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Journal of Constructional Steel Research 66 (2010) 542–555

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Journal of Constructional Steel Research

journal homepage: www.elsevier.com/locate/jcsr

Analytical behaviour of concrete-filled double skin steel tubular (CFDST)stub columns

Hong Huang a, Lin-Hai Han b,∗, Zhong Tao c, Xiao-Ling Zhao d

a College of Civil Engineering and Architecture, East of China Jiao Tong University, Jiangxi, 330013, PR Chinab Department of Civil Engineering, Tsinghua University, Beijing 100084, PR Chinac College of Civil Engineering, Fuzhou University, Fuzhou, Fujian Province 350108, PR Chinad Department of Civil Engineering, Monash University, Clayton, VIC 3168, Australia

a r t i c l e i n f o

Article history:

Received 13 June 2009

Accepted 30 September 2009

Keywords:

Concrete-filled double skin tubes (CFDST)Axial compression

FE modelling

Composite action

Concrete

Hollow steel tubes

Sectional capacity

a b s t r a c t

This paper reports a finite element analysis of the compressive behaviour of CFDST stub columns withSHS (square hollow section) or CHS (circular hollow section) outer tube and CHS inner tube. A set of test

data reported by different researchers were used to verify the FE modelling. Typical curves of averagestress versus longitudinal strain, stress distributions of concrete, interaction of concrete and steel tubes,

as well as effects of hollow ratio on thebehaviour of CFDST stub columns, were presented. The influencesof importantparameters thatdeterminesectionalcapacities of the composite columns wereinvestigated.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Concrete-filled double skin steel tubular (CFDST) members arecomposite members which consist of an inner and outer steel skinwith the annulus between the skins filled with concrete. This typeof sandwich cross-section was shown to have high bending stiff-ness that avoids instability under external pressure. Some back-ground information can be found in [1].

In recent years, many studies have been performed on CFDSTstub columns, such as [2–13]. A state-of-the-art review was givenby Zhao and Han [1]. A summary of research conducted on

CFDST stub columns is presented in Table 1. It can be seen fromTable 1 that the past studies concentrate mainly on experimentalinvestigations or predicting the load-bearing capacities of stubcolumns.

According to Han et al. [3] and Tao et al. [6], hollow ratio χ isan important parameter that affects column behaviour. This ratiois defined as d/(D−2t so), where d and D are the major dimensionsof the inner and outer tubes, respectively, and t so is the thicknessof the outer tube. If hollow ratio χ is equal to 0 for a column, the

∗ Corresponding author. Tel.: +86 10 62787067; fax: +86 10 62781488.

E-mail address: [email protected] (L.-H. Han).

column is actually a conventional concrete-filled steel tube (CFST).Generally,the CFDST columns have almost allthe same advantagesas conventional CFST members.

In this paper, a finite element (FE) modelling was developedbased on the commercial FE package, ABAQUS [14], to study thecompressive behaviour of CFDST stub columns. Several key issuesin the FE modelling are introduced briefly, i.e. the material modelsforconcrete andsteel,interface model to simulate the concrete andsteel interface, element type, mesh, and boundary conditions.

For CFDST columns, there are four possible combinations of square hollow section (SHS) and circular hollow section (CHS) as

outer or inner tubes.Since a CHSis less susceptible to local bucklingthan a SHS, it is good to use CHSs as both inner and outer tubes fora CFDST in practice. However the beam–column joint for a squarecolumn is easier to be fabricated and installed compared with thatof a circular column. For this reason, two types of CFDST columns,i.e., section with CHS inner and CHS outer, and section with CHSinner and SHS outer are investigated.

The main objectives of this paper are threefold: first, a set of test results reported by different researches are used to verifythe FE modelling. Second, typical curves of average stress versuslongitudinal strain, stress distributions of concrete, interaction of concrete and steel tubes and hollow ratio effect are investigated.Third, the influence of important parameters that determine thesectional capacities of the composite columns is identified.

