Experimental and Analytical Modeling of Concrete-Filled FRP Tubes Subjected to Combined Bending and Axial Loads

Transcription

1 Experimental and Analytial Modeling o Conrete-Filled FRP Tubes Subjeted to Combined Bending and Axial Loads Amir Fam 1, Bart Flisak 2 and Sami Rizkalla 3 Abstrat This paper presents test results o an experimental program and proposes an analytial model to desribe the behavior o onrete-illed iber reinored polymer (FRP) tubes subjeted to ombined axial ompression loads and bending moments. The experimental program inluded ten speimens subjeted to eentri axial loads, two speimens tested under onentri axial loads and two speimens tested in bending. Glass-FRP tubes with two dierent laminate strutures were onsidered. Axial load - bending moment interation urves are presented. The paper presents an analytial model, whih aounts or variable oninement o onrete and gradual hange o the bi-axial state o stresses developed in the tube as the eentriity hanges. The model utilizes the lassial lamination theory or the FRP tubes and aounts or their gradual redution o stiness as a result o the progressive ailure o dierent FRP layers. A parametri study was onduted to evaluate the eets o diameter-to-thikness ratio and laminate struture o the tube inluding iber proportions in the axial and hoop diretions. The study evaluated the oninement as aeted by the eentriity o the applied axial load as well as the inluene o the FRP laminate struture. Researh indings indiate signiiant inrease o the lexural strength by inreasing the ratio o ibers in axial diretion. Inreasing the ratio o ibers in the hoop diretion inreases the axial ompressive strength o onrete-illed thin tubes. Key words: FRP, tubes, onrete, beam, olumn, ombined loading, oninement, interation urve. 1 Assistant Proessor, Queen s University, Kingston, Ontario, Canada k7l 3N6 2 Graduate Student, The University o Manitoba and ISIS Canada Network o Centers o Exellene, Winnipeg, MB, Canada R3T 5V6 3 Distinguished Proessor o Civil Engineering and Constrution, Diretor o the Construted Failities Laboratory, Civil Engineering Department, North Carolina State University, Raleigh, NC

2 Introdution Conrete-illed iber reinored polymer (FRP) tubes provide a new and attrative use o omposite materials in several appliations inluding piles, olumns, bridge piers, poles and highway overhead sign strutures. Traditional pile materials inluding steel, onrete, and timber have limited servie lie and high maintenane osts, speially i they are used in harsh marine environments (Lampo et al., 1998). It has been estimated that repair and replaement o piling systems osts the U.S. over $1 billion annually (Lampo, 1996). High repair and replaement osts have led North Amerian highway agenies and researhers to investigate the easibility o using omposite materials or ivil engineering inrastrutures inluding bridge pile oundations (Iskander and Hassan, 1998). FRP tubes provide a permanent, non-orrosive, lightweight ormwork or the onrete and reinorement element at the same time. The laminate struture o the omposite tube an be ontrolled to provide dierent proportions o strength and stiness in the longitudinal and transverse diretions, depending on the appliation and nature o loading. Under axial loads, the FRP tube onines the onrete by reduing its lateral expansion, thereore, inreases its ultimate strain and strength. Several researhers have studied the strutural behavior o onrete-illed FRP tubes under axial loads (Fam and Rizkalla 2001(a) and (b) and Mirmiran and Shahawy 1997). Flexural behavior o these members was also studied by Fam and Rizkalla (2002) or Glass-FRP tubes and by Karbhari et al (1998) or arbon-frp tubes. Seible (1996) proposed the onrete-illed CFRP tubes or dierent bridge systems. Researh related to the behavior o onrete-illed FRP tubes under ombined axial load and bending moments is still very limited. Mirmiran et al (2000) studied both thin and thik wall tubes to investigate under- and over-reinored setions subjeted to a onstant axial load and inreasing bending, using transverse loads, in order to ompare the behavior o onrete- 2

3 illed FRP tubes with that o onventional prestressed piles. The study onluded that bond ailure is not a onern in members subjeted to ombined bending and axial loads and also overreinored setions were reommended or design due to their higher strength and stiness. Teng et al (2002) have onduted a theoretial study on reinored onrete irular members wrapped with FRP sheets and subjeted to ombined bending and axial loads in order to establish the interation diagrams using dierent oninement models proposed by dierent researhers. The study emphasized the signiiant eet o oninement as the axial load inreases and also showed almost no eet o oninement on the pure bending strength, whih was also reported earlier by Fam (2000) based on beam tests using onrete-illed FRP tubes. Researh Signiiane This paper provides experimental results o large-sale onrete-illed FRP tubes using two dierent laminate strutures tested under bending, onentri and eentri axial loads, in order to establish the interation diagrams. The FRP tube is the sole reinorement in both longitudinal and irumerential diretions, thereore, the analytial modeling aounts or the gradual hange o the state o bi-axial stresses developed in the tube as the eentriity o the axial load hanges. The lamination theory and the method o ultimate laminate ailure are adopted to aount or the gradual redution o stiness due to the progressive ailure o dierent FRP layers. Failure o the FRP tubes under ombined axial ompressive and hoop tensile stresses is deteted by the Tsai-Wu ailure riteria. Three dierent oninement mehanisms o onrete are examined, inluding an upper bound ull oninement model whih is based on a ixed level o oninement, independent o the eentriity o the applied load, a lower bound unonined onrete model, and a partial oninement model, whih is variable and untion o the 3

