Behaviour of restrained structural subassemblies of steel

Engineering Structures 46 (2013) 471–492

Contents lists available at SciVerse ScienceDirect

Engineering Structures

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

Behaviour of restrained structural subassemblies of steel beam to CFT columnin fire during cooling stage

S. Elsawaf, Y.C. Wang ⇑School of Mechanical, Aerospace and Civil Engineering, University of Manchester, United Kingdom

a r t i c l e i n f o

Article history:Received 23 March 2012Revised 31 July 2012Accepted 17 August 2012Available online 21 September 2012

Keywords:ConnectionJointFire resistanceCoolingNumerical modellingConcrete filled tubesReverse channel connectionFin plate connection

0141-0296/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.engstruct.2012.08.023

⇑ Corresponding author.E-mail address: [email protected] (Y.C

a b s t r a c t

During the well publicised Cardington structural fire research programme, parts of some connections suf-fered fracture during cooling. This led some to believe that fire spread and structural collapse may occurduring the cooling stage of a fire and therefore this issue should be considered in structural fire engineer-ing design. This paper focuses on steel framed structures using concrete filled tubular (CFT) columns andthe objective of this paper is to find means of reducing the risk of structural failure during cooling. Itreports the results of a study using the general finite element software ABAQUS to numerically modelthe behaviour of restrained structural subassemblies of steel beam to CFT columns and their joints bothin fire, emphasising on the cooling stage. Validation of the finite element model was achieved by compar-ing the simulation and test results for the two fire tests investigating cooling behaviour, recently con-ducted at the University of Manchester on similar structures. In these two tests, the test assembly washeated to temperatures close to the limiting temperature of the steel beam and then cooled down whilestill maintaining the applied loads on the beam. One of the tests used reverse channel connection and theother test used fin plate connection. The finite element models give very good agreement with the exper-imental results and observations. Remarkable differences in tensile forces in the connected beams wereobserved during the tests depending on the beam temperature at which cooling started. This leads to thesuggestion that in order to avoid connection fracture during cooling, it may be possible to reduce the lim-iting temperature of the connected beam by a small value (<50 �C) from the limiting temperature calcu-lated without considering any axial restraints in the beam.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Collapse of the World Trade Center buildings [1,2] and results ofthe Cardington full-scale eight-storey steel framed building firetests in the UK [3] have demonstrated that steel joints are vulner-able during both the heating and cooling phases of fire. Jointbehaviour in fire is currently one of the most important topics ofresearch on structural fire resistance; however, most of the presentresearch studies have focused on the heating phase.

The authors [4] undertook detailed numerical simulations of thefire tests by Ding and Wang [5] to validate their numerical simula-tion model during the heating stage using a 3-D finite elementmodel similar to that of Dai et al. [6]. The validated numerical mod-el was used to conduct a comprehensive programme of parametricstudies to find ways of enhancing the strength and deformationcapacities of reverse channel connections to CFT columns to pro-long the development of catenary action in the connected beam[7] as a means of improving structural robustness in fire.

ll rights reserved.

. Wang).

During the cooling stage of a fire, when the beam temperaturedecreases, if thermal shortening of the beam is restrained, large ten-sile forces may be induced in the beam [8,9]. In the meantime, be-cause of the larger thermal mass of the connection region comparedto the beam, the connection temperature may still be rising soreduction in the connection strength continues. This coupling ofconnection strength reduction and beam tensile force increasemay result in fracture of some connection components [14], leadingto possible structural failure. Although this has caused concern, theauthors are not aware that any systematic research has been under-taken to find ways of preventing connection failure during cooling.

This research extends the experimental study of Ding and Wang[5] and will conduct extensive numerical simulations to exploredifferent methods of enabling reverse channel connection to sur-vive the entire fire exposure, particularly during the cooling phase.This study has the following two specific objectives:

(1) To develop and validate a three-dimensional (3-D) FE modelusing ABAQUS software for modelling the behaviour ofrestrained structural subassemblies of steel beam to con-crete filled tubular (CFT) columns using reverse channel con-nections during cooling.

http://dx.doi.org/10.1016/j.engstruct.2012.08.023

mailto:[email protected]

http://dx.doi.org/10.1016/j.engstruct.2012.08.023

http://www.sciencedirect.com/science/journal/01410296

http://www.elsevier.com/locate/engstruct

Fig. 1. Elevation view of schematic arrangement of test.

183.719

140

FW 8mm

4060

40Fire protection15mm fibre blanket

10mm gap 35 45

90

5

90x140x8fin plate

22mm holes for M20 bolt

Fig. 2. Geometrical details of fin plate connection in Test 9 of Ding and Wang [5].

Fig. 3. FE mesh for Test 9 of Ding and Wang [5] (fin plate connection).

472 S. Elsawaf, Y.C. Wang / Engineering Structures 46 (2013) 471–492

(2) To conduct parametric studies to find means of connectiondesign to reduce the risk of structural failure during cooling.

This research will focus on steel structures due to their relativesimplicity compared to composite steel–concrete structures. How-ever, since the issue of joint fracture during cooling also occurredin steel–concrete composite structures, the findings of this re-search will be relevant to steel–concrete composite structures.

2. Validation of thenumerical simulation model against the testresults of Ding and Wang [5]

2.1. Description of the finite element model

Fig. 1 shows the experimental set up and details of the fire testsas provided in Ding and Wang [5]. The columns were horizontallyrestrained and provided axial restraints to the steel beam. As in theauthors’ recent research studies [4,7], three-dimensional solid ele-ments (C3D8) were used to model the main structural members.The tested structure was symmetrical in geometry. Therefore, tosave computational time, it was decided to include only half ofthe test assembly in the finite element model. Furthermore, to re-

0

100

200

300

400

500

600

700

800

900

0 20 40 60Time (min.)

Tem

pera

ture

(°C

)

Bottom flangeBeam webConnectionTop flangeSteel tubeCon. fill

(a) Before 60 min.

0

100

200

300

400

60 80 100 120 140 160 180 200Time (min.)

Tem

pera

ture

(°C

)


(b) After 60 min.

Fig. 4. Time–temperature relationships used for Test 9 of Ding and Wang [5] (fin plate connection).

Fig. 5. Deformation pattern of Test 9 of Ding and Wang [5] (fin plate connection).

Table 1Mechanical property values for different steel members used for Test 9 of Ding and Wang [5] (fin plate connection).

Component Beam web Beam flange Column Fin plate

Elastic modulus (MPa) 206,606 206,378 200,001 190,386Yield strength (MPa) 352 309 406 311Maximum strength (MPa) 493 477 539 468Ultimate strain (%) 32.1 34.9 29.5 37.2

-80

-60

-40

-20

0

20

40

60

80

100

Beam bottom flange mean temp.(°C)

Axi

al fo

rce

(N)

TestAbaqus

(a) Beam axial force – temperature relationships -300

-250

-200

-150

-100

-50

00 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800


Def

lect

ion

(mm

)

Test

Abaqus

(b) Beam mid-span deflection – temperature relationships

Fig. 6. Comparison between modelling and experimental results for mid-span deflection and axial force in the beam with fin plate connections, Test 9 of Ding and Wang [5

S. Elsawaf, Y.C. Wang / Engineering Structures 46 (2013) 471–492 473

].

