Behaviour and design of beam-to-column connections under ﬁre...

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Fire Safety Journal 42 (2007) 437–451

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Behaviour and design of beam-to-column connections under fireconditions

N.H. Ramli-Sulong, A.Y. Elghazouli�, B.A. Izzuddin

Department of Civil and Environmental Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

Received 28 July 2006; accepted 9 September 2006

Available online 21 June 2007

Abstract

In this paper, the main approaches used for developing a component-based connection model are presented and discussed. The model

is capable of simulating the behaviour of typical connection configurations in both steel and composite framed structures under

monotonic and cyclic loading conditions at ambient as well as elevated temperatures. Validation of the proposed connection model is

carried out by comparison against a range of available experimental results, and implementation is undertaken within an advanced finite

element program that accounts for material and geometric non-linearities. A series of sensitivity studies are then presented in order to

demonstrate the scope of application of the proposed model, and to examine the influence of connection behaviour on the overall

structural performance in fire. A number of structural configurations are investigated starting from isolated members and reaching more

detailed representations. Several factors are assessed including connection type, boundary conditions and temperature effects. Finally,

key parameters and considerations related to connection design are examined.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Steel structures; Composite floors; Connection behaviour; Component models

1. Introduction

Recent experimental and analytical investigations deal-ing with the performance of steel and composite buildingsunder fire conditions e.g. [1–3] have provided greaterinsight into the actual behavioural mechanisms that occurat elevated temperature. This has led to a wide recognitionof the inadequacy of conventional design procedures,which are largely based on the response of isolatedmembers with idealised end conditions. Consequently,there has been a growing need for the development ofperformance-based design procedures, which can provide amore rational representation of the behaviour. In order toperform further studies for the purpose of implementingnew findings into design guidance, it is important toprovide analytical tools, which are capable of capturingkey features of the behaviour in a realistic manner. Itshould be noted that under fire situations, the effects ofbeam thermal expansion and membrane action can induce

e front matter r 2007 Elsevier Ltd. All rights reserved.

esaf.2006.09.003

ing author. Tel.: +440 20 75946021.

ess: [email protected] (A.Y. Elghazouli).

significant axial forces in the connection. In addition, dueto load redistributions that take place during a fire, strainreversals frequently occur. Consequently, it is importantthat a connection model is able to incorporate axial loadinteraction effects as well as cyclic loading conditions.This paper firstly gives a brief description of an

analytical model for connections using the component-based approach. The model is capable of representingconnection response under ambient and elevated tempera-ture, and generalized loading conditions including possibleload reversals. The model is implemented within the non-linear finite element program ADAPTIC [4]. Severalstudies are carried out in order to verify the reliabilityand stability of the model for various connection config-urations under ambient and elevated temperature condi-tions. Sensitivity studies are also presented in order toillustrate the influence of salient parameters on localconnection behaviour as well as overall structural response.Several configurations are considered covering isolatedmembers as well as frame and floor sub-assemblages.Finally, some design considerations related to connectionresponse are discussed.

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Nomenclature

Ab area of bolt shankdb bolt diameterdcw column clear depthe distance from the centreline of the last bolt to

end of plateE elastic modulus of steel materialEb bolt elastic modulusF flange forceFcwc strength of column web in compressionfi bolt-row forcefycw column web yield stresshb beam depthKbt stiffness of bolt in tensionKcfb stiffness of column flange in bendingKecwc initial stiffness of column web in compressionKepb stiffness of end plate in bendingKi tangent stiffness of connectionKpbr stiffness of plate in bearingKpcwc post-yield stiffness of column web in compres-

sionKe

T connection elastic stiffness at temperature T

KpT connection plastic stiffness at temperature T

KmT connection reduced strain hardening stiffness at

temperature T

Lb effective length of boltLeff effective width in a bolt-rowm distance from the bolt centreline to the flange-

to-web filletM connection momentMp moment capacity in pure bendingMult ultimate moment capacity

n distance from end of the flange to the boltcentreline; number of the bolt-row

N axial forceNc axial compressive capacitypb minimum bolt pitchQ prying forcer root radiustcf column flange thicknesstcw column web thicknesstep end plate thicknesstf flange thicknessu connection horizontal displacementyi distance of the bolt-row i to the beam centreline

Greek Letters

a coefficient for non-circular pattern effectivewidth below the tension flange of the beam orbelow the continuity plates; ratio between mand db

b ratio between the flexural resistance or stiffnessof the flanges to the axial resistance or stiffnessof the bolts

di bolt-row displacementdp permanent displacementduT ultimate plastic displacement at temperature T

dyT first yield displacement at temperature T

f connection rotationm strain hardening coefficientc coefficient which accounts for the restraint

condition and the reduction of the flange spandue to bolt action

N.H. Ramli-Sulong et al. / Fire Safety Journal 42 (2007) 437–451438

2. Connection models

2.1. Component representation

The component-based method is employed for theconnection models as it combines relatively realisticrepresentation, based on actual geometric and materialproperties, with computational efficiency. The approachrequires identification of active components, evaluation offorce–deformation relationships and assembling of com-ponent characteristics to obtain the overall joint response.

