Experimental Behaviour of Stiffened Concrete-filled Thin-walled Hollow Steel Structural (HSS) Stub Columns

Journal of Constructional Steel Research 61 (2005) 962–983

www.elsevier.com/locate/jcsr

Experimental behaviour of stiffened concrete-filledthin-walled hollow steel structural (HSS) stub

columns

Zhong Tao∗, Lin-Hai Han, Zhi-Bin Wang

College of Civil Engineering and Architecture, Fuzhou University, Gongye Road 523, Fuzhou,Fujian Province 350002, PR China

Received 14 June 2004; accepted 9 December 2004

Abstract

Test results on concrete-filled steel tubular stub columns with inner or outer welded longitudinalstiffeners under axial compression are presented in this paper. The research was mainly focused onsquare hollow section (SHS) columns; two rectangular hollow section (RHS) columns were alsotested. A longitudinal stiffener was provided on each side of the stiffened SHS column, while onlytwo stiffeners were welded to the longer sides of the stiffened RHS column. The main experimentalparameters considered were the height-to-thickness ratio and stiffener rigidity. In addition, emptytubes with or without stiffeners, as well as unstiffened concrete-filled steel tubes were also testedfor comparison. Requirements for stiffener rigidity are developed by modifying a formula presentedin the literature. Existing theoretical model and design codes were used to predict the load versusaxial strain relationships and load-carrying capacities of the adequately stiffened composite sectionsrespectively; reasonable results were achieved.© 2005 Elsevier Ltd. All rights reserved.

Keywords: Concrete-filled steel tube; Concrete; Thin-walled; Stub columns; Axial compression; Stiffener; Steelhollow section; Local buckling

∗ Corresponding author. Tel.: +86 591 3716182; fax: +86 591 3737442.E-mail address: [email protected] (Z. Tao).

0143-974X/$ - see front matter © 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2004.12.003

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Z. Tao et al. / Journal of Constructional Steel Research 61 (2005) 962–983 963

Nomenclature

Ac Cross-sectional area of concrete

Asc Sum of cross-sectional areas of steel tube and concrete(=As,t + Ac)

As,s Cross-sectional area of steel stiffeners

As,t Cross-sectional area of steel tube

B Width of square or rectangular steel tube

bs Width of the steel stiffener

D Height of rectangular steel tube

Ec Concrete modulus of elasticity

Es Steel modulus of elasticity

fc Characteristic compressive concrete strength(=0.4 f 7/6cu )

fck Characteristic compressive strength of concrete (fck = 0.67 fcu for normalstrength concrete)

fcu Characteristic cube strength of concrete

f ′c Characteristic compressive cylinder strength of concrete

fscy Nominal average strength of the steel tube after filled with concrete

fs,s Yield strength of the stiffener

fs,t Yield strength of the steel tube

Is Moment of inertia of stiffener about its centroidal axis parallel to the panelelement

L Length of column

N Axial load

Nu,e Experimental ultimate strength

t Wall thickness of the steel tube

ts Thickness of the steel stiffener

σ Stress

ε Strain

ξ Confinement factor(= As,t · fs,t

Ac · fck

)

1. Introduction

The use of concrete filled steel tubular (CFT) columns has become increasingly popularin civil engineering structures. In China, itis reported that more than thirty high-risebuildings and two hundred arch bridges have been built due to their high strength andductility, as well as large energy-absorption capacity [1]. The enhancement of the CFTcolumns in structural properties can be reached because the steel tube provides confinementfor the concrete, and the concrete core can prevent the inward buckling of the tube.

964 Z. Tao et al. / Journal of Constructional Steel Research 61 (2005) 962–983

However, many studies have shown that the performance of a concrete-filled squareor rectangular steel tube is not as good as its circular counterpart [2,1]. This isdue to the fact that a square or rectangular steel tube cannot provide as muchconfining pressure to the concrete core, and that local buckling is more likely tooccur [3,4]. With a large aspect ratio of section,the maximum axial strength of stubcolumns is even less than the combination of the steel and concrete components dueto the effects of local buckling [5,6]. With the development of high strength steel,it has become extremely attractive to use in thin-walled tubes when local bucklingis eliminated in a column design. Accordingly, adequate stiffening measures forsquare or rectangular concrete-filled tubes are highly desirable when thin-walled tubesare used.

