Design of a continuous concrete filled steel tubular column in fire

Thin-Walled Structures 131 (2018) 192–204

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Full length article

Design of a continuous concrete filled steel tubular column in fire a,⁎

a

a

b

T c

Kingsley U. Ukanwa , G. Charles Clifton , James B.P. Lim , Stephen J. Hicks , Umesh Sharma , Anthony Abud a

Department of Civil and Environmental Engineering, The University of Auckland, Auckland, New Zealand New Zealand Heavy Engineering Research Association, HERA House, Auckland, New Zealand Department of Civil Engineering, India Institute of Technology, Roorkee, India d Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand b c

A R T I C LE I N FO

A B S T R A C T

Keywords: Fire resistance Concrete-filled steel tubular columns Design procedure Fibre reinforced concrete

Concrete filled steel tubular (CFST) columns used in multi-storey buildings are generally designed as continuous members. The fire behaviour is predicted based on the results of experimental standard fire testing of CFST members where the same temperature is applied to the column over the full column height. Over the past 36 years, 238 experimental tests have been reported in the literature on CFST columns; different types of concrete infill have been considered: plain, steel fibre and bar reinforced concrete. In these tests, the columns were loaded axially under either concentric or eccentric load, and subjected to the standard ISO 834 fire or its equivalent in a furnace. This paper has focused on the in-depth analysis of behaviour of a continuous CFST columns in fire and provided a simple design procedure to calculate the axial capacity of the CFST columns at elevated temperature. The examples given in the later section gives a step by step design procedure for practicing engineers to calculate the axial capacity of both concentrically and eccentrically loaded CFST columns in fire.

1. Introduction Engineers and building owners are becoming more aware of the benefits of using concrete filled steel tubular (CFST) columns, due to their combination of excellent stability during construction, high strength in service and clean lines for both appearance and durability. One of the most demanding loading conditions for multi-storey building design is the impact of severe fire. The columns play a critical role in ensuring the dependable behaviour of the building under severe fire attack. Design of these columns is based on the columns retaining their load carrying capacity for a specified time of exposure to Standard Fire conditions, known as a Fire Resistance Rating (FRR). During the design stage of the building, designers have to ensure column stability under compression or compression and bending for FRRs from 30 to 90 min typically, but up to a maximum of 300 min for firecells with very high fire load and limited ventilation, both of which generate high structural fire severity. Design equations have been developed by various researchers [1–4] to calculate the design compression capacity of unprotected CFST columns in fire. However, some of these equations are too conservative for columns requiring FRR higher than 90 min, principally because they underestimate the contribution of the structural steel jacket at longer durations of fire

⁎

Corresponding author.

https://doi.org/10.1016/j.tws.2018.07.001 Received 5 March 2018; Received in revised form 26 June 2018; Accepted 1 July 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.

exposure. The structural steel yield strength reduction factors given in AS/ NZS 2327 [5] and Eurocode 4 Part 1–2 [6] were developed for bare structural steel sections; however, in the case of CFSTs, the structural steel and concrete act together to provide a composite resistance greater than that of the individual materials acting alone. The concrete core acts as a heat sink, keeping the steel jacket cooler than would be the case for a hollow bare steel section without concrete infill. The proposed design equations presented in this paper and elaborated in a paper by the author [7,8] have been developed and validated against the results of 238 Standard Fire tests undertaken worldwide over the past 36 years (121 square, 104 circular and 13 rectangular). These also include laboratory tests conducted by the Authors [9,10]. Three different types of concrete infill have been used; plain, steel fibre and bar reinforced concrete. These tests are for columns subjected to Standard Fire exposure. This means that, if a natural fire is being used for the design, the time equivalent must be determined from first principles for an insulated structural steel member to give the time of standard fire exposure required. The thickness of insulation used for this time equivalent determination should be such as to give the maximum temperature reached in the structural steel member in the natural fire at around 550–600 °C.

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Notation Ac,T Ar,T As,T Am / V

Ec,sec,T Er,T Es,T Eƒi,Exp (EI)fi ƒc,T ƒsy ƒy ƒsy,T ƒy,T Ic,T Ir,T Is,T ke

kc kec kesy key ksy ky Le,T Nc,ƒi,Rd

concrete strength reduction factor concrete strain corresponding to ƒc,T bar reinforcement modulus of elasticity reduction factor structural steel modulus of elasticity reduction factor bar reinforcement reduction factor structural steel reduction factor buckling length of column in fire situation design section compression capacity at the fire limit state Nƒi,d design value of the axial load under fire condition Nƒi,d,ε design value of the eccentric axial load under fire condition Nc member capacity at ambient temperature Nc,ε member capacity for the eccentric axial load at ambient temperature Ps perimeter of structural steel section exposed to fire R Structural fire resistance αc member slenderness reduction factor T Temperature axis distance of bar reinforcement us λr relative slenderness of column at room temperature λr,T relative slenderness of column in fire situation ηfi design load level in fire condition φc , φs φr design compression load in fire modification factor for concrete, structural steel and bar reinforcement ϕc , ϕs and ϕr capacity factor impacting a limit state for concrete, structural steel and bar reinforcement e distance of eccentricity

cross-sectional area of concrete cross-sectional area of bar reinforcement cross-sectional area of structural steel profile section factor of structural member per unit length, calculated including the volume of the concrete core in determining V temperature dependent secant modulus of elasticity of concrete temperature dependent modulus of elasticity of bar reinforcement temperature dependent modulus of elasticity of structural steel design effect of actions in fire situation for laboratory experiment effective flexural stiffness under fire conditions compressive strength of concrete, at a temperature T characteristics yield strength of bar reinforcement yield strength of the structural steel yield stress of bar reinforcement, at a temperature T yield stress of structural steel, at a temperature T temperature dependent second moment of area of concrete temperature dependent second moment of area of bar reinforcement temperature dependent second moment of area of structural steel effective length factor

= 80 MPa. For the steel fibre reinforced concrete, Dramix hooked end steel fibre specification 5D 65/60BG were used. The length of the fibres were 60 mm, diameter was 0.9 mm and the dosage was 50 kg/m3. For the rebar reinforced concrete infill, longitudinal reinforcement bars were tied using 6 mm diameter stirrups, shape code 51 according to BS 8666:2005 [14]. Fig. 4 show the arrangements of reinforcements inside the steel tubes before pouring of the concrete.