A mechanical model, which consists of two rigid barsrepresenting the column centreline and the beam end, istypically utilised. These bars are connected by a series ofnon-linear springs that model the various components. Inevaluating the force–deformation relationship of eachidealised component, the strength and stiffness propertiesare determined based on underlying mechanics principles,coupled with evidence from available experimental studies.Tri-linear monotonic force–deformation characteristics are

formulated, and then extended to account for cyclicloading, as illustrated in Fig. 1.End plate connections (flush and extended forms),

connections with angles (top and seat and/or web angles)and fin-plate connections have been considered. Withinthese connection configurations, the active componentsidentified include: bolts in tension/shear, end plate inbending, column flange in bending, column web incompression/shear, beam flange in bearing, beam web inbearing/bending/tension, top/seat angle in bearing/bend-ing/tension and plate in bearing/shear/tension.In developing the cyclic response of the component

force–deformation curve for all connection types, Mas-sing’s rule is adopted for the construction of the unloadingand reloading paths. In tension, active components varydepending on their geometry and position within theconnection. For the compression components, it istypically assumed that only the column web in compressionsignificantly contributes to the behaviour. On the otherhand, for the shear panel, the column web governs the

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δuT

F

δyT

KuT

KpT

KeT

O δ

FyT

FuT

Tension

δO δuT δy

T

F

FyT

FuT

KuT

KpT

KeT

Compression

δuT

F

δyT

KuT

KuT

KpT

KpT

KeT Ke

T

DE

B

O

F

A

p δ

C

FyT

FuT

O δp δ

uT δy

T

F

FyT

FuT

δ

A

B

KuT

KeT

KpT

KeT

D

F

C

EKuT

KpT

Compression

Tension

Fig. 1. Tri-linear force–displacement relationships: (a) tension-type components: monotonic response; (b) compression-type components: monotonic

response; (c) tension-type components: cyclic response; and (d) compression-type components cyclic response.

N.H. Ramli-Sulong et al. / Fire Safety Journal 42 (2007) 437–451 439

behaviour but this component only needs to be activatedwhen unbalanced moments exist in the connection.Detailed relationships and representations of force–displacement curves for the various active connectioncomponents can be derived [5]. As an example and forbrevity, only the relationships for end plate connections,which are given the main emphasis in the parametric anddesign studies presented in this paper, are summarisedhereafter.

For extended and flush end plate connections, the maincomponents in tension apart from the bolts include thecolumn flange and end plate in bending which arerepresented through the T-stub idealisation shown in Fig.2. As proposed in EC3 [6], three capacity modes can beobtained depending on the ratio between the flexuralresistance of the flanges and the axial resistance of the bolts(b): Mode 1—complete yielding of the flanges, Mode 2—yielding of flange and bolt fracture and Mode 3—boltfailure without end plate yielding. The correspondingcomponent strength for these three modes can be readilydetermined [6].

The joint rotational stiffness is calculated based on theresultant stiffness of individual components. For a rowwith two bolts in tension, the axial stiffness Kbt can becalculated, with due account of prying action [7], as

Kbt ¼1:6EbAb

Lb, (1)

where Eb is the bolt elastic modulus, Ab is the bolt shankeffective cross-sectional area and Lb is the effective lengthof the bolt [6].By means of an equivalent beam model, the stiffness Kcfb

of the column flange of thickness tcf and the stiffness Kepb

of the end plate of thickness tep in bending are given, as afunction of Leff and m of the T-stub [6], as:

Kcfb ¼1

2

ELeff t3cf

m3, (2)

Kepb ¼1

2

ELeff t3ep

m3. (3)

In order to include the effect of bolt preloading on theconnection rotational stiffness, the coefficient c [8] (whichaccounts for the restraint condition and the reduction ofthe flange span due to bolt action) is multiplied by theelastic stiffness of the T-stub flange, where

c ¼ 0:57tf

db

ffiffiffiap

� ��1:28, (4)

in which tf is the flange thickness, db is the bolt diameterand a ¼ m/db.On the compression side, the flexibility of the compres-

sion zone in an unstiffened connection is considered. Forstiffened connections, the column web is assumed to berigid. Similar to the components in tension, the column

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Q

n m

Q

F

B B

0.8r

r

Mode 1 Mode 2 Mode 3

Fig. 2. T-stub idealisation in tension components of end plate connections: (a) T-stub components in end plate connections; (b) force diagram of T-stub

components; and (c) failure modes of a T-stub.


web in compression is determined for each bolt-row toaccount for the possible effect of cyclic loading in the jointor when compressive actions are activated in the respectivebolt rows. The strength of the column web in compressionwhen first yielding occurs is given as

F cwc1 ¼ Leff tcwf ycw, (5)

where fycw is the yield stress of the column web, tcw is thecolumn web thickness, and Leff is the effective width of thecolumn web in compression transmitted by the connection.For flush and extended end plate connections, the effectivewidth is equal to the depth of the end plate divided by thenumber of bolt rows. For the outermost bolt-row, taking intoconsideration the possibility that the beam flange might exert acompression force on the column web at large displacement,the effective length for these layers are determined as

Leff ¼hb � pbðn� 2Þ

2, (6)

where hb is the beam height, pb is the bolt pitch and n is thenumber of bolt-row.

