STRENGTH AND DUCTILITY OF HYBRID FRP ... - CiteSeerX

STRENGTH

AND

DUCTILITY OF HYBRID FRP-CONCRETE BEAM-COLUMNS

By Amir Mirmiran,1 Member, ASCE, Mohsen Shahawy,2 and Michael Samaan3 ABSTRACT: High strength-to-weight ratio and resistance to electro-chemical corrosion have made fiber-reinforced plastic (FRP) materials attractive to civil engineers. This paper presents a study on the beam-column behavior of a high-performance structural member made of concrete-filled FRP tubes (CFFT). The angle-ply FRP tube is a stay-in-place formwork, providing confinement as well as flexural and shear reinforcement. It also acts as a protective jacket for concrete core in harsh environments. A total of five 178 ⫻ 178 ⫻ 1,320 mm specimens were tested at various combinations of axial and transverse loads to develop a full moment-thrust interaction diagram for the hybrid column. In the compression control region, CFFT columns proved as strong as equivalent conventional reinforced concrete (RC) columns with as high as 6% reinforcement. Failure of CFFTs was ductile, and with considerable warning. Furthermore, toughness and energy-based ductility of CFFTs were quite comparable to those of conventional RC columns. It was also shown that the Euler-Bernouli beam theory is applicable to CFFTs, provided that composite action between the tube and the concrete core is fully developed.

INTRODUCTION High strength-to-weight ratio, electro-chemical corrosion resistance, and orthotropic properties of fiber-reinforced plastics (FRP) have made them attractive to civil engineers, faced with deteriorating infrastructure. Fiber wrapping is perhaps one of the more successful applications of FRP, simply because strength enhancement is accompanied by considerable cost savings over traditional retrofitting alternatives (Saadatmanesh et al. 1994). In new construction, hybrid FRP-concrete systems offer the same benefits by combining the mass, stiffness, damping, and low cost of concrete with the fabrication speed, low weight, high strength, and durability of FRP. Deskovic et al. (1995) proposed a hybrid beam consisting of a fiberglass box section with a concrete layer cast onto the compression flange and a thin carbon fiber laminate bonded to its tension flange. Similarly for beam columns, concrete can be cast in an FRP tube, which acts as permanent formwork, protective jacket, confinement, and shear and flexural reinforcement (Mirmiran and Shahawy 1996). Cost savings include eliminating formwork and the need for its removal, reinforcement cage, and high maintenance of reinforced concrete (RC) in corrosive environments. Though an extension of concretefilled steel tubes (CFSTs), concrete-filled FRP tubes (CFFTs) are considered the better alternative because orthotropic properties of FRPs allow uncoupling the axial and hoop directions. Therefore, fiber architecture of the tube and its fabrication technique become very important. The tube may be made by filament winding, SCRIMP, or centrifugal methods. Fibers may be carbon (with higher stiffness and strength) or glass (with lower costs). PREVIOUS RESEARCH Prion and Boehme (1994) tested 26 152-mm-diameter CFSTs with 1.7 mm tube thickness and 73–92 MPa concrete 1 Assoc. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Cincinnati, Cincinnati, OH 45221. 2 Dir., Struct. Res. Ctr., Florida Dept. of Transportation, Tallahassee, FL 32310. 3 Struct. Des. Engr., Dr. Sabri Samaan Consulting, Giza, Egypt; formerly Grad. Stud., Dept. of Civ. and Envir. Engrg., Univ. of Central Florida, Orlando, FL. Note. Associate Editor: Julio A. Ramirez. Discussion open until March 1, 2000. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on March 11, 1998. This paper is part of the Journal of Structural Engineering, Vol. 125, No. 10, October, 1999. 䉷ASCE, ISSN 0733-9445/99/0010-1085– 1093/$8.00 ⫹ $.50 per page. Paper No. 17889.