2435

6035

23.8

152.4

130

35

130

30

Grade 8.8M20 bolts

152x89channel

130 long

8

4.8

130x130x8endplate

152x89channel

130 long

130x130x8endplate

FW 6mm

22mm holes for M20 bolt

Fire protection15mm fibre blanket

152x89channel

130 long

C/L

41.2

41.2

70

5 183.7

FW 6mm

FW 8mm

88.9

FW 8mm

Fig. 7. Geometrical details of reverse channel connection in Test 10 of Ding and Wang [5].

Fig. 8. FE mesh for Test 10 of Ding and Wang [5] (reverse channel connection).


duce the number of elements and nodes in the FE model, the col-umn was divided into three parts and only the central part con-nected by the joint and exposed to fire in the furnace wasactually modelled using the solid elements. The other two partsaway from the joint zone were modelled using general beam ele-ments with ‘‘box’’ cross section for the steel tube and ‘‘rectangular’’

0

100

200

300

400

500

600

700

800

0 20 40 60Time (min.)

Tem

pera

ture

(°C

)


(a) Before 60 min.

Fig. 9. Time–temperature relationships used for Test 10

cross section for the concrete infill. The ABAQUS ‘‘Coupling’’ func-tion was used to join the three column parts. A series of ABAQUSmodels were built and run to assess sensitivity of the simulationresults to FE mesh. The reduction factors for strength and elasticmodulus of carbon steel at elevated temperatures provided in EN1993-1-2 [10] were used. In the test structures, many contact pairsexisted in the joints. The ABAQUS contact function was used tosimulate the interaction between the contact pairs. In order to re-duce the computational cost, a contact was defined as surface tosurface contact with a small sliding option. ‘‘Hard contact’’ was as-sumed for the normal contact behaviour and a friction coefficientof 0.3 was used in the tangential direction of the contact pairs.The friction coefficient values have been found to have little effecton the simulation results. The boundary conditions of the FE modelwere according to those in the test: the bottom of the columns waspinned in all three directions and the top of the columns was pin-ned in two directions but movement along the column longitudinalaxis was allowed. Since only half of the beam was included in theFE model due to geometrical and loading symmetry as discussedearlier, the beam mid-section was fixed in the axial direction atall nodes, which effectively prevented rotation about any axis inthe beam cross-section, but allowed the beam to twist about itslongitudinal axis.

0

100

200

300

400

60 80 100 120 140 160 180 200 220 240Time (min.)

Tem

pera

ture

(°C

)


(b) After 60 min

of Ding and Wang [5] (reverse channel connection).

Table 2Mechanical property values for different steel members used in Test 10 of Ding andWang [5] (reverse channel connection).

Component beamweb

Beamflange

Column Endplate

Reversechannelweb

Reversechannelflange

Elasticmodulus(MPa)

206,606 206,378 200,001 – 192,280 207,811

Yieldstrength(MPa)

352 309 406 – 397 351

Maximumstrength(MPa)

493 477 539 – 562 561

Ultimatestrain(%)

32.1 34.9 29.5 – 27.1 32.6


The test beam had no lateral restraint and could move sideways.But in the test, in order to ensure that the loading jacks remainedattached to the beam, each loading jack was inserted into a steelbracket which was then clamped on the top flange of the beam.

Fig. 10. Behaviour of Test 10 of Ding and W

-50

-40

-30

-20

-10

0

10

20

30

0 100 200 300 400 500 600 700 800


Axi

al fo

rce

(KN

)

Test

Abaqus

(a) Beam axial force – temperature relationships

Fig. 11. Comparison between modelling and experimental results for mid-span deflectioWang [5].

Therefore, in the numerical model the four corners of the loadingplate were laterally restrained. As in the test, the FE modelling ap-plied the loads in two steps: (i) two point loads were applied to thebeam at ambient temperature; (ii) while maintaining the structuralloads, the structural temperatures were exposed to fire attack untilthe end of the fire test. In the FE model, six different temperaturecurves based on the test measurements were adopted for differentparts of the structure: a total of three temperature curves for thebottom flange, web and top flange of the beam; one temperaturecurve for the joint zone which included all the bolts, nuts and con-nection components as well as 100 mm length of the beam in thejoint zone; one temperature curve for the steel tubular column inthe joint region; one temperature curve for concrete fill in the jointregion. The temperature of the column away from the joint zonewas set at ambient temperature. Since the column was not loaded,it was not necessary to refine the concrete infill model.

2.2. Finite element results

In order to evaluate reliability of the 3D finite element model,test results of two different fire tests recently conducted at the

ang [5] (reverse channel connection).


-80

-70

-60

-50

-40

-30

-20

-10

0 0 100 200 300 400 500 600 700 800

Def

lect

ion

(mm

)

Test

Abaqus

Thermal bowing

(b) Beam mid-span deflection – temperature relationships

n and axial force in the beam with reverse channel connections, Test 10 of Ding and

4.0

m4.

0 m

3.0 m 4.0 m 3.0 m

10.0 m

Fig. 12. Dimensions and boundary condition of structure assembly.

Table 3Mechanical property values for different steel components at ambient temperature(based on Test 4 of Ding and Wang [5]).

Component Beamweb

Beamflange

Column End plate, reversechannel

Elastic modulus(MPa)

210,050 226,690 203,210 210,000

Yield strength (MPa) 396 379 492 355Maximum strength

(MPa)550 572 536 560

Ultimate strain (%) 25.3 27.2 19.4 20


University of Manchester [5], one using reverse channel connectionand the other using fin plate connection, are used for direct com-parison. The test results included deformation patterns, beammid-span deflections and beam axial forces. As detailed in the fol-lowing sections, this comparison demonstrates that the 3-D finiteelement model is able to successfully simulate the fire tests duringboth the heating and cooling stages.

2.2.1. Test 9 of Ding and Wang [5]: fin plate connectionTest 9 of Ding and Wang [5] used CHS 193.7 � 5 mm tubes and

fin plate connection. Referring to Fig. 2, a fin plate of 8 mm thick-ness was welded to the middle of the tubular wall with 8 mm Fillet

Beam 457x15

Beam 457x

230x90channel

260 long 40

260

230

35

260x170x14endplate

Grade 8.8M20 bolts

FW

40

9

90

230x90channel

260 long

35

260x170x14endplate

FW 9040

90

300

FW

Fig. 13. Basic geometrical details of flexible e

Weld (FW) on both sides and bolted to the beam with two M20Grade 8.8 bolts. There was no fire protection on the joints. Duringthe test, the furnace fire exposure was stopped and fan-assistedcooling started just after the beam changed its behaviour frombending to catenary action.

Fig. 3 shows the FE mesh and Fig. 4 presents the input temper-ature–time relationships for the beam web and flanges, the steeltube, the connection zone and the concrete fill. In the numericalmodel, the yield strength, ultimate strength and elastic modulusof the steel members at ambient temperature were obtained fromtensile coupon tests and they are given in Table 1. For the concretein Test 9 of Ding and Wang [5], the average cube strength was45.3 MPa and the density was 2212 kg/m3.

