journal of constructional steel research of passive confinement...w.l.a. de oliveira et al. /...

Journal of Constructional Steel Research 66 (2010) 487–495

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Journal of Constructional Steel Research

journal homepage: www.elsevier.com/locate/jcsr

Evaluation of passive confinement in CFT columns

Walter Luiz Andrade de Oliveira a, Silvana De Nardinb, Ana Lúcia H. de Cresce El Debs a,∗,Mounir Khalil El Debs a

a Department of Structural Engineering, University of São Paulo, Brazilb Department of Civil Engineering, Federal University of São Carlos, Brazil

a r t i c l e i n f o

Article history:Received 16 September 2009

Accepted 23 November 2009

Keywords:Concrete-filled steel tubular columns

Confinement effect

Analytical models of confinement

Experimental analysis

Circular cross section

a b s t r a c t

This paper presents the experimental results of 32 axially loaded concrete-filled steel tubular columns

(CFT). The load was introduced only on the concrete core by means of two high strength steel cylinders

placed at the column ends to evaluate the passive confinement provided by the steel tube. The columns

were filled with structural concretes with compressive strengths of 30, 60, 80 and 100 MPa. The outer

diameter (D) of the column was 114.3 mm, and the length/diameter (L/D) ratios considered were 3, 5, 7

and 10. The wall thicknesses of the tubes (t) were 3.35 mm and 6.0 mm, resulting in diameter/thickness

(D/t) ratios of 34 and 19, respectively. The force vs. axial strain curves obtained from the tests showed, in

general, a good post-peak behavior of the CFT columns, even for those columns filled with high strength

concrete. Three analytical models of confinement for short concrete-filled columns found in the literature

were used to predict the axial capacity of the columns tested. To apply these models to slender columns,

a correction factor was introduced to penalize the calculated results, giving good agreement with the

experimental values. Additional results of 63 CFT columns tested by other researcherswere also compared

to the predictions of the modified analytical models and presented satisfactory results.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Concrete-filled steel tubular (CFT) columns have many con-structional advantages, such as high energy absorption, formworkeconomy and high ductility because the steel tube effectively con-fines the concrete core. Many researchers have studied this type ofcolumn in recent decades, e.g., [1–14].

There are various analytical models proposed by differentcodes and researchers for evaluating the strength of CFT columnsconsidering the confinement effect or not. However, to be realistic,the prediction of the axial load capacity of these columns mustconsider the confinement effect provided by the steel tube. In thisway, the axial load capacity of the CFT columns inmost of the casesis higher than the sumof the resistance of their components, whichare the steel tube (Aa · fy) and the concrete core (Ac · fc).

Observing two international code provisions, the differencesare clear. The Eurocode 4 [27] has a complex expression to predictthe axial capacity of CFT columns, in which the confinement isconsidered. On the other hand, the ANSI/AISC [16] has a moresimple equation, and the basic difference lies in the considerationof the confinement contribution for the CFT column axial capacity.

∗ Corresponding address: Departamento de Engenharia de Estruturas, Av.

Trabalhador Saocarlense, 400, São Carlos - SP CEP: 13566-590, Brazil. Tel.: +55 16

3373 9469; fax: +55 16 3373 9482.

E-mail address: [email protected] (A.L.H.C. El Debs).

Beck et al. [17] conducted a reliability analysis on CFT columnsby considering four different code provisions (CAN/CSA S16:2001[18], Eurocode 4:2004 [27], ANSI/AISC:2005 [16] and ABNT NBR8800:2008 [19]). The errors of the resistance models weredetermined by comparing 93 experimental results for ultimateloads with code-predicted column resistances. Regression analysiswas used to describe the variation of the model error with thecolumn slenderness and also to describe the model uncertainty.As a result, it was found that the prediction given by ANSI/AISCis overly conservative for very short columns, while the predictionby EC4 is not conservative. This occurred because the confinementeffect is over-estimated by the EC4 formula, even for shortcolumns. For large slenderness ratios, concrete confinement isminimal, column behavior is mainly elastic, and resistance modelsof the four design codes become slightly conservative.

2. The passive confinement in CFT columns

The confinement effect has been studied for many years. One ofthe first works on this subject was conducted by Richart et al. [20]and Considère [28] (apud [20], where the behavior of reinforcedconcrete columns using spiral reinforcement was studied. Richartet al. [20] concluded that the internal pressure provided by thespiral reinforcement should be multiplied by 4.1 to allow for theconfinement effect.

