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Journal of Constructional Steel Research 60 (2004) 867896

www.elsevier.com/locate/jcsr

Experimental and analytical investigationof the tension zone components within a

steel joint at elevated temperatures

S. Spyroua

, J.B. Davisonb,

, I.W. Burgessb

, R.J. Plankc

a HFS Engineering, 42 Arch. Makariou III Avenue, 3065 Limassol, Cyprusb Department of Civil and Structural Engineering, The University of Sheffield, Sheffield S1 3JD, UK

c School of Architecture, The University of Sheffield, Sheffield S10 2TN, UK

Received 20 July 2003; received in revised form 22 October 2003; accepted 24 October 2003

Abstract

When steel-framed structures are subjected to fire, their ability to sustain loads is severely

impaired and the action of the joints is of particular concern. To date, data on the responseof steel joints at high temperatures has been gathered from full-scale furnace tests. In anattempt to establish simplified methods to estimate the full response of a steel joint at elev-ated temperatures the principles of the component method have been investigated exper-imentally and analytically. The originality of the component method is to consider anyjoint as a set of individual basic components. When a steel joint is subjected to bending itmay be considered as three major zones (tension, shear and compression) with each zonesub-divided into the relevant components.

The objective of the work reported herein was to investigate experimentally and analyti-cally the tension zone within an end-plate steel joint at elevated temperatures. A series ofexperiments has been carried out, and these are described in the paper. Simplified analytical

models of the component behaviour have been developed, and these have been validatedagainst the tests results. Development of a suitable component model for the compressionzone is the subject of a companion paper.# 2003 Elsevier Ltd. All rights reserved.

Keywords: Steel joints; Component method; Tension zone; T-subs; Elevated temperatures

Corresponding author. Tel.: +44-114-222-5354; fax: +44-114-222-5700.

E-mail address: [email protected] (J.B. Davison).

0143-974X/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2003.10.006

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Nomenclature

af Weld thicknessdbl Deflection at the bolt line of the T-stub assemblydbolt Elongation of the boltdcl Deflection at the centre line of the T-stub assemblydIbl Deflection at the bolt line of the T-stub assembly at Failure Mode IdIcl Deflection at the centre line of the T-stub assembly at Failure Mode IDdbolt Incremental elongation of the boltDdcl Incremental deflection at the centre line of the T-stub assemblyDdIcl Incremental deflection at the centre line of the T-stub assembly after

yielding of the bolts at Failure Mode ID

FIncremental tension forceDQ Incremental prying forceDw Incremental uniform distributed bolt loadDwIbolt,pl Incremental uniform bolt load after yielding of the bolts, at Failure

Mode IDwk Incremental bolt forceDwkIbolt,pl Incremental bolt force after yielding of the bolts, at Failure Mode Ihb Bolt temperaturehs Steel temperatureq Ratio of the tension force and the bolt force

As Bolt shank areaE T-stub flange Youngs modulusEb Bolt Youngs modulusEs Youngs modulus of steelEs,h Youngs modulus of steel at elevated temperaturesEt 1.5% of the T-stub flange Youngs modulusEtb 1.0% of the bolt Youngs modulusF Tension forceF1st First plastic hinge forming at T-stub flange, or yielding of the boltsFbl,pl Plastic tension force at the bolt line of the T-stub flange

Fbolt,pl T-stub tension force due to yielding of the boltsfbu Bolt ultimate stressfby Bolt yield stressFcl,pl Plastic tension force at the centre line of the T-stub flangeFIbolt,pl T-stub tension force due to yielding of the bolts at Failure Mode IFIIbl,pl 2nd plastic hinge formation (tension force) at the bolt line of the T-

stub flange at Failure Mode IIFIIbolt,pl Tension force (yielding of bolts) after the formation of a 2nd plastic

hinge at the bolt line (T-stub flange) at Failure Mode IIFIIbolt,ultTension Force after yielding of the bolts (F

IIbolt,pl) at Failure Mode II

fy Yield stressfy,h Yield stress at elevated temperature

S. Spyrou et al. / Journal of Constructional Steel Research 60 (2004) 867896868

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1. Introduction

Structural steel frames usually consist of universal beams and columns assem-

bled together by means of bolted connections. The performance of the completeframe is affected by the behaviour of the joints, which should be accounted for in

the global analysis of the structure. For simplicity, in conventional analysis and

design of steel and composite frames, beam-to-column joints are assumed to

behave either as pinned or as fully rigid. Although the pinned or fixed assump-

tion simplifies significantly analysis and design procedures for the engineer, in prac-

tice the actual joint behaviour exhibits characteristics over a wide spectrum

between these two extremes. The majority of joints regarded as pinned possess

some rotational stiffness, whilst joints, which are regarded as rigid display some

flexibility. Designers may choose to include a more accurate representation of jointbehaviour in analysis and design but many do not as the simplified methods con-

tinue to produce cost-effective and reliable structures.