4 eentriity o the load. FRP tubes with dierent wall thikness and various proportions o strength and stiness in the axial and hoop diretions have been evaluated using parametri study to examine the eets o both reinorement ratio and laminate struture on the interation diagrams o onrete-illed FRP tubes subjeted to ombined bending and axial loads. Experimental Program The experimental program inluded testing o onrete-illed Glass-FRP (GFRP) irular tubes under onentri and eentri axial loads as well as under pure bending. Two dierent laminate strutures were used or the GFRP tubes. Table 1 provides details o test speimens inluding the type o loading (bending, axial ompression and ombined bending and axial ompression), the type o GFRP tube, the eentriity o the axial load, e (or the eentrially loaded olumns) the span o the beam (L) as well as the height o the onentrially and eentrially loaded olumns (H), the average ompressive strength o the onrete used to ill the tubes based on standard ylinder tests, the measured axial load P n and bending moment M n at ailure. The GFRP tubes had 51 perent iber volume ration and were abriated using the ilament winding method. Table 2 provides details o the two types o GFRP tubes inluding the diameter, wall thikness, staking sequene o dierent layers inluding the angle o the ibers and iber/matrix types. Table 2 also provides the eetive mehanial properties o the laminates based on the lassial lamination theory inluding the eet o progressive laminate ailure. Type I tubes have almost equal iber perentages, oriented at 3 and 88 degrees with the longitudinal diretion, while Type II tubes have 70 perent o the ibers oriented at ± 34 degrees and 30 perent at 80 degrees with the axial diretion. Coupons rom the longitudinal diretion o the tubes were tested in tension in order to veriy the predition by the lamination theory and progressive ailure 4

5 method. The experimental and predited stress-strain behavior in the longitudinal diretion is given in Fig. 1 or the two types o tubes. Fabriation o speimens The hollow GFRP tubes were plaed in an inlined position on a steel rame. Wooden plugs were installed at the top and bottom ends o the tubes. High slump onrete was pumped rom a ready mix truk into the tube through a hole in the upper plug. External vibrator was ixed to the steel rame. The onrete mix design inorporated an expansive agent to overome any possible shrinkage during the uring proess. Ater suiient uring time, test speimens were ut rom the long tubes using a diamond blade saw. Beam speimens Table 1 provides details o B1-I and B1-II beam speimens using FRP tubes Types I and II. The speimens were tested using our-point bending as shown in Fig. 2(a). Two idential speimens were tested or B1-I and B1-II. The span o the beams was 5.5 m while the distane between the two applied loads was 1.5 m. Speimens were instrumented within the onstant moment region to measure the longitudinal and irumerential strains along the depth. Mid-span deletion and applied load were also measured. The beams were tested to ailure to determine the lexural apaity M n. Fig. 3 shows the load-deletion behavior o the two beams. The behavior indiates that the raking load is quite low in omparison to the ultimate load and behavior is almost linear, ater raking, up to ailure. Conentrially loaded olumn speimens Table 1 provides details o C1-I and C1-II olumn speimens using FRP tubes, Types I and II. Both speimens were tested under onentri axial load to ailure, as shown in Fig. 2(b), to provide the axial strength P n. Two idential speimens were tested or C1-I. Axial and 5

6 irumerential strains were measured using both displaement and strain gauges along the perimeter o the tube at mid-height. Fig. 4 shows the axial load-axial strain behavior o the olumns based on an average value o three strain gauges and an average value o three displaement gauges. The two types o gauges were staggered around the perimeter, 60 degrees apart. The unonined onrete had a relatively high ompressive strength, and thereore, the onrete laks the post-peak strain sotening response typially observed in unonined low strength onrete stress-strain urve. Due to the brittle nature o this onrete, the load reahed a peak value, orresponds approximately to and dropped slightly, in C1-I speimens, ater development o ew major internal raks. Beyond this stage, the behavior o C1-I speimens showed plasti behavior and the peak load was gradually reovered until the tube was ratured and the olumns ailed. For C1-II speimen, larger drop in the load was observed without notieable reovery, mainly due to the laminate struture o Type II tubes, whih has low stiness in the hoop diretion and relatively high Poisson s ratio value. In a typial situation, where low or normal strength onrete is onined, internal raks are very uniorm and well distributed within the onrete mass, resulting in bi-linear load-strain behavior or FRP tubes with adequate stiness (Fam and Rizkalla 2001(a) and Mirmiran and Shahawy 1997). In this test, ew internal raks ourred due to the brittle nature o the relatively high strength onrete used. The measured axial load apaity o C1-II was slightly higher than C1-I in spite o the better oninement eetiveness o Type II tubes in omparison to Type I tubes. This is attributed to value o the onrete illing, whih was higher in C1-II (67 MPa) than in C1-I (60 MPa). In general, both olumns exhibited small oninement eet, mainly due to the brittle nature o the onrete ore, whih resulted in limited expansion in the transverse diretion under axial loading, and onsequently, low oninement pressure. Also, axial loading o the FRP tube 6