Fig. 5 compares the modelling and experimental results fordeformation modes of the beam and the joint. It can be seen thatthe observed deformations of the joint components and the beamwere closely followed by the numerical model. As shown in Fig. 5a,there was no fracture and failure of the sub-frame. Due to expan-sion and bending of the steel beam, the bottom flange of the beamwas bearing against the CFT columns during the heating stage, as

2x67

152x67

C/L

40

260

230x90channel

260 long90

9040

40 90 40

260x170x14endplate

FW

nd plate connection to reverse channel.

Fig. 14. Mathematical model for stress–strain relationships of steel at elevated temperatures (EN 1993-1-2).

0

100

200

300

400

500

600

700

800

0 20 40 60Time (min.)

Tem

pera

ture

(°C

)

Gas (fire) temperatureBeam (bottom flange&web)ConnectionBeam (top flange)Steel tubeCon Fill

(a) Before 60 min.

0

100

200

300

400

500

600

700

800

60 80 100 120 140 160 180 200Time (min.)

Tem

pera

ture

(°C

)Gas (fire) temperatureBeam (bottom flange&web)ConnectionBeam (top flange)Steel tubeCon Fill

(b) After 60 min.

Fig. 15. Input time–temperature curves for different parts of the simulation structure.


shown in Fig. 5a and b. Apart from these, there was no noticeabledeflection in the steel tubes. Due to large twist in the beam, the finplates were also twisted to one side as shown in Fig. 5b. Fig. 6 com-pares the measured and simulated beam axial force and beam mid-span deflection as functions of the beam lower flange temperatureat mid-span. The test structure experienced high compression butsmall lateral deflection during the thermal expansion stage. Be-cause cooling started just after the beam reached its limiting tem-perature for bending, the beam also developed high tension forcesduring the cooling stage. The simulation results have accuratelycaptured the entire cycle of beam behaviour.

2.2.2. Test 10 of Ding and Wang [5]: reverse channel connectionTest 10 of Ding and Wang [5] used CHS 193.7 � 5 mm tubes and

reverse channel connection. Referring to Fig. 7, the flanges of a re-verse channel section 152 � 89 were welded to the tubular wallwith 8 mm FW on the outside. A flexible endplate of 8 mm thick-ness was welded to the beam with 6 mm FW on both sides andthen bolted to the reverse channel with four (2 by 2) M20 Grade8.8 bolts. There was no fire protection on the joints.

Fig. 8 shows the FE model and Fig. 9 presents the input temper-ature–time relationships for the beam web and flanges, the steeltube, the connection zone and the concrete fill. Table 2 lists theaverage yield strength, ultimate strength and elastic modulus ofthe steel members at ambient temperature used in the numericalmodel, based on steel tensile coupon tests. For Test 10 of Dingand Wang [5], the average concrete cube strength was 46.2 MPaand the concrete density was 2305 kg/m3.

Fig. 10 compares the modelling and experimental results fordeformation modes of the beam and the joint. It can be seenthat the deformation patterns obtained by the simulation andfrom the test are very close. No failure was observed in boththe test specimen and numerical model. The beam was bentslightly, as shown in Fig. 10a. There was no visible deformationin the steel tube and the connection region, as shown inFig. 10b. Fig. 11 shows that both the numerical and measuredbeam axial force match well. The numerical results for beamdeflection during the heating stage are considerably higher thanthe experimental results. This was also the case in the previouscomparison (Fig. 6). This difference in the beam mid-span deflec-tion may be due to the difficulty in the experiment recording thebeam deflection when it was small. The beam deflection wasmeasured by attaching the LVDT to a ceramic rod through thefurnace lid and the ceramic rod may not have been able topromptly follow the movement of the beam. To substantiate thisclaim, the beam’s thermal bowing deflection was calculated andthe results are shown in Fig. 11b. Since the beam’s deflection be-fore experiencing accelerated rate of change was mainly thermalbowing deflection, the close agreement between the numericalsimulation results and the analytical calculation results indicatesthat the numerical results are credible. The beam’s thermal bow-ing deflection at mid-span can be calculated using the followingequation:

dth ¼a � DT � L2

h

0

5

10

15

20

25

30

0 50 100

150

200

250

300

350

400

450

500

550

600

650

Beam bottom flange temp. (°C)

Str

ain

%

Max Strain

Failure during heating phase

Failure during cooling phase

(c) Maximum plastic strain in reverse channel – beam temperature relationships

-160

-120

-80

-40

0

40

80

120

160

200

240

0 50 100

150

200

250

300

350

400

450

500

550

600

650


Axi

al fo

rce

(KN

)

Failure during heating

Failure during cooling

(a) Beam axial force – beam temperature relationships

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

- 50 100

150

200

250

300

350

400

450

500

550

600

650


Def

lect

ion

(mm

) Failure during heating phase

Failure during cooling phase

(b) Beam mid-span deflection – beam temperature relationships

Fig. 16. Beam mid-span deflection–beam temperature, beam axial force–beam temperature and maximum plastic strain–beam temperature relationships.


where a is the thermal expansion coefficient of steel (0.000014 m/m.C), DT the temperature difference between the top and bottomflanges, L the beam span (2 m) and h the overall beam depth(178 mm).

The test structure experienced large compression during thethermal expansion stage. However, unlike Test 9 of Ding and Wang[5], because in this test cooling started just before the beamreached its limiting temperature in bending, the beam was still

Fig. 17. Failure modes of connection.

0

50

100

150

200

250

300

350

400

450

0

0.05 0.1

0.15 0.2

Strain

Stre

ss [N

/mm

2 ] A

E

D

B

C

T1=585°C

T2=100°C

Fig. 18. Movement of critical strain between two different temperatures.


in substantial compression when cooling started. As a result, theresidual tensile force in the beam was quite small when comparedwith Test 9 of Ding and Wang [5]. This is closely predicted by theFE model.

The above comparisons demonstrate that the authors’ ABAQUSmodel is valid.

3. Behaviour of restrained structural subassemblies of steelbeam to CFT column in fire during cooling stage

The validated numerical model is used to conduct extensivenumerical simulations in order to investigate the behaviour of re-verse channel connections between steel beams and CFT columnsunder cooling. The aim of this investigation is to find means of reduc-ing the risk of joint failure during the cooling stage. Fig. 12 shows thestructure arrangement to be simulated in this research. It representsa steel beam connected to two concrete filled tubular (CFT) columns.The top and bottom of the columns are rotationally unrestrained butare horizontally restrained to simulate the lateral stability system ina real structure. This structural arrangement is the same as used inthe fire tests of Ding and Wang [5] but the dimensions are more real-istic. The beam was assumed to be fully restrained in the lateraldirection to represent the effect of the concrete slab.

3.1. Basic case

– Compared to flush and extended endplate connections, aflexible end plate connection is more likely to fail duringcooling. Therefore, this research focuses on reverse channelconnection using a flexible endplate. Fig. 13 shows detailsof the connection.

Other basic parameters were:

– Beam section size: 457 � 152 � 67UB (flange width153.8 mm, overall height 458 mm, flange thickness 15 mm,web thickness 9 mm).

– Beam span: 10 m.– Total column height: 8 m (2 storeys of 4 m).– Channel section size: 230 � 90 (overall depth 230 mm, over-

all width 90 mm, leg thickness 14 mm, web thickness7.5 mm).