core. Beam-column specimens failed in a ductile mode by rupture of steel in tension zone, while failure of eccentrically loaded columns was abrupt in the form of lateral buckling. Significant slippage between steel and concrete was reported in flexure tests (10–13 mm at each end). It was also noted that secondary moments due to P-⌬ effect accounted for 20% of the ultimate moments. Fardis and Khalili (1981) tested five 76 ⫻ 152 ⫻ 1,220 mm plain concrete beams wrapped with glass fibers. Even though specimens were capped with fabric at both ends, some slippage was reported. Failure was noted as crushing of concrete followed by bursting of FRP on the compression side. Nanni and Norris (1995) tested 19 152-mmdiameter circular and 7 152 ⫻ 203 mm square, 1,500 mm long RC specimens wrapped with either braided aramid/epoxy tapes (at 0 or 25 mm pitch) or preformed glass-aramid/epoxy shells. All specimens were subjected to a cyclic lateral load at midspan, while for some a constant axial load was also applied through a concentric prestressing rod. Significant improvement in ductility was reported. Previous research on CFFTs was initially directed to developing a confinement model from uniaxial compression tests of FRP-encased concrete cylinders (Mirmiran and Shahawy 1997a,b; Samaan et al. 1998). The model was then expanded to consider the effect of cross-sectional shape, column length, and tube-core interface bond (Mirmiran et al. 1998b). Flexural behavior of CFFTs presents additional issues to consider. After short beam shear tests showed considerable slippage between the tube and the core, new FRP tubes with shear ribs were manufactured and tested with success (Mirmiran et al. 1998a). In this paper, beam-column behavior of CFFTs is studied by developing an experimental moment-thrust interaction diagram. Applicability of Euler-Bernouli beam theory to hybrid members is examined, and finally their strength and ductility are compared with equivalent RC columns. It should be noted that this study focuses on short-term static loading of CFFTs. Other issues of concern for the proposed system include creep of fiber composites under sustained loads, fatigue of the hybrid system, behavior under seismic loading, long-term durability, glass-alkali reaction, ultraviolet effects, fire protection, damages due to impact and vandalism, possible repair schemes, and finally, connections of the proposed system with beams and columns, pier caps, and footings. EXPERIMENTAL PROGRAM Materials and Fabrication A total of five 178 ⫻ 178 ⫻ 1,320 mm concrete-filled FRP tubes were tested. The core was ready-mix concrete with an JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999 / 1085

FIG. 1. TABLE 1. ter Resina

Cross Section of Ribbed FRP Tube

Mechanical Properties of Glass Fibers and Polyes-

Property (1) Specific gravity Tensile strength (MPa) Tensile modulus (MPa) Shear modulus (MPa) Poisson’s ratio

450-yield E-glassb (2)

Polyester resin (3)

2.58 2,186 69,640 30,130 0.22

1.41 72 4,344 1,600 0.36

a

Manufacturer’s data (average values). Resin-impregnated (ASTM Standard D-2343).

b

average 28-day compressive strength of 18.75 MPa. As shown in Fig. 1, the tubes were made of one interior ply of bidirectional 24-oz E-glass woven roving on all its four sides, and 15 E-glass angle plies with a winding angle of ⫾75⬚. The glass fibers were 67B-RO99 from Vetrotex/CertainTeed, and the resin was DION-FR-6692T polyester from Reichold (see Table 1 for the average material properties). The tubes were filamentwound over a collapsible mandrel made of four 63 1/2 ⫻ 63 1/2 ⫻ 9 1/2 mm aluminum angles (1,676 mm long), placed with a 25 mm gap in between. On each face of aluminum angles, a series of 51 ⫻ 46 ⫻ 6.4 mm beveled maple-wood plates were mounted with a 12.7 mm gap in between. The spaces between the plates were filled with a special paste as catalyst. It consisted of DION 33-611 polyester resin (from Ashland Chemicals), silica fume, 1% (by volume) 6.4 mm long chopped glass fibers from PPG, and 1.5% (by volume) MEKP (methyl ethyl ketone peroxide as catalyst). This paste would form a series of 42 mm wide longitudinal and 19 mm wide transversal shear connector ribs on the interior surface of the tube, all ribs being 6.4 mm thick. Once the paste cured, the E-glass woven roving and polyester resin was placed on each side of the mandrel by hand lay-up, and then 15 plies of E-glass/polyester were added on the filament-winding machine. For more details on the specimen fabrication, see Mirmiran (1997). Test Procedure Of the five concrete-filled tubes, one (Specimen B) was subjected to a four-point pure flexure test and another (Specimen 1086 / JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999

