Size and Relative Stiffness Effects on Compressive Failure of Concrete Columns Wrapped with Glass FRP

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Size and Relative Stiffness Effects on Compressive Failureof Concrete Columns Wrapped with Glass FRP

Manuel A. G. Silva1 and Carlos C. Rodrigues2

Abstract: Structural design relies essentially on tests made on cylinders of small size to estimate the probability of failure of prototypemembers, since full-scale testing of structures to determine their strength is not feasible. The confidence that such scale modeling deservesin terms of representation of actual behavior needs careful examination, due to such factors as material nonlinearities, difficulties of scalerepresentation of particulate materials, and sometimes the impossibility of simultaneously satisfying independent dimensionless param-eters. Some failures explained by linear fracture mechanics are associable with strong size effects, as opposed to the cases where smallcracks are a material property. Besides research centered on these problems, a number of studies of scale effects have been associated withthe increased probability of finding a flaw in larger objects. In fact, geometric similitude may coexist with microscopic randomness offlaws that cause size effects to appear. The type of material of the object under study may also be a decisive factor. For example, scatterof the mechanical properties in unidirectional fiber-reinforced polymers �FRPs� is much larger than in metals due to a larger density offlaws. Thus the strength of FRP laminates may depend on the volume of material involved. Strengthening reinforced concrete columnswith FRP wraps leads to new constitutive laws for the overall response of the columns and requires small-scale testing followed byextrapolation for design use. The present paper focuses on the difficulties of this step, based on the experimental data obtained. Thequestions mentioned above are addressed, and the relevance of the adequate representation of the lateral stiffness of the FRP jacket in thescaled cylinders is emphasized. The paper also addresses the problem of testing confined cylinders with a given slenderness ratioH /D=height/diameter, within the range usually characteristic of short columns, and extrapolating the results for columns of differentH /D. The importance of the parameter �thickness of jacket/diameter of column, representative of stiffness of jacket/stiffness of concretecore� is also examined. The influence of the parameter is shown to be relatively minor, whereas the nonscaling of the relative stiffness ofthe core and jacket would be a major cause of error. The experimental data, in terms of strain and strength, are also compared withnumerical models proposed in the literature, and the quality of the approximations is analyzed.

DOI: 10.1061/�ASCE�0899-1561�2006�18:3�334�

CE Database subject headings: Fibers; Fiber reinforced plastics; Concrete columns; Scale effect; Retrofitting; Confinement.

Introduction

The characterization of fiber-reinforced polymers �FRPs�, usedeither as composite laminates or as textile wraps to repair andstrengthen structures such as columns, beams, or slabs of rein-forced concrete, is essential for adequate design of the structuralelements. Reliability of the characterization of failure by suppliersis questionable, due in part to scattering of data, variety of resinsused, scarcely known curing conditions, poorly controlled in situapplication, environmental aging, and diverse stacking and layoutof the material. These uncertainties require testing prior to appli-cation. Full-scale testing of the structures is out of the question,

1Full Professor, Centro de Investigação em Estruturas e Construção—UNIC, Faculdade de Ciências e Tecnologia, Universidade Nova deLisboa, 2829-516 Caparica, Portugal.

2Assistant Professor, Centro de Investigação em Estruturas eConstrução—UNIC, Faculdade de Ciências e Tecnologia, UniversidadeNova de Lisboa, 2829-516 Caparica, Portugal.

Note. Associate Editor: Houssam A. Toutanji. Discussion open untilNovember 1, 2006. Separate discussions must be submitted for individualpapers. To extend the closing date by one month, a written request mustbe filed with the ASCE Managing Editor. The manuscript for this paperwas submitted for review and possible publication on March 2, 2004;approved on July 12, 2005. This paper is part of the Journal of Materialsin Civil Engineering, Vol. 18, No. 3, June 1, 2006. ©ASCE, ISSN
0899-1561/2006/3-334–342/$25.00.
334 / JOURNAL OF MATERIALS IN CIVIL ENGINEERING © ASCE / MAY/JU

J. Mater. Civ. Eng. 200

both for logistic and cost reasons, and also because data areneeded prior to the design of the structure. Engineers thus have torely on scale-model tests to predict the behavior of the prototypesand consequently to know how to estimate ultimate strains andstresses in the structures from the results obtained in scaled-downspecimens.

