Journal of Constructional Steel Research 64 (2008) 1473–1482www.elsevier.com/locate/jcsr

Seismic behaviour of square CFT beam–columns underbiaxial bending moment

Jiepeng Liua,∗, Xuhong Zhoub, Sumei Zhanga

a School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, Chinab School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China

Received 11 March 2007; accepted 11 January 2008

Abstract

This paper investigates the behaviour of square concrete-filled steel tubular (CFT) beam–columns subjected to biaxial moment. Nine tests onbeam–columns are reported here under a combined loading of constant axial load and cyclic lateral load applied at varying angles to the axis ofthe cross-section, referred to as ‘diagonal’ loading. The specimens were prepared in order to evaluate the influence of different parameters onthe overall structural response, their ductility and their energy dissipation ability; the parameters included the effects of axial load ratio, width-to-thickness ratio, concrete compressive strength, slenderness ratio and load angle on the moment strength. The experimental results indicate thatthe ductility and energy dissipation ability of biaxially loaded square CFT columns decrease with increasing the axial load ratio. Their ductilityand energy dissipation ability was also observed to decrease as the concrete compressive strength increased while the ductility was barely affectedby the load angle. An increase in the load angle of biaxially bent square CFT beam–columns led to a slight decrease of the moment strength.Both EC4 and AIJ code provisions were shown to predict with reasonable accuracy the moment strength capacity observed in the tests, while theACI-predicted moment strength gave to slightly conservative values. On the other hand, the LRFD code provisions greatly underestimated theirmoment strength.c© 2008 Elsevier Ltd. All rights reserved.

Keywords: Concrete-filled steel tubular (CFT); Diagonal lateral load; Biaxial bending moment; Axial load ratio; Energy dissipation ability

1. Introduction

Concrete-filled steel tubular (CFT) structures are rapidlyemerging as one of the dominant structural systems inthe construction industry due to their high strength, easyconstruction and excellent antiseismic performance [1,2]. CFTmembers combine the advantages of both steel (high tensilestrength and ductility) and concrete (high compressive strengthand stiffness and relative cheapness). The steel tube serves asa form for casting the concrete, which as a result, reduces theconstruction cost. Once the composite action is established, thesteel tubular of CFT columns offer confinement to the concrete,thus improving its compressive strength and ductility [2–4]. Atthe same time, the concrete infill delays the local buckling of the

∗ Corresponding address: PO Box 2551, 202 Haihe Road, Nan’gang District,Harbin Institute of Technology (2th District), Harbin 150090, China. Tel.: +86(0) 451 8628 2083; fax: +86 (0) 451 86282083.

E-mail address: liujp@hit.edu.cn (J. Liu).

0143-974X/$ - see front matter c© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2008.01.013

columns [5,6]. The use of steel at the perimeter of the sectionis efficient as it provides the highest contribution of the steel tothe section second moment of area and flexural capacity [7].

Landmark use of the CFT system includes the 63-storeyComerzbank building in Germany, which is the tallest buildingin Europe, the 57-storey Two Union Square in the USA,the 43-storey Casselden Place in Australia, the 68-story SEGplaza in China and the 68-storey Hongkong Centre Edificein Hongkong, which is the world’s tallest building utilizingCFT columns. In order to minimize the size of the structuralmembers, high strength concrete (HSC) should be usedfor high-rise buildings as well as for bridges and offshoreplatforms. Excellent mechanical performance and durabilityis achieved using high-strength concrete and this results ininitial and long term cost reduction. However, HSC is morebrittle than conventional normal strength concrete. Therefore,it cannot be used in engineering applications without specialconsideration of its brittleness. Despite this, previous work hasshown that steel tubes filled with HSC can still lead to ductile

