FE modelling and fire resistance design of concrete filled double skin tubular columns

Journal of Constructional Steel Research 67 (2011) 1733–1748

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Journal of Constructional Steel Research

FE modelling and fire resistance design of concrete filled double skin tubular columns Hui Lu a, b, Xiao-Ling Zhao a,⁎, Lin-Hai Han c a b c

Department of Civil Engineering, Monash University, Melbourne, VIC 3800, Australia Pitt&Sherry, Melbourne, VIC 3025, Australia Department of Civil Engineering, Tsinghua University, Beijing, 100084, PR China

a r t i c l e

i n f o

Article history: Received 7 February 2011 Accepted 28 April 2011 Available online 8 June 2011 Keywords: Concrete-filled double skin tubes (CFDST) Columns Fire resistance Finite element analysis

a b s t r a c t Concrete filled double skin tubular columns (CFDST) have excellent structural behaviour. They have been used as transmission towers and have potential to be used as building columns and bridge piers. Performance of the CFDST columns under ambient temperature has been well studied, whereas fire resistance of such columns is still a major concern. A summary of a series of fire tests on CFDST columns conducted by the authors is briefly presented in the paper. A finite element numerical model is developed to analyse the fire behaviour of CFDST columns, namely thermal and structural responses under fire exposure. The model is verified by the test results and then used to perform parametric analyses. Parameters which have significant effect on the fire behaviour of CFDST columns are identified. Based on the parametric studies, suggestions on the fire resistance design of such columns are made. Practical design tables are derived for the fire resistance design of some typical CFDST columns. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Concrete filled double skin steel tubular (CFDST) columns consist of two concentrically placed steel hollow sections and the gap between the tubes filled with concrete. It is one kind of double skin composite construction [9,14–17,22,23]. CFDST has already been used in transmission towers and has potential to be used as building columns or bridge piers. In the last decade, a great deal of research has been conducted on the behaviour of CFDST columns as reviewed by Zhao and Han [26]. The behaviour of the CFDST columns under static and cyclic loading has been intensively investigated (e.g. [6,10,19,24,25]. However, research so far on CFDST has been focused on its behaviour under ambient temperature. There is a lack of understanding of fire resistance of such columns. This needs to be addressed before CFDST columns could be confidently used in building structures. There are four possible combinations of the outer and inner tubes in terms of square hollow section (SHS) and circular hollow section (CHS), i.e. SHS + SHS, CHS + CHS, SHS + CHS and CHS + SHS [6,20,27]. A series of standard fire tests on CFDST columns have been completed by the authors [12,13]. They are SHS + SHS and CHS + CHS combinations. Six CFDST columns and 16 CFDST stub columns were tested under standard fire condition. The thermal and structural responses of the columns, such as temperature distribution, failure modes and fire

⁎ Corresponding author. Tel.: + 61 3 99054972; fax: + 61 3 99054944. E-mail address: [email protected] (X.-L. Zhao). 0143-974X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.04.014

resistance were measured or observed. In the mean time, methodologies to improve the fire resistance of such columns were also investigated, i.e. the use of fibre reinforcement concrete and fire protection coating. The fire test result showed that CDFST columns can achieve better fire performance due to the interaction of concrete and steel tubes in the columns under elevated temperature and due to the low temperatures in the inner tube. Fire resistance of CFDST columns can be improved with the use of steel fibre reinforced concrete and fire protection coating. These tests also provided useful data to calibrate numerical models. Standard fire tests have been a traditional mean to study the fire behaviour of structural elements. Although fire testing is a straightforward method to investigate the fire behaviour of structural elements, fire tests are generally conducted on limited numbers of specimens under specific conditions due to their high cost and timeconsuming nature. Another methodology which has become wellaccepted in the study of the fire behaviour of structural elements is numerical modelling, as one of the obvious advantages of the numerical method is its cost-effectiveness. Numerical modelling can be used to investigate in details the fire behaviour of structural elements, such as the influence of a number of parameters on the fire resistance of the elements. Fire design guidelines and practical fire design methods can be further developed based on the numerical modelling. There are numerical models proposed to investigate the fire behaviour of concrete filled steel tubular columns [3]. Such modelling has resulted in developing of fire design guidelines and practical fire design methods for concrete filled steel tubular columns [5,7]. However, there is no numerical modelling and fire design guidelines for CFDST columns.

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Notation Cross-sectional area of outer steel tube As,out Ac,nominal Nominal cross-sectional area of concrete (i.e. the void area enclosed by the outer tube) B Width of square hollow section Bo Width of outer square hollow section Bi Width of inner square hollow section D Diameter of circular hollow section Do Diameter of outer circular hollow section Di Diameter of inner circular hollow section fc Cylinder strength of concrete fck Characteristic strength of concrete = 0.67 fc fy Yield stress of steel fyo Yield stress of outer steel tube fyi Yield stress of inner steel tube fy(T) Yield stress of steel at elevated temperature Gf Fracture energy of concrete Gft Fracture energy of concrete at elevated temperature hi Heat contact conduction coefficient hv Heat convective coefficient L Length of column Le Effective length of column q Heat flux Tc Temperature in concrete Tf Temperature of fire Ts Temperature in steel T0 Temperature of absolute zero t Wall thickness of steel hollow section to Wall thickness of outer steel hollow section ti Wall thickness of inner steel hollow section ε Strain εf Emissivity of fire εm Emissivity of steel surface

procedure in the package was utilised in the analysis. This procedure is used in cases where the stress/displacement solutions are dependent on a temperature field but there is no inverse dependency [1]. This procedure generally consists of two analysis steps. Thermal analysis step is conducted first to obtain the temperature distribution in the objects, followed by a stress/displacement analysis step in which temperature elevation in the objects is obtained from the thermal analysis step. The advantage of the sequentially-coupled analysis procedure is that it is more efficient in the calculation. There are some requirements in creating the finite element model so that temperatures obtained in the thermal analysis step can be transferred to the structural analysis step. Firstly, the type of elements should come from the same element families. In the current study, 3D solid elements were selected for concrete and shell elements were selected for the steel tubes in the CFDST columns. The 3D solid elements for thermal and structural analyses were DC3D8 and C3D8R respectively. The shell elements for thermal and structural analyses were DS4 and S4R respectively. Secondly, the time in the thermal analysis step should match the time in the structural analysis step so that the temperatures in both steps have the same meaning. In addition, the finite element mesh should be selected to be identical in two steps so that data can be transferred more efficiently between steps. The CFDST columns in this study use either CHS or SHS as inner and outer tubes, the columns are symmetrical in geometry. In addition, the fire temperature around the columns and load on the columns are also symmetrical. Therefore, only half of the columns were used in the modelling and the symmetrical boundary conditions were applied on the symmetric edges and surfaces. A typical finite element mesh for columns is shown in Fig. 1. In the thermal response analysis, only the columns were used in the modelling, whereas two rigid end plates were added to the model in the structural response analysis for the purpose of applying load and assigning column-end boundary conditions to the columns.