I Moment of inertiakE,h Reduction factor for Youngs modulus of steel at elevated tempera-

turesky,h Reduction factor for yield stress of steel at elevated temperaturesLb Effective length of the boltLe Width of the T-stub assemblyLeff Effective length of the T-stub assemblyMbl Moment at the bolt line of the T-stub flangeMcl Moment at the centre line of the T-stub flangeMp Plastic moment resistanceQ Prying forceQI Prying force at Failure Mode I

QII

Prying force at Failure Mode IIr Root radius of the steel sectiontf Flange thicknessw Bolt uniform distributed loadwk Bolt loadwkIIbl,pl Bolt load at the formation of a 2nd plastic hinge at the bolt line

(T-stub flange) at Failure Mode IIwkIIbolt,pl Bolt yielding load after the formation of a 2nd plastic hinge at the

bolt line (T-stub flange) at Failure Mode IIwkIIbolt,ult Ultimate bolt load after yielding of the bolts (wk

IIbolt,pl) at Failure

Mode IIA, B, C, D Constants of integrationn, k, m Dimensions defined in Fig. 5

869S. Spyrou et al. / Journal of Constructional Steel Research 60 (2004) 867896

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Although these simplified approaches are sufficient for design at ambient tem-peratures, when steel-framed structures are subjected to fire the behaviour of thejoints within the frame exerts an even greater influence on overall response. Most

research into the behaviour of beam-to-column joints has concentrated on themoment-rotation characteristics. But in fire, the joints are also subjected to highaxial forces, which are created by restraint to the thermal expansion of beams. Todate, data on the real response of joints at elevated temperatures have only beengathered from full-scale furnace tests [13] on cruciform arrangements, which haveconcentrated exclusively on moment-rotation behaviour in the absence of axialthrusts. If momentrotationthrust surfaces were to be generated this processwould require prohibitive numbers of complex and expensive furnace tests for eachjoint configuration.

As an alternative, this paper and its companion reports on an investigation to

extend the principles of the Component Method to the elevated-temperature situ-ation. The basic theme of the Component Method is to consider any joint as anassembly of individual simple components as shown in Fig. 1.

Each of these components is simply a non-linear spring, possessing its own levelof strength and stiffness in tension, compression or shear, and these will degrade asits temperature rises. The main objective of this study was to investigate exper-imentally and analytically the behaviour of tension and compression zones ofend-plate connections at elevated temperatures. A series of experiments has beencarried out, and simplified analytical models developed for both the tension and

compression zones, and these have been validated against tests and detailed finiteelement simulations.In a bolted end-plate joint the major components within the tension zone ( Fig. 1)

are the plate in bending, the column flange in bending and the bolts in tension. Allthese components are modelled using an equivalent T-stub, i.e., two T-elements con-nected through the flanges by means of one or more bolt rows as shown in Fig. 2.

Fig. 1. The three zones and their components within an end-plate steel joint.


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Early attempts [4] to design end-plate connections assumed the column flange to

be infinitely stiff and estimated the minimum required end-plate thickness by calcu-

lating the plastic moment capacity using various collapse mechanisms. In the early

1970s researchers realised that the flexibility of the column flanges could affect the

behaviour of the connecting tension bolts by inducing prying action. Zoetemeijer

[5] took into account the inter-dependence between these components and pro-

duced straight-line yield patterns to represent the failure of both end-plate and col-

umn flange T-stubs in bending. Packer and Morris [6] used curved yield lines to

predict the column flange capacity in both stiffened and unstiffened joints. Agers-kov [7] used the principles of simple bending theory to analyse T-stub behaviour

and based on the same principles Yee and Melchers [8] calculated the elastic stiff-

ness response of the T-stub assembly. Zoetemeijers work is of particular impor-

tance because it contains the basic principles of the component method which is

extensively applied throughout Europe.Simple bending theory is the basis for the simplified formulae for calculating the

elastic strength and stiffness behaviour of a T-stub assembly given in Eurocode 3:

Annex J [9] and the British design guides [10]. The full elasto-plastic response of

T-stub assemblies is not covered in design codes, so information is limited to ahandful of papers extending the model up to complete failure of the T-stub speci-

men [1115].

Fig. 2. T-stub identification and orientation for extended end-plate joint.


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In this paper a simplified mathematical model is presented to predict the elastic-plastic behaviour of the T-stub assemblies at both ambient and elevated tempera-tures. The model has been verified against elevated-temperature test results, thus

extending the component approach for use in fire engineering studies.

2. Simplified mathematical model

The deformation of each equivalent T-stub assembly (either end-plate or columnflange such as that shown in Fig. 3) arises from the elastic and plastic flexure of thecolumn flange and end-plate, and the elastic and plastic elongation of the bolts.Fig. 3 shows the effective width (Leff) as proposed by Faella et al. [16] assuming a

45

v

spread of the bolt action starting from the washer edge and finishing at 0.8 rfrom the face of the web in a rolled section (where r is the root radius of the col-umn flange) or 0.8af

p2 where af is the weld thickness, at a section to end-plate

interface.T-stub assemblies can fail by one of three possible collapse mechanisms, as

shown in Fig. 4. In Failure Mode I, yielding occurs first in the T-stub flange fol-lowed by yielding and fracture of the bolts. Failure Mode II involves completeyielding of the T-stub flange before failure of the bolts and in Failure Mode III theT-stub remains elastic and failure occurs by fracture of the bolts.

