Thin-Walled Structures 64 (2013) 83–93

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Thin-Walled Structures

0263-82

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Experimental study of rectangular CFST columns subjectedto eccentric loading

Xiushu Qu, Zhihua Chen n, Guojun Sun

Structural Engineering, School of Civil Engineering, Tianjin University, Tianjin 300072, PR China

a r t i c l e i n f o

Article history:

Received 16 February 2012

Accepted 14 December 2012Available online 22 January 2013

Keywords:

Biaxial bending

Concrete contribution ratio (CCR)

Concrete-filled steel tube (CFST)

Uniaxial bending

31/$ - see front matter Crown Copyright & 2

x.doi.org/10.1016/j.tws.2012.12.006

esponding author.

ail address: zhchen@tju.edu.cn (Z. Chen).

a b s t r a c t

To study the behavior of rectangular CFST columns subjected to eccentric loading, a total of 17

rectangular CFST columns uniaxial and biaxial bending tests were carried out. Concrete compressive

strength, steel strength, cross-sectional proportion and eccentricity were selected as the variables to

be investigated. The relationship between the load and the lateral displacement at the mid-height of

the columns in the directions of both the strong and weak axes and the relationships of load versus

end shortening for each specimen were duly recorded. The influences of the constraining factor and

eccentric ratio in relation to the strength and ductility indexes of the specimens were investigated.

Moreover, in order to achieve the ultimate bearing capacity of the relative rectangular hollow sections

with a load of the same eccentricity, the rectangular hollow section models were established by means

of the FEM. The concrete contribution ratio necessary for the rectangular CFST columns to be able to

resist the eccentric loading was obtained also through comparison of the simulated results and the test

data. Finally, based on the definitions and conclusions obtained for the design strength of rectangular

CFST columns relying on the ‘‘Technical specification for design of steel structure dwelling houses in

Tianjin’’ code (DB 29-57-2003), a factor b was proposed to enhance the steel strength in order to take

into account the concrete contribution to the resistance. The modified equation can subsequently

provide improved understanding and a more accurate predictive ability or value.

Crown Copyright & 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction

In the normal course of events the composite columns willnecessarily be subjected to eccentric loads in practical engineer-ing. In addition, the corner columns usually need to be subjectedto a combination of both compression and biaxial bending.

The related information that refers to the bearing capacity ofCFST columns under this combination of compression and bend-ing are currently provided in the form of the design codes, suchas EC4 [1], ACI318M-05 [2], GJB(4142-2000) [3]and AISC 2005 [4].The thrust–moment (P–M) interaction curve is usually used infact for predicting the bearing capacity of the reinforced concretestructure under eccentric loading. This method has also beenfound to be adopted in the design of composite structures too. Theexact P–M interaction curves found in current design codes arebased on a summary of test results or alternatively through thefiber analysis method. However, to make it more convenient forthe purposes of design, some codes have adopted a simplifiedP-M interaction curve to predict the design resistance strength ofcomposite columns. The current typical interaction curves are the

012 Published by Elsevier Ltd. All

AISC 2005 simplified bilinear interaction curve and the simplified4-line interaction curve proposed by EC4. The AISC 2005 simplifiedbilinear curve was revised based on changes in approach providedby AISC 2001 [5]. On account of the AISC 2001 approach notsuitably taking consideration of the contribution of the concrete;as a result the code does not realize the differences in behaviorbetween pure steel members and composite members: in fact itusually provides an overly conservative estimation. To make itmore accurate and safe for design, the revised version-AISC2005 provides two new simplified interaction curves for compositestructure. One of them is the rigid-plastic approach, which issimilar with the EC4 simplified interaction curve. However, it isstill different in relation to how it calculates the concrete stressvalue and, as well, as to how the concrete contributes in resistingthe pure bending: this as well should be considered.

Some researchers have undertaken an investigation into thebehavior of CFST columns subjected to eccentric loading [6–16].Of all these experimental studies on CFST columns, greatestefforts were placed on research intending to determine the failuremode as well as the bearing capacity for the tested specimens.However, as to the concrete contribution to the columns ability toresist combined compression and bending, and especially to resistcombined compression and biaxial bending: this type of researchanalysis is still lacking and in need of further research.

rights reserved.