2. Experimental investigation 2.1. General The fire tests were conducted in a furnace having dimensions of 2 m height × 1.5 m length × 1.5 m width, in accordance with EN 1364-1: 2012 [11]. The furnace temperature was controlled to match the ISO 834 [12] time-temperature curve. Fig. 1 shows the typical average furnace temperature to the ISO 834 fire curve for a typical test. Axial loads were applied for approximately 30 min before each fire test and were maintained throughout.

2.3. Experimental result The structural fire resistance (R) of the columns are summarized in Table 3. The variation of axial deflection against time is shown in Fig. 2a–c for columns filled with plain concrete, rebar reinforced concrete and steel fibre reinforced concrete respectively; the structural fire resistance is the time from commencement of test until the load bearing capacity criterion specified in EN 1363-1 was achieved (corresponding to the limiting rate of vertical contraction). (Fig. 5) As can be seen from Fig. 6, the initial longitudinal elongation of the

2.2. Test specimens Table 1 gives a summary of test specimens; two different crosssectional dimensions of square hollow section (SHS) were tested: 200 mm × 200 mm × 6 mm (P, F or R; 1–4) and 220 mm × 220 mm× 6 mm (P, F or R; 5–8). The first letter for each specimen represents the type of concrete infill used (P = Plain, F = Steel Fibre and R=Rebar). All columns had a length of 3200 mm, with fire exposure only to the middle 2000 mm. It should be noted that the bottom 500 mm and the top 700 mm of the column were outside the furnace. Fig. 2 shows the column inside the furnace before the start of the experiment. From Table 1 it can be seen that sixteen columns had fixed-pinned boundary conditions to allow for the load eccentricity to be applied in uni-axially. The pin-end boundary condition was provided through a ball (see Fig. 3). The fixed-fixed boundary was applied to the column by welding a boxed steel section having a depth of 200 mm to restrain the top of the column from rotational and translational movement; this was discussed in details by the authors [8,9,13]. Three types of concrete were used for the steel tube infill, namely: plain concrete; steel fibre reinforced concrete; and rebar reinforced concrete. Table 2 shows the mix used for the concrete infill. The specified compressive concrete cylindrical strength after 28 days was fck

Fig. 1. Measured furnace temperature (ISO 834 shown for comparison). 193

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Table 1 Details of test specimens. Specimen

ƒs N/mm2

ƒc N/mm2

Eccentricity mm

Boundary condition

P1 P2 P3 P4 P5 P7 P8 R1 R2 R3 R4 R5 R7 R8 F1 F2 F3 F4 F5 F6 F7 F8

569 569 525 525 461 461 461 569 525 525 525 461 461 461 525 525 569 569 461 461 461 461

86.9 81.3 89.6 78.8 84.4 76.8 73.8 86.1 94.5 88.2 90.1 86.1 85.7 90.3 90.9 91.9 93.1 95.1 79.7 94.3 101.6 97.7

0 0 25 50 0 25 50 0 0 25 50 0 25 50 0 0 25 50 0 0 25 50

F-F F-P F-P F-P F-F F-P F-P F-F F-P F-P F-P F-F F-P F-P F-F F-P F-P F-P F-F F-P F-P F-P

Fig. 3. Pin ended boundary condition.

F-F=Fixed-Fixed and F-P = Fixed-Pin.

Table 2 Concrete mix proportions. Cement

Water kg/m3

Coarse agregate kg/m3

Fine aggregate kg/m3

Silica fumes kg/m3

Super plasticizers kg/m3

kg/m3 500

150

1045

618

51

5.18

tubular column. The measured values from laboratory experiments were compared to the calculated values using an analytical approach; it was observed that the analytical approach could predict with acceptable accuracy the fire resistance of circular hollow steel columns filled with bar-reinforced concrete. For the evaluation of columns using the following parameters within stated ranges; column sizes, column lengths, applied load ratios and percentage of bar reinforcement, this analytical approach was also sufficient. Using this approach, the cross section of the column is divided into various sections. Lie and Irwin [17] conducted further investigation to develop a mathematical model to predict the temperature, deformation and fire resistance ratings of a square CFST column filled with bar reinforced concrete. The model was validated against experimental test results obtained by Chabot and Lie [18]. Various parameters such as the column section size, column length, load level and percentage of bar reinforcement were used for purpose of validation. It was observed that the mathematical model predicted the fire resistance ratings of the column to a level of acceptable standard. Wang and Kodur [25] also developed a mathematical equation to calculate the axial capacity of CFST columns at elevated temperatures. The design approach was based on the procedure given in Eurocode 4 Part 1–1 [26] with modifications to the provisions for determination of the column buckling curve, determination of the column temperature and calculations of the squash load. The equation was validated using laboratory experiments and a step by step design procedure was provided to aid engineers to calculate the axial capacity using the equation. Kodur [27], through various experimental and numerical studies, developed a simplified design equation to calculate the fire resistance ratings of a CFST column, as given in Equation 2.1.

