EFFECT OF COLUMN PARAMETERS ON FRP-CONFINED CONCRETE

By Amir Mirmiran,t Mohsen Shahawy,2 Michel Samaan/ Hazem EI Echary,4Juan Carlos Mastrapa,! and Odell Pico6

ABSTRACT: Confinement effectiveness of fiber reinforced plastic (FRP) jackets (shells) in concrete columnsdepends on several parameters, including concrete strength, types of fibers and resin, fiber volume and fiberorientation in the jacket, jacket thickness, shape of cross section, length-to-diameter (slenderness) ratio of thecolumn, and the interface bond between the core and the jacket. In this paper effects of shape, length, and bondon FRP-confined concrete are studied. Square sections are shown to be less effective in confining concrete thantheir circular counterparts. Their effectiveness is measured by a modified confinement ratio that is a function ofthe corner radius and the jacket's hoop strength. Length effect in short columns of up to 5: I is shown to besimilar to ACI provisions for tied columns, Le., 10% eccentricity and 20% strength reduction in pure compres­sion. While chemical adhesive bond does not change the confinement effectiveness of the jacket, mechanicalshear connectors can enhance the load-carrying capacity of the column by providing an effective load distributionmechanism.

SHAPE EFFECT

TABLE 1. Mechanical Properties of Resin-Impregnated GlassFibers and Polyester Resin'

concrete (Mirmiran and Shahawy 1997a,b), resulting in a newconfinement model (Samaan et al. 1998). This paper reportson a series of experiments with over 100 specimens to studythree aspects of column variables that have received less at­tention in the literature: (I) shape of cross section; (2) columnlength-to-diameter ratio; and (3) interface bond.

To investigate the effect of cross section on FRP-confinedconcrete, a series of uniaxial compression tests was carried outon a total of twelve 152.5 X 152.5 X 305 mm and thirty152.5 X 305 mm cylindrical specimens. Three different tubethicknesses of 1.45, 2.2 I, and 2.97 mm (with 6, 10, and 14plies, respectively) were tested for both cross sections. Thetubes were filament-wound of unidirectional E-glass fibers(Vetrotex CertainTeed 678 R099, 450 yield) at =75 0 angle(with respect to the longitudinal axis of the tube) and ReicholdDION FR 6692T polyester resin. Table I shows the mechan­ical properties of the fibers and the resin. The actual hoopstrength and modulus for the =750 filament-wound tubes werecalculated using the split-disk test and the classical laminatetheory (Samaan 1997). A special collapsible aluminum man­drel was prepared for the square tubes. Details of the mandreland the fabrication process were the same as those reported inMirmiran et al. (1998), except that the internal surface of alltubes in this study were smooth and no internal ribs wereprovided. The square tubes had a 6.35 mm corner radius. Thetube in all specimens was grooved at 19 mm from both endsto ensure that it acted only as a hoop tension band for theconcrete core. All specimens were capped with sulfur mortar.Instrumentation included hoop strain gauges on the surface ofthe tubes at their midheights and 3 or 4 linear variable differ­ential transducers (LVDTs) to measure the average axialstrains. Some specimens were further fitted with an embeddedgauge and two or more surface gauges in the axial direction.Tests were performed using a 2,500-kN MTS machine, and

1.4172

4,3441,6000.36

Polyester resin(3)

2.582,186

69,64030,1300.22

450-yield E-glassb

(2)

"Manufacturer's data.bResin impregnated single-ply.

Property(1 )

Specific GravityTensile Strength (MPa)Tensile Modulus (MPa)Shear Modulus (MPa)Poisson's Ratio

INTRODUCTION

Fiber reinforced plastic (FRP) jackets are shown to enhanceboth strength and ductility of concrete columns by providingconfinement to the concrete core (Nanni and Bradford 1995).The jacket can be used for retrofitting of existing columns(Saadatmanesh et al. 1994), or as a pour form for new con­struction of cast-in-situ or precast columns (Mirmiran and Sha­hawy 1996). Design of FRP shells for such systems requiresanalytical tools that predict the level of performance enhance­ment for the concrete core. Studies have shown that the useof steel-based models can lead to unsafe design (Nanni andBradford 1995; Mirmiran and Shahawy 1997a). As a result, anumber of studies were conducted to evaluate the confinementeffectiveness of FRP jackets, taking into account the mechan­ics of fiber composites as well as the triaxial state of stressesin concrete core (Picher et al. 1996; Rochette and Labossiere1996). Parameters that affect strength and ductility of FRP­confined concrete include concrete strength, types of fibers andresin, fiber volume fraction and fiber orientation in the jacket,jacket thickness (or number of plies), and interface bond be­tween the core and the jacket (e.g., mechanical or chemical).Also, shape of cross section can directly impact the confine­ment effectiveness of the jacket. Finally, column length-to­diameter ratio may affect the strength due to slenderness ef­fects and secondary moments. For the last four years theFlorida Department of Transportation has sponsored a detailedinvestigation into the behavior and design of concrete-filledFRP tubes and fiber-wrapped concrete columns. The studieshave shed some light on the characteristics of FRP-confined

'Assoc. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Cincinnati,Cincinnati, OH 45221.

2Dir., Struct. Res. Ctr., Florida Dept. of Transp., Tallahassee, FL 32310.'Struct. Des. Engr., Dr. Sabri Samaan Consulting, Giza, Egypt; for­

merly, Grad. Student, Dept. of Civ. and Envir. Engrg., Univ. of CentralFlorida, Orlando, FL 32816-2450.

'Struct. Des Engr., Wilbur Smith & Assoc., 3535 Lawton Rd., Orlando,FL 32803; formerly, Grad. Student, Dept. of Civ. and Envir. Engrg., Univ.of Central Florida, Orlando, FL.

'Struct. Des. Engr., Boyle Engrg., Orlando, FL 32801; formerly, Grad.Student, Dept. of Civ. and Envir. Engrg., Univ. of Central Florida, Or­lando, FL.