In recent years, many authors have presented analytical modelsto predict the confinement effect in reinforced concrete columnsand also in concrete-filled steel tubular columns.

0143-974X/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jcsr.2009.11.004

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488 W.L.A. de Oliveira et al. / Journal of Constructional Steel Research 66 (2010) 487–495

Nomenclature

fck compressive strength of concretefc mean compressive strength of concretefy yield strength of steelD external diameter of tubet steel tube thicknessL length of columnEcm Young’s modulus of the concrete given by Eurocode

2

Those models take into account the conclusions given by

Richart et al. [20], where the compressive strength of the concrete

in the column core is increased by the confinement effect

promoted by the ties in the case of concrete columns, and by the

steel tube for CFT columns.

Fig. 1 shows the passive confinement for concrete columns and

CFT columns. The confining stress distribution is very complex

in concrete columns confined by ties and spirals since the lateral

restraint of concrete expansion is highly localized, as seen in Fig. 1a,

b and c, for circular, square and rectangular concrete columns,

respectively,where the arching action in confined concrete column

can be seen [21].

The problem with the localized expansion of concrete does not

occur in CFT columns. According to [4,5,8], the circular CFT columns

present better gain of load capacity due to the confinement effect,

as shown in Fig. 1e. The square or rectangular cross sections

present some loss of the confinement effect compared to circular

sections, but they are still better than concrete columns, as

shown in Fig. 1d (the separation of steel and concrete is slightly

exaggerated in the caption).

3. Research significance

There are many variables that affect the confinement effect in

CFT columns, such as the concrete compressive strength, length-

to-diameter ratio (L/D), diameter-to-thickness ratio (D/t), typeof loading (in the concrete core or in both materials), shape of

cross section, eccentricity of loading, etc., and there is no analytical

model able to take into account all variables. Thus, in this work, the

ability of three analytical models to predict the axial load capacity

of CFT columns was tested. The models chosen were proposed

by Susantha et al. [9], Johansson [11] and Hatzigeorgiou [12],

which are able to predict axial strength of CFT short columns

with good accuracy. However, for CFT usual columns, the models

overestimate the load capacity.

To correct the values of the axial load capacity for regular CFT

columns and find a tool to predict their axial capacity, a slenderness

correction factor was introduced in the three models.

The results of the analytical models were compared to the

results for 116 CFT columns, where 32 were tested by the authors

and 63were from the literature: 15 from [22], 13 from [23], 18 from

[24] and 17 from [25].

4. Experimental program

Thirty-two CFT columns with different values of concrete

compressive strength (fc), L/D and D/t ratio were tested under

concentric loading to analyze the influence of those parameters

on the general behavior and load capacity of CFT columns. These

tests are part of a research program on the subject, in which 64

CFT columns were studied by the authors, and the results of 16 of

them have already been presented in [14].

The main geometric characteristics of the tested specimens are

the external diameter D = 114.3 mm; the thickness of the

steel tube t = 3.35 mm and 6.0 mm; L/D = 3, 5, 7 and 10;

and fc = 32.7 MPa, 58.7 MPa, 88.8 MPa and 105.5 MPa. The

Young’s modulus of the concrete was calculated according to the

expression of EC2 [15] (Eq. (1)).

Ecm = 22 000 ·(fck + 8 MPa

10

)0.3

. (1)

The small diameter was chosen based on the load capacity of the

test machine. All specimens were tested with concentric loading

applied on the concrete core.

The columns were identified with names such as: C1 (t =3.35 mm — black tubes) or C2 (t = 6.0 mm — painted white

tubes) + concrete compressive strength + L/D ratio + C (load

applied in concrete core). For example: C1-60-5D-C , C1 means a

columnwith a wall thickness of the tube of t = 3.35mm, 60 refers

to the concrete strength class (in MPa), 5D is the length of column

(5× diameter), and C indicates that the loadwas introduced in the

concrete core.

The yielding stress of the steel tube was obtained by tension

tests, according to ASTM A370-07a [26] with I specimens. The

average value adopted for the yielding stress (fy) was 287.33 MPa

for C1 and 342.95 MPa for C2 tubes, and the corresponding strain

was 1.4� for C1 and 2.0� for C2 tubes. The elasticmodulus for the

steel was taken as Es = 206.000 MPa.