0143-974X/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2009.09.014

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H. Huang et al. / Journal of Constructional Steel Research 66 (2010) 542–555 543

Nomenclature

Ac Cross-sectional area of concrete

Ace Nominal cross-sectional area of concrete Asco Cross-sectional area of the outer steel tube and the

sandwich concrete (= Aso + Ac ) Asc Cross-sectional area of CFDST (= Aso + Ac + Asi)

Asi Cross-sectional area of inner steel tube Aso Cross-sectional area of outer steel tubeCFDST Concrete-filled double skin tube

CFST Concrete-filled steel tubed Outer diameter of inner steel tubeD Outer dimension of outer steel tube

f ck Characteristic concrete strength ( f ck = 0.67 f cu for

normal strength concrete) f cu Characteristic 28-day concrete cube strength f c Concrete cylinder strength f syi Yield strength of inner steel tube f syo Yield strength of outer steel tubeN Axial compressive loadN u Ultimate strength of CFDST stub column

N uc Predicted ultimate strength of CFDST stub columnby using FE modelling

N ue Experimental ultimate strength of CFDST stubcolumn

p1 Interaction stress between the concrete and outer

tube p2 Interaction stress between the concrete and inner

tubet so Wall thickness of outer steel tube

t si Wall thickness of inner steel tubeαn Nominal steel ratio, given by αn = Aso/ Ace

χ Hollow ratio, given by d/(D − 2t so)ε Strain

µ Coefficient of friction between the steel tube and

core concreteτ bond Bond strength between the steel tube and coreconcrete

ξ Confinement factor (=αn f syo/ f ck)

2. Finite element modelling

2.1. Material models

(1) Steel

A steel constitutive model for structural steel presented in [15]

is utilised to represent uniaxial stress–strain relation of steel. For

carbon steel tubes, an elastic–plastic stress–strain relation model,

consisting of five stages (i.e. elastic, elastic–plastic, plastic, hard-

ening and fracture) is used. More details of the stress–strain rela-

tionship can be found in [15]. Mises yield function with associated

plastic flow is used in the multiaxial stress states.

The steel is assumed to have isotropic hardening behaviour, i.e.,

the yield surface changes uniformly in all directions so that yield

stresses increase or decrease in all stress directions when plasticstraining occurs [14]. Elastic modulus (E s) and Poisson’s ratio for

steel are taken as 2 × 105 (N/mm2) and 0.3, respectively.

(2) Concrete

Concrete is a brittle material with different failure mechanism

in compression and tension, i.e., crushing in compression and

cracking in tension. The damage plasticity model defined in

ABAQUS is used in the analysis [14]. The concrete damage plas-

ticity model adopts a unique yield function with non-associated

flow and a Drucker–Prager hyperbolic flow potential function to

describe the plasticity of concrete. Therefore, independent uniaxial

stress–strain relations for concrete both in compression and ten-

sion are the basic input data due to the difference in strength and

failure mechanism in compression and tension.

It is expected that the inner tube can restrict the inner indentof the concrete core if the hollow ratio is not too large, so the

sandwich concrete in the gap has the same behaviour with that

in a fully in-filled steel tube without the inner void. It was found

that in this case the failure features of the CFDST specimens were

very similar to those of CFST columns [3,6]. Therefore, uniaxial

stress–strain relation for concrete in CFSTs is used for the analysis

of CFDST members in this paper. The increasing of the plasticity

of core concrete as a result of the passive confinement of the

steel tube depends on the confinement factor ξ [15–17]. The

confinement factor for a CFDST can be defined as:

ξ = αn

f syo

f ck

(1)

in which, αn is the nominal steel ratio of CFDST columns, which isgiven by αn = Aso/ Ace. Ace is the nominal cross-sectional area of

concrete, which is given by Ace = π

4(D − 2t so)2 for section with

CHS inner and CHS outer, and Ace = (D − 2t so)2 for section with

CHS inner and SHS outer. Aso is the cross-sectional area of outer

steel tube, f syo is the yield stress of outer steel tube, and f ck is the

characteristic compression strength of concrete. The value of f ck is

approximately equal to 67% of the compressive strength of cube

blocks ( f cu) for normal strength concrete.

