Han 2004

� Corresponding author

E-mail address: hanlin

0263-8231/$ - see front m

doi:10.1016/j.tws.2004.03

. Tel.: +86-591-789-2459; fax: +86-591-373-7442.

[email protected] (L.-H. Han).

atter # 2004 Elsevier Ltd. All rights reserved.

.017

Thin-Walled Structures 42 (2004) 1329–1355

www.elsevier.com/locate/tws

Concrete-filled double skin (SHS outer andCHS inner) steel tubular beam-columns

Lin-Hai Han a,�, Zhong Tao a, Hong Huang a, Xiao-Ling Zhao b

a College of Civil Engineering and Architecture, Fuzhou University, Gongye Road 523, Fuzhou,

Fujian Province 350002, People’s Republic of Chinab Department of Civil Engineering, Monash University, Clayton, Vic. 3168, Australia

Received 26 June 2003; received in revised form 13 February 2004; accepted 13 February 2004

Abstract

A series of tests on concrete-filled double skin steel tubular (CFDST) stub columns (14),beams (four) and beam-columns (12) were carried out. The specimens had square hollowsection (SHS) as outer skin and circular hollow section (CHS) as inner skin. A mechanicsmodel is developed in this paper for the CFDST stub columns, columns and beam-columns.A unified theory is described where a confinement factor (n) is introduced to describe thecomposite action between the steel tubes and the sandwiched concrete. The load versus axialstrain relationship for CFDST stub columns is predicted. Simplified model is derived for sec-tion capacities of CFDST. The predicted beam-column strength is compared with thatobtained in beam and beam-column tests. The load versus mid-span deflection relationshipfor CFDST beams and beam-columns is predicted. A simplified model is developed for cal-culating the member capacity of the CFDST beams. Simplified interaction curves are derivedfor CFDST beam-columns.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Concrete-filled; Beams; Columns; Beam-columns; Design; Hollow sections; Double-skin;

Mechanics model

1. Introduction

1.1. Background

‘‘Double skin’’ composite construction was originally used in submerged tube

tunnels for pressure vessels [1–5], which consisted of an inner and outer steel skin

Nomenclature

Ac concrete cross-sectional areaAc,nominal nominal cross-sectional area of concrete, given by B2 � Aso

Asc cross-sectional area of the composite section, given by Aso þ Ac þ Asi

Asco cross-sectional area of the outer steel tube and the sandwichedconcrete, given by Aso þ Ac

Asi cross-sectional area of the inner steel tubeAso cross-sectional area of the outer steel tubeB outer width of square tubeCFDST concrete-filled double skin steel tubeCFST concrete-filled steel tubeD outer diameter of the inner circular tubee load eccentricitye=r load eccentricity ratios, r can be given by B=2Ec concrete modulus of elasticityEs steel modulus of elasticityfsyo yield strength of the outer steel tubefsyi yield strength of the inner steel tubefcu characteristic 28-day concrete cube strengthfck characteristic concrete strength (fck ¼ 0:67fcu for normal strength

concrete)i radius of gyration of CFDST, given by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIsc=Asco

pIsc moment of inertia for CFDST cross-sectionL effective buckling length of column in the plane of bendingMu ultimate strength of CFDST beamsMuc,mm predicted moment capacity using mechanics modelMuc,sm predicted moment capacity using simplified modelMue maximum test momentMi,u moment capacity of the inner tubeMosu,u moment capacity of the outer steel tube filled with concreteNu ultimate strength of the composite columnsNuc,mm predicted ultimate strength using mechanics modelNuc,sm predicted ultimate strength using simplified modelNi,u compressive capacity of the inner tubeNosu,u compressive capacity of the outer steel tube filled with concreteNue experimental ultimate strengthtso wall thickness of the outer steel tubetsi wall thickness of the inner steel tubeWscm section modulus of the outer steel tube and the sandwiched concrete,

given by B3=6� pD4=ð32BÞWsi plastic section modulus of the inner tubev hollow ratio, given by D=B

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551330

r stresse strain/ curvaturek slenderness ratios, given by L=in confinement factor (¼ ðAso � fsyoÞ=ðAc;nominal � fckÞ)

1331L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

with the annulus between the skins filled with concrete. This type of sandwich

cross-section was shown to have high bending stiffness that avoids instability under

external pressure.In recent years, a similar concept called concrete-filled double skin tubes

(CFDST) was developed, and reported by Wei et al. [6,7], Nakanishi et al. [8],

Yagishita et al. [9], Lin and Tsai [10], Elchalakani et al. [11], Zhao and Grzebieta