In the past, the effects of longitudinal stiffeners on the behaviour of square CFTstub columns have been experimentally studied by Ge and Usami [7] and Kwon et al.[8]. The preliminary test results demonstrated the effectiveness of the stiffeners in delayinglocal buckling of the tube. Compared with traditional CFT members, it is also expectedthat the stiffened CFT columns will have higher shear strength, higher bond strengthbetween the steel tube and the concrete core, as well as higher fire resistance capacitiesif the stiffeners are welded internally. However,only two stiffened stub columns wereincluded in the above-mentioned literature. Whilst Ge and Usami [7] reported that thestiffened composite stub column had a lower section capacity than the combined capacityof the components acting alone, Kwon et al. [8] concluded that its ultimate strengthhad a higher section capacity than the sum of those of the concrete, the steel tubeand the stiffeners. It seems more experiments covering a wider range of parametersshould be carried out to verify these conclusions. Moreover, no research has beenconducted to evaluate the rigidity requirement on stiffeners, as well as their influences onductility.

In recent years, Fuzhou University in China has been engaged in research to determinethe strength and behaviour of concrete-filled thin-walled hollow steel structural (HSS)columns. Both theoretical and experimental studies have been carried out, such asTao et al. [9], Han et al. [10], Han [11], Han and Yang [12], Han et al. [13], Han [1],Han andYao [14,15], Han et al. [16,17], Tao et al. [18]. The research results reported inthis paper arepart of a wider study on concrete-filled thin-walled HSS columns.

This paper studies mainly the behaviour of stiffened concrete-filled square steel tubularstub columns under concentric compression. The stif feners are typically arranged as shownin Fig. 1(b)–(d). The primary parameters considered in the test program were the height-to-thickness ratio(D/t) of the steel tube and the stiffener rigidity. For comparison,experiments were also conducted on empty tubes with or without stiffeners, as well asunstiffened CFT columns. Moreover, a novel stiffening measure with longitudinal steelstiffeners welded on the outer surfaces of the steel tube was also adopted in the testprogram. This kind of stiffeners is easier to weld compared to the inner-welded ones,and may be used when the aesthetic requirement is not highly emphasized or whenfireproof panels are used to protect the column from fire. The outer welded stiffenersare especially suitable for cold-formed thin-walled tubes which are manufactured in thefactory.


Fig. 1. Test specimens: (a) unstiffened SHS; (b) inner stiffened SHS; (c) outer stiffened SHS (d) inner stiffenedRHS.

2. Experimental program

2.1. General

Nineteen specimens, including thirteen square CFT stub columns, two rectangular CFTstub columns and four empty square steel stub columns, were tested to failure underconcentric compression.

According to design code AS 4100 [19], local buckling stress for a rectangular platesubjected to uniaxial compression can be expressed as

fol = π2Es

12(1 − ν2s )

k

(b/t)2 (1)

where the elastic modulusEs can be taken as 200,000 MPa, Poisson’s ratioνs can betaken as 0.3,b and t are the width and the thickness of the steel plate, respectively, andk is the buckling coefficient which dependson the boundary conditions. Based on finite-strip analysis, the value ofk for a rectangular plate in contact with concrete has beenrecommended by Bridge and O’Shea [20] and Uy and Bradford [21] as 9.99 and 10.31,respectively. A value of 10 was used in this paper as the buckling coefficient(k) for steelplates in a square or rectangular CFT column. If the yield strength( fy) of the plate is takenas 234.3 MPa, the local buckling slenderness limit for structural steel can be determinedfrom Eq. (2):

b

t≤ α

√kπ2Es

12(1 − ν2s ) fy

= 57.2 (2)

where α is a reduction factor used to account for plate imperfections and residualstresses [22]. For heavily welded tubes, it can be derived from the yield slenderness limitsspecified in AS 4100 [19] as 0.651. This has been further developed by Uy [23]. Accordingto the local buckling slenderness limit determined from Eq. (2), the height-to-thicknessratios (D/t) of tubes were chosen as 52, 76 and 100, respectively. It is therefore expectedthat stiffening measures should be taken to compensate the local buckling effects of thethin-walled tubes.


Table 1Specimen labels, material properties and section capacities

No. Specimen B D L D/t bs × ts Is f ′c Nue N0 Nue/N0 Stiffener

label (mm) (mm) (mm) (mm) (mm4) (MPa) (kN) (kN) type

1 SCFT25-1 249.9 250.2 750 100 35× 2.5 8932 50.1 3700 3483 1.062 Inner2 SCFT25-2 248.0 251.0 750 100 35× 2.0 7146 50.1 3530 3478 1.015 Inner3 SCFT25-3 248.7 252.3 750 100 25× 2.5 3255 50.1 3500 3476 1.007 Inner4 SCFT25-4 248.6 252.6 750 100 35× 2.5 8932 50.1 3620 3497 1.035 Outer5 UCFT25 249.0 250.4 750 100 – – 50.1 3230 3409 0.947 NA6 SS25 249.5 250.3 750 100 35× 2.5 8932 – 492 662 0.744 Inner7 US25 250.0 250.0 750 100 – – – 220 580 0.379 NA

8 SCFT19-1 190.1 190.2 570 76 25× 2.5 3255 54.8 2250 2166 1.039 Inner9 SCFT19-2 189.1 190.3 570 76 25× 2.0 2604 54.8 2240 2167 1.034 Inner