C) was tested in uniaxial compression, while the other three (Specimens BC1, BC2, and BC3) were subjected to combined axial-flexural loading at three different levels of axial loads, corresponding to 1/8 Po, 1/2 Po, and 3/4 Po, respectively, where Po is the maximum capacity of the section under uniaxial compression. Po was determined from the average strength of short columns, as explained later in ‘‘Ancillary Tests.’’ The schematic of test setup is shown in Fig. 2. All five specimens were tested horizontally between two reaction walls, 1 ton concrete blocks, strong floor, and a top 915 mm reaction beam. The specimens were supported on two smooth half-cylinders 1,220 mm apart. Flexural loads were applied by a vertical jack reacting on the top steel beam. The load was transferred through a 510 mm long steel I-beam to two 51 mm diameter rollers on the top surface of the specimens at third points of span. Axial loads were applied by a horizontal jack reacting on the walls. End surfaces of specimens were grinded, and a 6.4 mm lead plate at each end further secured a smooth loading surface. End pin conditions were simulated with a 51 mm diameter roller between two end plates. Beam columns were loaded in two phases. In Phase 1, axial load was applied to the desired level. In Phase 2, while maintaining the axial load, the specimen was subjected to a monotonically increasing transverse load (in four-point loading) until failure. Instrumentation Test data were collected by a Megadac data acquisition system. Axial and flexural loads were monitored by 1,780 kN and 220 kN load cells, respectively. Also, pressure from hydraulic jacks was monitored through pressure transducers. Specimen B was instrumented with nine strain gauges, mounted on the surface of the tube at midspan, with one transverse gauge at the top, and eight others in the axial direction as follows: one at the top, one at the bottom, and three on either side evenly distributed across the depth of the section. No embedded gauge was used. Three LVDTs, one at the midspan and two under the load points, monitored the deflections. Additional LVDTs were used to monitor any uplift from the support, though results determined that to be negligible. Specimen C was instrumented with 12 axial and 12 transverse gauges mounted at the top quarter, centerline, and the bottom

FIG. 2.

Schematic of Beam-Column Test Setup

quarter, on all four sides of the specimen. Also, two LVDTs, one at each end of the specimen, monitored its axial shortening. Specimens BC1, BC2, and BC3 were instrumented exactly the same as Specimen B with two additional axial gauges mounted on the soffit at the quarter-span points. A total of seven LVDTs were used; three to measure vertical deflections at the midspan and under the load points, two to measure axial deformations at each end, and two to measure any uplift at the supports. All strain gauges were 60 mm long polyester wire gauges. Observed Behavior Specimen B. As the load increased, white patches and flexural cracking developed at the soffit near the midspan, then spread along the beam. The white patches indicated flow of resin in the tube, leaving only white glass fibers to take the load. Total lateral load peaked at 51.5 kN when a major crack developed on the tension side at the midspan. The failure was, however, gradual and progressive. The ultimate deflection was 20 mm, which is 1/60 of the span length. In Specimen B (and all others), no slippage or relative movement was observed between the tube and the concrete core at the end surfaces. This indicated that the ribs had arrested any potential slippage and a perfect bond existed between the tube and the concrete. Specimen C. At 50% of the ultimate load, cracking of concrete could be heard. Significant white patches and transverse cracks were observed between the midspan and the south end of the specimen at 80–90% of the ultimate load. Axial load peaked at 1,026 kN, over twice the strength of unconfined concrete core (0.85f⬘A c g). The specimen failed with noticeable buckling, an axial shortening of 2.3%, and bursting of the tube on the top surface at about 0.08 L from the midspan, where L = specimen length. Transverse strains were noted to be much lower than the equivalent circular sections (Mirmiran and Shahawy 1997a), indicating lower confinement effectiveness for square sections. This has also been verified in a separate shape effect study (Mirmiran et al. 1998b). Specimen BC1. A slight camber was developed in the specimen while applying axial loads. Cracking of concrete was heard late in Phase 2 of loading (lateral loads). The tension face of the tube cracked at about 75% of the peak lateral load. The cracks gradually increased in intensity and depth, resulting in a tension failure. It is necessary to note that a balanced condition in an FRP-reinforced concrete section (FRP-RC) is defined as one where the concrete crushes at the same time that the FRP reinforcement ruptures (‘‘State-of-the-art’’ 1996). This is clearly different from the conventional steel-RC section, in which balanced condition is defined for yielding (and not failure) of steel reinforcement. However, based on the def-

inition of balanced condition for FRP-RC sections, reinforcement ratios less than the balanced ratio would result in a tension failure and rupture of FRP. The specimens in this study had only a single ply of woven roving, and therefore failed in tension at low levels of axial load. After the test, the tension side of the tube was removed and concrete was found intact except for a single major crack across the depth at the midspan (Fig. 3). The ribs clearly contained the concrete core in tension and further controlled opening of the cracks. The ultimate moment was twice that of Specimen B. Specimen BC2. The camber due to axial loads was larger than Specimen BC1. Concrete cracking was first heard at 50% of the ultimate lateral load. The tube cracked near the midspan at about 85% of the ultimate lateral load. As the load in-

FIG. 3.

Cracking of Concrete Core in Specimen BC1

FIG. 4.

Specimen BC3 at Failure

JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999 / 1087

TABLE 2.