Fig. 2. Column inside the furnace before fire test.

steel tube in all tests is less than 3 mm. This initial longitudinal elongation is much less than that previously reported in the literature, e.g. [15–22], where initial longitudinal elongation values above 15 mm are typical. Columns elongating in fire due to thermal heating are subjected to an additional axial load which will cause the steel tube to lose its structural integrity earlier; this is an important consideration in design of bare steel columns [23]. 3. Existing design equations Lie [24] developed a mathematical model to calculate the deformation, temperature and fire resistance of a concrete filled steel

R=f× 194

(fc′ + 20) (KL − 1000)

× D2 ×

D C

(3.1)

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a

b

Fig. 5. Position of thermocouples within 200 × 200 SHS.

length of the column in mm; f is a parameter to account for the type of concrete filling (PC, RC and FC) the type of aggregate used (carbonate or siliceous), the percentage of reinforcement, the thickness of concrete cover, and the cross-sectional shape of the hollow steel section column (circular or square). Yin et al. [22] investigated the fire behaviour of the axially loaded square and circular CFST columns at elevated temperatures and observed that the structural steel strength can be calculated using the Eurocode reduction factors at elevated temperature. However, the concrete strength was more complicated to calculate. Comparing square and circular columns of similar cross-sectional area, the circular column would usually have a higher FRR, due to the greater confining effect of the structural steel jacket on the concrete. Espinos et al. [3] reviewed the current design guidelines available worldwide for calculating the fire resistance of CFST columns, with the recommendations focusing on the Eurocode 4 part 1–2 [6] design approach. The aim was to demonstrate a new method for calculating the fire resistance of axially loaded unreinforced concrete filled circular hollow section columns. In order to determine the important parameters which affect the fire behaviour of CFST columns, a parametric study using validated numerical models was required. For the concrete model, it was assessed that the flexural stiffness reduction coefficient can be taken as 0.8 to account for the thermal stresses. The structural steel tube required a more conservative value for its reduction coefficient. The method proposed was validated against laboratory experiments and it was observed that the equations can predict the axial capacity of circular columns filled with un-reinforced concrete loaded concentrically. The proposed equations were further extended by Espinos [29] to cover reinforced concrete infill and elliptical CFST columns. Yu et al. [30] developed a method to calculate the fire resistance of axially loaded CFST columns filled with plain concrete. This approach was based on the calculation for ambient temperature given in Eurocode 4 Part 1–1 [26]. The procedure was applied to columns at elevated temperature by first calculating the equivalent strength and elastic modulus, using the corresponding reduction factor, then determining the compression capacity using Eq. (3.2) below.

Fig. 4. Concrete longitudinal reinforcement arrangement, a) 200 × 200 SHS Column, b) 220 × 220 SHS Column. Table 3 Experiment results. Specimen

λr

Eƒi,Rd kN

Load Level

R Mins

Failure mode

P1 P2 P3 P4 P5 P7 P8 R1 R2 R3 R4 R5 R7 R8 F1 F2 F3 F4 F5 F6 F7 F8

86.9 81.3 89.6 78.8 84.4 76.8 73.8 86.1 94.5 88.2 90.1 86.1 85.7 90.3 90.9 91.9 93.1 95.1 79.7 94.3 101.6 97.7

1378 1378 1068 872 1415 1127 912 1485 1485 1120 899 1604 1208 969 1378 1378 1068 872 1415 1415 1127 912

0.37 0.38 0.38 0.41 0.35 0.38 0.38 0.37 0.37 0.39 0.38 0.35 0.35 0.35 0.37 0.37 0.36 0.37 0.36 0.33 0.33 0.33

37 26 48 26 38 80 41 46 23 65 34 72 72 97 24 25 98 42 85 51 132 66

Euler Euler Euler Plastic Local Plastic Plastic Euler Euler Euler Euler Plastic Euler Euler Euler Euler Plastic Euler Euler Euler Plastic Euler

N0, T = (1 + ηT ) [Ac fck, Tc + As f y, Ts ] Where R is the fire resistance time in minutes; fc′ is the specified 28 day concrete strength in MPa; D is the outside diameter or width of the column in mm; C is the applied load in kN; K is the effective length factor as per CAN/CSA-S16.1-M89 [28] standard; L is the unsupported

where: ηT is the enchanced confining coefficient under fire;

ηT = 0.5ke ξT /(1 + ξT );

ξT is the confining coefficient and ξT = As f y, Ts / Ac fck, Tc ; 195

(3.2)

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a

compared to when it was modelled using a perfect contact between the structural steel tube and concrete. The results of the analysis were used to develop the fire design of axially loaded CFST columns based on Eurocode 4 Part 1–1 [26]. The strength and stiffness properties of the column in the room temperatures were substituted with those in elevated temperatures and effective values were calculated using the reduction factors for the structural steel and concrete, thereby making it possible to apply the buckling curves modification factor. The simple method, however, is very conservative when compared to the experimental data over much of the range of application. More recently, Albero et al. [2] conducted a parametric study using numerical models developed by Universitat Politècnica de València (UPV) and Centre Technique Industriel de la Construction Métallique (CTICM). The numerical study was validated against laboratory experiments conducted within the FRISCC (Fire Resistance of Innovative and Slender Concrete Filled Tubular Composite Columns) project in Europe. The new method was used in calculating the fire resistance time of unprotected CFST columns subjected to loads under a standard fire condition. The new method also allows for displacement to occur between the concrete core and the outer structural steel tube and the axial capacity of the column is thereby calculated using the methods given in section 6.7.3 of Eurocode 4 Part 1–1 [26] but, taking into account the equivalent temperatures.

b

4. Development of new design equations 4.1. General The proposed design procedure in this paper were developed using laboratory experiments carried out on CFST columns loaded axially (concentrically and eccentrically) by various researchers [15–18,20,24,32–38] over the past 36 years, including those of the authors [9,10]. The proposed procedure follows the same steps as that given in EN 1994-1-1 [26] and AS/ NZS 2327 [5] for the design of CFST columns at ambient temperature, but utilises strength reduction factors that are dependent on member temperature and introduces a modification factor dependent on the structural fire rating, distance of eccentricity (e) and section factor of the column. These modifications have been made to improve the accuracy of the equations and reduce variability in relation to the experimental tests.

c

4.2. Conditions applicable to the proposed procedure The following conditions and restrictions apply when using the proposed procedure to calculate the axial capacity of CFST columns in fire.