An equivalent stress–strain model presented by Han et al. [17],

which is suitable for the FE analysis using ABAQUS software for

CFSTs, is used in this paper for the analysis of CFDSTs. Fracture

energy versus displacement cross crack relation is used to describe

Table 1Summary of research conducted on CFDST stub columns.

Researchers Combinations Research results

Wei et al. [8,9]

CHS outer and CHS inner

Test results; An analytical model is presented, and an empirical formula is presented for the peak strength.Lin and Tsai [4] Test results.

Zhao et al. [10]Test results; Mechanics models and simplified models are developed.

Tao et al. [6]

Zhao and Grzebieta [13]SHS outer and SHS inner

Test results; Theoretical models are developed to predict the ultimate strength.

Zhao et al. [11] Test results; Plastic mechanism methods are used to predict the unloading behaviour.

Elchalakani et al. [2] CHS outer and SHS inner Test results; A simplified formula is derived to determine the compressive capacity.

Han et al. [3]SHS outer and CHS inner

Test results; Mechanics models and simplified models are developed.

Zhao et al. [12] Test results; Theoretical models are developed to predict the ultimate strength.

Tao et al. [7]RHS outer and RHS inner Test results; Mechanics models are developed.Tao and Han [5]

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544 H. Huang et al. / Journal of Constructional Steel Research 66 (2010) 542–555

(a) Circular section. (b) Square section.

Fig. 1. A schematic view of the element divisions.

Fig. 2. A schematic view of boundary conditions.

the tensile behaviour of concrete. More details of the modelcan befound in [17].

The initial modulus of elasticity (E c ) and Poisson’s ratio (µc )of concrete are determined according to the recommendations inACI Committee 318 [18], given as E c = 4730

f c and µc = 0.2

respectively.

2.2. Element type, element mesh and boundary conditions

The inner and outer steel tubes of a CFDST are modelled byreduced-integration shell elements (S4R), while the concrete core,as well as the end plates, are modelled by 8-node brick elements(C3D8R). The finite element meshes for typical members withcircular and square sections are shown in Fig. 1.

Due to symmetry of loading and geometry, only one eighth of the CFDST columns are modelled in the analysis. Boundary condi-tions of a model are shown in Fig. 2. The uniform loading in the z direction is applied to the top surface of the end plate. Load is sim-ulated by applying displacement instead of directly applying load.The stiffness of the end plate is large enoughthat its deformation inthe whole loading process is very little. Theend plate connects withthesteel tube by ‘SHELL TO SOLID’ (an interface model in ABAQUS),which ensures the displacements and rotational angles of the con-

tact elements keep the same in the whole loading process. The‘‘Hard contact’’ relation is selected for the end plate and concrete.

2.3. Steel-tube–concrete interface

The model to simulate the interaction of steel and concrete

in CFDST is the contact interaction in ABAQUS [14]. The contact

interaction is defined in two aspects, the geometric property and

the mechanical property.

The geometric property of the contact surfaces is defined by se-

lecting appropriate contact discretization, tracking approach and

determination of master and slave surfaces for the contact [14].

The surface-to-surface contact discretization is used in which two

of the contact surfaces are defined as master and slave surfaces

respectively. Some individual nodes in the master surface may

penetrate into the slave surface; however, large, undetected pen-

etrations of master nodes into the slave surface do not occur

with this discretization. Such penetrations can be further reduced

through careful selection of the master surface and finite element

discretization of contact surfaces. A smallsliding tracking approach

is selected for the contact. This approach is more efficient in the

calculation since the actualsliding between steel and concrete sur-

faces in CFDST is relatively small.