7 and the design o the FRP laminate, whih provided a limited ration o the ibers in the hoop diretion, have ontributed to the low oninement pressure and the limited gain in axial strength in this ase. Eentrially loaded olumn speimens Table 1 provides details o the eentrially loaded olumn speimens (BC1-I to BC5-I) o Type I tubes as well as (BC1-II to BC5-II) o Type II tubes. Rigid steel aps were installed at the top and bottom o the speimens, as shown in Fig. 2(), to allow or variation o the eentriity o the applied axial load, thereore, provide dierent ombinations o axial loads P n and bending moments M n at ailure. Longitudinal and irumerential strains as well as the net lateral deletion at mid-height were measured. Due to the nature o the load appliation, the applied axial ore and bending moment were oupled. The total maximum moment M n at mid-height, whih is reported in Table 1 or all eentrially loaded olumn speimens, is omposed o the primary moment, based on the initial eentriity, and the seondary moment due to the lateral deletion at ailure at mid-height. Table 1 also presents the eentriity based on the inal M n and P n, whih ranged rom 55 to 839 mm or Type I tubes and rom 11 to 329 mm or Type II tubes. These values are equivalent to eentriity e - to - outer diameter D o ratios o to or Type I and to or Type II tubes. Fig. 5 shows the axial load-bending moment interation diagrams or Type I and II speimens. The behavior relets very well the transition rom tension to ompression ailure through the balaned point. The interation diagrams are disussed in more details in the analytial modeling setion. Failure modes Fig. 2 shows the dierent ailure modes o some o the test speimens. Beam speimens B1-I and B1-II ailed by rupture o the ibers in the tension side within the onstant moment region in 7

8 a similar ashion to the eentrially loaded olumn speimens, whih ailed in tension as shown in Fig. 2 (). The axial strains measured on the ompression side o the tubes o beams B1-I and B1-II were and respetively (with no sign o ompression damage), when the beams ailed in tension at 0.02 and 0.15 axial tensile strains, respetively. The C1-I and C1-II olumn speimens ailed by rature o the tube under a state o bi-axial stresses inluding axial ompressive and hoop tensile stresses as shown in Fig. 2 (b). C1-II olumn also showed minor loal bukling o the tube under axial ompression. The axial stresses in both types o speimens is a result o the diret axial loading on the tube, while the hoop stresses results mainly rom expansion o the onrete inside the tube under high axial stresses. The behavior o C1-II speimen suggests that onrete expansion did not engage the FRP tube to produe signiiant level o oninement. Eentrially loaded olumn speimens ailed either in tension or ompression, depending on the eentriity o the applied load. BC1-I, BC2-I, BC3-I, BC1-II, and BC2-II ailed in tension by rupture o the ibers, similar to the beams B1-I and B1-II, while BC5-I, BC3-II, BC4-II and BC5-II ailed in ompression by rushing o the ibers in the ompression side as shown in Fig. 2(). BC4-I had a balaned ailure inluding rupture o ibers in tension side, almost simultaneously with rushing o the ibers in the ompression side. Both tension and ompression ailure modes are illustrated in Fig. 2() or speimens o both Type I and Type II tubes. Analytial Modeling The objetive o the proposed analytial model is to establish the axial load-bending moment interation diagram o onrete-illed FRP tubes. The model is based on the equilibrium and strain ompatibility approah. The layer-by-layer method is used or the integration proess o 8

9 the stresses over the ross-setion o the member, in order to determine the ultimate axial load and bending moment ating on the ross-setion under dierent eentriities. The lassial lamination theory is used to establish the eetive stress-strain urves o the laminate o FRP tubes in the axial and hoop diretions, utilizing the progressive ailure approah o dierent layers o the laminate. Failure o the laminate is determined by the Tsai-Wu ailure riteria (Daniel and Ishai 1994). For the stress-strain urve o onrete in the ompression zone, three dierent oninement mehanisms are examined, inluding an upper bound representing the ull oninement model, whih represent ixed level o oninement, independent o the eentriity o the applied load, a lower bound unonined onrete model, and a partial oninement model, whih is variable and dependent on the eentriity o the load. Coninement o onrete Three dierent mehanisms simulating the behavior o onrete in the ompression zone an be ategorized as ollows: Full oninement mehanism (Upper bound) In this ase, the stress-strain urve o the onined onrete an be determined using any o the oninement models available in the literature or the ase o pure axial loading ondition. The analysis in this ase utilizes the same onined stress-strain urve, shown in Fig. 6(a), in the ompression zone, or the ull range o eentriity, to establish the interation diagram. The oninement model by Fam and Rizkalla (2001 b) has been adopted in this analysis. The model is well suited or this ase beause it aounts or the bi-axial state o stress developed in the tube, inluding the axial ompressive stresses, whih results rom the omposite ation, and the hoop tensile stresses resulting rom oninement. The model adopts Tsai-Wu ailure riteria to target the ailure point o the tube. The ultimate onined strength and orresponding strain are 9

10 and ε respetively. For FRP tubes with adequate stiness, the model is almost bi-linear with the transition point near the unonined peak strength,. Unonined onrete model (Lower bound) In this ase, an unonined stress-strain onrete model, shown in Fig. 6(a), is adopted in the ompression zone or the ull range o eentriity to establish the interation diagram. In this analysis the model by Popovis (1973) is used due to its aurate simulation, espeially or the strain sotening behavior. In this model, the stress at a given axial strain ε is given as a untion o the unonined strength and the orresponding strain ε as ollows: x r = (1) r r 1 + x Where x = ε / ε and r = Eo / ( Eo - Ese ). E o is the tangent elasti modulus o unonined onrete, and an be estimated as 5000 ( MPa). E se is the seant modulus o unonined onrete and an be estimated as ε. The urve ould be terminated at strain, whih is the ultimate strain, speiied by ACI , or ould be extended to strain ε o. Fam and Rizkalla (2002) have shown that or the ase o pure bending the eet o oninement on onrete strength is insigniiant, however, the dutility and strain o onrete are inreased signiiantly beyond It is also well established that ailure o the system is normally governed by ailure o the FRP tube beore omplete ailure o the onrete inside. Thereore, ε o is assumed equal to the ultimate ompressive strain o the FRP tube in the axial diretion. 10