Subsequent to the onset of plasticity, the ultimatecapacity of the column web can be determinedby substituting the yield stress with the ultimate stressin Eq. (5). On the other hand, the initial stiffness ofthe column web in compression Kecwc can be consideredas

Kecwc ¼ ELeff tcw

dcw, (7)

where E is the Young’s modulus, tcw is the column webthickness, and dcw is the clear depth of column web.

For the post yield stiffness, a strain hardening stiffnessKpcwc is calculated as

Kpcwc ¼ mKecwc, (8)

where m is the strain hardening coefficient.To account for the influence of elevated temperature,

parameters such as the elastic modulus, yield stress andultimate strength, which represent the stiffness andstrength of components, are varied with temperature.Default temperature-dependent properties are based onavailable information for plate and bolt materials [6,9], butthese properties are user-defined and can be modified ifnecessary. The model can also incorporate temperaturedistributions within the joint, as each component can betreated separately. Quadratic temperature variation alongthe depth of a segment is adopted, which enables anaccurate representation of temperature in each component.It should however, be noted that the effect of thermalexpansion within the connection components is notincluded in this study.

2.2. Overall joint response

Non-linear procedures, based on the cyclic representa-tion of the load–deformation temperature-dependentmodels of the active components, have been developedand implemented within ADAPTIC [4]. For connectionssubjected to combined axial force and bending moment,the displacement, di at any connection layer ‘i’ is given as

di ¼ u� fyi (9)

in which: ‘u’ is the horizontal displacement due to axialforce, ‘f’ is the rotation of the connection, and ‘yi’ is thedistance of the layer ‘i’ to the beam mid-depth.Knowing a layer deformation ‘di’, the layer force ‘fi’ is

obtained from the non-linear load–deformation curve ofthe weakest component in the spring series. The layer force

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0

20

40

60

0 10 14 16 18 20

Test-200C Test-420CTest-570C Test-745CModel-200C Model-420CModel-570C Model-745C

Forc

e (k

N)

220

200

180

160

140

120

100

80

-20 2 4 6 8

Displacement (mm)

12

Fig. 3. Force-displacement response of T-stub at elevated temperature for

Test AA1 [10].

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70 80 90

Tem

pera

ture

(C

)

Test M=4kNm Test M=8kNm

Test M=13kNm Test M=17kNm

Model M=4kNm Model M=8kNm

Model M=13kNm Model M=17kNm

Rotation (mrad)

Fig. 4. Anisothermal temperature–rotation response for flush end plate

test [11].


is summed up to obtain the total connection axial force ‘N’and consequently the connection moment ‘M’, for ‘n’number of layers, as follows:

N ¼Xn

i¼1

f ðdiÞ, (10)

M ¼ �Xn

i¼1

f ðdiÞyi. (11)

The connection stiffness matrix, K is then represented as

K½ � ¼

qN

qu

� �qN

qf

� �

qM

qu

� �qM

qf

� �26664

37775. (12)

The stiffness matrix entity related to axial deformations ofthe beam-column connection is:

qN

qu

� �¼Xn

i¼1

Ki. (13)

The entities related to interaction between axial androtational deformation are as follows:

qN

qf

� �¼

qM

qu

� �¼ �

Xn

i¼1

Kiyi. (14)

The second diagonal entity of the stiffness matrix isrelated to the rotational deformation of the beam-columnconnection given as

qM

qf

� �¼Xn

i¼1

Kiy2i , (15)

where Ki is the tangent stiffness of the connection layer i.A full account of the numerical and implementation

procedures is given elsewhere [5].

2.3. Validation studies

The connection models developed were extensivelyvalidated against available experimental results on connec-tions subjected to ambient monotonic and cyclic loading. Itshould be noted however that connection tests at elevatedtemperature are limited, hence comparisons were madewith available experimental results which do not cover alltypes of connection incorporated in the models. This alsopoints out to the need for further experimental studies. Ingeneral, good agreement was obtained between thenumerical simulations and experimental results. Only acouple of representative results, from an extensive valida-tion study [5], are presented in this section to illustrate thegeneral reliability of the models, focusing on elevatedtemperature situations.

As a typical example for results under elevatedtemperature, Fig. 3 shows the comparison betweenanalytical simulations using ADAPTIC and experimentalforce–displacement curves obtained for a T-stub compo-

nent (Specimen AA1) [10] for different steady-statetemperatures. Another example is depicted in Fig. 4 for aflush end plate connection tested at elevated temperature[11]. The figure shows the case of anisothermal loading atfour levels of constant moment. The analytical-experimen-tal comparisons are shown in terms of temperature–rota-tion response. As in other validation studies, goodcorrelation between numerical simulations and experimen-tal results is generally observed. However, some discre-pancies are inevitable due to the sensitivity of the results tomodelling idealisations and simplified temperature-depen-dent material representations.