As;out ⋅fy;out ðT Þ Ac;no minal ⋅fck

ξ

ξ=

σ CFDST CFST SHS

Stefan Boltzmann constant or stress Concrete filled double skin steel tube Concrete filled steel tube Square hollow section

This paper presents a finite element numerical model to simulate the thermal and structural responses of CFDST columns subjected to fire conditions. A commercial finite element package, ABAQUS [1], is used for modelling. Fire testing results are utilised to verify the numerical model. Then, the verified model is used to perform parametric studies to identify major parameters which influence the fire behaviour of CFDST columns. Based on the results of the parametric study, suggestions on fire resistance design of CFDST columns are made, in terms of selecting parameters for CFDST columns to achieve certain fire resistance level. Practical design tables are developed for several typical CFDST columns that could be potentially used in multistorey buildings. The same approach can be adopted to develop more practical tables or diagrams for the fire resistance design of CFDST columns with wider range of geometry and material properties.

2.2. Thermal response analysis The thermal response of CFDST columns under fire exposure is actually a transient heat transfer process in which the heat of the fire transmits to the exterior surface of the outer tube and then conducts into the inner tubes. The numerical method used to solve this heat

(a) For thermal analysis

(b) For structural analysis P/2

Rigid end plates

2. Numerical model 2.1. Procedure of analysis A finite element analysis package, ABAQUS [1], was used to simulate the non-linear behaviour of the columns under both thermal and mechanical actions. A sequentially-coupled thermal-stress analysis

P/2 Fig. 1. Typical finite element mesh for CFDST column.

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

transfer process in ABAQUS includes procedures of spatial discretization, time integration and solution for non-linear equations. Heat is transmitted from the fire to the exterior surface of the outer tubes by convection and radiation. When the fire temperatures are available, the heat can be input through convection and radiation respectively in the ABAQUS package. Heat flux for convection and radiation can be expressed by the following equations: qconvection = hv ðTf −Ts Þ

ð1Þ 4

4

qradiation = εf εm σ½ðTf + T0 Þ −ðTs + T0 Þ 

ð2Þ

where, q is the input heat flux, Tf, Ts and T0 are the temperature of fire, exterior surface of outer tube and absolute zero respectively, hv is heat convective coefficient, εf and εm are emissivity of fire and steel surface, σ is the Stefan Boltzmann constant. For the standard fire condition, the following values are recommended by Eurocode 4 [4] for composite elements: hv = 25 (W/m 2K), εf = 0.8 and εm = 0.7. These values were used in the current analysis. Apart from the fire-exposed surface of the outer tubes, there is another boundary condition for CFDST which is at the inner surface of the section. The heat may radiate in the void within the inner tube when the temperature increases in the inner tube. However, for the CHS and SHS CFDST columns, there is no heat radiation in the inner void of the CFDST because the cross-sections are symmetrical. As heat transmitted through the interior surface of the inner tube, part of the heat is dissipated to rise the air temperature in the void. However, the amount of air in the void is very limited thus the dissipated heat can be ignored in the heat transfer modelling. Hence, this boundary condition is simulated by a free heat boundary condition, which means that no heat boundaries apply on the interior surface of the inner tube. In this study, the concrete thermal model and the steel thermal model proposed by Lie [8] were used. In addition, the effect of the moisture content on the thermal properties of concrete and the transformation of water from liquid to vapour was considered in the concrete thermal model [11]. In CFDST columns, the interface of steel and concrete is not in perfect contact when observed using a microscope. Hence, when heat transmits through the steel and concrete interface, there is a thermal resistance. A contact conductance concept in ABAQUS was used to simulate such thermal resistance which is expressed by the following equation. q = hi ðTs −Tc Þ

ð3Þ

where q is heat flux transmitting through interface, Ts and Tc is the temperature at the steel and concrete respectively and hi is a heat contact conduction coefficient. The authors have compared several available heat contact conduction coefficient models for steel– concrete interface [11]. It has been found that all the models are applicable for predicting the temperature in concrete filled steel tubular columns. A contact conduction coefficient of 100 (W/m 2K) [2] is used in the current study.

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increment, a series of iterations was performed to find an equilibrium solution. In order to implement structural response analysis, some related parameters needed to be established for the finite element model, such as material mechanical properties, interaction of concrete and steel tubes and boundary conditions. 2.3.1. Material mechanical properties Material properties required in the analysis generally include elastic and inelastic mechanical properties and thermal expansion coefficient. For concrete and steel, all these mechanical properties are temperature-dependent at elevated temperature. Elastic modulus and Poisson's ratio are two basic parameters related to the elastic mechanical properties of material in ABAQUS. A uni-axial stress– strain relationship, a yield function and a plastic flow rule to describe material behaviour under multi-axial stress state are required to represent the inelastic properties of material. In the ABAQUS package, different types of material models are available, such as models for classic metal and concrete. In these material models, the yield function and plastic flow rule have been predefined. Hence, inelastic material properties can be determined by selecting an appropriate material model and a uni-axial stress–strain relationship. The thermal expansion coefficient of steel and concrete used in this analysis is the model proposed by Lie [8]. The stress–strain relationship for steel used in the analysis is from Lie [8]. Elastic modulus of steel is taken as the initial secant elastic modulus in the stress–strain relationship. A classic metal material model in ABAQUS is chosen for steel. This model follows von Misses' yield function and associated plastic flow rule. A concrete damaged plasticity model in ABAQUS was used for the constitutive relationship of concrete. This model uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behaviour of concrete, and consists of a combination of non-associated multi-hardening plasticity and scalar (isotropic) damaged elasticity to describe the irreversible damage that occurs during the fracturing process [1]. Concrete has different behaviours and failure mechanisms under compression and tension. Therefore, the stress–strain relationship for concrete needs to be defined in compression and tension separately. It is well known that there is an interaction between the steel tubes and concrete in CFDST columns. Such interaction can lead the concrete to achieve better performance at ambient temperature. However, this interaction may weaken when the columns are under fire exposure due to the rapid degradation in the mechanical property of the outer tube at elevated temperature. The concrete compression stress–strain relationship in this study is a modification of that proposed by Han et al. [5] for CFST columns. The original stress–strain relationship was proposed to predict the structural response of CFST columns under fire exposure by using the fibre model method. The modified compressive stress–strain relationship for concrete is defined by the following equations: y = 2x−x2