[12], and Zhao et al. [13–15]. Similar to fully concrete-filled steel tubes (CFST),

advantages of CFDST include: increased section modulus; enhanced global stab-

ility; lighter weight; utilization of the space in the inner tube if necessary, good

damping characteristics and good cyclic performance. CFDST columns may have

reasonable fire resistance period because that the inner tubes are protected by the

sandwiched concrete under a fire. Recently, CFDST have been used as high-rise

bridge piers in Japan [9] to reduce the structure self-weight, while maintaining a

large energy absorption capacity against earthquake loading. There may be a

potential for CFDST to be used in building structures, as observed for concrete-

filled steel tubes (CFST) in the past few decades [16]. Therefore, there is a need

to study the behavior of CFDST stub columns, columns and beam-columns.The research conducted so far on CFDST is summarized in Table 1 where refer-

ences are listed. It can be seen that there are four combinations of square hollow

section (SHS) and circular hollow section (CHS) as outer and inner tubes. This

paper focuses on CFDST with SHS as outer skin and CHS as inner skin. Only

Table 1

Summary of research Conducted on CFDST

Combinations M

Stub columns

CHS outer and CHS

inner

W

L

ei et al. [6,7],

in and Tsai [10]

Lin and Tsai [10] –

SHS outer and SHS

inner

Z

[

hao and Grzebieta

12], Zhao et al. [13,14]

Zhao and

Grzebieta [12]

–

CHS outer and SHS

inner

E

SHS outer and CHS

inner

Z

p

hao et al. [13], this

aper

This paper T

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551332

some stub column tests were reported on this combination in the past [15] wherecold-formed SHS and CHS were used. The contribution of this paper can be sum-marized as follows:

1. More realistic sizes of SHS and CHS are used. The tube sizes used in the currentstudy are up to about three times that used by Zhao et al. [15].

2. The ratio of the inner tube diameter (D) to the outer tube width (B) varies from0 to 0.75 compared with that ranging from 0.49 to 0.60 by Zhao et al. [15].

3. Beams, columns and beam-columns are tested in the current study.4. Mechanics models and simplified models are developed for stub columns,

beams, columns and beam-columns.

1.2. This paper

Tests on 14 CFDST stub columns, four CFDST beams and 12 CFDST beam-columns were carried out. The main parameters varied in the testing program are:(1) hollow section ratio (v ¼ D=B) from 0 to 0.75, where D is the inner tube diam-eter and B is the outer tube width; (2) outer tube width to thickness ratio from 40to 100; (3) column slenderness (k), from 29 to 58; and (4) load eccentricity (e), from15 to 80 mm, for beam-columns.Mechanics models were developed to predict the behavior of CFDST stub

columns, beams, columns and beam-columns. The unified theory [17] was adoptedin the derivation, where a confinement factor (n) was introduced to describe thecomposite action between the steel tube and the sandwiched concrete. The loadversus axial strain relationship is established for concrete-filled SHS stub columns.The load versus mid-span deflection relationship is established for CFDST beamsand beam-columns. Simplified models were developed to estimate the strength ofCFDST stub columns, beams, columns and beam-columns. All predictions werecompared with test results with reasonable agreement achieved.

2. Experimental investigations

2.1. Materials and specimen preparation

A series of tests on concrete-filled double skin steel tubular (CFDST) stub col-umns, beams and beam-columns were carried out. The experimental study was notonly to determine the maximum load capacity of the specimens, but also to investi-gate the failure modes up to and beyond the ultimate load.A schematic view of the cross-section is shown in Fig. 1 where the outer skin is a

square box and the inner skin is a CHS. The tubes were all manufactured frommild steel sheet. Four sheet plates were cut, tack welded into a square shape andthen welded with a single bevel butt weld along the corners to form the outer tube.One sheet plate was cut, rolled to a circular shape and then welded with a singlebevel butt weld. A 25 mm thick plate was welded to one end of each specimen.

1333L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

Standard tensile coupon tests were conducted to measure material properties ofthe steel sheet. Three coupons were taken from each steel sheet used for manufac-turing specimens. The average yield stress of the outer tube (fsyo), and that of theinner tube (fsyi) for each specimen is listed in Tables 2–4. The modulus of elasticityof the outer and the inner tubes were found to be approximately 200,000 MPa.One type of concrete, with a nominal compressive cube strength (fcu) at 28 days

of 40 MPa, was designed. The mix proportions of the concrete were as follows:

– C

– W

– S

– C

For each batch of concrete mixed, three 150 mm cubes were also cast and curedin conditions similar to the related specimens. The average cube strength at thetime of testing was 46.8 MPa. The modulus of elasticity (Ec) of concrete was foundto be 33,300 MPa.The concrete was filled in the annulus between the outer and inner skins. The

specimens were vibrated by poker vibrator. They were placed upright to air-dryuntil testing. During curing, a very small amount of longitudinal shrinkage of0.6–0.8 mm or so occurred at the top of the columns. A high-strength epoxy wasused to fill this longitudinal gap so that the concrete surface was flush with thesteel tube at the top. Prior to testing, this surface was ground smooth and flat

Fig. 1. Column specimen details and dimensions (schematic view).

