CFT Subjected to Pure Bending, Elchalakani, 2001

Journal of Constructional Steel Research 57 (2001) 1141–1168www.elsevier.com/locate/jcsr

Concrete-filled circular steel tubes subjected topure bending

M. Elchalakani*, X.L. Zhao, R.H. GrzebietaDepartment of Civil Engineering, Monash University, Melbourne, Victoria 3800, Australia

Received 19 February 2001; revised 26 June 2001; accepted 25 July 2001

Abstract

Current design codes and standards provide little information on the flextural behaviour ofcircular concrete filled tubes (CFT) as there have been few experimental studies. There aresignificant differences ind/t-limits recommended in various codes for CFT under bending.This paper presents an experimental investigation of the flexural behaviour of circular CFTsubjected to large deformation pure bending whered/t = 12 to 110. The paper compares thebehaviour of empty and void-filled, cold-formed circular hollow sections under pure plasticbending. It was found that for the range ofd/t�40, void filling prevented local buckling forvery large rotations, whereas multiple plastic ripples formed in the inelastic range for speci-mens with 74�d/t�110. In general, void filling of the steel tube enhances strength, ductilityand energy absorption especially for thinner sections. Based on the measured material proper-ties, the plasticd/t-limit was found to be 112. A simplified formula is provided to determinethe ultimate flexural capacity of CFT. The existing design rules for the ultimate momentcapacity of CFT may be extended conservatively to a new slenderness range of 100�ls�188. 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Circular tubes; Composite section; Plastic bending; Thin-walled sections

1. Introduction

Composite members consisting of circular steel tubes filled with concrete areextensively used in structures involving very large applied moments, particularly inzones of high seismicity. Composite circular concrete filled tubes (CFT) have been

* Corresponding author.E-mail address: [email protected] (M. Elchalakani).

0143-974X/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S0143 -974X(01)00035-9

1142 M. Elchalakani et al. / Journal of Constructional Steel Research 57 (2001) 1141–1168

Nomenclature

a shear span defined in Fig. 2(a)CHS circular hollow sectionsd outside diameter of CHSeu percentage elongation at fractureE modulus of elasticity of CFT sectionEs measured initial Young’s modulus of steel tubeEc predicted elastic modulus of the concretefy measured yield stress (0.2%)fc concrete cylinder strengthfu measured ultimate tensile strengthIm second moment of area based on measured dimensionsL beam length under constant momentM applied momentMu ultimate momentMp plastic momentMpt plastic moment based on measured dimensions and material

propertiesMptH plastic moment of hollow tubesMtheory predicted ultimate moment capacityMu ultimate moment obtained in a testN axial forceN0 squash loadrm mean radius of the tuberi inside radius of the tubeR rotation capacityRu limit rotation angleSH plastic section modulus for hollow tubest thickness of CHSa slenderness parameterap slenderness parameter plastic limit� curvature�pt curvature corresponding to Mpt

ls section slenderness defined in AS4100 [39]g0 angular location of the plastic neutral axisq relative angle of rotationqmax rotation corresponding to Mu

qy rotation corresponding to My

1143M. Elchalakani et al. / Journal of Constructional Steel Research 57 (2001) 1141–1168

used increasingly as columns and beam-columns in braced and unbraced frame struc-tures [1]. Their use worldwide has ranged from compression members in low-rise,open floor plan construction using cold-formed steel circular or rectangular tubesfilled with precast or cast-in-place concrete, to large diameter cast-in-place membersused as the primary lateral resistance columns in multi-story buildings. Concretefilled steel box columns fabricated from four welded plates and concrete filled steelfabricated circular sections have been used in some of the world’s tallest structures[2]. In addition, concrete filling is widely used in retrofitting of damaged steel bridgepiers after the 1995 Hyogoken-Nanbu earthquake in Japan and the Northridge earth-quake in 1994 in the USA [3].

The CFT structural members have a number of distinctive advantages over con-ventional steel reinforced concrete members. CFT members provide excellent seismicresistance in two orthogonal directions as well as good damping characteristics.These members also have excellent hysteresis behaviour under cyclic loading, com-pared with hollow tubes [1]. The use of CFT members in moment resisting frameseliminates the use of additional stiffening elements in panel zones and zones of highstrain demand. The CFT columns have been proven to be cost effective in buildingstructures compared to conventional reinforced concrete ones [4]. In general, voidfilling is an efficient way to delay premature local buckling and to enhance ductilityof tubular structures built with cold-formed hollow sections. Concrete filling not onlydelays local buckling but also prevents the detrimental effect of ovalization on thebending capacity of circular hollow sections (CHS).

In spite of the bulk literature written over the last four decades on the techniqueof concrete filling of circular steel tubes, little of it was devoted to the large defor-mation flexural behaviour of these members. CFT beams were studied under 3-pointbending by Kilpatrick and Rangan [5] and 4-point bending by Hosaka et al. [6].CFT stub columns were studied by Furlong [7], Gardner and Jacobson [8], Schneider[9], Uy [10] and Bridge and O’Shea [11]. CFT beam columns were investigated byPrion and Boehme [12], Neogi et al. [13], Eltawil et al. [14], Tomii [15] and Trezonaand Warner [16]. Bonds between concrete and steel tubes stub columns have beenexperimentally studied by Shakir-Khalil [17]. Hajjar [1] has recently provided a state-of-the-art literature review, where the results of research on CFT members undermonotonic and cyclic loading over the last four decades are summarised.