ðx ≤ 1Þ x y= ð x N 1Þ βðx−1Þ4 + x

ð4Þ

2.3. Structure response analysis where; x = ε/ε0 and y = σ/σ0; The structural response analysis is divided into two sub-steps. In the first sub-step, the columns are loaded through two rigid endplates at ambient temperature. In the second sub-step, temperatures are read from the solutions of thermal analysis to simulate the action of fire while the load is maintained until the failure of the columns. The structural response analysis involves solving nonlinear equations. The full Newton method was chosen to solve the nonlinear equations to obtain the structural response of the columns. To solve nonlinear equations, each analysis sub-step was divided into increments. In each

8 h i 0 −9 3:21 > < fc = 1 + 1:986 × 10 ðT−20Þ σ0 = h i > : f 0 = 1 + 9:45 × 10−8 ðT−20Þ2:66 c



 fc0 ≤ 55MPa



 0 fc N 55MPa

  0 0:2 −6 ε0 = 1300 + 12:5fc + 800⋅ξ ⋅10   −4 −6 2 × 1:03 + 3:6 × 10 ⋅T + 4:22 × 10 T

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β=

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

8 <

ðT ≤ 100-C Þ ð100-C b T ≤ 400-C Þ ðT N 400-C Þ

0:1 6:45 × 10−4 T + 0:087 : 0:345

where, f c’ is the concrete cylinder strength at ambient temperature in MPa, α = 1.25dmax + 10, dmax is the maximum diameter of coarse aggregate in millimetre.

and β ≥ (0.0338 − 0.00125ξ) ⋅ f c' 0.5. In the equations, ξ is a parameter relating to the interaction of steel tubes and concrete. It is defined as: ξ=

As;out ⋅fy;out ðT Þ Ac;nominal ⋅fck

ð5Þ

where, As,out is the cross-sectional area of outer steel tube; Ac,nominal is the nominal cross-sectional area of concrete which equals to the void area enclosed by the outer tube; fck is the characteristic strength of concrete which equals to 0.67f c’ and fy(T) is defined as:

fy ðT Þ =

8 > < > :

ðT b 200 -C Þ

fy 0:91fy 1 + 6:0 × 10

−17

⋅ðT−10Þ

6

ðT ≥ 200 -C Þ

:

ð6Þ

There are several options in the concrete damaged plasticity model to define the tensile stress–strain relationship of concrete. A traditional tensile stress–strain relationship for concrete may cause convergent problems in the finite element model if cracks occur in the concrete. The concept of using fracture energy to define the tensile behaviour of concrete is a better solution to achieve a convergent result. Therefore, the tensile property of concrete at elevated temperature is defined as a stress and fracture energy relationship provided in the concrete damaged plasticity model. The fracture energy of concrete at elevated temperature is defined as:   −4 −6 2 Gft = Gf ⋅ 0:2882 + 8 × 10 T−1 × 10 T

ð7Þ

where Gf is the fracture energy of concrete at ambient temperature which is calculated by the following equation (N/mm):  Gf = α⋅

fc0 10

0:7 ⋅2:5 × 10

−3

ð8Þ

2.3.2. Steel and concrete interface properties In finite element modelling, the steel tubes and concrete are modelled as individual parts. Although steel tubes and concrete have geometry interfaces in the finite element model, they are independent parts and deform independently unless the interaction between tubes and concrete is defined. In the actual situation, interaction between tubes and concrete has been recognised as a factor which significantly influences the behaviour of the columns. Hence, interaction between tubes and concrete needs to be considered in the modelling. An approach of contact interaction in ABAQUS [1] is used to simulate the interaction of tubes and concrete in this study. The surfaces of concrete and tube at the interface are defined as a contact pair, one as master surface and the other as slave surface. The master and slave surfaces may contact each other or remain separate. A nodeto-surface formulation is used in the simulation. The contact condition is established if nodes in the slave surface effectively interact with a group of points in the master surface. The mechanical properties of the contact pair are defined along normal and tangential directions to the interface respectively. “Hard contact” was selected for the normal directional behaviour. When a contact pair is in contact, there is pressure between the master and slave surfaces, whereas two contact surfaces separate as the pressure comes to zero. A Coulomb friction model was used to simulate the tangential behaviour of the contact pair. When the shear stress in the interface is smaller than a certain value or the bond strength between surfaces, no slipping occurs, otherwise slipping occurs between surfaces. When two contact surfaces have relative slipping, there is a frictional or shear stress between surfaces. This stress is determined by the frictional coefficient and the pressure between surfaces. Therefore, a friction coefficient and the bond strength between surfaces are two parameters to determine the mechanical behaviour along the tangential direction. A friction coefficient of 0.2 has been found to be satisfactory in analysing the fire behaviour of CFST columns [3]. In the current study, this value was adopted. The bond between tubes and concrete was ignored, based

Table 1 Parameters of CFDST columns in fire tests. No

Label

Outer tube Do × to or Bo × to mm

Inner tube Di × ti or Bi × ti mm

Load kN

Load eccentricity mm

Fire protection mm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

CC1 CC2 CC3 SC1 SS1 SS2 C1-C3-SCC2 C1-C3-SCC2SF C1-C3-SCC2SFP C2-C4-SCC2 C2-C4-SCC2SF C2-C4-SCC2SFP S1-S3-SCC2 S1-S3-SCC2SF S1-S3-SCC2SFP S2-S4-SCC2 S2-S4-SCC2SF S2-S4-SCC2SFP C2-C4-SCC1 C2-C4-SCC1SF S2-S4-SCC1 S2-S4-SCC1SF

CHS 300 × 5 CHS 300 × 5 CHS 300 × 5 SHS 280 × 5 SHS 280 × 5 SHS 280 × 5 CHS 406 × 8 CHS 406 × 8 CHS 406 × 8 CHS 291.1 × 5 CHS 291.1 × 5 CHS 291.1 × 5 SHS 350 × 8 SHS 350 × 8 SHS 350 × 8 SHS 200 × 6 SHS 200 × 6 SHS 200 × 6 CHS 291.1 × 5 CHS 291.1 × 5 SHS 200 × 6 SHS 200 × 6

CHS 125 × 5 CHS 125 × 5 CHS 225 × 5 CHS 140 × 5 SHS 140 × 5 SHS 140 × 5 CHS 165.1 × 3 CHS 165.1 × 3 CHS 165.1 × 3 CHS 101.6 × 3.2 CHS 101.6 × 3.2 CHS 101.6 × 3.2 SHS 150 × 5 SHS 150 × 5 SHS 150 × 5 SHS 89 × 3.5 SHS 89 × 3.5 SHS 89 × 3.5 CHS 101.6 × 3.2 CHS 101.6 × 3.2 SHS 89 × 3.5 SHS 89 × 3.5

1810 570 2000 2050 1200 1100 4100 4000 3400 1821 1785 1821 4420 4420 4420 1900 1860 1900 1923 1964 2567 2615

0 75 0 0 75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

10 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Note: Tests No. 1 to No. 6 were reported in Lu et al. [12], whereas Tests No. 7 to No. 22 were reported in Lu et al. [13].