1474 J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482

Notations

Ac area of the concrete of the cross-section;As area of the steel tubular of the cross section;D width of the steel tubular;fco compressive strength of unconfined concrete;f 10cu 100 mm concrete cubic strength;

fy yield strength of the steel tubular;L length of the column;Mu tested ultimate moment strength of the cross-

section;MEC4 the moment strength predicted using EC4 code;MAIJ the moment strength predicted using AIJ code;MACI the moment strength predicted using ACI code;MLRFD the moment strength predicted using LRFD code;N applied axial load of the columns;n0 axial load ratio, n0 = N/( fco Ac + fy As);P lateral load;Pu ultimate lateral load strength of the specimen;t thickness of the tubular;∆ lateral deflection of the column;

behaviour of the composite member and give large energyabsorption [7,8], a property which is especially necessaryin seismic regions. After many applications of CFT withcircular sections in high-rise buildings and bridges in China,more attention is currently being devoted to CFT columnswith square sections whose shape is more suitable for simpleconnection detail design and construction. In such columnsthe axial load, namely the dead load resulting from the upperstructures, usually acts eccentrically producing an additionalbending moment which affects their load-carrying capacity.Due to the randomness of seismic loading, it is also possiblethat transverse loads are not applied in a plane parallel to thesquare side over which the bending moment due to the eccentricload acts.

Experimental studies on circular CFT columns undera combination of flexure and axial compression havebeen conducted by Forlong [9], Knows [10], Neogi [11],Priestley [12], Elremaily [7], Boyd [13], Wang [14],Morino [15]. Tests on rectangular CFT Columns subjectedto combined flexure and axial compression were reported byFurlong [16], Rangan [17], Grauers [18], Varma [19] andHan [20]. Analytical method for predicting the static andcyclic behaviour of rectangular CFT beam–columns have alsobeen proposed by Hajjar [21], Zhang [22], Zhong [2] andVarma [19]. Research on the seismic behaviour of rectangularCFT has mainly focused on uniaxial bending beam–columnsfor the moment with only very limited work on biaxial loadedbeam–columns. For biaxial loaded square members, additionalcomplications arise when the applied moment does not coincidewith the square axis of the cross-section. Extensive research onthe behaviour of biaxial loaded reinforced concrete membershave been carried out in the past years. This work has shownthat the moment capacity of square section reinforced concretebeam–columns about the diagonal axis can be 20% less than

the square axis moment capacity [16,23]. Researches on thedifference between uniaxial and biaxial loaded square CFTbeam–columns have not been reported.

The aim of this paper is to investigate the strength andductility of diagonally loaded square CFT beam–columns filledwith normal strength and high strength concrete. As part of thisstudy, nine specimens were prepared and tested. The specimenswere subjected to a constant axial load, of 35%–58% of theaxial load-bearing capacity of the columns, and a diagonalcyclic transverse load. The effect of axial load ratio, width-to-thickness ratio, concrete compressive strength, slendernessratio and diagonal load angle on the moment strength, ductilityand energy dissipation ability of square CFT beam–columnsunder this loading regime was investigated in detail and the testresults recorded.

2. Experimental programme

2.1. Details of specimens

A total of nine square CFT beam–columns, including fivespecimens filled with normal and four with high strengthconcrete, were tested as part of this study. The specimenswere subjected to a combination of constant axial load andcyclic biaxial bending moment. Fig. 1 shows schematically theexperimental setup. Based on Fig. 1 it can be noted that thecolumn is under biaxial bending moment if the diagonal loadangle is between 0◦ and 45◦, while 0◦ angle corresponds tothe uniaxial bending case. In order to reproduce the type ofrestraint provided to a column in a real building frame, the testspecimens were fixed at their ends by rigid steel beams.