10 SCFT19-3 189.5 190.9 570 76 15× 2.5 703 54.8 2195 2153 1.020 Inner

11 SCFT13-1 129.7 130.5 390 52 20× 2.5 1667 54.8 1310 1105 1.185 Inner12 SCFT13-2 129.6 130.5 390 52 20× 2.0 1333 54.8 1300 1109 1.172 Inner13 SCFT13-3 129.7 130.2 390 52 15× 2.5 703 54.8 1300 1094 1.189 Inner14 SCFT13-4 129.7 130.5 390 52 20× 2.5 1667 54.8 1270 1105 1.149 Outer15 UCFT13 128.2 129.1 390 52 – – 54.8 1150 1047 1.099 NA16 SS13 130.2 131.4 390 52 20× 2.5 1667 – 398 347 1.145 Inner17 US13 130.5 130.9 390 52 – – – 200 300 0.666 NA

18 SCFT-R25 126.0 249.0 750 100 35× 2.5 8932 50.1 2010 1861 1.080 Inner19 SCFT-R13 65.8 129.6 390 52 20× 2.5 1667 54.8 695 614 1.132 Inner

Four types of steel tubes, shown as inFig. 1 were fabricated, i.e. unstiffened squaretubes (Fig. 1(a)), inner stiffened square tubes (Fig. 1(b)), outer stiffened square tubes(Fig. 1(c)) and inner stiffened rectangular tubes (Fig. 1(d)). The minimum stiffener rigidityfor each of theD/t series was determined from formulae presented by Rhodes [24]. Largerstiffeners were also provided to determine the influence of stiffener rigidity on stiffeningeffects. A summary of the specimens is presented inTable 1where the measured sectionsizes, material properties andD/t ratio are given. InTable 1, specimen designationsstarting with a U refer to columns without stiffeners, and those starting with an Srefer to columns with stiffeners. Follows the U or S, the character S represents emptysteel tubes, and CFT represents concrete filled steel tubes. It should be noted that thespecimens of SCFT25-4 and SCFT13-4 are outer stiffened CFT columns as shown inFig. 1(c), and the specimens of SCFT-R25 and SCFT-R13 are rectangular CFT columnsas shown inFig. 1(d). The length of the stub columns(L) was chosen to be threetimesthe height of the SHS or RHS columns to avoid the effects of overall buckling and endconditions [1].

2.2. Material properties

All tubes were manufactured from mild steel sheet with a measured thickness of2.5 mm. The stiffeners were fabricated from two kinds of mild steel sheet with thicknessesof 2 and 2.5 mm respectively. The widths of the stiffeners ranged from 15 to 35 mm toget a varied flexural stiffness. The material properties of the steel are shown inTable 2,


Table 2Material properties of steel

Thickness Elastic modulus Yield strength Yield strain Poisson’s Ultimate strength Ultimate strain(mm) (GPa) (MPa) (%) ratio (MPa) (%)

2 208 311.0 0.189 0.242 430.7 28.72.5 208 234.3 0.137 0.247 343.7 31.6

and were determined from tension tests on three coupons in each series. To fabricate aspecimen, four steel plates were cut. If stiffening was specified, the stiffeners were weldedon the plates with fillet welds. After that the four plates were tack welded into a square orrectangular shape, and then welded with a single bevel butt weld along the corners to formthe tube.

The concrete used in the test program had a water/cement ratio of 0.38, made withordinary Portland cement. The mix proportions of the concrete were as follows: cement:528 kg/m3; water: 201 kg/m3; sand: 585 kg/m3; and coarse aggregate: 1086 kg/m3. Thecoarse aggregate was well graded with a maximum size of 15 mm. Two batches of concretewith the same mix design were used to fill thesteel tubes. Todetermine the compressivestrength of concrete, three 150 mm cubes and three standard cylinders(150 mm×300 mm)

were cast from each batch of the concrete and cured in conditions similar to the relatedspecimens. The average cube strength( fcu) for each batch of concrete at the time of testswas59.8 and 61.8 N/mm2 respectively, while the average cylinder strength( f ′

c) was50.1and 51.8 N/mm2 respectively. The average modulus of elasticity(Ec) of concrete wasfound to be 35,100 N/mm2.

2.3. Specimen preparation and test procedure

In the case of the CFT columns, the concrete was filled in layers and was vibrated by apoker vibrator. These specimens were then placed upright to air-dry until testing. Duringcuring, a very small amount of longitudinal shrinkage occurred at the top of the columns. Ahigh-strength epoxy was used to fill this longitudinal gap so that the concrete surface wasflush with the steel tube at the top. Prior to testing, the top surfaces of the CFT specimenswere ground smooth and flat using a grinding wheel with diamond cutters. A ruler wasused to check for the flatness. This was to ensure that the load was applied evenly acrossthe cross-section and simultaneously to the steel and concrete.