"Deceased, June 1998; formerly, Grad. Student, Dept. of Civ. and En­vir. Engrg., Univ. of Central Florida, Orlando, FL.

Note. Discussion open until April 1, 1999. To extend the closing dateone month, a written request must be filed with the ASCE Manager ofJournals. The manuscript for this paper was submitted for review andpossible publication on March 27, 1998. This paper is part of the Journalof Composites for Construction, Vol. 2, No.4, November, 1998.©ASCE, ISSN 1090-0268/98/0004-0175-0185/$8.00 + $.50 per page.Paper No. 17783.

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/175

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

TABLE 2. Test Results for Shape Effect Specimens

t} Number Sample f~c f~u

Cross section Batch number (mm) of plies number (MPa) (MPa) Ea. E",

(1 ) (2) (3) (4) (5) (6) (7) (8) (9)

Circle (152.5 X 305 mm) Batch 1 (f:o =30.9 MPa) 1.45 6 1 - 53.66 0.031 -0.0122 - 56.50 0.033 -0.018

2.21 10 1 - 72.92 0.041 -0.0152 - 65.67 0.029 -0.0123 - 77.99 0.044 -0.017

2.97 14 1 - 85.72 0.044 -0.0142 - 86.76 0.047 -0.016

Batch 2 (f;o =29.6 MPa) 1.45 6 1 - 67.12 0.029 -0.0182 - 55.29 0.038 -0.0163 - 60.23 0.038 -0.018

2.21 10 1 - 74.56 0.043 -0.0162 - 93.02 0.043 -0.0193 - 71.74 0.039 -0.015

2.97 14 1 - 86.22 0.046 -0.0132 - 114.66 0.053 -0.0193 - 87.44 0.041 -0.015

Batch 3 (f:o =32.0 MPa) 1.45 6 1 - 59.06 0.034 -0.0192 - 60.79 0.034 -0.018

2.21 10 I - 77.35 0.038 -0.0152 - 77.08 0.038 -0.014

2.97 14 1 - 86.11 0.042 -0.0132 - 83.99 0.043 -0.013

Square (152.5 X 152.5 X 305 mm) Batch 1 (f;' =40.6 MPa) 1.45 6 I 47.78 22.75 0.008' -0.004'2 40.20 2S.S1 0.010' -O.OOS'3 42.82 26.20 0.008' -0.004'

2.21 10 1 4S.23 26.89 O.OIS' -0.008'2 46.47 34.48 0.017' -0.009'3 43.30 34.48 0.017' -0.009'

2.97 14 I 41.92 31.03 0.011' -0.006'2 4S.16 37.92 0.009' -0.005'3 47.92 33.10 0.011' -0.006'

Note: /;0 = strength of unconfined concrete core (from control cylinders);/;c = peak strength of confined concrete (same as/:. for circular sections);and /:. = ultimate strength of confined concrete (postpeak for square sections).

'Tests were stopped after load stabilized, therefore strains shown are lower than ultimate strains.

data was recorded with MegaDAQ. Loading was applied at aconstant rate of 5.6 nun/min in a displacement control mode.

Table 2 summarizes the results for the entire test matrix,where tj ::: tube thickness, I;c = peak (maximum) strength ofconfined concrete, I;. = ultimate strength of confined concrete,1;0 = compressive strength of unconfined concrete (from av­erage strength of control cylinders), and Ee• and Ero = ultimateaxial and lateral (radial) strains of concrete, respectively. Theultimate strength of square sections is lower than their peakstrength, whereas for circular section, the peak and ultimatestrengths are the same, since there is no postpeak descendingbranch in their response. Fig. I shows typical failure modesof circular and square sections. In cylindrical specimens,patches of white could be seen near the midheight of the tubeat about 60-70% of the ultimate load, an indication that theresin has yielded, leaving only the white glass fibers to takethe hoop tension. For the square tubes, these patches appearedonly along the edges, where stress concentration was present.Failure of a cylindrical specimen was generally marked byfiber rupture at or near its midheight, after which the specimencould not carry additional load. In square specimens, a signif­icant load drop would accompany a popping noise, after whichthe load would stabilize at a lower value.

Fig. 2 shows the normalized stress-strain curves for the cy­lindrical and square specimens with different tube thickness.A number of different concrete batches were used in the study.In order to eliminate the effect of different concrete batches,and to isolate the shape effect, the curves are normalized withrespect to the peak stress and corresponding strain of the re­spective unconfined concrete core. It is clear from the figurethat square sections are less effective than their circular coun-

terparts in confining concrete. This may be explained by thedistribution of confining pressure in circular and square sec­tions. For circular sections, the confining pressure is uniform,and is a function of hoop strength of the jacket. On the otherhand, for square sections, the confining pressure varies froma maximum at the corners to a minimum in between the edges.The confining pressure at the corners is due to the membraneaction in the transverse sides of the tube, whereas at otherpoints it depends on the flexural rigidity of the FRP plate.Therefore, both the corner radius and the dimensions of thetube affect the level of confinement exerted on the concretecore. Fig. 2 also shows that while jacket thickness greatly af­fects the response of circular sections, for square sections, thiseffect is minimal. It appears that the descending branch of theresponse is stabilized at about 70% of the peak strength ofunconfined concrete, irrespective of the tube thickness. Ofcourse, there seems to be a threshold thickness (e.g., between6 to 10 plies for the materials in this study), below which littleor no postpeak plasticity is present.