The plastic slenderness limits are widely used in the current design rules to classifythe cross-sectional behaviour. Three types of sections are commonly used in thisclassification: compact, non-compact and slender. The plastic d/t-limit is used toidentify a compact section suitable for plastic design of frames. Currently, there arelarge differences in this limit for CFT members specified in different codes andstandards as shown in Table 1. The plastic d/t-limits specified by most of the inter-national design codes for a nominal yield strength of 350 MPa (grade C350) areconsistent and lower than 70. However, the AIJ [18] adopts a larger plastic d/t-limitof 120 for C350. It is worth noting that this limit results from beam column tests[19]. In Japan, the limit values are about 1.5 times larger than those for unfilled steeltubes. This recommendation stems from the concept of ensuring fully plastic strengthof CFT cross section [19]. This means that the cross section can locally buckle before

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Tab

le1

The

d/t-

limits

for

CFT

mem

bers

inin

tern

atio

nal

code

s

Cou

ntry

Cod

ed/

t-lim

it

Form

ulae

(usi

ngno

min

alpr

oper

ties)

a(u

sing

mea

sure

dpr

oper

ties)

b

Japa

nA

IJ[1

8]36

000/

Fc

120

98C

hina

CA

IP[4

1]85

√ 235

/f y70

64U

SAA

ISC

-LR

FD[2

0]√ 8

Es/f

y68

62A

CI

318

[38]

√ 8E

s/fy

6862

Eur

ope

EC

4[2

2]90

(235

/f y)

6050

CID

EC

T[4

0]90

(235

/f y)

6050

Uni

ted

Kin

gdom

BS

5400

,Pa

rt5

√ 8E

s/fy

6862

[33]

af y

=35

0M

Pa,

f u=

430

MPa

and

Es

=20

0,00

0M

Pa.

bf y

=41

9M

Pa,

f u=

523

MPa

and

Es

=20

4,00

0M

Pa.

cF

(in

MPa

)is

the

less

erof

0.7f

uan

df y

.


reaching the full plastic moment. In the USA, the specified limit (d/t = 68 for C350)is used to prevent local buckling before attainment of full plastic moment [20]. Thesetwo different concepts may explain the large differences in the plastic d/t-limits. InAustralia, it is proposed [21] to use the same limit specified in EC4 [22] for CFTunder axial compression (d/t = 60 for C350). Therefore, it is required to perform aseries of plastic bending tests on CFT beams to determine a suitable plastic d/t-limit.

Early research at Monash University on square hollow section (SHS) beams sub-jected to large deformation cyclic bending showed that a plastic mechanism mayform in the flange of SHS and the residual strength rapidly reduces after a few cycles[23]. This is true even for compact sections that have adequate rotation capacityunder static bending. Recent research on void-filled SHS beams subjected to largedeformation cyclic bending demonstrated the significant increase in ductility of thesemembers [24]. Similar phenomenon is expected for CHS. Therefore, it is necessaryto investigate empty and void-filled CHS subjected to large deformation pure bendingfor a single half cycle test before extending the study to multiple cycle tests.

This paper presents an experimental investigation of the flexural behaviour ofcircular CFT beams subjected to large deformation pure bending where d/t = 12 to110. The paper examines the strength, ductility and energy absorption of CFT con-structed from cold-formed steel tubes filled with normal concrete. The failure modesof hollow and CFT members under pure bending are compared. A suitable plasticd/t-limit is determined and recommended for the plastic design of CFT subassembliesand frames. The differences between the design rules in the ultimate bending capacityof CFT are quantified. A simplified formula is derived to determine the ultimateflexural capacity of CFT under pure bending.

2. Material properties

The steel sections used for the construction of the specimens are cold-formedcircular hollow sections grade C350 with nominal yield stress of 350 MPa producedby Palmer Tube Mills in Australia. The tubes are manufactured to meet the qualityof cold-formed standards AS 1163 [25]. Tensile coupons were taken from pointsaway from the seams in the tubes to avoid the variability in strength due to welding.The tensile coupons were prepared and tested according to the Australian StandardAS 1391 [26] to determine the initial Young’s modulus (Es), the yield stress (fy),the ultimate tensile strength (fu) and the percentage elongation (eu) at fracture. Theaverage measured mechanical properties are fy = 419 MPa, fu = 523 MPa andeu = 26%. The average measured yield stress and ultimate tensile strength are 19.7%and 21.6% larger than their corresponding nominal values, respectively. The averageratio of the measured fu/fy is 1.25.

A total of eight concrete standard cylinders (100 mm in diameter and 200 mmlong) were tested in a 200 kN capacity Amsler universal testing machine to AS1012.9 [27] on the day the pure bending experiments were carried out. The averageunconfined compressive strength of concrete cylinder was fc = 23.4 MPa. The densityof the concrete was 2440 kg/m3.

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3. Pure bending test specimens and procedure

3.1. Specimens

A total of 12 specimens (1500 mm long) were tested. The average measureddimensions of the composite specimens and the calculated effective stiffness EI,plastic moment capacity (Mpt) and plastic curvature (�pt) are listed in Table 2. Themeasured material properties are used in calculating Mpt which was determined fromrigid plastic stress block analysis and �pt = Mpt/EI. The effective stiffness of thecomposite section was determined as [22]:

EI � EsIs � 0.8EcIc (1)

Ec � 0.043r1.5√fc (2)

where Es and Ec are the elastic moduli of steel and concrete in MPa, respectively.Is and Ic are the moments of inertia of the steel tube and the concrete, respectivelyand r is the concrete density in kg/m3.