– Endplate thickness: 10 mm.– Material properties: the stress–strain constitutive relation-

ships adopted in the FE model for the steel beam, columnsand connection components were based on the steel tensilecoupon tests at ambient temperature (Table 3) of Test 4 ofDing and Wang [5]. For ABAQUS simulation, the nominalengineering stress–strain relationship obtained from thesteel tensile coupon test was converted to the true stress–strain relationship.

– Fig. 14 shows the adopted engineering strain–strain curvesat different temperatures. According to EN 1993-1-2, allstress–strain curves enter the descending branches at 15%strain and completely lose stress at 20% strain.

– In the fire tests of Ding and Wang [5], all the columns wereunloaded and sufficiently strong to resist the axial loadsfrom the beam. However in reality the columns will beloaded. In this research, the load ratio in the columns isabout 0.5, based on combined axial load and bendingmoment as a result of the maximum catenary force in the

Table 4Summary of parametric study results.

SimulationID

Fire protection schemefor connection

Span(m)

Ultimatestrain (%)

Revere channel webthickness (mm)

Loadratio

BLT Reduction intemperature (�c)

The beam’s axialrestraint level (%)

Results

1 – 10 20 7.5 0.7 585 0 7.5 F2 CFP A 10 20 7.5 0.7 585 0 7.5 F3 CFP B 10 20 7.5 0.7 585 0 7.5 F4 CFP C 10 20 7.5 0.7 585 0 7.5 F5 – 10 27 7.5 0.7 585 0 7.5 NF6 – 10 20 10 0.7 585 0 7.5 NF7 – 10 20 7.5 0.5 648 0 7.5 F8 – 10 20 7.5 0.4 673 0 7.5 NF9 – 10 20 7.5 0.7 585 10 7.5 F

10 – 10 20 7.5 0.7 585 25 7.5 NF11 – 10 20 7.5 0.8 545 25 7.5 F12 – 10 20 7.5 0.8 545 50 7.5 NF13 – 10 20 7.5 0.7 570 0 15 F14 – 10 20 7.5 0.7 565 0 25 F15 – 10 20 7.5 0.7 561 0 50 F16 – 10 20 7.5 0.7 570 50 15 NF17 – 10 20 7.5 0.7 565 50 25 F18 – 10 20 7.5 0.7 561 50 50 F19 – 10 20 7.5 0.7 565 75 25 NF20 – 10 20 7.5 0.7 561 125 50 NF21 – 10 20 7.5 0.4 670 30 15 F22 – 10 20 7.5 0.4 670 50 15 NF23 – 10 20 7.5 0.5 640 30 15 F24 – 10 20 7.5 0.5 640 50 15 NF25 – 10 20 7.5 0.6 605 30 15 F26 – 10 20 7.5 0.6 605 50 15 NF27 – 10 20 7.5 0.8 540 50 15 F28 – 10 20 7.5 0.8 540 60 15 NF29 – 7.5 20 7.5 0.7 572 0 15 F30 – 7.5 20 7.5 0.7 572 50 15 NF31 – 12.5 20 7.5 0.7 575 0 15 F32 – 12.5 20 7.5 0.7 575 50 15 F33 – 12.5 20 7.5 0.7 575 65 15 NF

F = failure, NF = no failure.CFP = connection fire protection.BLT = beam limiting temperature.

0

100

200

300

400

500

600

700

0 30 60 90 120 150 180 210 240Time (min.)

Tem

pera

ture

(°C

)

Protected beam AProtected beam BProtected beam CProtected connection AProtected connection Bprotected connection C

Fig. 19. Calculated time–temperature curves for protected and non-protected connections.


connected beam. Based on this calculation, a Square HollowSection (SHS) 300 � 35 mm section was used for thecolumns.

– Initial applied load ratio in the beam = 0.7. Here the load ratiois defined as the ratio of the maximum bending moment inthe simply supported beam to the plastic moment capacityof the beam at ambient temperature.

The temperature profiles (see Fig. 15) for different parts of the struc-ture were obtained based on the following calculation procedure:

– The ISO834 standard time–temperature curve (ISO 1980)was applied to calculate the fire temperature during theheating phase. The standard curve is given by hg =20 + 345log10(8t + 1).

-140

-100

-60

-20

20

60

100

140

180

0 50 100

150

200

250

300

350

400

450

500

550

600

650


Axi

al fo

rce

(KN

)

UnprotectedProtected AProtected BProtected C

(a) Beam axial forces – beam temperature relationships 0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450 500 550 600 650Beam bottom flange temp. (°C)

Str

ain

%

Max Strain UnprotectedProtected A Protected BProtected C

Unprotected

Protected A

Protected C

Protected B

(b) Plastic strain – temperature relationships

Fig. 20. Comparison between three different fire protection schemes for beam axial force and reverse channel web strain–beam temperature relationships.

0

50

100

150

200

250

300

350

0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

0.27 0.3

Plastic strain

Stre

ss [N

/mm

2 ]

400 [°C]-15%/20%

500 [°C]-15%/20%

600 [°C]-15%/20%

700 [°C]-15%/20%

400 [°C]-22%/27%

500 [°C]-22%/27%

600 [°C]-22%/27%

700 [°C]-22%/27%

Fig. 21. Stress–strain relationships of steel at elevated, temperatures. EN 1993-1-2 values and Ding and Wang [5] values of a ‘‘ductile’’ steel.

-160

-120

-80

-40

0

40

80

120

160

200

240

0 50 100

150

200

250

300

350

400

450

500

550

600

650


Axi

al fo

rce

(KN

)

Unprotected- steel strain limits 22%/27%


(a) Beam axial forces – beam temperature relationships 0

5

10

15

20

25

30


Str

ain

%

Max Strain limit 27%




failure



22%/27%

15%/20%

(b) Plastic strains– beam temperature relationships

Fig. 22. Effects of steel strain limits on connection failure.


– At the maximum heating period (tmax), the maximum tem-perature in the unprotected steel beam reached its limitingtemperature (585 �C). The fire temperature–time relation-ship during the cooling phase was determined using thefollowing equations, based on the parametric fire curve in

EN 1993-1-2 [11]. Fig. 15 shows a set of typical time–tem-perature curves for different parts of the simulationstructure.

hg;t ¼ hmax � 625ðt � tmaxÞ for tmax 6 0:5

Fig. 23. Comparison of deformed shapes of reverse channel with different web thicknesses (simulations 1 and 6).

0

5

10

15

20

25

0 50 100

150

200

250

300

350

400

450

500

550

600

650


Str

ain

%


Reverse channel web thickness=10mm

Reverse channel web thickness=7.5mm

Fig. 24. Effects of reverse channel web thickness on connection strain: maximum plastic strain–beam temperature relationships.

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700Beam bottom flange temp. (°C)

Str

ain

%

Max Strainapplied load ratio 0.7applied load ratio 0.5applied load ratio 0.4

Fig. 25. Effects of beam load ratio on connection behaviour: maximum plastic strain–beam temperature lationships.


hg;t ¼ hmax � 250ð3� tmaxÞðt � tmaxÞ for 0:5 < tmax < 2:0

hg;t ¼ hmax � 250ðt � tmaxÞ for 2:0 6 tmax

where t is the time, hg,t the gas temperature at time t, hmax the valueof the gas temperature at the end of the heating phase, and tmax isthe maximum heating period.

