RESILIENT INFRASTRUCTURE June 1 4, 2016

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1 RESILIENT INFRASTRUCTURE June 1 4, 2016 FLEXURAL BEHAVIOUR OF RECTANGULAR FRP-TUBES FILLED WITH REINFORCED CONCRETE: EXPERIMENTAL AND ANALYTICAL INVESTIGATIONS Ahmed Abouzied, PhD Postdotoral Fellow, University o Sherbrooke, Canada Radhouane Masmoudi, PE., PhD Proessor, University o Sherbrooke, Canada ABSTRACT This paper presents experimental and analytial investigations on the lexural behaviour o retangular onreteilled iber-reinored polymer (FRP) tube (CFFT) beams with steel rebar. Eight ull-sale CFFT beams and two ontrol reinored onrete (RC) beams were tested under a our-point bending. Several parameters as the FRP tubes thikness, iber laminates, and steel reinorement were studied. The experimental results indiate outstanding perormane o the CFFT beams in terms o strength and dutility ompared to the RC beams. Some CFFT beams attained lexural strength and dutility 540% and 1430% higher than that o the RC beams, respetively. Theoretial analysis was developed to determine the lexural apaities o the CFFT beam system through raking, yield, and ultimate stages. A strain ompatibility/equilibrium model was developed to predit the moment-urvature response o the CFFT beams addressing the issue o oninement and tension stiening o onrete. The analytial model an predit well the lexural moments, urvature, deletion, strains, and neutral axis loation. Keywords: Beams, Fiber-Reinored Polymer, Flexural behaviour, Strain Compatibility, Deletion. 1. INTRODUCTION Considerable researh has been onduted to validate the appliation o iber-reinored polymer (FRP) omposites in the onstrution industry. One o the innovative appliations is the onrete-illed FRP tubes (CFFT). Extensive studies have been onduted to investigate the behaviour o CFFTs as olumns, but omparatively limited researh was arried out on CFFTs as beams espeially CFFTs with irular setions. The onstrution and arhitetural requirements preer the retangular setion o beams due to its stability during installation and its workability during onneting to other strutural members like slabs and olumns. Atually, limited studies have been reported on the lexural behaviour o CFFT beams with retangular setions (Fam et al. 2005, Belzer et al. 2013). However, none o them reinored the retangular CFFT beams with steel rebar or analytially studied the deletion response o the omposite setion. The ompression ailure in most tested irular CFFT beams was predominantly governed by the ompression ailure o the tube lange under longitudinal ompressive stresses where the tensile hoop strains (i.e., oninement eet) were insigniiant (AASHTO 2012). This notie is based on lexural tests o irular CFFT beams without steel reinorement. More investigations are required to veriy that notie on retangular CFFT beams with steel rebar. Unlike steel-or-frp-rc beams, the steel-reinored CFFT beams an exhibit superior additional lexural apaities in the post-yielding stage (Abouzied and Masmoudi 2014, 2015). This is attributed to the onining ation o the FRP tube on the onrete ore to withstand higher strains, and the FRP tube reinorement ontribution in the axial diretion, in addition to the reinorement ation o the steel bars in their plasti hardening status. New design equations are required to get beneit o the outstanding lexural apaity at the post-yielding stage, and simultaneously, equations to predit the expeted deletion with reasonable auray. STR-938-1

2 Analytial models have been developed to predit the lexural apaity and load-deletion response or irular CFFT beams (Cole and Fam 2006, Fam and Son 2008, Mohamed and Masmoudi 2010). These models are based on strain ompatibility, internal ores equilibrium, and material onstitutive relationships. The ores within the CFFT ross setion were alulated by integrating the stress over the area o eah individual material. Despite the limited number o tested speimens, these models predit well the lexural behaviour o their irular CFFT beams. Their theoretial analysis depends mainly on a omputer-based analysis and requires some sophistiated alulation proedures. Also, these proposed models require veriiation and adjustment to be valid or the retangular CFFT beams, and need to be simpliied to be appliable or ommon designers. This paper investigates the lexural behaviour o retangular CFFT beams with steel rebar, partiularly in terms o lexural apaities at various stages during the loading, deletion response, and modes o ailure, or whih very limited published data exist. Also, it attempts to establish a theoretial basis or the development o design proedure inspired by the North Amerian design odes provisions. 