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

on the consideration that bond strength in the interface may degrade quickly at elevated temperatures. From the above definition of contact properties, it is clear that concrete confinement produced by steel tubes is simulated by the normal contact property, whereas the tangential contact behaviour simulates the transmission of shear force on the surfaces. 2.3.3. Boundary conditions and initial eccentricity As shown in Fig. 1, only half of an actual CFDST column is used to create a finite element model. There are two rigid end plates, on the top and bottom of the column, which are used to apply load

(a) CC1

and assign column-end boundary conditions on the column. Fixed, pinned or other constraining boundary conditions can be applied on the end plates to simulate the actual boundary conditions. In addition to column-end boundary conditions, symmetry boundary conditions need to be defined on the symmetry faces and edges. During analysis of the behaviour of columns under axial load, imperfection in the straightness of the columns is one of the parameters which should be considered in the modelling. Ding and Wang [3] conducted a sensitive analysis to investigate the initial straightness imperfection on the fire behaviour of CFST columns. The initial straightness imperfection was converted into load initial eccentricity at

(b) CC2 1000

800

d=0

Temperature (oC)

Temperature (oC)

1000

d=83 mm

600 400 200

800 600

0

400 200

60

120

180

240

300

0

30

60

Time (min)

1000

Temperature (oC)

Temperature (oC)

120

(d) SC1

1000

d=16 mm

800 600

d=0

400 200 0

800

d=33 mm

d=65 mm

600 400 200 0

0

20

40

60

0

30

Time (min)

60

90

120

Time (min)

(e) SS1

(f) SS2

1200

1200

d=0

1000

Temperature (oC)

Temperature (oC)

90

Time (min)

(c) CC3

800 600 400

d=33 mm

200

d=65 mm

1000

d=33 mm

800 600 400 200 0

0

30

60

90

120

150

180

0

30

Time (min)

60

90

120

150

180

Time (min)

(g) C1-C3-SCC2

(h) C1-C3- SCC2SF 1200

d=0

1000

d=43 mm

800

d=86 mm

600 400 200 0 0

30

Time (min)

60

90

Temperature (oC)

1200

Temperature (oC)

d=83 mm

d=41 mm

0

0

0

1737

d=0

1000 800

d=43 mm

600

d=86 mm

400 200 0

0

30

60

90

120

Time (min)

Fig. 2. Comparison of predicted and measured temperatures in CFDST columns.

150

180

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H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(i) C1-C3- SCC2SFP

(j) C2-C4- SCC2 1000

d=0

1000

Temperature (oC)

Temperature (oC)

1200

800

d=43 mm

600

d=86 mm

400 200

800 600

d=54 mm

400 200 0

0 0

30

60

90

120

150

180

0

20

Time (min)

1000

800

d=27 mm

d=0

600

d=54 mm

400 200

Temperature (oC)

Temperature (oC)

60

(l) C2-C4- SCC2SFP

1000

800

d=27 mm

d=0

600

d=54 mm

400 200

0

0 0

20

40

60

0

20

Time (min)

40

60

Time (min)

(m) S1-S3- SCC2

(n) S1-S3- SCC2SF 1200

d=0

1000

d=46 mm

800

d=92 mm

600 400 200

Temperature (oC)

1200

Temperature (oC)

40

Time (min)

(k) C2-C4- SCC2SF

d=46 mm

1000

d=0

800 600

d=92 mm

400 200

0

0 30

0

60

90

0

120

30

Time (min)

60

90

120

150

180

Time (min)

(o) S1-S3- SCC2SFP

(p) S2-S4- SCC2 1000

d=46 mm

d=0

1000 800

d=92 mm

600 400 200

Temperature (oC)

1200

Temperature (oC)

d=27 mm

d=0

d=50 mm 800

d=0

600

d=99 mm

400 200

0

0 0

30

60

90

120

0

Time (min)

20

40

60

Time (min) Fig. 2 (continued).

the ends of the columns. This study showed that initial eccentricity has a minimal influence on the fire behaviour of the CFST columns when the initial eccentricity varies from L/2000 to 3L/1000, where L is the length of the columns, and an initial eccentricity of L/1000 was used in the analysis. In the current study, the initial eccentricity was also taken as L/1000. 2.4. Verification of the model Fire test results on six CFDST columns and 16 stub CFDST columns [12,13] are used to verify the above proposed finite element model.

The parameters of these columns are shown in Table 1 and details of the fire tests can be found in Lu et al. [12,13]. The predicted temperatures, axial deformation, failure modes and fire resistance are compared to those obtained from the fire tests to verify the finite element model. 2.4.1. Temperatures Comparisons of the predicted temperatures to the temperatures obtained from the fire tests are shown in Figs. 2. In these figures, the solid lines represent the temperatures measured in the fire tests and dashed lines represent the predicted temperatures.

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(q) S2-S4- SCC2SF

(r) S2-S4- SCC2SFP

Temperature (oC)

d=50 mm

800

d=0

600

d=99 mm

400 200

Temperature (oC)

1000

1000

d=50 mm 800

d=0

600

d=99 mm

400 200 0

0 0

20

40

60

0

20

Time (min)

60

(t) C2-C4- SCC1SF 800

d=27 mm d=0

600

d=54 mm

400 200

Temperature (oC)

800

Temperature (oC)

40

Time (min)

(s) C2-C4- SCC1

d=27 mm d=0

600

d=54 mm

400 200

0

0 0

10

20

30

0

10

Time (min)

20

30

Time (min)

(u) S2-S4- SCC1

(v) S2-S4- SCC1SF 800

d=0

d=50 mm

600

d=90 mm

400 200

Temperature (oC)

800

Temperature (oC)

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d=0

d=50 mm

600

d=90 mm

400 200

0

0 0

10

20

0

30

Time (min)

10

20

30

Time (min) Fig. 2 (continued).

