period belong o an elaic age. The following age i elao-plaic age in which he developing rae of u i apparenly faer han ha of N. The curve begin o drop afer N u,cr, and in hi age he increae of u i uch faer while he decreae of N i gradual Specien CC A- 8 Specien CC A-1 Specien CC A-2 Specien CC A Specien CC B- 8 Specien CC B-1 Specien CC B-2 Specien CC B (a) Specien of 12 (b) Specien of Specien CC C- 8 Specien CC C-1 Specien CC C-2 Specien CC C Specien CC D- 8 Specien CC D-1 Specien CC D-2 Specien CC D (c) Specien of 18 (d) Specien of Specien CC E- 7 Specien CC E-1 Specien CC E-2 Specien CC E Specien CC F- 7 Specien CC F-1 Specien CC F-2 Specien CC F (e) Specien of 36 (f) Specien of 54

10 272 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio Specien CC G- 6 Specien CC G-1 Specien CC G-2 Specien CC G Specien CC H- Specien CC H-1 Specien CC H-2 Specien CC H (g) Specien of 72 (h) Specien of 9 Figure 8. Teed N- u Curve Teed N- curve Figure 9 how he N- curve of he pecien, where i he axial horening of he pecien Specien CC A- 8 Specien CC A-1 Specien CC A-2 Specien CC A Specien CC B- 8 Specien CC B-1 Specien CC B-2 Specien CC B (a) Specien of 12 (b) Specien of Specien CC C- 8 Specien CC C-1 Specien CC C-2 Specien CC C Specien CC D- 8 Specien CC D-1 Specien CC D-2 Specien CC D (c) Specien of 18 (d) Specien of 24

11 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng Specien CC E- 7 Specien CC E-1 Specien CC E-2 Specien CC E Specien CC F- 6 Specien CC F-1 Specien CC F-2 Specien CC F (e) Specien of 36 (f) Specien of Specien CC G- 6 Specien CC G-1 Specien CC G-2 Specien CC G Specien CC H- Specien CC H-1 Specien CC H-2 Specien CC H (g) Specien of 72 (h) Specien of 9 Figure 9. Teed N- Curve Coparion beween longiudinal Srain and Tranvere Srain Figure 1 how coparion beween l (longiudinal rain of he eel ube) and (ranvere rain of he eel ube) a poin 1 and poin 5 for pecien CC E-2, where i he rain of he eel ube. The ign of l and a ae poin are differen: i i negaive in longiudinal direcion while poiive in ranvere direcion and vice vera. Sudie on CF-CFRP-ST ub colun (Che e al. [19]; Wang and Shao [34]) and CF-CFRP-ST flexural eber (Wang and Shao [28]; Wang e al. [36]) provided ae concluion. I can alo be found ha poin 1 on he eel ube i under enion longiudinally and under copreion ranverely afer N, which ake i clear ha hi poin ogeher wih he around eel ube ha no u,cr confineen o concree, and he reaon ay be lied a follow: he nearby concree i alo in a enile ae when he eel ube i under enion in longiudinal direcion, and hu i doe no need ranvere confineen provided fro eel ube. The ranvere rain of he eel ube i under copreion due o he correponding enion in longiudinal direcion Plane Secion Aupion Figure 11 how he diribuion of l over he deph on he cro-ecion of he pecien wih a lenderne raio 24. A hown in Figure 11, he diribuion of l i baically aified wih he plane ecion aupion. Sudie on CF-CFRP-ST flexural eber (Wang and Shao [28]; Wang e al. [36]) provided ae concluion.

12 274 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio of Poin 1 l of Poin 1 of Poin 5 l of Poin () Figure 1. Coparion beween l and of Poin 1 and Poin 5 for Specien CC E-2 2.N u, cr 1.N u, cr.32n u, cr.34n u, cr l () N u, cr.87n u, cr.95n u, cr l () N u, cr.91n u, cr.95n u, cr D 1.N u, cr D (a) Specien CC F- (b) Specien CC F-1 1.N u, cr 15.N u, cr 3.N u, cr.38n u, cr.36n u, cr l () N u, cr.92n u, cr.96n u, cr l () N u, cr.92n u, cr.97n u, cr D 1.N u, cr D (c) Specien CC F-2 (d) Specien CC F-3 Figure 11. Diribuion of over Deph of Cro-Secion for 24 Specien l 1.N u, cr 3. FE SIMULATION 3.1 Sre-Srain Relaionhip of Maerial A 5-age re-rain relaionhip of eel aerial (Han e al. [1]) i ued in he FE iulaion. The coniuive relaionhip of he concree confined by circular CFRP-eel ube under copreion a well a under enion (Che e al. [19]) are adoped. The CFRP i aued o be ubjeced o enion only, and he ree in oher direcion are aued o be.1mpa. Before fracure, he re-rain relaionhip i in accordance wih Hooke Law E (8)