Table2

Specim

enlabels,materialproperties

andsectioncapacities

(stubcolumns)

No.

Specim

en

label

Outertube

dim

ension

B�t so(m

m)

Inner

tube

dim

ension

D�t si(m

m)

vL (m

m)

f syo

(MPa)

f syi

(MPa)

Nue

(kN)

Nuc,mm

(kN)

Nuc;mm=N

ue

1scc1-1

&-120�3

–0

360

275.9

–982

882

0.898

2scc1-2

&-120�3

–0

360

275.9

–990

882

0.891

3scc2-1

&-120�3

U32�3

0.27

360

275.9

422.3

1054

967

0.917

4scc2-2

&-120�3

U32�3

0.27

360

275.9

422.3

1060

967

0.912

5scc3-1

&-120�3

U58�3

0.48

360

275.9

374.5

990

976

0.986

6scc3-2

&-120�3

U58�3

0.48

360

275.9

374.5

1000

976

0.976

7scc4-1

&-120�3

U88�3

0.75

360

275.9

370.2

870

947

1.089

8scc4-2

&-120�3

U88�3

0.75

360

275.9

370.2

996

947

0.951

9scc5-1

&-180�3

U88�3

0.49

540

275.9

370.2

1725

1785

1.035

10

scc5-2

&-180�3

U88�3

0.49

540

275.9

370.2

1710

1785

1.044

11

scc6-1

&-240�3

U114�3

0.48

720

275.9

294.5

2580

2756

1.068

12

scc6-2

&-240�3

U114�3

0.48

720

275.9

294.5

2460

2756

1.120

13

scc7-1

&-300�3

U165�3

0.50

900

275.9

320.5

3240

3855

1.190

14

scc7-2

&-300�3

U165�3

0.50

900

275.9

320.5

3430

3855

1.124

15

Empty

tube

&-120�3

––

360

275.9

–376

––

Mean

1.014

COV

0.009

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551334

Table3

Specim

enlabels,materialproperties

andsectioncapacities

(beams)

No.

Specim

en

label

Outertube

dim

ension

B�t so(m

m)

Inner

tube

dim

ension

D�t si(m

m)

vL (m

m)

f syo

(MPa)

f syi

(MPa)

Mue

(kN)

Muc,mm

(kN)

Muc;mm=M

ue

1scb1

&-120�3

–0

1400

275.9

–24.37

19.79

0.812

2scb2

&-120�3

U32�3

0.27

1400

275.9

422.3

25.87

22.46

0.868

3scb3

&-120�3

U58�3

0.48

1400

275.9

374.5

26.90

25.87

0.962

4scb4

&-120�3

U88�3

0.73

1400

275.9

370.2

28.98

33.49

1.156

5Empty

tube

&-120�3

––

1400

275.9

–17.44

––

Mean

0.950

COV

0.023

1335L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

Table4

Specim

enlabels,materialproperties

andmem

ber

capacities

(columnsandbeam-columns)

No.

Specim

en

label

Outertube

dim

ension

B�t so(m

m)

Inner

tube

dim

ension

D�t si(m

m)

vL (m

m)

kf syo

(MPa)

f syi

(MPa)

e (mm)

Nue

(kN)

Nuc,mm

(kN)

Nuc;mm=N

ue

1scbc1-1

&-120�3

U58�3

0.48

1070

29

275.9

374.5

4856

912.

1.065

2scbc1-2

&-120�3

U58�3

0.48

1070

29

275.9

374.5

4872

912

1.046

3scbc2-1

&-120�3

U58�3

0.48

1070

29

275.9

374.5

14

667

755

1.132

4scbc2-2

&-120�3

U58�3

0.48

1070

29

275.9

374.5

14

750

755

1.007

5scbc3-1

&-120�3

U58�3

0.48

1070

29

275.9

374.5

45

480

483

1.006

6scbc3-2

&-120�3

U58�3

0.48

1070

29

275.9

374.5

45

486

483

0.994

7scbc4-1

&-120�3

U58�3

0.48

2136

58

275.9

374.5

0920

860

0.935

8scbc4-2

&-120�3

U58�3

0.48

2136

58

275.9

374.5

0868

860

0.991

9scbc5-1

&-120�3

U58�3

0.48

2136

58

275.9

374.5

15.5

596

602

1.010

10

scbc5-2

&-120�3

U58�3

0.48

2136

58

275.9

374.5

15.5

570

602

1.056

11

scbc6-1

&-120�3

U58�3

0.48

2136

58

275.9

374.5

45

380

389

1.024

12

scbc6-2

&-120�3

U58�3

0.48

2136

58

275.9

374.5

45

379

389

1.026

Mean

1.024

COV

0.002

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551336

1337L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

using a grinding wheel with diamond cutters. This was to ensure that the load

was applied evenly across the cross-section and simultaneously to the steel and

concrete.