Concrete of four different compressive strengths (C30, C60, C80and C100) were used as column filling material. The mixes were

produced using the available materials, and the details are pre-

sented in [14]. The axial compressive strength was determined by

tests on 10×20 cm cylindrical specimens at 28 days, the same day

of the columns tests.

The testswere performed using an Instron 8506 servo hydraulic

actuator. The details of the test machine, the loading ratios and the

instruments used are also presented in [14].

5. Tests results

The failure mode of the specimens was a function of the L/DandD/t ratios and also of the concrete strength. The short columns

(L/D = 3) failed due to the crushing of the concrete core, aggra-

vated by the local buckling of the steel tube after having reached

the yielding stress of the steel. In Fig. 2a and b, for C1 and C2columns, respectively, it can be observed that the C2 columns can

better restrain the expansion of the concrete core for the same con-

crete compressive strength (30 MPa). The increase in the lateral

strain in columns with t = 6.0 mm is uniform along the height

compared to columns with t = 3.35 mm, where the lateral strain

is more localized at the middle height. The specimens filled with

normal strength concrete (C30 and C60) showed a significant in-

crease in the cross section dimensions without any sudden loss of

load capacity, as seen in diagrams of Fig. 6a. For C1 columns, filled

with high strength concretes (C80 and C100), the confinement ef-

fect provided by the steel tube was not enough to give ductility to

the columns, but for C2 columns the steel tube was able to confine

the concrete core even for high strength concrete.

C1 columns with L/D = 5 presented shear failure of the

concrete core for all concrete compressive strengths considered

(Fig. 3a). For C2 columns, the thickness of the steel tube was ca-

pable of restraining shear in the concrete core. This columns failed

by buckling, as seen in Fig. 3b. Both C1 and C2 columns presented


W.L.A. de Oliveira et al. / Journal of Constructional Steel Research 66 (2010) 487–495 489

a b c d e

Fig. 1. Effectively confined concrete for concrete columns and CFT columns.

a b

Fig. 2. (a) C1-3D tested column; (b) C2-3D tested column.

a b


good ductile behavior when filled with normal strength concrete,but that was not observed for C1 columns, where high strengthconcrete was used (Fig. 6b).

Columns with L/D = 7 and L/D = 10 and a tube thicknessof 3.35 mm (C1 columns) presented failure by shear at the middleheight of the columns (Figs. 4a and 5a). For high strength concrete,there was a significant loss of load capacity after the peak load wasreached (Fig. 6c and d). For normal strength concrete the columnswere still able to show ductility after the peak load.

For C2 columns with L/D = 7 and L/D = 10, the failureoccurred by overall buckling. Fig. 4b shows a columnwith L/D = 7before testing, and in Fig. 5b the buckling of columns with L/D =10 can be seen.

In general, thick tubes were able to prevent shear in columns,independent of the column slenderness, which was not observedwhen thin tubes were used.

The specimens filled with normal strength concretes showedelasto-plastic post-peak behavior with strain-hardening, while the



a b

Fig. 4. (a) C1-7D tested column; (b) C2-7D columns before testing.

a b


oneswith high strength concrete presented elasto-plastic behaviorwith strain-softening, as observed by Johansson [11].

The specimens with L/D ≥ 7 exhibited insufficient radial strainfor mobilizing the confinement effect. This was confirmed by thereadings of the two strain gauges placed around the column. Themeasured radial strain at the peak load was about 1.5� for thecolumnswith L/D = 10 andmore than 10� for the short columns.

6. Analytical models and comparisons

Three analytical models were studied and used to predict theaxial capacity of CFT tubular columns: [9,11,12]. The models arebased in the same theory of lateral pressure promoted by the steeltube, but they show different procedures to predict the confinedconcrete strength (fcc). The sequence of procedures to predict theaxial strength of CFT columns using each one of the analyticalmodels is shown in Table 1.

Table 2 shows the measured concrete compressive strength(fc) for specimens C1 and C2, the confined concrete strength (fcc)calculated by each model and the relations between experimentalresults of the axial capacity (Fexp) and the predicted values using

the analytical models. Table 2 also shows the results for the32 tested columns. Despite the differences between the threecalculated values for the confined concrete strength, the predictedaxial capacities of the CFT columns are quite similar.