– For unprotected steel elements (beams and unprotectedconnections), the change in temperature Dha,t during afire exposure time interval Dt should be determined fromEN 1993-1-2 [10]:

Dha;t ¼ kshAm=Vcaqa

hnet;dDt

0

5

10

15

20

25


Str

ain

%

Max StrainBeam max. temp.=B.L.TBeam max. temp.=B.L.T-10°CBeam max. temp.=B.L.T-25°C

(c) Maximum plastic strain– beam temperature relationships

-160

-120

-80

-40

0

40

80

120

160

200

240

0 50 100 150 200 250 300 350 400 450 500 550 600 650

Beam bottom flange temp. (°C)A

xial

forc

e (K

N)

Beam max. temp.=B.L.T

Beam max. temp.=B.L.T-10°C



-700

-600

-500

-400

-300

-200

-100

0

- 50 100

150

200

250

300

350

400

450

500

550

600

650


Def

lect

ion

(mm

)

Beam max. temp.=B.L.T




Fig. 26. Effects of the beam’s maximum temperature on connection failure, BLT = beam limiting temperature.


where ksh is correction factor for the shadow effect (taken as 1.0 inthis study); Am/V is the section factor for the steel element; in whichAm is the surface area of the element per unit length, and V is thevolume of the element per unit length. ca is the specific heat of

steel; hnet,d is the design value of the net heat flux per unit area;Dt is the time interval; qa is the density of steel; ha,t is the steel tem-perature at time t; hg,t is the gas temperature at time t; and Dhg,t isthe increase in gas temperature during the time interval Dt.

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400 450 500 550 600Beam bottom flange temp. (°C)

Str

ain

%

Max Strain

LR=0.8-Beam max. temp.=B.L.T-25°C


Fig. 27. Effects of load ratio on the beam’s maximum safe temperature during cooling:maximum plastic strain–temperature relationships.


– For protected steel elements (columns and protected connec-tions), the change in temperature Dha,t during a time intervalDt should be determined from:

Dha;t ¼kpAp=Vdpcaqa

ðhg;t � ha;tÞð1þ /=3Þ Dt � ðe/=10 � 1ÞDhg;t

where

/ ¼cpqp

caqadpAp=V

where Ap/V is the section factor of the steel section insulated by fireprotection; in which Ap is the appropriate area of the fire protectionmaterial per unit length of the element, and V is the volume of thesteel element per unit length. cp is the temperature dependent spe-cific heat of the fire protection material; dp is the thickness of thefire protection material; Dt is the time interval; kp is the thermalconductivity of the fire protection system; and qp is the density ofthe fire protection material.– The section factor for the top flange was calculated as for a rect-

angular section exposed to fire on three sides using the follow-ing formula:

Am=V ¼ bþ 2tf

tf

where b is the flange width and tf is the flange thickness.– For the reverse channel web and the endplate, Ding and Wang

[12] suggested that the section factor may be calculated as fora steel plate with the combined thickness, i.e.

2=ðt1 þ t2Þ

where t1 is the end plate thickness and t2 is the reverse channel webthickness.– The tubular column was assumed to be fully protected. The

steel tube in a CFT column may be treated as an empty tubefor the purpose of calculating the steel tube temperature [13].The equivalent steel tube thickness may be calculated asfollows:

tse ¼ ts þ tce

� with tce = 0.15bi for bi (or di) < 12p

T� or tce = 1.8

pT for bi (or di) P 12

pT

where ts is the original steel tube thickness (mm), tce is the increasein steel tube thickness for temperature calculation (mm); bi is theminimum dimension of the concrete core (mm); and T is the fireresistance time (min).

3.2. Simulation results for the basic case

Fig. 16a shows axial force developments in the beam withcontinuous heating only and with heating up to the beam’s lim-iting temperature followed by cooling. At the beginning of fireexposure, due to restrained thermal expansion, an axial com-pression force is present in the beam and the compression forceincreases with increasing temperature until reaching the maxi-mum value (113 kN) at 437 �C. Afterwards, the beam mid-spandeflection starts to increase more rapidly until reaching658 mm (more than span/20) at the maximum beam tempera-ture of 585 �C (the beam’s limiting temperature), as shown inFig. 16b. For the beam with continuous heating, failure occursat 618 �C after some catenary action has developed in the beam.For the beam in cooling, the beam deflection changes within anarrow range because the beam deflection is mainly plastic.However, due to restrained cooling, the beam develops tensionforce at decreasing temperature. Eventually, the connection failsat near ambient temperature (22 �C) when the beam tensionforce reaches about 168 kN, as a result of excessive plasticstrains (larger than 20% strain, see Fig. 16c) in the connection.As shown in Fig. 17, failure is caused by fracture of the reversechannel web around the bolt holes and fracture at the reversechannel web/flange junctions.

Fig. 18 may be used to explain the variation of plastic strain dur-ing the cooling phase shown in Fig. 16c. Assume a point in the struc-ture is at temperature T1 (585 �C, cooling start temperature), and itsstress–strain state is at point A on the stress–strain curve at T1. Oncooling, due to the change of the beam axial force from compressionto tension, the stress decreases to point B and then starts to increaseelastically. During this stage, although the stress within the steel in-creases as a result of the increasing tensile force in the connectiondue to restrained thermal contraction, the total strain is lower ow-ing to increased stiffness at lower temperatures. Therefore, for aconsiderable period of time, the plastic strain is unchanged. Nearambient temperature (T2), the stress–strain relationships atdifferent temperatures are almost identical. Therefore, further in-crease in tensile force in the connection can only be accommodated


by further strain increase shown as point C in the figure. Once thestrain exceeds 15% (point D), the stress–strain curve enters thedescending branch and accelerated straining is necessary to main-tain structural equilibrium. Connection failure occurs at 20% strain(point E).

0

5

10

15

20

25

0 50 100 150 200 250 300Beam bottom

Str

ain

%

(c) Maximum plastic strain –

-220-180-140-100-60-202060100140180220260300

0 50 100 150 200 250 30

Beam bottom flange temp. (

Axi

al fo

rce

(KN

)

(a) Beam axial force – bea

-850

-750

-650

-550

-450

-350

-250

-150

-50

- 50 100 150 200 250 300Beam bottom

Def

lect

ion

(mm

)

max. temp.=B.L.Tmax. temp.=B.L.Tmax. temp.=B.L.Tmax. temp.=B.L.T-50max. temp.=B.L.T-50max. temp.=B.L.T-50

K−K−K−

(b) Beam mid-span deflection

Fig. 28. Effects of axial restraint level o

4. Parametric studies

The above simulation results for the basic case suggest thatthere is a risk of connection fracture during the cooling stage.A parametric study has been conducted to investigate the effects

350 400 450 500 550 600 650flane temp. (°C)

Max Strainmax. temp.=B.L.T-50°Cmax. temp.=B.L.T-50°Cmax. temp.=B.L.T-50°Cmax. temp.=B.L.Tmax. temp.=B.L.Tmax. temp.=B.L.T

BAAK25.0K =−

BAAK50.0K =−

BAAK50.0K =−

BAAK15.0K =−

BAAK15.0K =−

BAAK25.0K =−

beam temperature relationships

0 350 400 450 500 550 600 650

°C)

max. temp.=B.L.Tmax. temp.=B.L.Tmax. temp.=B.L.Tmax. temp.=B.L.T-50°Cmax. temp.=B.L.T-50°Cmax. temp.=B.L.T-50°C

BAAK15.0K =−

BAAK15.0K =−

BAAK50.0K =−

BAAK50.0K =−

BAAK25.0K =−

BAAK25.0K =−

m temperature relationships

350 400 450 500 550 600 650flange temp. (°C)

°C°C°C

BAAK15.0K =−

BAAK15.0=

BAAK25.0=

BAAK25.0K =−

BAAK50.0=

BAAK50.0K =−

– beam temperature relationships

n beam behaviour during cooling.