In order to research the deformation mode for a T-stub assembly under various

bending moments, a mathematical model has been developed to consider theelasto-plastic deformations.

From classical beam theory [17], if the tension force acting on a T-stub assemblyis F(Fig. 5; note that Q is the prying force), it can be shown (Appendix A) that thedeflection dcl at x n km is:

dcl FL3e

48EI wkEI

L3e24

m k=23

6 m k=2

2Le

4 k

2n k=224

1

where E is the T-stub flange Youngs modulus; I 2Lefft3f=12, Leff is the effectivelength for the T-stub flange (Fig. 3); F is the tension force applied to the T-stub;wk is the bolt tension force; n, k and m are defined in Fig. 3; Le is the width of theT-stub shown in Fig. 5.

The equation above is more useful if the bolt force wk is expressed in terms ofthe T-stub force F. This can be obtained from the compatibility condition requiringthat at the bolt line x n k=2, the deflection of the T-stub flange must be equalto the bolt elongation. From beam bending theory the deflection at the bolt linex n k=2 is given by:

dbl FEI

nk=2L2e16

nk=23

12 ::::::::::::wk

EI

nk=236

k2nk=2

24nk=2mk=2

2

2nk=2L

2e

8 k

3

384

2


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which should be equal to the bolt elongation given by

dbolt wkLbEbAs

3

where Lb is the effective length of the bolt (measured from centre of nut to centre ofbolt head); Eb is the Youngs modulus of the bolt; As is the shank area of the bolt.

Therefore, from Eqs. (2) and (3) above, the bolt force wkcan be expressed as:

wk

F

EI

n k=2L2e16

n k=23

12

LbEbAs

1EI

n k=23

6 k

2

n k=224

n k=2m k=22

2 n k=2L

2

e8

k3

384

4

Fig. 3. Equivalent column flange and end-plate T-stubs respectively.


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Further simplification of the formula above gives the bolt force as a ratio q of the

total T-stub force F, i.e. p F=wk where p is a function of the geometry andmaterial properties only,

q 1

EI

n k=2L2e16

n k=23

12

Lb

EbAs 1

EI

n k=236

k2n k=2

24 n k=2m k=2

2

2 n k=2L

2e

8 k

3

384

5

and the prying force Q as shown in Fig. 5 is then given by:

Q

wk

F

F

q

1

6

By substituting Eq. (4) into Eq. (1) the maximum deflection dcl in the middle span

of the T-stub flange can be written as a function of F.The next step in the calculation procedure is to determine the magnitude of the

total T-stub force F and the position of the first plastic hinge. The first plastic

hinge will appear when the maximum bending moment in the T-stub flange exceeds

Fig. 5. Forces on T-stub assembly.

Fig. 4. Failure modes for the T-stub flange.


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the plastic moment resistance Mp given by:

Mp 2Leff

t2ffy

4 7

where fy is the yield stress of the T-stub flange; Leff is the effective length as shown

in Fig. 3 and tf is the flange thickness.In order to calculate the minimum tension force (F1st) required to form the first

plastic hinge or yielding of the bolts, the minimum value (Fcl,pl, Fbl,pl, Fbolt,pl) is

taken from Eqs. (8)(10). These equations represent the first plastic hinge forming

in either:

. the middle of the T-stub assembly, at x n km,

. the bolt line of the T-stub assembly, at x n k=2,

. the T-stub force due to yielding of the bolts.

Mcl wkn k=2 Fcl;pln km2

Mp 8

Mbl

wk

n

k=2

Fbl;pln k=2

2 wk

k

8 Mp

9

wk 2Asfby qFbolt;pl 10

where fby is the yield stress for the bolt.Eqs. (8) and (9) have been derived by substituting Q wk Fcl;pl=2 and

Q wk Fbl;pl=2 respectively into the moment expressions at the middleof the T-stub (Mcl wkm k=2 Qn k m) and the bolt line(Mbl Qn k=2 wkk=8).By further substitution of wk pF into Eqs. (8) and (9) the minimum value ofFcl,pl, Fbl,pl, Fbolt,pl gives the total tension force F1st and also the position of the first

plastic hinge.

F1st minFcl;pl;Fbl;plFbolt;pl 11

After the formation of the first plastic hinge, which for Failure Modes I and II

occurs in the middle of the T-stub flange, at x n k m, a failure may developin one of two ways (and whichever happens will define the failure mode of theT-stub flange). Either the bolts start to yield (Failure Mode I), or a second plastic

hinge forms in the T-stub flange at the bolt line x n k=2 (Failure Mode II).


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2.1. Failure mode I

After the formation of the first plastic hinge, if the bolts start to yield then part

of the flange remains elastic and the total T-stub force F

I

bolt,pl is given by:Mp wk Dwk m k=2

wk Dwk F1st DF2

n km 12

FIbolt;pl F1st DF 2Mp

Pwk Dwk n k=2 n km 13

where

Pwk Dwk 4Asfby and Mp is given by Eq. (7).