The confined concrete strength and the predicted axial capacityare denoted as fcc,Sus and FSus for the model proposed by Susanthaet al. [9], respectively, fcc,Joh and FJoh for the model proposed byJohansson [11] and fcc,Hat and FHat for the model proposed byHatzigeorgiou [12].

Table 2 shows the comparisons between the experimentalresults and predicted ones, for mean values. They are close, buton the unsafe side, since the predicted results are a little higherthan the experimental ones. This happened because the analyticalmodels are adequate to predict the axial capacity only for shortcolumns, and the results considered take into account slender andshort columns.

In an attempt to correct the prediction for slender columns,a correction factor (λOliveira) was introduced. This factor wascalibrated by the 32 experimental results. A logarithmic regressionwas made considering the relation between the experimentalresults and the resistance of the cross section of CFT columns



Table 1Sequence to calculate the predicted axial capacity by using the three analytical models studied.

Model Expressions Observations

Susantha et al. [9]

ν ′c = 0.881

106· ( D

t

)3 − 2.58

104· ( D

t

)2 + 1.953

102· ( D

t

) + 0.4011 Empirical factor

νc = 0.2312 + 0.3582 · ν ′c − 0.1524 ·

(fcfy

)+ 4.843 · ν ′

c

·(

fcfy

)− 9.169 ·

(fcfy

)2

Poisson ratio of a steel tube filled with concrete

β = νc − νs νs is the Poisson ratio of a steel tube, taken equal to 0.5

frp = β · 2·tD−2·t · fy Lateral pressure at the peak load

fcc = fc + 4 · frp Confined compressive strength of the concrete

FSus = Ac · fcc + Aa · fy Axial capacity of CFT column

Johansson [11]

νa = 0.3 | νc = 0.2 | εv = 0.002 (2�) Initial considered values here

εahr = εv ·(νa−νc )[1+ 2·t·Ea

(D−2·t)·Ec] Restrained steel strain

εah = −νa · εv + εahr Final lateral strain of steel

σah = Ea1−ν2a

· (εah + νa · εal) and σal = Ea1−ν2a

· (εv + νa · εah) Steel’s lateral and longitudinal stresses

σlat = σah · 2·t(D−2·t) Compressive confining pressure

k = 1.25 ·(1 + 0.062 · σlat

fc

)· f −0.21

c fc in MPa Parameter that reflects the effectiveness of

confinement

fcc = fc ·(

σlatfct

+ 1

)kConfined compressive strength of the concrete.

For fct was used here the expression of Eurocode 2.

FJoh = Ac · fcc + Aa · σal Axial capacity of CFT column

Hatzigeorgiou [12]

σh = fy · exp [ln

( Dt

) + ln(fy) − 11

]fy in MPa Hoop stress of the steel

frp = 2·σh ·tD−2·t Mean confining stress

fcc = fc + 4.3 · frp Confined compressive strength of the concrete

fyc = 0.5 ·(σh −

√4 · f 2y − 3 · σ 2

h

)Compressive yield stress

FHat = Ac · fcc + Aa · fyc Axial capacity of CFT column

Table 2Values of compressive strength of concrete (fc ), confined compressive strength of concrete (fcc ) and the ratios between experimental results of CFT tested columns and axial

capacity of columns predicted for each analytical model.

Specimen fc (MPa) fcc,Sus fcc,Joh fcc,Hat Fexp (kN) Fexp/FSus Fexp/FJoh Fexp/FHat