-700

-600

-500

-400

-300

-200

-100

0


Def

lect

ion

(mm

)




LR=0.7-Beam max. temp.=B.L.T-125°C BAAK50.0K =−

BAAK50.0K =−

BAAK25.0K =−

BAAK25.0K =−


0

5

10

15

20

25

- 50 100 150 200 250 300 350 400 450 500 550

0 50 100 150 200 250 300 350 400 450 500 550Beam bottom flange temp. (°C)

Str

ain

%

Max Strain





BAAK25.0K =−

BAAK25.0K =−

BAAK50.0K =−

BAAK50.0K =−

(c) Maximum plastic strain – beam temperature relationships

-240-200-160-120-80-4004080120160200240280

0 50 100 150 200 250 300 350 400 450 500 550


xial

forc

e (K

N)

max. temp.=B.L.T-50°C




BAAK25.0K =−

BAAK25.0K =−

BAAK50.0K =−

BAAK50.0K =−


Fig. 29. Effects of cooling temperature at different levels of axial restraint.


of different design parameters and how they may be changed toprevent joint failure during the cooling stage. Table 4 lists all thesimulations carried out in the parametric study, which coveredthe six parameters identified in the previous section: (1) jointfire protection scheme (temperature); (2) ductility (ultimatestrain) of steel; (3) reverse channel web thickness; (4) applied

load ratio; (5) difference between the beam’s limiting tempera-ture and the temperature (before reaching its limiting tempera-ture) at which cooling starts, and (6) the beam’s axial restraintlevel. Table 4 also indicates whether the connection has failedor not.

0

5

10

15

20

25


Str

ain

%

Max Strainmax. temp.=B.L.T-30°C-LR= 0.5max. temp.=B.L.T-50°C-LR= 0.5max. temp.=B.L.T-30°C-LR= 0.6max. temp.=B.L.T-50°C-LR= 0.6


-200

-150

-100

-50

0

50

100

150

200

0 50 100

150

200

250

300

350

400

450

500

550

600

650

Beam bottom flange temp.(°C)A

xial

forc

e (K

N)

max. temp.=B.L.T-30°C-LR= 0.5max. temp.=B.L.T-50°C-LR= 0.5max. temp.=B.L.T-30°C-LR= 0.6max. temp.=B.L.T-50°C-LR= 0.6


-650

-550

-450

-350

-250

-150

-50

- 50 100

150

200

250

300

350

400

450

500

550

600

650


Def

lect

ion

(mm

)



Fig. 30. Effects of cooling temperature at different beam applied load ratios: applied load ratio = 0.5 and 0.6.


4.1. Effect of fire protection scheme for the connection zone(simulations 2–4)

In the basic case, the connection zone temperature was quitehigh. To examine whether it is possible to prevent connection

failure during the cooling stage by reducing the connectiontemperature, three connection fire protection (temperature)schemes were considered: the connection zone was protectedby the same fire protection thickness as the beam which reachedits limiting temperature at 30, 60 and 90 min of standard fire

-650

-550

-450

-350

-250

-150

-50

- 50 100

150

200

250

300

350

400

450

500

550

600

650

700


Def

lect

ion

(mm

)



0

5

10

15

20

25


Str

ain

%

Max Strainmax. temp.=B.L.T-30°C-LR= 0.4max. temp.=B.L.T-50°C-LR= 0.4max. temp.=B.L.T-50°C-LR= 0.8max. temp.=B.L.T-60°C-LR= 0.8


-200

-150

-100

-50

0

50

100

150

200

250

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700


xial

forc

e (K

N)



Fig. 31. Effects of cooling temperature at different beam applied load ratios: applied load ratio = 0.4 and 0.8.


exposure respectively (fire protection (mineral wool) thickness tobeam = 3.3, 8.2 and 13.7 mm respectively). Fig. 19 shows thetime–temperature curves for the protected connection zone and

the beam. In all three cases, the connection zone temperaturewas quite low. Fig. 20a compares the beam axial force–tempera-ture relationships and Fig. 20b the reverse channel strain (the

0

10

20

30

40

50

60

70

0.4 0.5 0.6 0.7 0.8The beam applied load ratio

Red

uctio

n in

BLT

(°C

)

BAAK15.0K =

BAAK075.0K =

Fig. 32. Effects of the beam applied load ratio on required reduction from beam limiting temperature when cooling starts.


reverse channel web)–beam temperature relationships for thethree fire protection schemes. All the connections failed duringthe cooling stage by the same mode of failure as shown inFig. 17 (the reverse channel web). This is expected. Since connec-tion failure occurred during the cooling stage, the heating historyin the connection has little effect.

4.2. Effects of increasing connection ductility (simulation 5)

In EN 1993-1-2, the maximum strain of steel at yield stress is15% and the fracture strain of steel is 20%. It is possible for steelto reach higher strains. For example, Ding and Wang [5] reportedfracture strain of 27% from their steel coupon tests. Since connec-tion fracture is due to its strain limit being exceeded, it is possibleto prevent connection fracture if the connection steel has higherstrain capacity. To investigate this claim, a simulation was carriedout in which the steel strain limits were changed from the above15%/20% to 22%/27% respectively. Fig. 21 shows the alternativestress–plastic strain relationships with the higher strain limitsat different temperatures.

Fig. 22 compares the reverse channel maximum plastic straindevelopments between using 20% and 27% steel strain limites. At15%/20% strain limits, the connection fails before complete cool-ing to room temperature with the strain increasing at rapid ratesbefore fracture at around 36 �C. At 22%/27% strain limits, there isno connection fracture during cooling and the strucure remainsintact because the maximum steel strain when cooled down tothe ambient temperature is still much lower than 27% strainabove which fracture is considered to have started. Whilst the27% strain limit is based on only one set of mechanical test re-sults, it clearly indicates the benefits of using ductile steel andthe necessity of better quantifying the strain limits of steel.

4.3. Effects of reverse channel web thickness (simulation 6)

Because the failure mode in the previous simulation cases wasreverse channel fracture, it was expected that increasing the re-verse channel thickness would prolong integrity of the structure.This is confirmed. Fig. 23 compares the deformed shape and theequivalent Mises plastic strain for two reverse channel web thick-nesses: 7.5 mm and 10 mm. The thicker reverse channel (10 mm)develops much lower plastic deformation than the thin one, asshown in Fig. 24. Increasing the reverse channel web thicknessfrom 7.5 mm to 10 mm prevented the fracture of the reverse chan-nel web around the bolt holes.