11 Variable oninement mehanism The proposed variable oninement model assumes that the oninement level o onrete is gradually redued as the eentriity o the axial load inreases. This mehanism is very representative to observed behavior. Test results indiated that inreasing the eentriity results in a strain gradient that subjet large part o the ross-setion to tensile strains, whih would signiiantly redue the level o oninement. Fig. 6(b) shows the variable stress-strain urve o onrete, whih ranges rom the upper limit o the ully onined onrete (zero eentriity) to the lower limit o the unonined stress-strain urve with extended dutility or the ase o ininite eentriity (pure bending). The proposed model assumes that the initial asending part o the urve is similar or both unonined and onined onrete as observed by several researhers [Fam and Rizkalla (2001 a) and Samaan et al (1998)]. The part o the urve beyond the peak point o unonined strength, is variable and dependent on the eentriity o the applied load. For a given general eentriity e, the ultimate strength o onrete, is alulated as a untion o the ully onined strength and the unonined stress o at ultimate strain, rom the ollowing proposed equation: Where Do ( ) o = o + (2) Do + e Do is the outer diameter. This expression satisies the upper and lower limits. For a ase o pure axial load (e = 0), = and or the ase o pure bending (e = ), = o. Fam and Rizkalla (2001 b) have shown that or the ase o axial load (e = 0), a bi-axial state o stress is developed in the FRP tube and thereore, a bi-axial strength ailure riteria suh as Tsai- Wu should be used to detet ailure. Fig. 6() shows the stress path (point 0 to 1) during the 11

12 loading history under pure axial load. By inreasing the eentriity, less oninement is generated, and thereore, less hoop tensile stresses are developed and the stress path would gradually shits rom (point 0 to 1) to (point 0 to 2). As the eentriity reahes ininity (pure bending), the stress path would be rom point 0 to 3. Thereore, the path between points 1 and 3 on Fig. 6(b) orresponds to the path between points 1 and 3 on the ailure envelope in Fig. 6(). Aordingly, the lous o ailure points between and o in Fig. 6(b) is analogous to Tsai- Wu ailure envelope and is approximated as elliptial. The strain ε strength and ranges rom, whih orresponds to the ε to ε o, is alulated rom the ollowing elliptial equation: The shape o the urve between 2 o ε = ( εo ε ) 1 + ε (3) o and ranges rom approximately linear at e = 0 to the nonlinear untion o Popovis at e =, whih is given in Equation 1, depending on the value o. In order to allow or the gradual and smooth transition between the upper and lower bounds, a modiied expression o Equation 1 is used, as shown in Equation 4, where a shape parameter α has been introdued. x ( αr) ( αr ) ( αr) 1 + x = (4) Where between x = ε / ε. Knowing and ε, Equation 4 an be solved or α. The ull urve and an then be established using the same equation, Equation 4, to get dierent points (stresses and orresponding strains) using the obtained value o α. A trial and error proedure would be used to solve Equation 4 or α, due to its omplex nature. Fig. 7 shows a 12

13 amily o urves representing the solution o the equation or (α r), or a wide range o x = ε /. ε Setion analysis or establishing the interation diagram Conrete-illed FRP irular tubes under axial load and bending moment are subjeted to variable axial stresses along the depth o the member, whih are also distributed over an area o variable width. The reinorement onsists o the FRP tube, whih is a ontinuous surae. Due to the omplex nature o the geometry and stress distribution, numerial integration o stresses is used to alulate the ores, utilizing the layer-by-layer approah [Fam 2000]. The setion is subdivided into several horizontal layers as shown in Fig. 8(a). The reinorement within eah layer onsists o the portion o the FRP tube available within the depth o the layer. Fig. 8(a) shows the original and idealized setions used or analysis. Linear strain distribution and ull omposite ation are assumed. The axial ompressive and tensile stresses in the FRP tube are based on the eetive stress-strain urves o the FRP laminate in the axial diretion. The ompressive stresses in onrete are based on the dierent oninement mehanisms. The analysis is perormed or a given eentriity e, by assuming values or the extreme ompressive strain, ε, and a neutral axis depth. The strains ε(i) and orresponding stresses in FRP, (i), and onrete, (i), are alulated and used to determine the ompressive ores in the FRP and onrete, CF(i) and CC(i) respetively, as well as the tension ores in FRP, TF(i), at eah layer, i. The resultant o all the internal ores, N, as well as the orresponding moment, M, are alulated and used to alulate the eentriity [e = M / N]. I the alulated eentriity is dierent rom the value assumed initially, the neutral axis depth is hanged and the proess is repeated until the alulated eentriity is equal to the assumed one, and (M, N) are obtained as shown in Fig. 8(b) as point 1. The whole proess is repeated or dierent values o the 13