C1-30-3D-C 32.68 55.88 44.41 45.28 816.2 0.967 0.913 1.058

C1-30-5D-C 32.68 55.88 44.41 45.28 749.4 0.888 0.838 0.972

C1-30-7D-C 32.68 55.88 44.41 45.28 736.8 0.873 0.824 0.955

C1-30-10D-C 32.68 55.88 44.41 45.28 563.6 0.668 0.630 0.731

C1-60-3D-C 58.68 87.17 71.95 71.28 995.7 0.883 0.870 0.988

C1-60-5D-C 58.68 87.17 71.95 71.28 937.0 0.831 0.818 0.930

C1-60-7D-C 58.68 87.17 71.95 71.28 932.9 0.827 0.815 0.926

C1-60-10D-C 58.68 87.17 71.95 71.28 904.2 0.801 0.790 0.897

C1-80-3D-C 88.78 109.97 105.78 101.38 1242.2 0.930 0.855 0.969

C1-80-5D-C 88.78 109.97 105.78 101.38 1281.4 0.959 0.882 1.000

C1-80-7D-C 88.78 109.97 105.78 101.38 1206.5 0.903 0.830 0.942

C1-80-10D-C 88.78 109.97 105.78 101.38 1200.0 0.899 0.826 0.936

C1-100-3D-C 105.45 116.41 124.01 118.05 1610.6 1.155 0.995 1.124

C1-100-5D-C 105.45 116.41 124.01 118.05 1598.9 1.147 0.988 1.116

C1-100-7D-C 105.45 116.41 124.01 118.05 1513.5 1.086 0.935 1.056

C1-100-10D-C 105.45 116.41 124.01 118.05 1481.2 1.063 0.915 1.034

C2-30-3D-C 32.68 64.10 49.74 51.56 1380.0 1.125 1.094 1.191

C2-30-5D-C 32.68 64.10 49.74 51.56 1218.7 0.993 0.966 1.052

C2-30-7D-C 32.68 64.10 49.74 51.56 1000.4 0.815 0.793 0.863

C2-30-10D-C 32.68 64.10 49.74 51.56 909.7 0.741 0.721 0.785

C2-60-3D-C 58.68 98.95 78.38 77.56 1425.3 0.942 0.951 1.038

C2-60-5D-C 58.68 98.95 78.38 77.56 1389.3 0.918 0.927 1.012

C2-60-7D-C 58.68 98.95 78.38 77.56 1244.4 0.822 0.831 0.907

C2-60-10D-C 58.68 98.95 78.38 77.56 1141.3 0.754 0.762 0.831

C2-80-3D-C 88.78 118.11 114.31 107.66 1673.9 1.002 0.933 1.033

C2-80-5D-C 88.78 118.11 114.31 107.66 1564.7 0.936 0.872 0.966

C2-80-7D-C 88.78 118.11 114.31 107.66 1509.3 0.903 0.841 0.932

C2-80-10D-C 88.78 118.11 114.31 107.66 1389.1 0.831 0.774 0.857

C2-100-3D-C 105.45 118.95 133.47 124.33 1943.4 1.158 0.996 1.106

C2-100-5D-C 105.45 118.95 133.47 124.33 1827.1 1.089 0.936 1.040

C2-100-7D-C 105.45 118.95 133.47 124.33 1788.9 1.066 0.916 1.018

C2-100-10D-C 105.45 118.95 133.47 124.33 1613.5 0.962 0.827 0.918

Mean 0.936 0.871 0.974

Standard dev. 0.127 0.092 0.100

C.O.V. 13.6% 10.6% 10.3%



Table 3Results of tested columns and ratios with predicted values from analytical models using the slenderness correction factor.

Specimen L/D D (mm) t (mm) fc (MPa) fy (MPa) Fexp (kN) Fexp/FSus Fexp/FJoh Fexp/FHat