The probability of finding a serious flaw in a structural mem-ber increases with its size and varies with the type of material.Tests of unidirectional FRP cylinders show, for example, greaterscatter of mechanical properties than do tests of metal specimens.The question arises of whether this fact, due partially to the largerdensity of microdefects in the FRP, should make the designstrength �or equivalent parameter� dependent on the volume ofmaterial involved. The answer to this and other questions in thesearch for adequate design values requires understanding of thefollowing problems:• What scale laws permit prediction of full-scale performance?• Are size and geometry dependence of test data a legitimate

issue?• What minimum size �or threshold of the geometry� can be

suggested for the models that allows reliable use of the testdata in design?In the special case of concrete cylinders wrapped with FRP

jackets, the following question is also relevant:• Do the parameters �FRP thickness/effective diameter, or more

adequately, stiffness of outer layers of FRP/stiffness of inner

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core of concrete, also govern the behavior of the columns, andhow can they be attended to?The paper concentrates on these questions, which essentially

concern models of circular cylindrical columns of concrete withFRP jackets subjected to axial loading for different heights ofcylinders of constant diameter d=150 mm, as well as those with adiameter changed to 250 mm. Both plain concrete models, con-sidered as reference cases, and concrete models wrapped withglass fiber-reinforced polymer �GFRP� were tested.

The available literature is next briefly commented upon, andfor the sake of more complete insight into the field, mention ismade of previous work in fracture mechanics. In fact, the issue ofscale effects on fracture was taken up much earlier, and pioneer-ing work developed by Atkins and Caddell �1974� and May andAtkins �1975, 1978� sheds light on various aspects to be analyzed.The first paper quoted, for example, reminds engineers that theuse of laboratory toughness data in the design of large structuresrequires care in the establishment and use of similitude laws. Infact, formulae such as K=��a, where �=applied stress, a=halfof crack length, K=stress intensity factor, when used to obtainprototype stress �p based on laboratory values obtained for K,cannot overlook the fact that in the prototype, �p is lower than thestress �m, causing cracking in a geometrically similar but smallermodel structure. Results published by May and Atkins �1975� fornonlinear elastic structures, although obviously not directly appli-cable to concrete, make an interesting contribution to the analysesof scaling effects, namely showing that stresses that cause crack-ing in large nonlinear elastic structures are smaller than corre-sponding stresses in large linear elastic structures ��p /�m=1/�

versus �p /�m=1/��.Wang �1984� derived an approach with particular relevance for

FRP based on the observation that microcracks, voids in the ma-trix, lack of perfect bond at interfaces, broken fibers, and mis-alignment are common flaws that interact and lead to failurethrough a synergy of effects that make their scaling very complex.Wang shows that scaling effects are governed by a characteristicdimension of the composite substructure.

Planas et al. �1999� show that, for failure depending solely ontwo fracture parameters, it is possible �in principle� to determinethose parameters on scaled-down models if the peak load is mea-sured for two different geometries. They proceed to characterizethe methodology by using tests of split cylinders and three-point-bend notched beams, but the procedures are fairly complex tofollow in current civil engineering applications. Brocca andBažant �2001� call attention to the fact that codes predict the samenominal strength for geometrically similar columns of differentsizes, made of the same concrete, although confined reinforcedconcrete columns exhibit size effects of fracture mechanics type.Brocca and Bažant work experimentally with very small couponsand recommend that a restriction on the size of the damagedregion be introduced and associated with the constitutive law, asin the crack band model, which assumes that the damage propa-gates as a band with a minimum characteristic size.

Tests to characterize reinforced concrete �RC� are normallyconducted on cylinders with height H=300 mm and diameterD=150 mm, for a slenderness ratio H /D=2. It is important toverify the eventual change that strength data would experience fordifferent values of H /D and ultimately for values found in actualconstruction. The influence of H /D on ultimate compressive val-ues, also due to the constraints created by the plates of the press,has been the object of numerous studies for concrete specimens,leading for example to rules to ensure that failure takes place
outside the conic zones adjacent to the plates. Recommendations
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of H /D from H /D�3 to H /D�5 can also be found.The problem of comparing failure loads for geometrically dif-