Fig. 6. The variation of axial deflection against time, (a): Plain concrete infill axial displacement with time, (b): Rebar reinforced concrete infill axial displacement with time, (c): Steel fibre reinforced concrete infill axial displacement with time.

4.2.1. The bar reinforcement ratio shall be less than or equal to 6% of the concrete core cross section area The relative slenderness of the column at ambient temperature lies within the limits 18 ≤ λ η ≤ 108 given in AS/NZS 2327 [5] table 4.1.3.3(c), where λ η is calculated in accordance with Clause 4.1.3.3. This corresponds to the relative slenderness given in Eurocode 4 [26] clause 6.7.3.3(2). The standard fire resistance required is between 30 and 300 min; any well designed and detailed column meeting the geometrical and loading limits given herein or in [5] for ambient temperature will achieve R = 30 min. The ratio of e/D for circular or e/B for square and rectangular ratio must be less than 1 for eccentrically loaded columns. Note: “e” is the eccentricity calculated as Md/Nd, where Md is the design moment and Nd the design axial load. This represents the limit on eccentricity that has been experimentally tested. The axial capacity of the column loaded eccentrically at ambient temperature Nc, ε shall be calculated in accordance to clause 4.2 given in AS/NZS 2327 [5]. This shall be used to calculate the axial capacity of eccentrically loaded columns in fire.

ke is the effectiveness coefficient, ke = (1 − ψ)(n2 − 4)/(n2 + 20) ; hollow ratio, ψ = Ak /(Ac + Ak ) f y, Ts, fck, Tc are the equivalent strengths of structural steel and concrete. Ibanez et al. [31] conducted a parametric study, which was used to develop a set of equations for calculating the axial capacity of circular CFST columns in fire. The parametric study was carried out by computing numerically the thermal and stress analysis of composite columns filled with normal strength concrete. The main parameters of the model were the steel–concrete interface gap, moisture content of concrete and thermal properties of structural steel and concrete. The set of equations were derived from a parametric study, which was validated against laboratory experiments. The effect of air gap in the interface between the steel section and concrete core was taken into account by presenting thermal conductance for the gap. The inclusion of the gap conductance into the analysis resulted in a more accurate prediction, 196

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Member slenderness reduction factor “αc” is calculated from AS/ NZS 2327 Clause 4.1.3 or NZS 3404 [39] or AS 4100 [40] Clause 6.3 using the following:

concrete temperature is taken as the average temperature across the whole concrete section when divided into various sections. However, Albero et al. [2] used the concept of an equivalent temperature for developing the equations for the design temperature of the concrete core. It should be noted that the structural steel temperature is constant regardless of the steel tube thickness, due to the high conductivity of steel and the heat sink of the concrete; the bar reinforcement temperature is dependent on the concrete cover. The temperatures can be calculated using Eqs. 5.1 to 5.4.

• Plain concrete infill: Compression member section constant α = 0.5 • Steel fibre or bar reinforced concrete infill: Compression member b

section constant αb= 0

4.3. Step by step design approach

– Concrete core temperature

This section presents the key factors used in calculating the axial capacity of CFST columns when using the proposed approach. An example of how to apply the design procedure is given in a Section 6.

Rectangular and Square

Tc = −112.35 + 13.194R − 0.0778R2 + 0.0001654R3 − 4.101(As / Ps ) 4.3.1. Calculation of equivalent temperatures for the cross-sectional components The evaluation of design temperatures for the cross-section components (concrete, structural steel and bar reinforcement) is presented in this Section. The design temperatures of the components are a key factor which influences the axial capacity of the column in fire. The

≤ 650 °C

(5.1)

Circular

Tc = −34.617 + 11.845R − 0.0698R2 + 0.000149R3 − 4.101((As / Ps ) ≤ 650 °C

a

b

c

d

e

f

(5.2)

Fig. 7. Comparison of the temperature values from the design procedure against the experimentally recorded ones, (a): Temperature of steel section for circular column, (b): Effective temperature of concrete core for circular column, (c): Temperature of reinforcing bars for circular column, (d): Temperature of steel section for square column, (e): Effective temperature of concrete core for square column, (f): Temperature of reinforcing bars for square column.

197

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– Temperature of the structural steel section

Ts = 448.573 + 9.734R −

0.0552R2

+

0.000106R3

1 ⎧ ⎪ 0.98 + 0.00185T − 0.0000045T2 ⎪ ky and ksy = 2 ⎨ 4.43 − 0.0102T + 0.000006T ⎪ 0.51 − 0.0005T ⎪ 0.24 − 0.0002T ⎩

(5.3)

– Temperature of the reinforcing bars

Tr = 28.09 + 5.728R − 0.0092R2 − 0.0003851us3.186

(5.4)

1.05 − 0.0005T kc = ⎨ 1.15 − 0.001T ⎪ 1.35 − 0.0015T ⎩

for 20 °C ≤ T ≤ 100 °C for 100 °C ≤ T ≤ 200 °C for 200 °C ≤ T ≤ 400 °C for 400 °C ≤ T ≤ 650 °C

(5.6)

⎫ ⎪ ⎬ ⎪ ⎭

(5.7)

4.3.3. Effective flexural stiffness of the fire exposed column The flexural stiffness of the column in fire is calculated using Eq. (5.8). The modulus of elasticity reduction factor for structural steel and bar reinforcement is calculated using Eq. (5.9), while, the secant modulus of concrete is calculated using Eq. (5.10). Eqs. (5.9 and 5.10) were developed using values obtained in Eurocode 4 [6], this was to allow design engineers input the values easily into excel spreadsheets.