2. EXPERIMENTAL PROGRAM 2.1 Materials and Beam Speimens Five types o retangular FRP tubes with idential internal ross setions were abriated at the laboratory o Composites Materials or Inrastrutures at Sherbrooke University using the ilament-winding proess. The FRP tubes were omposed o typial E-glass ibers and vinyl-ester resin. The tubes thikness ranged rom 3.4 mm to 14.2 mm. The ibers are oriented at dierent winding angles, 90 o, ±30 o, and ±45 o as shown in Table 1. This orientation aims to inrease the lexural strength and stiness o the FRP tube in the axial diretion as well as the transverse diretion. Standard tests were arried out to evaluate the physial and mehanial properties o the ilament-wound FRP tubes. Tension and ompression tests were arried out aording to ASTM D3039 (2014) and ASTM D695 (2010), respetively, on idential ive oupons to obtain the tensile and ompressive strength in eah diretion. Table 1 lists the detailed physial and mehanial properties o the abriated FRP tubes. The results o the oupons tests indiate a non-linear behaviour o the FRP omposite when inreasing the winding angle as shown in Figure 1. The inner suraes o the tubes were oated by a layer o vinyl-ester resin and oarse sand partiles to produe a rough texture in order to enhane the bond between the onrete ore and the tubes to ahieve a ull omposite ation under lexure. Ten beams 3200 mm long were abriated or this study as shown in Table 2; two idential steel-rc beams, two idential CFFT beams o OR2 30, OR4 30, and OR8 30, one beam o OR12 30, and one beam o OR All the tested beams were reinored at the tension side with steel bars 4Φ15M. Aording to the results o a standard tension test ASTM A615 (2009) arried out on three speimens o a steel bar 15M, the average yield tensile strength ( y) is 467 MPa and the modulus o elastiity E s is about 200 GPa. The beams were asted with a ready-mixed normal weight onrete. The RC beams were asted horizontally in a wooden box ormwork, while the CFFT beams were ixed on inlined strong rames and the onrete was poured into the tubes rom top end gates. The RC beams were ured in a onventional way by spraying water or 7 days. The CFFT beams were overed tightly with plasti sheets and the moisture surrounded the beams was kept at high level or 7 days. Ater 28 days o asting, onrete ylinders tests were perormed aording to ASTM C39 (2012). The average unonined ompressive strength or the ylindrial onrete speimens at 28 days old ( ) is listed in Table Test Setup and Instrumentations The beams were tested using a our-point bending load setup over a simply supported span o 2920 mm and a distane between the applied onentrated loads o 720 mm entered with the beam as shown in Figure 2. The beams were loaded under displaement ontrol with a rate o 1 mm/min using MTS mahine with a apaity o kn. The beams were unloaded at 0.5Δ y, Δ y, 2Δ y, and 4Δ y and then reloaded where Δ y is a pre-alulated deletion at yielding o the steel rebar. The unloading and reloading sheme was intended or the assessment o stiness at various load levels and to evaluate the dutility o suh beam system. STR-938-2