Table 1 shows the parameters of the specimens in the testseries. In particular, these are defined as follows: D was thewidth of the square tube; t was the thickness of the tube; D/twas the width-to-thickness ratio of the tube; L was the length ofcolumn; f 10

cu was the 100 mm concrete cubic strength; fco wasthe uniaxial compressive strength of concrete obtained fromfrom f 10

cu ; fy was the yield strength of the steel tube; N was theapplied axial load on the column; n0 was the axial load ratio,n0 = N/(As fy + Ac fco), where Ac and As were the cross-sectional area of the concrete and steel tube, respectively; θ wasthe diagonal load angle (0◦

≤ θ ≤ 45◦); Pu was the testedultimate lateral load strength of the columns. The concretecubic strength f 10

cu was measured for each specimen on the dayof the column test based on the results of three 100 mm cubicspecimens prepared from the same concrete batch used to fillthe member tested. The material properties of the steel tubeswere measured from the tension tests on three coupons in eachseries.

2.2. Test setup and instrumentation layout

In the test procedure, the axial compressive load was appliedand maintained constant before the cyclic transverse (horizon-tal) load was applied. Fig. 2 shows schematically the test setup.It consists of the rigid L beam and a movable truss system whichallows the L beam to move freely in vertical and horizontal di-rections with no rotation. This loading system guarantees the

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(a) Typical diagonalbending momentspecimen.

(b) Diagonal load angle (θ). (c) Schematic of testedspecimen.

Fig. 1. Schematic of beam–columns under biaxial bending moment.

Fig. 2. Schematic of test setup.

Table 1Parameters of test specimens

Specimen D (mm) t (mm) D/t L (mm) f 10cu (MPa) fco (MPa) fy (MPa) N (kN) n0 θ (◦) Pu (kN)

CCFT1 150 2.65 56.6 1100 48.8 35.2 328 662 0.52 45 80.0CCFT2 150 2.65 56.6 1100 48.8 35.2 328 452 0.35 45 74.7CCFT3 150 4.82 31.1 1100 48.8 35.2 340 592 0.35 45 122.5CCFT4 150 2.65 56.6 845 48.8 35.2 328 452 0.35 45 109.3CCFT5 150 2.65 56.6 1100 48.8 35.2 328 452 0.35 22.5 78.5HCFT1 150 4.78 31.4 1100 100.5 81.4 317 1300 0.52 45 164.1HCFT2 150 2.89 51.9 1100 100.5 81.4 319 1300 0.58 45 125.8HCFT3 150 2.89 51.9 1100 100.5 81.4 319 1000 0.45 45 130.4HCFT4 150 2.89 51.9 800 100.5 81.4 319 1000 0.45 45 160.4

boundary condition of the columns. The axial load was appliedby two 1000 kN hydraulic jacks on which two 1000 kN pressuretransducers were positioned to measure the axial loads. Thelateral load was applied by a 630 kN MTS hydraulic actuatorsystem which was controlled by a computer. On the pressuretransducer and under the 1000 kN hydraulic jacks were the dis-tribution beams that transfer the axial load to the specimen and

the reaction frame. Rollers were placed between the rigid beamand the spreader beam so that the rigid L beam was able tomove freely with negligible friction. Since the moveable trusssystem was not designed to bear the vertical or horizontal load,the axial and horizontal load are resisted by the test specimen.

Fig. 3 shows the instrumentation layout for the specimens.Seven linear variable differential transducers (LVDT) were used

1476 J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482

Fig. 3. Instrumentation layout.

during each test. The horizontal displacement of specimens wasmeasured by three horizontally placed LVDTs. Four LVDTswere placed vertically to observe if the rigid beams of thetest specimen were fixed firmly enough during the test. Theaxial load was applied before the cyclic lateral load. Twelvelongitudinal strain gauges were glued to the steel tubes at theends and at midheight of the columns and four hoop straingauges were bonded at the midheight of the columns. Thesestrain gauges enabled a check on whether the columns wereaxially loaded during the application of the vertical axial load.

3. Results of the experiment

3.1. Failure mode

Fig. 4 shows the failure modes of three specimens. In allnine columns, local buckling of the tube occurred after thepeak lateral load was reached. The steel element buckled at thecolumn ends where the moment reached its maximum value.