Nomenclature

Ac cross-sectional area of concrete core;As cross-sectional area of steel tube;B width of the rectangular steel tube;CFST concrete-filled steel tube;CHS circular hollow section;D depth of the rectangular steel tube;DIx ductility index about x-axis;DIy ductility index about y-axis;Ec Young’s modulus of concrete;Es Young’s modulus of rectangular steel tube;fcu compressive cube strength of concrete;fy yield strength of steel;fu ultimate strength of steel;L length of the rectangular steel tube;Mx available flexural strength about x-axis;My available flexural strength about y-axis;Nu ultimate axial compression bearing capacity;

Nu,e ultimate test resistance of concrete-filled rectangularspecimens;

Nu,hollow ultimate strength of the empty hollow steel member;NEx Euler’s critical load about x-axis;NEy Euler’s critical load about y-axis;Wx net section resistance moment about x-axis;Wy net section resistance moment about y-axis;RHS rectangular hollow section;SI strength index;SHS square hollow section;t wall thickness of the steel tube;x constraining factor;d specimen end shortening;d85% axial deformation corresponding to the 85% of the

ultimate strength of CFST columns measured after theultimate strength was reached;

du axial deformation at the ultimate strength;jx stability factor for compression about x-axis;jy stability factor for compression about y-axis.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–9384

As distinct from square and circular CFST columns, the flexuralstrength of rectangular CFST columns is different along both of thetwo symmetry axes. The aim of this paper is to study the behavior ofrectangular CFST columns subjected to combined compression andbending (including uniaxial and biaxial bending). Seventeen eccen-trically loading tests were carried out on rectangular CFST columns.The results obtained from the testing, including the ultimate load,maximum lateral and vertical displacement and strain develop-ment of the steel tubes, were each, in turn, recorded and analyzed.Furthermore, the strength index, ductility index and concrete con-tribution ratio for the tested specimens were investigated. Finally,based on the analysis of these test results, as well as test data drawnfrom other literatures, a factor b was proposed to enhance the steelstrength so as to take account of the concrete contribution to theresistance for the design strength for the rectangular CFST columns inthe ‘‘Technical specification for design of steel structure dwellinghouses in Tianjin’’ code (DB 29-57-2003).

2. Experimental study

2.1. General

A total of 17 RCFST stub columns tests were carried out atTianjin University to investigate the behavior of rectangular CFSTcolumns subjected to eccentric loads. All the test specimens wereclassified into two groups—Group PYA and Group PYB. Specimensin Group PYA were subjected to combined compression and uniaxialbending about the strong axis, whilst specimens in Group PYB weresubjected to combined compression and biaxial bending. The inves-tigated variables were selected accordingly: electricity, concretecompressive strength, steel strength grade and cross-sectional pro-portions. Table 1 provides details of the ranges of values covered. Thesection labeling convention is shown in Fig. 1.

2.2. Fabrication of specimens

All specimens of the same size of steel tube were cut from thesame cold-formed rectangular steel tube. The concrete was verticallycast into the steel tube in layers. Each layer was compacted using apoker vibrator. All specimens were kept in an indoor environmentto cure.

2.3. Material properties

The nominal tube thicknesses are 4 mm, 5 mm and 6 mmrespectively. The basic stress–strain characteristics of the rectan-gular steel tubes were obtained by means of tensile coupon tests.Coupons were machined from the complete sections of the wider-width regions (see Fig. 1) and subsequently tested in accordancewith Code (GB/T 228-2002) [17]. The key results from the coupontests are summarized in Table 2.

Three different grades of commercial concrete strengths – C30,C40, and C50 – were used in the test. Nine cubes (100 mm) ofeach batch were cast for material testing [18], the concrete elasticmodulus and the average cubic strength (f cu) at the testing timeare illustrated in Table 3.

2.4. Test set-up

All column tests were performed in a 5000 kN capacity testingmachine (see Fig. 2). Since the standard accessories of the testingmachine were unable to produce eccentric loading, knife edgesand ball edges were constructed which allowed the load from thetesting machine to be applied at given eccentricities to the speci-men. More details about the bearing plates employed at bothends of the specimens are shown in Fig. 3. The knife edges and balledges were employed at both the bottom and the top to enableeach Group PYA specimen and Group PYB specimen respectively tosimulate the required pin-pin boundary conditions.

For the specimens subjected to compression and uniaxialbending, the axial shortening was captured by means of two linearvariable displacement transducers (LVDTs) positioned between theend platens of the testing machine. While the lateral displacementsof specimens were measured by means of three LVDTs at thelocations of L/4, L/2 and 3L/4 mm respectively for the specimenssubjected to compression and biaxial bending, the axial shorte-ning was captured by means of four linear variable displacementtransducers (LVDTs) positioned at each corner between the endplatens of the testing machine. Meanwhile the lateral displace-ments of the specimens on the two perpendicular sides weremeasured by means of two LVDTs at the locations of L/2 mm. Allthe relevant details as to the measurement arrangement are shownin Fig. 4.

Strain gauges were used to measure the axial longitudinalstrains and transverse strains at the different locations along the

Table 1Measured geometric properties for tests specimens.