3 Three displaement potentiometers (DPs) were used to monitor the deletion proile along the beam span, whereas another two DPs were loated at the ends o the beams to reord any relative displaement (slip) between the onrete ore and the tube. Eletrial strain gages were bonded on the steel reinoring bars beore asting at the most ritial setion at mid-span. In addition, axial and transverse strain gages were bonded diretly on the tubes suraes at dierent levels along the beams depth to reord the strains and the onining ation around the setion. Additional Linear variable dierential transduers (LVDTs) were aixed at the beams top and bottom aes to monitor the extreme axial ompressive and tensile strains. Strain rosettes were loated at the enter o the shear span to investigate the shear response o the beams. The load, deletion, and strains were reorded during the tests using a data aquisition system. Tube OR230 OR430 OR830 OR1230 Cross Setion Table 1: GFRP tubes onigurations and mehanial properties Staking sequene % t Mehanial Fibers properties [90 o, ±30 o, 90 o ] [90 o, ±30 o, 90 o, ±30 o, 90 o ] [90 o, ±30 o 2, 90 o , ±30 o 2, 90 o ] [90 o, ±30 o 6, 90 o ] Elo (GPa) Axial diretion Flo (Mpa) εlo Etr (Gpa) Transverse diretion Ftr (Mpa) εtr Ten. Test 14.3±2 158± ±5 16.0±1 257± ±2 Comp. test 14.0±3-92±9-7.0±1 17.8±2-175±9-10.4±1 Ten. Test 14.5±1 173±9 15.3±2 14.4±1 249± ±3 Comp. test 15.5±1-165±7-12.5±1 14.5±1-293± ±3 Ten. Test 16.2±1 197± ±2 13.7±1 168±6 19.2±1 Comp. test 17.7±1-189±9-11.8±1 13.8±1-211± ±1 Ten. Test 18.6±1 242± ±1 13.4±1 125±9 16.6±2 Comp. test 20.1±2-176±12-9.5±1 12.2±1-217± ±3 [90 o, ±45 o 4, Ten. Test 10.5±2 100± ±6 13.0±1 164±3 24.5±2 OR o , ±45 o 4, 90 o ] Comp. test 11.1±1-110±6-20.7±1 12.2±1-171±7-21.4±2 E, F, and ε are the elastiity modulus, stress, and strain, respetively. Figure 1: Typial oupons test results in the axial diretion STR-938-3

4 Figure 2: Shemati o test setup (Dimensions are in mm) Group Beam ID Setion shape Table 2: Beam speimens and summary o test results Conrete Steel Outer Moment (kn.m) strength reinorement tube (MPa) Mr My Mu Ultimate Deletion Dutility (kn.m 2 ) Failure mode RC beams RC #1 Top 2Φ10M Tension Bot. 4Φ15M RC #2 Ties Φ10M/150 mm Tension CFFT beams OR230 # Tension OR OR230 # Tension OR430 # Tension OR OR430 #2 Bot Tension 4Φ15M OR830 # Balaned OR OR830 # Balaned OR1230 OR Comp. OR1645 OR Balaned 3. TEST RESULTS 3.1 Flexural Behaviour o Retangular CFFT Beams All the beams ailed under lexure without any signs o shear ailure, slip, or web bukling. The yli loading did not aet the load-deletion response sine the maximum gab in the deletion within the yles did not exeed 1 mm until the peak load. This is attributed to the elasti behavior o this type o hybrid CFFT beams. Figure 3 shows the typial ailure patterns o the CFFT beams and their moment-deletion responses (outer envelopes) in addition to the strains at the top ae o the FRP tubes. OR2 30 with FRP tube thikness o 3.4 mm ailed in tension with axial rupture o ibers at the tension side. Also, OR4 30 with FRP tube thikness o 5.7 mm experiened a tension ailure however there was inlate and minor signs o outward bukling at the top lange beore the ultimate ailure. The ailure o OR8 30 with FRP tube thikness o 8.7 mm started with outward bukling o the tube ompression lange with a limited drop in strength. Aordingly, the lexural stiness dereased. Nevertheless, the tube ontinued to arry additional loads depending mainly on the tube bottom lange at the tension side and the onined onrete at the ompression side. Shortly thereater, an axial rupture o ibers at the tension side happened. OR12 30 with FRP tube thikness o 9.9 mm ailed in ompression by outward bukling o the ompressive lange with a limited loss o strength, but the beam ould not arry any additional loads aterwards. OR16 45 with FRP tube thikness o 14.2 mm behaved in the same way as OR8 30. Note that, OR16 45 experiened the maximum lexural apaity due to its high resistane to bukling. This is attributed to the high perentage o the transverse ibers in OR16 45 that resisted the STR-938-4

5 bukling o the axial ibers unlike the ase in OR Aordingly, the bukling o the tube ompression lange aeted the lexural apaity o OR Figure 3(b) shows that the oninement eiieny appear in the thik tubes (OR8 30, OR12 30, and OR16 45) more than the thin tubes (OR2 30 and OR4 30). This onirms the transverse rupture o ibers at the top ae o OR16 45 shown in Figure 3(). Based on the notied patterns o ailure o the tested CFFT beams, OR2 30 and OR4 30 ould be onsidered as under-reinored CFFT beam setions, while OR12 30 ould be onsidered as over-reinored CFFT beam setions, while OR8 30 and OR16 45 ould be onsidered as balaned CFFT beam setions as listed in Table 2. Even ater the ultimate ailure, the reinored CFFT beams kept a residual strength due to the existene