3.2. Lateral load versus lateral deflection (P–∆) relationship

Fig. 5 shows the lateral load (P) versus lateral deflection(∆) responses for the normal strength concrete-filled tubular(CCFT) columns. CCFT1 was not as ductile as CCFT2 due toits higher axial load level despite all other parameters beingsimilar; also its energy dissipation ability was lower than theone observed for CCFT2. This leads to the conclusion that theductility and energy dissipation ability of biaxially bent CCFTbeam–columns decrease with an increase in their axial loadratio.

The P–∆ hysteresis loop of CCFT3 is plumper than that ofCCFT2 due to the fact that the D/t ratio of CCFT3 was lowerthan for CCFT2 despite the remaining parameters being similar.

CCFT2 and CCFT5 had the same parameters except the loadangle. The test results highlighted that the there is no obviousdifference between the energy dissipation ability of specimensCCFT2 and CCFT5 despite their load angle being different,i.e. 45◦ for CCFT2 and 22.5◦ for CCFT5.

Fig. 6 shows the lateral load (P) versus lateral deflection (∆)

responses for the high-strength concrete-filled tubular (HCFT)columns. The load-deflection responses of HCFT1 and HCFT2

show that the ductility and energy dissipation ability of HCFTcolumns under high axial load levels (n0 > 0.5) was relativelylow.

The parameters of HCFT2 were the same as those of HCFT3except that the axial load ratio of HCFT3 was less than thatof HCFT2. The test results indicate that the ductility andenergy dissipation ability of HCFT3 were better than the oneof HCFT2, denoting that the ductility and energy dissipationability of biaxially bent HCFT columns decrease with anincrease in the axial load ratio.

The parameters of HCFT3 were the same as those of HCFT4except that HCFT3 was longer than HCFT4. The test resultsindicate that the ductility and energy dissipation ability ofbiaxially bent HCFT columns increased with an increase inslenderness ratio.

The test results of CCFT and HCFT columns indicate thatthe P–∆ hysteresis loops of CCFT columns are plumperthan those of HCFT columns, which denotes that the energydissipation ability of biaxially bent square CFT columnsdecreased with an increase in concrete compressive strength.

4. Discussion of the test results

4.1. Comparison between the envelopes of CCFT columns

Fig. 7 shows the comparison between the envelopes ofCCFT1 and CCFT2. The parameters of CCFT1 and CCFT2were the same except for the axial load ratio. The axialload ratio of CCFT1 (0.52) was higher than that of CCFT2(0.35). The ultimate lateral load strength (Table 1) of CCFT1was 7.1% higher than that of CCFT2, while the ductility ofCCFT1 was much lower compared to that of CCFT2. Thetest results indicate that normal strength concrete-filled squaretubular columns are not sufficiently ductile when subjected totransverse seismic load when the axial load ratio is higher than0.5. The lateral load strength was not obviously affected by theaxial load ratio when the axial load ratio was between 0.35 and0.52 for biaxially bent CCFT columns. While the ductility wasobviously affected by the axial load ratio when the axial loadratio was between 0.35 and 0.52.

Fig. 8 shows the comparison between the envelopes ofCCFT2 and CCFT3. The parameters of CCFT2 and CCFT3were the same except that the D/t ratio of CCFT2 was higherthan that of CCFT3. It is obvious that the lateral load strength ofCCFT2 was less than that of CCFT3, while CCFT3 was not asductile as CCFT2; the possible reason was that as the axial loadof CCFT3 was higher than that of CCFT2, it produced highersecond-order effects.

Fig. 9 shows the comparison between the envelopes ofCCFT2 and CCFT4. The parameters of CCFT2 and CCFT4were the same except that the column of CCFT2 was longerthan CCFT4. It is obvious that the lateral load strength ofCCFT4 was greater than that of CCFT2, while CCFT4 was notas ductile as CCFT2; these test results indicate that the ductilitydecreases with a decrease in slenderness ratio.

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Fig. 4. Failure modes of the specimens.