4.3.2. Design of section compression capacity at the fire limit state When calculating the design compression resistance of the composite cross-section, modification factors for the capacities of concrete, structural steel and bar reinforcement are applied. The thickness factor (As/Ps) is the ratio of the area of the structural steel member (not including the concrete core) to the perimeter of the structural steel exposed to fire, which is used to calculate the modification factor for the design compression load in fire. The current design guide [5] is conservative for columns developing higher structural fire resistance, because the structural steel, concrete and bar reinforcement reduction factors at elevated temperatures have been developed for individual members and not for composite members. For a composite member, the structural steel will be prevented from buckling inwardly due to the concrete infill. The concrete will also have a higher compressive strength because it is confined by the structural steel. The modification factors developed herein account for the composite action of the structural steel tube and concrete core for varying structural fire ratings. It was also observed that the AS/NZS 2327 provisions are too conservative for columns having R values greater than 90 min. Eq. (5.5) is used to calculate the section capacity, Eqs. (5.6 and 5.7) are used to calculate the reduction factors based on Eurocode 4 [6].

Nc, ƒ i,Rd = φc × Ac × fc, T + φs × As × f y, T + φr × Ar × fsy, T

1

⎧ ⎪

Fig. 7a–f shows a comparison between the laboratory experiments, the proposed equation for the temperatures for structural steel section, concrete core and reinforcing bars. The conservativeness of temperature evaluation was judged by dividing the temperature obtained experimentally with the temperature calculated using the three design procedures. The average values obtained that are lower than 1 are unsafe. The values obtained were then used to compute the coefficient of variation (CoV). The CoV values closer to zero (see Table 4a–c) are a better match with the experimental test values.

for 20 °C ≤ T ≤ 400 °C ⎫ for 400 °C ≤ T ≤ 600 °C ⎪ ⎪ for 600 °C ≤ T ≤ 800 °C ⎬ for 800 °C ≤ T ≤ 900 °C ⎪ for 900 °C ≤ T ≤ 1200 °C ⎪ ⎭

(EI ) fi = Ec, Sec, T × Ic, T + Es, T × Is, T + Er , T × Ir , T

(5.8)

where:

Ii, T =second moment of area, of part i of the cross-section for bending around the affected axis (i is structural steel, concrete or bar reinforcement) Ec, Sec, T =characteristic value for the secant modulus of elasticity of concrete in fire condition Ec, sec, T = fc, T / kec Es,T =modulus of elasticity of the structural steel in fire condition Es, T = Es × key Er,T =modulus of elasticity of the bar reinforcement in fire condition Er , T = Er × kesy ⎧ ⎪ ⎪ k esy and k ey =

(5.5)

⎧ ⎪

φc = (0.02945 × R0.864 ) × a × b ≥ cφs = (0.02793 × R0.883) × a × b

1 1.1 − 0.001T

2 ⎨ 3.7 − 0.00895T + 0.0000055T ⎪ 0.41 − 0.0004T ⎪ 0.27 − 0.000225T ⎩

for 20 °C ≤ T ≤ 100 °C ⎫ for 100 °C ≤ T ≤ 500 °C ⎪ ⎪ for 500 °C ≤ T ≤ 700 °C ⎬ for 700 °C ≤ T ≤ 800 °C ⎪ for 800 °C ≤ T ≤ 1200 °C ⎪ ⎭

0.0021 − 0.00001875T

2 kec = 0.004 − 0.000005T + 0.00000005T 2 ⎨ 0.04 − 0.000175T + 0.00000025T ⎪ 0.025 ⎩

≥ cφr = (0.02257 × R0.889) × a × b ≥ c where:

φc is the modification factor for concrete applicable over the range 0.2 ≤ φc ≤ 1.2 . φs is the modification factor for structural steel applicable over the range 0.2 ≤ φs ≤ 1.2 . φr is the modification factor for bar reinforcement applicable over the range 0.2 ≤ φr ≤ 1.2 . Ai, T =area of material i, at any given temperature T (i is structural steel, bar reinforcement or concrete) fiy, T =yield stress of material i, at any given temperature T (i is either structural steel or bar reinforcement) fc, T =concrete compressive stress, at a temperature T R=the structural fire resistance. Ps =perimeter of structural steel section Am / V =section factor e / D =eccentricity/diameter or width of steel tube

(5.9)

for 20 °C ≤ T ≤ 100 °C ⎫ for 100 °C ≤ T ≤ 400 °C ⎪ for 400 °C ≤ T ≤ 600 °C ⎬ ⎪ for T ≥ 600 °C ⎭ (5.10)

Table 4 Comparison of the temperature values from the design procedure against the experimentally recorded ones. (a): Temperature of steel section Circular Proposed Average 0.97 ST. Dev 0.05 COV 0.05 (b): Effective temperature of concrete core Average 0.92 ST. Dev 0.31 COV 0.34 (c): Temperature of reinforcing bars Average 0.78 ST. Dev 0.22 COV 0.28

a = 1.11 − 0.04 × As / Ps b = −0.17 + 0.04 × (Am / V ) c = ((As /Ps)/(Am / V ) − e / D)

198

AS/NZS 1.14 0.81 0.72 0.99 0.77 0.78 0.65 0.23 0.35

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– Design temperatures in the column section

4.3.4. Euler buckling load at elevated temperature and relative slenderness in fire The Euler buckling load in fire is calculated using Eq. (5.11) with the effective lengths of the column calculated in accordance to Section 4.8.3 of NZS 3404 [40]. The relative slenderness is calculated in accordance with Section 5.3.2 of this paper, using Eq. (5.12).