Specimen

reference

D�B� t� L Concrete

strength grade

Steel grade x ex ey e

PYA-1 150�100�4.065�700 C30 Q235b 1.704 10 0 10

PYA-2 150�100�4.065�800 C50 Q235b 1.007 15 0 15

PYA-3 150�100�4.065�900 C40 Q235b 1.278 20 0 20

PYA-4 200�150�4.433�700 C40 Q235b 0.78 20 0 20

PYA-5 200�150�4.433�800 C30 Q235b 1.04 30 0 30

PYA-6 200�150�4.433�900 C50 Q235b 0.614 40 0 40

PYA-7 300�200�5.730�800 C50 Q345b 0.781 50 0 50

PYA-8 300�200�5.730�900 C40 Q345b 0.992 60 0 60

PYA-9 300�200�5.730�1000 C30 Q345b 1.322 70 0 70

PYB-1 150�100�4.065�700 C30 Q235b 1.704 8.321 5.547 10

PYB-2 150�100�4.065�800 C50 Q235b 1.007 12.48 8.321 15

PYB-3 150�100�4.065�900 C40 Q235b 1.278 16.64 11.09 20

PYB-4 200�150�4.433�700 C40 Q235b 0.78 16 12 20

PYB-5 200�150�4.433�800 C30 Q235b 1.04 24 18 30

PYB-6 200�150�4.433�900 C50 Q235b 0.614 32 24 40

PYB-7 300�200�5.730�800 C50 Q345b 0.781 38.41 32.01 50

PYB-8 300�200�5.730�900 C40 Q345b 0.992 46.09 38.41 60

x

Flat coupon

x

y

y

Weld

B

D

t

ex ey e

Fig. 1. Section labeling convention and location of flat tensile coupons.

Table 3Concrete properties (Young’s modulus, compressive strength).

Concrete strength

grade

Young’s modulus

Ec ðMPaÞ

Compressive strength

f cu ðMPaÞ

C30 26690 39

C40 29380 52

C50 38070 66

Table 2Key material properties from tensile coupons tests

Specimen Young’s modulus

Es (MPa)

Yield stress

fy (MPa)

Ultimate

strength fu (MPa)

RHS150�100�4.065 212300 295 496

RHS200�150�4.433 216800 242 410

RHS300�200�5.730 216400 336 533

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–93 85

steel tubes. For specimens with an unaxial eccentric loading,two vertical strain gauges and two transverse strain gauges wereaffixed to two perpendicular faces (wide face and narrow facerespectively) of the steel tube at mid-height to record strains. Forspecimens subjected to biaxial eccentric loading, four verticalstrain gauges were affixed to each of the faces of the steel tube atmid-height to record longitudinal strains and, in addition, twotransverse strain gauges: which were affixed to two perpendicu-lar faces of the steel tube at mid-height to record transversestrains. The locations of the strain gauges are shown in Fig. 4.

2.5. Test procedure

Knife edges and ball edges were selected to be used for eachspecimen in accordance with the pre-designed load. Taking testPYA-1 as an example, due to the designed eccentricity in Y-axisbeing zero, knife edges were, as a result, selected for use. Prior tothe test, the bottom alpha edge (see Fig. 3(a) A) was placed at thebottom platen of the testing machine. Then, in turn, the bottom

beta edge (see Fig. 3(b) B) was positioned onto the alpha edgewith the specific position of the knife edge being determinedby the required load eccentricity. The specimen was then subse-quently placed on the bottom knife edge. And finally, to followthat, the top knife edge was placed onto the top part of thespecimen. At the same time as this alignment actions were takento ensure that the center points of the beta edges coincided withthe centers of the platens of the testing machine. A load intervalof less than one tenth of the estimated strength was used and theload was applied in a monotonous way from the beginning of thetest to the point at which the load caused failure in the columnitself. From the point of the ultimate load onwards, the load wasapplied in a downward trend. For each of these columns thetest observations would include observation of the failure load,load–displacement response, and load–strain vibration at severalpoints along the steel tube.

3. Experimental results

3.1. Failure mode

All the specimens showed a favorable ductility performance.For some specimens, slight local buckling can be found before theload reached the point of the ultimate load. After the tests, it canbe found that all the specimens failed on account of cracking ofthe concrete in the tension zone and buckling of the steel inthe compression zone; with the typical failure mode being shownin Fig. 5.

Because the tested columns were stub columns, the mainfailure mode throughout these tests was a form of material failure.The overall buckling failure mode which normally will occur onaccount of the columns being slender is not, in fact, found withinthe results of these tests.

A (alpha edge)A (alpha edge) B (beta edge) B (beta edge)

1 1 2 2

1-12-2

33 4 4

4- 43- 3

Fig. 3. Details of the bearing plate: (a) knife edges and (b) ball edges.

Fig. 2. Test set-up: (a) Group PYA with knife edges and (b) Group PYB with ball edges.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–9386

The different phenomenon observed respectively throughoutthe course of the two Groups’ experiments does in fact representthe local buckling distribution that exists throughout the lengthof the cross-sections. For the specimens subjected to unaxialbending (Group PYA), the local buckling could be found on threefaces (that is to say the compression narrow face and the twoadjacent wide faces). While, for specimens subjected to biaxialbending, local buckling could only be found on the two compres-sion faces. It should be noted that the corner of the steel tube forspecimen PYB-8 was cracked during the unloading stage. Thismay be due to the concrete being crushed and expanded at thecorner and the constraining force from the steel tube to the coreconcrete not being sufficient so as to resist the expanding of theconcrete. The consequence was that the steel tube was crackedunder the overall complicated force.