A 5000 kN capacity testing machine was used for the compression tests of all specimensas shown inFig. 2. A computerized IMP data acquisition system was used for data logging.To assure uniform compression, preliminary tests within the elastic range were conductedby carefully adjusting the position of the specimen, based on the measurements of straingauges attached at the mid-height of the test specimen. The adjustment was terminateduntil the difference between the measured strain and the average value was no more than5%. In addition, two displacement transducers (seeFig. 2) were used to measure the axialshortening during the tests. A load interval of less than one tenth of the estimated loadcapacity was used. Each load interval was maintained for about 2 to 3 min.


Fig. 2. Test set-up.

3. Test results and discussion

Typical failure appearances of the test specimens are shown inFig. 3, and the bucklingmodes of the plate panel after collapse of these specimens are shown inFig. 4. As expected,the steel plates buckled alternately in convex and concave surfaces for the unstiffened steelcolumn, with the nodes at the corners of columns (Fig. 4(a)); and for the stiffened steelcolumn, the buckling did not occur at the stiffeners unless the stiffeners buckled (Fig. 4(b)).For all steel columns, it was also observed during the experiment that the steel panelsbuckled near the mid-height of the column. In the case of the CFT column, all the steelpanels buckled outward (Fig. 5(c)–(e)). Local plate buckling occurred initially near theupper end, because it is impossible to apply theload perfectly evenly across the cross-section of the upper end, although the above mentioned measure has been taken. Thenthe steel plates buckled at different locations, including the central part of the specimen.Finally, buckling deformations developed quickly at one of these locations, normally nearthe mid-height of the column. It must be noted that for the buckling modes of the stiffenedcomposite columns, the stiffeners contributed to a great extent to the overall shape of thebuckling of columns even when stiffener rigidity was small. The steel plates in the stiffenedCFT specimens buckled later than those in the unstiffened CFT columns. However, thesmaller the stiffener rigidities, the earlier the stiffener buckled, thus affecting the stiffeningeffects to some extent. Compared to the inner stiffened specimen, the plate panels buckledearlier when outer stiffeners were used. The reason is that the buckling of the formerlongitudinal stiffeners was delayed or even prevented by the filled-in concrete.

It was also observed that the plate buckling of all specimens withD/t ratios of 100and 76 initially occurred before the maximum load was reached, as well as empty steeltube US13 with aD/t ratio of 52. The larger theD/t ratio, the earlier the local bucklingoccurred in each series. Although both specimens UCFT13 and SCFT25-1 had almost the


Fig. 3. Typical failure appearances of test specimens.

Fig. 4. Local buckling modes of test specimens: (a) steel column; (b) stiffened steel column; (c) CFT column;(d) inner stiffened CFT column; (e) outer stiffened CFT column.

same width-to-thickness ratio for subpanel plates, it is quite interesting to note that platebuckling of the specimen UCFT13 was initially observed after the maximum load wasreached, whereas specimen SCFT25-1 was to the contrary. The reason may be attributedto residual stresses from welding of the stiffeners. This was once again confirmed by thefact that the stiffened RHS columns buckled(local buckling) initially at the longer side.

The tested curves of load versus axial strain are shown inFig. 5. The axial strain wascalculated from measured axial shortening divided by the overall length. The maximumloads(Nue) obtained in the test are summarized inTable 1. It can be seen that all thecurves tend to drop after peak load, but the specimen with largerD/t ratio drops morequickly in each series.

In order to quantify the effect of stiffeners on section ductility, a ductility index (DI) isdefined inthis paper as

DI = ε85%

εy(3)

whereε85% is the axial strain when the load falls to 85% of the ultimate load, andεy isequal toε75%/0.75,ε75% is the axial strain when the load attains of 75% the ultimate loadin the pre-peak stage.

The ductility indexes (DI) so determined are plotted inFig. 6 against the normalizedmoment of inertia of stiffener(Is/Is,max) for inner stiffened square CFT columns, whereIsis the moment of inertia of stiffener about its centroidal axis parallel to the panel element,


(a) SHS withD/t = 100.

(b) SHS withD/t = 76.

Fig. 5. Load versus axial strain curves.

andIs,max is the maximum moment of inertia of stiffener in the sameD/t series. It can beseen fromFig. 6 that Is does not significantly influence the ductility of the stiffened CFTspecimens, although a very slight drop is observed with the increasing ofIs/Is,max. Thebeneficial effect of stiffeners on ductility may be counteracted by the residual stresses fromwelding of the stiffeners. The slight drop can be explained by the fact the ultimate strengthincrease with the increase ofIs/Is,max, thus inducing a decrease in the value ofε85%.