An end cap (thin steel plate) was used to cast the concrete while the steel tubewas in the vertical position. The specimens were cast from two batches and curedunder polyethylene until the time of testing. The end cap was removed and the endsof the specimens were left uncapped to allow slippage to occur. This was believedto be the worst case in regards to loss of composite action. The necessary d/t ratiorequired to examine slender specimens (CBC0-A, B, C) was obtained by machininga CHS 114.3×3.2 to the required thickness. Machining of circular tubes was usedin the past [28] to examine the effect of section slenderness on the inelastic flexuralbehaviour of CHS. Machining was found to have a negligible effect on the behaviourof the members [28]. The free deformation length for the non-machined specimensis equal to the pure-moment span in the tests. This distance is equal to the distancebetween the internal supports in the rig (LAB�a = 800 mm as shown in Fig. 2(a)).The free deformation length for the machined specimens was 600 mm. This makesthe minimal free deformation length-to-diameter ratio 7.86 for non-machined speci-mens and 5.41 for machined ones. These ratios were believed to be adequate toallow the formation of local buckles without end effects and the development of fullinelastic rotation of the cross section.

3.2. Test procedure

A unique pure bending rig was used to test the bending specimens. This rig wasdesigned and fully commissioned at Monash University [29]. The advantage of thisrig is its ability to apply a pure bending moment over the middle span of the testspecimen without inducing significant axial or shear forces. A front view on speci-men CBC9 during the test is shown in Fig. 1(a). It can be seen that the rig comprisestwo load application wheels mounted on right and left carriages at either end of thespecimen. The right carriage is fixed in place by holding down bolts and the left oneis attached to floor wheels by a needle bearing to reduce friction during movement of

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Sticky Note

Why 0.8EcIc

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Tab

le2

Mec

hani

cal

prop

ertie

sof

CFT

spec

imen

s

Spec

imen

Prop

ertie

sof

stee

ltu

bePr

oper

ties

ofco

mpo

site

sect

ion

no.

d×t

(mm

)d/

tf y

(MPa

)f u

(MPa

)e u

(%)

Es

(GPa

)M

pt

(kN

m)

EI

(101

0N

k pt

(mm

–1)

a/d

mm

2)

CB

C0-

C10

9.9×

1.0

109.

940

053

330

191

6.71

23.0

2.92

2.7

CB

C0-

B11

0.4×

1.25

88.3

400

533

3019

18.

6125

.53.

382.

7C

BC

0-A

110.

9×1.

573

.940

053

330

191

10.4

728

.13.

732.

7C

BC

110

1.83

×2.5

340

.236

546

930

200

9.96

28.0

3.56

3.0

CB

C2

88.6

4×2.

7931

.843

253

823

210

9.60

18.5

5.19

3.4

CB

C3

76.3

2×2.

4531

.241

553

424

218

6.00

10.4

5.77

3.9

CB

C4

89.2

6×3.

3526

.641

250

228

211

10.9

421

.45.

113.

4C

BC

560

.65×

2.44

24.9

433

508

2421

13.

824.

88.

055.

0C

BC

676

.19×

3.24

23.5

456

548

2420

58.

2512

.36.

713.

9C

BC

760

.67×

3.01

20.2

408

503

2820

44.

335.

57.

905.

0C

BC

833

.66×

1.98

17.0

442

511

2320

70.

920.

519

.17

8.9

CB

C9

33.7

8×2.

6312

.846

056

822

209

1.21

0.7

18.1

18.

9M

ean

419

523

2620

4C

OV

0.06

0.05

0.12

0.04


Fig. 1. The pure bending rig. (a) Front view on the rig while testing CBC 9. (b) Side view on the rigwhile testing specimen CBC3.

the carriage. This movement is necessary to prevent any significant axial force frombuilding up during the full course of the experiment, particularly at large defor-mations. A side view on specimen CBC3 during the test is shown in Fig. 1(b). Thebending moment, shear force diagrams and relative angle of rotation (q) of a testspecimen are shown in Fig. 2.

Adequate modelling of the boundary conditions is of prime importance in theanalysis of buckling problems. Therefore, the test specimen was carefully mountedon the two load application wheels and positioned using saddle clamps that were


Fig. 2. Bending moment, shear force diagrams and load transfer model.


fabricated to suit each tube size. The intention of these clamps was to provide fullbearing of the load onto the specimen thus reducing the localised stress raiser parti-cularly at the inside 40 mm diameter loading pins. The specimen was positionedhorizontally on the saddles to have its weld seam levelled with its centroid. Themoment was applied to the specimen using a hydraulic pump connected to twohydraulic jacks through a manifold. The presence of the manifold ensured that theload applied by both jacks was approximately the same. The jacks are connected tothe load application wheels on either side of the test specimen. Extension of thejacks causes the load application wheels to rotate opposite to each other and henceapply a bending moment to the specimen via four load application pins.