2.2. Stub column tests

A total of 12 stub columns were tested. A summary of the specimens is presented

in Table 2, where the section sizes, material properties and hollow ratio (v) are

given. The length of stub columns (L) was chosen to be three times the width of

outer SHS sections to avoid the effects of overall buckling and end conditions [17].All the tests were performed on a 5000 kN capacity testing machine. The speci-

mens were sitting on the machine base plate. The load was applied through a load-

ing ram. Eight strain gauges were mounted on each specimen to measure strains at

the middle height, two on each flat face of the outer tube. Four strain gauges were

placed along the direction of loading while the other four were placed perpendicu-

lar to the loading direction. Two displacement transducers were used to measure

the axial deformation. A load interval of less than one-tenth of the estimated load

capacity was used. Each load interval level was maintained for about 2 min.Typical failure mode of the outer tube was local (outward folding) failure mech-

anism. This is the same as that observed by Zhao et al. [15] for CFDST with SHS

outer and CHS inner. This failure mode is also similar to that observed for con-

crete-filled steel tubes (CFST) by many other researchers, such as Ge and Usami

[18], Han et al. [17], O’Shea and Bridge [19], and Song and Kwon [20], just to list a

few. The typical failure mode is shown in Fig. 2(a). The failure mode of the inner

CHS behaves differently from that for empty CHS in compression where an

‘‘elephant foot’’ occurs. The failure mode shown in Fig. 2(b) is very much the same

as that observed for the inner CHS tube of CFDST [13,14]. One test on empty

outer tube was also carried out for comparison purpose. The details are listed in

Table 2.Load versus axial strain curves are shown in Fig. 3. The maximum loads (Nue)

obtained in the test are summarized in Table 2. It can be found from Fig. 3(d) that

the ultimate strength and the ductility of CFDST stub columns are much larger

than those of the empty stub columns.

2.3. Beam tests

Four CFDST beam specimens with different hollow ratio (v) were tested in the

same machine that was used for the stub column tests. The specimens were labeled

as shown in Table 3.A four-point bending rig was used to apply the moment similar to that described

by Zhao and Grzebieta [12]. The mid-span deflection was measured using a dis-

placement transducer. The strains in the outer tube were measured at mid-span of

the beam by strain gauges on both top and bottom surfaces.Failure modes of the current tested beams were very similar to those described

by Zhao and Grzebieta [12] for CFDST (SHS outer and SHS inner) beams. No

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551338

tensile fracture was observed on the tension flange. The failure modes of inner con-

crete and inner tubes are shown in Fig. 4(a) and (b), respectively.One empty beam with the same tube dimension as the outer tube was also car-

ried out for comparison purposes. The details of the specimen were listed in

Table 3.The bending moment is plotted in Fig. 5 against the compressive and tensile

strains of the extreme fiber at mid-span. The bending moment versus mid-span

deflection curves are given in Fig. 6. The maximum experimental moment (Mue) is

listed in Table 3. It can be found from Table 3 and Fig. 6(a) that both the ultimate

strength and the ductility of CFDST beams are much larger than those of the

empty tube beam.

2.4. Beam-column tests

Fourteen tests on composite columns and beam-columns were carried out. A

summary of the specimens is presented in Table 4 where the section sizes, slender-

ness ratios (k), load eccentricities (e), and sectional hollow ratio (v) are given. The

load eccentricity (e) ranges are from 0 to 45 mm. The slenderness ratio (k) ranges

Typical failure mode of the of CFDST stub columns. (a) Specimen after testing and (b)

tube.

1339L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

Fig. 3. Load versus axial strain curves.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551340

are from 29 to 58. The value of slenderness ratio (k) is defined as

k ¼ L

i; ð1Þ

where L is the effective length of a column, which is the same as the physical length

of the column (L) with pin-ended supports. i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIsc=Asco

p, is the section radius of

gyration, Isc and Asco are the moment of inertia and area of CFDST composite

cross-section, respectively.The desired eccentricity was achieved by accurately machining grooves that are

6 mm deep into the stiff endplate that was welded to the steel tubes. For the con-

centrically loaded column, the groove was in the middle of the plate. The endplate

was considered very stiff with a thickness of 30 mm. The axial load was applied

through a very stiff top platen with an offset triangle hinge, which also allowedspecimen rotation to simulate pin-ended supports. Both the endplate and the top

platen were made of very hard and very high-strength steel. Eight strain gauges

were used for each specimen to measure the longitudinal and transverse strains at

the middle height. Two displacement transducers were used to measure the axial

deformation. Five transducers were used to measure the lateral deflection. Fig. 7

gives a general view of the test arrangement.A load interval of less than one-tenth of the estimated load capacity was used.