Test Results of CFFT Specimens

Specimen (1)

Nominal axial loada (kN) (2)

Actual axial loadb (kN) (3)

Primary moment (kN-m) (4)

Secondary moment (kN-m) (5)

Total moment (kN-m) (6)

Ultimate axial deflection (mm) (7)

Ultimate lateral deflection (mm) (8)

C B BC1 BC2 BC3

1,026 — 150 600 890

1,026 — 132 587 882

— 10.41 20.89 23.76 11.13

— — 2.75 10.42 8.97

— 10.41 23.64 34.18 20.10

30.2 — 3.3 22.9 33.0

— 20.3 27.9 38.4 53.3

a

Applied axial load. Actual axial load at the peak lateral load (includes some drift).

b

creased, the cracks became deeper and wider and spread along the beam. The failure, even though markedly compression, was gradual and progressive. The ultimate lateral deflection was 38.4 mm. The uplift at the supports was negligible. Specimen BC3. High axial loads in Phase 1 of loading caused cracking of the concrete core and a considerable camber in the specimen. In Phase 2, the compression flange of the tube cracked at about 90% of the peak lateral load. The failure was progressive, even though with less warning than those in Specimens BC1 and BC2. Fig. 4 shows the specimen at failure.

FRP tube were prepared, and capped with 6.4 mm lead plates. Four LVDTs were used to measure the axial deformations. The specimens were tested in the 2,500-kN MTS machine at a displacement rate of 1.3 mm/min according to ASTM Standard D 3410-95. An average compression modulus of 3,805 MPa and an ultimate strain of 3% were recorded. For more details on beam columns and ancillary tests, see Samaan (1997) and Mirmiran (1997). DISCUSSION OF RESULTS

Short Columns. Three 178 ⫻ 178 ⫻ 305 mm specimens were prepared of the same concrete mix and the same tube, except that they lacked the woven roving. The end surfaces of the tubes were ground and then capped with a 5 mm lead plate. The specimens were tested in uniaxial compression with a 2,500-kN MTS machine. The axial load (Po) and ultimate axial strain averaged at 1,200 kN, and 0.05, respectively. Tension Coupons. Four 102 ⫻ 380 mm coupon specimens were cut off the sides of the FRP tubes from the middle of each side such that the central rib was centered in the middle of each specimen. The specimens were tabbed at both ends by four layers of 24-oz E-glass woven roving and polyester resin to serve as the gripping area. All specimens were tested in pure tension at a displacement rate of 1.3 mm/min according to ASTM Standard D3039-95a. Each specimen was instrumented with two 60 mm long polyester wire gauges, one on each side. Also, two LVDTs, one on each side, were used to monitor axial displacements. An average tensile modulus of 3,340 MPa and an ultimate strain of 2% were recorded. Compression Coupons. Because of the hybrid structure of the tube, the full section, rather than flat strips, were tested in uniaxial compression. Four 127 mm long sections of the

Test results are summarized in Table 2. Axial deflection for Specimen C represents an ultimate strain of 2.3%, which is less than half that of short columns. This is attributed to the length effects, which also caused buckling of the specimen. It was further noted that hoop strains (average of four surface gauges at the midspan of Specimen C) were about 60% of those seen in comparable circular sections, indicating a much lower level of confinement in square sections (see Mirmiran et al. 1998b). Figs. 5–8 show the moment-deflection-curvature plots for Specimens B, BC1, BC2, and BC3, respectively. The bending moment is plotted versus midspan deflection and curvature. Curvatures are calculated from readings of the top and bottom strains at the midspan. For the beam-column specimens, three curves are plotted: M1 is the primary moment due to lateral loads, M2 is the secondary moment due to P-⌬ effect, and MTOT is the total moment and the section capacity. The negative deflections denote a camber in the specimen due to axial loads in Phase 1 of loading. A general bilinear trend is clear for all primary moment-curvature curves. Specimens B and BC1 both fail in tension, signifying the fact that the section was reinforced with less than balanced ratio with only a single layer of glass woven roving. Here, it is important to note that M2/MTOT ratio for Specimens BC1, BC2, and BC3 is 12, 30, and 45%, respectively. Such large P-⌬ effects, too, are due to low bending stiffness of the tube,

FIG. 5. B

FIG. 6. BC1

Ancillary Tests

Moment-Deflection-Curvature Diagrams for Specimen

1088 / JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999


FIG. 7. BC2

FIG. 8. BC3



which can be remedied either by using carbon fibers in the axial direction, or by adding to the number of layers of glass woven roving. The maximum compressive strain of 0.0034 and the hoop strain of 0.0006 for Specimen B indicate that practically no confinement was developed in pure flexure. Although compressive strain for Specimen BC1 was 0.0176— more than five times that of plain concrete—the hoop strain (from surface gauge on the compression side of the section) was only 0.0032. Therefore it appears that for this specimen, too, confinement did not play a significant role, and that the reason for the considerable section capacity was the containment of cracked concrete by the tube. On the other hand, confinement was significant for both Specimen BC2 and Specimen BC3, due to high levels of axial load. Test results were also used to develop the moment-thrust interaction diagrams for CFFTs, as explained further in the next two sections. Analytical Modeling A sectional analysis by fiber model was carried out to examine the applicability of Euler-Bernouli beam theory to CFFTs. A perfect bond was assumed between the ribbed tube and the core, as no slippage was observed in the experiments. The tube material was assumed to be linear-elastic, with properties determined from coupon tests. Since concrete is confined by the tube, its tensile strength cannot be neglected. Tension stiffening was modeled after Vecchio and Collins (1986), with an ultimate tensile strain of 2.0% as verified by tension coupon tests. Tensile modulus of concrete was taken to be the same as its initial compressive modulus. A bilinear stress-strain