3.2. Load–end shortening responses

The longitudinal deflection of all specimens was recorded andplotted against the applied load, taking the typical specimensPYA-1 and PYB-1 for examples, as shown in Fig. 6. The relation-ship between the load and the deflection was non-linear and was

characterized by an upwards trend leading to the ultimateload followed by a slightly declining trend to the failure load. Forspecimen PYB-1, the longitudinal deformations on the four faceswere quite different and the bigger longitudinal deformations werefound on the wide and narrow faces near to the point of appliedloading. It can be concluded as a result that all the specimensshowed a favorable ductility performance.

3.3. Load–transverse displacement responses

Fig. 7 shows the relationship between the applied load andthe transverse displacement for all the test specimens. Since thespecimens in Group PYB were subjected to biaxial bending, thetransverse displacement along the strong and the weak axes wasin each case recorded respectively. Instead of the expected idealfigure being achieved, the biggest lateral transverse displacementfor each specimen was in fact not always found at the mid-heightposition. The main reason may be that the test machine is anaxial testing machine and the eccentric load was added by meansof the knife or ball edges. In most cases the rotation angle of thespecimen is determined simultaneously by a combination of threefactors: the available rotation angle of the edges, the slenderness

Strain

gauge1

LDVT5

LDVT1

Strain

gauge3

LDVT3

LDVT4 Strain

gauge2Strain

gauge4

LDVT6 LDVT8

Strain

gauge7

LDVT10

LDVT7 Strain

gauge 6

Strain

gauge 5 Strain

gauge 9

Strain

gauge 10LDVT11

LDVT6

LDVT10

Strain gauge 5,9

LDVT9

Strain gauge 7

LDVT11

LDVT8

Strain gauge 6,10 LDVT7

Strain gauge 8

Strain gauge 1,3 LDVT2

LDVT3,4,5

LDVT1 Strain gauge 2,4

y

x

0 E

S

W

N

Fig. 4. Details of the measurement arrangement.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–93 87

of the specimen and the value of the eccentric load. Moreover, theavailable rotation angle of the edges is determined not only by thedesignated angle but also by the total weight of the specimen.Another way to say this is that if the specimen has a smallerslenderness ratio while possessing a large weight: then, when itis subjected to an eccentric load using such experimental equip-ment, the beta edge and the alpha edge may contact eachother very quickly if the available rotation angle is insufficient.As a consequence the specimen’s rotation would of course berestrained.

The ultimate loads and the corresponding maximum recordedlateral displacements for each specimen are reported in Table 4.Meanwhile these lateral displacements were to be used forcalculating the maximum bending moments within the columns’lengths.

3.4. Load–strain responses

Figs. 8 and 9 give complete illustrations as to the load–strainvariations of all the tested columns. The common feature of thesecurves is that variation is non-linear and that the yield strains ofthe compressed side were reached at the point of failure and wereexceeded in the post-failure stage. The calculated yield strain forthe three steel tubes (RHS150�100�4.065, RHS200�150�4.433and RHS300�200�5.730) were 1390, 1116 and 1553 respec-tively. As shown in Fig. 8, for specimens of Group PYA the long-itudinal strains in the compression side were observed to be higherthan the calculated steel yield strains. The strains at the mid-depthof the cross-section (strain gauge (2)) were also once again higherthan the calculated yield strength. This indicates that the steelsection from the compressed side to the point of mid-depth withinthe cross-section had yielded before the point of load failure forspecimens in Group PYA.

Within the category of specimens of Group PYB, each speci-men was subjected to biaxial loading. The longitudinal strainsin the compression sides (strain gauge (5) and (6)) were higherthan the yield strain itself with exceptions supplied by specimensPYB-4, 5, 6. As shown in Fig. 8(e) and (f), and, again with the excep-tion of the specimens PYB-1, 2, 3, the tension sides of the specimenswere experiencing compression but that level of compression fellwithin the elastic range available at the point of failure load. For thetransverse strains, and at the point before the loading reached thepoint of failure load, the transverse strains were essentially withinthe elastic range as applied to all specimens.

4. Performance indices

4.1. Strength index (SI)

Strength index can be taken as an important parameter todetermine the behavior of specimens subjected to the designedload. Therefore the SI, with the same definition as described inSection 5, was adopted to investigate the influence of both theconfinement factor and the eccentricity ratio in relation to thestrength index.