Each load interval was maintained for about 2 min. At each load increment, the

Typical failure modes of the of CFDST beams. (a) Sandwiched concrete and (b) inner

1341L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

Fig. 5. Moment versus extreme fibre strains at mid-span of beam specimens.

Fig. 6. Load versus mid-span deflection of beam specimens (a) scb1; (b) scb2; (c) scb3; (d) scb4.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551342

strain readings and the deflection measurements were recorded. All specimens wereloaded to failure. Each test took approximately 30 min to reach the maximum loadand 1.5 h to complete. All the test specimens behaved in a relatively ductile mannerand testing proceeded in a smooth and controlled way.Typical failure mode was overall buckling failure. When the load was small, the

lateral deflection at middle height is small and approximately proportional to theapplied load. When the load reached about 60–70% of the maximum load, thelateral deflection at middle height started to increase significantly. Specimenno. scbc5-1 is selected to illustrate the lateral deflection in the middle-span of thecomposite beam-column with different axial loads (N), as shown in Fig. 8, wherethe ratio of n is given by N=Nue.The axial load (N) versus extreme fiber strain curves are shown in Fig. 9. The

load (N) versus mid-height deflection (um) curves for the composite columns arepresented in Fig. 10. The maximum loads (Nue) obtained in the test are summar-ized in Table 4.

3. Mechanics models

3.1. Mechanics model for stub columns

Mechanics models were developed by Han et al. [17] for concrete-filled SHSs.Stress versus strain relations were given in Han et al. [17] for steel tubes and con-

Fig. 7. A general view of beam-column test.

1343L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

fined concrete. In this paper, the same stress–strain relations were adopted for steeltubes and concrete in the analysis.A typical stress–strain curve for steel consists of five stages as shown in Fig. 11.

Detailed expressions were given in Han et al. [17].It is assumed that the inner tube can restrict the inner indentation of the con-

crete core, so the sandwiched concrete in the annulus was confined in the same wayas that in a fully in-filled steel tube. A typical stress–strain curve for the confinedconcrete with fck ¼ 41 MPa is shown in Fig. 12, where the confinement factor (n) isdefined as

n ¼ Aso � fsyoAc;nominal � fck

; ð2Þ

in which Aso is the cross-section area of the outer steel tube, Ac,nominal is the nom-

inal cross-section area of concrete, given by B2 � Aso, fsyo is the yield stress of theouter steel tube, and fck is the compression strength of concrete. The value of fckfor normal strength concrete is determined using 67% of the compression strengthof cubic blocks. Detailed expressions are given in Han et al. [17].It can be seen from Fig. 12 that the higher the confinement factor (n) is, the

higher the compression strength of confined concrete is. It can also be seen fromFig. 12 that the higher is n, the more ductile is the confined concrete. The confine-ment factor (n), to some extent, represents the ‘‘composite action’’ between steeltubes and concrete.The fabrication of concrete-filled steel SHS columns involves welding which

introduces residual stresses in the specimens. Fig. 13 shows a typical residual stress

lateral deflection along the column at different loa

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551344

distribution for a steel plate in a column that has been fabricated with four steel

plates and a longitudinal fillet weld [21]. The residual stresses in steel plates for

concrete-filled steel SHS columns were found to be 0:15fsy � 0:25fsy in compression

and about fsy in tension [21]. The average value of 0.2fsy in compression is adopted

in this paper as shown in Fig. 13.The load versus axial strain relations can be established based on the following

assumptions:

Fig. 9. Axial load versus extreme fibre strains at mid-height of test specimens.

1345L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

1. There is no slip between the steel and concrete.2. Longitudinal stress–strain models of steel and concrete given in Han et al. [17]

are adopted in the analysis.3. Residual stress distribution for a steel plate of a column shown as in Fig. 13 is

used in the analysis.

Fig. 10. Load (N) versus mid-height lateral deflection (um) curves.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551346

. Typical stress–strain curves for steel (schematic

Fig. 12. r versus e relations of concrete core.

sidual stress distribution across plate of steel bo

1347L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

4. Force equilibrium and deformation consistencies are considered along the longi-tudinal direction, i.e.

N ¼ Nsi þNc þNso; ð3Þesil ¼ ecl ¼ esol; ð4Þ

in which Nsi, Nc and Nso are longitudinal forces carried by the inner steel tube,the sandwiched concrete, and the outer steel tube, respectively; esil, ecl and esolare longitudinal strains in the inner steel tube, the sandwiched concrete, and theouter steel tube, respectively.