The total bolt force and the total prying force are given below as functions of

the T-stub force from Eq. (12) above.

wkIbolt;pl wk DwkF1st DF

2n k m Mp

n k=2 14

QI Q DQ F1st DF

2m k=2 Mp

n k=2 15

The deflection when the bolts start to yield can be calculated using the same

analysis as in the calculation of initial deflection dcl. In this case though the totalbolt and T-stub forces have to be taken into account in the bending moment equa-tions as well as the plastic moment Mp at the middle of the flange,x n k m. By integrating the bending moment equations twice, the constantscan be calculated using the same boundary conditions as before, except at x n k=2 where the total bolt deflection is equal to dIbl dbl DwkLbEbAs . The totaldeflection of the T-stub flange at x n k m is given by:

dIcl

dcl

Ddcl

wk Dwk

EI

n k m3

6 m k=23

6

F1st DF2EI

n k m36

An kmEI

BEI

16

in which the constants A and B are:

A wk Dwk k3

384n k=2 n k=22

6 k

2

24

F1st DF2

n k=226

EIdbln k=2 DwkEILb

EbAsn k=2

B wk Dwk k2n k=2

24


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By substituting

wk

Dwk

from Eq. (14) into the displacement Eq. (16) the

total displacement dIcl at which the bolts yield can be expressed as a function of theT-stub force FIbolt,pl.

After yielding of the bolts, the prying force cannot be increased any further and

the bolts take any increase of the T-stub force until they fracture. Hence,

DwkIbolt;pl DF

2 2Asfbu wkIbolt;pl 17

DQ 0 18

where fbu is the ultimate stress of the bolt.The incremental deflection due to the final increment of force on the T-stubflange can be calculated using beam theory (Appendix A), but with the system as

shown in Fig. 6. The incremental deflection is given by:

DdIcl DF

EI

m k=4 2 m k=2 8

m k=4 3

24 k

3

1536 EILb

2EtbAs

" #19

Note that Etb is taken as 1.0% of the bolt elastic Youngs modulus Eb (205 kN/mm2). Shi et al. [11] report that the tangent modulus for the bolt should be taken

as 5% of the elastic Youngs modulus, and this value is derived from an ambient-temperature finite element analysis. Studies performed by Theodorou [18] on grade

8.8 bolts at elevated temperatures concluded that the value of 1.0% could be used

for defining the bolt tangent modulus value. For the T-stub flange, Piluso et al. [13]

performed 12 coupon tests and reported that the tangent modulus of the flange (upto ultimate stress) ranged from 1.0 to 1.6% of the elastic Youngs modulus. For the

current study a value of 1.5% was chosen.

2.2. Failure mode II

The formation of the first plastic hinge is analysed as described in section 2. If asecond plastic hinge is formed in the flange at the bolt line, x n k=2 the T-stubforce FIIbl,pl can be calculated as shown below:

Fig. 6. System for calculating the final displacement.


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By taking

PMA 0 then Mp is equal to:

Mp wk Dwk n 3k=8 F1st D

F2 n k=2 20and for the other part of the T-stub flange (Fig. 7), when

PMC 0 the total force

is equal to:

FIIbl;pl F1st DF4Mp 2wk Dwk k

8m k=2 21

Solving Eq. (20) with respect to wk Dwk and substituting into Eq. (21) theT-stub force when the second plastic hinge forms is given by:

FIIbl;pl F1st DF2Mp2n 7k=8

mn 3km=8 3kn=8 k 2=8 22

The bolt force and prying force increments are given by the following formulae:

Dwk DF2

m k=2n k=2 1

23

DQ

DF

2

m k=2

n

k=2

24

The total bolt force is equal to wkIIbl;pl wk Dwk and the total prying force is

equal to QII Q DQ. The deflection at x n k m can be calculated usingthe same bending equations as in the calculation of initial deflection dcl but thistime using the incremental forces. After the second integration the constants can becalculated using the same boundary conditions as before except at x n k=2where the bolt deflection according to the incremental bolt force is equal to

Ddbolt DwkLbEbAs . The incremental deflection Ddcl of the T-stub flange at x n k m is given below:

Ddcl DQEI

n km36

Dwk

EI

m k=236

Cn kmEI

DEI

25

Fig. 7. Free body diagram for half of the T-stub flange.


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in which the constants C and D are given as:

C

Dwk

k3

384n k=2 k2

24 EILb

EbAsn k=2 DQn k=22

6

D Dwk k2n k=2

24

By substituting Eqs. (23) and (24) into the equations for constants C and D andthen those into Eq. (25) the deflection Ddcl can be calculated according to theincremental T-stub force DF.

After the appearance of the second plastic hinge in the fillet at x n k=2 theprying force cannot be increased any further and any increase of the T-stub force is

taken by the bolts until they yield. Hence,

Dwk DF2

2Asfby wkIIbl;pl 26

DQ 0 27where wkIIbl;pl wk Dwk, fby is the yield stress for the bolt, the total bolt force isequal to wkIIbolt;pl wkIIbl;pl Dwk, and the total T-stub force is equal to FIIbolt;pl FIIbl;pl DF.