Another important comparison between the square and cir­cular sections is in their volumetric response. Fig. 3 shows theaxial stress versus volumetric strain for both shapes with dif­ferent tube thickness. The curves are again normalized withrespect to the peak stress and the corresponding strain of theirrespective unconfined concrete core. The change in volume perunit volume of concrete is calculated as

(1)

where lOu = volumetric strain; E1 = axial strain; lOr = lateral

176/ JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

(2)

(3)

(4)

+ = 2fAJr D

(circular, square, and rectangular), fiber type (carbon and ar­amid), comer radius, and number of composite plies or wraps(2-5 plies for carbon, and 3-12 plies for aramid). The con­crete strength ranged between 29-44 MPa. Rochette con­cluded that, as discussed above, comer radius of the tube af­fects its confinement effectiveness. In this paper, a modifiedconfinement ratio MCR is defined as

MCR = (2R) frD f;"

where R = comer radius; D = inside dimension of the tube;and f,. = confinement pressure given by

where jj = hoop strength of the tube. The (fr/f;o) is the con­finement ratio for circular sections. Fig. 4 shows a plot ofU;./f;c) versus MCR for specimens tested by Rochette (1996)as well as the square specimens of the present study. In thisfigure, f;. = ultimate strength of confined concrete (postpeakfor square sections), and f;c = maximum (peak) strength ofconfined concrete (same asf;. for circular sections). As shownin the figure, MCR dictates whether or not a postpeak descend­ing branch will be present in the response curve. It appearsthat for MCR <15%, the jacket is not very effective instrengthening the concrete core, and though there may be ad­ditional ductility due to crack dilatancy containment, nostrength enhancement should be expected. Low confining ef­fects may be due to thin jackets (i.e., low confinement pres­sure), or sharp edges in noncircular sections. As the sharp cor­ners are rounded, the jacket becomes more effective. A carefulexamination of the data in Fig. 4 reveals that for low levelsof MCR a logarithmic trend can produce a reasonable estimateof the postpeak response. Although such a logarithmic trenddoes not render a value for MCR = 0, it is not expected thatexact sharp comers or zero confinement be of any concern inthe confinement analysis. Therefore, the following relationshipis proposed for the postpeak stress level:

~~. =0.169 In MCR + 1.32 for MCR < 0.15J cc

(b)

FIG. 1. Typical Failure of Concrete-Filled FRP Tubes: (a) Cir­cular Section; (b) Square Section

(a)

strain; and where tensile strains are negative. A positive Ev

represents volume reduction (compaction), whereas a negativevalue indicates volume expansion (dilation). The figure showsthat all specimens, regardless of their shape, are compactedunder axial load until they reach a critical stress level, at whichpoint they begin to expand volumetrically. Whereas for plainconcrete there is no recovery beyond this point; both circularand square sections appear to effectively reverse the dilationprocess of concrete core. Previous studies have shown that nosuch dilation recovery exists for steel-confined concrete.Therefore, it can be concluded that the reversal of volumetricstrain is only a function of the tube materials and not the shapeof cross section. Such response represents a form of plasticityfor the hybrid system, although concrete itself is fully crackedbeyond the critical stress level. It is further noted that this formof plasticity in circular sections is accompanied by a strain­hardening process, unlike the square sections that show a pe­scending postpeak response.

Comparison with Fiber-Wrapped Specimens

A similar study in nature, though limited to fiber-wrappedspecimens, has been conducted by Rochette (1996) who tested33 fiber-wrapped concrete cylinders under uniaxial compres­sion. The parameters studied included cross-sectional shape

For values of MCR >15%, the confinement model of Sa­maan et al. (1998) could be used to predict the stress-strainresponse. For more details on the shape effect experiments,see Mirmiran (1997b) and Pico (1997).

LENGTH EFFECT

A total of 24 concrete-filled cylindrical tubes with three tubethicknesses of 1.45, 2.21, and 2.97 mm (6, 10, and 14 plies,respectively) and four different lengths (305, 457, 610, and762 mm) were tested. For each tube length and thickness, twosamples were prepared for repeatability verification. The plyarrangement, fibers and resin, and the winding angle were thesame as the shape effect series. The inside diameter of all tubeswas 145 mm as controlled by the diameter of the mandrel usedfor making the tubes. Therefore, the diameter-to-thickness (DIt) ratios of the 6, 10, and 14-ply tubes were approximately100, 65, and 50, respectively. Generally, concrete-filled steeltubes with (Dlt) ratios <50 are considered stocky, while veryslender tubes have a (Dlt) ratio of >100 (U.S.-Japan 1992).Although different from steel tubes, the tubes under study arestill considered to be in the intermediate range between thestocky and very slender columns. As for the length-to-diameter(LID) ratio of the tubes, a range from approximately 2: 1 to 5:1 was selected, which would still qualify as a short column.The concrete was ready mix with an average strength off;o =

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/ 1n

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

2,5 r------------------------------==-----...,

14,012,010,04,02,0

0,0 l.- ~ _+_----'------'-----+_----+------J0,0 6,0 8,0

Normalized Axial Strain

FIG. 2. Normalized Stress-Strain Curves for Concrete-Filled Circular and Square Tubes

2,0

tiltil

t<J:l;;j 1,5

'>1<"0

Q)

.~;;j 10

E0Z

0,5

2.51-----~::;;:;:;;::;;;;::;::;:;:~----------_=71

:.::E 2.0&I)G)COuiII,- 1.51.!~~

'iii~ 1.0

jCi 0.5

~

1412108642a-2-4

+-1Volwne Expansion IVolwne Compaction~

0.0 +-~--=+:====i=~-f---=+====:;::==~~-+__-_+_--+__-~-6

Volumetric Strain

FIG. 3. Normalized Volumetric Curves for Concrete-Filled Circular and Square Tubes

1,2

1.0

0.8

~ 0,6il

0,4

•

••

•I

0,2

• Tests by Rochette (1996)

.. Present Study-Proposed Model for MCR < 0.15

0,140,0 !------I------'------+-----+-----I-----I-------+----'

0.00 0.02 0.04 0.06 0.08 0.10 0,12

MeR

FIG. 4. Ultimate Strength Ratio versus (2RJ0)( '.J ,~o) Ratio

178/ JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

44.8 MPa. All specimens were made of the same concretebatch. The grooving and capping of specimens were done thesame as the shape effect series. The 2: 1 and 3: 1 cylinders wereonly instrumented at their midheights with two sets of verticaland horizontal strain gauges placed at 1800 opposite from eachother. In each set, the horizontal and vertical gauges were at­tached to the surface of the tube with one gauge located ontop of the other. The 4: 1 and 5: 1 cylinders were instrumentedat the top and bottom quarters as well as midheight with atotal of 12 strain gauges arranged similar to that explained

previously. In addition to surface gauges, three LVDTs wereused for each specimen to measure the average axial strains.Test procedures were the same as the shape effect series.