ferent specimens �e.g., a cylinder with d=150 mm, H=300 mmwith another one with d�=150 mm, H�=750 mm� shifts the at-tention to the “size effect” caused by reduced model tests and tothe examination of whether larger �brittle� bodies fail at lowerstress levels when subjected to the same uniformly distributedaxial compressive load, and how to bring that property into de-sign. Size effects on reinforced concrete structures have been sys-tematically studied by Bažant and coworkers at NorthwesternUniversity, who have published a wealth of data. Without at-tempting thorough coverage of their publications, insight andvaluable information can be found in papers published in the lasttwo decades, such as Bažant �1984, 1993�, Bažant and Zhengzhi�1996�, and Bažant and Novak �2000�. These authors emphasizethat deformation and fracture of heterogeneous materials such asconcrete or fiber composites cannot be modeled by local con-tinuum material models, nor by linear-elastic fracture theory.

A model was proposed as applicable to either aggregate com-posite materials, such as concrete, or to unidirectionally rein-forced fiber composites loaded in the transverse plane. Based onthe assertion that, for stress or strain yield failure load criteria,geometrically similar specimens of different sizes must fail at thesame axial stress, these authors performed tests on geometricallysimilar specimens of H /D=8/3, for H=96, 192, and 384 mm.They observed that the load-deflection curves were coincidentuntil the peak load was attained, but that thereafter the slope wassteeper as the specimen size increased. The results show that scaleeffects can then be of importance when postfailure performanceof concrete may have influence on the structural behavior, aneventual situation found for axially loaded columns confined withFRP wraps. The existence of a size effect reflected in the variationof the nominal stress with �d /da�, the ratio of the depth of thespecimen d by the diameter da of the largest aggregate �12 mm�,was also shown. Additional studies as well as proposed scaleeffect laws can be found in the articles cited.

If one focuses attention on concrete wrapped with GFRP, bothmaterials contribute to the strength of the cylinders and the com-plexity increases. Separate studies of both GFRP and concretehave to be concerted and complemented to analyze the results ofcompressive tests of cylinders with outer protection of GFRP andspecific features of reinforced concrete need also consideration.

Zweben �1984�, who favors the theory that there is a sizeeffect in reinforced polymers, even though it is sometimes uni-dentified because it is masked by a number of factors, notices thefollowing:• Tensile failure of 1D composites is linked to accumulation of

fiber ruptures;• Increasing the number of piles of 1D cylinders shows a rela-

tive decrease in global flexural strength; and• Mean tensile strength of glass, carbon, and aramidic filaments

decreases with increasing length.Davies and Petton �1999� studied scale effects on marine com-

posites, namely polyester resins reinforced with glass fibers. Thequestion posed by these authors has to do with the establishmentof whether or not test methods used to characterize these compos-ites provide intrinsic material properties, prior to addressing theadditional problem of eventual scattering of structural perfor-mance. The conclusions drawn are of qualitative interest: �1�small specimens can be used unless they are excessively thin; and�2� shear strength for 45° tensile test is strongly dependent oncross-sectional area.

Size effects related to concrete composition are also known to

ATERIALS IN CIVIL ENGINEERING © ASCE / MAY/JUNE 2006 / 335

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exist and affect the constitutive relationship. On the macroscopiclevel, concrete is a two-phase system, known in rheology asconcrete-sol, consisting of coarse aggregate embedded into mor-tar; the bond between the two phases disturbed by a large numberof bond microcracks is present even before the first loading isapplied. Owing to the random orientation of aggregate and initialmicrocracks, the concrete can be phenomenologically treated asinitially homogeneous and isotropic.

The subsequent growth of the microdefects, their propagationthrough the mortar, and their coalescence into macrocracks �as aresult of the loading process� depend also on the relative size andproportion of the aggregates and are the main source of the non-linearity in the stress–strain relationship for the concrete. There-fore, it appears that a rational model for the mechanical behaviorof concrete should be based on the continuous damage theory ofKrajcinovic and Silva �1984�. The general damage theory forbrittle materials was developed by Krajcinovic and Fonseka�1981� and later applied to concrete for a 3D state of stress byKrajcinovic and Selvaraj �1983�. The application of this rathercomplex theory to the present problem would introduce great anddisproportionate complexity and was not attempted.