In order to determine the M–� curve, it was necessary to measure the change ofsix key angles, jack loads and strains. Four inclinometers were attached to the rig,one on each side of the load application wheels and one on each side of the hydraulicjacks. In addition, two inclinometers where attached directly (by a magnet) to thetop side of the specimen to measure the relative angle of rotation. The applied bend-ing moment was determined from the measured angular rotations and forces fromthe load cells attached to the jacks. The inclinometers were calibrated using a DividedHead set to a 30° range and 2.0 kN intervals. The load cells were calibrated usinga Mohr and Federhaff Universal testing machine set to a 10 kN range and 1.0 kNintervals. Two electric resistance strain gauges at the top and bottom of the sectionat the middle of the specimen were used to determine the point at which bucklingoccurred. The curvatures were determined from the inclinometers (attached directlyto the ends of the specimen) and then were used in plotting M–� curves. The curva-ture was determined as � = q/(LAB�a). The load cells, strain gauges and incli-nometers were connected to a standard data logger through an amplifier. The sam-pling rate was done at 2-s intervals. The test was stopped for a few minutes at 5°relative rotation to allow for measurements and photographs.

4. Pure bending test results

In the following, the results are given in two sections. The first one is devoted tothose CFT constructed using compact tubes where d/t�40. The second sectiondescribes the results for those specimens constructed using slender tubes where74�d/t�110.

4.1. CFT constructed from compact steel tubes

In general, the CFT specimens (from CBC1 to CBC9) had a better performancethan the hollow tubes (from BC1 to BC9 [30]). Figure 3 shows a kink typicallyformed in the hollow tube after a considerable inelastic rotation [30]. Unlike thehollow tubes, the CFT did not exhibit any form of buckling, plastic ripples or asingle local buckle, or even a tensile fracture during the test.

The numerical values of the ultimate moment (Mu) obtained in the tests for theCFT are listed in Table 3. Figure 4 shows three typical responses of the normalised

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Fig. 3. Flexural behaviour of unfilled [BC1 100.6×2.6 (top) to BC9 33.7×2.6] and filled circular tubes[CBC1 100.6×2.6 (top) to CBC9 33.7×2.6].

bending moment (M/Mpt) versus the normalised curvature (�/�pt) for the filled andunfilled tubes. The term �pt is the plastic curvature (�pt = Mpt/EI) and the term Mpt

is the plastic moment capacity.The behaviour of the filled and unfilled specimens was similar until a point, where

the filled curve separated from the corresponding curve of the hollow specimen. Theratio of the maximum normalized curvature obtained for the filled section[(�/�pt)max�filled] to the normalized curvature at the separation point [(�/�pt)separation]is given in Table 3. This ratio is larger for specimens with larger slenderness. Thisindicates that there is more enhancement in ductility due to concrete filling for thin-ner sections.

The ratios of the maximum moment, ductility and energy absorption obtained inthe tests for CFT and the corresponding values for hollow tubes are also given inTable 3. There is a considerable increase in the bending strength of CFT over thehollow tubes, particularly for large slenderness. The maximum increase is 37% forBC3 (ls = 54.92), while the minimal increase is 3% for BC9 (ls = 23.85). The termls is the section slenderness which is given by ls = (d/t)(fy/250). This level ofincrease in strength is consistent with the range of 10–30% reported by Lu and

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Table 3Test results and comparison between filled and unfilled sections

Specimen Maximum Ultimateno. rotation moment (�/�pt)max�filled

(�/�pt)separation

(Mu)filled

(Mu)unfilled

(qmax)filled

(qmax)unfilled

Efilled

Eunfilledqmax (°) Mu (kN

m) (to θmax)

CBC0-C 11.10 7.60CBC0-B 17.5 9.10CBC0-A 36.9 11.00CBC1 38.2 11.33 5.63 1.29 2.27 4.34CBC2 69.2 10.86 7.08 1.36 6.87 9.36CBC3 66.6 6.92 4.72 1.37 7.94 9.31CBC4 30.5 10.47 1.06 2.29 2.36CBC5 71.0 3.78 1.23 2.29 2.51CBC6 70.9 9.87 3.84 1.30 5.44 1.80CBC7 66.6 4.75 3.01 1.14 2.42 1.90CBC8 63.6 0.90 1.12 1.76 1.52CBC9 60.8 1.17 1.0 1.03 1.12 1.09

Fig. 4. Typical normalized moment versus curvature response for filled and unfilled tubes withd/t�40.


Kennedy [31] for flexural tests on rectangular CFT, and 15–35% obtained by Zhaoand Grzebieta [24] for square CFT beams. In addition, Kilpatrick and Rangan [5]found that concrete filling increases the strength by 47% over the hollow steel tubefor ls = 64 and 31% for ls = 75. Prion and Boehme [12] measured a larger increaseof the order of 93% for ls = 96.4 and 67% for ls = 121 where fc = 73 MPa. Hosakaet al. [6] measured an increase of 65% for CFT for ls = 108 where fc = 46 MPaunder 4-point bending.

The ductility of the CFT under pure plastic bending was determined using themaximum inelastic rotation qmax, which was the maximum stroke of the machine.qmax for the CFT corresponds to the maximum moment (Mu) obtained at the end ofthe test. The numerical values of qmax for the CFT and its normalised values usingthe corresponding values for the hollow tubes are given in Table 3. qmax for thehollow tubes is measured up to a rotation which corresponds to Mu. It can be seenthat the CFT has a significant increase in the inelastic rotation over the hollow tubes,particularly for larger slenderness (larger values of d/t). The absorbed energy of theCFT was determined from the moment–curvature response (up to qmax) and it wasnormalised using the energy absorbed by the hollow tubes (again up to qmax for thehollow tubes). This ratio is given in Table 3, which is larger for the CFT with largerslenderness. Due to capacity limitations of the testing machine, specimens CBC1and CBC4 were not tested to the desired q = 60� bend angle. This explains the smallratio of energy absorption obtained for these two specimens.