Fig. 10(a) and (b) shows that the strength index increases withan increase in the confinement index: and especially in the case ofspecimens subjected to biaxial bending. Furthermore the ultimatebearing capacity for the specimen experiencing an eccentric loadapplied to its major and minor axes is to be determined by meansof the bending resistance capacity of the minor axis. As such it canbe concluded that specimens with possessing a higher confine-ment factor have a higher bearing capacity and therefore abilityto resist the pressure of eccentric loading. Moreover Fig. 11(a)–(c)

0 2 4 6 8 10 12 14 160

200

400

600

800

1000

SN

z (mm)

N (k

N)

0 5 10 15 20 25 30 35 40 450

200

400

600

800

1000

1200

WE S N

z (mm)

N (k

N)N

)

Fig. 6. Load–vertical deflection relationships of columns: (a) PYA-1 and (b) PYB-1

Fig. 5. Typical failure modes of tested columns: (a) PYA-1 and (b) PYB-8.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–9388

0 5 10 15 20 25 300

500

1000

1500

2000

2500

3000

3500

4000

δx(mm)

PYA-1

PYA-2

PYA-3

PYA-4

PYA-5

PYA-6

PYA-7

PYA-8

PYA-9

N (k

N)

0 5 10 15 200

500

1000

1500

2000

2500

3000

δx(mm)

PYB-1

PYB-2

PYB-3

PYB-4

PYB-5

PYB-6

PYB-7

PYB-8

N (k

N)

0 5 10 15 200

500

1000

1500

2000

2500

3000

δy(mm)

PYB-1

PYB-2

PYB-3

PYB-4

PYB-5

PYB-6

PYB-7

PYB-8

N (k

N)

Fig. 7. Load–lateral deflection relationships of columns: (a) Group PYA, (b) Group

PYB and (c) Group PYB.

Table 4Test results

Specimen

reference(du)x (du)y SI DI CCR Nu,e Nu,hollow

PYA-1 3.15 – 0.81 1.33 0.85 750 884

PYA-2 2.955 – 1.01 2.89 1.3 1040 803

PYA-3 5.435 – 0.7 1.67 1.02 810 795

PYA-4 1.29 – 0.91 3.88 1.64 1750 1069

PYA-5 4.34 – 0.97 2.51 1.43 1400 978

PYA-6 6.02 – 0.75 1.54 1.41 1250 884

PYA-7 4.735 – 0.91 2.91 1.53 3450 2250

PYA-8 12.68 – 0.62 1.42 1.22 2650 2170

PYA-9 2.99 – 0.74 2.37 1.22 2445 2009

PYB-1 2.3 3.86 1.06 1.55 1.11 980 884

PYB-2 5.787 5.224 0.92 1.4 1.24 950 766

PYB-3 3.33 8.9 0.85 1.31 1.23 980 795

PYB-4 3.048 4.981 0.68 2.46 1.31 1300 993

PYB-5 1.17 3.497 0.9 3.72 1.31 1300 992

PYB-6 4.45 2.852 0.96 3.22 1.75 1600 914

PYB-7 3.765 8.579 0.69 4.63 1.14 2600 2284

PYB-8 7.67 4.008 0.6 0.56 1.18 2550 2152

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–93 89

further indicates that the strength index decreases with the eccentricratio (ex/D, ey/B).

4.2. Ductility index (DI)

Compared to the steel and reinforced concrete structures, thecomposite structure shows more favorable ductility. The conceptof a ductility index (DI) is adopted to study the behavior of testspecimens subjected to combined compression and bending.

It is defined as the ratio between the lateral displacement atmid-height that corresponds to 85% of the ultimate strengthof CFST columns, measured after the ultimate strength has beenreached, and the displacement from the maximum load. Due tothe eccentricity load not being exclusively applied to the strong axisfor specimens PYB-1–8, the lateral deflection on the wide face that

runs in parallel to the weak axis is also significant and as such cannotbe ignored. Therefore, the DIx and DIy are determined herein by

DIx ¼d85%ð Þx

duð Þxð1Þ

DIy ¼d85%ð Þy

duð Þyð2Þ

where (d85%)x is the mid-height lateral deformation to the major axiscorresponding directly to the 85% of the ultimate strength of the CFSTcolumns as measured after the ultimate strength point.

(du)x is the mid-height lateral deformation to the major axis atthe point where the load reaches its point of application of theultimate load.

(d85%)y is the mid-height lateral deformation to the minor axiscorresponding directly to 85% of the ultimate strength of the CFSTcolumns measured after the ultimate strength.

(du)y is the mid-height lateral deformation to the minor axis atthe point where the load reaches application of its ultimate load.

Fig. 12(a)–(c) shows the relationship between the DI and theconstraining factor. It is apparent that the ductility of the testspecimens decreases with the increase in size of the constrainingfactor; and especially this is so for the Group PYB specimens. Thiscan be explained by the fact that the confinement factor representsthe ability of the steel tube itself to constrain the infilled concrete.Furthermore specimens with a higher confinement factor mayhave higher strength and performance in relation to their ability toresist deformation.