Typical failure, similar to that observed in the shape effectseries, was marked by fiber rupture at points of maximumstress concentration, preceded by snapping of the inner pliesof the tube, appearance of white patches, and some noise frominside the tube. Sounds heard during the early-to-middle stagesof loading were attributed to the cracks in concrete and shift­ing and settling of aggregates. Snapping of the inner plies of

14 r--------II---------;:::========:::l

0.030.0250.020.Ql50.010.005o-0.005-0.01

oL-__'--__"'--__"'--__.l:..-__"'--__"'--__"'--__"'--__"'--_----J

-0.02 -0.015

12

2

Lateral Strain Axial Strain

FIG. 5. Biaxial Stress-Strain Curves for Length Effect Specimens

TABLE 3. Test Results for Length Effect Specimens

Stram gauge broke before reachmg ultimate load.bLower ultimate load for this specimen is due to premature failure at top groove.<Specimen fell down and was damaged prior to loading.

Eccentricity Ratio (alh)

Bottom

~ Number of Sample t:,., Top quarter Midheight quarterUD ratio (mm) plies number (MPa) Eeu Eru ("!o) ("!o) ("!o)

(1 ) (2) (3) (4) (5) (6) (7) (8) (9) (10)

2:1 1.45 6 1 63.02 0.025 -0.019 - 2.48 -2 57.02 0.022 -0.014 - -0.71 -

2.21 10 1 83.22 0.029 -0.018 - . -2 75.36 0.024 -0.014 - -3.13 -

2.97 14 1 104.53 0.030 -0.015 - -1.78 -2 89.01 b 0.027 -0.011 - -0.80 -

3:1 1.45 6 1 51.57 0.013 -0.009 - 2.46 -2 48.89 0.008 -0.009 - -9.17 -

2.21 10 1 69.64 0.021 -0.011 - -1.24 -2 67.43 0.020 -0.010 - -4.76 -

2.97 14 1 84.39 0.025 -0.010 - 4.62 -2 85.02 0.025 -0.012 - 5.46 -

4:1 1.45 6 1 52.75 0.013 -0.011 -2.07 -0.62 3.792 42.68< 0.008 -0.009 -3.59 0.73 1.34

2.21 10 1 64.61 0.016 -0.010 - . -1.53 -2.212 63.23 0.014 -0.009 11.80 -2.16 -11.51

2.97 14 1 88.81 0.026 -0.010 . -0.29 -10.672 89.22 0.023 -0.012 0.17 -5.82 -5.15

5:1 1.45 6 1 47.78 0.011 -0.009 6.00 -8.06 -7.982 52.40 0.013 -0.011 6.07 -3.72 -9.09

2.21 10 1 65.23 0.016 -0.010 4.55 -2.18 -6.182 57.23 0.011 -0.007 5.98 -6.12 -9.40

2.97 14 1 82.26 0.019 -0.009 9.40 -2.29 -8.242 84.46 0.019 -0.009 4.99 -4.23 -9.62.

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/179

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

the tube could be heard near the end of the loading process.Failure, while sudden, was physically detectable and predict­able. Although some local buckling was observed, shear fail­ure was noted as the primary mode of failure for the tubes. Itwas also noted that specimens typically remained intact afterfailure, as no form of violent failure was observed. Of the 2:1 specimens, all but two failed at or around the middle band.Of the 3: 1 specimens, on the other hand, all but two failed atthe top or bottom quarters. Of the 4: 1 specimens, all but onefailed somewhere away from the midheight. Finally, no single5:1 specimen fractured at its midheight. However, no bucklingas a result of slenderness was noticeable, and as will be dis­cussed later, only minor eccentricities were present at any sec­tion of any of the specimens.

Fig. 5 shows the biaxial stress-strain curves for the 6, 10,and 14-ply tubes with different (UD) ratios. Test results are

also summarized in Table 3, which shows considerable in­crease in strength and ductility for all specimens. It is clearthat length effects are not significant within the range of (UD) ratios studied here. There is no difference in eithcr theinitial or the secondary slopes of the comparable tubes of dif­ferent lengths. It appears, however, that the bend and failurepoints are somewhat affected by the tube length. One canquantify such effects in comparison with the standard 2: 1 spec­imens. Fig. 6 shows the normalized ultimate strengthU;u/f;u2:1) versus (UD) ratio, where f:U21 is the average ulti­mate strength of the corresponding 2: I specimens with thesame number of plies. A parabolic curve fit is given by

1.2

f 'O/f '02:1 = 0.0288(Lffi)2 - 0.263(Lffi) + 1.418~

,:; 1.0=~b.l:l 0.8....CJ)

=~[;i.fl 0.6eo:..;5a:l 0.4.!::l-;e..i. 0.2

•-• •

•ISpecimen damaged before testing~ •

= .••

5:14:13:1

0.0 L.. ----"- ~ ___"_ ~ _'

2:1

LID Ratio

FIG. 6. Normalized Ultimate Strength versus (UO) Ratio

.'