The procedures to calculate load versus axial strain are expressed as follows.For a given (ith) increment in axial strain deli ! ith axial strain e1;iþ1 ¼

eli þ deli ! ith axial stress rsil;iþ1; rcl;iþ1 and rsoil;iþ1 ! ith forces Nsi;i; Nc;i and

Nso;i ! ith force Ni.The predicted curves of load versus axial strain are compared in Fig. 3 with

experimental curves. Good agreement is obtained between the predicted and testedcurves. The predicted section capacities using mechanics model (Nuc,mm) are com-pared in Table 2 with those obtained in the current tests (Nue). A mean ratio(Nuc=Nue) of 1.014 is obtained with a coefficient of variation (COV) of 0.009.

3.2. Mechanics model for the composite beam-columns

A member subjected to compression is shown in Fig. 14, where N is the com-pression force, e is the load eccentricity and um is the mid-span deflection. Whenthe load eccentricity (e) equals zero, the member under compression is called a col-umn. Otherwise, the member is called a beam-column, i.e. it is under combinedbending and compression.The load versus mid-span deflection relations can be established based on the

following assumptions:

1. The stress–strain relationship for steel given in Han et al. [17] is adopted forboth tension and compression. The stress–strain relationship for concrete givenin Han et al. [17] is adopted for compression only. The contribution of concretein tension is neglected.

2. Original plane cross-sections remain plane.3. The effect of shear force on deflection of members is omitted.

Fig. 14. A schematic view of a beam-column.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551348

4. The deflection curve of the member is assumed as a sine wave.5. Residual stress distribution for a steel plate of a column shown as in Fig. 13 is

used in the analysis.

According to the assumption no. 4, the deflection (u) of the member can be

expressed as:

u ¼ um � sin pL� z

� �; ð5Þ

where um is the mid-span deflection, L is the length of the member and z is the

horizontal distance from the left support as defined in Fig. 14.The curvature (/) at the mid-span can be calculated as:

/ ¼ p2

L2� um: ð6Þ

The strain distribution is shown in Fig. 15, where eo is the strain along the

geometrical centre line of the section. The term ei is the strain at the location yi as

defined in Fig. 15. Along the line with y ¼ yi, the section can be divided into three

kinds of elements (dAso,i and dAsi,i for outer and inner steel tubes, respectively, and

dAci for concrete) with unit depth. The strain at the centre of each element can be

expressed as:

ei ¼ eo þ / � yi: ð7Þ

The stress at the centre of each element (rso,i and rsi,i for outer and inner steel

tubes, respectively, or rc,i for concrete) can be determined using the stress–strain

relationship given in Han et al. [17]. The internal moment (Min) and axial force

Fig. 15. Distribution of strains.

1349L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

(Nin) can be calculated as:

Min ¼Xi

ðrso;i � dAso;i � yo;i þ rc;i � dAc;i � yc;i þ rsi;i � dAsi;i � yi;iÞ; ð8Þ

Nin ¼Xi

ðrso;i � dAso;i þ rc;i � dAc;i þ rsi;i � dAsi;iÞ: ð9Þ

According to the equilibrium condition

Min ¼ Mapplied; ð10ÞNin ¼ Napplied: ð11Þ

From the above equations, the load versus mid-span deflection relations can beestablished for a certain eccentricity (e). The geometrical imperfection is taken asL=1000 [17].The predicted curves of load versus lateral deflection are compared in Figs. 6

and 11 with those obtained in the current beam and beam-column tests. A reason-able good agreement is achieved between the predicted and tested curves.The predicted ultimate capacities for beams and beam-columns are compared

with the experimental values in Tables 3 and 4, where a mean of 1.072 and 0.95,and COV of 0.023 and 0.020 are obtained for the CFDST beams and beam-col-umns, respectively.Fig. 16 illustrates a typical calculated interaction relationship between compress-

ive strength ratio (N=Nu) and bending strength ratio (M=Mu) of a CFDST beam-column with different column slenderness ratio (k). Nu and Mu are the sectioncapacity in compression and bending moment capacity of CFDST, respectively. Itcan be found that the member capacities of the composite beam-columns decreasewith the increasing of member slenderness ratio (k). A careful examination of thepredicted results also revealed an interesting phenomenon, i.e. the N=Nu �M=Mu

dicted axial load (N=Nu) versus moment (M=Mu) interaction

&-600� 600� 14 mm, v ¼ 0:5, fsy ¼ 345 MPa, fck ¼ 26:8 MPa).

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551350

relationships of the CFDST beam-columns are very similar to those of the CFST

members [17].

4. Simplified models

4.1. Section capacity

It is assumed that the total capacity (Nu,sm) of CFDST is a sum of the inner tube

capacity (Ni,u) and a capacity (Nosu,u) which contributed by the outer tube togetherwith the concrete, i.e.