13 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 275 where and are he re and he rain of CFRP, repecively. When longiudinal CFRP reache i rupure rain ( lr ), i loe longiudinal renghening effec o he pecien. When ranvere CFRP reache i rupure rain ( r ), i loe ranvere confineen o he eel ube. 3.2 FE Model Eleen ype elecion and eh dicriizaion The adoped eleen in he eh of he eel ube i hell eleen S4 wih full inegraion. Sipon inegraion wih 9 inegraing poin in he hell hickne direcion i ued. For he eh of he concree, 3-D brick eleen C3D8R wih reduced inegraion i ued. Mebrane eleen M3D4 wih 4-node i ued for odelling CFRP. The convergen analyi i carried ou by uing refined eh in finie eleen analyi, deail can be found in Ref. (Che e al. [19]) Inerface odel Hard conac i ued for conac inerface beween he eel ube and he concree, i.e., he preure perpendicular o he conac urface (p) can be ranferred copleely beween he wo urface. The angenial force beween he eel ube and he concree i iulaed by uing Colub odel, i.e., hear force can be ranferred beween wo conac urface. In he angenial direcion of he conac urface beween he end plae and he concree, here i no lipping, and hard conac aupion i ued in noral direcion of he conac urface. Figure 12 how he coparion of he rain beween he eel ube and he CFRP, where, l and are he longiudinal rain and he ranvere rain repecively, and l and are he rain of he longiudinal CFRP and he ranvere CFRP, repecively. A hown in Figure 12, l and l, a well a and, are approxiaely ae. Addiionally, afer cuing he CFRP-eel ube ino halve afer he e, i i found ha he adherence beween he CFRP and he eel ube i ill inac excep a he region where CFRP rupured. All above indicae ha he eel ube and he CFRP could cooperae well in boh longiudinal and ranvere direcion. Sudie on CF-CFRP-ST ub colun (Che e al. [19]; Wang and Shao [34]) and CF-CFRP-ST flexural eber (Wang and Shao [28]; Wang e al. [36]) provided ae concluion. According o he above e reul, he CFRP i bound o he eel ube in he finie eleen odel, and i i aued ha no lip exi beween he CFRP and he eel ube. Sae nodal freedo are ued for he conac eleen beween he CFRP and he eel ube Boundary condiion Boundary condiion (a hown in Figure 13) are iulaed a he ae iuaion in he experienal proce. According o he yery of boh he geoery and he boundary condiion, 1 4 of he enire odel i eleced for FE analyi. On he yerical plane of he odel, yerical conrain are applied. A one end, he diplaceen in x-, y- and z- direcion are all rerained. A he oher end, line loading i applied (conidering iniial eccenriciy of L 1 ). Increen ieraion ehod i ued o olve he proble in which conrolled diplaceen loading ehod i ued.

14 276 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio l of poin 1 l of poin 5 l of poin 1 l of poin l () (a) N- l Curve of poin 1 of poin 5 of poin 1 of poin () Figure 12. Coparion beween (b) N- Curve and for Specien CC F FE Reul Failure ode Figure 13. Boundary Condiion To verify he reliabiliy of he above preened FE ehod, overall 32 axially copreed C-CF-CFRP-ST colun are analyzed by uing ABAQUS ofware. Figure 14 how he deforaion ode of he pecien in he e and in FE iulaion. Fro Figure 14, i can be

15 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 277 found ha he iulaed reul agree reaonably well wih he experienal reul. (a) Teed Reul N- curve (b) Siulaed Reul Figure 14. Deforaion Mode The FE N- u curve ogeher wih he eaured reul of everal pecien are ploed in Figure 15. The FE reul agree reaonably well wih he experienal reul. The average raio of he criical buckling load beween he FE and he experienal reul ( N ) i.848, and he COV i u, cr.92. The iulaed reul for he pecien wih large lenderne are relaively aller, and i i ainly caued by he following reaon: The iniial eccenriciie for all he eed pecien are roughly equal in he experien. However, uch iniial eccenriciy i precribed o be L/1, which iplie ha he pecien wih a larger lenderne ha a bigger iniial eccenriciy and hence i ha a lower iulaed reul FEM reul Teed reul FEM reul Teed reul (a) Specien CC A-1 (b) Specien CC B FEM reul Teed reul FEM reul Teed reul (c) Specien CC C-1 (d) Specien CC D-1