4.4. Effects of applied load ratio (simulations 7 and 8)

In simulations 1–6, the applied load ratio (0.7) was high so themaximum connection plastic strain was already quite high beforecooling started. The risk of connection failure during the coolingphase was high. Connection behaviour for three load levels wascompared, the load ratios being 0.4, 0.5 and 0.7. Here the load ratiois defined as the ratio of the applied load in fire to the beam’s ambi-ent temperature plastic bending moment capacity with simplysupported boundary conditions.

Fig. 25 compares the simulation results for the maximum plas-tic strain in the connection. Connection failure is prolonged whenthe load ratio is lower and at the lower load ratio of 0.4, the con-nection is able to survive during the cooling stage.

4.5. Effect of the beam maximum temperatures (simulations 9–12)

Results of the above parametric studies indicate that connec-tions may fail during the cooling stage. While it is possible to re-duce this risk by changing one or more structural parameters (forexample, using lower load ratio, thicker reverse channel or moreductile steel), it is necessary to for the designer to evaluate detailedstructural behaviour, which may not be available in many cases.Therefore, there is a need to find an alternative, much simpler ap-proach. One possibility is to start cooling at a temperature lowerthan the beam’s limiting temperature based on bending. In an axi-ally restrained beam, the axial force in the beam is compression attemperature lower than the limiting temperature. If the maximumbeam temperature when cooling starts is lower than the beam’slimiting temperature in bending, then the axial load in the beamis compressive when cooling starts and this compression forcecan be used to offset the tensile force in the connection whenthe beam cools.

Fig. 26 compares the beam’s axial force–beam temperature andvertical deflection–temperature relationships between three cases:the beam’s maximum temperature is equal to the beam’s limitingtemperature (case 1), the beam’s maximum temperature is 10 �Cless than the beam’s limiting temperature (case 2) and the beam’smaximum temperature is 25 �C less than the beam’s limiting tem-perature (case 3). From Fig. 26a, it can be seen that a very large ten-sion force (183 kN) was generated in the beam, causing failure ofthe connection before it had cooled down to room temperature,Fig. 26c showing the maximum connection strain exceeding thestrain limit of steel. Starting cooling at 10 �C below the beam’s lim-iting temperature prolonged the connection’s survival time during

0.00

5.00

10.00

15.00

20.00

25.00

0 50 100 150 200 250 300 350 400 450 500 550 600Beam bottom flange temp. (°C)

Stra

in %

Max Strainmax. temp.=B.L.T-L=7.5 mmax. temp.=B.L.T-L=10 mmax. temp.=B.L.T-L=12.5 mmax. temp.=B.L.T-50°C-L=7.5 mmax. temp.=B.L.T-50°C-L=10 mmax. temp.=B.L.T-50°C-L=12.5 mmax. temp.=B.L.T-65°C-L=12.5 m


-200

-160

-120

-80

-40

0

40

80

120

160

200

240

280

0 50 100 150 200 250 300 350 400 450 500 550 600

0 50 100 150 200 250 300 350 400 450 500 550 600

Beam bottom flange temp.(°C)

Axi

al fo

rce

(KN

)

max. temp.=B.L.T-L=7.5 mmax. temp.=B.L.T-L=10 mmax. temp.=B.L.T-L=12.5 mmax. temp.=B.L.T-50°C-L=7.5 mmax. temp.=B.L.T-50°C-L=10 mmax. temp.=B.L.T-50°C-L=12.5 mmax. temp.=B.L.T-65°C-L=12.5 m


-1100

-900

-700

-500

-300

-100


Def

lect

ion

(mm

)

max. temp.=B.L.T-L=7.5 mmax. temp.=B.L.T-L=10 mmax. temp.=B.L.T-L=12.5 mmax. temp.=B.L.T-50°C-L=7.5 mmax. temp.=B.L.T-50°C-L=10 mmax. temp.=B.L.T-50°C-L=12.5 mmax. temp.=B.L.T-65°C-L=12.5 m


Fig. 33. Effects of the beam span to depth ratio on the beam safe temperature during cooling.


cooling but the connection still failed before cooling down to ambi-ent temperature. In contrast, because the beam in case 3 was stillexperiencing high compression when cooling started, the residualtension force in the beam was reduced (to 168 kN) so that the max-imum connection tension strain was lower than the strain limit of

steel throughout the cooling phase. Therefore, there was no con-nection failure in case 3.

The reduction from the beam’s limiting temperature (BLT) tothe beam’s maximum temperature before cooling starts increasesas the load in the beam increases because of the existing higher


connection tensile strain at a higher load ratio. For example, in thecase of a high load ratio (0.8), the reduction in temperature (differ-ence between beam limiting temperature and maximum beamtemperature at which cooling starts) approaches 50 �C, as shownin Fig. 27.

4.6. Effect of different levels of axial restraint (simulations 13–20)

The level of axial restraint is obviously an important parameter affect-ing beam and connection behaviour during cooling. All other conditionsbeing the same, the tension force in the connection (and the beam) in-creases as the axial restraint stiffness increases and therefore the risk ofconnection failure during cooling increases. For example, Fig. 28c com-pares the maximum connection strain at three levels of axial restraintstiffness (15%, 25% and 50% of beam axial stiffness KBA). The maximumbeamtemperaturewhencoolingstartsisthesame,being50 �Clowerthanthe beam’s limiting temperature. The results in Fig. 28 show that the con-nection in all three cases failed when the beam starts to cool at the beam’slimiting temperature but failure occurred at different temperatures.Whenthebeamstarts tocoolat50 �Clowerthanthebeam’s limitingtem-perature in case of KA = 0.15KBA there is no failure during cooling. But con-nection failure occurs if the axial restraint stiffness is higher. It should bepointed out that the axial restraint stiffnesses used are high compared tothat inrealisticdesign.Toenablethebeamwithhigheraxial restraintstiff-nesses to survive the cooling phase without a connection failure, furtherreductions from the beam’s limiting temperature to the maximum tem-perature at which cooling starts should be considered. For example,Fig.29 showsthatareductionof75 �Cisnecessaryforthecaseof25%axialrestraint stiffness and 125 �C for the case of 50% restraint stiffness.

4.7. Effect of applied load ratio with 15% axial restraint (simulations21–28)

In order to investigate the effects of the beam applied load ra-tio on the behaviour of the beam and connection during cooling,different applied load ratios were applied to the 10 m beam. Theapplied load ratios were 0.4, 0.5, 0.6, 0.7 and 0.8. Here the loadratio is defined as the ratio of the applied load in fire to thebeam’s ambient temperature plastic bending moment capacitywith simply supported boundary conditions. The axial restraintstiffness was 15% of the respective beam axial stiffness KBA. Allother conditions were kept the same. Figs. 30 and 31 comparethe results for the beams that start cooling at different tempera-tures before reaching the beam’s limiting temperature, the differ-ences being 30 �C, 50 �C or 60 �C. Because the load ratios aredifferent, the beam’s limiting temperatures are also different. Itis clear that the beam deflection and axial force vary with the ap-plied load ratio, having larger deflections, lower compressionforces and higher tension forces at a higher load ratio, as shownin Figs. 30a, b, 31a and b. When the beam starts to cool at30 �C lower than the beam’s limiting temperature, beams at allapplied load ratios experience connection failure during cooling.But connection failure is prevented if the beam starts to cool at50 �C lower than the beam’s limiting temperature for applied loadratios 0.4, 0.5, 0.6 and 0.7, as shown in Fig. 30c. A higher reduc-tion in temperature, about 60 �C, is needed for load ratio 0.8, asshown in Fig. 31c.