C1-30-3D-C 3 114.3 3.35 32.68 287.33 816.2 0.967 0.913 1.058

C1-30-5D-C 5 114.3 3.35 32.68 287.33 749.4 0.976 0.921 1.067

C1-30-7D-C 7 114.3 3.35 32.68 287.33 736.8 1.028 0.970 1.124

C1-30-10D-C 10 114.3 3.35 32.68 287.33 563.6 0.850 0.803 0.930

C1-60-3D-C 3 114.3 3.35 58.68 287.33 995.7 0.883 0.870 0.988

C1-60-5D-C 5 114.3 3.35 58.68 287.33 937.0 0.912 0.899 1.021

C1-60-7D-C 7 114.3 3.35 58.68 287.33 932.9 0.973 0.959 1.089

C1-60-10D-C 10 114.3 3.35 58.68 287.33 904.2 1.020 1.005 1.142

C1-80-3D-C 3 114.3 3.35 88.78 287.33 1242.2 0.930 0.855 0.969

C1-80-5D-C 5 114.3 3.35 88.78 287.33 1281.4 1.054 0.969 1.099

C1-80-7D-C 7 114.3 3.35 88.78 287.33 1206.5 1.063 0.977 1.108

C1-80-10D-C 10 114.3 3.35 88.78 287.33 1200.0 1.144 1.051 1.192

C1-100-3D-C 3 114.3 3.35 105.45 287.33 1610.6 1.155 0.995 1.124

C1-100-5D-C 5 114.3 3.35 105.45 287.33 1598.9 1.260 1.085 1.226

C1-100-7D-C 7 114.3 3.35 105.45 287.33 1513.5 1.278 1.100 1.243

C1-100-10D-C 10 114.3 3.35 105.45 287.33 1481.2 1.353 1.165 1.316

C2-30-3D-C 3 114.3 6.00 32.68 342.95 1380.0 1.125 1.094 1.191

C2-30-5D-C 5 114.3 6.00 32.68 342.95 1218.7 1.091 1.061 1.155

C2-30-7D-C 7 114.3 6.00 32.68 342.95 1000.4 0.960 0.933 1.016

C2-30-10D-C 10 114.3 6.00 32.68 342.95 909.7 0.944 0.918 0.999

C2-60-3D-C 3 114.3 6.00 58.68 342.95 1425.3 0.942 0.951 1.038

C2-60-5D-C 5 114.3 6.00 58.68 342.95 1389.3 1.008 1.019 1.112

C2-60-7D-C 7 114.3 6.00 58.68 342.95 1244.4 0.968 0.977 1.067

C2-60-10D-C 10 114.3 6.00 58.68 342.95 1141.3 0.960 0.970 1.058

C2-80-3D-C 3 114.3 6.00 88.78 342.95 1673.9 1.002 0.933 1.033

C2-80-5D-C 5 114.3 6.00 88.78 342.95 1564.7 1.029 0.958 1.061

C2-80-7D-C 7 114.3 6.00 88.78 342.95 1509.3 1.063 0.990 1.096

C2-80-10D-C 10 114.3 6.00 88.78 342.95 1389.1 1.058 0.986 1.092

C2-100-3D-C 3 114.3 6.00 105.45 342.95 1943.4 1.158 0.996 1.106

C2-100-5D-C 5 114.3 6.00 105.45 342.95 1827.1 1.196 1.028 1.142

C2-100-7D-C 7 114.3 6.00 105.45 342.95 1788.9 1.255 1.078 1.198

C2-100-10D-C 10 114.3 6.00 105.45 342.95 1613.5 1.224 1.052 1.169

Mean 1.057 0.984 1.101

Standard dev. 0.126 0.078 0.084

C.O.V. 11.9% 7.9% 7.6%

Table 4Results of columns tested by O’Shea and Bridge [22] and ratios with predicted values from analytical models using the correction factor if applicable.


S30CS50B 3.52 165 2.82 48.3 363.3 1662 0.907 0.967 0.878

S20CS50A 3.49 190 1.94 41.0 256.4 1678 1.116 0.974 1.005

S16CS50B 3.50 190 1.52 48.3 306.1 1695 1.059 0.943 0.861

S12CS50A 3.50 190 1.13 41.0 185.7 1377 1.105 0.928 0.997

S10CS50A 3.47 190 0.86 41.0 210.7 1350 0.885 0.961 0.959

S30CS80A 3.52 165 2.82 80.2 363.3 2295 0.914 0.964 0.914

S20CS80B 3.49 190 1.94 74.7 256.4 2592 1.118 0.978 1.011

S16CS80A 3.49 190 1.52 80.2 306.1 2602 1.095 0.970 0.922

S12CS80A 3.49 190 1.13 80.2 185.7 2295 1.075 0.894 0.940

S10CS80B 3.49 190 0.86 74.7 210.7 2451 0.969 1.050 1.056

S30CS10A 3.50 165 2.82 108 363.3 2673 0.895 0.904 0.875

S20CS10A 3.47 190 1.94 108 256.4 3360 1.139 0.941 0.974

S16CS10A 3.48 190 1.52 108 306.1 3260 1.099 0.945 0.914

S12CS10A 3.47 190 1.13 108 185.7 3058 1.155 0.916 0.958

S10CS10A 3.48 190 0.86 108 210.7 3070 0.896 0.943 0.952

Mean 1.029 0.952 0.948

Standard dev. 0.103 0.037 0.055

C.O.V. 10.1% 3.9% 5.8%

(Ac ·fc+Aa·fy). Eq. (2) shows the correction factor, recommended foruse only if the relation L/D is larger than 3; otherwise λOliveira = 1.

λOliveira = −0.18 · ln(

LD

)+ 1.2. (2)

The comparisons between the analytical models and the resultsfrom the literature are presented in Tables 3–7. Table 3 showsresults for the 32 tested columns using the correction factor topenalize the analytical model results. Tables 4–7 show the resultsfrom [22–25], respectively. The correction factor was used for L/Dratios greater than or equal to 3.