16 278 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio FEM reul Teed reul FEM reul Teed reul (e) Specien CC E-1 (f) Specien CC F N- curve 5 FEM reul Teed reul FEM reul Teed reul (g) Specien CC G-1 (h) Specien CC H-1 Figure 15. Coparion of N- u Curve beween FEM Reul and Teed Reul for Several Specien The FE N- curve ogeher wih he eaured reul of everal pecien are alo given in Figure 16. The FE reul agree reaonably well wih he experienal reul FEM reul Teed reul FEM reul Teed reul (a) Specien CC A-1 (b) Specien CC B FEM reul Teed reul FEM reul Teed reul (c) Specien CC C-1 (d) Specien CC D-1

17 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng FEM reul Teed reul FEM reul Teed reul (e) Specien CC E-1 (f) Specien CC F N- curve 5 FEM reul Teed reul FEM reul Teed reul (g) Specien CC G-1 (h) Specien CC H-1 Figure 16. Coparion of N- Curve beween FEM Reul and Teed Reul for Several Specien The coparion of he rain in he eel ube of pecien CC E-1 i hown in Figure 17. Experienal and FE reul are denoed in hin line and in hick line repecively, and he iulaed reul of he ube rain agree well wih he experienal reul Poin 1 6 Poin 5 Poin 1 Poin () 12 Poin 1 6 Poin 5 Poin 1 Poin l () (a) Tranvere rain (b) Longiudinal rain Figure 17. Coparion beween Seel Tube Srain of Specien CC E-1 4. THEORETICAL ANALYSIS On he bai of he above odel and approach, a large nuber of paraeric analye how ha he validiy range of he odel in he preened approach i: f 2 4MPa, f 3 12MPa,.2 4,. 6,. 9. In he above validiy range, a ypical odel i eleced o carry ou heoreical analyi, and he deail of he ypical odel are lied a follow: y cu

18 28 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio D 4, 9.3, MPa f y 345, f 6 cu MPa, 8, 383.,. 163, elaiciy Poion raio of concree v. c 2, E 47 ' c fc (where f c' i he copreive rengh of cylinder concree pecien and i uni i in MPa). Five ypical poin a hown in Figure 18 are eleced for furher analyi. In Figure 18, he load i proporional o he laeral deflecion before poin 1, and he re of he eel ube reache i proporional lii a poin 1. Plaic region occur on he cro-ecion a he id-heigh beween poin 1 and poin 2, and he criical buckling load i reached a poin 2. Area of he plaic region increae gradually afer poin 2, and he ranvere CFRP on he longiudinally copreive region rupure a poin 3. The longiudinal CFRP on he longiudinally enile region rupure a poin 4. Deflecion a he id-heigh i very large (abou L 25 ) a poin N Poin Poin 1 Poin 2 Poin 3 Poin 4 Poin Figure 18. Typical N- u Curve of Axially Copreed C-CF-CFRP-ST Colun wih Moderae Slenderne Raio 4.1 Sre analyi Sre in concree Figure 19 illurae he diribuion of he longiudinal re in he concree on he cro-ecion a he id-heigh for axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio. All he cro-ecion of he concree i found o be under copreion before he criical buckling load i reached. Afer he criical buckling load, enile region iniiae on he concree ecion. Wih he increaing deflecion a he id-heigh of he colun, he area of he copreive region reduce and he area of he enile region enlarge coninuouly. Figure 2 how he diribuion of he longiudinal re in he concree in axial direcion. I can be found ha uch diribuion i no unifor and he ree of he concree in he copreive region on he cro-ecion a he id-heigh increae gradually. Tenile region (a) Poin 1 (b) Poin 2 (c) Poin 3

19 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 281 Tenile region Tenile region (d) Poin 4 (e) Poin 5 Figure 19. Diribuion of Longiudinal Sre in Concree on Cro-Secion a Mid-Heigh Cro-ecion (a) Poin 1 Cro-ecion (b) Poin 2 Cro-ecion Tenile region (c) Poin 3 Cro-ecion Tenile region (d) Poin 4