The procedure to calculate the deflection Ddcl due to the incremental force DF isthe same as described in section 2.1,

Ddcl DFEtI

m k=42m k=28

m k=43

24 k

3

1536 EtILb2EbAs

28

where Et is taken as 1.5% of the flange elastic Youngs modulus E.The incremental T-stub force, between yielding and fracture of the bolts is given

below:

Dwk

DF

2 2Asfbu

wkIIbolt;pl

29

DQ 0 30

where fbu is the ultimate stress for the bolt.The total bolt force is equal to wkIIbolt;ult wkIIbolt;pl Dwk and the total T-stub

flange force is equal to FIIbolt;ult FIIbolt;pl DF.The deflection Ddcl due to the incremental force DF is given by:

Ddcl DFEtI

m k=42m k=28

m k=43

24 k

3

1536 EtILb2EtbAs 31

where Et is taken as 1.5% of the flange Youngs modulus E and Etb is taken as1.0% of the bolt Youngs modulus Eb.


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2.3. Failure mode III

In this failure mode the T-stub flange remains elastic and the bolts cause the

failure. The procedure is to calculate the force required to yield the bolts ( F1st)and then the increment necessary to fracture the bolts. As all the extra load istaken only by the bolts, the incremental T-stub force is given by Eq. (29) (wherewkIIbolt,pl is replaced by Eq. (10)) and the displacement is given by Eq. (31). Thevalue for Etb is taken as 1.0% of the bolt Youngs modulus Eb.

3. Taking account of temperature effects

3.1. Degradation of steel strength

Design codes have adopted the concept of Strength Reduction FactorSRF(or more precisely a strength retention factor) to represent the degradation ofmaterial strength at elevated temperatures. This is the residual strength of the steelat a particular temperature relative to its basic yield strength at room temperature.At ambient temperature, the stressstrain characteristics of steel are approximatelybi-linear with a distinct yield plateau. At high temperatures, however, the stressstrain curves degrade and are no longer bi-linear, making it difficult to define theexact yield point and elastic modulus. To overcome the problem, a limiting strainis specified and the relationship between strength reduction factor and temperature

will depend on the limit chosen. The design codes BS5950: Part 8 [19] and EC3:Part 1.2 [20] have adopted 0.5%, 1.5% and 2.0% strain limits for the fire limit state.The appropriate limit depends on whether the steel is bare or composite and thestrain limit of any protective material used.

3.2. Degradation of steel stiffness

The stiffness of steel is defined by Youngs (elastic) modulus, which is the initialslope of the tangent of the stressstrain curve. At elevated temperature the tangentmodulus must be used because of the non-linear nature of the stressstrainrelationship. However this depends on the proof strain at which the elastic modu-

lus is measured. Therefore, a bi-linear relationship is often used, with the elasticmodulus expressed as a function of temperature. The differences in the strengthand stiffness reduction factors between BS5950: Part 8 code and EC3: Part 1.2 arevery small.

Table 1 shows the Strength Reduction Factors for S275 steel at 2% strain and theStiffness Reduction Factor taken from EC3: Part 1.2. These SRF values have beenused in the mathematical model at elevated temperatures in order to model thebehaviour of the T-stub assemblies.

3.3. Degradation of bolts at elevated temperatures

Kirby [21] conducted a series of tests to determine the deterioration of thestrength of grade 8.8 bolts in fire. The bolts suffer a significant decrease in capacity


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in the temperature range 300700v

C. Based on these results, the following tri-linear relationship, shown in Fig. 8, was proposed by Kirby for the SRF:

SRF 1:0; for hb 300 vC

SRF 1:0 hb 3002:128 103

for hb < 300

v

C 680v

C;SRF 0:17 hb 6805:13 104 for hb < 680 vC 1000 vC

where hb is the temperature of the bolt.Theodorou [18] carried out a separate study on the behaviour of bolts at elev-

ated temperatures. His results verified the SRFs proposed by Kirby [21] and theapplicability to bolts of the SRFs of EC3: Part 1.2 and BS5950: Part 8, which arefor S275 steel. Bolt ductility was found to increase with temperature. Full details ofthis test programme and its results have been reported by Theodorou [18].

4. Experimental programme

A specially designed experimental arrangement was constructed, including a fur-nace and an image acquisition and processing system [22,23]. Developments invideo camera and digital image processing technology now permit real-time dis-placement measurements to be taken from a video image. The technique measuresdisplacements by tracking two contrasting targets. A purpose-built fan-assistedelectric furnace, with an internal capacity of 1 m3, was commissioned with view-ports to accommodate three video cameras.

The load was applied to the specimen by the use of a 500 kN capacity hydraulicjack, which was attached to a reaction frame outside the furnace, as shown in Fig. 9.The jack was connected to a control device capable of controlling the movement

Table 1Reduction factors for stressstrain curves of steel at elevated temperatures

Steel temperature, hs (v

C) Reduction factors for yield stress fy, and Youngs modulus Es, at

steel temperature hs

ky;h fy;h=fy kE;h Es;h=Es20 1.000 1.000100 1.000 1.000200 1.000 0.900300 1.000 0.800400 1.000 0.700500 0.780 0.600600 0.470 0.310700 0.230 0.130800 0.110 0.090900 0.060 0.06751000 0.040 0.04501100 0.020 0.02251200 0.000 0.000


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of the hydraulic jack either in load or displacement mode. A fire-protected loadintroduction device was designed in order to keep the hydraulic jack outside thefurnace but at the same time applying the tension or compression forces to thespecimen effectively.