The mechanical property of the contact interaction is defined

along normal and tangential directions to the interface respec-tively.The ‘‘Hardcontact’’ relation is selected as normalmechanical

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(1) Circular sections.

(2) Square sections.

Fig. 3. Comparison of predicted versus measured axial load N —Deformation curves.

property. This property can be described in a pressure–overclosure

relation, i.e. surfaces transmit no contact pressure unless the nodes

of the slave surface contact the master surface. There is no limita-

tion on pressure development when surfaces are in contact. Fur-thermore, the contact surfaces are allowed to separate each other

after they have contacted. The tangential mechanical property of

the contact interaction is simulated by an isotropic Coulomb fric-

tion model [14]. According to the Coulomb friction model, the sur-

faces can transfer shear stress until the shear stress is greater thanthe limit value (τ crit). After the relative slip is formed between the

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(a) Outer steel tubes of circular sections. (b) Outer steel tubes of square sections.

(c) Inner steel tubes of circular sections. (d) Inner steel tubes of square sections.

Fig. 4. Comparisons between predicted and observed typical failure modes of specimens.

surfaces, the shear force is taken as a constant (τ crit). More detailsof the model can be found in [17].

Up to now, there is no research reported regarding the bondbehaviour of CFDST columns. It is expected that, however, the

behaviour of CFDST stub columns is not sensitive to the bondbetween the concrete and the inner or outer steel tube since thethree components are loading together. This is also confirmed by

changing the bond value in certain scope by using the FE modellingin this paper. Therefore, the bond model used for conventional

CFST columns is also used in this paper to simulate CFDSTcolumns.

2.4. Verification of the FE modelling

The predicted ultimate strengths (N uc) by using the FE mod-elling are compared with the measured ones (N ue) taken from Taoet al. [6], Lin and Tsai [4], Han et al. [3] and Zhao et al. [12], as

shown in Table 2. A mean(N uc/N ue) of 0.936 and a COV (coefficientof variation) of 0.045 formembers with circular section anda mean

(N uc/N ue) of 1.022 and a COV (coefficient of variation) of 0.061 formembers with square section are obtained. Typical predicted axialload N versus axial strain ε or axial displacement curves using FE

modelling are compared with the measured curves in Fig. 3. It can

be found that, in general, good agreement is obtained between thepredicted and test results.

Comparisons between predicted and observed typical failuremodes are presented in Fig. 4, where the failure modes for theouter CHS and SHS are shown in Fig. 4(a) and (b), respectively, andFig. 4(c) and (d) show the failure modes of the inner steel tubes. Ascan be seen, the failure modes of the outer steel tubes are outwardbuckling occurred near the specimen mid-height, while that fortheinner steel tubes is inwardbucklingsince itsoutward displacementis restricted by the concrete. In general, thepredicted failure modesof both inner and outer steel tubes agree well with the observed

ones.

3. Mechanism analysis

3.1. Analysis of the load–deformation relation

Typical calculated curves of average stressσ sc (=N / Asc, Asc isthecross-sectional area of CFDST)versus longitudinalstrain ε is shownin Fig. 5. Four characteristic points are also marked on the curves.At Point A, the outer steel tube begins to come into elastic–plasticstage. Yielding of the outer steel tube occurs at Point B. At Point C,ultimate axial load is reached. At Point D, the longitudinal strainattains the value of 0.02.

Fig. 6 shows the distributions of longitudinal stress (S 33 in the

graphs) at these characteristic points for the sandwich concrete inthe cross-section at the mid-height. The basic parameters used in

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Table 2

Test data of CFDST stub columns under axial compression.