20 282 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio Cro-ecion (e) Poin 5 Tenile region Figure 2. Diribuion of Longiudinal Sre in Concree in Axial Direcion Longiudinal re in eel ube Figure 21 how he diribuion of he longiudinal re in he eel ube in axial direcion. The cro-ecion of he concree i under copreion before he criical buckling load (poin 2), while he longiudinal re on he cro-ecion varie fro copreion o enion over he deph on he cro-ecion afer poin 3, which proce perfor fro a poiive o a negaive value of he ree. The axiu copreive and he axiu enile ree are locaed a he op and a he boo urface repecively. Figure 22 how he diribuion of he Mie re in he eel ube. The loading a poin 1 i relaively aller and he eel ube i in elaic age. A poin 2, he copreed eel ube begin o yield and he cro-ecion a he id-heigh yield firly. A hi ie, he enioned eel ube doe no ye yield. Before he fracure of he ranvere CFRP, he copreed eel ube i ill in a yielding ae. Afer he fracure of he ranvere CFRP, he eel ube ener ino a hardening age. (a) Poin 1 Cro-ecion (b) Poin 2

21 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 283 Cro-ecion Tenile region (c) Poin 3 Cro-ecion Tenile region (d) Poin 4 Cro-ecion Tenile region (e) Poin 5 Figure 21. Diribuion of Longiudinal Sre in Seel Tube in Axial Direcion (a) Poin 1 Cro-ecion (b) Poin 2

22 284 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio Cro-ecion Tenile region (c) Poin 3 Cro-ecion Tenile region (d) Poin 4 Cro-ecion Tenile region Sre in CFRP (e) Poin 5 Figure 22. Diribuion of Mie Sre in Seel Tube Figure 23 how he diribuion of he re in he ranvere CFRP. Such re ha a unifor diribuion in he longiudinal direcion in he elaic age (poin 1). Before he criical buckling load, he re in he copreive region on he cro-ecion a he id-heigh increae gradually. However, he ranvere CFRP i ill no fracured (he axiu value of re i abou.17 f ). Wih he increaing deflecion a he id-heigh, uch re increae coninuouly ill he CFRP i fracured and doe no work (poin 3) which indicae ha he ranvere CFRP in he copreive region in longiudinal direcion provide confineen bu he ranvere CFRP in he enile region canno produce uch acion in he enire loading proce. Figure 24 how he diribuion of he re in he longiudinal CFRP. I i found ha he re in he longiudinal CFRP ha a unifor diribuion in he elaic age (poin 1). Before he criical buckling load (poin 2), he re in he enile region on he cro-ecion a he id-heigh i very all (abou.1mpa) becaue he deflecion i abou only L/25, which indicae ha he longiudinal CFRP doe no provide renghening effec o he colun a hi ie. A poin 3, he deflecion i abou L/5 and he re in he longiudinal CFRP increae rearkably (he axiu value of he re i abou.57 f l ). Wih he increaing deflecion a he id-heigh, he

23 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 285 re in he enile region increae coninuouly ill he CFRP i fracured and doe no work. Thi how he longiudinal CFRP in he enile region deain he flexural deforaion of he colun. The longiudinal CFRP in he copreive region canno produce uch acion in he enire loading proce. Cro-ecion (a) Poin 1 Cro-ecion (b) Poin 2 Copreive region Cro-ecion (c) Poin 3 Copreive region Cro-ecion (d) Poin 4

24 286 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio Copreive region Cro-ecion (e) Poin 5 Figure 23. Diribuion of Sre in Tranvere CFRP Cro-ecion (a) Poin 1 Cro-ecion (b) Poin 2 Tenile region Cro-ecion (c) Poin 3 Tenile region Cro-ecion (d) Poin 4