As can be seen, the predicted temperatures are generally consistent with the temperatures measured in the fire tests. It should be noted that the thermal conductivity of the insulation coating increased to 2.5 times of its original value after 100 min of fire exposure being used to predict the temperature of SS2 shown in the figure to consider the effect of local buckling of the outer SHS on the integrity of the fire protection system. 2.4.2. Axial deformations The comparison of the predicted and measured axial deformation for the CFDST columns is shown in Fig. 3. As can be seen, there is generally a well correlation between the predicted axial deformation and the measured values. 2.4.3. Failure models A comparison of the predicted and observed failure modes of SS2 (as an example) when the column reaches fire endurance and the corresponding failure mode of the outer and inner tubes are shown in Fig. 4(a) to (c). There is an obvious lateral deflection in the column. This suggests that the column failed due to the combination of local and overall buckling. Local buckling occurred in the outer tube and the most severe local buckling appeared at the position where maximum lateral deflection occurred. Local buckling also appeared in the inner tube at the position where maximum lateral deflection was present. It

shows that the predicted failure mode matches well with the observed failure mode. The observed failure mode of a CFDST stub column, C1-C3SCC2SF (as an example), is further used to compare to the predicted failure mode as shown in Fig. 5. As can be seen, there is an obvious outward bulge in the outer tube. However, there is no obvious lateral deflection in the column. This is a typical compression failure mode for CFDST stub columns. The outer tube is forced to outward bulging because of the presence of the concrete. In contrast, the inner tube is forced to inward bulging by the concrete. Again, the finite element model can well predict the failure modes of the CFDST stub columns. It should be noted that the predicted failure modes are under hot condition without cooling, while the observed failure modes are after specimens have cooled down. During the experiments, failure modes of the steel tube and the overall columns before and after cooling were both observed. The difference in the failure modes under these two stages is not significant. Hence, it is reasonable to use the failure modes of steel and overall columns after cooling in the experiments to compare to the predicted failure modes under hot condition. 2.4.4. Fire resistance The comparison between the predicted and measured fire endurance of the CFDST columns is shown in Fig. 6. It can be seen that

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10

Deformation (mm)

(b) CC2

10

Deformation (mm)

(a) CC1 0 -10 -20 -30 -40

Test Predicted

-50 -60

0

60

120

180

240

0 -10 -20 -30 -40 -60

300

Test Predicted

-50 0

30

60

Time (min)

10

Deformation (mm)

(d) SC1

10

Deformation (mm)

(c) CC3 0 -10 -20 -30 -40

Test Predicted

-50 -60

0

20

40

-40

0

30

60

Time (min)

Deformation (mm)

Deformation (mm)

10

-10 -20 -30

Test Predicted 60

90

120

0 -10 -20 -30 -40 -60

150

Test Predicted

-50 0

60

120

Time (min)

Time (min)

(g) C1-C3- SCC2

(h) C1-C3- SCC2SF 10

Deformation (mm)

Deformation (mm)

10

Test Predicted

0 -10 -20 -30

0

30

60

90

120

0 -10 -20 -30

150

Test Predicted 0

30

60

Time (min)

120

150

(j) C2-C4- SCC2

10

10

Deformation (mm)

Deformation (mm)

90

Time (min)

(i) C1-C3- SCC2SFP 0 -10 -20 -30

240

Test Predicted

-50 -60

60

0

30

180

-30

(f) SS2

0

120

-20

10

-60

90

0

(e) SS1

-50

120

-10

Time (min)

-40

90

Time (min)

Test Predicted 0

30

60

90

Time (min)

120

150

Test Predicted

0 -10 -20 -30

0

20

40

Time (min)

Fig. 3. Comparison of predicted and measured deformation in CFDST columns.

60

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(k) C2-C4- SCC2SF

(l) C2-C4- SCC2SFP 10

Deformation (mm)

Deformation (mm)

10 0 -10 -20 -30

Test Predicted 0

20

40

-10 -20 -30

60

Test Predicted

0

0

20

Time (min)

0

Deformation (mm)

Deformation (mm)

10

Test Predicted

-10 -20

30

60

90

120

-10 -20 -30

150

Test Predicted

0

0

30

60

Time (min)

Deformation (mm)

Deformation (mm)

0 -10 -20

60

90

120

0 -10 -20 -30

150

Test Predicted 0

Time (min)

40

60

40

60

(r) S2-S4- SCC2SFP

10

10

Deformation (mm)

Deformation (mm)

20

Time (min)

(q) S2-S4- SCC2SF 0 -10 -20 -30

150

10

Test Predicted

30

120

(p) S2-S4- SCC2

10

0

90

Time (min)

(o) S1-S3- SCC2SFP

-30

60

(n) S1-S3- SCC2SF

10

0

40

Time (min)

(m) S1-S3- SCC2

-30

1741

Test Predicted 0

20

40

60

0 -10 -20 -30

Test Predicted 0

Time (min)

20

Time (min) Fig. 3 (continued).

the finite element model can well estimate the fire endurance of the CFDST columns. 3. Parameters influencing fire resistance of CFDST columns The above proposed finite element model is used to analyse the effect of parameters on the fire resistance of CFDST columns. Some parameters have insignificant influence on the fire resistance of the columns, whereas some parameters have moderate or significant influence on the fire resistance of the columns which are summarised as follows. Parameters of CFDST columns which are used in the parametric study are shown in Table 2.

3.1. Load level The effect of load level on fire resistance is shown in Fig. 7. Load level has a significant influence on the fire resistance of CFDST columns. Fire resistance decreases dramatically as the load level increases. Such influence is more pronounced when the load level is smaller than 0.4. Load level represents the ratio of the load applied in fire test to the ultimate capacity at ambient temperature. Columns with a higher load level obviously possess less remaining capacity up to the ultimate capacity. The higher the stress level of the components, the less fire exposure time is required to allow the material strength to deteriorate

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H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(s) C2-C4- SCC1

(t) C2-C4- SCC1SF 10

Test Predicted

0

Deformation (mm)

Deformation (mm)

10

-10 -20 -30

0

15

30

-10 -20 -30

45

Test Predicted

0

0

15

Time (min)

10

Deformation (mm)

Deformation (mm)

10 0 -10 -20

Test Predicted 0

10

45

(v) S2-S4- SCC1SF

(u) S2-S4- SCC1

-30

30

Time (min)

20

30

Test Predicted

0 -10 -20 -30

0

10

Time (min)

20

30

Time (min) Fig. 3 (continued).