.-

1/2 Ultimate Load

~IStrain Distribution

I~

381

254

635

127

e.! 508

e~o=:IeoJ:.."=~

'"Q

762 r-:-------,------i------;:::=======::--,

0.030.020.01oAxial Strain

-0.01-0.02

o~====::'.. ---'- --l _'____--..-.!======:!..-.J

-0.03

FIG. 7. Typical Strain Distribution along 24" and 30" Specimens

180 I JOURNAL OF COMPOSITES FOR CONSTRUCTION I NOVEMBER 1998

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

TABLE 4 Test Results for Bond Effect Specimens

Number Sample f' f~ucc

Jacket type Batch number Bond type of plies number (MPa) (MPa) Ecu E",

(1 ) (2) (3) (4) (5) (6) (7) (8) (9)

Multilayered Batch I (29.8 MPa) Bonded 1 1 33.65 30.82 0.010 -0.0212 33.16 26.00 0.023 -0.0233 33.23 28.55 0.020 -0.016

3 1 - 63.02 0.027 -0.0212 - 65.16 0.030 -O.oI83 - 65.23 0.028 -0.005

5 1 - 93.70 0.043 -0.0202 - 92.26 0.039 -0.0213 - 96.46 0.044 -0.019

7 1 - 111.97" 0.047 -0.0162 - 111.15R 0.040 -O.oI83 - 111.29R 0.039 -0.018

Unbonded I 1 31.03 29.30 0.010 -O.oI82 34.06 32.82 0.013 -0.0193 35.58 26.68 0.015 -O.oI 1

3 1 - 63.02 0.027 -0.0212 - 49.02 0.018 -0.0093 - 58.68 0.030 -O.oI5

5 I - 86.81 0.033 -0.0152 - 88.32 0.036 -0.0193 - 93.63 0.038 -0.017

7 1 - 109.15R 0.037 -0.0152 - 111.84R 0.038 -0.0203 - 110.80R 0.052 -0.016

Single-wrap Batch 2 (3 1.2 MPa) Bonded 3 1 - 67.50 0.030 -0.0232 - 64.68 0.031 -0.020

5 1 - 91.01 0.053 -0.0182 - 96.87 0.063 -0.018

Unbonded 3 1 - 63.09 0.031 -0.0232 - 65.43 0.031 -0.022

5 1 - 91.91 0.043 -0.0202 - 89.01 0.050 -0.018

'The 7-layer specimens did not fail. and these values are merely maximum stresses they sustamed.

Similarly, for the ultimate strains (Ecu ), a parabolic functionis derived as

Ecu = E",21 [0.0529 (~r-0.5214 (~) + 1.8506] (6)

where Ecu 2:1 = average ultimate strain of corresponding 2:1specimens with the same number of plies.

Another consideration is the eccentricities due to length ef­fects. Fig. 7 shows the strain distributions along the length ofthe column for a 4: 1 specimen with 10 plies, and a 5:1 spec­imen with 14 plies. On each side and for each specimen, fourgraphs are shown that represent the strain distribution on thatside of the specimen at 1/4, 1/2, 3/4, and full ultimate load.As the load increases, some variation in strains are observed,reflecting a bending curvature along the specimen. For thespecimens shown, while only a single curvature is present,points of maximum strains are different. If the stress resultantat a section were concentric, strain readings on both sides ofthe section would be the same. Different strain readings in­dicate either an eccentric stress resultant at the section, or anonuniform distribution of the confining pressure. Noting thebilinear stress-strain response of FRP-confined concrete, forall points on the second slope, one can write

(7)

where fc and Ec =axial stress and strain in the concrete section,respectively; j" = intercept stress of the second slope with thestress axis; and £2 = second slope of the stress-strain of FRP­confined concrete. From (7) it is clear that beyond the bendpoint, one can assume the same distribution for the stresses asfor the strains. Therefore, the centroid of the trapezoidal areabetween the two strain readings (see inset in Fig. 7) can, in

TABLE 5. Mechanical Properties of S-2 Glass/Epoxy Compos­Ite

Property ASTM standard Typical value"(1) (2) (30

Longitudinal Modulus 03039 55,850 MPaTransverse Modulus 03039 17,950 MPaShear Modulus 03518 7,600 MPaPoisson's Ratio 03039 0.27Longitudinal Tensile Strength 03039 1,800 MPaLongitudinal Compressive Strength 03410 950 MPaTransverse Tensile Strength 03039 62 MPaTransverse Compressive Strength 03410 155 MPaLongitudinal Tensile Strain 03039 0.030Unit Weight 0792 15.67 N/m3

"Average of manufacturer's data at 22°C and dry conditions.

fact, show the location of the stress resultant (i.e., the appliedload at that particular section). The distance between that cen­troid and the centerline of the section is the eccentricity (e) ofthe load at that section. Table 3 shows the eccentricity ratio(e/h, h = outside diameter) at the top and bottom quarters, aswell as the midheight of each specimen, except for the 2: 1 and3:1 specimens that were only instrumented at their midheights.It should be noted that part of the difference in the strainreadings may be due to nonuniform distribution of the confin­ing pressure, stress concentrations, or local flaws in the tube.Therefore, the values in Table 3 may be treated as the upperbound eccentricities present in the tests. However, the singlemost important conclusion from these calculations is that themaximum eccentricity is within 10-12% of the section width.Note that ACI (Building 1995) requires a minimum eccentric­ity of 10% for tied columns and further recommends reducing

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/181

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

(8)

the ultimate strength by 20% to allow for the inherent eccen­tricity. Using (5) a reduction factor of 18% results for a col­umn with UD ratio of 5:1. It is therefore concluded that thestandard 2: 1 cylinders may be considered adequate to repre­sent the confinement of concrete sections. Also, longer speci­mens possess an inherent eccentricity that results in lower ul­timate loads. However, these eccentricities are within thecurrently prescribed range of 10% of the section width and donot necessarily qualify for any slenderness effect. For moredetails on the length effect experiments see Mirmiran (1997b)and EI Echary (1998).