Nf , omb =

λr , T =

Ts = 448.573 + 9.734 × 150 − 0.0552 × 1502 + 0.000106 × 1503 = 1024 °CTc = −112.35 + 13.194 × 150 − 0.0778 × 1502 + 0.0001654 × 1503 − 4.101 × 6.15 = 649 °CTr = 28.09 + 5.728 × 150 − 0.0092 × 1502 − 0.0003851 × 233.186 = 672 °C

– Modification factors for the design capacity of the column cross-section

π 2 (EI ) fi Le2, T

(5.11)

(2 × (203 + 203)) × 1000 Am = V 203 × 203 A 4995 1 − = 19.7 m Thickness factor = s = Ps 203 × 4

Section factor =

Nc, fi, Rd Nf , omb

(5.12)

= 6.15 mma = 1.11 − 0.04 × 6.15 = 0.864b

4.3.5. Design load in fire for concentrically and eccentrically loaded columns The design member compression capacity of fire exposed CFST columns loaded concentrically or eccentrically is calculated from Eqs. (5.13) or (5.14), respectively.

Nfi, d = α c × Nc, fi, Rd Nfi, d, ε =

Nc, ε × Nfi, d Nc

= −0.17 + 0.04 × 19.7 = 0.618c = (6.15/19.7 − 0) = 0.31φc = ⎜⎛0.02945 × 1500.864⎟⎞ × 0.86 × 0.618 = 1.19φs ⎝ ⎠

(5.13)

= ⎜⎛0.02793 × 1500.883⎟⎞ × 0.864 × 0.618 ⎝ ⎠

(5.14)

= 1.24 Therefore, use 1.2φr = ⎜⎛0.02257 × 1500.889⎟⎞ ⎝ ⎠ × 0.864 × 0.618 = 1.04

Where Nc, ε and Nc is calculated from Section 4 of AS/NZS 2327 [40] but, taking ϕc , ϕs and ϕr as 1. To determine the conservativeness of the proposed equations, the compression load used in the experiments has been divided by the axial capacity obtained using the proposed equations. Similar to the comparison carried out in the previous section, it is observed that the proposed equations yield results that are more conservative (where Exp/Cal > 1) and accurate (COV closer to zero) while many of the AS/ NZS 2327 results are either too conservative or in some cases un-conservative. The various parameters which shows the accuracy of the design procedure when compared to AS/NZS 2327 is given in Table 5a–c and shown graphically in Fig. 8 when the columns are safe or unsafe. The structural fire rating of the columns corresponding to the conservativeness of the columns for each of the equations used can be seen in Table A1 of Appendix 1.

– Design compression capacity at the fire limit state

Nc, ƒ i,Rd = φc × Ac × fc, T + φs × As × f y, T + φr × Ar × fsy, T kc (649°C ) = 0.376k y (1024°C ) = 0.035ksy (672°C ) = 0.285Nc, ƒ i,Rd = 1.19 × 35410 mm2 × 47MPa × 0.376 + 1.2 × 4995 mm2 × 370 MPa × 0.035 + 1.04 × 804 mm2 × 400 MPa × 0.285 = 916 kN – Effective flexural stiffness in fire (EI ) fi = Ec, Sec, T × Ic, T + Es, T × Is, T + Er , T × Ir , T k ec (649 °C ) = 0.025k ey (1024 °C ) = 0.04k esy (672 °C ) = 0.169(EI ) fi = ((47MPa × 0.376)/0.025) × 105978701 mm4 + 200000 MPa × 0.04 × 32226781 mm4 + 200000 MPa × 0.169 × 3309658 mm4

5. Design examples

= 442 kNm2

5.1. Comparison with experimental test for concentrically loaded column

– Euler buckling load at elevated temperature

The design example presented is taken from a laboratory fire test carried out by Lie & Irwin [17] on a square CFST column filled with bar reinforced concrete. The column was located on the intermediate floor, therefore, it was considered to be fixed ended. During the fire test, the column achieved a structural fire rating of 150 min. This R value was used to obtain the axial capacity of the column and thereby, comparing this with the applied load during the laboratory experiment. The test data used for the calculation are given below:

Nf , omb =

π 2EIfi Le2, T

Nf , omb =

22 2 7

( )

× 442 × 109 Nmm2

(0.7 × 3810 mm)2

= 613 kN

Table 5 Comparison of design provisions with experimental test. (a): Circular columns (experiment/calculated) values Experiment Proposed Average 1.56 ST. Dev 0.51 COV 0.33 (b): Square columns (experiment/calculated) values Average 1.52 ST. Dev 0.43 COV 0.28 (c): Rectangular columns (experiment/calculated) values Average 2.83 ST. Dev 1.57 COV 0.56

R= 150 min Column Length= 3.81 m Fixed – Fixed “ke”= 0.7 Square hollow section= 203 mm × 203 mm× 6.35 mm Yield strength of structural steel, ƒy = 350 MPa Compressive strength of concrete, ƒc= 47 MPa Yield strength of reinforcing bars, ƒsy= 400 MPa Diameter of reinforcing bars= 16 mm Number of reinforcing bars= 4 Axis distance of reinforcing bar, us = 23 mm

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AS/NZS 1.12 0.60 0.54 1.32 0.89 0.68 1.94 1.18 0.61

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a

b

c

Fig. 8. Comparison of design axial capacity of the column between proposed procedure, AS/NZS 2327 and experimental test, (a): Square Columns, (b): Circular Columns, c: Rectangular Columns.

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– Relative slenderness in fire

λr , T =

Nc, fi, Rd Nf , omb

λr , T =

φc = (0.02945 × 570.864) × 0.61 × 0.416 = 0.245 ≥ c = 0.36 Therefore use 0.36φs = (0.02945 × 570.883) × 0.61 × 0.416

916 = 1.22 613

= 0.265 ≥ c = 0.36 Therefore use 0.36φr = (0.02945 × 570.889) × 0.61

Therefore,λ η, T = λr , T × 90 = 110 Reduction factor “αc”= 0.48, accounting for the column slenderness, is taken from Table 6.3.3(2) of NZS 3404 using 0 as the value of αb as given in subsection 3.3.6 of this paper.