14 extreme ompressive strain ε, until the maximum values o M and N are obtained. (M, N) max are shown in Fig. 8(b) as point 2. These values normally orrespond to reahing the ultimate ompressive or tensile strength o the material in most ases. Dierent ombinations o (M, N) max are used to establish the ull interation diagram or the setion at dierent eentriities. Stress-strain urves o the FRP tube The lassial lamination theory [Daniel and Ishai, 1994] is used to alulate the eetive elasti modulus o the multi-layer laminate o the tube in the axial and hoop diretions assuming a lat membrane element subjeted to in-plane ores. This assumption is valid sine all The ultimate laminate ailure approah (ULF), whih is based on progressive ailure o dierent layers, is used to estimate the omplete stress-strain urve o the laminate, inluding the gradual redution o stiness as shown in Fig. 8(). The predited stress-strain urves o the FRP tubes in the axial diretion are shown in Fig. 1 and used in the setion analysis, whih is illustrated in Fig. 8(a). Proposed analysis proedure The analysis proedure, using the variable oninement model, an be summarized as ollows: (a) Use any available oninement model, suh as the one by Fam and Rizkalla (2001 b), to establish the stress-strain urve o onined onrete under axial ompression, inluding the values o and ε at ultimate as shown in Fig. 6(a). (b) Use the model by Popovis (1973), given in Equation 1, to establish the unonined stressstrain urve o unonined onrete as shown in Fig. 6(a). The urve is terminated at axial strain ε o equals to the ultimate axial ompressive strain o the FRP tube, obtained rom lamination theory. The axial stress orresponding to ε o is o. 14

15 () At eah eentriity e, Equations 2 and 3 are used to alulate the ultimate strength and orresponding strain ε. (d) Using and ε, Equation 4 or Fig. 7 an be used to alulate the shape ator α. (e) Using α, Equation 4 an be used again to establish the ull stress-strain urve ( - ε ) between and as shown in Fig. 6(b). The part o the urve beore, is assumed similar to the unonined urve. () The obtained stress-strain urve o onrete is used in the setion analysis or that partiular eentriity, to obtain a point on the interation diagram as shown in Fig. 8. Veriiation o the Model The model has been applied to the test speimens, rom Types I and II, in order to predit the interation diagrams, using the proedure desribed above. Also, the load-strain behavior o the olumns under pure axial load as well as the load-deletion behavior o the beams under pure bending, have been predited. Fig. 1 shows the stress-strain urve o the FRP tubes o Types I and II under axial tension, based on oupon tests as well as the predition using the lamination theory. Fig. 1 also shows the measured FRP longitudinal ultimate tensile strains in the beam tests o the onrete-illed FRP tubes, whih indiate that oupon tests ould underestimate the tensile strength o irular ilament-wound FRP tubes. In general, the predition using the lamination theory shows good agreement with test results, however, it underestimated the longitudinal ultimate strains o the tubes by 1.4 and 18.7 perent or Type I and Type II tubes respetively. Similarly, the strength and stiness o the tubes under axial ompression and hoop tension have been predited and given in Table 2. 15

16 Fig. 9(a) shows the predited stress-strain urves o onrete or Type I speimens, inluding the ull oninement model (upper bound), the unonined model (lower bound) and the variable oninement model, whih results in a dierent urve or dierent eentriities. Fig. 9(b) shows the predited stress-strain urves o onrete or Type II speimens, inluding the upper and lower bounds. It is evident that the tubes in Type II speimens provide low level o oninement, whih is also onirmed by the measured load-axial strain behavior o olumn C1- II in Fig. 4. Low oninement is attributed to the laminate struture o Type II tubes, whih resulted in low stiness in the hoop diretion as well as a high value o Poisson s ratio, and aordingly, resulted in separation between the onrete ore and the tube and delay o the oninement mehanism. Interation diagrams Using the predited stress-strain urves o the FRP tube and onrete, the setion analysis using layer-by-layer approah has been onduted in order to establish the ull interation diagram or Types I and II speimens. Fig. 5 (a) and (b) shows the experimental results as well as the predited interation diagrams using dierent oninement mehanisms, or speimens o Types I and II respetively. Fig. 5(a) shows that the variable oninement mehanism provides the best predition. It however over-estimated the moment at the balaned point by 1.6 perent and under-estimated the axial load by 17.8 perent. It is also noted that the ull oninement mehanism provides reasonable predition o the interation diagram, however, it overestimates the bending apaity under low axial loads or under pure bending. The unonined onrete model signiiantly underestimated the interation diagram. However, under pure bending, the unonined onrete model with extended strain sotening predits the bending apaity very well, whih was also reported by Fam and Rizkalla (2002). Lak o oninement in bending is 16

17 attributed to the small area o onrete in ompression as well as the strain gradient. The unonined onrete model with ultimate strain limited to underestimates the bending apaity. Fig. 5 also shows the ontribution o the plain onrete ore (without the eet o the tube) to the interation diagrams. Fig. 5(b) shows that the ull oninement model provides good agreement with the test results, inluding the ase o pure bending, mainly due to the very low level o oninement o this type o tube in the irst plae, in omparison to Type I. This is evident by the at that both the onined and unonined models provided very similar preditions at high axial load level or Type II speimens. For this reason, there was no attempt to use the variable oninement model in Type II speimens, as the predited interation urve would have been very lose to that predited using the ull oninement model. The ull oninement model underestimated the moment at the balaned point by 4.6 perent and over estimated the axial load by 7.4 perent or Type II speimens. By examining the interation diagrams, our distint zones an be reognized as shown in Fig. 5 (a) and (b). Zone 1 represents the ontribution o plain onrete ore alone. Zone 2 relets the ontribution o the FRP tube, provided that the oninement eet on the onrete ore is ignored. In this ase, it an be notied that the ontribution o the tube (zone 2) to the bending moment is muh more signiiant than it is to the axial load, sine it provides the lexural tension reinorement element to the system. It should also be noted that the sizes o zones 1 and 2 are very similar or both Type I and II speimens. Zone 3 relets the eet o the oninement mehanism imposed by the FRP tube, whih is muh more signiiant in ase o Type I speimens than it is in Type II, due to the better laminate struture o the tube. The oninement eet is insigniiant under pure bending, however, the ontribution o zone 3 beomes more signiiant as the axial load inreases, due to the larger portion o the setion beoming under 17