BOND EFFECT

Bond between the FRP jacket and the concrete core can bedeveloped using either an adhesive such as epoxy (e.g., infiber-wrapped columns), or a series of mechanical shear con­nectors (e.g., in concrete-filled tubes with internal ribs). Theinterface bond affects the state of stress in the shell, and mayalso affect the capacity of the column. Orito et al. (1987) re­ported that unbonded construction for concrete-filled steeltubes results in a higher load-carrying capacity than thebonded tubes. They reasoned that unbonded tubes are onlysubjected to hoop tension, and will not buckle under columnload. On the other hand, bonded jackets are subject to hooptension as well as axial compression, a combination that maylower the fracture strength of the jacket. In this section, effectof adhesive and mechanical bonds in FRP-concrete columnsis studied to see if modeling for confinement in fiber-wrappedcolumns and concrete-filled FRP tubes should be any different.

Adhesive Bond

A total of 32 composite specimens with and without inter­face bond, two methods of fabrication for the jacket (multi­layered or single-wrap), and different numbers of plies (1-7)were tested. For each case, two or three identical samples wereprepared for repeatability verification. The test matrix is shownin Table 4. All specimens were made of S-glass fabric andpolyester resin with a core diameter of 152.5 mm and a lengthof 305 mm. The fabric was Hexce1 SA 120, a unidirectionalstitched Owens Corning S-2 glass yarn with 0.61 warp permm, 610 mm width, 13.0 mils nominal thickness, and 12.2 ozper square yard aerial weight. Table 5 shows the manufac­turer's data for the 5-2 glass fibers in a unidirectional epoxycomposite with 57 -63% fiber volume fraction. The resin wasDIaN 6692T polyester, material properties of which were pro­vided in Table 1. The fiber volume fraction was controlled bythe equivalent weight fractions of the fibers and the resin

W r Pr(1 - vf - v,,)

Wf PfVf

where W r = weight of the resin; Wf = weight of the fibers; Vf =fiber volume fraction; v" = void ratio; Pf = specific gravity ofthe fibers taken as 1.39; and Pr = specific gravity of the resintaken as 2.48. For each length of the fabric the required weightof the resin, including the methyl ethyl ketone peroxide cata­lyst, was then calculated using a 3% void ratio and a 37%fiber volume fraction. Of the resin mix, 1.5% (by volume) wasthe catalyst.

In these experiments, two methods of fabrication for thejacket were compared, multilayered and single-wrap. In thelatter method, the jacket was made of a continuous single sheetof the fabric with a total overlap of about 32% of the perimeterof the shell. In the multilayered shell, on the other hand, eachply of the shell was cut and placed separately with individualoverlaps of about 17% of the perimeter of the shell. The splicelocation was varied from one ply to another to avoid stressconcentration at one location.

For each method of fabrication, two types of jackets wereprepared: (1) bonded; and (2) unbonded. The unbonded tubeswere prepared by wrapping the fabric around a collapsiblemandrel. The mandrel was made of two half-cylinders of a152.5 mm o.d. aluminum pipe with a circumferential gap of12.7 mm and a total length of 813 mm to allow making two305 mm tubes. The half-cylinders were tied together by clampsat both ends, and were placed on a wooden dowel and twowooden disks. The fabrication sequence consisted of cuttingthe fabric into proper lengths, weighing the resin to the rightamount, mixing with the catalyst, placing the sheet on waxpaper, applying and spreading about 85% of the resin on thesheet, wrapping the sheet around the mandrel, and finally, ap­plying the remainder of the resin onto the sheet. A roller wasused to remove air voids from the sheet before placing thenext ply. The procedure was repeated for the desired numberof plies in the multilayered jackets. The tubes would be lefton the mandrel to cure for 24 h. The mandrel would then becollapsed and the tubes removed. The bonded specimens were

(a)

(b)

FIG. 8. Typical Fracture of 7-Ply Specimens after RemovingTube: (a) Unbonded; (b) Bonded

182/ JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

made by wrapping fabric around concrete cylinders at the ageof 28 days. Prior to placing the first ply, the surface of theconcrete was saturated with additional resin of half as muchas needed for one ply of fabric.

Two batches of concrete were used in these experiments.Batch 1 was used for all the multilayered jackets. whereasBatch 2 was used for the single-wrap specimens. Concrete forBatch 1 was ready mix with an average strength of/;o = 29.8MPa, whereas concrete for Batch 2 was mixed on site with anaverage strength of/;0 = 31.2 MPa. Only unbonded specimenswere grooved at the top and bottom, similar to that explainedfor the shape effect series. Instrumentation, loading rate, andtest procedure were also the same as the shape effect series.Test results are shown in Table 4.

Failure in almost all specimens was initiated by the for-

mation of a narrow band or ring as a result of the shearing offand separation of the fabric in the hoop direction. Some spec­imens failed with simultaneous band separations rather than asingle major one. The bandwidth was in the order of 5-60mm. The band was generally formed at or near the midheightof the specimen. Once the band was formed, delamination atthe splice would result in the snapping of the ring and a slippagein the order of 12-38 rom. Mode of failure was attributed tothe 90° orientation of the fibers, i.e., hoop direction. The patchesof high stress concentration were not as significant as thosereported for the other series, perhaps because of the color ofthe resin. However, popping noises heard during various stagesof loading were the same as those reported for the other series.

The 7-ply specimens did not fail within the capacity of thetesting machine. Four of these specimens were then subjected

180 ,..------------r---------------------,

Axial Strain

_ Unhonded SpecimensBonded Specimens

16.0

.. 14.0

~It'l 120~QO

~

II

] 10.0

~ 3-Ply=-~ 8.0'-'

'"f 6.0....V'.J0;

~ 4.0

2.0

0.0-0.03 -0.02 -0.01 0.00 0.01

Lateral Strain

0.02 0.03 0.04

7-Ply

0.05

Biaxial Stress-5train Curves for Bond Effect Specimens with Multilayer Shells

Effect of Shell Layup on Stress-Strain Response of Bond Effect Specimens

Lateral Strain

0.040.03

I 3-Ply Shell I

0.02

Axial Strain

- Unhonded SpecimensBonded Specimens

0.010.00-0.01-0.02

FIG. 9.