25 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 287 Tenile region Cro-ecion (e) Poin 5 Figure 24. Diribuion of Sre in Longiudinal CFRP 4.2 Ineracion Force beween Concree and Seel Tube The ineracion force beween he eel ube and he concree (p)-deflecion ( ) curve for poin A, B and C on he cro-ecion a he id-heigh of he colun i hown in Figure 25. The ineracion force in he copreive region i bigger han he correponding one in he enile region before he ranvere CFRP in he copreive region (poin A) i fracured (poin 3). Afer he longiudinal CFRP in he enile region (poin C) i fracured (poin 4), he ineracion force a poin B becoe bigger han he one a poin A becaue he ranvere CFRP a poin B i no fracured and i ha ill oe confineen o he inernal C-CFST. The p- u curve of he colun a a heigh of L 2, 3L 8 and L 4 o he end plae repecively in he copreive region are hown in Figure 26. The reul how ha he ineracion force a he id-heigh in he copreive region i bigger. Wih he increaing diance o he id-heigh, he ineracion force reduce gradually. A een fro Figure 25 and 26, for axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio, he ineracion force reduce coninuouly fro he copreive region o he enile region. In he copreive region, he ineracion force alo decreae gradually wih he increaing diance o he id-heigh of he pecien. p (MPa) C Tenile region Poin A Poin B Poin C B Copreive region A Poin 3 Poin Figure 25. p- u Curve over Deph of Cro-Secion of Colun

26 288 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio p (MPa) L/2 3L/8 L/ Analyi on Adheive Srengh Figure 26. p- u Curve along Heigh of Colun To inveigae he effec of he adheive rengh beween he eel ube and he concree on he perforance of he axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio, differen fricion facor ( ) wih he value of,.3 and.6 repecively are eleced in he iulaion. Figure 27 how he effec of he adheive rengh on he N- curve of he colun, which how ha he adheive rengh alo ha no effec on he criical buckling load and he iffne of he pecien in he elaic age. Figure 28 how he effec of he adheive rengh on he p- u curve of he colun. In he copreive region, p increae wih he increaing value of he fricion facor (. A value fro.3 o.6 ee o have no clear effec on p in he enile region, which i oe differen wih he cae ha he value of i zero = =.3 = Figure 27. Influence of Adheive Srengh on N- u Curve of Colun

27 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng 289 p (MPa) = =.3 =.6 p (MPa) = =.3 = (a) Copreive region (b) Tenile region Figure 28. Influence of Adheive Srengh on p- u Curve of Colun 5. CRITICAL BUCKLING LOAD 5.1 Calculaion Expreion Many calculaed reul ( f y 2 4MPa, f cu 3 12MPa,.2 4,. 6,.9, E 26 GPa, v. 3, v. 2, c E 47 ' c fc MPa) how ha he relaionhip beween (abiliy coefficien of he axially copreed C-CF-CFRP-CT colun wih oderae lenderne raio) and can be decribed by uing he curve ha hown in Figure 29 (a). The curve can be divided ino hree age: when, 1, he colun fail in rengh; when p, he colun fail in elao-plaic buckling; when p, he colun fail in elaic buckling. and p are he liied lenderne raio for an axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio in elao-plaic buckling and elaic buckling repecively, and heir value can be deerined fro he following equaion (where he uni of f and f are in MPa): y ck 42 fcy π 55 (9) p 1743 f y (1) where i he global confineen facor (Che e al. [19]); f cy i he index of load carrying capaciy of he axially copreed C-CF-CFRP-ST ub colun (Che e al. [19]), where (11) f cy ck 1 f (12) By uing regreion analyi ehod (Han e al. [11]), relaionhip of - can be expreed a follow

28 29 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio 1 2 a b c p (13) 2 d 35 p 1 d/( p +35) 2 N u, cr (kn) '= pecien '=1 pecien '=2 pecien '=3 pecien 3 p N u, cr =N u, cr N (kn) u, cr (a) - curve (b) Coparion beween N u, cr and N u, Figure 29. Criical Buckling Load where e 2 2 a p p, b e 2a, c 1 a p b, e d 3 p 35, he expreion of he coefficien d i obained fro aoun of calculaed reul baed on regreion analyi, and i i lied a follow.3.5 d ln 1. 9 y ck 5 f f.1 (14) cr where A A i he eel raio. c The expreion for he criical buckling load of he C-CF-CFRP-ST colun wih oderae lenderne raio ( N ) i hen expreed a follow N u, cr Nu u, cr (15) where N u i he load carrying capaciy of he C-CF-CFRP-ST ub colun (Che e al. [19]), N A f (16) u c cy where raio. A c i he cro-ecional area of he C-CF-CFRP-ST colun wih oderae lenderne 5.2 Validaion of Expreion Figure 29 (b) diplay he coparion beween N u, cr and N u,cr for he eed pecien. The average value of N u, cr N i.97, and he ean quare error i.8 which ean he wo u, cr reul agree well and he calculaed reul are conervaive in overall.