to the stress level. Hence, the fire resistance of the columns decreases drastically when the load ratio increases. 3.2. Capacities of inner and outer steel tubes The capacity of the inner and outer tubes depends on the crosssectional area of the tubes and the yield stress of the tubes. Here, variation in the tube capacity is achieved by changes in the tube wall thickness and yield stress of the tube. When studying the effect of the inner tube, the load level, outer steel tubes and column length are kept constant. Similarly when studying the effect of the outer tube, the load level, inner steel tube and column length are kept constant. The effect of inner tube capacity on fire resistance is illustrated in Fig. 8. In the figure, the inner tube capacity increases from left to right. An increase in the capacity of the inner tube can lead to an increase in the fire resistance of the columns. The fire resistance is more sensitive to the thickness increase than to yield stress increase. As the inner steel tubes in CFDST columns are well insulated by the concrete, temperatures in the inner steel tubes are generally quite low even when the columns reach fire endurance. Therefore, the inner steel tubes fail due to the yield or/and local buckling of the steel tubes with minor influence of elevated temperatures. Inner steel tubes offer an extra load transfer path for CFDST columns under fire exposure in addition to concrete. Hence, the capacity of inner steel tube in a CFDST column has a significant influence on the fire resistance of the column. Fig. 9 shows the effect of outer tube capacity on the fire resistance of the CFDST columns. Similarly, the outer tube capacity increases from left to right in the figure. Generally, an increase in the outer tube capacity (while the load level and the inner tube are kept constant) leads to a decrease in the fire resistance of the CFDST columns. However, when the tube wall is thick enough, an increase in the outer tube capacity can result in an increase in the fire resistance of the columns. It is clear that fire resistance increase is more sensitive to yield stress than to tube thickness. 3.3. Fire protection The comparison of fire resistance between unprotected and fire insulated CFDST columns is shown in Fig. 10. The fire resistance of

the counterpart CFST columns is also shown in the figure for comparison. The fire protection coating is a cement mortar based material incorporating light weight filler. The thermal properties of the insulation material are shown in Table 3. The thickness of the fire protection coating is 5 mm. As shown in the figure, fire insulation is a very effective way to enhance the fire resistance of CFDST columns even when the fire protection coating is only 5 mm. However, the extent of the enhancement in the fire resistance for CFDST columns is found more than that for the CFST columns with the same outer diameter/width and thickness. 3.4. Effective length It is well-known that column capacity at ambient temperature depends on the geometrical properties (e.g. length and radius of gyration) and the boundary conditions of the columns. The effective length is commonly used to represent such conditions. This concept is also used here for CFDST columns under fire exposure to account for the influence of the boundary conditions on the capacity of the columns at elevated temperature. The columns used for the current parametric studies are all pinned boundary conditions, i.e. the effective length is the same as the column length. Therefore, the influence of slenderness on the fire resistance of the columns is equivalent to the influence of column length to diameter (or width) ratio. Fig. 11 shows the relationship between fire resistance and length to diameter or width ratio. As shown in the figure, fire resistance of CFDST columns decreases with the increase in column slenderness. When the length to diameter (or width) ratio is less than five for CHS CFDST (or four for SHS CFDST), the effect of slenderness on the fire resistance is minimal. However, such effect becomes pronounced when the length to diameter (or width) ratio is greater than that value. Hence column slenderness has a significant effect on the fire resistance of slender CFDST columns. Variation in the slenderness or length of the CFDST columns does not affect the thermal response of the columns. In other words, degradation in the strength and stiffness of the concrete and steel in the columns due to elevated temperatures is not affected by variation

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(a) Comparison of failure mode of the overall column

1743

the columns are concentrically loaded in this study, an initial straightness imperfection has been considered in the modelling. The initial straightness imperfection is transferred into an initial load eccentricity at both ends of the columns. This value is taken as the straightness tolerance in AS 4100 [18], the larger value of L/1000 or 3 mm, where L is the length of the column in millimetres. Initial eccentricity induced by straightness imperfection is proportional to the length of the columns as the length of the columns is over 3 m. Initial bowing accompanied by the second order effect in the columns results in a decrease in the capacity or fire resistance of the columns at elevated temperature as the slenderness of the columns increases. 3.5. Perimeter of outer steel tube

(b) Comparison of failure mode of the outer tube

The effect of outer tube perimeter on the fire resistance of the CFDST columns is shown in Fig. 12. It seems that the increase in the outer tube perimeter leads to a moderate increase in the fire resistance of the columns. Variation in the outer tube perimeter has little influence on the thermal response of the columns [11]. However, such variation affects the structural response of the columns. Fig. 13 shows the effect of the outer tube perimeter on the ratios of cross-sectional area of each component to total cross-sectional area of the RHS columns defined in Fig. 12(b). As shown in the figure, an increase in the outer tube perimeter leads to a decrease in the outer tube area and an increase in the inner tube area. Thus, increase in the outer tube perimeter is beneficial to the structural response and finally the fire resistance of the columns. 3.6. Use of steel fibre reinforced concrete

(c) Comparison of failure mode of the inner tube

The comparison of fire resistance between normal and steel fibre reinforced concrete-filled double skin tubular columns is shown in Fig. 14. CFDST columns filled with steel fibre reinforced concrete can achieve a higher fire resistance compared to the counterpart CFDST columns filled with normal concrete. The difference in the fire resistance of the columns becomes larger as the load level decreases. The fire resistance of the columns filled with steel fibre reinforced concrete increases by 20 to 30% compared to those filled with normal concrete. The influence of steel fibre on the concrete mechanical property manifests only at the post-peak stress stage. The steel fibre in the concrete can effectively prevent cracking of the concrete at postpeak stress stage. Thus, the descending branch of the stress–strain relationship curve declines less suddenly for steel fibre reinforced concrete compared to normal concrete. Steel fibre reinforced concrete possesses higher capacity than normal concrete in the post-peak stress stage. Hence, steel fibre reinforced concrete can make a greater contribution than normal concrete to retain the capacity of CFDST columns at elevated temperature. Therefore, CFDST columns filled with steel fibre reinforced concrete can achieve higher fire resistance. 4. Suggestions for fire resistance design of CFDST columns

Fig. 4. Comparison of observed and predicted failure modes of SS2.

Parameters which have significant influence on the fire resistance of CFDST columns have been identified in the previous section. Better fire performance of CFDST columns can be achieved by appropriately selecting these parameters. Suggestions to enable CFDST columns to achieve better fire resistance are made as follows:

in the slenderness. For slender CFDST columns, column capacities are determined by the critical buckling load of the columns. Geometrical non-linearity, i.e. the second order effect, is an important factor influencing the buckling load of slender columns. The second order effect is more pronounced when the slenderness increases. Although

• The inner steel tube is the most important component in a CFDST column contributing to the fire performance of the column. Increasing the capacity of the inner tubes is an effective way to increase the fire resistance of CFDST columns. • The outer steel tube is the most vulnerable component in CFDST columns under fire exposure due to the direct fire exposure of the tube. Reducing the capacity of the outer steel tubes can benefit the

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H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(a) Comparison of failure mode of the outer tube

(b) Comparison of failure mode of the inner tube

Fig. 5. Comparison of observed and predicted failure mode of C1-C3-SCC2SF.