Fig. 32 summarises the simulation results, showing the requiredreduction in beam temperature from limiting temperature to cool-ing temperature for the two different axial restraint levels of 7.5%and 15%. In the case of 7.5% restraint, no reduction is required forload ratio = 0.4 and 50 �C reduction is required if the load ratio is0.8. However, in case of the higher axial restraint level (15%), morereduction in temperature is needed. Even so, if the load ratio isrealistic (not exceeding 0.7), connection failure does not happen

if the cooling temperature is 50 �C lower than the beam’s limitingtemperature.

4.8. Effects of beam span to depth ratio (simulations 29–33)

The beam span to depth ratio is another parameter which hasnoticeable effect on the beam and connection behaviour duringcooling. A number of simulations were performed to investigatethe effects of beam span to depth ratio. In these simulations, theapplied load ratio was 0.7. The beam spans were 7.5, 10 and12.5 m, giving span/depth ratios of about 17, 22 and 27 respec-tively. The axial restraint stiffness was 15% of the respectivebeam axial stiffness KBA. All other conditions were kept thesame. Fig. 33 compares the results for the beams that start cool-ing at different temperatures before reaching the beam’s limitingtemperature, the differences being 0 �C, 50 �C or 65 �C. Becausethe relative stiffness of the axial restraint to that of the beamis the same in all beams, the initial developments of axial forcein the beams are identical irrespective of the beam span. Becausethe load ratio is also the same, the beam’s limiting temperaturesare also very close. Although the beam deflection increases withincreasing beam span (Fig. 33b), strains in the connections dur-ing heating are very similar (Fig. 33c). During the cooling stage,the main difference is that the longer beams experience slightlymore rapid increase in strain after the plateau stage. This makesthe connections to the longer beams slightly more prone to frac-ture. The results in Fig. 33c show that if the beam starts coolingat 50 �C before reaching the limiting temperautre, the 7.5 m and10 m beams do not experience connection failure during cooling.But connection failure occurs for the 12.5 m beam span. To pre-vent connection failure during cooling for the 12.5 m beam, cool-ing has to start slightly earlier, at 65 �C before reaching thebeam’s limiting temperature.

5. Conclusions

This paper has presented detailed simulation results of twofire tests carried out on beam to concrete filled tubular (CFT) col-umn assemblies using reverse channel and fin plate connectionsfor validation of the numerical simulation model during coolingstage; and reports the results of an intensive parametric study,using the validated numerical simulation model, to investigatedifferent methods of reducing connection failure occurring duringthe cooling stage of a fire event. The following conclusions maybe drawn:

1. The proposed finite element models give very good agreementwith the experimental results and observations, for thedeformed shapes and, and the beam axial force–temperatureand beam vertical deflection–temperature relationships.

2. There are high risks of failure in the reverse channel connectionusing flexible endplate during cooling. However, such failuremay be prevented by increasing the reverse channel’s webthickness. Connection failure may also be reduced by usingmore ductile steel. While it would not be feasible to make moreductile steel just to enable the structure to pass the coolingstage of a fire attack without failure, more precise quantifica-tion of the strain limits of steel at elevated temperatures wouldhelp more accurate estimate of the connection’s ability to sur-vive cooling.

3. For beams with realistic levels of axial restraint stiffness (con-nection tensile stiffness <15% of beam axial stiffness) and prac-tical levels of loading (load ratio not exceeding 0.7), a moreeffective and simple method is feasible. In this method, thebeam is forced to cool at a temperature below its limiting tem-


perature in bending. If the temperature at which beam coolingstarts is lower than the beam’s limiting temperature by 50 �C,the risk of connection fracture is drastically reduced. The prac-tical implication of this conclusion is to design the beam for alimiting temperature that is 50 �C lower than calculated with-out considering beam axial restraint.

Acknowledgements

The first author of this paper would like to thank the EgyptianMinistry of Higher Education and Al-Azhar University in Cairo,Egypt for providing scholarship to enable him to pursue PhD studyat the University of Manchester.

References

[1] National Institute of Standards and Technology (NIST 2008). Federal buildingand fire safety investigation of the world trade center disaster: structuralresponse and probable collapse sequence of world trade center building 7, vol.2. National Institute of Standards and Technology Report NIST NCSTAR 1–9,2008.

[2] Federal Emergency Management Agency (FEMA 2002). World Trade Centerbuilding performance study. FEMA, USA.

[3] Newman GM, Robinson JT, Bailey CG. Fire safety design: a newapproach to multi-storey steel-framed buildings. The Steel ConstructionInstitute; 2004.

[4] Elsawaf S, Wang YC, Mandal P. Numerical modelling of restrained structuralsubassemblies of steel beam and CFT columns connected using reversechannels in fire. Eng Struct 2011;33:1217–31.

[5] Ding J, Wang YC. Experimental study of structural fire behaviour of steel beamto concrete filled tubular column assemblies with different types of joints. EngStruct 2007;29:3485–502.

[6] Dai XH, Wang YC, Bailey CG. Numerical modelling of structural fire behaviourof restrained steel beam column assemblies using typical joint types. EngStruct 2010;32:2337–51.

[7] Elsawaf S, Wang YC. Methods of improving the survival temperature in fire ofsteel beam connected to CFT column using reverse channel connection. EngStruct 2012;34:132–46.

[8] Wang YC. Steel and composite structures, behaviour and design for firesafety. Spon Press; 2002.

[9] Wang YC. Performance of steel–concrete composite structures in fire. ProgStruct Eng Mater 2005;7(2):86–102.

[10] EN 1993-1-2, Eurocode 3: design of steel structures. Part 1.2: General rules-structural fire design. London: British Standards Institution; 2005.

[11] EN 1991-1-2. Eurocode 1: actions on structures. Part 1–2: Generalactions on structures exposed to fire. London: British StandardsInstitution; 2002.

[12] Ding J, Wang Y. Temperatures in unprotected joints between steel beam toconcrete filled tubular columns in fire. Fire Saf J 2009;44:16–32.

[13] Wang Y, Orton A. Fire resistant design of concrete filled tubular steel columns.Struct Eng 2008(October):40–5.

[14] Wald F, da Silva SL, Moore D, Lennon T, Chladná M. Experimental behaviour ofa steel structure under natural fire. Fire Saf J 2006;41(7):509–22.

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具

http://www.xuebalib.com/cloud/

http://www.xuebalib.com/

http://www.xuebalib.com/cloud/


http://www.xuebalib.com/vip.html

http://www.xuebalib.com/db.php

http://www.xuebalib.com/zixun/2014-08-15/44.html


Documents

Behaviour of restrained structural subassemblies of steel