Fig. 8. Comparison between bolt and steel SRFs.

Fig. 9. Arrangement for the experimental work.


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To verify the analytical model, the experimental investigation was conducted to

collect data on the behaviour of the T-stub assemblies at elevated temperatures and

to investigate the three failure modes resulting from the different geometrical

properties of each specimen. 45 T-stub specimen tests were conducted at elevatedtemperatures. Details of the geometrical and mechanical properties of the T-stub

specimens are reported elsewhere [24]. In the following section typical test results

are compared with the results from the mathematical model.The three failure modes are summarised below, with illustrations of the T-stub

specimens from the actual elevated-temperature tests.Failure Mode I. The T-stub specimen first forms a plastic hinge in the flange next

to the web (1), and then the bolts start to yield and finally fracture (2,3). Fig. 10

shows a typical test image for Failure Mode I.Failure Mode II. The T-stub specimen first forms a plastic hinge in the flange

next to the web (1), then it forms another plastic hinge in the flange at the bolt line

(2), and then the bolts start to yield and finally fracture (3,4). Fig. 11 shows a typi-

cal test image for Failure Mode II.Failure Mode III. In this failure mode the T-stub flange remains elastic and

essentially flat, but the bolts start to yield and finally fracture (1,2). Fig. 12 shows a

typical test image for Failure Mode III.

4.1. Investigation of each of the three failure modes

The tests were monitored using two video cameras placed in the front view-port

of the furnace. The first camera captured images for accurate displacement mea-

surements and the other for general observation of the T-stub distortion. Typical

images of distorted specimens at 570v

C taken from the two cameras are shown in

Fig. 13.The 25 tests (Series CA to CE), whose basic details are summarized in Tables 2

and 3, were devised to study each of the three failure modes. This was achieved by

Fig. 10. Typical test image for Failure Mode I.


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Fig. 11. Typical test image for Failure Mode II.

Fig. 12. Typical test image for Failure Mode III.

Fig. 13. Typical distorted images at 570v

C. (a) Image from first camera showing targets, 0.5 mm holes(boxed); (b) Image from second camera.


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Table2

Geometricalpropertiesofspecimensforp

haseCtests

h(mm)

Le(mm)

do

(mm)

a(mm)

tw(mm

)

tf(mm)

Rootradius(mm)W

eldaf(mm)

PhaseC

Column(UC20320360)

C

A1

174.2

5

203.9

5

22.00

56.9

7

10.0

0

13.70

10.2

0

N

o

C

A2

174.4

9

203.2

5

22.15

56.5

0

9.9

0

13.90

10.2

0

N

o

C

A3

173.9

6

203.3

5

22.12

56.5

5

9.9

5

13.90

10.2

0

N

o

C

A4

174.9

2

203.2

5

22.45

56.2

5

9.9

6

13.90

10.2

0

N

o

C

A5

173.3

5

203.2

0

22.25

56.2

2

9.9

0

13.80

10.2

0

N

o

End-plate(20020020)

C

A1

194.1

6

196.0

0

22.00

47.7

5

10.2

0

20.20

No

1

1.00

C

A2

193.9

5

195.6

5

22.30

47.7

5

10.2

5

20.20

No

1

1.00

C

A3

194.5

8

195.6

5

22.20

47.7

5

10.2

7

20.16

No

1

1.00

C

A4

194.2

9

195.7

8

22.36

47.5

9

10.3

2

20.22

No

1

1.00

C

A5

194.2

2

196.2

5

22.20

47.8

5

10.2

0

20.15

No

1

1.00

Column(UC15215230)

C

B1

157.0

2

153.6

6

22.22

32.2

6

6.1

5

9.1

5

7.6

N

o

C

B2

157.0

6

153.6

0

22.05

31.9

2

6.1

5

9.2

0

7.6

N

o

C

B3

156.9

0

153.6

5

22.10

31.7

0

6.2

0

9.1

5

7.6

N

o

C

B4

156.8

2

153.7

5

22.10

31.8

5

6.1

0

9.2

0

7.6

N

o

C

B5

156.8

2

154.0

0

22.10

32.2

3

6.1

0

9.1

5

7.6

N

o

End-plate(20020020)

C

B1

194.0

5

196.3

4

22.10

48.0

2

10.2

8

20.15

No

1

1.00

C

B2

194.0

0

195.7

3

22.20

47.8

1

10.1

5

20.15

No

1

1.00

C

B3

194.3

0

196.1

0

22.10

47.7

4

10.2

6

20.15

No

1

1.00

C

B4

193.9

5

196.0

5

22.10

48.2

9

10.3

2

20.15

No

1

1.00

C

B5

194.1

2

195.6

8

22.20

47.9

3

10.2

2

20.17

No

1

1.00

Column(UC20320386)

C

C1

179.0

0

204.5

5

22.25

57.4

9

12.4

5

19.12

10.2

0

N

o

C

C2

179.0

2

204.6

2

22.35

57.2

2

12.3

0

19.02

10.2

0

N

o

C

C3

179.5

5

204.0

5

22.30

56.9

2

12.2

5

19.46

10.2

0

N

o

C

C4

179.6

0

204.6

5

22.25

57.2

6

12.3

5

19.26

10.2

0

N

o

C

C5

178.8

0

203.7

0

22.25

56.6

0

12.3

0

19.47

10.2

0

N

o

End-plate(20020020)