The amount of the aggregate and not its gradation affects themechanical properties; the compressive strength of concrete de-creases with the increase of aggregate fineness. The variation ofthe tensile strength with the diameter D of specimens, for a givenconcrete, is known to decrease with D, but reaches an asymptoticvalue for D=150 mm �actually, 6 in.�. The importance of aggre-gate scaling on model concretes has been studied, and an earlyarticle by Sabnis and Mirza �1979� pinpoints the major aspects tobe considered. Kim and Seong-Tae �2002� observed from statis-tical analyses of the existing experimental data that, within limitsrespected by the maximum aggregate size �also respected in thepresent study, where it is 15 mm�, the effect of the size of aggre-gates can be neglected. In any case, much earlier modeling of theimpact of concrete blocks had shown that the influence of the sizeof aggregates on the compressive strength of concrete is negli-gible when the ratio of the characteristic length of the aggregateto that of the tested specimen is as small as in the present study, inwhich it is essentially 1:10, with a still smaller maximum ratio of1:20 with respect to the height of the cylinders. This aspect is ofstill less importance for concrete cylinders confined by unidirec-tionally reinforced FRP jackets, where the ultimate failure is as-sociated with tensile rupture of the fibers.

The literature survey showed a relative paucity of conclusivedata and some difficulty in recognizing the causes for some typesof size effect encountered in composites of polymeric matrix.Designers have coped with the problem of integrating this reduc-tion of capacity due to size and scale effects by lowering thestrength already affected by other factors. These factors account,for example, for uncertainties due to degree of cure, environmen-tal effects, aging, processing, and method of application. In thetechnical literature, proposals of reduction factors for strengthbased on tests can range from 0.80 to 0.50 and smaller. Furtherstudies and guidelines appear desirable to reduce the amplitude ofthe interval.

The importance of the relative stiffness of the outer shell ver-sus that of the inner concrete core for the performance of thecolumns cannot be neglected. Typically, if laboratory tests on cyl-inders of D=150 mm are made to estimate the strength of actualcolumns of D=350 mm, wrapped with three layers of FRP andwith the same number of plies as used in the lab, then the com-parability of behavior and the transfer of results are difficult. The
reason is the much different relative stiffness of the jacket and the


concrete core, providing much weaker confinement to the proto-type columns. The discontinuity in the incremental thicknesscaused by the discrete number of plies that can be used and thestandard diameter of the tested cylinders often leads to differentdegrees of confinement of tested cylinders versus correspondingprototypes. Then, besides an eventual size effect resulting fromdifferent H /D ratios, there is a violation of similitude laws on the�non�scaling of jacket strength that requires attention.

The ensemble of questions summarized above motivated thestudy described below, in which some of the problems areaddressed.

Materials and Tests

Eighteen concrete cylinders 150 mm in diameter were preparedfor testing, as well as six standard cubes and three cylinders of250 mm. Concrete was mixed in the usual manner and mechani-cal characteristics evaluated in the normalized way, by testingspecimens at a 0.01 mm/s rate on a press of 3,000 kN nominalcapacity. Ultimate tensile stress obtained by the Brazilian test�2.23; 2.04; 2.71 MPa� led to an average value of 2.33 MPa. Thediameter of the cylinders was either 0.15 or 0.25 m, and concretehad an unconfined compressive strength of fco=27.4 MPa testedat 28 days. Experimental values obtained for GFRP cylinderswith two layers led to Ef =21.3 GPa and � f =2.18%.

Cubic compressive strength was determined from tests that ledto an average value of 33.11 MPa. The usual relation of cubicversus cylindrical strength would generate a cylindrical strength�83% of cubic, as often recommended� of 27.46 MPa, whereasexperimental results with standard cylinders gave 27.37 MPa. TheYoung’s modulus of concrete was experimentally found to be21.2 GPa. Eight cylinders of plain concrete, without externalcomposite reinforcement, three of them with H=300 mm and theother five with H=750 mm, were axially tested to failure. Two ofthe latter cylinders had D=250 mm and the remaining hadD=150 mm.