× 0.416 = 0.272 ≥ c = 0.36 Therefore use 0.36 – Design compression capacity at the fire limit state

Nc, ƒ i,Rd = φc × Ac × fc, T + φs × As × f y, T + φr × Ar × fsy, T kc (390°C )

– Design load in fire

= 0.76k y (844°C ) = 0.09ksy (276°C ) = 1Nc, ƒ i,Rd

Nfi, d = α c × Nc, fi, Rd 0.48 × 916 = 437 kN

= 0.36 × 47759 mm2 × 37 MPa × 0.76 + 0.36 × 10776 mm2

Using the proposed design procedure, the column axial capacity is 437 kN for 150 min FRR. However, during the standard fire test, the column was subjected to an axial load of 500 kN which is 15% higher than the calculated axial load. This indicates that the design for the column is conservative.

× 370 MPa × 0.035 + 0.36 × 2513 mm2 × 566 MPa × 1 = 1, 113 kN – Effective flexural stiffness in fire

(EI ) fi = Ec, Sec, T × Ic, T + Es, T × Is, T + Er , T × Ir , T kec (390°C )

5.2. Comparison with experimental test for eccentrically loaded column

= 0.0096key (844°C ) = 0.08kesy (276°C ) = 0.82(EI ) fi The design example presented was taken from laboratory fire test carried out by Espinos et al. [35] on circular CFST column filled with bar reinforced concrete. During the fire test, the column achieved a structural fire rating of 57 min, therefore, this R value was used to obtain the axial capacity of the column and thereby, comparing this with the applied load during the laboratory experiment. The test data used for the calculation are given below:

= ((37 MPa × 0.76)/0.0096) × 193766549 mm4 + 210000 MPa × 0.08 × 71540925 mm4 + 210000 MPa × 0.82 × 7351933 mm4 = 3, 040 kNm2 – Euler buckling load at elevated temperature

Nf , omb =

R= 57 min Column Length = 3180 mm Pin – Pin “ke”= 1 Circular hollow section= 273 mm × 10 mm Steel Yield strength, ƒy = 369 MPa Concrete Strength, ƒc = 37 MPa Reinforcement yield strength, ƒsy = 566 MPa Diameter of reinforcing bars = 20 mm Number of reinforcing bars = 8 Axis distance of reinforcing bar, us = 40 mm Eccentricity = 136.5 mm

π 2EIfi Le2, T

22 2 7

( ) =

× 3040 × 109 Nmm2

(1 × 3180 mm)2

= 2, 969 kN

Relative slenderness in fire

λr , T =

Nc, fi, Rd Nf , omb

1, 113 = 0.61 2, 969

Therefore,

λ η, T = λr , T × 90 = 55.1 Member slenderness reduction factor “αc”= 0.83 taken from NZS 3404 Table 6.3.3(2), using 0 as the value of αb. – Design of concentrically loaded column in fire

– Modification factors for the design capacity of the column cross-section

Nfi, d = α c × Nc, fi, Rd 0.83 × 1, 113 = 924 kN

Am 4 × 1000 A = = 14.65 m−1Thickness factor = s V 273 Ps 10775 = = 12.56 mm pi × 273

Design of eccentrically loaded columns in fire

Section factor =

e / D = 136.5/273 = 0.5Nuc = 6, 087 kNNuc, ε = 2, 010 kNNfi, d Nuc, ε 2, 010 kN = 924 kNNfi, d, ε = × Nfi, d Nfi, d, ε = × 924 kN = 305 kN Nuc 6, 087 kN

– Design temperature in the column section

Ts = 448.573 + 9.734 × 57 − 0.0552 × 572 + 0.000106 × 573 = 844 °CTc = −112.35 + 13.194 × 57 − 0.0778 × 572 + 0.0001654 × 573 − 4.101 × 12.56 = 390 °CTr = 28.09 + 5.728 × 57 − 0.0092 × 572

The applied load in this experiment, for which the column withstood the Standard Fire exposure for 57 min, was 392 kN, 30% higher than the design capacity calculated using this procedure. 6. Conclusions

+ 0.0003851 × 403.186 = 276°C During the design stage of buildings, the column is usually designed to withstand compression loads or compression and bending loads for a FRR of 30–90 min typically, but can be as high as 300 min. The longitudinal expansion of the steel tube relative to the concrete will be restrained by the length of column above and below the floor in a continuous column construction system. The proposed design equations presented in this paper have been developed and validated against 238

– Design compression capacity modification factor – a = 1.11 − 0.04 × 12.56 = 0.61 – b = −0.17 + 0.04 × 14.65 = 0.416 – c = (12.56/14.65 − 0.5) = 0.36

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CFST columns, therefore, a further validation of the design procedure using laboratory experiment data for rectangular CFST columns will be pragmatic.

(121 square, 104 circular and 13 rectangular) Standard Fire test results undertaken worldwide over the past 36 years. The proposed procedure has been shown to be conservative for CFST columns filled with either plain, steel fibre or bar reinforced concrete. Following a sensitivity analysis, a new member section constant “αb” value has been proposed for columns having different concrete infill type to calculate the buckling member factor of the column in fire. The proposed design procedure has shown to be more accurate than the current AS/NZS 2327 method. Limited experimental data was found in the literature for rectangular CFST columns in fire when compared to square and circular

Acknowledgements The authors wish to express gratitude to the New Zealand Heavy Engineering Educational & Research Foundation (HEERF) for their scholarship support, also to the Department of Civil Engineering, IIT Roorkee for providing the laboratory used for the experiments.

Appendix 1 Please check Table A1 here.