Test

series

Specimen

label

Outer tube

dimensions

D × t so (mm)

Inner tube

dimensions

d × t si (mm)

χ f syo (MPa) f syi (MPa) f c ( f cu) (MPa) N ue (kN) N uc (kN) N uc/N ue Test data

resources

CHSouter

cc2a Φ 180 × 3 Φ 48 × 3 0.28 275.9 396.1 47.4 1790 1622 0.906

Tao et al. [6]

cc2b Φ 180 × 3 Φ 48 × 3 0.28 275.9 396.1 47.4 1791 1622 0.906

cc3a Φ 180 × 3 Φ 88 × 3 0.51 275.9 370.2 47.4 1648 1497 0.908

cc3b Φ 180 × 3 Φ 88 × 3 0.51 275.9 370.2 47.4 1650 1497 0.907cc4a Φ 180 × 3 Φ 140 × 3 0.80 275.9 342.0 47.4 1435 1258 0.877

cc4b Φ 180 × 3 Φ 140 × 3 0.80 275.9 342.0 47.4 1358 1258 0.926

cc5a Φ 114 × 3 Φ 58 × 3 0.54 294.5 374.5 47.4 904 807 0.893cc5b Φ 114 × 3 Φ 58 × 3 0.54 294.5 374.5 47.4 898 807 0.899

cc6a Φ 240 × 3 Φ 114 × 3 0.49 275.9 294.5 47.4 2421 2337 0.965

cc6b Φ 240 × 3 Φ 114 × 3 0.49 275.9 294.5 47.4 2460 2337 0.950

cc7a Φ 300 × 3 Φ 165 × 3 0.56 275.9 320.5 47.4 3331 3195 0.959

cc7b Φ 300 × 3 Φ 165 × 3 0.56 275.9 320.5 47.4 3266 3195 0.978

DS-2 Φ 300 × 2 Φ 180 × 2 0.61 290 290 28 2141 2155 1.007Lin and Tsai [4]

DS-6 Φ 300 × 4 Φ 180 × 2 0.61 290 290 28 2693 2765 1.027

SHS outer

scc2-1 -120 × 3 Φ 32 × 3 0.28 275.9 422.3 46.8 1054 993 0.942

Han et al. [3]

scc2-2 -120 × 3 Φ 32 × 3 0.28 275.9 422.3 46.8 1060 993 0.937

scc3-1 -120 × 3 Φ 58 × 3 0.51 275.9 374.5 46.8 990 1020 1.030

scc3-2 -120 × 3 Φ 58 × 3 0.51 275.9 374.5 46.8 1000 1020 1.020

scc4-1 -120 × 3 Φ 88 × 3 0.77 275.9 370.2 46.8 870 977 1.123

scc4-2 -120 × 3 Φ 88 × 3 0.77 275.9 370.2 46.8 996 977 0.981

scc5-1 -180 × 3 Φ 88 × 3 0.51 275.9 370.2 46.8 1725 1835 1.064scc5-2 -180 × 3 Φ 88 × 3 0.51 275.9 370.2 46.8 1710 1835 1.073

S1C1 -100.2 × 6.12 Φ 48.5 × 3.01 0.55 500 425 70 1677 1651 0.984Zhao et al. [12]

S2C1 -100.4 × 4.13 Φ 48.5 × 3.01 0.53 476 425 70 1253 1337 1.067

Fig. 5. Typical σ sc versus ε relations.

the calculations are: D = 400 mm, t so = 9.3 mm, d = 191 mm,t si = 3.18 mm, L = 1200 mm, f syo = f syi = 345 MPa, f cu = 60 MPa,χ = 0.5, where t si and f syi are the wall thickness and yield strengthof the inner steel tube respectively, and L is the column height.

It is clear from Fig. 5 that a curve can be generally divided intofour stages, i.e.

Stage 1: Elastic stage (from Point O to Point A). During this stage,steel and concrete bear axial load independently. It can be seenfrom Fig. 6(1)(a) and (2)(a) that the longitudinal stress of concreteuniformly distributes across the cross-section on the whole.