10.0

9.0

.. 8.0

~It'l 7.0~QO

~

II 6.0]~ 5.0

=-~ 4.0'"'"b

3.0V'.J0;.;:;-< 2.0

1.0

0.0-0.03

FIG. 10.

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/183

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Transverse Rib

Angle Plies

Longitudinal Rib

Woven Rovings

Fig. 9 shows plots of axial stress versus axial and radialstrains for multilayered bonded and unbonded jackets. Eachcurve is an average of three identical samples. The stress-straincurves for the 3, 5, and 7-ply specimens have the same bilinearshape as those observed in the previous series. However, theconfinement provided for the I-ply specimens was not suffi­cient to enhance the strength of the concrete core, as a de­scending branch is present in the response. The figure showsno marked difference between the response of bonded andunbonded specimens. Note that the stress-strain curves of the7-ply specimens do not represent their ultimate strength asthey did not fail within the capacity of the machine. The effectof shell layup and fabrication technique is shown in Fig. 10for the 3- and 5-ply bonded and unbonded specimens. No sig­nificant difference exists whether the jacket is made of a singlecontinuous wrap or a series of wraps that are spliced together.For more details on the adhesive bond experiments see Mir­miran (1997b) and Mastrapa (1997).

FIG. 11. FRP Tube with Shear Connector RibsMechanical Bond

TABLE 6. Test Results for Concrete-Filled Ribbed Tubes

Specimen Loading of pu" Au" f~u

number tube (kN) (mm) (MPa) Ecu

(1 ) (2) (3) (4) (5) (6)

SCI Direct 1,237 17.3 39.1 0.053SC2 Direct 1,121 14.5 35.4 0.047SC3 Indirect 1,308 17.5 41.4 0.051

to 3 cycles of loading and unloading that also did not result ina failure. To study the difference between the bonded and un­bonded construction, the jacket was removed from two of thetested 7-layer specimens by an electric handsaw. The tube inthe unbonded specimen separated with ease, showing no signof distress and no attachment to the core [Fig. 8(a)]. The con­crete core, however, had horizontal cracks and split in twohalves when dropped on the floor. In the bonded specimens,once the jacket was cut, its stresses were suddenly released,causing the concrete core to crack circumferentially, and leavingthe exterior portion of the core attached to the jacket [Fig. 8(b)].

Bond between the concrete core and the FRP shell can alsobe provided by means of shear connector ribs on the interiorsurface of the tube. Such shear connectors are normally usedin flight and marine structures as longitudinal and transversestiffeners for FRP shells. Fig. 11 shows the interior shear ribsof the FRP tubes used for this study. The tube was made usinga special collapsible mandrel (for details see Mirmiran et al.1998). The ribs were made of a special polyester paste thatconsisted of Ashland Chemicals polyester resin (DION 33­611), 1% (by volume) PPG chopped glass fibers (6.4 mmlength), and 1.5% (by volume) methyl ethyl ketone peroxidecatalyst. The longitudinal and transverse ribs were 42 mm and19 mm wide, respectively. All ribs were 6.4 mm thick. Thetube consisted of 15 plies of ±75° E-glass/polyester of thesame material properties as those in Table 1. The outer di­mensions of the tubes were approximately 178 X 178 X 305mm. Three tubes were filled with!;o = 18.6 MPa concrete, andtested under uniaxial compression with the same procedure asthat indicated for the shape effect series. No groove was madein anyone of the tubes. The end surfaces of the tubes were

4

3

3

'"'"t..rJ:J

~2

-< 15-Ply Square1l Mechanical Bond.Ql 2 R/D=O.18';a..<:>Z

14-Ply SquareNo Bond

R/D-O.04

0.060.050.040.030.020.01oL-----------------------------------'0.00

Axial Strain

FIG. 12. Effect of Mechanical Bond on Stress-5traln Response of Concrete-Filled Tubes

184/ JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

Vft Vv

wfl Wr =A.ult

fit Er, Ev =Eeu , £ru =

PI' pr =

grinded. The specimens were capped with a 5 mm lead platecovering the entire cross section for Specimens SCI and SC2,and only the concrete core for Specimen SC3. Table 6 showsthe test results, where PUll = ultimate axial load capacity, and/i.ult = ultimate axial deflection. As shown in the table, Speci­men SC3 failed at a higher load, which may be attributed tothe fact that the axial load was not directly applied to thejacket, but rather indirectly through the internal ribs. Fig. 12shows the stress-strain curves for a I5-ply ribbed tube (Spec­imen SCi), a typical I4-ply square tube with no ribs (fromthe shape effect series), and a typical I4-ply circular tube withno ribs. The stresses in the figure are normalized with respectto the corresponding unconfined strength of concrete core. Itis clear that the ribs help improve the load-carrying capacityof the tube by distributing the confinement pressures moreeffectively around the circumference of the tube. The longi­tudinal stiffeners act as stringers, and help the tube resist axialand lateral loads. They also divide the shell into small panels,thereby increasing its buckling and compressive strength.Moreover, they help arrest the growth of cracks in the shellby accepting tensile loads that the shell can no longer carry.The transverse ribs help maintain the cross-sectional shape ofthe skin, redistribute stresses around structural discontinuities,provide end restraints for the longitudinal ribs, and, finally, actwith the shell in resisting the hoop stresses. For more detailson the mechanical bond experiments see Mirmiran (1997a)and Samaan (1997).

CONCLUSIONS

Effects of shape, length, and interface bond on FRP-con­fined concrete were investigated on over 100 specimens sub­jected to uniaxial compression. The following conclusionswere made:

1. Square sections are less effective than their circularcounterparts. Confinement effectiveness is measured byMCR that is a function of the corner radius and thejacket's hoop strength. No strengthening may be ex­pected for MCR <15%.