Nu;sm ¼ Nosc;u þNi;u; ð12Þ

in which Ni;u ¼ Asi � fsyi and Nosu,u is determined similarly to that of fully concrete-filled steel tubular sections [17] with the relevant concrete section area for CFDST.Nosu,u can be expressed by:

Nosc;u ¼ fscy � Asco; ð13Þ

in which Asco ¼ Aso þ Ac;

fscy¼ 1:212þ 0:138� fsyo235

þ0:7646

� ��nþ �0:0727� fck

20þ0:0216

� ��n2

� �fck; ð14Þ

where the units for fscy and fck are N/mm2.The section capacities predicted using the simplified model are compared in

Fig. 17(a) with those obtained in stub column tests by Zhao et al. [15] and in the

current study. Good agreements are obtained.

4.2. Bending moment capacity

Similar to the approach used for stub columns, the bending moment capacity ofCFDST (Mu,sm) can be expressed as:

Mu;sm ¼ Mosc;u þMi;u ð15Þ

in which Mi;u ¼ Wsi � fsyi is moment capacity of the inner tube, Mosc,u is determinedsimilarly to that of fully concrete-filled steel tubular sections [17] with the relevant

concrete section area for CFDST. Mosu,u is given by:

Mosc;u ¼ cm �Wscm � fscy ð16Þ

in which cm ¼ �0:2428n þ 1:4103ffiffiffin

p; Wscm ¼ ðB3=6Þ � ðp �D4=32BÞ, fscy is given

by Eq. (14).The flexural capacities predicted using the simplified model are compared in

Fig. 17(b) with those obtained in current tests. Results in this figure clearly show

that the predicted values are slightly lower than experimental ones.

1351L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

alculated capacity between simplified model and tes

beams and (c) beam-columns.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551352

4.3. Interaction curves

The interaction equation suggested by Han et al. [17] for concrete-filled beam-columns are used in this paper to predict the CFDST beam-columns with relevantcapacities for CFDST defined in Eqs. (12) and (15). The interaction curves wererewritten here as

11� 0:25N=NE

¼ 1� g=u1� 2g0o=u

for g � 2g0o; ð17aÞ

11� 0:25N=NE

¼ a � gu

� �2

þb � gu

� �þ 1 for g < 2g0o; ð17bÞ

in which

g ¼ N

Nu;sm; 1 ¼ M

Mu;sm;

Nu,sm, Mu,sm are the sectional capacity and bending moment capacity of CFDSTsection given by Eqs. (12) and (15), respectively;

NE ¼ p2 � Eelasticsc � Asco

k2;

Asco ¼ Aso þ Ac;

Eelasticsc is the section modulus of concrete-filled steel SHS in elastic stage [17]; u is

the stability reduction factor for the composite slender columns [17].

a ¼ ð1� 10oÞ=g0o2;

b ¼ �2g00ð1� f0oÞðu � g0oÞ;

g00 ¼ u3go;

f0o ¼ 1þ u5ðfo � 1Þ;

go ¼ 0:2 � fck20

� �0:65

� 235

fsyo

� �0:38

� 0:1

a

� �0:45

;

fo ¼ 1þ 0:11fck20

� �1:46

� 235

fsyo

� �1:65

� 0:1

a

� �1:4

;

where the units for fsyo and fck are N/mm2.The member capacities predicted using the simplified model are compared with

the experimental results in Fig. 17(c). Fig. 18 shows the axial load (N) versusmoment (M) interaction curves for the current specimens with dimensions of theouter and the inner tubes are &-120� 3 and U58� 3, respectively. It can be foundfrom the above comparisons that the accuracy with which the formula predictedthe experimental strength is reasonable, and in general, the predictions are some-what conservative.

1353L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

5. Conclusions

A series of tests, including 14 stub columns, four beams and 12 beam-columnson CFDST (SHS outer and CHS inner) sections have been performed. Mechanicsmodels have been established for CFDST stub columns, beams and beam-columns.A confinement factor has been used to describe the ‘‘composite action’’ betweensteel tubes and the sandwiched concrete. The following observations and conclu-sions can be drawn based on the limited research reported in the paper:

1. Enhanced strength and ductility have been observed for CFDST (CHS innerand SHS outer) stub columns, beams and bean-columns due to the ‘‘compositeaction’’ between the steel tubes and the sandwiched concrete.

2. Mechanics models have been developed to predict the behavior of CFDST stubcolumns, beams, columns and beam-columns.

ersus moment (M) interaction curves for the tested spec

scbc1-2, scbc2-1, scbc2-2, scbc3-1, scbc3-2 and (b) scb3, scbc4-1, scbc4-2, scbc5-1, scbc5-2, scbc6-1,

scbc6-2.