The maximum measured ovalization in the tests of CFT was 1.5% for CBC5, butgenerally less than 1% for the other eight specimens. This is significantly less thanthe 10% uniform ovaling measured in bending tests of hollow tubes [30]. The radialdeformation of the steel tube in the CFT tests was mostly outward, i.e. away fromthe tube’s axial centre line. Unlike hollow tubes, the ovaling of the CFT was small,non-uniform with loading and asymmetric due to the opposing effect of concretedilation (Poisson’s ratio effect). Therefore, the effect of ovalization can be neglectedin any theory to predict the flexural strength of CFT sections.

4.2. CFT constructed from slender steel tubes

Figure 5 shows the graphs of normalized bending moment (M/Mpt) versus thenormalized curvature for the specimens constructed using slender tubes, i.e. CBC0-A, B, C. Based on strain measurements, the behaviour of CFT beams constructedfrom thin CHS can be idealised as shown in Fig. 6. The CFT beam first followeda linear elastic response during which the yield stress was reached first at the extremetensile fibres (bottom) at point B. The extreme compressive fibres then yielded atpoint C. The tube starts to bend at point D at an angle of rotation of q = qy. At earlyrotations, a plastic ripple started to form in one location when q�1.5qy at point F.Between points F and G, the specimen exhibited significant strain hardening in thetension zone, particularly for larger slenderness. The ripples were uniformly growingwith loading and also were uniformly distributed along the length of the tube. Theultimate moment was reached at point G. Between G and I the load slightly droppedand the unloading curve was gradual, while the tensile strains were accumulating at

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Fig. 5. Normalized moment versus curvature response for filled tubes with 40�d/t�110.

the extreme tensile fibres. The drop in load was 6.5% and 2% for CBC0-A andCBC0-C, respectively. The unloading curve (between points G and I) was notobtained for specimen CBC0-B. This may be because the weld seam was slightlybelow the centroid of the tube, thus it may have triggered the fracture at a relativelysmaller curvature. The failure occurred at point I suddenly when fracture strain ofthe steel tube was reached accompanied with significant thinning in the tube’s wall.Measurements indicated 25–30% thinning. The failure mechanism of CBC0-C andthe plastic ripples after failure are shown in Fig. 7. The fracture occurred at thedominant buckle. The fracture extended from the extreme tensile (bottom) fibres toslightly above the predicted location of the neutral axis.

4.3. Bond between concrete and steel tube

The effects of slip on the flexural behaviour of square hollow sections (SHS) under4-point bending were studied by Lu and Kennedy [31]. They found that slip hasslightly reduced the ultimate bending capacity. A model similar to that shown inFig. 2(e) was suggested to explain the load transfer. In this figure, the load transferfrom the loaded steel tube (at the outside loading pins) to the concrete is solely byfriction (i.e. no mechanical means such as shear keys, bolts, etc.) by friction andadhesion within the shear span (distance a in Fig. 2). The values of the shear spanto diameter ratio (a/d) are given in Table 2. Strain gauge measurements in the tests


Fig. 6. Idealised behaviour of CFT under pure bending where 74�d/t�110.

indicated no sudden increase in strains and no sudden drop was observed in themoment–curvature responses. These observations suggest that no slippage occurredduring testing of CFT specimens. This emphasises the significance of the bindingaction arising from longitudinal curvature. Similar phenomenon was observed in testsby Kilpatrick and Rangan [5]. It seems that a value of a/d = 2.7 was sufficient fora full load transfer without slip. Test results from Kilpatrick and Rangan [5] on non-compact circular tubes filled with high strength concrete (fc = 80 MPa) under 3- or4-point bending showed that the bond between concrete and the steel tube has littleeffect on the strength of CFT under flexure. Therefore, a perfect bond between con-crete and CHS is assumed in the ultimate strength model discussed in Section 6.


Fig. 7. Progressive bending of specimen CBC0-C, d/t = 110.

5. Determination of plastic slenderness limits

5.1. Plastic hinge rotation capacity

Two different methods are compared in this paper to determine the rotationcapacity (R) for CFT members. One is based on normalised rotation angles determ-


ined from pure or constant moment bending tests. This method was found to besuitable for the plastic analysis of circular hollow tubes [30, 32]. The other methodis based on a limit rotation angle determined from beam column tests. This latermethod is used for the plastic analysis of CFT members as part of the US–JapanCooperative Research Program [34, 35]. These two methods are discussed to somedepth in the following.

5.1.1. Method based on normalized rotation angleR = qu/qp�1 was used by Stranghoner and Sedlacek [36] for rectangular hollow

section (RHS) beams and Gioncu et al. [37] for wide flange I-beams. The termqu/qp is the dimensionless rotation angle at which the dimensionless moment–rotationangle test curve falls through M/Mp = 1. The term qp is the rotation correspondingto Mp (the plastic moment). R = qu/qy was used by Sherman [32] for CHS beamssubjected to constant bending. The term qu = qmax�qy where qmax is the rotationcorresponding to the maximum moment obtained in the test (Mu) and qy is therotation corresponding to the first yield moment (My). The expression of R can berewritten as R = qmax/qy�1. The value of qy can be determined using the elastic

beam theory, i.e. qy =2·fy·LE·d

for a CHS beam under 4-point bending, where fy is the

yield stress, L is the beam length under constant moment region and d is the diameterof the CHS.