3. Parametric investigations

A number of sensitivity and parametric studies aredescribed in this section in order to assess various factorsinfluencing the response of steel and composite structures.Emphasis is given to the influence of axial effects on the

ARTICLE IN PRESSN.H. Ramli-Sulong et al. / Fire Safety Journal 42 (2007) 437–451442

response. Three connection types are examined, namelydouble web angles, flush end plate and extended end plate,as indicated in Fig. 5. In all cases, the connection is used inconjunction with a beam of size UB 305� 127� 37,column of size UC 254� 254� 73 and Grade 8.8 M20bolts.

The ambient monotonic response of the three selectedconnections in tension, compression and moment areshown in Fig. 6. The capacity of the double web angleconnection (dwa) is reached by yielding of the angle inbending followed by yielding of the column flange inbending. For the flush end plate connection (fep), plasticityis governed by yielding of the end plate in bending,followed by yielding of the column flange in bending. Asimilar plastic mechanism is also observed in the extendedend plate configuration (extep). In order to study theinfluence of connection type on the beam response, anunrestrained beam of span 5m is subjected to a point loadat mid-span. The relationship between load and displace-ment at mid-span is depicted in Fig. 7, showing thedifference in response between the three connection types.Subsequent sections focus on the influence of boundaryconditions and temperature effects.

3.1. Boundary conditions

The support conditions of a steel beam may vary fromfull restraint to unrestrained conditions with a range ofintermediate cases offering various levels of axial androtational restraint. Clearly, these conditions may have asignificant effect on the distribution of internal forces anddeformations within a member. More accurate beamresponse can be represented by incorporating the actualconnection details.

Three support conditions are considered herein, namelyrigid, pinned and the flush end plate connection (represent-ing a semi-rigid partial strength case) with and withoutaxial restraint. These are adopted to investigate the

200

90

360

9090

8595

20090

425

9090

60100

5040

Fig. 5. Selected connection configurations: (a) flush end plate; (b

influence of the axial and rotational restraint of the jointon the beam response. The beam is subjected to aconcentrated load at mid-span (with a load ratio of 0.6)followed by a linearly increasing temperature. The tem-perature vs. mid-span deformation curves for restrainedbeams with and without thermal expansion (i.e. Res. (Exp)and Res. (NoExp), as well as the case of an axiallyunrestrained beam (Unres), are shown in Fig. 8a–crespectively.Generally, for all support conditions, the beam failure

temperature is higher for restrained cases compared tounrestrained beams. For a restrained beam, thermalexpansion causes an early buckling of the beam due tocompressive loading followed by a rapid rise in displace-ment at mid-span. The response of the two restrained cases(with and without thermal expansion) is similar afteraround 730 1C, when tensile membrane action prevails dueto large displacement and loss of bending stiffness.By comparing the restrained beam response with three

connection conditions, as shown in Fig. 9, the effect ofrotational restraint can be observed. The restrained beamwith pinned connection shows larger mid-span deforma-tion at lower temperature due to the absence of rotationalrestraint at the beam end. On the other hand, beams withflush end plate and rigid connections show very similarresponse. By examining the axial forces at the support, theinduced compressive forces vary for different supportconditions depending on the rigidity of the connection.The compressive forces increase with increasing rotationalrestraint due to lower flexural buckling length of the beamand higher axial buckling capacity. Also, using the flushend plate connection reduces the mid-span momentcompared to the pinned connection.

3.2. Temperature effects

In this section, the effect of temperature on the beam andconnection response is examined. Two factors are con-

3570

70

55

210

90

) extended end plate; and (c) double web angle connection.

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0

20

40

60

80

140

0.1 0.3 0.5 0.7 0.9

extep

fep

dwa

Load (

kN

)

120

100

0.0 0.2

Displacement (m)

0.4 0.6 0.8 1.0

Fig. 7. Load–displacement curves for unrestrained beam incorporating

the three connections.

0

200

400

600

800

1000

1200

0.000

Load (

kN

)

extep

fep

dwa

0

200

400

600

800

1000

1200

1400

1600

1800

0.002

Load (

kN

)

extep

fep

dwa

0

20

40

60

80

100

120

140

160

0.07 0.08 0.09

Mom

ent (k

Nm

)

extep

fep

dwa

Rotation (rad)

Displacement (m)

Displacement (m)

0.002 0.004 0.006 0.008 0.010 0.012

0.000 0.004 0.006 0.008 0.010 0.012 0.014 0.016

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.10

Fig. 6. Ambient monotonic response of the selected connections: (a)

load–displacement curves in tension; (b) load–displacement in compres-

sion and; (c) moment–rotation curves.


sidered here: thermal expansion and cooling. A fullyrestrained steel beam of 5m span incorporating a flushend plate connection (Fig. 5a) is subjected to an initial loadrepresenting a load ratio of 0.6. Subsequently, a lineartemperature history is applied uniformly along the beamup to a centroidal beam temperature T of 1000 1C. For allcases, the temperature is assumed as 0.9 and 1.0T at the topand bottom of the beam section, respectively, and theconnection temperature is considered as 0.7T, uniformlydistributed along its depth.