In order to gain an insight into the effects of stiffening and local buckling, the ultimatestrength of a stiffened CFT column is estimated firstly using the sum of the sectioncapacities of concrete, the steel tube and the steel stiffeners, i.e.

N0 = fcAc + fy,t As,t + fy,sAs,s (4)


(c) SHS withD/t = 52.

(d) RHS.

Fig. 5.(continued).

where Ac, As,t, As,s are the areas of the concrete, the steel tube and the steel stiffeners,respectively;fy,t and fy,s are the yield strengths of the steel tube and the steel stiffenersrespectively;fc is the characteristic concrete strength, and can be calculated by the formulapresented in [25]:

fc = 0.4 f 7/6cu . (5)

For steel columns or unstiffened CFT columns, Eq. (4) is also used to calculateN0 bytaking one or both of the cross-sectional areas of the concrete and the stiffeners as zero.

The predicted ultimate strength(N0) is compared inTable 1with the experimental data(Nue). Tested ultimate strengths of specimens with different section configurations areshown inFig. 7 for specimens with aD/t ratio of 100 and 52, respectively. It can be seenfrom Fig. 7 andTable 1that the maximum loads and post-buckling strengths were almost


Fig. 6. Effect of stiffeners on ductility.

the same for unstiffened steel columns US25 and US13, although the former had largercross-sectional areas. On the other hand, the stiffened steel columns SS25 and SS13 hadmuch higher compression capacities than theirunstiffened counterparts. This means thatlongitudinal stiffeners were very effective against the local buckling of the plate panels. It isalso noted that the column SS25 hasattained a maximum strength with anNue/N0 ratio of0.744 and has not developed its full strength, while the column SS13 has anNue/N0 ratioof 1.145 due to the effects of strain-hardening. It seems more stiffeners should be providedto further reduce the width-to-thickness ratios of the subpanel plates, thus to increase theultimate strength of the column SS25.

Compared with the steel columns, the ultimate strength of the composite columns wasgreatly increased because of the filled-in concrete. In the case of unstiffened compositecolumns, it can be seen fromTable 1that Eq. (4) underestimates the load carrying capacityof specimen UCFT13. This is due to the effect of concrete confinement which is notconsidered in the model. However, it can also be seen that Eq. (4) overestimates theload-carrying capacity of specimen UCFT25 because the effect of local buckling is notconsidered in the model. In the case of stiffened composite columns, each specimen hada higher ultimate strength thanN0, and the strength was also higher than that of theunstiffened composite column. It is concluded that the longitudinal stiffeners can not onlydelay the local buckling of the plate panel, but also improves the lateral confinement on theconcrete core and, thus enhances its strength.The smaller the height-to-thickness ratio ofthe specimen, the more apparent the confinement enhancement.

It can also be seen fromTable 1and Fig. 7 that the outer stiffened specimens haveshown almost the same behaviour as the inner stiffened ones with the same size stiffeners.However, the ultimate strength of the outer stiffened specimen was slightly lower thanthat of the inner stiffened one in each series. As explained above, the local buckling oflongitudinal stiffeners in the latter specimenswas delayed or even prevented by the filled-in


(a) D/t = 100.

(b) D/t = 52.

Fig. 7. Tested ultimate strengths of specimens with different section configurations.

concrete, and thus could exert their influences more effectively. Therefore, it is concludedthat the outer welded stiffeners should have higher flexural rigidity than the inner weldedones.

4. Stiffener rigidity requirement

Fig. 8shows the effect of stiffener rigidity on the load-bearing capacity of the stiffenedCFT column. In order to make meaningful comparisons, a normalized ultimate strength is


Fig. 8. Effect of moment of inertia of stiffener on normalized ultimate strength.

defined as follows:

Nn,ult = Nue − fy,sAs,s

fcAc + fy,t As,t. (6)

The above equation essentially subtracts the contribution of the longitudinal stiffenersfrom the ultimate strength for a given column and then divides this number by thecontributions of the concrete core and the steel tube. It can be seen fromFig. 8that the valueof Nn,ult does not increase with the increment ofIs for stiffened composite specimens witha nominalD/t ratio of 52. It seems that the flexural rigidity requirement of the stiffenersin this case can be met with a minimum size of 15× 2.5 mm. However, for stiffenedcomposite columns in other series, the value ofNn,ult does increase with the incrementof Is. This demonstrates the fact that the larger is theD/t ratio, the larger the rigidityrequirement of stiffeners.

By comparing the axial strain at the stiffener–plate juncture with the strain at the cornerof the tube, the relative support provided by different stiffener rigidities could be assessedas pointed out in [26]. It was observed that the strain variations at these locations werevirtually the same for some specimens when they reached their ultimate strength. Allthese specimens are shown inTable 3. Therefore, the stiffeners in these specimens canbe recognized as sufficiently strong to support the steel plates. In contrast, the strain atthe longitudinal stiffener of a specimen with a relatively small stiffener showed a strainreversal tendency.