o the steel that has a high plasti strain (see the horizontal yielding plateau ater the ultimate ailure in Figure 3(a)), unlike the FRP-onrete omposite beams that ommonly lose their lexural strength entirely one their FRP reinorement ails. The overall moment-deletion behaviour o the retangular CFFT beams reinored with steel rebar is non-linear. The lexural stiness was very high beore raking due to the high value o the gross moment o inertia (I g) and then it dereased ater raking o the onrete. The lexural stiness dereased more ater yielding o the steel, but there was an asending lexural apaity that annot be negleted as in the RC beams. The results indiate also the signiiant gain in strength, stiness, and dutility o the retangular CFFT beams ompared to the RC beam. The dutility o the beams were indiated by the energy absorption determined by the area under the moment-deletion urves until the peak apaity as listed in Table 2. The results indiate that the dutility o the CFFT beams attained values 1430% greater than that o the RC beam as in OR The moment at the yield o steel (M y) o the CFFT beams is also greater than that o the RC beams, and inreases with inreasing the FRP tube ontribution by its thikness and/or axial strength. For example, M y o the CFFT beams OR2 30 with 3.4 mm tube thikness is 32% higher than that o the RC beams. While M y o the CFFT beam OR12 30 with 9.9 mm tube thikness is 114% higher than that o the RC beams. The ultimate lexural apaity (M u) o the CFFT beams attained value 540% higher than that o the RC beam as in OR STR-938-5

6 Figure 3: Beam test results 3.2 Craking Strength in CFFT Beams One o the advantages o the CFFT system is that the outer FRP tube ats as a jaket that protets the inner strutural elements, suh as onrete and steel, against orrosion even i the inner onrete ore is raked. It is important or eetive design o FRP-onrete omposite struture to study the raking behaviour or servieability requirements related to deletion and rak width ontrol. Although the onrete ore was hidden behind the tubes surae, the moment at the irst rak (M r) was obtained rom the readings o the steel strains and the urvature response hange. In this study, the experimental M r and the moment o inertia o the gross transormed setion (I g) were used to develop an expression or the modulus o rupture o onrete ( r) using the ollowing equations: [1] =M Y I k r r [2] I g=i (ns-1 )I s n I t g Where I, I s, and I are the moment o inertia o the onrete, steel bars, and FRP tube, respetively. Y t is the distane o the extreme tension iber o onrete rom the entroid. n s is the steel modular ratio (n s = E s /E o). n is the FRP STR-938-6

7 modular ratio (n = E /E o). E is the elastiity modulus o the FRP tube approximated as the average o the axial elastiity modulus in tension and ompression. E o is the elastiity modulus o the onrete ( E = 4500 ). o Based on this study, the oeiient k = 0.69 in ase o alulating I g onsidering reinorement (FRP tube + steel) and k = 0.8 in ase o alulating I g negleting reinorement. Note that, ACI-318 (2014) uses k = 0.62 and reommends negleting reinorement in alulating I g. By omparing the k values o the urrent study and ACI- 318, it an be seen that the raking strength an be inreased by 30% in the CFFT beams. It is attributed to many ators: 1. The FRP tubes ontributed positively in the gross setion inertia I g. 2. The bond between the FRP tubes suraes and the onrete delayed the generation o the raks. 3. Conining the onrete with FRP tubes restrained it against raks propagation. 4. The onrete expansion during uring was restrained by the tube induing hemial pre-stressing on the onrete (Fam and Rizkalla 2002). 