fire performance of the columns. This can be achieved by the use of steel tubes with lower yield stress and smaller wall thickness. • For CFDST columns without fire protection, limiting the load level at a low value is the most effective way to increase the fire resistance of the columns. CFDST columns without fire protection may achieve 1 to 2 h of fire resistance when an appropriate load level is selected. • For CFDST columns with higher load level or requiring more than 2 h of fire resistance, steel fibre concrete or fire protection should be used. The fire resistance of CFDST can be increased by 20% to 30% when steel fibre concrete is used to replace plain concrete in CFDST. The fire resistance of CFDST with fire protection can reach 3 h or more depending on the thickness of the fire protection system. • The concrete in CFDST columns should be appropriately determined to delay as long as possible the time to reach the critical temperature in the inner tube. From the practical point of view, the minimum

Predicted fire endurance (min)

300

CFDST columns CFDST stub columns

250

thickness of the concrete should be greater than 50 mm so that the concrete can be conveniently placed into the space between the tubes. • Drain holes must be provided in the outer steel tube to prevent bursting of the steel tubes when steam pressure is generated as water in the concrete transfers into vapour at elevated temperature. 5. Practical design table for fire resistance of some typical CFDST columns The principles described in Section 4 are used to derive practical design tables for some typical CFDST columns which could be potentially used in multi-storey buildings. It should be pointed out that the design tables are developed for CFDST columns under standard fire conditions. The cross-section size of the outer steel tubes is selected as 400 mm width for SHS and 500 mm in diameter for CHS. Columns with cross-section sizes in this range are commonly used in multi-storey buildings. A column effective length of 4 m and concrete strength of 40 MPa are selected for the columns. These are typical values for columns in buildings. 5.1. Outer steel tube

200

As the outer steel tube is the component making the least contribution to the fire resistance of CFDST columns, values for tube thickness and yield stress should be as low as possible. Based on this consideration, the yield stress of the outer steel tube is chosen as

150

100

50

Table 2 Parameters of CFDST columns.

0 0

50

100

150

200

250

300

Measured fire endurance (min) Fig. 6. Comparison of predicted and measured fire resistance.

CFDST

Outer tube mm

Inner tube mm

fy MPa

f’c MPa

L m

SHS CHS

700 × 25 700 × 25

300 × 20 300 × 20

350 350

40 40

4.2 4.2

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

500

(a) CHS CFDST

CFDST without protection CFDST with protection CFST with protection

240 400

Fire resistance (min)

Fire resistance (min)

D o × t o=700 × 25, D i × t i =300 × 20, f yo =350, f yi =350, f c =40, L =4200

180

120

300 200 100 0

60

Fig. 10. Effect of fire insulation on fire resistance.

0

0.2

0.4

0.6

0.8

1

Load level

Table 3 Thermal properties of insulation material.

(b) SHS CFDST 240

B o × t o=700 × 25, B i × t i =300 × 20, Fire resistance (min)

SHS

CHS

0

f yo =350, f yi =350, f c =40, L =4200

180

Density (kg/m3)

Conductivity (W/mK)

Specific heat (J/kgK)

500

0.0907

1.047 × 103

250 MPa. The wall thickness of the outer steel tube can be determined by the minimum allowable value to prevent local buckling at ambient temperature as required in design codes for composite columns. Here, Eurocode 4 [4] is used as an example to determine the minimum wall

120

60

(a) CHS CFDST

0 0

0.2

0.4

0.6

0.8

150

1

D o × t o=700 × 25, D i × t i =300 × 20,

Fig. 7. Effect of load level on fire resistance.

150 t=10, fy=350 120 90

t=20, fy=350 t=20, fy=700

Fire resistance (min)

Load level

Fire resistance (min)

1745

f yo =350, f yi =350, f c =40

120

90

60

30

t=70, fy=350

60 0 30

0

3

6

9

12

15

L/Do

0 CHS column

SHS column

(b) SHS CFDST 150

B o × t o=700 × 25, B i × t i =300 × 20,

Fig. 8. Effect of inner tube capacity on fire resistance.

f yo =350, f yi =350, f c =40

Fire resistance (min)

120

Fire resistance (min)

150 120 90

t=10, fy=350 t=25, fy=350 t=25, fy=700 t=100, fy=350

60

90

60

30

30 0 0

0 CHS column

SHS column

Fig. 9. Effect of outer tube capacity on fire resistance.

3

6

9

12

L/Bo Fig. 11. Effect of column slenderness on fire resistance.

15

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H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

(a) CHS CFDST

(a) Load level=0.5

150

180

Fire resistance (min)

Fire resistance (min)

t o= 25, t i = 20, f yo =350, f yi =350, f c =40, L=4200

120

90

60

150 120

NC SFC

90 60 30 0 CHS

30

SHS

(b) Load level=0.3 180

0 1000

2000

3000

4000

5000

Fire resistance (min)

0

Outer tube perimeter (mm)

(b) SHS CFDST 150

t o= 25, t i = 20, f yo =350, f yi =350, f c =40, L=4200

Fire resistance (min)

120

NC SFC

120 90 60 30 0 CHS

90

SHS

Fig. 14. Effect of steel fibre concrete on fire resistance.

60

where fy is the yield stress in MPa. The geometric and mechanical properties of the outer steel tubes so determined are listed in Table 4.

30

5.2. Inner steel tube

0 0

1000

2000

3000

4000

5000

Outer tube perimeter (mm) Fig. 12. Effect of outer tube perimeter on fire resistance.

thickness of the outer tubes. The maximum diameter to wall thickness ratio is as follows: sffiffiffiffiffiffiffiffiffi 235 ðSHSÞ fy

ð9Þ

sffiffiffiffiffiffiffiffiffi 235 D=t = 90 ðCHSÞ fy

ð10Þ

B=t = 52

Outer tube

Concrete

Inner tube

1.00

Cross-sectional ratio

150

As described in Section 4 an inner tube with higher yield stress and greater wall thickness should be selected to enable the columns to achieve better fire resistance performance. Hence, the yield stress of the inner steel tube is chosen as 450 MPa, which is considered as high strength structural steel in engineering practise. When selecting an appropriate wall thickness for the inner tube, one factor which should be considered is the size of the tube. The diameter (width)-to-wall thickness of the tube should be within a practical range. The crosssection size of the inner tube must be at least 100 mm smaller than that of the outer tube so that the concrete thickness is greater than 50 mm. Hence, the cross-section sizes of the inner tube should be less than 400 and 300 mm as the sizes of the outer tube are 500 and 400 mm respectively. Considering the possible cross-section of the tubes, the wall thickness of the inner tube is chosen as 20 mm. The diameter (width) to wall thickness ratio is about 15 to 20, which is a typical value in engineering applications. 5.3. Concrete thickness

0.80

It was suggested in Section 4 that a minimum concrete thickness of 50 mm be used due to construction requirement. A sufficient concrete thickness offers insulation for the inner steel tube to maintain its

0.60 0.40

Table 4 Parameters of outer steel tube.