18 ompression, as the neutral axis shits. Zone 4 relets the eet o the extended strain sotening (dutility) or onrete beyond the axial strain. Load-deletion behavior o beams Fig. 3 shows the measured and predited load-deletion diagrams o beams B1-I and B1-II. The predition is based on the stress-strain urve o unonined onrete with extended strain sotening. Tension stiening eet has also been onsidered (Fam 2000). The setion analysis using layer-by-layer approah is perormed or the ase o pure bending and the momenturvature response o the setion is obtained. The deletion at mid span is alulated by integrating the urvatures along the span using the moment-area method. The model showed good agreement with the measured response, where the dierene between the predited and measured moment apaities were 1.82 and 8 perent or B1-I and B1-II respetively. Load-axial strain behavior o onentrially loaded olumns Fig. 4 shows the measured and predited axial load-axial strain behavior o the olumns o Type I and II speimens. The response was predited using the stress-strain urve o the onined onrete (given in Fig. 9 or the ase o zero eentriity), whih is based on the model by Fam and Rizkalla (2001 a). Mirmiran et al (1998) have shown that or length-to-diameter ratios (L/D) higher than 2:1, the strength o the onined onrete, u, is slightly redued aording to Equation 5. u u 2:1 2 L L = (5) D D Where = i the strength at ultimate is the peak value, while u < when the strength at u ultimate is less than the peak strength in the ase o low oninement eet suh as in C1-II olumn. For a 3:1 ratio, the redution is 12 perent, whih has been aounted or. Due to the 18

19 brittle nature o the relatively high strength onrete, the load-strain urves do not show a smooth response. Instead, a number o load drops are observed. For the C1-I olumn, the predited response shows a reasonable agreement with the observed behavior. For the C1-II olumn the model over estimated the post-peak response o the strain-sotening portion. The dierene between the measured and predited axial load apaities o both C1-I and C1-II was 11 perent. Parametri Study A parametri study has been onduted using the proposed analytial model in order to study the eets o the thikness o the FRP tube as well as dierent ratios o stiness in the axial and hoop diretions, whih are ontrolled by the laminate struture. The parametri study onsidered a GFRP tube o 300 mm inner diameter and [0/90] s symmetri ross ply, E-glass/epoxy laminate, illed with 40 MPa onrete. Three dierent laminate strutures o the tube are onsidered by varying the proportions o ibers in the axial [0] and hoop [90] diretions, inluding 1:9, 1:1 and 9:1 ratios. A 1:9 laminate has 90 perent o the ibers oriented in the hoop diretion, whih is seleted to provide high level o oninement. A 9:1 laminate has 90 perent o the ibers oriented in the axial diretion and is seleted to provide high lexural apaity and less oninement level or axial strength. A 1:1 laminate represents a balaned eiieny o the tube under bending and axial load. For eah laminate, three values o wall thikness, t, have been onsidered, inluding 2, 8 and 16 mm, whih are equivalent to reinorement ratios o 2.7, 10.4 and 20.3 perent respetively. The variable oninement model o onrete was adopted in the analytial model to establish the interation diagrams or the 9 ases under onsideration. Fig. 10 shows the interation diagrams obtained using the proposed variable oninement model, inluding three urves representing the three laminate strutures or eah tube s speii wall 19

20 thikness. The axial load and bending moments are normalized with respet to the diameter D o and onrete ompressive strength. The igure learly demonstrates the inreased axial and bending apaities as the thikness o the tube is inreased, as evident by the enlarged size o the interation diagram or a speii laminate struture. Fig. 10 also demonstrates that inreasing the axial stiness o the tube (1:9 to 9:1) inreases the pure lexural apaity signiiantly, or all range o wall thikness. On the other hand, the inrease in pure axial strength might not neessarily be attributed to the inrease o the hoop stiness o the tube (9:1 to 1:9) or all the range o wall thikness. For example, in the ase o 2 mm thik tube, the pure axial strength is inreased as the hoop stiness o the tube is inreased, while in the ase o 16 mm thik tube, the pure axial load has inreased when the hoop stiness o the tube was redued. This interesting behavior an be explained by examining Equation 6, whih represents the total ultimate axial load P n in terms o the ontributions o the onrete ore, P, and the FRP tube, P is the produt o the onined strength o onrete while P (Fam 2000). and the area o the onrete ore, A, P is the produt o the stiness o the tube in the axial diretion in terms o the eetive axial elasti modulus, E, the ross setional area o the tube A, and the ultimate axial strain, ε, whih is assumed equal or both the tube and onrete ore based on omposite ation. P = P + P n = A + A E ε (6) As the hoop stiness o the tube is redued (1:9 to 9:1 or example), is also redued, and onsequently, the irst term o Equation 6 is also redued. However, the seond term o Equation 4 is inreased simultaneously due to the inreased axial stiness o the tube E, on the expense o the redued hoop stiness (or the same wall thikness). For a small wall thikness, 20