3.3 Yield and Ultimate Moments An analytial model based on strain ompatibility/equilibrium was developed to predit theoretially the lexural apaity o retangular CFFT beams as shown in Figure 4(a). The model is based on the assumption that plain setions remain plain ater deormation, whih means linear strain distribution along the depth o the CFFT setion subjeted to bending. This model assumes also ull bond between the onrete ore, steel bars, and the FRP tubes (no slip). By assuming the depth o the ompression zone () and the strains at any level (steel level or tube top and bottom aes), the internal tension and ompression ores along the ross setion an be determined as shown in Table 3. The parts o the retangular FRP tube above and below the neutral axis were onsidered eetive in resisting the ompression and tension ores, respetively. A linear stress-strain relationship was assumed or the FRP with maximum limits or strength and strains obtained rom oupon tests results (See Table 1). Thereore, Seant s moduli are used to model the FRP tube in tension and ompression as E ten=f lo(ten)/ε lo(ten) and E omp=f lo(omp)/ε lo(omp), respetively. The steel was modeled by a bilinear model in two parts: (1) a linear elasti part up to the yield strain (ε s = y /E s = ), (2) a yield plateau up to the ultimate plasti strain with a zero plasti hardening elastiity modulus. Two models or onrete in ompression are examined in this study as shown in Figure 4(b). The irst onrete model is an unonined onrete model with extended strain sotening using Popovis s model (1973) as suggested by AASHTO guidelines (2012) and shown in Eq. 3. [3] ( r 1 / ) r r ( / ) and r E E o o E se Where, the seant modules o onrete E ompressed ylinder test results. se and the maximum ompressive strain ε = based on the The seond onrete model is a partially onined onrete model, whih is based on a untion similar to the Popovis s model up to ollowed by plasti behaviour with onstant ompressive strength equals as shown in Figure 4(b). This model was hosen to present intermediate level o oninement that is adequate or beams, instead o ull oninement models that are adequate or olumns. The tensile strength and tension stiening o onrete in tension are also onsidered in the model as shown in Figure 4(b). The maximum tensile strength o onrete and the orresponding tensile strain ε r = r /E o. For r ε ε r, the onrete tension stiening model proposed by Collins and Mithell (1997) was used as ollows: [4] r 500( r ) STR-938-7

8 Where, α 2 is a ator aounting or the nature o loading and was taken as 0.7 or repeated loading. α 1 is a ator aounting or the bond harateristis and was taken as 1.0 beause o the ull omposite ation. Due to the non-linearity o the onrete material, the onrete parts above and below the neutral axis are divided into n number o strips, whih have the same thikness h i. Where h i = / n or the strips in the ompression zone and h i = (h )/n or the strips in the tension zone. The entroid o eah strip, i, is loated at its mid-thikness. The distane rom eah ompression strip entroid to the neutral axis, YC i, and the strain ε i at its mid-thikness are alulated rom Eq. 5. The distane rom eah tension strip entroid to the neutral axis, YT i, and the strain ε ti at its midthikness are alulated rom Eq. 6. [5] YC i (i 0. 5 ) YC i i...for strips in the ompression zone n [6] h YT i (i 0. 5 ) YT i ti...for strips in the tension zone t n h These strain values are retrieved in Eq. 3 and Eq. 4 to obtain the orresponding ompressive stress or tensile stress in onrete, respetively. Then, the internal ompression or tension ore, C i or T i, inside eah strip is alulated as: [7] Ci ibh...( i i rom Eq. 3) [8] T i i bh i...( i rom Eq. 4) Figure 4: Analytial model Table 3: The internal ores and their positions in retangular CFFT beams Internal Fore ID Expression o the ore Distane rom the neutral axis Tension ore in steel T s Es. s. As y. As YT s d ε t t Tension ore in tube lange ( bot TTube lange bt Eten ) YTTube lange h Tension ore in tube webs T (h )t E (h ) 3 Tube webs ten t YT Tube webs Tension ore in onrete strips i Ti ibh i n i1 T T i ε top Compression ore in tube lange CTube lange bt Eomp ( ) 2 Compression ore in tube two webs Compression ore in onrete strips C t Tube webs E omp i Ci ibh i n i1 ε C C i h YT i ( i 0.5) n t YCTube lange 2 2 YC Tube webs 3 YC i ( i 0.5) n STR-938-8