2. Effect of length-to-diameter ratios within the range of 2:1 and 5: I is not significant for either strength or ductilityof the section. Both eccentricities and strength reductionsare within the limits prescribed by ACI 318-95 for tiedcolumns.

3. Whereas adhesive bond does not affect load-carrying ca­pacity of FRP-confined concrete, mechanical bond (shearconnectors) significantly improves the performance ofthe section by distributing the confinement pressure moreeffectively around the circumference of the tube.

ACKNOWLEDGMENTS

This paper is dedicated to Odell G. Pico, former graduate student atthe University of Central Florida, who passed away so unexpectedly andat such a young age. Financial support for this study was provided bythe Florida and U.S. Departments of Transportation (Contracts B-9135and B-9895) and the National Science Foundation (Grant CMS-9625070).The writers are grateful to Mr. Parks of Marine Muffler Corp. for pro­viding the specimens, and Mr. Beitelman of the Florida Department ofTransportation for his invaluable assistance with the experiments. Theopinions and findings expressed here, however, are those of the writersalone, and not necessarily the views of the sponsoring agencies.

APPENDIX I. REFERENCES

Building code requirements for structural concrete and commentary.(1995). ACI 318-95, American Concrete Institute, Farmington Hills,Mich.

EI Echary, H. (1998). "Length effect on behavior of concrete columnsconfined by fiber composites using acoustic emission," MS thesis,Univ. of Central Florida, Orlando, Fla.

Mastrapa, J. C. (1997). "Effect of construction bond on confinement withfiber composites," MS thesis, Univ. of Central Florida, Orlando, Fla.

Mirmiran, A. (1997a). "Analytical and experimental investigation of re­inforced concrete columns encased in fiberglass tubular jackets and useof fiber jacket for pile splicing." Final Rep., Contract No. B-9135,Florida Dept. of Transp., Tallahassee, Fla.

Mirmiran, A. (1997b). "FRP-concrete composite column and pile jacketsplicing-Phase II." Final Rep., Contract No. B-9895, Florida Dept.of Transp., Tallahassee, Fla.

Mirmiran, A., Samaan, M., Cabrera, S., and Shahawy, M. (1998). "De­sign, manufacture, and testing of a new hybrid column." Constr. andBuild. Mat., 12(1), 39-49.

Mirmiran, A., and Shahawy, M. (1996). "A new concrete-filled hollowFRP composite column." Composites Part B: Engrg., 27B(3-4),263-268.

Mirmiran, A., and Shahawy, M. (1997a). "Behavior of concrete columnsconfined 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., Int. J., 2(3),237-249.

Nanni, A., and Bradford, N. M. (1995). "FRP-jacketed concrete underuniaxial compression." Constr. and Build. Mat., 9(2), 115-124.

Orito, Y, Sato, T., Tanaka, N., and Watanabe, Y (1987). "Study on theunbonded steel tube structure." Proc., Int. Con! Composite Construc­tion in Steel and Concrete, ASCE, 786-804.

Picher, E, Rochette, P., and Labossiere, P. (1996). "Confinement of con­crete cylinders with CFRP." Proc., 1st Int. Con! Composites in Infra­structure, H. Saadatmanesh and M. R. Ehsani, eds., Tuscon, Ariz.,829-841.

Pico, O. (1997). "Confinement effectiveness of square FRP tubes in hy­brid columns," MS thesis, Univ. of Central Florida, Orlando, Fla.

Rochette P. (1996). "Confinement of short square and rectangular col­umns with composite materials," MS thesis, Univ. of Sherbrooke, Que­bec, Canada.

Rochette, P., and Labossiere, P. (1996). "A plasticity approach for con­crete columns confined with composite materials." Adv. CompositeMat. in Bridges and Struct., M. M. EI-Badry, ed., Canadian Soc. forCiv. Engrg., Montreal, Canada, 359-366.

Saadatrnanesh, H., Ehsani, M. R., and Li, M. W. (1994). "Strength andductility of concrete columns externally reinforced with fiber compositestraps." ACI Struct. J.. 91(4), 434-447.

Samaan, M. (1997). "Analytical and experimental investigation of FRP­concrete composite columns," PhD thesis, Univ. of Central Florida,Orlando, Fla.

Samaan, M., Mirmiran, A., and Shahawy, M. (1998). "Model of concreteconfined by fiber composites." J. Struct. Engrg., ASCE, 124(9),1025-1031.

U.S.-Japan Planning Groups. (1992). "Recommendations for U.S.-Ja­pan cooperative research program-Phase 5 composite and hybridstructures." Rep. UMCEE 92-29, Univ. of Michigan, Ann Arbor, Mich.

APPENDIX II. NOTATION

The following symbols are used in this paper:

D = core diameter or column diameter;£2 second slope of stress-strain curve of FRP-confined

concrete;e = load eccentricity;

f;,/;o strength of unconfined concrete;f;c peak strength of confined concrete;f;u = ultimate strength of confined concrete;jj = hoop strength of FRP jacket;fa = intercept stress of stress-strain curve of FRP-confined

concrete;f,. = confining pressure;h outside dimension of section;L = column length;

MeR modified confinement ratio;Pult = ultimate axial load;t, tj tube (jacket) thickness;

V, A. V = volume and change of volume;fiber volume fraction and void ratio;weight of fibers and resin;ultimate axial deflection;axial, lateral, and volumetric strains in concrete;ultimate axial and lateral strains in concrete; andspecific gravity of fibers and resin.

JOURNAL OF COMPOSITES FOR CONSTRUCTION / NOVEMBER 1998/185

J. Compos. Constr. 1998.2:175-185.

Dow

nloa

ded

from

asc

elib

rary

.org

by

NE

D U

nive

rsity

of

Eng

inee

ring

and

Tec

hnol

ogy

on 0

9/04

/15.

Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.