Availability of studies of size effects on plain concrete, asmentioned earlier, showed a large research gap on columns exter-nally strengthened with GFRP, and the study was based on cylin-ders wrapped with GFRP with varying heights of H=300, 450,600, and 750 mm, as partially shown in Fig. 1. This picture also

Fig. 1. Cylinders and strain gauges �H=300, 450, 600, 750 mm�

shows the location and number of strain gauges used to obtain

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strains at intermediate points. That number varied with the heightof the cylinders, from 2 �one circumferentially opposite to theother� for H=300 mm, to 6 for H=450, 600 mm, and 9 forEE-75-C. Transversal gauges were not placed on specimensEE-30-B, EE-45-B, EE-60-B, and EE-75-B. Specimen EE-75-Awas instrumented with 6 strain gauges, and EE-75-D was instru-mented only at midsection.

GFRP jackets were made of unidirectional SEH51/Tyfo GFRPfabric, with sparse Kevlar fibers orthogonal to the glass fiber. TyfoS epoxy was the resin used as advised by the supplier. Each jacketwas composed either of two or three layers of composite appliedby the wet layup technique. Data on the tested specimen are sum-marized in Table 1, including axial strains and failure stresses.The location of part of the gauges is shown in Table 2 and illus-trated in Fig. 2, for H=750 mm; there were three gauges at eachlevel for �250 mm, H=750 mm. Fig. 2 shows one cylinder of750 mm, wrapped with GFRP, ready to be tested, as well as twoother cylinders of the same height, one of plain concrete and theother with outer layers of GFRP, after failure. The readings from

Table 1. Location of Strain Gauges

hi

�a� �150 mm

H=450 mm H=600 mm H=750 mm

h3,h6 287.5 400 512.5

h2,h5 225.0 300 375.0

h1,h4 162.5 200 237.5

�b� �250 mm; H=750 mm

h3,h6,h9 500

h2,h5,h8 375

h1,h4,h7 250

Note: Measures are in mm from bottom.

Table 2. Identification and Characterization of 21 Cylinders Tested

SpecimenH

�mm��

�mm� Layers of GFRPAge at test

�days�

EE-30-1EE-30-2EE-30-3

300 150 Plain 282828

EE-75-1EE-75-2EE-75-3

750 150 Plain 241241248

EE-75-4EE-75-5

750 250 Plain 344345

EE-30-AEE-30-BEE-30-C

300 150 2 336248335


450 150 2 339248342


600 150 2 342342342

EE-75-AEE-75-B

750 150 2 339248

EE-75-C 750 250 2 343

EE-75-D 750 150 3 —

Note: fcm , t �adjustment of fcm to t days at testing�; �max*= fcm,t �1.5+� /H
strength.
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the strain gauges placed on the GFRP skin to obtain the circum-ferential strain at different levels are displayed in Table 3.

At both ends of the cylinders, two extra wraps of approxi-mately 35 mm height were placed to avoid eventual rupture dueto singular stress distribution next to the loading plates. Placinggauges at intermediate sections to obtain more reliable measure-ments of ultimate strains in the GFRP, rather than assuming thatrupture occurs at the vicinity of midheight, did not lead to signifi-cantly different results. However, readings from the gauges forcircumferential strains show that specimens EE-45-A andEE-60-C fail near the bottom, whereas EE-45-C, 60-A, andEE-75-A fail nearer midheight, confirming that placement ofgauges at different heights was wise. The general failure patternsin this set of tests are well illustrated by Figs. 3 and 4, and nospecific difference is identified that can be attributed to the heightof the cylinders, that is, a qualitative inspection of results does notidentify size effects worth mentioning.

Stress–Strain Curves

Ductility and strength changes attributable to different values ofthe H /D parameter, as well as data on the lateral tensile stressesdeveloped while the FRP jackets confine the different cylinders,require analysis. Examination of Figs. 5–7 allows comments oneventual differences in behavior and failure mechanisms that aresummarized next.