The influence of thermal expansion (i.e. with andwithout thermal expansion) under transient response isdepicted in Fig. 10a in terms of temperature–axial load.Initially, restraint to thermal expansion induces highcompressive force in the connection. Due to the appliedinitial load, the compressive effect is released around T of

100 1C. At higher temperature (around T ¼ 750 1C), thebeam deflection with and without thermal expansionconverge when beam tensile membrane action in the beamstarts to dominate the response.Recent fire tests have shown that the response in the

cooling phase can also be important. This is particularlythe case if significant tensile forces develop in connections.In order to illustrate this effect, the beam is assumed tofollow a more realistic time–temperature representation[12]. During the cooling stage, high tensile forces areinduced in the flush end plate connection as depicted inFig. 10b, approaching its tensile capacity. This highlightsthe importance of accounting for the full duration of fireloading in assessing structural response where in somecases the connection capacity may prove to be a limitingfactor.

3.3. Sub-frame response

This section presents analytical studies on idealised steelsub-frames. The analysis considers uniform heating in allbays as well as the effect of fire spread (non-uniformheating) from the original fire compartment to adjacentbays. Only an idealised internal frame configuration isconsidered herein, as shown in Fig. 11. The main objectiveis to study the effect of fire loading of the beam on the sub-frame response under different support conditions, namelyrigid, pinned and semi-rigid/partial-strength (for which thesame flush end plate connection utilised previously in theisolated beam studies is also adopted).Two idealised fire scenarios are considered. Firstly, the

fire is assumed to occur simultaneously over the entirebeams and, secondly, the fire is confined to the middle bay(bay 2) and spreads to adjacent bays (bays 1 and 3) after aspecified time. The time–temperature curve for these firescenarios, as adopted in other studies [12], is depicted inFig. 12a and b for the cases of simultaneous heating and

ARTICLE IN PRESS

-1.4

-1.3

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00 100 200 300 400 500 600 700 800 900 1000

Dis

plac

emen

t (m

)

Res (Exp)Res (NoExp)Unres

-1.4

-1.3

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00 100 200 300 400 500 600 700 800 900 1000

Dis

plac

emen

t (m

)

Temp. (Deg C)

-1.4

-1.3

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 100 200 300 400 500 600 700 800 900 1000

Dis

plac

emen

t (m

)

Temp. (Deg C)

Temp. (Deg C)



Fig. 8. Displacement–temperature response for a steel beam with various

connections: (a) rigid connection; (b) flush end plate connection; and (c)

pinned connection.

-1.4

-1.3

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

00 100 200 300 400 500 600 700 800 900 1000

Dis

plac

emen

t (m

)

Temp. (Deg C)

RigidFepPinned

-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

0 100 200 300 400 500 600 700 800 900 1000

Axi

al F

orce

(kN

)

Temp. (Deg C)

RigidPinnedFep

-20

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700 800 900 1000

Sagg

ing

Mom

ent (

kNm

)

Temp. (Deg C)

RigidPinnedFep

Fig. 9. Action effects in a an axially restrained beam with various

connection configurations: (a) deflection at mid-span; (b) axial forces at

beam ends; and (c) mid-span moments.


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-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

0 100 200 300 400 500 600 700 800 900 1000

Axi

al F

orce

(kN

)

Temp. (Deg C)

Res (Exp.)Res (NoExp.)

0

0 20 40 60 80 100 120 140 160 180

Axi

al F

orce

(kN

)

Time (mins)

800

600

400

200

-200

-400

-600

-800

200

Fig. 10. Influence of temperature on connection response: (a) effect of thermal expansion on the connection axial force and (b) time-axial force in the

connection under the effects of heating and cooling.

Beams: 305x127x37UB

Columns: 254x254x73UC

5m 2.5m2.5m

3.5m3.5m

Bay 1 Bay 2 Bay 3

Fig. 11. Internal sub-frame configuration.


fire spread, respectively. For a reference applied tempera-ture T, the top and bottom of the beam are assumed to beat 0.9 and 1.0T, respectively, whilst the connectiontemperature is considered as 0.7T, uniformly distributedalong its depth. The column temperature in the firecompartment is considered as 0.5T whilst the uppercolumns are assumed to remain at ambient temperature.