Fig. 10 shows the comparison between the envelopes ofCCFT2 and CCFT5. The parameters of CCFT2 and CCFT5were the same except for the diagonal load angle which was45◦ and 22.5◦, respectively. There is no obvious difference onthe envelopes of CCFT2 and CCFT4 except that the lateralload strength of CCFT4 (78.5 kN) was slightly higher than thatof CCFT2 (74.7 kN). The test results indicate that the lateralload decreases slightly with an increase in diagonal load angle(0◦

≤ θ ≤ 45◦), while the ductility of square CFT columns isbarely affected by the diagonal load angle.

4.2. Comparison between the envelopes of HCFT columns

Fig. 11 shows the comparison between the envelopes ofHCFT1 and HCFT2. The applied axial load during the test ofHCFT1 and HCFT2 was the same (1300 kN), while the lateralload strength of HCFT1 was greater than that of HCFT2 despitethe D/t ratio of the former being less than that of HCFT2.Neither HCHF1 nor HCFT2 were ductile enough due to thehigh axial load level (0.52 and 0.58). The test results indicatehigh-strength concrete-filled square tubular columns are notsufficiently ductile under transverse seismic load if the axialload ratio is greater than 0.5.

Fig. 12 shows the comparison between the envelopes ofHCFT2 and HCFT3. The parameters of HCFT2 and HCFT3were the same except that the axial load ratio of HCFT2 (0.58)was greater than that of HCFT3 (0.45). The lateral load strengthof HCFT3 was 3.65% higher than that of HCFT2, while theductility of HCFT3 was obviously higher than that of HCFT2.The test results indicate that the lateral load strength was barelyaffected by the axial load ratio when the axial load ratio wasbetween 0.45 and 0.58 for biaxially bent HCFT columns. It canbe concluded that the ductility is affected by the axial load ratiowhen it varies between 0.45 and 0.58.

Fig. 13 shows the comparison between the envelopes ofHCFT3 and HCFT4. The parameters of HCFT3 and HCFT4were the same except that HCFT3 was longer than HCFT4. It isobvious that the lateral load strength of HCFT4 was higher thanthat of HCFT3, while HCFT4 was not as ductile as HCFT3. Thetest results indicate that the ductility decreases with a decreasein slenderness ratio for HCFT columns.

4.3. Comparison between the envelopes of CCFT and HCFTcolumns

Fig. 14 shows the comparison between the envelopes ofHCFT2 and CCFT1. The parameters of the two columns weresimilar and only differed in their concrete compressive strength;the lateral load strength increased with an increase in concretecompressive strength. Neither HCFT2 nor CCFT1 was ductileenough due to the high axial load ratio (0.58 and 0.52).

Fig. 15 shows the comparison between the envelopes ofHCFT4 and CCFT4. The parameters of the two columns weresimilar and only differed in their concrete compressive strength;the lateral load strength increased with an increase in concretecompressive strength. HCFT4 was not as ductile as CCFT4 forthe reason that HCFT 4 was under higher axial load ratio (0.45)and was filled with higher-strength concrete.

5. Comparison of experimental results with strengthpredictions based on current code provisions

The experimental results in this paper were comparedwith moment strength predictions based on current Eurocode4 (EC4) [24], Architectural Institute of Japan (AIJ) [25],American Concrete Institute (ACI) [26] and American Instituteof Steel Construction-Load and Resistance Factor Design(LRFD) [27] code provisions for CFT columns. The width-to-thickness ratio (D/t) of all test specimens have been reportedin Table 2 together with the relevant limiting values specified bythe current codes considered. In summary, The D/t ratio of testspecimens satisfied the width-to-thickness-ratio limit of currentcode AIJ, ACI and LRFD code provisions. CCFT3 and HCFT1satisfied the D/t limit of EC4 code provision, while CCFT1,CCFT2, CCFT4, CCFT5, HCFT2, HCFT3 and HCFT4 violatedthe D/t limit of EC4 code provisions.