According to Desmond et al. [26], the requirement on stiffener rigidity was developedfor longitudinally stiffened compression elements of thin-walled members based primarilyon experimental results. The requirement(Is,ad) is expressed as

Is,ad

t4= 100w/t

(w/t)a− 50 for 0.5(w/t)a ≤ w/t < 1.5(w/t)a (7a)

Z.Tao

etal./JournalofConstructional

SteelResearch

61(2005)

962–983975

Table 3Comparisons of experimental and predicted stiffener rigidities and ultimate strengths for specimens in this paper

No. Specimen Is Is,ad Is,re Nue NP/Nue NACI/Nue NAISC/Nue NBS5400/Nue NEC4/Nue NDBJ/Nuelabel (mm4) (mm4) (mm4) (kN)

1 SCFT25-1 8932 3677 8960 3700 0.964 0.866 0.861 0.830 0.987 0.9552 SCFT19-1 3255 2124 3429 2250 0.985 0.886 0.881 0.851 1.003 0.9793 SCFT13-1 1667 994 909 1310 0.866 0.783 0.779 0.756 0.875 0.8704 SCFT13-2 1333 994 909 1300 0.875 0.792 0.788 0.765 0.885 0.8795 SCFT13-3 703 994 909 1300 0.863 0.780 0.785 0.753 0.873 0.8766 SCFT-R25 8932 3677 8960 2010 0.969 0.858 0.849 0.825 0.968 0.9567 SCFT-R13 1667 994 909 695 0.938 0.828 0.826 0.803 0.912 0.945


Is,ad

t4 = 257w/t

(w/t)a− 285 forw/t ≥ 1.5(w/t)a (7b)

wherew is the width of the subpanel plate, and can be taken approximately asb/2,b is theoverall width of theplate;(w/t)a = 580

√fy,t, theunit of fy,t is MPa.

The above equation is simplified in [24] as:

Is,ad = 0.045(w

t

)2 fy,t

280t4. (8)

Eq. (8) gives quite close prediction of the value of rigidity requirement on stiffenerscompared with that from Eq. (7).

The actual stiffener rigidities(Is) and values calculated from Eq. (8) (Is,ad) are listed inTable 3for those adequately stiffened specimens reported in this paper. As can be seen fromTable 3, all actually required stiffener rigidities are larger than the calculated values exceptSCFT13-3. This can be explained from the confining mechanisms: the tube exerts confiningstress on the concrete core, and the counter-stress from the concrete core promotes the localbuckling of the steel tube. However, for the specimen with smallerD/t ratio, this effectis counteracted because the stiffeners were embedded in the concrete, while the pushingeffect from concrete core is not significant. So the adequate rigidity required on stiffenersis smaller than that determined from Eq. (8). According to the above analysis, Eq. (8) ismodified as follows

Is,re = 3.1 × 10−4 ·(w

t

)3.5 fy,t

280t4. (9)

The calculated values ofIs,re are given inTable 3. As can be seen, Eq. (9) givesreasonable results in predicting adequate rigidities required. It should be noted that Eq. (9)can only be used for inner-welded stiffeners, more research should be conducted to evaluatethe rigidity requirement onouter-welded stiffeners.

Two stiffened SHS stub columns have been experimentally studied by Ge and Usami[7] and Kwon et al. [8], respectively. A summary of the specimens is presented inTable 4where the component areas, material properties and stiffener sizes are given. The actualstiffener rigidities, as well as values calculated from Eqs. (8) and (9) are alsolisted inTable 4. As can be seen fromTable 4, thestiffener rigidities in [7] seem too small to meetthe rigidity requirements according to Eq. (8) or (9), while the stiffener sizes in [8] seem alittle too large. Therefore, specimens SC15-1 and SC15-2 reported in [8] can be recognizedas adequately stiffened specimens.

5. Prediction of load versus axial strain relationships using existing model

A theoretical model was developed in [10] for concrete-filled SHS stub columns,columns and beam columns. The predicted load versus axial strain relationship is in goodagreement with stub column test results. As pointed out in [1], the model can also be usedfor concrete-filled RHS stub columns. Therefore, the load versus axial strain relationshipsfor adequately stiffened stub columns in the current test are predicted using this model.The comparison is shown inFig. 9. The agreement between the predicted curves and thetested ones appears generally good. The experimental failure loads(NP) are summarized in


Table 4Comparisons of experimental and predicted stiffener rigidities for specimens from independent experiments

Specimen t D/t Ac As,t As,s f ′c fy,t fy,s bs × ts Is Is,ad Is,re

label (mm) (mm2) (mm2) (mm2) (MPa) (MPa) (MPa) (mm) (mm4) (mm4) (mm4)

(a) [7]