5.1.2. Method based on limit rotation angleSakino [34] and Toshiyuki et al. [35] reported beam column tests with

0�N/N0�0.5 to examine the effect of axial force on the deformation capacity ofCFT members. N0 is the squash load of the composite section. They used the limitrotation angle (Ru) to classify the CFT section. It is a characteristic point on theenvelope curve of the shear force versus rotation angle. It is defined as the slope ofa line connecting the two ends of the beam column segment at a point where 95%of the maximum shear is maintained after reaching maximum shear (see Fig. 8). TheCFT members are classified using Ru into four classes from the viewpoint of ductility,i.e. FA (very ductile) when Ru�2.0, FB (ductile) when 1.5�Ru�2.0, FC (semiductile) when 1.0�Ru�1.5 and FD (semi brittle) when Ru�1.0. For circular CFT:

Ru � 8.8�6.7NN0

�0.04dt�0.012fc (3)

where N is the applied axial force, N0 is the squash load, d is the outside diameterof the tube, t is the thickness of the tube, and fc is the concrete cylinder strength.This parameter (Ru) is examined in the current paper to determine its suitability topredict the rotation capacity under pure flexure.

5.2. Plastic slenderness limits

In this paper, the plastic slenderness limit will be determined from pure bendingtests. The plastic slenderness limit is determined from the graphs of rotation capacity(R) versus the slenderness parameter (a) which is defined as [32]:


Fig. 8. Limit rotation angle method, Sakino [34].

a �Es/fy

d/t(4)

The transition between sections that have large rotation capacity (compact) andthose where it is limited (non-compact and slender) is rather sharp. The value of awhich corresponds to this sharp transition is called the slenderness parameter limit(ap). This limit can be converted to the plastic slenderness limit (lp) where E isexpressed in MPa:

lp � �dt�limit

·� fy250� � �Es/fy

ap�·� fy

250� �Es

ap·250(5)

The rotation capacity is defined in this paper as

R �qmax

qy

�1 (6)

where qmax is the rotation corresponding to the maximum moment (point G) and qy

is the rotation corresponding to the first yield moment (My).The rotation capacities determined from Eq. (6) are listed in Table 4. They are

plotted against the slenderness parameter (a) in Fig. 9. Specimens CBC4 and CBC1are excluded for the same reasoning stated in Section 4.1. Figure 9 also shows themeasured rotation capacity in 4-point bending by Prion and Boehme [12] whereR = 25.2 for a CFT having a slenderness parameter of a = 8.3. They also measured


Table 4Rotation capacity of CFT beams

Specimen ls a qmax (deg.) qy (deg.) R [Eq. (6)] Ru [Eq. (3) withN=0]

CBC0-C 184.33 4.34 11.14 1.81 5.15 4.08CBC0-B 147.87 5.41 17.50 1.78 8.83 4.99CBC0-A 123.84 6.46 36.85 1.82 19.25 5.56CBC1 57.05 14.02 38.20 1.67 21.85 6.91CBC2 59.08 13.54 69.20 2.13 31.56 7.25CBC3 54.92 14.57 66.60 2.28 28.21 7.27CBC4 45.78 17.47 30.54 1.96 14.58 7.45CBC5 45.41 17.62 71.00 3.04 22.36 7.52CBC6 43.38 18.44 70.88 2.56 26.66 7.58CBC7 33.93 23.57 66.60 3.04 20.91 7.71CBC8 29.79 26.85 63.56 5.76 10.03 7.84CBC9 23.85 33.54 60.80 5.42 10.22 8.01

Fig. 9. Variation of the inelastic rotation with the slenderness parameter.

slightly lesser R = 22.3 for the same a under 3-point bending. In Fig. 9, a sharptransition is observed to occur around a = 4.34. The plastic slenderness limit can bedetermined using Eq. (5) with ap = 4.34 and the average measured elastic modulusEs = 204,000 MPa given in Table 2, i.e.

lp �Es

ap·250�

204,0004.34×250

� 188


This limit corresponds to d/t = 112 based on the average measured fy of 419 MPa,which is slightly higher than d/t = 98 (Table 1) specified in AIJ [18] if the averagemeasured material properties are used. A plastic d/t-limit of 134 is obtained if thenominal yield stress of 350 MPa is used, which is slightly higher than the d/t-limitof 120 specified in AIJ [18] if the nominal material properties are used. This differ-ence in the plastic d/t-limit may arise from the presence of axial forces in beamcolumn tests used to derive the limit specified in AIJ [18]. The axial force tends tolimit the inelastic rotation of CFT beams [34, 35]. The value of lp = 188 is approxi-mately three times the limit obtained recently for CHS from plastic bending tests[30]. Concrete filling fully prevents local buckling and ovalization for cold-formedsteel tubes when 13�d/t�40, whereas multiple plastic ripples formed in the inelasticrange for CFT with 74�d/t�110. The rotation capacity determined for hollow tubes[30] is also shown in Fig. 9, where a similar trend is observed with a sharp transitionoccurs at a = 14.