29 Q.L. Wang, S.E Qu, Y.B. Shao and L.M. Feng CONCLUSIONS Baed on he preened reul in hi udy, he following concluion can be drawn: (1) for he axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio, he pecien end o fail in rengh when he lenderne raio i all while he one wih large lenderne raio end o fail in buckling. Load-deflecion curve a he id-heigh of he pecien can be divided ino hree age: elaic, elao-plaic and dropping age. (2) The eel ube and he CFRP ube could cooperae well boh in he ranvere and in he longiudinal direcion. The diribuion of he longiudinal rain of he pecien over he deph on he cro-ecion approxiaely ee he plane ecion aupion. The longiudinal and he ranvere rain a ae poin have oppoie ign, and he enioned eel ube in longiudinal direcion ha no confineen o he concree. (3) The finie eleen iulaion reul of he defored ode, he N- curve and he N- curve of he eber a well a he ree in he eel ube agree well wih experienal reul. The re diribuion of differen copoed aerial have been analyzed, and he copued reul have a good agreeen wih experienal reul. (4) In he copreive region, wih he increaing diance o he id-heigh of he pecien, he ineracion force beween he ouer ube and he concree reduce gradually. The adheive rengh ha alo no effec on he criical buckling load and on he iffne in he elaic age of he pecien, bu i can iprove he confineen o he concree. (5) The calculaing equaion of he criical buckling load of he axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio i given. ACKNOWLEDGEMENTS The reearch repored in he paper i par of he Projec uppored by Naural Science Foundaion of China (NSFC) and he Projec uppored by Public Welfare Foundaion of Liaoning Province, P. R. China. Their financial uppor are highly appreciaed. NOMENCLATURE A c A l c : Cro-ecional area of concree : Cro-ecional area of longiudinal CFRP A : Cro-ecional area of C-CF-CFRP-ST colun wih oderae lenderne raio A A C-CF-CFRP-ST C-CFST CF-CFRP-ST CF-FRP-T CFRP CFST D E c E E f l : Cro-ecional area of ranvere CFRP : Cro-ecional area of eel ube : Circular concree filled CFRP-eel ube : Circular concree filled eel ube : Concree filled CFRP-eel ube : Concree filled FRP ube : Carbon fiber reinforced plaic : Concree filled eel ube : Ouer diaeer of eel ube : Elaiciy odulu of concree : Elaiciy odulu of carbon fiber hee : Elaiciy odulu of eel ube : Uliae enile rengh of longiudinal CFRP

30 292 Saic Behavior of Axially Copreed Circular Concree Filled CFRP-Seel Tubular (C-CF-CFRP-ST) Colun wih Moderae Slenderne Raio f : Index of load carrying capaciy of axially copreed C-CF-CFRP-ST ub cy colun f : Uliae enile rengh of ranvere CFRP ' f : Tenile rengh of carbon fiber hee f ck : Characeriic axial copreive rengh of concree f c' : Copreive rengh of cylinder concree pecien f cu : Cubic rengh of concree pecien FRP : Fiber reinforced plaic f y : Yield rengh of eel ube GFRP : Gla fiber reinforced plaic L : Lengh of pecien LVDT : Linear variable differenial ranforer : Nuber of ranvere CFRP layer ' : Nuber of longiudinal CFRP layer () N : Axial load N u : Load carrying capaciy of C-CF-CFRP-ST ub colun N u,cr : Calculaed value of criical buckling load of C-CF-CFRP-ST colun wih oderae lenderne raio Nu,cr : Teed value of criical buckling load of C-CF-CFRP-ST colun wih oderae lenderne raio p : Ineracion force beween concree and ouer ube S-CF-CFRP-ST : Square concree filled CFRP-eel ube : Thickne of 1 layer carbon fiber hee : Wall hickne of eel ube u : Deflecion of colun v c : Elaiciy Poion raio of concree v : Elaiciy Poion raio of eel ube w : Deniy of carbon fiber hee : Seel raio : Elongaion percenage of carbon fiber hee Δ : Axial horening of pecien : Srain of CFRP l : Srain of Longiudinal CFRP lr : Rupure rain of longiudinal CFRP : Srain of ranvere CFRP r : Rupure rain of ranvere CFRP l : Longiudinal rain : Srain of eel ube l : Longiudinal rain of eel ube : Tranvere rain of eel ube : Tranvere rain : Sabiliy coefficien of axially copreed C-CF-CFRP-ST colun wih oderae lenderne raio

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