S75-C-1 4.51 73.8 104,616 6030 684 40.6 266 309 38× 4.36 19,937 24,082 37,186S75-C-2 4.51 73.8 104,850 6030 450 40.4 266 301 25× 4.34 5,719 24,082 37,186

(b) [8]

SC15-1 3 74.3 46,549 2694 540 22.05 235.2 235.2 45× 3 22,781 4226 6591SC15-2 3 74.3 46,549 2694 540 22.05 235.2 235.2 45× 3 22,781 4226 6591

Table 3. A mean ratio(NP/Nue) of 0.923 is obtained with a COV (coefficient of variation)of 0.053. As can be seen fromFig. 9 andTable 3, the experimental failure loads are ingeneral in excess of the determined values by the model. This could be explained by thebeneficial effect of the confinement enhancement from stiffeners. It can also be seen fromFig. 9 that, for theoretical curves, the loads decrease gradually after the specimens haveattained their ultimate loads, unlike the experimental curves where the loads drop morequickly at the point of peak loads. This phenomenon is more apparent when the tubethickness becomes thinner. This isbecause the model presented in [10] is not calibratedfor thin-walled CFT columns. Therefore, more future research is required to modify themodel presented in [10], thus giving a more accurate prediction of load versus axial strainrelationships.

6. Load-carrying capacity prediction

There are several widely used design codes for calculating the capacity of CFTs, suchas ACI [27], AIJ [28], AISC [29], BS5400 [30], EC4 [31]. More recently, a new codeDBJ1351-2003 [32] was enacted by the construction department of Fujian province inChina. The design equationsrecommended in the codes mentioned above are applied tocalculate section capacities of adequately stiffened CFTs in this section. It must be notedthat these codes are not applicable to design thin-walled CFT columns. Therefore, thewidth-to-thickness ratios for subpanel plates of the stiffened CFT column must be smallerthan the value determined from Eq. (2). At the same time, some necessary modificationsshould be made to take the contribution of stiffeners into account. It should also benoted that all partial safety factors have beentaken as unity, as well as reduction factorsaccounting for accidental eccentricities.

6.1. ACI and AIJ methods

ACI [27] and AIJ [28] gave the sameequation to calculate nominal strength of CFTshort columns:

NACI = As fy + 0.85Ac f ′c. (10)


(a) SCFT25-1.

(b) SCFT19-1.

Fig. 9. Comparison of load versus axial strain curves between predicted and tests for adequately stiffened stubcolumns.

For stiffened CFT stub columns in this paper, the term ofAs fy is replaced byAs,t fy,t +As,s fy,s.

The predicted strength using ACI [27] or AIJ [28] is compared with the currentexperimental values of adequately stiffened specimens inTable 3. Ultimate strengths ofspecimens listed inTable 4are also predicted using Eq. (10) as shown inTable 5. As canbe seen fromTables 3and5, Eq. (10) underestimates the strength of stiffened CFT stubcolumns except specimens S75-C-1 and S75-C-2 which were reported by Ge and Usami[7]. The reasons for specimens S75-C-1 and S75-C-2 showing a lower strength maybetwofold: first, the concrete may not have been properly poured into the tube accordingto Ge and Usami [7]. Secondly, the stiffener sizes seemed too small to be fully effective


(c) SCFT13-1.

(d) SCFT-R25 and SCFT-R13.

Fig. 9.(continued).

as mentioned above. Therefore, the comparisons for specimens S75-C-1 and S75-C-2 areignored in the following sections.

A mean ratio(NACI/Nue) of 0.831 is obtained for adequately stiffened CFT stubcolumns with a COV (coefficient of variation) of 0.038. It seems that Eq. (10)underestimates the strengths of the stiffened columns.

6.2. AISC method

The nominal strength for composite compression members is given as:

NAISC = AsFcr (11)


Table 5Comparisons of experimental and predicted ultimate strengths for specimens from independent experiments

No. Specimen Nue (kN) NP/Nue NACI/Nue NAISC/Nue NBS5400/Nue NEC4/Nue NDBJ/Nuelabel

(a) [7]

1 S75-C-1 5030 1.233 1.079 1.073 1.073 1.205 1.2112 S75-C-2 5158 1.186 1.035 1.030 1.030 1.158 1.164

(b) [8]

3 SC15-1 1935 0.930 0.844 0.841 0.841 0.924 0.9154 SC15-2 2001 0.899 0.816 0.813 0.813 0.893 0.884

where Fcr = (0.658λ2c )Fmy (for stub column);λc = kL

rmπ

√FmyEm

; Fmy = fy +0.85 f ′

c(Ac/As); Em = Es + 0.4Ec(Ac/As); Es is the modulus of elasticity of steel;Ec isthe modulus of elasticity of concrete;rm is the radius of gyration of the tube.