Fig. 13(a)–(c) shows the tendency of the DI to change inresponse to changes in the eccentric ratio. It appears that theDIx decreases with an increase in the eccentric ratio (ex/D) for thespecimen when subjected to a combined circumstance of com-pression and uniaxial bending. Meanwhile for specimens sub-jected to combined compression and biaxial bending, the DIx andDIy increases along with the increase in the eccentric ratio (ex/D

and ey/B respectively). The dissimilar results may be as a con-sequence of the designated variations of the tested specimensbeing multitudinous and, in addition, the specimens used in eachfigure possessing different parameters in terms of their concretestrength, steel strength and cross-sectional dimensions. In con-trast to what has been observed in relation to the constrainingfactors, the eccentric ratio is not a wholly typical parameterand it is not appropriate for use in providing descriptions ofgeometric and material information beyond what is already foundin relation to the specimen.

0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

PYB-2

PYB-6

PYB-7

PYB-8

PYB-1

PYB-4

PYB-5

PYB-3

Longitudinal strain in steel ε (με)

Load

N (k

N)

0 500 1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

3000

PYB-1PYB3 -

PYB-4

PYB-7

PYB-2

PYB-6

PYB-8

PYB-5

Longitudinal strain in steel ε (με)

Load

N (k

N)

-500 0 500 1000 1500 20000

500

1000

1500

2000

2500

3000

PYB-3

PYB-2

PYB-5

PYB-7

PYB-1

PYB-6

PYB-8

PYB-4

Longitudinal strainin steel ε (με)

Load

N(k

N)

-500 0 500 1000 1500 20000

500

1000

1500

2000

2500

3000

PYB-3

PYB-2

PYB-7

PYB-9

PYB-1 PYB-4

PYB-8

PYB-5

Longitudina lstrain in steel ε (με)

Load

N (k

N)

0 1000 2000 3000 4000 5000 6000 70000

500

1000

1500

2000

2500

3000

3500

4000

PYA-3PYA-1

PYA-7

PYA-9PYA-8

PYA-2

PYA-4

Longitudinal strain in steel ε (με)

Load

N (k

N)

PYA-5

0 500 1000 1500 2000 2500 30000

500

1000

1500

2000

2500

3000

3500

4000

PYA-2PYA-1

PYA-7

PYA-9

PYA-3PYA-4

PYA-8

PYA-5

Longitudinal strain insteel ε (με)

Load

N (k

N)

Fig. 8. load–longitudinal strain variations of columns: (a) strain gauge (1), (b) strain gauge (2), (c) strain gauge (5), (d) strain gauge (6), (e) strain gauge (7) and (f) strain

gauge (8).

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–9390

4.3. Concrete contribution ratio (CCR)

As we know, within the current design code there is a conflict inrelation to the determination of the concrete contribution to theflexural strength of composite structures. One of the objectives of thissection is to determine the concrete contribution as compared to thebearing capacity of rectangular CFST columns subjected to eccentricloading. In the event there is a lack of experimental value with regardto the empty steel tube, the behavior of the relative rectangularhollow section (RHS) under the same eccentric loading pressure is tobe obtained by means of a numerical simulation model. Here, in thisinstance, the ANSYS FEM software was used to establish the RHSmodels. The numerical model of RHS150�100�4.065�700 isshown in Fig. 14 as an example. The ultimate bearing capacities ofthe RHSs (numerical data) and the relative rectangular CFST columns(experimental data) are both shown in Table 4. The concretecontribution ratio (CCR), which is defined as the ratio between theultimate strength of the composite column and the empty hollowsteel member, is adopted within the confines of this paper to

illustrate the infilled concrete contribution to the improvement inthe bare steel columns themselves:

CCR¼Nu,e

Nu,hollowð3Þ

5. Discussion for the cross-sectional resistance

In China, some provinces have their own design codes to assistbuilding design, an illustrative example being the ‘‘technical speci-fication for design of steel structure dwelling houses in Tianjin’’. Forthis code the design resistance of square and rectangular CFSTcolumns for combined compression and bending is determined asfollows:

(1)

The design resistance strength for the CFST columns shouldsatisfy:

NrNcþNs ð4Þ

0 500 1000 1500 20000

500

1000

1500

2000

2500

3000

3500

4000

Transverse strain in steel ε ( ε)

Load

N (k

N)

PYA-7

PYA-8 PYA-9

PYA-1

PYA-5

PYA-4

PYA-3

PYA-2

0 500 10000

500

1000

1500

2000

2500

3000

3500

4000

Transversestrain in steel ε ( ε)

Load

N (k

N)

PYA-7

PYA-8

PYA-9

PYA-2PYA-5

PYA-4

PYA-1PYA-3

0 200 400 600 800 10000

500

1000

1500

2000

2500

3000

PYB-3

Transverse strain in steel ε ( ε)

Load

N (k

N)

PYB-8PYB-7

PYB-4PYB-6

PYB-1PYB-2

0 300 600 900 1200 15000

500

1000

1500

2000

2500

3000

PYB-3

PYB-4

PYB-5 PYB-7 PYB-6

PYB-8

PYB-1

Transversestrain in steel ε ( ε)

Load

N (k

N)

PYB-2

Fig. 9. load–transverse strain variations of columns: (a) strain gauge (3), (b) strain gauge (4), (c) strain gauge (9) and (d) strain gauge (10).