FIG. 9. crete

Idealized Stress-Strain Model for FRP-Confined Con-

FIG. 10. Comparison of Experimental and Analytical Interaction Diagrams for CFFTs

curve was assumed for concrete in compression based on the model of Samaan et al. (1998), as fc =

(E1 ⫺ E2)εc

冋冉 1⫹

冊册

(E1 ⫺ E2)εc fo

n

1/n

⫹ E2εc

(1)

where εc and fc = axial strain and stress of concrete; E1 and E2 = first and second slopes; fo = intercept of the second slope with the stress axis; and n = curve-shape parameter, which mainly controls the curvature in the transition zone (Fig. 9). E2 depends on the level of confinement developed in the compression zone. An upper bound of 320 MPa was obtained for E2 from the average second slopes of the stress-strain curves for the short columns. Rochette and Labossie`re (1996) proposed a lower bound of 0 for E2 as an elastic–perfectly plastic material with no strain hardening. A similar approach was suggested by Ziara et al. (1995) for conventional RC beams with considerable transverse reinforcement. The intercept stress fo is obtained from the geometry of the stress-strain curve in Fig. 9, as given by fo = f ⬘co ⫺ E2εco

(2)

where εco is the peak strain of plain concrete. Using the upperand lower-bound values of E2, and the experimental top strains, two analytical interaction diagrams were developed for partial and full confinement. Fig. 10 shows the predicted and the experimental interaction curves. It is clear that in the case of pure flexure (Specimen B), strain hardening of concrete does not affect the moment capacity of the section. On the other hand, confinement effect is most pronounced for SpecJOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999 / 1089

FIG. 11. Interaction Diagrams of CFFTs versus Conventional RC Columns

FIG. 13. Cyclic Response of Circular CFFT in Axial and Lateral Directions

FIG. 14. Load-Deflection Curves for Specimen B versus Its Equivalent RC Beam

␻=

FIG. 12. (a) Elastic Energy Released at Failure (Naaman and Jeong 1995); (b) Equivalent Elasto-Plastic Yield (Park 1989)

imen BC3, for which the upper bound value of E2 results in a much closer prediction of the section capacity. Since effect of confinement increases with the level of axial load, it is logical to assume that strain hardening of concrete, i.e., E2, is a function of PA/Po, where PA is the applied axial load and Po is the axial capacity of the section. Comparison with Conventional RC Columns Strength For concentric loading, capacity of Specimen C is compared with that of an equivalent conventional RC section, defined as one that has the same reinforcement index, ␻, given by 1090 / JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999

␳j fj ␳s fy = f ⬘c f ⬘c

(3)

where ␳j = glass reinforcement ratio in the FRP tube; ␳s = steel reinforcement ratio in the equivalent conventional RC section; fj = ultimate compressive strength of the tube; fy = yield strength of steel; and f c⬘ = 28-day compressive strength of concrete. It is important to note that the ‘‘equivalent conventional RC section’’ does not have external confinement and therefore does not experience the same level of confinement as the CFFTs at high axial loads. The glass reinforcement ratio is about 5%, including the woven roving and the axial component of angle plies. However, compressive strength of the tube is only 115 MPa, less than 28% of the yield strength of Grade 60 steel. Therefore, the equivalent steel reinforcement ratio is only 1.4% for which the capacity of an equivalent 178 ⫻ 178 mm conventional RC section of the same concrete mix (18.75 MPa), is given by Pn = [0.85f ⬘c ⫹ ␳s( fy ⫺ 0.85f ⬘)]A c g

(4)

where Ag = gross area of the section. The above equation results in a 680 kN capacity. Therefore, CFFT is over 75% stronger than its equivalent conventional RC section. For eccentric loading, the experimental moment-thrust interaction diagram of CFFT is compared with analytical interaction diagrams for conventional RC columns with 1–6% reinforcement ratios (Fig. 11). A fiber element model was developed to analyze RC columns by discretizing the cross section into a series of strips (for uniaxial bending) or fibers (for biaxial bending). The following assumptions were employed (for details, see Samaan 1997):