Observing the results in Tables 2 and 3, the mean results forrelations between the experimental axial load and predicted ones

are close to 1 for both the Susantha and Johansson models. Theaxial capacities of the CFT columns given by the three modelsbenefited by the correction factor. Only Johansson’s model stillpresented a mean less than 1, 1.6% on the unsafe side.

The Hatzigeorgioumodel presented the best approach, in termsof the mean, before using the correction factor: 2.6% under theexperimental values. After using the correction factor, those valuesbecame 10.1% higher than the experimental ones and therefore onthe safe side.

Analyzing the mean values presented in Table 4, only the onespredicted by Susantha’s model were higher than the experimentalones, with a difference of 2.9%. However, the standard deviationof the values presented the higher value, 10.1%, showing a large



Table 5Results of columns tested by Giakoumelis and Lam [23] and ratios with predicted values from analytical models using the correction factor if applicable.


C3 2.62 114.43 3.98 24.6 343 948 1.065 1.044 1.067

C4 2.62 114.57 3.99 74.9 343 1308 0.893 0.929 0.976

C5 2.62 114.43 3.82 27.7 343 929 1.014 1.015 1.033

C6 2.63 114.26 3.93 77.8 343 1359 0.922 0.955 1.003

C7 2.62 114.88 4.91 27.8 365 1380 1.264 1.281 1.277

C8 2.61 115.04 4.92 83.9 365 1787 1.060 1.096 1.137

C9 2.61 115.02 5.02 46.1 365 1413 1.042 1.114 1.127

C10 2.61 114.49 3.75 46.1 343 1038 0.902 0.957 0.981

C11 2.62 114.29 3.75 46.1 343 1067 0.930 0.986 1.011

C12 2.62 114.30 3.85 25.5 343 998 1.126 1.113 1.132

C13 2.63 114.09 3.85 25.5 343 948 1.072 1.059 1.079

C14 2.62 114.54 3.84 79.1 343 1359 0.917 0.951 0.996

C15 2.62 114.37 3.85 79.1 343 1182 0.799 0.828 0.868

Mean 1.000 1.025 1.053

Standard dev. 0.122 0.113 0.101

C.O.V. 12.2% 11.0% 9.6%

Table 6Results of columns tested by Gupta et al. [24] and ratios with predicted values from analytical models using the correction factor if applicable.


D2M3C1 7.19 47.28 1.87 25.15 360 215 1.504 1.530 1.496

D2M3C2 7.19 47.28 1.87 28.89 360 215 1.424 1.475 1.449

D2M3C3 7.19 47.28 1.87 28.22 360 210 1.404 1.450 1.423

D3M3C1 3.81 89.32 2.74 25.15 360 610 1.209 1.256 1.180

D3M3C2 3.81 89.32 2.74 28.89 360 635 1.184 1.252 1.183

D3M3C3 3.81 89.32 2.74 28.22 360 630 1.187 1.251 1.181

D4M3C1 3.02 112.56 2.89 25.15 360 754 0.996 1.044 0.950

D4M3C2 3.02 112.56 2.89 28.89 360 730 0.903 0.962 0.882

D4M3C3 3.02 112.56 2.89 28.22 360 745 0.932 0.991 0.907

D2M4C1 7.19 47.28 1.87 37.60 360 250 1.483 1.584 1.569

D2M4C2 7.19 47.28 1.87 40.00 360 225 1.299 1.397 1.386

D2M4C3 7.19 47.28 1.87 37.77 360 246 1.456 1.557 1.542

D3M4C1 3.81 89.32 2.74 37.60 360 644 1.061 1.156 1.104

D3M4C2 3.81 89.32 2.74 40.00 360 620 0.992 1.087 1.041

D3M4C3 3.81 89.32 2.74 37.77 360 650 1.069 1.165 1.113

D4M4C1 3.02 112.56 2.89 37.60 360 822 0.891 0.977 0.908

D4M4C2 3.02 112.56 2.89 40.00 360 788 0.827 0.912 0.850

D4M4C3 3.02 112.56 2.89 37.77 360 801 0.866 0.950 0.883

Mean 1.149 1.222 1.169

Standard dev. 0.233 0.230 0.251

C.O.V. 20.2% 18.8% 21.5%

Table 7Results of columns tested by Yu et al. [25] and ratios with predicted values from analytical models using the correction factor if applicable.