Fig. 5 displays results for typical cylinders of height H=300,450, and 600 mm and �150 mm. The circumferential strains atultimate load are slightly higher for H=300 and 450 mm than forH=600 mm, but the differences are minimal and may be partiallydue to the greater closeness of the corresponding strain gauges tothe section where failure first took place. Otherwise, the usualbehavior of concrete confined by a jacket of initially passive lay-

�max

/mm2�

Average�max,m

�N/mm2� fcm , t �max*

�max, v�%�

Average�max, vm

�%�

29.227.125.8

27.4 27.4 — 0.210.190.20

0.20

26.6—

26.4

26.5 29.5 27.2 0.190.180.21

0.19

34.929.4

32.2 31.2 31.1 0.250.22

0.24

91.689.487.5

89.5 31.129.631.1

— 2.612.722.28

2.54

91.989.891.9

91.2 31.129.631.2

— 2.342.322.31

2.32

81.288.787.5

85.8 31.231.231.2

— 2.052.552.21

2.27

89.186.0

87.6 31.129.6

— 2.432.65

2.54

55.8 55.8 31.2 — 1.09 1.09

128.1 128.1 37.6 — 2.44 2.44

as per Concrete Society Technical Rep. No. 11: Concrete core testing for

�N

� /1.84


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ers of FRP under compressive axial load is observed. Values ofclose magnitude were attained for maximum axial compressivestrength for all specimens.

Fig. 6 associates stress–strain curves for two cylinders of thesame H /D=3, characterized by either H=750, D=250 mm orH=450, D=150 mm, thus introducing geometric scaling, that is,both height and diameter increased by the same factor. By keep-ing the same number of GFRP layers, as in all other tests reportedabove, the confinement is less effective for the cylinders of largerdiameter, and loss of strength ought to be expected. In fact, theexpected decrease of strength was exceeded, while the failurestrain was also reduced. The cylinder of �250 mm reached amaximum axial stress of 55.8 MPa, at a strain of 1.09%, while thecylinder of the same H /D and �150 mm failed for an averagestress of 91.2 MPa at �=2.32%.

These values raise an important question regarding laboratorytests, since the column being designed or repaired is almost al-ways of larger diameter than the cylinder tested in the laboratory.The decrease in the lab of the number of layers of reinforcementdecided by the designer so that there is similitude of confinement

Table 3. Failure Circumferential Strains Obtained from Gauge Measurem

Specimen�max

h1�max

h2�max

h3�max

h4�

EE-30-A 2.03 1.94 — —

EE-30-B — — — —

EE-30-C 2.03 1.75 — —

EE-45-A 2.05 2.04 1.71 1.92 1

EE-45-B — — — —

EE-45-C 1.72 2.02 1.94 2.03 1

EE-60-A 1.76 1.65 1.60 1.14 1

EE-60-B — — — —

EE-60-C 1.73 1.68 1.23 1.73 1

EE-75-A 1.87 2.09 2.01 1.42 1

EE-75-B — — — —

EE-75-C 0.84 0.98 0.73 0.79 0

EE-75-D 1.14 1.93 — —

Fig. 2. Specimens of 750 mm: �a� prio



is difficult to implement, mostly because the thickness of thejacket has to vary discontinuously and cannot be reduced to lessthan one ply.

Fig. 7 provides some more insight into the importance of therelative stiffness of the outer layer and the concrete core. First, itallows the comparison of the response of cylinders of same height�750 mm� and diameter �150 mm� for two and three layers ofGFRP. The cylinders with two layers exhibited an average axialstrength of 87.6 MPa and an ultimate strain 2.54%; the specimenof the same H and D, but with three layers of GFRP, failed for128.1 MPa and 2.44%, respectively. The stress fcm found experi-mentally was 30.3 MPa �2 layers� and 37.6 MPa �3 layers�. Interms of circumferential strain registered with gauges, the strainfor �150 mm with two layers was larger, 2.09%, than for threelayers when it was found 1.93%. Second, Fig. 7 allows also thecomparison of results for H=750, two layers of GFRP, and both�150 and �250 mm. The most important result detected is thesubstantially lower strength and ductility observed in the�250 mm cylinders as compared with the specimens with�150 mm, keeping the same number of layers of GFRP. The

in %�

�max

h6�max

h7�max

h8�max

h9

Averageof maximum

�max,hmi

— — — — 2.03

— — — —

— — — —

1.70 — — — 2.04

— — — —

1.99 — — —

1.17 — — — 1.74

— — — —

0.83 — — —

1.25 — — — 2.09

— — — —

1.01 0.83 1.00 1.16 1.16

— — — — 1.93

st; �b and c� after compressive failure

ents �

max

h5

—

—

—

.77

—

.85

.45

—

.32

.35

—

.63

—

r to te

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curves also confirm that replacing H=450 mm with H=750 mm,that is, different H /D for the same D, again does not cause sig-nificant changes.

