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Journal of Constructional Steel Research 66 (2010) 542–555
Contents lists available at ScienceDirect
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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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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(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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H. Huang et al. / Journal of Constructional Steel Research 66 (2010) 542–555 545
(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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546 H. Huang et al. / Journal of Constructional Steel Research 66 (2010) 542–555
(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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548 H. Huang et al. / Journal of Constructional Steel Research 66 (2010) 542–555
(1) Circular section.
(2) Square section.
Fig. 6. The distributions of longitudinal stress of concrete (MPa).
(a) Circular section. (b) Square section.
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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(a) Circular section. (b) Square section.
Fig. 8. Confinement to the sandwiched concrete provided by the steel tubes.
(a) Circular section. (b) Square section.
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).
Fig. 14. (continued)
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(f) Width to thickness ratio of inner steel tube ( d/t si).
Fig. 14. (continued)
THU) (No. J2008G011), the National Basic Research Program of China (973 Program) (Grant No. 2009CB623200). The financialsupport is greatly appreciated.
References
[1] Zhao XL, Han LH. Double skin composite construction. Progress in StructuralEngineering and Materials 2006;8(3):93–102.
[2] ElchalakaniM, Zhao XL,Grzebieta R. Testson concrete filleddouble-skin(CHSouter and SHSinner) compositeshort columns under axial compression.Thin-Walled Structures 2002;40(5):415–41.
[3] Han LH, Tao Z, Huang H, Zhao XL. Concrete-filled double skin (SHS outer andCHS inner) steel tubular beam–columns. Thin-Walled Structures 2004;42(9):1329–55.
[4] Lin ML, Tsai KC. Behavior of double-skinned composite steel tubularcolumns subjected to combined axial and flexural loads. In: Proceedingsof the first international conference on steel & composite structures. 2001.p. 1145–52.
[5] Tao Z, Han LH. Behaviour of concrete-filled double skin rectangular steeltubular beam–columns. Journal of Constructional Steel Research 2006;62(7):631–46.
[6] Tao Z, Han LH, Zhao XL. Behaviour of concrete-filled double skin (CHS inner
and CHS outer) steel tubular stub columns and beam–columns. Journal of Constructional Steel Research 2004;60(8):1129–58.
[7] Tao Z, Han LH, Zhao XL. Tests on stub columns of concrete filled doubleskin rectangular hollow sections. In: Proceedings of the 4th internationalconference on thin-walled structures. 2004. p. 885–92.
[8] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwichtube under axial loading: Experiment. Journal of Structural Engineering ASCE1995;121(12):1806–14.
[9] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwichtube under axial loading: Analysis. Journal of Structural Engineering ASCE
1995;121(12):1815–21.[10] ZhaoXL, GrzebietaRH, Elchalakani M. Tests of concrete-filleddouble skin CHScomposite stub columns. Steel and Composite Structures—An International Journal 2002;2(2):129–46.
[11] Zhao XL, Han BK, Grzebieta RH. Plastic Mechanism analysis of concrete filleddouble skin (SHS inner and SHS outer) stub columns. Thin-Walled Structures2002;40(10):815–33.
[12] Zhao XL, Grzebieta RH, Elchalakani M. Tests of concrete-filled double skin and(SHS outer and CHS inner) composite stub columns. In: Proceedings of thethird international conference on advances in steel structures. Vol. 1. 2002.p. 567–74.
[13] Zhao XL, Grzebieta RH. Strength and ductility of concrete filled double skin(SHSinnerand SHSouter)tubes.Thin-WalledStructures2002;40(2):199–233.
[14] Hibbitt, Karlson & Sorensen Inc. ABAQUS/standard user’s manual, version6.4.1. Pawtucket (RI): Hibbitt, Karlsson, & Sorensen, Inc.; 2003.
[15] Han LH. Concrete-filled steel tubular structures-theory and practice. Beijing(China): Science Press; 2007 [in Chinese].
[16] Han LH, Yao GH, Zhao XL. Tests and calculations of hollow structural steel(HSS) stub columns filled with self-consolidating concrete (SCC). Journal of
Constructional Steel Research 2005;61(9):1241–69.[17] Han LH, Yao GH, Tao Z. Performance of concrete-filled thin-walled steel tubes
under pure torsion. Thin-Walled Structures 2007;45(1):24–36.[18] ACI 318-02.Buildingcode requirementsfor reinforced concrete andcommen-
tary. Farmington Hills (MI, Detroit, USA): American Concrete Institute; 2002.