Comparisons of the experimental moment strength oftest specimens with predictions based on the current codesprovisions are shown in Table 3, in which Mu is theexperimentally measured ultimate moment strength of thecolumns. In Table 3, MEC4, MAIJ, MACI and MLRFD are themoment strength predicted using the current EC4, AIJ, ACIand LRFD code provisions. The purpose of the comparisonswas to evaluate the accuracy of the current code provisions in

1478 J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482

(a) CCFT1 (D/t = 56.6, n0 = 0.52, L = 1100, θ = 45◦). (b) CCFT2 (D/t = 56.6, n0 = 0.35, L = 1100, θ = 45◦).

(c) CCFT3 (D/t = 31.1, n0 = 0.35, L = 1100, θ = 45◦). (d) CCFT4 (D/t = 56.6, n0 = 0.35, L = 845, θ = 45◦).

(e) CCFT5 (D/t = 56.6, n0 = 0.35, L = 1100, θ = 22.5◦).

Fig. 5. Lateral load–lateral deflection response of common strength concrete-filled tubular (CCFT) columns.

J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482 1479

(a) HCFT1 (D/t = 31.4, n0 = 0.52, L = 1100, θ = 45◦). (b) HCFT2 (D/t = 51.9, n0 = 0.58, L = 1100, θ = 45◦).

(c) HCFT3 (D/t = 51.9, n0 = 0.45, L = 1100, θ = 45◦). (d) HCFT4 (D/t = 51.9, n0 = 0.45, L = 800, θ = 45◦).

Fig. 6. Lateral load–lateral deflection response of high strength concrete-filled tubular (HCFT) columns.

Fig. 7. Comparison between the envelopes of CCFT1 and CCFT2.

predicting the moment capacities of square CFT beam–columnsunder biaxial bending moment. The comparison results indicate

Fig. 8. Comparison between the envelopes of CCFT2 and CCFT3.

that although 6 test members in this paper violated the D/t limitof EC4 code provisions, the EC4-predicted moment strength

1480 J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482

Fig. 9. Comparison between the envelopes of CCFT2 and CCFT4.

Fig. 10. Comparison between the envelopes of CCFT2 and CCFT5.

was reasonably accurate. The predicted moment strength withAIJ code provisions was also reasonably accurate. The ACI-predicted moment strength was slightly conservative. TheLRFD code provisions greatly underestimate the momentstrength of square CFT beam–columns under biaxial bendingmoment. The average ratio of the tested moment strength to theLRFD-predicted moment strength is as high as 1.99 and 3.34for CCFT and HCFT columns respectively. The axial load ratioof HCFT2 was the highest (0.58) in this paper, and the ratio ofthe tested moment strength to the LRFD-predicted moment wasthe highest (4.09). The axial load ratios of the CCFT membersin this paper were 0.52 for CCFT1 and 0.35 for the other four.The axial load ratio of CCFT1 was the highest (0.52) among thefive CCFT columns, and the ratio of the tested moment strengthto the LRFD-predicted moment strength was the highest (2.57)among the five CCFT columns. Conclusion can be drawn fromthe above analysis that the higher axial load level, the moreconservative the LRFD-predicted moment strength. In LRFDprovisions, when the axial load is zero, no composite actionis assumed to occur and the moment capacity (at zero axialload) is determined from a plastic stress distribution on the steelsection alone. Therefore the calculated moment strength for the

Fig. 11. Comparison between the envelopes of HCFT1 and HCFT2.

Fig. 12. Comparison between the envelopes of HCFT2 and HCFT3.

Fig. 13. Comparison between the envelopes of HCFT3 and HCFT4.

CFT cross-section will be relative conservative using the LRFDaxial load-bending moment interaction curve for the CFT cross-section.

J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482 1481

Fig. 14. Comparison between the envelopes of HCFT2 and CCFT1.

Fig. 15. Comparison between the envelopes of HCFT4 and CCFT4.