Stage 2: Elastic–plastic stage (from Point A to Point B). During thisstage, with the increasing of the axial load, the concrete cracksand begins to increase in volume. The confinement provided bythe outer steel tube enhances as the transverse deformation of concrete increases. It was found from Fig. 6(1)(b) that for thecircular member the longitudinal stress of concrete distributes stilluniformly in the cross-section, but for the square member shownin 6(2)(b) the maximal longitudinal stress of concrete occurs at the

corner because of the non-uniform confinement provided by theouter steel tube.

Stage 3: Plastic stage (from Point B to Point C). During this

stage, due to the increasing of the confinement provided by theouter steel tube, the average longitudinal stress in the concrete

cross-section exceeds the concrete cylinder strength f c . But thelongitudinal stress of the concrete distributes unevenly for both

the two types of column. For the member with CHS inner and CHSouter, the closer the location to the outer steel tube, the larger the

longitudinalstress is,which canbe seen from Fig.6(1)(c). This is at-tributed to the fact that the confinement is mainly from the outer

steel tube.

Stage 4: Descending or hardening stage (from Point C to Point D).Duringthis stage,the average stress σ sc of CFDST beginsto decrease

if ξ < ξ 0. If ξ > ξ 0, no descending stage will occur due to thestrainhardening of outer steel tube and its higher confinement on the

concrete. Based on a parametric analysis, the value of ξ 0 is equalto 1 or so for members with circular section, and is equal to 4.5 or

so for members with square section. It can be seen from Fig. 6(1)that, for the CFDST column with CHS outer, the distribution of the

concrete stresses at Point D is similar to those at Points B and C,although the values of concrete stresses decrease obviously. For

the CFDST column with SHS outer, however, a notable change instress distribution is found (see Fig. 6(2)) at different points (B, C

and D) with the maximum stress of concrete occurs near the inner

steel tube at Point D.Fig. 7 shows theloads carried by the outersteel tube, inner steel

tube, sandwich concrete, and overall CFDST versus longitudinalstrainrelations. It can be seen that the sandwich concrete bears thelarge part of the load, while the inner steel tube contributes little

to the load bearing of the CFDST.

3.2. Interaction of steel and concrete

Fig. 8 shows the confinement to the sandwiched concrete

provided by the steel tubes, in which p1 is the interaction stressbetween the concrete and outer steel tube, and p2 is that between

the concrete and inner steel tube.

Due to the influence of theend plate, theinteraction stresses p1

and p2 vary along the tube height as shown in Fig. 9, in which H is the distance to the top end, and L is the length of the composite

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(1) Circular section.

(2) Square section.

Fig. 6. The distributions of longitudinal stress of concrete (MPa).


Fig. 7. The loads (N ) carried by outer steel tube, inner steel tube, sandwich concrete, and CFDST respectively versus longitudinal strain (ε).

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Fig. 8. Confinement to the sandwiched concrete provided by the steel tubes.


Fig. 9. The variety of interactions p1 and p2 along the stub column height.

(a) Different locations. (b) Interaction stress p1. (c) Interaction stress p2.

Fig. 10. Interaction stresses p1 and p2 across the cross-section for a member with square section.

member. In Fig. 9, the stresses are shown when the peak loads arereached. It shouldalso be noted that, the interaction stresses p1 and

p2 shown in Fig. 9(b) are average values around the cross section.It can be seen that the influence of the end plate on the interactionis not significant if H > 0.1L.

For members with circular section, the interaction stresses p1

and p2 are almost constant across the cross-section. But this isnot the case for members with square section. To eliminate the

influence of the local buckling of the outer steel tube formed atthe mid-height, the interaction stresses shown in Fig. 10 are taken

from the section with a distance of L/5 away from the mid-height.

It can be seen from Fig. 10(b) that the stress of p1 at the corner

is much higher, which indicates the confinement provided by the

outer steel tube at the corner is the strongest across the cross-

section. The interaction stress p1 isalmost equal to0, ifthe distance

to the corner is larger than D/7, such as those points from 3 to 8

shown in Fig. 10(a). It can be seen from Fig. 10(c) that the values of

p2 do not vary too much around the cross-section compared withthose of p1.