9 3.4 Proedure o Analysis 1. Speiy the tube dimensions, thikness, material properties, loation and area o steel rebar, and number o onrete strips, n. 2. Assume a strain value, i.e., ε s = F y/e s i M y is required or ε bot = ε lo(ten) i M u is required. 3. Assume a value or the ompression zone depth. 4. Calulate the strains at dierent levels, i.e., the strain at steel rebar (ε s), the strain at the top ae o the FRP tube (ε top), the strain at top ae o onrete (ε ), the strain at the bottom ae o onrete (ε t), and the strain at the bottom ae o the FRP tube (ε bot). 5. For eah onrete strip in ompression and tension, ompute the strains at its mid-thikness (ε i or ε ti) and the orresponding ompressive or tensile stresses. 6. Calulate the total ompressive and tensile ores in the onrete, rebar, and the FRP tube. 7. Chek or equilibrium by satisying with allowable tolerane. 8. I the equilibrium is not satisied, go to step 3 and assume another value or. The proess is repeated until the equilibrium is satisied. 9. One the equilibrium is satisied, the internal moments are alulated or all the internal ores around the neutral axis as = ( F. Y i ) theo i C T ψ=. M, and the orresponding urvature is alulated as ε top t The previous steps an be repeated many time by assuming sequential values o strains rom zero to maximum oupons strains in order to onstrut moment-urvature response. One the urvature is obtained, the deletion (Δ) o a our-point loading system an be estimated rom orresponding urvatures at any level (servie load or ultimate load) by Eq. 9 where L is the span between the supports and a is the shear span. [9] ψ 2 2 Δ ( 3L 4a ) Analytial Results Two typial examples or CFFT beams with thin FRP tube and thik FRP tubes are shown in Figure 5 whih plots the eet o using the unonined-or-onined onrete models on the neutral axis loation and orresponding moments. The partially onined onrete model indiates good predition or the lexural behaviour o all tested CFFT beams. While the unonined onrete model an be used in the FRP tubes that have small tube thikness only. For example in the CFFT beam OR2 30, the response o the unonined and onined onrete model was idential until the ultimate predited moment. While in the CFFT beam OR12 30, the response that uses the unonined onrete model was not able at all to predit well their lexural response and deviates rom the experimental results at about 60% o the ultimate moments. Aordingly, the unonined onrete model is onservative espeially in the thik tubes. These theoretial results math well with the experimental results indiated in Figure 3(b) that indiates oninement presene in the CFFT beams with thik FRP tubes unlike the CFFT beams with thin FRP tubes. Figure 5: Eet o onrete oninement model Until yield, both unonined and onined onrete models give the same results sine the oninement has not been ativated yet (ε top ε as shown in Table 4). Table 4 lists the predited versus experimental yield moments o the CFFT beams and the tension stiening o the onrete is onsidered or ignored. The results indiate that the tension STR-938-9

10 stiening an be onsidered in the thik tubes and should be ignored in the thin tubes to math well the experimental results. It is attributed to, the thik tubes onine well the inner onrete ore and prevent it rom exessive raks unlike the thin tubes. Nevertheless, ignoring the tension stiening o onrete underestimates the experimental results and ahieves sae design. The same observation an be seen in Table 5 that lists the predited versus experimental ultimate moments o the CFFT beams. The analytial results justiy the use o the partially onined onrete model in modelling the retangular CFFT beams. Figure 6 shows the experimental versus the analytial results o moment-deletion responses or two examples o the tested CFFT beams using the partially onined onrete model. Good agreement is observed, however in CFFT beams with thin FRP tubes, ignoring the tension stiening shows better agreement with the experimental proiles o deletion than onsidering it. CFFT Beam My(exp.) (kn.m) εs Table 4: Theoretial versus experimental yield moments Unonined or partially onined onrete model Considering tension stiening εtop εbot My(th.) (kn.m) M M y y (exp.) (th.) Ignoring tension stiening εtop εbot My(th.) (kn.m) M M y y (exp.) (th.) OR230 # OR230 # OR430 # OR430 # OR830 # OR830 # OR OR CFFT Beam Mu(exp.) (kn.m) Table 5: Theoretial versus experimental ultimate moments Partially onined onrete model Considering tension stiening εtop εbot Mu(th.) (kn.m) M (exp.) M (th.) u εtop u Ignoring tension stiening εbot Mu(th.) (kn.m) M u (exp.) M (th.) OR230 # OR230 # OR430 # OR430 # OR830 # OR830 # OR OR u STR