Analyses of Results

The average experimental data found for axial strength of theconfined cylinders with two layers of GFRP were 91.2 MPa for150 mm diameter and 55.8 MPa for 250 mm. Recall thatEf =21.3 GPa and � f =2.18% for GFRP cylinders with two layersand thickness tf =2.54 mm and that concrete had initial uncon-fined compressive strength fco=27.4 MPa. Estimates of the com-pressive strength of concrete confined by FRP has been the objectof several proposals based on experimental data obtained fromtests of confined cylinders, namely those cited by Lam and Teng�2002�, many of them expressed by

f cc� = fcm,t�1 + k1�1

fc0� �1�

�1 =2� fEftf

D�2�

where fcc� , fcm,t�confined and age corrected unconfined concretecompressive strength; �1�confining pressure provided by thejacket; and tf, Ef, and � f�thickness, Young’s modulus, and tensile

Fig. 3. Specimens of H=300, 450, an

Fig. 4. Cylinders of H

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strength at the rupture of the GFRP. It is understood that the useof the peak values for the GFRP reinforcement causes an exag-geration of the confinement pressure, since at global rupture ofthe cylinders, the fibers are not uniformly submitted to the ulti-mate stress. However, the procedure is maintained in the absenceof alternatives less prone to errors.

The values of kl that generate predicted fcc� consistent withaverage experimental data are kl=3.9 for �150 mm and kl=2.6for �250 mm. The value for D=150 mm is higher than thoseassociated with most proposed formulae for fcc� , raising doubts onadequacy of the formula for small diameters and high confine-ment. Karbhari and Gao’s �1997� Model 1, for example, led tokl=2.26 and 2.30 by application of the expression

k1 = 2.1� �1

f c0�� 3�

Hereafter, kl=2.3 and Eq. �1� are selected for the sake of sim-plicity, leading to estimated values of 66.3 and 52.9 MPa, stillsignificantly below those found in the experiments, especially for�150 mm. These results suggest that the expressions representedEq. �1� are rather conservative for the smaller diameters andstronger confinement.

Returning to the tests, if the increase of the diameter from�150 to �250 mm were accompanied by a simultaneous and pro-portional increase of the thickness of the composite, that is, thelarger cylinder had, for example, t=4.23 mm, then the strength

mm, with GFRP jacket, after failure

mm—Rupture modes

d 750

=600


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would be expected to be of the same order of magnitude, aspredicted by Eq. �1�. So long as a press with sufficient capacity isavailable, tests on �250 mm cylinders are recommended for threeand four plies of composite so as to allow interpolation for f cc� ,corresponding to an intermediate thickness. Estimates of f cc� , fordesign, from experimental data can then be made based on thistype of procedure.

Alternatively, the model proposed by Spoelstra and Monti�1999� was shown to lead to more accurate predictions by Rod-rigues and Silva �2001�, notwithstanding the additional effort ofthe iterative process, as mentioned by Mirmiran and Singhvi�2001�. The application of such a procedure is shown in Fig. 8 forcylinders of H=750 mm and diameters of 250 and 150 mm, con-fined with two plies of GFRP. For the same stress level, the modelestimated an axial strain a little larger than that found experimen-tally, while the lateral strain is a little underestimated forD=150 mm. For D=250 mm, the results generated by the modelproposed by Spoelstra and Monti �1999� were found to be stillmore representative for the stress fc versus axial strain �c while itsunderestimate of �1 is more accentuated in the region of lowlateral strain.