A comparison is made between the rotation capacity determined from the puremoment setup [Eq. (6)] and the beam column setup [Eq. (3)]. The R and Ru valuesdetermined from Eqs (6) and (3) are given in Table 4. In general, the Ru values aresmaller than the corresponding R values for the same d/t. The Ru values for all theCFT specimens are larger than 2.0, thus they are classified as Class 1, very ductile.This conclusion is consistent with the experimental observation, i.e. all 12 sectionstested in this paper are ductile and achieved full plastic moment. A plastic d/t-limitof d/t = 111 can be obtained from Eq. (3) by using the minimum Ru of 4.08 (Table4) and substituting fc = 24.30 and N/N0 = 0. This value is in good agreement withthat of 112 obtained from the first method when using the measured yield stress.

6. Ultimate strength model

6.1. Model

A simplified rigid plastic approach was used to determine the flextural capacityof circular CFT. Local buckling was observed before reaching Mu in the tests for74�d/t�110. However, the concrete infill forced the buckles to be outward (awayfrom the tube’s longitudinal centre line) and this increased the effective sectionmodulus of the steel tube. Therefore, the full section of the CHS was assumed effec-tive in the derivation of the ultimate moment. Strain measurements indicated no sliphas taken place in the tests, thus perfect bond between the steel and concrete wasassumed. Based on a tied arch model, as discussed earlier, the friction between steeland concrete was sufficient to fully generate the concrete compressive force Fcc (seeFig. 10). The ultimate bending capacity of the composite section shown in Fig. 10can be written as

Mtheory � Mcc � Mst � Msc (7)

where, Mcc, Mst, Msc are the moments due to: concrete in compression; steel in ten-

rfenyves

Highlight


Fig. 10. Model for ultimate moment capacity of circular CFT.

sion; and steel in compression, respectively. By performing simple integration of therectangular stress blocks over the corresponding area of steel and concrete, the forceand moment components about the centroid of the cross section are:

Fcc � fcr2i (p/2�g0�0.5sing0)

Fst � fytrm(p � 2g0)

Fsc � fytrm(p�2g0)

Mcc �23fcr3

i cos3g0

Mst � Msc � 2fyr2mtcosg0

where fc is the concrete cylinder strength, fy is the yield stress of the steel tube, t isthe tube thickness, and rm [=(r0+ri)/2] and ri are the mean and inside radii of thetube, shown in Fig. 10.

Force equilibrium results in

Fst � Fcc � Fsc (8)

The angular location of the plastic neutral axis (g0) can be found from Eq. (8).An iterative procedure can be used to determine g0. A closed form solution for g0can be obtained by assuming sing0 = g0; thus

g0 �

p4�fc

fy

ri

rm

ri

t�2 �

12�fc

fy

ri

rm

ri

t �


The final expression for the bending strength (Mtheory) can be expressed as

Mtheory �23

fcr3i cos3g0 � 4fyr2

mtcosg0 (9)

6.2. Comparison

The specimens constructed using slender sections (CBC0-A, B, C) exhibited sig-nificant strain hardening, particularly in the tension side. Therefore, the ultimate ten-sile strength fu was used to replace fy in Eq. (9) when calculating their Mpt for theseslender sections. A comparison is made between the experimental ultimate moment(Mu) and the predicted ultimate moment using Eq. (9) in Table 5. Good agreementis obtained with a mean ratio (Mu/Mtheory) of 1.07 with a COV of 0.07. The averageconcrete contribution in bending strength determined by Eq. (9) is 11.8% withCOV=0.52. The maximum error resulting from assuming sing0 = g0 in determiningMtheory is 11.3% which occurs at specimen CBC0-C with the largest d/t=109.9. Table5 also lists the ratio of Mu to the corresponding strength determined using four designrules. The values in brackets were determined using fu instead of fy. Appendix Ashows the design equations as they appear in the codes. Predictions using the originalformulae underestimate the ultimate moment capacity especially for AISC-LRFDand AIJ codes. This is because some of the terms in the AISC-LRFD code becomezero when no reinforcement bars are used, and a reduction factor of 0.85 is usedfor concrete strength in AIJ code. Better predictions are obtained if fu is used forslender tubes, especially for CIDECT and EC4 formulae.

Table 5Comparison of flexure strengtha

Specimen Mu/Mtheory Mu/MAISC Mu/MAIJ Mu/MCIDECT Mu/MEC4

CBC0-C 1.31 (1.14) 1.61 (1.21) 1.53 (0.92) 1.35 (1.08) 1.30 (1.00)CBC0-B 1.28 (1.06) 1.53 (1.15) 1.49 (0.98) 1.31 (0.98) 1.27 (0.98)CBC0-A 1.29 (1.05) 1.53 (1.14) 1.50 (1.03) 1.33 (1.00) 1.28 (0.99)CBC1 1.14 1.24 1.24 1.13 1.09CBC2 1.13 1.22 1.22 1.14 1.10CBC3 1.15 1.25 1.24 1.16 1.12CBC4 0.96 1.03 1.03 0.96 0.93CBC5 0.99 1.06 1.06 1.00 0.96CBC6 1.20 1.25 1.25 1.19 1.16CBC7 1.10 1.16 1.16 1.11 1.07CBC8 0.98 1.03 1.02 0.98 0.96CBC9 0.96 0.99 0.99 0.96 0.94Mean 1.12 (1.07) 1.24 (1.14) 1.23 (1.10) 1.14 (1.05) 1.10 (1.03)COV 0.11 (0.07) 0.16 (0.08) 0.15 (0.10) 0.12 (0.08) 0.12 (0.07)

a The values in brackets were determined using fu instead of fy.