FIG. 15. Load-Deflection Curves for Specimen BC1 versus Its Equivalent RC Beam-Column


1. Plane sections remain plane and normal to the neutral axis after bending. 2. Perfect bond exists between concrete and the steel rebars. 3. The reinforcement is placed in two equal layers on the tension and compression sides. 4. An elastic–perfectly plastic stress-strain curve is assumed for Grade 60 steel. 5. The model of Mander et al. (1988) is used for confined concrete. Confinement for the concrete core in the RC section is provided by code-specified lateral ties (Building code 1995). The initial modulus of elasticity for concrete is taken after Carrasquillo et al. (1981). 6. The model of Mander et al. (1988) is also used for the unconfined concrete cover up to a strain of 2εco, where εco (equal to 0.002) is the strain corresponding to the peak stress of unconfined concrete. The descending branch is extended by a straight line to a strain of 3εco at zero stress. The initial modulus of elasticity for concrete is, again, taken after Carrasquillo et al. (1981). 7. Tension stiffening of concrete is included according to the model of Stevens et al. (1991). A linear-elastic relationship is assumed for tensile strains less than the cracking strain. The modulus of elasticity in tension is assumed to be the same as the one in compression. By examining the comparative plots in Fig. 11, it is evident that CFFT has an enhanced performance in the compression failure region, making it comparable to a 6% equivalent conventional RC section. In pure flexure, however, the CFFT specimen is comparable to a 1.2% RC section, which is


slightly lower than its equivalent steel reinforcement ratio of 1.4%. Higher capacity in compression is due to confinement, which results in higher ultimate strains. Moreover, the internal shear ribs effectively distribute the load and contain the cracked concrete core. It is important to note here that, contrary to conventional RC sections, if one were to compare the CFFTs with equivalent concrete-filled steel tubes (CFSTs), a similar level of confinement would be observed in both systems. Such comparison was made by Samaan et al. (1998) between published test results on two CFST and CFFT specimens with the same level of confinement ratio, i.e., ratio of confinement pressure to the unconfined strength of concrete core. The results indicated that whereas the confinement effectiveness (ratio of confined to unconfined strengths of concrete core) are reasonably close, the shape of the response curve is completely different. Moreover, the dilatancy and volumetric response of FRP-confined and steel-confined concrete are significantly different from each other. Ductility Ductility of a member is defined as its ability to sustain inelastic deformations prior to collapse, without substantial loss of strength. A ductile system displays sufficient warning before catastrophic failure. Ductility is generally measured by the ratio of the ultimate deformation—deflection, curvature, or rotation—to that at the first yielding of steel reinforcement. However, such definition of ductility is not directly applicable to FRP or FRP-reinforced concrete members. Therefore, toughness has been suggested (Smart and Jensen 1997) as a measure of deformability of such members, since it generally indicates the ability to resist crack growth (or fast fracture). Toughness is calculated by integrating the area under the loaddeflection curve. However, large deformations do not necessarily warrant a ductile failure, because they may be due to low stiffness. Linear-elastic response of FRP reinforcement often stores large amounts of elastic energy in the structure, release of which may prove devastating. Therefore, the following two measures of ductility are considered as the basis of comparison between CFFT and equivalent conventional RC sections: 1. The yield-based ductility index follows the conventional definition of ductility, as ␮D =

⌬u ⌬y

(5)

where ⌬u and ⌬y = ultimate and yield deflections, respectively. The yield deformation is defined as that of an equivalent JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999 / 1091

TABLE 3.

Toughness and Ductility of CFFT Specimens versus Equivalent RC Columns

Equivalent steel ratio

Toughness (kN-mm)

Energy-based ductility ratio

Yield-based ductility ratio

Specimen (1)

PA /Poa (2)

␳gg (3)

␳gs (4)

CFFT (5)

RC (6)

CFFT (7)

RC (8)

CFFT (9)

RC (10)

B BC1 BC2 BC3

0% 11.0% 48.9% 73.4%

1.4% 1.4% 1.4% 1.4%

1.3% 2.2% 4.0% 4.1%

623 2,373 2,549 678

859 1,028 434 157

3.65 2.59 2.64 2.36

17.99 5.71 2.27 2.42

10.24 4.73 2.16 1.43

13.12 6.88 2.64 2.34

a

PA = actual axial load at peak lateral load, and Po = nominal strength of the section (1,200 kN).

elasto-plastic system with the same elastic stiffness and ultimate load as those of the real system [Fig. 12(a)]. This definition was first suggested by Park (1989) for nonlinear materials or when various parts of a system commence their yielding at different load levels. 2. The energy-based ductility index takes into account the portion of the total absorbed energy, ETOT (i.e., toughness), that is released at failure, EEL. This definition was first suggested by Naaman and Jeong (1995) for concrete beams prestressed with FRP tendons, and is given by ␮* D =