The effect of H /D on f cc� was not clearly evident in the tests,perhaps because of converging factors: the number of tests is notlarge, the ultimate strains may occur at a distance from the straingauges �especially for H=750 mm�, and rupture occurs at thefibers. Mirmiran et al. �1998�, for an associated problem, pro-

posed an expression that relates f cc� with f̄ cc� , the latter obtainedfrom the standard cylinders with H /D=2

f cc�

f̄ cc�= 0.0288�H

D�2

− 0.263�H

D� + 1.418 �4�

This expression was derived for confinement provided bytubes of 6, 10, or 14 plies of E-glass, with fibers oriented at ±75°and polyester resin for the matrix. These characteristics are dif-ferent from those of the columns studied here and the differencesin relative strength and stiffness of the jacket and cylinder advisecare in comparing the corresponding results with those of thepresent study. In any case, Eq. �4� indicates decreasing values off cc� only until H /D reaches 4.56 �minimum strength 18.3% below

f̄ cc� �. Slenderer columns fall outside the range of application of

that formula. For f̄ cc� =89.5 MPa, and H /D=3 and 4, the predic-

Fig. 5. Compressive stress versus axial and circu

tions with that formula are 79.5 and 74.0 MPa and fall below



those registered in the present study, on which the average valuesof f cc� were 91.2 and 85.8 MPa for H /D=3 and 4.

Thériault et al. �2004� presented results on the size and slen-derness effects of FRP-confined columns, with similar conclu-sions on the compressive strength of specimens with D=152 and304 mm and 1 or 3 plies of GFRP. These authors do not reportstrains and concluded that no significant variations occur in themeasured compressive strengths for slendernesses H /D=2 and 6.

Fig. 7 displays curves that allow comparison of the changes onthe strength of the columns with �1� the increase in the number ofplies from two to three and �2� the change of diameter from150 to 250 mm, keeping the same number of two plies in thelatter cases. The comparison of the strains found at failure, forH /D=2 and D=150 mm, requires some care. Consulting Table 2for D=150 mm and varying H /D, one finds average strain valuesof 2.54 for H /D=2, 2.32 for H /D=3, and 2.27 for H /D=4, thatis, decreasing strain at failure, reversed at H /D=5, rebounding to2.54 when a value lower than 2.27 would be expected. At the timeof the experiments the record of this anomalous result went un-detected, perhaps because the gain in axial compressive strengthwas the parameter given most attention. Such gain is also dis-played in Table 2 �87.6 MPa for two layers and 128.1 MPa forthree layers�. The expression in Eq. �1�, making �=2.5% andkl=2.30, as before, provides results that were contrasted with theactual experimental values. The calculations predicted an increaseof axial strength of 25%, while the experimental tests showed an

ntial strains for cylinders of � 300 and 600 mm

Fig. 6. Comparison of H /D=3 for H=750 and H=450

mfere

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increase of 46%, suggesting a stronger confinement of the speci-mens with three layers of GFRP than predicted by the approxi-mate formulae.

Concluding Remarks

The experimental study has shown the following features for col-umns of concrete externally reinforced with a passive jacket ofGFRP:• Cylinders of �150 mm of varying heights �H �300 mm�, all

with same thickness of the outer layer of GFRP, led to closeresults for ultimate compressive strength and axial strain. Inthat strict sense, no significant size effect was identified.

Fig. 7. Two and three layers of GFRP for �150 mm, two differen

Fig. 8. Approximate results from appli

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• For a given size �H /D�, the increase in the number of layersled to an increase in the maximum load. This increase ex-ceeded the value predicted by available models.

• Increasing the diameter of the specimens, namely from�150 to �250 mm, causes a significant reduction in thestrength of the cylinders, even if H /D is kept constant, if thethickness of the outer reinforcement is not increased. In fact,the confinement provided by the composite outer shell be-comes relatively weaker for increasing diameters, and labora-tory results for which the stiffness of the jacket does notproperly scale the confinement effect cannot be directly usedfor design purposes.

• Estimates of strength based on expressions currently used pro-vided, in this study, results in general below those found in the

eters �=150, 250 mm, and same 2 layers of GFRP reinforcement

of Monti–Spoelstra iterative procedure

t diam

cation


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tests. The model that provided the best estimates, among thosetested, was the one due to Spoelstra and Monti �1999�.

• Circumferential strains show variation with increase of height,but registered changes may also be due to the proximity of themeasuring gauges to the section of actual rupture and no con-clusion could be drawn.

Acknowledgments

The authors thank engineers A. Paulo and P. Marques, who per-formed part of the tests. Research was made possible partiallythrough financing by Fundação para a Ciência e Tecnologia forProject POCTI/1999/ECM/36113.

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Documents

Size and Relative Stiffness Effects on Compressive Failure of Concrete Columns Wrapped with Glass FRP