For stiffened CFT stub columns in this paper:As = As,t + As,s; rm =√

Is,t+Is,sAs,t+As,s

where

Is,t and Is,s are the moment of inertia about the minor axis of section for the tube and thestiffeners, respectively.

The predicted strength using AISC [29] is compared with the experimental values inTables 3and5, where a mean of0.825 is obtained forNAISC/Nue with a COV of 0.036. Itseems AISC [29] is alittle more conservative than ACI [27] or AIJ [28].

6.3. BS5400 method

The cube strength of concrete( fcu) is used in BS5400 [30] to calculate the squash loadof composite cross section as:

NBS5400 = As fy + 0.675Ac fcu. (12)

For stiffened CFT stub columns in this paper,As fy is the same as that used in Eq. (12).fcu is taken as 1.25 f ′

c to calculate the values ofNAIJ for specimenslisted inTable 5sincenocube strength of concrete was provided in the literature.

The predicted strength using BS5400 [30] is compared with the experimental values inTables 3and5. A mean ratio(NBS5400/Nue) of 0.807 is obtained for adequately stiffenedCFT stub columns with a COV of 0.037. It can be seen that the predicted results fromBS5400 [30] are quite conservative.

6.4. EC4 method

The nominal strength for composite compression members is given as:

NEC4 = As fy + Ac f ′c. (13)

The predicted strength using EC4 [31] is compared with the experimental values inTables 3and5. A mean ratio(NEC4/Nue) of 0.927 is obtained with a COV of 0.049. It canbe seen that EC4 [31] can predict the strength of the stub column with reasonable accuracy,


although Eq. (13) slightly underestimates the load carrying capacity when theD/t ratio isequal to 52.

6.5. DBJ1351-2003 method

According to DBJ1351-2003 [32], a confinement factor(ξ) is used to describe the“composite action” between the steel tube and concrete as:

ξ = As,t · fs,tAc · fck

(14)

where fck is the compression strength of concrete. The value offck is determined using67% of the compression strength of cubic blocks( fcu). The squash load of the compositecross section is expressed as:

NDBJ = Asc fscy (15)

whereAsc is the sum of cross-sectional areas of the steel tube and the concrete core, givenby As,t + Ac. fscy is thenominal average strength of a square or rectangular steel tube afterfilling with concrete, which is given by

fscy = (1.18+ 0.85ξ) · fck. (16)

For stiffened CFT stub columns in this paper, the contribution from stiffeners isconsidered by adding a term ofAs,s fy,s to Eq. (15) as:

NDBJ = Asc fscy + As,s fy,s. (17)

The predicted strength using Eq. (17) is compared with the experimental values inTables 3and5 where a mean of 0.918 is obtained forNDBJ/Nue with a COV of 0.042.Generally good agreements are obtained.

7. Conclusions and recommended future research

Nineteen stub column specimens were tested to failure under concentric compression.The following observations and conclusions can be drawn based on the research reportedin the paper:

(1) The sectional capacity of the composite stub columns can be increased when stiffenerswere provided.

(2) Generally, the longitudinal stiffeners can not only delay the local buckling of the platepanel, but also improves the lateral confinement on the concrete core.

(3) It seems that no ductility improvement for stiffened CFT columns was observed in thecurrent test, and the increment of moment ofinertia of stiffenersdoes not significantlyinfluence the ductility of the stiffened CFT specimens.

(4) The outer stiffened specimens have shown almost the same behaviour as the innerstiffened ones, but the stiffeners should have higher flexural rigidities to ensure theireffectiveness.

(5) The larger the D/t ratio, the larger the rigidity requirement of stiffeners. Therequirement is developed by modifying a formula presented in the literature.Reasonable results are achieved.


(6) For adequately stiffened thin-walled CFT stub columns, existing design codes, suchas ACI [27], AIJ [28], AISC [29], BS5400 [30], EC4 [31] and DBJ1351-2003 [32],can be used to predict their load-carrying capacities with reasonable accuracy. Thelocal buckling effect can be ignored in the calculating process. Among them, EC4 andDBJ1351-2003 give the best results.

(7) It was found that, in general, the existing design codes mentioned above underestimatethe strength of the adequately stiffened stub columns. Future study shall be directed togivemore accurate formulae in predicting the load-carrying capacities of the columns,in which confinement enhancement effects from stiffeners should be considered.Another suggested future research topic is to present a more accurate model inpredicting load versus axial strain relationships.

Acknowledgements

The research work reported herein wasmade possible by the National NaturalScience Foundation of China, the Science and Technology Project from the ConstructionDepartment of Fujian Province and the Fujian Province Science and Technology BigProject (Grant No. 2002H007); the financial support is highly appreciated.

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Documents

Experimental Behaviour of Stiffened Concrete-filled Thin-walled Hollow Steel Structural (HSS) Stub Columns