Table 2Limit on D/t ratio according to current code provisions

Specimen D/t D/t limitEC4 AIJ ACI LRFD

CCFT columns CCFT1 56.6 45.2 63.4 75.2 75.2CCFT2 56.6 45.2 63.4 75.2 75.2CCFT3 31.1 45.2 62.4 73.8 73.8CCFT4 56.6 45.4 63.4 75.2 75.2CCFT5 56.6 45.2 63.4 75.2 75.2

HCFT columns HCFT1 31.4 45.4 64.5 76.5 76.5HCFT2 51.9 45.2 64.3 76.2 76.2HCFT3 51.9 45.2 64.3 76.2 76.2HCFT4 51.9 45.2 64.3 76.2 76.2

6. Summary and conclusions

The effects of axial load ratio, width-to-thickness ratio,concrete compressive strength, slenderness ration and loadangle on the behaviour of biaxially bent square CFTbeam–columns were studied by testing nine specimens. Thecolumns were subjected to combined constant axial load and

Table 3Comparisons of the test results of test specimens with predictions based on thecurrent codes provisions

Specimen Mu (kN m)Mu

MEC4Mu

MAIJMu

MACIMu

MLRFD

CCFTcolumns

CCFT1 46.82 1.07 1.21 1.31 2.57

CCFT2 46.07 0.95 0.96 1.02 1.81CCFT3 69.77 1.05 1.07 1.15 1.56CCFT4 49.22 1.13 1.14 1.21 2.16CCFT5 48.83 0.97 0.98 1.04 1.85Average Coefficientof Variation

1.03 1.07 1.15 1.99

0.07 0.11 0.12 0.39HCFTcolumns

HCFT1 78.71 1.07 1.23 1.29 3.00

HCFT2 53.34 1.06 1.19 1.17 4.09HCFT3 56.85 1.06 1.08 1.19 3.13HCFT4 57.38 1.04 1.05 1.09 3.15Average Coefficientof Variation

1.06 1.14 1.18 3.34

0.01 0.08 0.08 0.51

diagonal cyclic lateral load. Conclusions from the investigationpresented in this paper are summarized as follows:

1. The ductility and energy dissipation ability of biaxially bentCCFT and HCFT columns decreases with an increase in theaxial load ratio. Neither HCFT nor CCFT columns underseismic biaxial bending moment are sufficiently ductilewhen subjected to high axial load ratios, namely for n0 >

0.5.2. The moment capacity decreases as the width-to-thickness

ratio increases for both CCFT and HCFT columns subjectedto biaxial loading. The energy dissipation ability decreaseswith an increase in width-to-thickness ratio for biaxiallybent CCFT columns. However, the width-to-thickness ratiobarely affects the energy dissipation ability of biaxially bentHCFT columns.

3. The moment capacity of biaxially bent square CFTbeam–columns increases with increase in concrete compres-sive strength, while an opposite trend was observed for theirductility and energy dissipation ability.

4. The ductility and energy dissipation ability of biaxially bentCCFT and HCFT columns increases with an increase inslenderness ratio.

5. The ductility and energy dissipation ability of biaxially bentsquare CFT beam–columns are barely affected by diagonalload angle while their moment capacity slightly decreaseswith increase of the diagonal load angle.

6. These tests showed that the moment capacity of biaxiallybent square CFT columns can be predicted with reasonableaccuracy using the EC4 and AIJ code provisions. TheACI-predicted moment capacity was slightly conservativecompared with the test results while the LRFD codeprovisions greatly underestimated the capacity of squareCFT beam–columns under biaxial bending moment.

Acknowledgements

The research reported here was financially supported byNational Natural Science Foundation of China (59808004)

1482 J. Liu et al. / Journal of Constructional Steel Research 64 (2008) 1473–1482

and The Research Fund for the Doctoral Programmeof Higher Education (20030213045). Dr. Douglas Goodeprovided some advice and some of the referenced pa-pers were gained from the CFST column database web-site, http://web.ukonline.co.uk/asccs2, which is managed byDr. Goode.

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