1 2

冉

冊

ETOT ⫹1 EEL

(6)

For elasto-plastic materials such as steel, both measures of ductility result in exactly the same value. For nonlinear systems, Naaman and Jeong (1995) suggest that the unloading slope at failure s be approximated as the weighted average of the two initial slopes s1 and s2 of the load-deflection curve [Fig. 12(b)]. This has been justified for CFFTs by several uniaxial cyclic load tests (Mirmiran and Shahawy 1997a). For example, Fig. 13 shows a typical response of a 152 ⫻ 305 mm concrete-filled FRP tube made of S-glass/polyester and subjected to three cycles of axial loading and unloading to failure (Samaan 1997). No substantial degradation of the unloading slope is evident in either the axial or the lateral direction. Figs. 14–17 show the experimental P-⌬ curves for Specimens B, BC1, BC2, and BC3, respectively. In each figure, an analytical P-⌬ curve for the equivalent conventional RC section with the same maximum primary moment is shown. In order to develop the analytical P-⌬ curves, first the steel reinforcement ratios were calculated that would result in the same maximum primary moments as those of CFFTs. The moment-curvature (M-␾) curves were generated using the same assumptions as those explained earlier for the interaction diagrams. The M-␾ curves were then used to generate the P-⌬ curves by the conjugate beam method. As suggested by Park and Paulay (1975), the ultimate capacity of CFFT and RC sections was taken as 80% of their peak strength. The toughness and ductility of the two systems are compared in Table 3. The equivalent steel reinforcement ratio for the CFFT section is calculated from (3), whereas the steel reinforcement ratio for the equivalent conventional RC section is calculated such that it would result in the same maximum primary moments as those of CFFTs. It is clear that except for the case of pure flexure, the equivalent reinforcement ratio is much less for CFFTs than for their equivalent conventional RC sections. Moreover, the reinforcement ratios for RC sections include only the axial rebars, as the transverse steel is separate. This further indicates the effectiveness of CFFTs as compared with RC sections. The CFFTs also have toughness values higher than their equivalent conventional RC section, except in pure flexure. Higher toughness values, however, indicate larger deformations and lower stiffness for CFFTs, and not necessarily a more ductile failure. On the other hand, both ductility measures (yield-based and energy-based ratios) indicate that whereas CFFTs are not as ductile as the conventional 1092 / JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999

RC columns in the tension failure region, they are quite comparable to RC sections at higher levels of axial load. CONCLUSIONS Beam-column behavior of concrete-filled FRP tubes (CFFTs) was investigated by testing five 178 ⫻ 178 ⫻ 1,320 mm specimens at various combinations of axial and transverse loads to develop a moment-thrust interaction diagram. The following conclusions are made for the parameters considered in this study: 1. The Euler-Bernouli beam theory is applicable to CFFTs, provided that composite action between the tube and the concrete core is fully developed. 2. The shear connector ribs proved effective in arresting any potential slippage between the tube and the concrete. 3. Under concentric loading, CFFTs are considerably stronger than their equivalent conventional RC counterparts, mainly because of full-section enclosure and confinement of concrete. 4. In order to effectively utilize the confinement in beamcolumns, a compression failure is necessary. In the compression control region, CFFT columns proved as strong as equivalent conventional RC columns with as high as 6% reinforcement. 5. Failure of CFFTs was ductile, and with much warning. Furthermore, toughness, and ductility measures for CFFT beam-column specimens were quite comparable to those of their equivalent conventional RC sections. Clearly, CFFTs are more advantageous at higher levels of axial loads. Finally, is should be noted that since the tube governs the flexural behavior as well as the level of confinement, its design can be tailored to achieve the required strength and stiffness in the axial and transverse directions. ACKNOWLEDGMENTS Financial support for this study was provided by the Florida and U.S. Departments of Transportation, under Contract No. B-9135. Additional support was provided by the National Science Foundation CAREER Award to the first writer under Grant No. CMS-9625070. The writers are grateful to Marine Muffler Corp. for providing the materials and fabricating the FRP tubes, and to Mr. Beitelman of FDOT for his invaluable help with the experiments. The opinions and findings expressed here are those of the authors alone, and not necessarily the views of sponsoring agencies.

APPENDIX.

REFERENCES

Building code requirements for structural concrete. (1995). ACI 318-95, American Concrete Institute, Farmington Hills, Mich. Carrasquillo, R. L., Nilson, A. H., and Slate, F. O. (1981). ‘‘Properties of high strength concrete subject to short term loads.’’ ACI J., 78(3), 171– 178. Deskovic, N., Triantafillou, T. C., and Meier, U. (1995). ‘‘Innovative design of FRP combined with concrete: Short-term behavior.’’ J. Struct. Engrg., ASCE, 121(7), 1069–1078.