The first case, involving uniform heating over the entirebeam, causes the members in different bays to behavesimilarly. Hence, the overall response can be depictedthrough the mid-span displacement of the middle beam.The response of the beam with three different supportconditions (rigid, pinned and flush end plate connection) isshown in Fig. 13a. Clearly, the maximum displacement isobtained when the beam is subjected to the highesttemperature for all three support conditions. As expected,connection rotational restraint determines the maximum

displacement and residual deformation of the beam. Forthe flush end plate connection, the displacement reaches aplateau after about 80min, limited by the yielding of theend plate in bending. During heating, the compressive axialforces in the beam increase up to the point when thematerial properties of the beam begin to degrade, as shownin Fig. 13b. In all cases, the beam mid-span displacementbegins to recover during the cooling stage, and the beamstarts to carry its load through tensile membrane action.The tensile membrane forces evidently have a beneficialeffect in reducing the mid-span deflection in the beam andhence in maintaining the overall structural integrity.The second case, which assumes a fire spreading

scenario, is perhaps a more typical condition than theassumption that the temperatures change uniformlythroughout the fire-affected zone. Once a beam begins tocool, with its adjacent beam starting to heat at a muchfaster rate, extra compression is induced into the middlebeam, thus increasing its deflection. This deflectioncontinues to increase until the compressive axial forcesinduced by the adjacent heated beams begin to decrease.Both the maximum deflection and the residual deformationof the beam in the source bay are usually higher if firespread is considered.The displacement at the mid-span of the beam in bay 2,

after the full fire history is applied, is depicted in Fig. 14afor the three support conditions under consideration. Thesame pattern is observed for all cases: high mid-spandeflection following the end of the heating stage after36min, then the deflection continues to increase when thisbeam is in the cooling stage, and at the same time that thefire spreads to the adjacent bays. On the other hand,Fig. 14b depicts the mid-span displacement of the beamssubjected to the second phase of heating (bays 1 and 3). In

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0

100

200

300

400

500

600

700

800

0 50 100 200

Tem

pera

ture

(C

)

All bays

0

100

200

300

400

500

600

700

800

0 20 40 60 80 100 120 140 160 180 200 220 240 260

Tem

pera

ture

(C

)Time (mins)Time (mins)

150 250

Bay 1 and 3

Bay 2

Fig. 12. Applied temperature histories: (a) uniform heating and (b) non-uniform heating.

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 20 40 60 80 100 120 140 160 180 200 220

Dis

plac

emen

t (m

)

Time (mins)

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200 220

Axi

al F

orce

(kN

)

Time (mins)

Rigid

Pinned

Fep

Rigid

Pinned

Fep

Fig. 13. Response of beam in bay 2: (a) displacement response and (b) variation of axial forces.


this case, the beams start to be heated after 36min. Prior tothe heating stage, the deflection is not influenced signifi-cantly by the heating in the middle beam, where thedeformations are relatively small. The beams reach themaximum temperature at 72min, and the correspondingmaximum displacements are 70.285 and 160mm for therigid, pinned and flush end plate cases, respectively. Thesedeformation levels are largely maintained as residualdeflections thereafter.

By examining the axial forces in the middle beam (bay 2)and adjacent members (bays 1 and 3) as shown in Fig. 15aand b, respectively, it can be observed that fire spread isaffecting axial forces in both bays. When the middle beam

is first heated, it induces compressive forces into theadjacent beams. Although the middle beam starts to cooldown, further compression is applied to this member whenthe adjacent beams are heated. This explains the increase indisplacement in the middle beam during the cooling stageup to around 72min, since tensile axial forces are onlyinduced in the middle beam when adjacent beams begin tocool down.

3.4. Composite system

The influence of connection type on the responseof a restrained composite beam is examined by considering

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-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

00 20 40 60 80 100 120 140 160 180 200

Dis

plac

emen

t (m

)

Time (mins)

Rigid

Pinned

Fep

-0.3

-0.28

-0.26

-0.24

-0.22

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0 20 40 60 80 100 120 140 160 180 200

Dis

plac

emen

t (m

)

Time (mins)

Rigid Pinned Fep

Fig. 14. Mid-span deformation for the case of non-uniform heating: (a) beam in bay 2 and (b) beams in bays 1 and 3.

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Axi

al F

orce

(kN

)

Time (mins)

Rigid

PinnedFep

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Axi

al F

orce

(kN

)

Time (mins)

Rigid

PinnedFep

Fig. 15. Axial Forces for the non-uniform heating scenario: (a) beam in bay 2 and (b) beams in bays 1 and 3.


one of the full-scale fire tests (Test 1) carried out atCardington. Details of the composite floor modelsand connection configuration are given elsewhere [2,5].The structural model covers part of the floor as indicatedin Fig. 16a. Average temperature distribution in themain elements is considered as shown in Fig. 16b.The overall structural behaviour of the floor systemfor Test 1 is presented in the time–displacement curve atmid-span of the heated beam as shown in Fig. 16c. qItshould be noted that in this test the beam deflec-tion is largely driven by thermal expansion effectsdue to the high level of axial restraint from the surrou-

nding cold structure coupled with the low effective loadratio [2].The experimental result is compared with the predicted

deflection for three different beam-to-column and beam-to-beam connection conditions: (i) rigid (ii) pinned and (iii)actual joint configurations where partial end plate is usedfor beam-to-column connections and fin-plate is used forbeam-to-beam connections. Generally, the predicted mod-els show good agreement compared to the experimentalresults as shown in Fig. 16c. Slight discrepancies may beattributed to the idealisation used for material properties,temperature distribution, boundary conditions and the use

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D1/2 E1/2

E1/3D1/3

D2E2

Heated area

00 20 40 60 80 100 140 160 180 200

Tem

p. (

Deg

. C)

steel beamconcretes lab

0 20 40 60 80 100 120 140 160 180 200

Dis

plac

emen

t (m

)

Experiment

Analysis-Rigid Conn.