0.20

Profile of outer tube

Outer tube

fy MPa

CHS CHS SHS SHS

500 × 6 400 × 5 500 × 10 400 × 5

250 250 250 250

0.00 0

1000

2000

3000

4000

Outer tube perimeter (mm) Fig. 13. Effect of outer tube perimeter cross-sectional area ratio.

5000

H. Lu et al. / Journal of Constructional Steel Research 67 (2011) 1733–1748

temperature much lower than the critical temperature even after a certain period of fire exposure (e.g. 2 h). It can be proven that a concrete thickness of about 100 mm to 125 mm is sufficient for columns to achieve this goal. Therefore, the diameters (width) of the inner tubes are selected as 250 and 200 mm respectively. The geometric and mechanical properties of the columns and the temperatures in the inner tube after 2 h of fire exposure are listed in Table 5. It is clear that the temperature in the inner tube is below 200 °C after 2 h of fire exposure. 5.4. Use of fibre reinforced concrete and fire protection coating The required fire resistance of columns in buildings generally ranges from 1 h to 3 h. CFDST columns filled with plain concrete may not meet this requirement in some circumstances. The use of steelfibre reinforced concrete or fire protection is one of the options to improve the fire performance of the columns. The use of steel-fibre reinforced concrete seems a more attractive solution than the use of fire protection systems as it does not alter the appearance of the columns. However, the extent of the enhancement which steel-fibre reinforced concrete can offer for CFDST columns is generally about 20 to 30% compared to the plain concrete filled CFDST. Therefore, fire protection is necessary when load level is high or high fire resistance performance is needed. 5.5. Practical design tables The CFDST columns shown in Table 5 are selected as typical examples to derive practical design tables to achieve a fire resistance between 1 h and 3 h. The proposed finite element model is used to predict the fire resistance of the columns. The data from the calculation are used to create practical design tables as shown in Table 6. In the table, the load level varies from 0.3 to 0.7 which covers the load levels recommended for steel–concrete composite columns by Twile et al. [21]. Plain concrete is the first option for the columns to achieve a certain level of fire resistance. If the plain concrete filled CFDST columns cannot achieve a certain level of fire resistance, steel fibre reinforced concrete is chosen as the second option. Fire protection is used as the third option to enable the columns to achieve the required fire resistance. The material properties of the fire protection system used here is the same as those in Table 3. The three options are denoted “A” for plain concrete filled CFDST, “B” for fibre reinforced concrete filled CFDST and “C-xx” for plain concrete filled CFDST with fire protection. The digits “xx” in “C-xx” represent the thickness of the fire protection coating in millimetres. Here are some observations from Table 6. Plain concrete filled CFDST columns with an outer tube width (or diameter) of 400 to 500 mm can achieve a fire resistance up to 3 h if the load level is limited to a low value, i.e. 0.3. The use of steel fibre reinforced concrete to replace plain concrete in CFDST can lead to an increase in the fire resistance of the columns by about 0.5 h. Fire protection coating is the most effective way to further enhance the fire resistance performance of the columns. It should be noted that to achieve 3 h of fire resistance the fire protection thickness (5 to 15 mm) for CFDST columns is much less than that (20 to 40 mm) for steel tubular columns alone.

Table 5 Geometric and mechanical properties of the columns. CFDST profile

Outer tube mm

Inner tube mm

fyo MPa

fyi MPa

f’c MPa

Le m

Temperature °C

CHS + CHS CHS + CHS SHS + SHS SHS + SHS

500 × 6 400 × 5 500 × 10 400 × 8

250 × 20 200 × 20 250 × 20 200 × 20

250 250 250 250

450 450 450 450

40 40 40 40

4 4 4 4

108 196 102 173

1747

Table 6 Fire resistance tables for CFDST columns. Load level

FR 60 (min)

90 (min)

120 (min)

150 (min)

180 (min)

(a) CHS 500 × 6 + 250 × 20 0.3 A 0.5 A 0.7 C-5

A B C-5

A C-5 C-5

A C-5 C-10

A C-5 C-10

(b) CHS 400 × 5 + 200 × 20 0.3 A 0.5 B 0.7 C-5

A C-5 C-10

A C-5 C-10

A C-5 C-15

A C-5 C-15

(c) SHS 500 × 10 + 250 × 20 0.3 A 0.5 A 0.7 C-5

A A C-5

A B C-5

A C-5 C-5

A C-5 C-10

(d) SHS 400 × 8 + 200 × 20 0.3 A 0.5 A 0.7 C-5

A A C-5

A B C-5

A C-5 C-10

A C-5 C-15

6. Conclusions Based on the study reported in this paper, several conclusions can be drawn: (1) A finite element model was developed to simulate the fire behaviour of the CFDST columns. Thermal and structural responses of the columns under fires can be predicted by the model. A concrete mechanical property model at elevated temperature is also proposed for the analysis of the structural response of the columns. The proposed finite element model is verified by the fire tests results. The predicted temperatures, axial deformation, failure modes and fire endurance are in good agreement with the test results. (2) Parametric analysis is carried out. Parameters which have significant influence on the fire resistance of CFDST columns have been identified. The key parameters include load level, capacity of inner steel tube, the use of fire protection and effective length. (3) Suggestions are made on selecting parameters to achieve higher fire resistance. (4) Practical design tables are developed for some typical CFDST columns for multi-storey buildings. Three options are given to achieve fire resistance between 1 h and 3 h. The same procedures can be used to develop practical design tables or diagrams to cover a wider range of parameters. References [1] ABAQUS. ABAQUS analysis user's manual. Providence: SIMULIA; 2008. [2] CIDECT. Improvement and extension of the simple calculation method for fire resistance of unprotected concrete-filled hollow columns, CIDECT report 15Q. Paris: CTICM; 2004. [3] Ding J, Wang YC. Realistic modeling of thermal and structural behaviour of unprotected concrete filled tubular columns in fires. Journal of Constructional Steel Research 2008;64(10):1086–102. [4] Eurocode 4. Design of steel and concrete composite structures: part 1.2 general rules: structural fire design. Brussels: European Committee for Standardization; 2005. [5] Han LH, Zhao X-L, Yang Y-F, Feng J-B. Experimental study and calculation of fire resistance of concrete filled hollow steel columns. Journal of Structural Engineering, ASCE 2003;129(3):346–56. [6] Han LH, Tao Z, Zhao XL. Concrete-filled double skin (SHS outer and CHS inner) steel tubular beam-columns. Thin-Walled Structures 2004;42(9):1329–55. [7] Kodur VKR. Design equations for evaluating fire resistance of SFRC-filled HSS columns. Journal of Structural Engineering, ASCE 1998;124(6):671–7.

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