Ryan

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Figure 11 shows a plot of M/MptH ratio versus section slenderness ls, where M isthe moment obtained for CFT (either in the tests or using the design codes) andMptH = SHfy is the predicted plastic moment of hollow tubes. The plastic modulusSH = [(d3�d3

i )/6] is based on the measured dimensions and fy is the measured yieldstress of the steel tube. It is evident that the ratio (M/MptH) increases as the sectionslenderness ls increases. The plot is extended beyond the calibrated range (ls�100)for each design code to ls of 188. The curve based on the closed-form solution [Eq.(9)] is also shown in Fig. 11. This curve is located between the design curves givenby EC4 [22] and CIDECT [40]. A lower bound is given based on the limited testsavailable. For 25�ls�100, the lower bound line lies in-between various codes. Forls�100, the lower bound line lies much higher than those extended curves fromcurrent codes. It seems that the existing design rules can be conservatively appliedto circular CFT with 100�ls�188.

The lower bound bilinear curve can be expressed as

M/MptH � 0.00267ls � 0.933 for 25�ls�100

M/MptH � 0.00455ls � 0.745 for 100�ls�188} (10)

Fig. 11. Design rules for CFT beams.


7. Conclusions

The following observations and conclusions are made based on the limited testresults described in this paper.

� The plastic limit of d/t=112 (or lp=188) was obtained for CFT constructed fromcold-formed hollow section under pure bending. This value is slightly higher thand/t=98 specified in AIJ [18] if measured material properties are used.

� Concrete filling was found to induce more increase in flexural strength and duc-tility for thinner CHS than for thicker ones.

� Concrete filling was found to fully prevent local buckling and ovalization for cold-formed steel tubes with 13�d/t�40, whereas multiple plastic ripples wereobserved in the inelastic range for CFT with 74�d/t�110.

� A simplified formula to determine the ultimate bending capacity of circular CFTwas derived based on plastic stress blocks and was shown to agree with experi-mental results.

� The predicted ultimate moment capacity of cold-formed CHS beams by CIDECTand EC4 was in good agreement with test results.

� The existing design rules for moment capacity of circular CFT (with normalconcrete) can be conservatively extended to a new range of 100�ls�188.

Acknowledgements

The writers are grateful to the Australian Research Council and Monash Universityfor their financial assistance for the project. Thanks are given to Palmer Tube Millsfor providing the steel tubes. The experiments were carried out in the Civil Engineer-ing Laboratory at Monash University and the technical assistance of Mr GrahamRundle and Mr Jeoff Doddrell is gratefully acknowledged.

APPENDIX A. Design rules for CFT

The notation used in this appendix is the same as that used in the original code.

Steel reinforced concrete structures AIJ [18]—art. 45

In the original code the following are from equation (173) and Table B1:

Mu � sMu � Mu

cMu �112

(crufc)d3sin3q

where Mu is the ultimate moment of CFT cross section;


cMu

is the ultimate moment due to concrete;

sMu

is the ultimate moment due to steel tube; q is the angular location of the neutralaxis; d is the outside diameter of the steel tube;

sZp

is the plastic section modulus of the steel tube; and sy is the yield strength of thesteel tube.

AISC-LRFD [20]—commentary, chapter I4

The commentary of the code recommends using a simplified equation for theultimate strength of the composite section (original equation C-14-1):

Mn � Zfy �13(h2�2Cr)Arfyr � �h2

2�

Awfy1.7fch1

�Awfy

where Mn is the ultimate moment of composite cross section; Aw is the web area ofthe encased steel (Aw=0 for CFT); Ar is the area of reinforcing steel (Ar=0 for CFT);Z is the plastic section modulus of the hollow steel tube; Cr is the average distanceto the reinforcement (Cr=0 for CFT); h1 is the width of the member perpendicularto the plane of bending; h2 is the width of the member parallel to the plane ofbending; fc is the concrete cylinder strength; fyr is the yield strength of reinforcementsteel (fyr=0 for CFT); and fy is the yield strength of the steel tube.

Eurocode 4 [22]—Appendix C

The ultimate flexural capacity of circular CFT is given by Mpl.Rd:

Mpl.Rd � Mmax.Rd�Mn.Rd

Mmax.Rd � wpafyd � wpsfsd � wpcfcd/2

Mn.Rd � wpanfyd � wpsnfsd � wpcnfcd/2

wpcn � (d�2t)h2n

wpan � bh2n�wpcn�wpsn

hn �Npm.Rd�Asn(2fsd�fcd)2bfcd � 4t(2fyd�fcd)

Npm.Rd � Acfcd

fcd � 1.0×fck

Ryan

Highlight


where wpan is the plastic section modulus of the steel tube; wpsn is the plastic sectionmodulus of the steel reinforcement; wpcn is the plastic section modulus of the concretecore (region 2 in the original figure C.2); fyd is the design yield strength of the steel;fsd is the design yield strength of the reinforcement; fcd is the design yield strengthof the concrete; fck is the concrete cylinder strength; Asn is the area of the reinforce-ment; Ac is the area of the concrete; t is the thickness of the steel tube; and b is thediameter of the steel tube.

CIDECT [40]—Appendix C

From the original equation 28:

Mpl.Rd � m0

d3�(d�2t)3

6fyd

where m0 is a factor (see the original Table 11); fyd is the design yield strength ofthe steel; and d is the outside diameter of the steel tube.

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Documents

CFT Subjected to Pure Bending, Elchalakani, 2001