Fardis, M. N., and Khalili, H. (1981). ‘‘Concrete encased in fiberglassreinforced plastic.’’ ACI J., 78(6), 440–446. Mander, J. B., Priestley, M. J. N., and Park, R. J. T. (1988). ‘‘Theoretical stress-strain model for confined concrete.’’ J. Struct. Engrg., ASCE, 114(8), 1804–1826. Mirmiran, A. (1997). ‘‘Analytical and experimental investigation of reinforced concrete columns encased in fiberglass tubular jackets and use of fiber jacket for pile splicing.’’ Final Rep., Contract No. B-9135, Florida Dept. of Transportation, Tallahassee, Fla. Mirmiran, A., Samaan, M., Cabrera, S., and Shahawy, M. (1998a). ‘‘Design, manufacture, and testing of a newly hybrid column.’’ Constr. & Bldg. Mat., 12(1), 39–49. Mirmiran, A., Shahawy, M., Samaan, M., El Echary, H., Mastrapa, J. C., and Pico, O. (1998b). ‘‘Effect of column parameters on FRP-confined concrete.’’ J. Compos. for Constr., ASCE, 2(4), 175–185. Mirmiran, A., and Shahawy, M. (1996). ‘‘A new concrete-filled hollow FRP composite column.’’ Composites Part B: Engrg., 27B(3,4), 263– 268. Mirmiran, A., and Shahawy, M. (1997a). ‘‘Behavior of concrete columns confined by fiber composites.’’ J. Struct. Engrg., ASCE, 123(5), 583– 590. Mirmiran, A., and Shahawy, M. (1997b). ‘‘Dilation characteristics of confined concrete.’’ Mech. of Cohesive-Frictional Mat., An Int. J., 2(3), 237–249. Naaman, A. E., and Jeong, S. M. (1995). ‘‘Structural ductility of concrete beams prestressed with FRP tendons.’’ Proc., 2nd Int. RILEM Symp. (FRPRCS-2), L. Taerwe, ed., RILEM, Cachan, France, 379–384. Nanni, A., and Norris, M. S. (1995). ‘‘FRP jacketed concrete under flexure and combined flexure-compression.’’ Constr. & Bldg. Mat., 9(5), 273–281. Park, R. (1989). ‘‘Evaluation of ductility of structures and structural as-

semblages for laboratory testing.’’ Bull. New Zealand Soc. Earthquake Engrg., 22(3), 155–166. Park, R., and Paulay, T. (1975). Reinforced concrete structures. Wiley, New York. Prion, H. G. L., and Boehme, J. (1994). ‘‘Beam-column behavior of steel tubes filled with high strength concrete.’’ Can. J. Civ. Engrg., 21(2), 207–218. Rochette, P., and Labossie`re, P. (1996). ‘‘A plasticity approach for concrete columns confined with composite materials.’’ Proc., Adv. Composite Mat. in Bridges and Struct., M. El-Badry, ed., Canadian Society of Civil Engineers, Montreal, Canada, 359–366. Saadatmanesh, H., Ehsani, M., and Li, M. W. (1994). ‘‘Strength and ductility of concrete columns externally reinforced with fiber composite straps.’’ ACI Struct. J., 91(4), 434–447. Samaan, M. (1997). ‘‘Analytical and experimental investigation of FRPconcrete composite columns,’’ PhD thesis, University of Central Florida, Orlando, Fla. Samaan, M., Mirmiran, A., and Shahawy, M. (1998). ‘‘Model of concrete confined by fiber composites.’’ J. Struct. Engrg., ASCE, 124(9), 1025– 1031. Smart, C. W., and Jensen, D. W. (1997). ‘‘Flexure of concrete beams reinforced with advanced composite orthogrids.’’ J. Aerosp. Engrg., ASCE, 10(1), 7–15. ‘‘State-of-the-art report on fiber reinforced plastic reinforcement for concrete structures.’’ (1996). ACI 440R-96, American Concrete Institute, Farmington Hills, Mich. Vecchio, F. J., and Collins, M. P. (1986). ‘‘The modified compressionfield theory for reinforced concrete elements subjected to shear.’’ ACI Struct. J., 83(2), 219–231. Ziara, M. M., Haldane, D., and Kuttab, A. S. (1995). ‘‘Flexural behavior of beams with confinement.’’ ACI Struct. J., 92(1), 103–114.

JOURNAL OF STRUCTURAL ENGINEERING / OCTOBER 1999 / 1093