Table A1 Comparison of design provisions with experimental tests. Square columns

Circular columns

Rectangular columns

S/N

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

11 11 13 13 14 14 15 16 16 16 16 18 19 19 20 22 22 23 23 24 25 26 28 29 29 29 29 30 30 30 30 30 32 34 35 36 36 37 38 39 39 40 40 42 43 43 43 45 45 47 48 48

1.67 2.09 1.82 1.91 1.80 2.35 2.09 1.55 1.88 1.94 2.14 1.62 1.60 1.98 1.96 1.48 1.86 0.82 1.98 1.69 1.93 1.47 1.55 0.85 0.95 1.20 1.56 1.00 1.02 1.07 1.44 1.73 1.09 1.11 2.00 0.78 1.10 0.99 1.07 1.21 1.43 1.04 1.12 1.01 0.88 1.04 1.33 1.37 1.37 1.04 0.91 0.91

0.92 0.99 1.16 0.99 1.13 1.04 1.13 0.92 0.86 0.95 1.04 0.84 1.07 1.01 1.14 0.99 1.13 0.61 1.09 1.11 1.05 0.67 0.48 0.7 0.71 0.75 0.73 1.23 0.67 0.78 0.72 0.46 0.7 0.89 0.71 0.98 0.78 0.76 0.93 0.69 1.08 0.73 1.17 0.83 0.55 0.5 1 0.59 0.59 1.17 0.39 1.32

15 16 16 18 20 21 22 23 24 24 24 24 25 25 25 25 26 26 26 28 29 29 30 32 33 33 34 34 34 35 35 36 36 37 37 38 39 39 41 42 42 42 42 45 45 46 46 48 48 49 51 51

1.23 0.75 1.69 2.85 2.36 1.72 1.06 1.27 2.11 1.53 1.31 2.18 1.93 1.05 1.37 3.09 1.60 1.68 1.01 1.57 2.09 1.01 0.99 1.20 2.34 1.11 2.11 1.28 1.38 1.49 1.65 2.52 1.83 1.75 1.43 1.37 1.86 0.82 1.50 1.47 1.01 2.29 1.23 2.14 1.78 1.23 1.26 1.30 1.41 1.54 1.92 1.30

0.79 0.49 0.79 0.91 0.9 0.88 0.4 0.57 1.52 1.13 0.49 0.92 1.01 0.65 0.58 0.63 0.7 0.72 0.78 1.27 0.98 0.82 0.75 1.01 0.57 0.66 1.02 0.7 0.67 1.11 1.18 1.18 0.63 0.81 0.71 0.54 0.9 0.58 0.74 1.63 0.69 0.91 0.83 0.67 0.57 1.61 0.78 1.32 1.12 0.74 0.96 0.95

16 19 20 21 22 22 23 23 24 24 27 30 34

2.94 0.81 6.31 2.71 2.06 4.77 0.98 1.82 4.4 2.85 1.86 1.87 3.45

2.84 0.84 5.19 1.81 1.39 2.35 0.88 0.98 2.4 1.52 1.16 1.4 2.42

(continued on next page) 202

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Table A1 (continued) Square columns

S/N 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121

Circular columns

Rectangular columns

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

48 51 56 56 57 57 57 65 70 70 71 71 72 75 76 80 80 82 82 90 93 93 96 96 102 102 102 106 108 111 111 112 114 125 133 134 144 144 145 149 152 170 170 174 174 178 188 188 199 227 259 294

0.98 0.75 1.20 1.34 1.03 1.06 1.27 1.30 2.85 2.87 0.82 1.52 0.83 0.59 1.93 1.93 2.01 1.90 1.93 1.93 1.14 2.40 2.58 2.60 1.16 1.76 1.80 2.35 2.32 2.12 2.35 1.81 1.95 1.04 1.68 0.84 1.87 1.90 1.73 2.09 1.02 1.25 1.26 1.76 1.80 1.80 1.86 1.90 1.92 1.55 2.02 2.04

0.38 0.34 1.29 1.42 1.97 0.69 1.9 3.05 1.2 1.2 0.73 1.43 0.85 0.51 0.87 1.83 1.77 2.21 2.19 1.03 1 1.96 1.92 1.92 2.45 1.34 2.44 1.53 3.28 3.35 0.83 1.25 0.76 0.72 1.47 1.62 1.69 1.69 0.76 0.68 0.6 0.81 0.81 2.15 2.12 1.13 1.02 1.01 0.57 0.28 0.31 1

51 52 55 55 56 57 57 57 58 58 59 60 61 61 62 62 63 65 66 66 66 68 68 68 68 70 72 72 73 73 80 80 81 81 81 83 83 85 85 86 88 89 89 92 97 98 98 102 105 109 110 113 113 114 126 128 132 133 134 135 135 136 144 150 150 165 192 212 212

1.23 0.94 1.51 1.17 1.65 1.68 0.96 2.01 1.53 1.07 0.91 1.74 1.59 1.25 1.92 0.88 1.16 1.20 1.14 1.94 1.10 1.09 1.74 1.74 1.23 2.34 1.11 1.08 1.46 1.31 1.69 1.68 1.22 1.14 1.28 1.09 1.01 1.04 1.52 1.30 1.52 1.72 1.21 1.42 1.10 1.35 1.87 1.62 1.45 1.82 1.80 1.30 1.77 1.39 1.92 1.76 1.70 1.45 1.45 1.89 1.73 2.06 1.23 1.06 1.14 1.15 1.31 1.77 1.84

0.72 0.65 0.82 0.77 0.86 0.89 0.73 0.69 0.72 0.92 0.88 2.04 2.58 1.15 0.85 0.77 1.13 1.64 2.54 0.92 1.01 1.83 1.21 0.76 1.35 1.34 1.03 1.28 1.14 3.46 2.42 2.08 3.85 3.59 0.7 1.82 3.26 0.66 1.72 0.76 2.44 1.17 2.2 1.68 2.66 0.94 3.63 1.24 2.9 1.61 5.15 1.39 1.8 1.36 1.65 4.06 3.96 1.44 1.45 1.96 1.01 1.35 2.24 2.51 2.66 1.17 0.52 0.52 0.52

203

R Min

Proposed Exp/Cal

AS/NZS Exp/Cal

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