11 Figure 6: Theoretial versus experimental moment deletion response o CFFT beams 4. CONCLUSIONS The main onluded points o this study are as ollowing: 1. The retangular CFFT beams experiene signiiantly higher dutility, higher stiness, and superior strength than the RC beams. 2. The retangular CFFT beams with steel rebar ail gradually in a sequential manner (yielding o steel, bukling o ompressed tube lange, and inally rupture o the ibers). Even ater the ultimate ailure, the steel reinored CFFT beams keep a residual strength beause o the existene o the steel that withstands high strains and elongation. 3. The reinored CFFT retangular beams experiene high raking strength and the onrete modulus o rupture ( r) suggested by ACI-318 ould be inreased by 30% i the gross moment o inertia I g is alulated negleting reinorement. 4. The analytial model proposed in this study is apable o prediting well the moment-urvature, moment strains, neutral axis depth, and moment-deletion responses o ully-cfft retangular beams. The oninement and tension stiening issues o onrete are onsidered in the model. 5. Using partially onined model or onrete with plasti strain up to the ultimate ompressive strain o the FRP tube material indiate better agreement with the experimental results than using the unonined onrete model proposed by AASHTO guidelines (2012). 6. Conrete tension stiening an be onsidered in CFFT beams with thik tubes, and should be ignored in CFFT beams with thin tubes. ACKNOWLEDGMENTS The researh reported in this paper was partially sponsored by the Natural Sienes and Engineering Researh Counil o Canada (NSERC) and the Fonds de reherhe québéois-nature et Tehnologie. The authors also aknowledge the ontribution o the Canadian Foundation or Innovation (CFI) or the inrastruture used to ondut testing. The opinion and analysis presented in this paper are those o the authors. REFERENCES AASHTO. Guide speiiations or design o onrete-illed FRP tubes or lexural and axial members. 1st edition, Washington, DC; Abouzied, A. and Masmoudi, R Flexural behaviour o new partially onrete-illed ilament-wound retangular FRP tube beams. 4 th international strutural speialty onerene CSCE, Haliax, NS, Canada, 10 p. paper in CD-ROM proeedings. STR

12 Abouzied, A. and Masmoudi, R Strutural perormane o new ully and partially onrete-illed retangular FRP-tube beams. Constrution and Building Materials Journal, 101: Amerian Conrete Institute Building ode requirements or strutural onrete. ACI Detroit, USA. ASTM Standard speiiation or deormed and plain arbon steel bars or onrete reinorement. ASTM A615/A615M. West Conshohoken, PA. ASTM Standard test method or ompressive properties o rigid plastis. ASTM D695. West Conshohoken, PA. ASTM Standard test method or ompressive strength o ylindrial onrete speimens. ASTM C39. West Conshohoken, PA. ASTM Standard test method or tensile properties o polymer matrix omposite materials. ASTM D3039/D3039M. West Conshohoken, PA. Belzer, B., Robinson, M., and Fik, D Composite ation o onrete-illed retangular GFRP tubes. ASCE Composites or Constrution Journal, 17(5): Cole, B. and Fam, A Flexural load testing o onrete-illed FRP tubes with longitudinal steel and FRP rebar. ASCE Composites or Constrution Journal, 10(2): Collins, M. P. and Mithell, D Prestressed onrete strutures. Response Publiations, Canada. Fam, A. and Rizkalla, S Flexural behaviour o onrete-illed iber-reinored polymer irular tubes. ASCE Composites or Constrution Journal, 6(2): Fam, A. and Son, J. K Finite element modeling o hollow and onrete-illed iber omposite tubes in lexure: optimization o partial illing and a design method or poles. Engineering Strutures Journal, 30: Fam, A., Shnerh, D., and Rizkalla, S Retangular ilament-wound glass iber reinored polymer tubes illed with onrete under lexural and axial loading: experimental investigation. ASCE Composites or Constrution Journal, 9: Mohamed, H. and Masmoudi, R Flexural strength and behaviour o steel and FRP-reinored onrete-illed FRP tube beams. Engineering Strutures Journal, 32: Popovis, S A numerial approah to the omplete stress-strain urve o onrete. Cement and Conrete Researh Journal, 3(5): STR