Analysis-Pinned Conn.

Analysis-Actual Conn.

Time (mins)

Time (mins)

900

800

700

600

500

400

300

200

100

0.00-0.02-0.04-0.06-0.08-0.10-0.12-0.14-0.16-0.18-0.20-0.22-0.24-0.26-0.28

120

Fig. 16. Response of composite system: (a) modelled floor area; (b)

centroidal temperature in beam and (c) slab deflection at mid-span.


of a grillage model to represent the slab. More importantly,it is evident that the support condition has an insignificantinfluence on the overall response. This is because at ahigher temperature when the steel beam yields, the loadthat develops in the transverse rib slab is resisted by tensileforces [3]. The actual joint configuration gives virtually thesame result as the rigid case because throughout the

heating stage the connection is subjected to compression;due to the location of the joint in the minor axis of thecolumn, based on the model, high stiffness is provided bythe connection. However, by comparing with the pinnedjoint, the floor is stiffer if the actual joint configurations areconsidered.The effect of different connection conditions at the

beam-to-column and beam-to-beam joints in terms of axialforce is depicted in Fig. 17. Considerable levels of bothstrength and stiffness can be achieved by the connectioncompared to the pinned case and hence have a beneficialeffect on the survival time of the structure. For the heatedbeam, connected to the column minor axis (Grid line 2 inFig. 16a), the response of axial forces against time isdepicted in Fig. 17a. As shown in the figure, initially theforce in the beam end increases with temperature incompression due to the restraint to thermal expansion.Similar trends are observed for the three different supportconditions. The axial force in the flush end plate connec-tion is similar to the rigid case because the end plateconnection is very stiff in compression when the beam isconnected to the minor axis of the column and the responseis governed by the plastic capacity of the beam. After about60min, changes in the compression force result from thedegradation of material properties in the members.The effect of the support condition on the unheated

member at the beam-to-column joint (at the column majoraxis D2 in Fig. 16a) and the beam-to-beam joint (at Gridline D1/2) are shown in Fig. 17b and c respectively. Theoverall axial forces applied on the connection are smallcompared to the joint connected to the heated member.However, slight variations of axial forces appear forvarious connection conditions.

4. Design considerations

Important aspects of connection design are discussed inthis section, with particular emphasis on the influence ofinteraction between axial load and moment. Whilst this isnot considered in detail in current design guidance [6], itsimportance under fire and other loading conditions hasbeen highlighted in this work and in a number of previousstudies [13–16]. Hereafter, several design aspects, whichhave been examined for various connection types, arediscussed for the case of a flush end plate configuration asan example.

4.1. Rotational stiffness

Using the analytical model, the influence of the interac-tion between bending and axial loading on stiffnesscharacteristics is investigated. A flush end plate configura-tion, shown in Fig. 18 is assumed to be connected to abeam of size UB 305� 127� 37. The connection is semi-rigid based on the classification of EC3. It should be notedthat in Part 1.8 of EC3 connection design does not accountfor significant axial loading. To assess the influence of axial

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90

360

9090

8595

200

Fig. 18. Selected connection configuration.

0

15000

20000

25000

30000

800

Rot

atio

nal s

tiffn

ess

(kN

m/r

ad)

35000

10000

5000

Axial force (kN)

-2000 -1600 -1200 -800 -400 0 400 1200

FEP-Analytical [16] FEP-ADAPTIC

Fig. 19. Influence of axial load on initial rotational stiffness.

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

0 20 40 60 80 100 120 140 160 180 200

Axi

al f

orce

(kN

)

Time (mins)

Rigid

Pinned

Fep

-210

-180

-150

-120

-90

-60

-30

0

30

60

90

120

0 20 40 60 80 100 120 140 160 180 200

Axi

al F

orce

(kN

)

Time (mins)

Rigid

Pinned

Fep

-400

-360

-320

-280

-240

-200

-160

-120

-80

-40

00 20 40 60 80 100 120 140 160 180 200

Axi

al f

orce

(kN

)

Time (mins)

Rigid Pinned Finplt

Fig. 17. Axial force in connections: (a) Beam-to-column minor axis; (b)

beam-to-column major axis and (c) beam-to-beam connection.


loading on the rotational joint stiffness, the analyticalmodel is utilised whereby different levels of axial load areinitially applied, followed by increasing moment until theultimate capacity is reached. In Fig. 19, the results are alsocompared with available analytical expressions [16].As indicated in the figure, the initial rotational stiffness is

significantly affected by the axial loading. The slope ofrotational stiffness-axial force changes at the specific levelwhen the critical components, such as end plate, columnflange in bending or column web in compression, startyielding. It should be noted that under pure moment, EC3gives lower values compared to those obtained from theanalytical model [5]. This is due to simplifications used inEC3 in relation to the location of the centre of rotation.