1 2.97 219 4.78 41.91 350 3400 1.006 1.062 1.023

2 2.97 219 4.72 41.91 350 3350 0.997 1.052 1.012

3 2.97 219 4.75 34.08 350 3150 1.048 1.083 1.034

4 2.97 219 4.74 41.91 350 3160 0.938 0.991 0.953

5 2.97 219 4.73 34.08 350 3150 1.050 1.086 1.035

6 2.97 219 4.72 41.91 350 3380 1.006 1.062 1.021

7 2.97 219 4.73 41.91 350 3600 1.070 1.130 1.086

8 2.97 219 4.73 41.91 350 2900 0.862 0.910 0.875

9 2.97 219 4.74 41.91 350 2680 0.796 0.840 0.808

10 3.09 165 2.73 68.71 350 2080 0.915 0.957 0.912

11 3.09 165 2.76 68.71 350 2060 0.902 0.945 0.902

12 3.09 165 2.81 68.71 350 2160 0.939 0.986 0.943

13 3.09 165 2.81 68.71 350 2095 0.911 0.956 0.914

14 3.09 165 2.76 68.71 350 2250 0.985 1.032 0.985

15 3.09 165 2.72 48.45 350 1750 0.961 1.007 0.933

16 3.09 165 2.74 48.45 350 1785 0.976 1.024 0.951

17 3.09 165 2.75 38.43 350 1560 0.983 1.014 0.929

Mean 0.961 1.008 0.960

Standard dev. 0.071 0.072 0.070

C.O.V. 7.4% 7.1% 7.3%

scatter in predictions. Despite being on the unsafe side, withmeans of 4.8% and 5.2%, the values predicted by the Johansson andHatzigeorgioumodels presented the smallest standard deviation ofthe values:, 3.7% and 5.5%, respectively. In general the threemodels

were able to predict the results of the columns tested byO’Shea andBridge [22].

The columns tested by Giakoumelis and Lam [23] werecomparedwith the predictions in Table 5. The calculated values for



a b

c d

Fig. 6. Load vs. axial strain of 32 CFT tested columns: (a) L/D = 3, (b) L/D = 5, (c) L/D = 7 and (d) L/D = 10.

these columnswere the best predictions among all. The predictions

of themodels of Susantha, Johansson and Hatzigeorgiou presented

differences of 0%, 2.5% and 5.3% compared to the experimental

ones, on the safe side. However, they presented a large variability

in individual predictions.

Despite being on the safe side, the means of ratios between

the experimental results and the predicted ones for the columns

of Gupta et al. [24] (Table 6) presented the largest difference

and standard deviation. This can be attributed to the fact

that the columns tested presented higher variability of the

studied variables, such as L/D, diameter, thickness and concrete

compressive strength. Only the yielding strength of steel remains

constant. In addition, the correction factor made the results more

conservative. If the correction factor was not applied to these

columns, the mean values would be 1.060, 1.128 and 1.078 for the

models of Susantha, Johansson and Hatzigeorgiou, respectively.

Table 7 presents the comparisons of the results for the columns

tested by Yu et al. [25] and the predictions. The comparisons

indicate very close values and the smallest standard deviations

among all comparisons. In terms of the means, only Johansson’s

model gave predictions on the safe side, of only 0.8%.

7. Conclusions

This paper presented experimental results of 32 CFT columns

tested under concentric loading. In general, all columns filled with

normal strength concrete (C30 and C60) presented good ductile

behavior, without loss of capacity after reaching the peak load, as

seen in Fig. 6. For columns filled with high strength concrete, theC2 columns seem to have more ductility than C1 ones due to thedifference between the tube thickness, where the thicker tube isable to better promote the confinement of the concrete core.

Three analytical models for the axial capacity of CFT shortcolumns were studied so that the values of the axial capacity ofthe 32 tested CFT columns and another 63 from the literaturecould be evaluated. A factor was introduced to correct the values ofpredictions for slender columns when the L/D ratio is higher than3, presenting good results.

In general, the three analyticalmodels showed good predictionsfor the axial load capacity of CFT columns. In most cases, themean values of the relation between the experimental results andpredicted ones were higher than 1, therefore on the safe side. Evenwhen the values were lower than 1, they were close to 1, with adifference of 5.2% for the columns tested by O’Shea and Bridge [22]predicted by the Hatzigeorgiou model.

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