21 the rate o redution o P is higher than the rate o inrease o P when the hoop stiness is redued, and thereore, the over all ultimate load P n is redued. On the other hand, large thikness tubes would experiene an over all inrease in the ultimate axial load P n despite o the redution o the hoop stiness, mainly beause o the rate o inrease o P, whih is higher than the rate o redution o P. At a ertain intermediate wall thikness, the inrease o P almost balanes the redution o P, and P n remains almost onstant, as shown in zone A o Fig. 10 or the 8 mm thik tube ( D o t = 40). For tubes with larger wall thikness ( D o t = 40 to 21), the interation urves or dierent laminates do not interset eah other, while or smaller wall thikness ( D o t = 40 to 152), the interation urves interset at ertain points. This behaviour ould have a great impat on optimisation rom design point o view. For example, or tubes with small wall thikness, under small eentriities suh as e 1, shown in Fig. 10, the 1:9 laminate is the most eiient design out o all laminate strutures, sine it governs the outer envelope o the amily o urves at this region, while under large eentriities suh as e 2, the 9:1 laminate is the most eiient design as it orms the outer envelope or all the urves. At ertain intermediate eentriities suh as e 3, all laminates provide almost same eiieny, where the interation urves interset. On the other hand, or tubes with large thikness, the design eiieny or all range o eentriities seem to be governed by tubes with highest axial stiness suh as the (9:1) laminate. It is also evident rom Fig. 10 that a ertain design strength (ombination o M and N) an be ahieved by several ombinations o both laminate struture and wall thikness. 21

22 Summary and Conlusions The axial load bending moment interation diagrams o onrete-illed FRP tubes, o two dierent types, have been established experimentally and analytially. The two types o tubes have almost the same diameter and wall thikness, however, the laminate struture o Type I tube resulted in muh better oninement eiieny due to the lower Poisson s ratio and higher hoop stiness. Three oninement mehanisms o onrete are examined, inluding an upper bound ull oninement model, independent o the eentriity o the load, a lower bound unonined model, and a variable oninement model, aounting or the gradual hange o state o bi-axial stresses developed in the tube as the eentriity hanges. Lamination theory, using ultimate laminate ailure approah, was adopted to relet the gradual redution o stiness o the tube due to the laminate progressive ailure. Analytial model based on setion analysis using layer-by-layer approah was developed. The model has been veriied and extended to a parametri study to examine the eets o wall thikness and laminate struture o the tube using various proportions o ibers oriented in the axial and irumerential diretions. The ollowing onlusions are drawn: 1. Interation urves o onrete-illed FRP tubes o moderate diameter-to-thikness ratios are similar to that o reinored onrete members. As axial load inreases, the moment apaity also inreases and ailure is governed by rupture o the FRP tube at the tension ae. A balaned point is reahed, beyond whih, the moment apaity is redued by inreasing the axial load and ailure is governed by rushing o the FRP tube in the ompression side. 2. The variable oninement model o onrete provides best predition o interation diagrams. Full oninement model also provides reasonable predition, however, or 22

23 tubes with adequate oninement stiness (suh as Type I), it overestimates bending apaity at low axial loads. 3. The unonined onrete model signiiantly underestimates the interation diagrams or onrete-illed FRP tubes with adequate oninement stiness. However, the unonined model with extended strain sotening predits very well the pure bending strength. 4. Laminate struture o FRP tubes signiiantly aets the interation diagram. Type I tubes had higher eetive elasti modulus in the hoop diretion and signiiantly lower Poisson s ratio than Type II tubes, whih resulted in better oninement as evident rom the larger size o interation urve and load - strain behavior o the olumns o Type I. 5. For a given laminate struture, inreasing the wall thikness o the tube inreases the axial and bending strengths as evident rom the inreased size o interation diagram. The urve ould however hange rom the typial shape with the balaned point being the maximum moment (or small thikness tubes), to a shape with the pure bending strength being the maximum moment, and the ull urve is governed by ompression ailure (or large thikness tubes, partiularly or tubes with higher axial stiness). 6. For both onrete-illed thin and thik tubes, inreasing the ratio o ibers in axial diretion signiiantly inreases the lexural strength. 7. Inreasing the ratio o ibers in the hoop diretion would inrease the axial strength o onrete-illed thin tubes only. 8. Axial strength o onrete-illed thik tubes tends to inrease by inreasing the amount o ibers in the axial diretion rather than in the hoop diretion. In thik tubes, the ontribution rom axial stiness o the tube is more signiiant than the gain rom oninement. 23

24 9. For small thikness tubes, hanging the proportion o ibers in the axial and hoop diretions, results in a amily o interation urves, interseting at ertain points, whih provides an optimum laminate struture or any partiular eentriity, or a given wall thikness. For relatively thik tubes, the interation urves do not interset and the optimum laminate seems to be the one with maximum axial stiness and minimum hoop stiness, regardless o the eentriity. 10. There are several ombinations o wall thikness and laminate struture that satisies a partiular ombination o bending moment and axial load. Aknowledgements The authors wish to aknowledge inanial support provided by the Network o Centres o Exellene on Intelligent Sensing or Innovative Strutures (ISIS Canada), the University o Manitoba, North Carolina State University, and Lanaster Composite. The authors are also grateul to Moray MVey, Robert Greene, David Shnerh, and Jerry Atkinson or their assistane during the experimental program. Notations A = Cross-setional area o the onrete ore A = Cross-setional area o the FRP tube CC () i = Compression ore in onrete in a general strip i in a onrete-illed FRP tube CF () i = Compression ore in FRP within a general strip i in a onrete-illed FRP tube = Neutral axis depth D = Diameter o onrete-illed FRP tube 24