4.2. Strength interaction

Using the analytical model, strength–interaction curvesbetween moment and axial load can be readily constructed.This is illustrated in Fig. 20 for the flush end plate example.In this case, the connection is subjected to initiallyprescribed constant temperature and axial load followedby applied moment. Alternatively, any generalised loading

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-2

-1

0

1

0 0.2 0.6

amb

T=200C

T=400C

T=600C

T=800C

N/N

t

1.41.2

0.80.60.40.2

-0.2-0.4-0.6-0.8

-1.2-1.4-1.6-1.8

-2.2-2.4

0.4 0.8 1 1.2

COMPRESSION

TENSION

Mult/Mp

Fig. 20. Analytical M–N interaction at various temperature levels.

TENSION N

M

COMPRESSION

N/N

t

Mult/Mp

(a)

(c)

(d)

(b)

8595

9090

Fig. 21. Idealised M–N interaction curve for connections.


procedure can be considered. The M–N interaction isrepresented as the ratio of N/Nt against Mult/Mp, where N

is the applied axial force, Nt is the axial tensile capacity ofthe connection, Mult is the ultimate moment resistance, andMp is the moment capacity under bending action only.

In most other configurations, the shape of the normal-ised interaction curve is not notably influenced bytemperature effects. For end plate connections, dependingon the Nc/Nt ratio of the connection, the compressive axialforce increases the moment resistance of the joint as thepre-compression effect can benefit the components in thetension zone. However, the effect of the initial tensile forceson the joint may reduce the joint moment resistance as thetension force may activate earlier yielding of the compo-nents in tension. The M–N interaction curve in thecompression region varies with temperature, where higherMult/Mp ratio is obtained as the temperature increases.This is attributed to the change of plastic mechanisms ofthe end plate in bending (which governs the tensile capacityof the connection), mainly due to the degradation ofmaterial properties with temperature.

Based on numerical studies of several connection types[5], relatively simple relationships can be utilised in order toderive idealised M–N interaction curves of the form shownin Fig. 21. For a given connection, points (a–d) in the figurecan be determined without the need for detailed analysis. Ifcomponent ductility is not limited, full plastic distributioncan be assumed hence equilibrium considerations deter-mine the interaction curve. The variation of slope in thecurve indicates a change in the plastic mechanism in linewith the location of the plastic neutral axis along theconnection depth. Such idealised interaction curves can beused to determine the joint resistance subjected to anycombination of moment and axial load at any temperaturelevel. This can be beneficial not only for design considera-tions but also for assisting in interpreting experimental andanalytical response of framed structures under fire andother loading conditions.

4.3. Deformation capacity

The deformation capacity of a joint is obviouslygoverned by the ductility of its constituent components.Generally, the weakest component that governs the jointmoment resistance also provides the greatest contributionto the joint deformation capacity. Several studies have beenconducted on the ductility of connection components[17,18], but there is a need for further experimentalinvestigations to quantify these effects.As noted before, the strength–interaction illustrated in

Fig. 21 is based on plastic distribution. However, suchcurves can be readily modified to incorporate ductilitylimits imposed for the various components [5], henceleading to a reduced surface corresponding to lower tensile/compressive/moment resistance. For example, for a flushend plate configuration, the weakest component in tensionwould be the end plate in bending whilst in compressionthe column web would govern. Consequently, the deforma-tion ductility limits assigned to these components woulddetermine the reduced interaction curve. These ductility-modified interaction curves could be readily used inassessing limiting criteria in structural frame assembliesespecially for partial strength joints where the non-linearresponse of the joint can affect the overall response.

5. Conclusion

A component-based model is utilised in this paper toassess the behaviour of isolated members and structuralassemblages under fire conditions. The model can representconnection behaviour under generalised loading coveringambient and elevated temperature as well as monotonicand cyclic conditions. The influence of connection beha-viour on the response of a steel beam as well as an idealisedframe is first discussed, followed by an examination of oneof the Cardington full-scale fire tests carried out on a

ARTICLE IN PRESSN.H. Ramli-Sulong et al. / Fire Safety Journal 42 (2007) 437–451 451

composite arrangement. Whilst the connection can have asignificant effect on the overall response of steel beams andsub-assemblages, the contribution of the connection to theoverall response in a restrained composite beam becomessignificantly less pronounced, as expected. Nonetheless, anappropriate representation of the joint is shown to beimportant for the purpose of assessing the load anddeformation levels imposed on the connection itself.Finally, design aspects related to response of connectionsunder combined moment and axial load are examined,including stiffness and strength properties. Using theanalytical model, temperature-dependent strength-interac-tion curves can be derived for different connectionconfigurations. Alternatively, idealised forms of thesecurves can be obtained from simple equations based onequilibrium considerations. An important aspect of con-nection design is related to deformation capacity, whichcan be determined based on the ductility of constituentcomponents. In this context, strength interaction curvescan be readily modified to incorporate ductility limits invarious connection components although this is an aspectthat appears to require further experimental examination.

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[5] Ramli Sulong NH. Behaviour of steel connections under fire

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[6] European Committee for Standardisation, Eurocode 3: Design of

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