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Fig. 11. Interaction stresses p1 and p2 versus longitudinal stain ε relations.

Forconvenience of analysis, the interaction stresses of p1 and p2

are taken from the cross-section at the mid-height in the following

analysis, where the basic parameters used in the examples are:D = 400 mm, t so = 9.3 mm, d = 191 mm, t si = 3.18 mm,

L = 1200 mm, f syo = f syi = 345 MPa, f cu = 60 MPa, χ = 0.5.

For the circular CFDST column in the above example, Fig. 11

shows the interaction stresses p1 and p2 versus longitudinal stain

ε relations. It can be found that the lateral deformation of the

outer steel tube is larger than that of the concrete at the initial

loading stage due to the larger Poisson’s ratio of the outer steel

tube compared with that of the concrete. Therefore there is no

interaction developed between the concrete and outer steel tubein

this stage. However, it should be noted that the bonding strength

between the concrete and steel tube in the normal direction has

been ignored in the FE modelling. This bondingin reality will allow

small tensilestressdeveloped between the concrete andsteel tube.

Since the tensile stress has no significant influence on the overall

performance of thedoubleskin compositecolumns,it is reasonable

to ignore the tensile stress to simplify the FE analysis. With the

increasing of thelongitudinalstrain, thecracksin concrete develop,

and the lateral deformation rate of the concrete begins to exceed

that of the outer steel tube. Therefore, the confinement provided

by the outer steel tube occurs at this moment. As far as the

interaction stress p2 is concerned, very small p2 develops at the

initial loading stage since the inner steel tube will press against

the concrete outwardly. But this effect is negligible because the

concrete comes into the elastic–plastic state soon, and there is no

interaction between the inner steel tube and the concrete core.

After thepeak load is reached, compression will develop once again

at the interface of the inner tube and the concrete.Possible parameters affecting the interaction stress versus lon-

gitudinal stain ε relationship are hollow ratio (χ ), nominal steel

ratio (αn), strength of outer steel tube ( f syo), strength of concrete

( f cu), strength of inner steel tube ( f syi) and width to thickness ratio

of inner steel tube (d/t si). Since these parameters have no obvious

influence on the interaction stress p2, only the effects of these pa-

rameters on the p1 versus ε relations are shown in Fig. 12. It can

be found from this figure: (1) With the increasing of hollow ratio

and concrete strength, the interaction stress p1 decreases due to

the decreasing of the confinement provided by the outer steel tube.

(2) With the increasing of nominal steel ratio and strength of outer

steel tube, the interaction stress p1 increases. (3) The strength and

widthto thickness ratio of the inner steel tube have little influence

on the interaction stress p1.

3.3. Effects of hollow ratio

Hollow ratio (χ) is an important parameter affecting the com-pressive behaviour of CFDST. Fig. 13 shows the distributions of

longitudinal stress of concrete for CFDST members with different

hollow ratio (i.e. χ = 0, χ = 0.25, χ = 0.5, χ = 0.75) at peakloads. It can be seen from Fig. 13(1) that with theincreasing of hol-

low ratio, longitudinal stress of concrete decreases obviously for

member with circular section. If χ is equal to 0, themaximum con-

crete stress occurs in the centre of the cross-section. If χ is equal

to 0.25, the maximum concrete stress occurs in the centre of thesandwich concrete. If χ is equal to 0.5 or 0.75, the maximum con-

cretestress appears near the outersteel tube. As hollow ratio χ in-

creases, apparently, the location of the maximum concrete stress

moves from centre to the periphery of the cross-section. The value

of the maximum concrete stress also decreases with the increasing

of hollow ratio χ .Fig. 13(2) shows that the effect of hollow ratio on the stress dis-

tribution for members with SHS outer. As can be seen, the maxi-

mum concrete stress occurs at the corner and decreases a bit with

the increasing of hollow ratio. Generally, the influence of hollow

ratio on the concrete stresses for members with CHS outer is largerthan that for members with SHS outer.