C

C1

194.0

6

196.0

0

22.20

48.0

3

10.2

5

20.10

No

1

1.00

C

C2

193.9

2

196.7

0

22.45

48.3

5

10.2

0

20.10

No

1

1.00

C

C3

194.6

5

196.2

5

22.15

48.5

5

10.2

0

20.10

No

1

1.00

C

C4

194.1

5

196.7

0

22.05

47.9

8

10.2

5

20.15

No

1

1.00

C

C5

194.4

0

195.2

0

22.20

47.1

3

10.4

0

20.15

No

1

1.00

Column(UC254254107)

C

D1

180.7

0

255.6

1

22.25

83.2

2

12.8

0

21.12

12.7

0

N

o

C

D2

180.0

2

255.1

0

22.15

82.4

6

12.8

5

21.14

12.7

0

N

o

C

D3

181.8

3

258.3

5

22.20

84.3

0

12.8

0

20.80

12.7

0

N

o

C

D4

181.5

2

258.5

5

22.20

84.0

0

12.7

5

20.85

12.7

0

N

o

C

D5

181.3

9

258.4

5

22.25

84.1

6

12.7

5

20.82

12.7

0

N

o

End-plate(20020020)

C

D1

194.0

8

196.3

6

22.25

47.9

4

10.2

5

20.20

No

1

1.00

C

D2

194.2

5

195.8

5

22.25

47.5

1

10.4

0

20.25

No

1

1.00

C

D3

194.8

0

195.8

5

22.15

47.4

8

10.3

5

20.30

No

1

1.00

C

D4

194.2

0

195.6

5

22.28

47.8

9

10.3

2

20.16

No

1

1.00

C

D5

194.3

0

196.0

0

22.25

47.9

3

10.3

5

20.22

No

1

1.00

Column(UC20320386)

C

E1

179.9

0

204.7

0

14.50

57.4

2

12.3

0

19.21

10.2

0

N

o

C

E2

179.9

5

204.7

5

14.35

57.3

5

12.4

5

19.37

10.2

0

N

o

C

E3

180.1

7

204.1

0

14.45

57.2

2

12.4

0

19.66

10.2

0

N

o

C

E4

179.6

0

204.2

5

14.45

57.0

2

12.3

5

19.46

10.2

0

N

o

C

E5

180.3

7

204.5

0

14.40

57.4

0

12.3

8

19.30

10.2

0

N

o


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Table3

Testdataandmaterialproperties

Test

Temperature(vC)

Maximum

force(kN)

Actualyieldstress

(N/mm

2)

Youngsmodulus

(kN/mm

2)

Bolts

Measuredstress(N/mm

2)

Youngs

modulus

(kN/mm

2)

T-stub

Bolt

Column

End

-plate

Column

End-

plate

0.2

%Yield

Ultimate

stress

CA1

660

630

220

304

284

204

192

826

887

208

CA2

670

670

150

304

284

204

192

811

886

215

CA3

730

725

110

304

284

204

192

826

887

208

CA4

530

530

320

304

284

204

192

811

886

215

CA5

740

747

85

304

284

204

192

811

886

215

CB1

650

640

160

285

284

198

192

826

887

208

CB2

540

540

280

285

284

198

192

811

886

215

CB3

415

415

350

285

284

198

192

811

886

215

CB4

705

705

95

285

284

198

192

811

886

215

CB5

505

510

350

285

284

198

192

826

887

208

CC1

620

630

230

258

284

201

192

811

886

215

CC2

700

698

125

258

284

201

192

811

886

215

CC3

505

505

430

258

284

201

192

811

886

215

CC4

615

619

250

258

284

201

192

835

906

201

CC5

740

746

100

258

284

201

192

811

886

215

CD1

615

618

220

288

284

189

192

811

886

215

CD2

700

703

90

288

284

189

192

811

886

215

CD3

705

707

120

288

284

189

192

835

906

201

CD4

505

507

410

288

284

189

192

811

886

215

CD5

800

803

90

288

284

189

192

811

886

215

CE1

610

614

80

258

284

201

192

635

750

205

CE2

510

515

140

258

284

201

192

635

750

205

CE3

505

508

160

258

284

201

192

766

869

209.4

0

CE4

410

414

225

258

284

201

192

843

924

207

CE5

Room

Room

300

258

284

201

192

843

924

207


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keeping the geometrical properties of the right-hand side T-stub element the same(using a steel plate 200 200 20 mm to represent the end-plate found in realjoints) and changing the geometrical properties of the left-hand side T-stub speci-men by using different column sections. Thermocouples were arranged around thespecimen as shown in Fig. 14. One typical image demonstrating Failure Mode I isshown in Fig. 15.

In order to achieve complete failure of the bolts in Failure Mode II, without anyplastic hinges forming in the T-stub flanges, a smaller bolt size (M12) had to beused. In Failure Mode II, because of the extensive deformation of the column T-

stub, the bolts failed under a combination of shear and tension force, as illustratedin Fig. 16.