25 D o = Outer diameter o the tube E o = Initial tangential elasti modulus o onrete E se = Seant modulus o onrete at E = Eetive elasti modulus o FRP tube in the axial diretion e = Eentriity o axial load measured to the enter o the irle = Axial ompressive stress in onrete () i = Axial stress level in onrete at a general strip i in a onrete-illed FRP tube = Conrete ompressive strength = Peak axial strength o FRP onined onrete under onentri axial load o = Axial ompressive stress in onrete orresponding to ε o u = Compressive strength o FRP onined onrete at ultimate = Peak axial ompressive strength o partially onined onrete in presene o eentriity () i = Axial stress level in the FRP tube at a general strip i in a onrete-illed FRP tube H = Height o onentrially or eentrially loaded olumn speimens i = General strip within the ross-setion o a onrete-illed FRP tube L = Span o beams L = Length o olumn M = Bending moment M n = Flexural apaity N = Axial ompression ore P = Load arried by onrete in onrete-illed tube under axial ompression load 25

26 P = Load arried by the FRP tube in onrete-illed tube under axial ompression load P n = Axial ompression apaity r = Constant in Mander s equation relates the initial tangential modulus E o to the seant modulus o onrete E se TF () i = Tension ore in the FRP tube in a general strip i in a onrete-illed FRP tube t = Wall thikness o FRP tube α = Shape parameter or the stress-strain urve o partially onined onrete ε () i = Axial strain at a general strip i within the ross-setion o onrete-illed FRP tube ε = Axial ompressive strain orresponding to ε = Compressive strain at the extreme onrete ibers o the member ε o = Ultimate axial ompressive strain o onrete, whih equals to the ultimate axial strain o the FRP tube in ompression. ε = Axial ompressive strain o onrete orresponding to ε = Axial strain o onrete orresponding to ε = Axial ompressive strain orresponding to x = Ratio between any axial strain level ε and the strain ε x = The ratio ε / ε REFERENCES 1. ACI Committee 318 Building Code Requirements or Reinored Conrete and Commentary, ACI 318M-95/ACI 318RM-02, Amerian Conrete Institute, Detroit,

27 2. Daniel, I. M., and Ishai, O. Engineering Mehanis o Composite Materials, Ed. by Oxord University Press, New York, Fam, Amir Z., and Rizkalla, Sami H., Behavior o Axially Loaded Conrete-Filled Cirular Fiber Reinored Polymer Tubes, ACI Strutural Journal, Vol.98, NO.3, May-June 2001(a), pp Fam, Amir Z. and Rizkalla, Sami H., Coninement Model or Axially Loaded Conrete Conined by FRP Tubes, ACI Strutural Journal, Vol.98, NO.4, July-August 2001(b), pp Fam, Amir Z. Conrete-Filled Fiber Reinored Polymer Tubes For Axial and Flexural Strutural Members, Ph.D. Thesis, 2000, The University o Manitoba, pp Fam, Amir Z. and Rizkalla, Sami H., Flexural Behavior o Conrete-Filled Fiber-Reinored Polymer Cirular Tubes, Journal o Composites or Constrution, ASCE, Vol. 6, Issue 2, May 2002, pp Iskander, M., and Hassan, M. (1998), State o the Pratie Review in FRP Composite Piling, Journal o Composites or Constrution, ASCE, 1998, 2(3), pp Karbhari, V. M. et al Strutural Charaterization o Fiber-Reinored Composite Short- and Medium-Span Bridge Systems, Proeeding o European Conerene on Composite Materials (ECCM-8), June 1998, Vol. 2, June 1998, pp Lampo, R., Federal Interest Gives Reyled Plasti Lumber a Leg up, ASTM Standardization News, 1996, pp Lampo, R. et al. (1998). Development and Demonstration o FRP Composite Fender, Load bearing and Sheet Piling Systems, USACERL Tehnial Report 98/

28 11. Mirmiran, Amir and Shahawy, Mohsen Behavior o Conrete Columns Conined by Fiber Composites, Journal o Strutural Engineering, May 1997, pp Mirmiran, Amir et al Large Beam-Column Tests on Conrete-Filled Composite Tubes, ACI Strutural Journal, Title no. 97-S29, Marh-April 2000, pp Mirmiran, Amir et al Eet o Column Parameters on FRP-Conined Conrete, Journal o Composites or Constrution, ASCE, Vol. 2, No. 4, Nov. 1998, pp Popovis, S. A Numerial Approah to the Complete Stress-Strain Curves or Conrete, Cement and Conrete Researh, V.3, No.5, pp Samaan, M., Mirmiran, A., and Shahawy, M. Model o Conrete Conined by Fiber Composites, Journal o Strutural Engineering, Sept. 1998, pp Seible, Frieder Advaned omposites materials or bridges in the 21 st entury, Proeeding o the First International Conerene on Composites in Inrastruture (ICCI 96), Tuson, Arizona, Jan. 1996, pp Teng, J. G., Chen, J. F., Smith, S.T. and Lam, L. FRP Strengthened RC Strutures, Ed. by John Wiley & Sons Ltd., England,

29 List o Tables Table 1 Table 2 Details o test speimens Details o the GFRP tubes 29

30 List o Figures Fig. 1 Fig.2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Stress-strain urve o FRP tubes under axial tension Test setup and ailure modes o beams, onentrially loaded olumns and eentrially loaded olumns Load-deletion behavior o test beams Axial load-axial strain behavior o the olumn speimens Experimental and predited interation diagrams or test speimens Coninement mehanisms o onrete as aeted by the bi-axial state o stress in FRP tube Shape ator α at dierent axial stress levels Summary o the analysis o onrete-illed FRP tubes subjeted to ombined bending and axial loads Predited stress-strain urves o onrete or test speimens Normalized interation diagrams or onrete-illed FRP tubes o dierent thikness and laminate struture 30