3.4. Parametric studies

Possible parameters affecting the axial load (N ) versus longitu-

dinal strain (ε) relationship of stub columns are hollow ratio (χ),

nominal steel ratio (αn), strength of outer steel tube ( f syo), strengthof concrete ( f cu), strength of inner steel tube ( f syi) and width to

thickness ratio of inner steel tube (d/t si). Fig. 14 shows the effectsof these parameters on the N versus ε relations.

It can be found from Fig. 14(a) that axial strength of the com-

posite columns decreases as hollow ratio (χ ) increases. The reason

is that the area of concrete decreases as χ increases, and the con-crete carries the majority of load for a CFDST column as demon-

strated in Fig. 7. However, the stiffness at the elastic–plastic stage

increases with the increasing of χ because of the increased steel

ratio.

It can be found from Fig. 14(b)–(d) that the axial strength of thecomposite columns increases obviously as the nominal steel ratio

(αn), strength of outer steel tube ( f syo) or strength of concrete ( f cu)

increases.

It can be found from Fig. 14(e) and (f) that the strength of inner

steel tube ( f syi) and width to thickness ratio of inner steel tube(d/t si) have no obvious influence on the strength of the composite

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(a) Hollow ratio.

(b) Nominal steel ratio.

(c) Strength of outer steel tube.

Fig. 12. Effects of different parameters on p1 versus ε relations.

member and the shape of curves. The reason is that the inner steeltube contributes comparatively little to the column strength asshown in Fig. 7.

Comparing the load versus longitudinal strain curves in Fig. 14for the two different section types shown in Fig. 1 reveals that theresidual strength after experiencing large deformation is higher forcircular sections.

4. Conclusions

The following conclusions can be drawn based on the limited

research reported in this paper.

(1) Finite element method is used in this paper for the analysis of

CFDST stub columns. A comparison of results calculated using

this modelling shows good agreement with those of the test

results.

(2) Typical curves of average stress versus longitudinal strain

are analysed. The stress distributions of concrete at different

characteristic points are investigated. The average stress ver-

sus longitudinal strain relations show strain hardening or anelastic–perfectly-plastic behaviour with bigger confinement

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(d) Concrete strength.

(e) Strength of inner steel tube.

(f) Width to thickness ratio of inner steel tube.

Fig. 12. (continued)

factor (ξ ), while for composite sections with smaller ξ , the

curves were of a strain-softening type.

(3) Interaction between the concrete and steel tubes in the com-

posite columns is analysed. It is found that the influence of

hollow ratio on the concrete stress for stub columns with cir-

cular section is more significant than that on members with

square section.

(4) Important parameters affecting the axial load (N ) versus longi-

tudinalstrain(ε) relationship of stubcolumns areinvestigated.

It is found that the stiffness at elastic–plastic stage of N –ε rela-

tions increases with the increasing of hollowratio. The residualstrength after experiencinglargedeformation is higherfor stub

columns with circular section compared to those with square

section.

Based on the finite element modelling presented in this paper,

further efforts can be made in the future to take the effects of

concrete shrinkage and the concrete viscosity under long-term

loading into account.

Acknowledgements

The study of thispaperis supported by the Research Foundationof the Ministry of Railways and Tsinghua University (RFMOR &

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(1) Circular section.

(2) Square section.

Fig. 13. The distributions of longitudinal stress of concrete for CFDST members with different hollow ratios (unit: MPa).

(a) Hollow ratio (χ ).

Fig. 14. Effects of different parameters on N versus ε relations.

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(b) Nominal steel ratio (αn).

(c) Strength of outer steel tube ( f syo).

(d) Concrete strength ( f cu).

(e) Strength of inner steel tube ( f syi).


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(f) Width to thickness ratio of inner steel tube ( d/t si).


THU) (No. J2008G011), the National Basic Research Program of China (973 Program) (Grant No. 2009CB623200). The financialsupport is greatly appreciated.

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