0.3 0.6 0.9 1.2 1.5 1.80.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

ConsConstraining factor (ξ)

SI

Constraining factor (ξ)0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.6

0.7

0.8

0.9

1.0

1.1

1.2

SI

Fig. 10. SI versus x relations: (a) Group PYA and (b) Group PYB.

0.08 0.12 0.16 0.20 0.240.6

0.7

0.8

0.9

1.0

1.1

ex/D

SI

0.04 0.06 0.08 00.1 0.12 0.14 0.16

0.6

0.7

0.8

0.9

1.0

1.1

ex/D

SI

0.02 0.04 0.06 0.08 0.10 0.12 0.14

0.6

0.7

0.8

0.9

1.0

1.1

ey/B

SI

Fig. 11. SI versus ex/D and ey/B relations: (a) Group PYA, (b) Group PYB and (c) Group PYB.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–93 91

0.6 0.8 1.0 1.2 1.4 1.6 1.81.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Constraining factor (ξ)

DI x

0.6 0.8 1.0 1.2 1.4 1.6 1.80

1

2

3

4

5

Constraining factor (ξ)

DI x

0.6 0.8 1.0 1.2 1.4 1.6 1.8

1

2

3

4

Constraining factor (ξ)

DI y

Fig. 12. DI versus x relations: (a) Group PYA, (b) Group PYB and (c) Group PYB.

0.08 0.12 0.16 0.20 0.241.0

1.5

2.0

2.5

3.0

3.5

4.0

ex/D

DI x

0.04 0.06 0.08 0.10 0.12 0.14 0.160

1

2

3

4

5

ex/D

DI x

0.02 0.04 0.06 0.08 0.10 0.120.141

2

3

4

ey/B

DI y

Fig. 13. DI versus ex/D and ey/B relations: (a) Group PYA, (b) Group PYB and (c) Group PYB.

35 40 45 50 55 60 65 700.5

1.0

1.5

2.0

fcu(N/mm2)

CC

R

Test data

Average value

35 40 45 50 55 60 65 701.0

1.2

1.4

1.6

1.8

2.0

fcu(N/mm2)

CC

R

Test data

Average value

Fig. 14. CCR versus x relations: (a) Group PYA and (b) Group PYB.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–9392

Ns

Asþ

Mx

Wxþ

My

Wyr f y ð5Þ

where N is the required axial compressive strength;Nc is the design value of the concrete axial compressive strength,Nc ¼ Acf c;Ns is the design value of the steel axial compressive strength; itis equal to the remained of the value of N�Nc;

(2)

when the specimen is subjected to combined axial compressionplus flexure the required axial compressive strength and therequired flexural strength should satisfy the following equations:

Nrjx NcþNsð Þ ð6Þ

Nrjy NcþNsð Þ ð7Þ

Ns

jxAsþ

Mx

Wxð1�0:8ðN=NExÞÞþ

0:7My

Wyr f y ð8Þ

Ns

jyAsþ

My

Wyð1�0:8ðN=NEyÞÞþ

0:7Mx

Wxr f y ð9Þ

where jx is stability factor for compression about x-axis; jy

is stability factor for compression about y-axis; NEx is Euler’scritical load about x-axis; NEy is Euler’s critical load about y-axis;Wx is net section resistance moment about x-axis; Wy is netsection resistance moment about y-axis; Mx is available flexuralstrength about x-axis; My is available flexural strength abouty-axis.

It is not difficult to notice the fact that the concretecontribution to the flexural resistance is not mentioned in thisabove set of equations; and thus, as a result, these methods forcomputation of the resistance level will always be to someextent conservative. Furthermore, the axial load is, subject tothis method, shared with the concrete first of all; but, in fact,the axial load should be shared between the steel and theconcrete simultaneously.

10 20 30 40 500

1000

2000

3000

4000

N testN pre

Specimen numbers

N (

kN)

Fig. 15. Comparisons between test results and predicted value.

X. Qu et al. / Thin-Walled Structures 64 (2013) 83–93 93

One of the objectives of this research is to improve themethodological equation so as to gain a more accurate predictiveunderstanding in relation to the actual value of the design.

Within the confines of this thesis, and based on the analysis ofthese test results, as well as test data drawn from other literatures[14,19], a factor ‘‘b’’ was proposed to enhance the yield strengthof the steel to take account of the concrete contribution’s as itimpacts on the prevention of any steel local buckling effect. Whatthis essentially means is that the fy in the above equations can besubstituted bybf y. In this way, the modified equation can provideimproved understanding and a more accurate predictive ability ofthe value:

b¼ 0:009401� f cuþ1:1186�

ffiffiffiffiffiffiffiffiffi235

f y

s !�0:35207 ð10Þ

The predicted results, making use of the above discussingmethod, and the test results are shown in Fig. 15; and it can beseen that the modified equation provides a good prediction of thespecimens’ resistance to the test loading. The average value forthe Npre/Ntest is 0.9.