L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–13551354

3. The load versus axial strain relationship has been established for concrete-filledSHS stub columns. The load versus mid-span deflection relationship has beenestablished for CFDST beams and beam-columns. Simplified models have beendeveloped to estimate the strength of CFDST stub columns, beams, columnsand beam-columns. All predictions were compared with test results with reason-able agreement achieved.

Acknowledgements

The research work reported herein was made possible by the Fujian ProvinceScience and Technology Project, the financial support is highly appreciated. Theauthors also express special thanks to Mr. Zheng Yong-Qian, Mr. Liu Cheng-Chao,Miss Zheng Huai-Ying, and Mr. Zhuo Qiu-Lin for their assistance in the experi-ments.

References

[1] Montague P. A simple composite construction of cylindrical shells subjected to external pressures.

Journal of Mechanical Engineering Society 1975;17:105–13.

[2] Wright H, Oduyemi T, Evans HR. The experimental behaviour of double skin composite elements.

Journal of Constructional Steel Research 1991;19:91–110.

[3] Goode CD. Composite construction to resist external pressure. The International Speciality Confer-

ence on Concrete Filled Steel Tubular Structures, Harbin, China. 1988, p. 46–52.

[4] Shakir-Khalil H. Composite columns of double-skinned shells. Journal of Constructional Steel

Research 1991;19:133–52.

[5] McKinley B, Boswell LF. Behaviors of double skin composite construction. Journal of Construc-

tional Steel Research 2002;58(10):1347–59.

[6] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwich tube under axial

loading: experiment. Journal of Structural Engineering, ASCE 1995a;121(12):1806–14.

[7] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwich tube under axial

loading: analysis. Journal of Structural Engineering, ASCE 1995b;121(12):1815–21.

[8] Nakanishi K, Kitada T, Nakai H. Experimental study on ultimate strength and ductility of con-

crete filled steel columns under strong earthquakes. Journal of Constructional Steel Research

1999;51:297–319.

[9] Yagishita F, Kitoh H, Sugimoto M, Tanihira T, Sonoda K. Double-skin composite tubular col-

umns subjected cyclic horizontal force and constant axial force. Proceedings of the Sixth ASCCS

Conference, Los Angeles, USA, March 22–24. 2000, p. 497–503.

[10] Lin ML, Tsai KC. Behavior of double-skinned composite steel tubular columns subjected to com-

bined axial and flexural loads. Proceedings of the First International Conference on Steel and Com-

posite Structures, Pusan, Korea, 14–16 June. 2001, p. 1145–52.

[11] Elchalakani M, Zhao XL, Grzebieta R. Tests on concrete filled double-skin (CHS outer and SHS

inner) composite short columns under axial compression. Thin-Walled Structures 2002;40(5):415–41.

[12] Zhao XL, Grzebieta R. Strength and ductility of concrete filled double skin (SHS inner and SHS

outer) tubes. Thin-Walled Structures 2002;40(2):199–213.

[13] Zhao XL, Han B, Grzebieta RH. Plastic mechanism analysis of concrete-filled double-skin (SHS

inner and SHS outer) stub columns. Thin-Walled Structures 2002;40(10):815–33.

[14] Zhao XL, Grzebieta RH, Elchalakani M. Tests of concrete-filled double skin CHS composite stub

columns. Steel and Composite Structures—An International Journal 2002;2(2):129–42.

1355L.-H. Han et al. / Thin-Walled Structures 42 (2004) 1329–1355

[15] Zhao XL, Grzebieta RH, Ukur A, Elchalakani M. Tests of concrete-filled double skin (SHS Outer

and CHS inner) composite stub columns. In: Chan SL, Teng JG, Chung KF, editors. Advances in

steel structures, Vol. I. Elsevier; 2002, p. 567–74.

[16] ASCCS. Concrete filled steel tubes—a comparison of international codes and practices. ASCCS

Seminar, Innsbruck, Austria. 1997.

[17] Han LH, Zhao XL, Tao Z. Tests and mechanics model of concrete-filled SHS stub columns, columns

and beam-columns. Steel and Composite Structures—An International Journal 2001;1(1):51–74.

[18] Ge HB, Usami T. Strength analysis of concrete-filled thin-walled steel box columns. Journal of

Constructional Steel Research 1994;30:607–12.

[19] O’Shea MD, Bridge RQ. Behaviour of thin-walled box sections with lateral restraint. Department

of Civil Engineering Research Report, No. R739. The University of Sydney, 1997.

[20] Song JY, Kwon YB. Structural behaviour of concrete-filled steel box sections. International Con-

ference Report on Composite Construction–Conventional and Innovative, Innsbruck, Austria.

1997, p. 795–801.

[21] Uy B. Concrete-filled fabricated steel box columns for multistorey buildings: behaviour and design.

Progress in Structural Engineering and Materials 1998;1(2):150–8.