6. Conclusions

The aim of this section is to investigate the response ofrectangular CFST columns subjected to eccentric loading. A totalof 17 stub columns of varying steel strength grades, steel tubegeometric properties, eccentricities and infill concrete strengthswere tested. The results, together with the supporting materialand geometric properties, have been produced. The load–verticaldisplacement and load–lateral deflection and the strains at certainkey points were both recorded and analyzed. The relationshipbetween the strength index and ductility, subject to the constrain-ing factors, as well as the eccentricity ratio, were also studied.Generally, for all specimens, the strength index increases alongsidethe increase in x and the ductility index decreases with the increaseof x; while the strength index decreases with the eccentricity ratio.However, the influence of the eccentricity ratio to the ductilityindex was not regular. Furthermore the concrete contribution ratio

to the flexure resistance also required some investigation. By meansof the numerical simulation on the RHS columns, the concretecontribution ratio increased commensurate with the increase of theconcrete strength. Finally, based on the analysis of the designstrength for the rectangular CFST columns of the ‘‘technical speci-fication for design of steel structure dwelling houses in Tianjin’’code, a factor b was proposed to enhance the steel strength to takeaccount the concrete contribution tothe resistance. This modifiedequation can provide an improved understanding and a moreaccurate predicted value.

Acknowledgments

The authors are grateful to the China Standard ManagementGroup for the GB50017-2003 Structural Steel Design Code for theirspecial composite structure research funding (GB 5000172010-04),and would like to thank the Taian Kenuo profile steel stock companylimited for the supply of test specimens and Butler (Tianjin) Inc. fortheir help with this project and research students in the steelresearch group of Tianjin University for their assistance with thelaboratory work.

References

[1] EN 1994-1-1, Eurocode 4: Design of composite steel and concrete structures.[2] Building code requirements for structural concrete and commentary (ACI

318M-05). American Concrete Institute; 2005.[3] GJB 4142-2000. Technical specifications for early-strength model composite

structure used for navy port emergency repair in wartime; 2001 [in Chinese].[4] AISC 360-05. Specification for structural steel buildings. AISC; 2005.[5] AISC 360-05. Specification for structural steel buildings. AISC; 2001.[6] Stevens RF. Encased stanchions. The Structural Engineer 1965;43(2):59–66.[7] Wakabayashi M, Minami K, Komura K. An experimental study on elasto-

plastic characteristics of concrete members using an encased H-sectionsubjected to combined bending and axial force. Bulletin of Disaster Preven-tion Research Institute 1971.

[8] Naka T, Morita K, Tachibana M. Strength and hysteretic characteristics ofsteel-reinforced concrete columns. Transaction of AIJ 1977;250:47–58[inJapanese].

[9] Yamada M, Kawamura H, Zhang F. Research on the elasto-plastic deformationand fracture behaviors of wide flange steel encased reinforced concretecolumns subjected to bending and shear. Journal of Structural ConstructionEngineering, AIJ 1991;420:63–74[in Japanese].

[10] Ricles JM, Paboojian SD. Seismic performance of steel-encased compositecolumns. Journal of Structural Engineering, ASCE 1994;120(8):2474–94.

[11] Mirza SA, Hyttinen V, Hyttinen E. Physical tests and analyses of compositesteel–concrete beam-columns. Journal of Structural Engineering, ASCE1996;122(11):1317–26.

[12] Shakir-Khalil H, Zeghiche J. Experimental behavior of concrete filled rolledrectangular hollow-section columns. The Structure Engineer 1989;67(9):346–53.

[13] Zeghiche J, Chaoui K. An experimental behaviour of concrete-filled steeltubular columns. Journal of Constructional Steel Research 2005;61(1):53–66.

[14] Liu Dalin. Behaviour of eccentrically loaded high-strength rectangular concrete-filled steel tubular columns. Journal of Constructional Steel Research 2006;62(8):839–46.

[15] Xu Chang Cheng-Kui Huang, Chen Ya-Juan. Mechanical performance ofeccentrically loaded pre-stressing concrete filled circular steel tube columns bymeans of expansive cement. Engineering Structures 2009;31(11):2588–97.

[16] Portoles JM, Romero ML, Bonet JL, Filippou FC. Experimental study of highstrength concrete-filled circular tubular columns under eccentric loading. Journalof Constructional Steel Research 2011;67(4):623–33.

[17] GB/T228-2002. Metallic materials – Tensile testing at ambient temperature,Chinese Standard; 2002.

[18] GB50152-92. Standard methods for testing of concrete structures, ChineseStandard; 1992.

[19] Lu FW, Li SP, Sun Guojun. A study on the behavior of eccentricallycompressed square concrete-filled steel tube columns. Journal of Construc-tional Steel Research 2007;63(7):941–8.

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