In order to include this combined shear and tension bolt failure mechanism inthe simplified model the last image from each test was taken and the approximateshear force value applied to the bolts was calculated for the deformed geometry.

Fig. 14. Typical T-stub assembly and thermocouple arrangement.

Fig. 15. Typical image showing Failure Mode I.


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A reduced tensile capacity to account for the presence of shear was calculated using:

Applied tension

Tensile strength

2 Applied shear

0:63 Tensile strength 2

1:0 32

when the threads are in the shear plane [25], and

Applied tension

Tensile strength

2 Applied shear

0:79 Tensile strength 2

1:0 33

when the shank of the bolts is in the shear plane.

Fig. 17. Forcedeflection curves for the column T-stub for test programme CA.

Fig. 16. Bolt failure in a combination of shear and tension force.


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The test results compared with the mathematical model results are presented in

Figs. 1724. Note that in Figs. 1924 the results for column flange failure and end-

plate failure are shown separately.Both the test and simplified model results show the importance of correctly pre-

dicting the failure mode of the T-stub specimen. The total deformation of the T-stub flange varies significantly with failure mode. This is demonstrated by plotting

the three failure modes taken from different test programmes at 505v

C, as shown

in Fig. 25.

Fig. 18. Forcedeflection curves for the column T-stub for test programme CB.

Fig. 19. Forcedeflection curves for the column T-stub for test programme CC.


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4.2. Test and theoretical results

During the tests it was observed that, when using grade 8.8 bolts and nuts, the

nuts failed by thread stripping as shown in Fig. 26, in which a normal nut is com-

pared against two failed nuts.This nut-stripping failure happened in Failure Mode I, for specimens tested at

530v

C and 740v

C. As a result, for all the other tests it was decided to use HSFGnuts in order to avoid this kind of failure. Of course in practise this would not be

possible and the reduced capacity of the bolt and nut system would need to be

accounted for. This study aimed to research a full range of failure modes and thus

premature failure by nut thread stripping had to be avoided. During the experi-

Fig. 21. Forcedeflection curves for the column T-stub for test programme CD.

Fig. 20. Forcedeflection curves for end-plate T-stub for test programme CC.


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mental investigation of the tension zone it was very clear from the beginning thatbolts could influence the T-stub specimen behaviour significantly. The same behav-iour is highlighted by the simplified model results. The performance of bolt andnut assemblies at elevated temperatures is worthy of further investigation.

5. Conclusions

The current study demonstrates the potential for incorporating component-basedmodels, for different zones within a steel joint, in order to predict joint behaviour

Fig. 22. Forcedeflection curves for end-plate T-stub for test programme CD.

Fig. 23. Forcedeflection curves for the column T-stub for test programme CE.


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at elevated temperatures. Having the advantage of being able to predict the behav-

iour of any joint arrangement under fire conditions from geometrical and mechan-

ical properties minimises the need to carry out costly, time consuming and complex

tests at elevated temperatures.The tension zone components were tested and analytically investigated, at elev-

ated temperatures up to their failure point, and demonstrated that the component-based model accurately predicts the failure mechanism and the level of moment

and rotation that a particular joint can sustain. From the analytical part of the

investigation, a simplified model has been developed using plastic theory andmechanics. The model has been extended to predict the three failure modes of the

Fig. 25. Failure modes compared at 505v

C.

Fig. 24. Forcedeflection curves for end-plate T-stub for test programme CE.


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T-stub specimen from the geometrical and mechanical properties at ambient andelevated temperatures. Furthermore the load-deflection results, when compared

against the actual elevated-temperature tests, were in good agreement, especially

considering the complexity of the problem resulting from the interaction of flange

and bolt forces and the added elevated-temperature factor.From the tests at elevated temperatures it was obvious that bolt flexibility was akey parameter in the behaviour of a T-stub specimen. The use of grade 8.8 bolts

and nuts resulted in a nut-stripping failure, so instead high strength friction grip

nuts were used for the subsequent tests. In order to investigate the mechanical

properties of grade 8.8 bolts at elevated temperatures a separate study was carriedout at elevated temperatures. The results of the study verified the use of Kirbys

Strength Reduction Factors and EC3:Part 1.2 SRFs for analytical studies of the

behaviour of T-stubs at elevated temperatures.Using component-based models in the analysis of steel joints at elevated tem-

peratures is particularly advantageous when it is necessary to account for the effectof large axial forces generated in the beams during a fire. It is important to con-

sider these tensile or compressive axial forces when predicting steel joint behaviour,

because they could reduce the rotational ductility of the joint and limit the ductility

of the structural frame. In the latter stages of such an analysis the net axial force isusually tensile. With the conventional approach to frame analysis, moment

rotationtemperaturethrust relationships would be required, making the problem

two degrees more difficult than an ambient-temperature semi-rigid frame problem.Clearly these would be extremely cumbersome to predict and input into frame

analysis programs. Using the temperatureloaddeflection relationships for the indi-vidual zones directly in the analysis removes this complication and allows different

temperatures to be used for different zones or components.

Fig. 26. Nut stripping failure mechanism.


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Acknowledgements

The work described herein was funded by the Engineering and Physical Sciences

Research Council of Great Britain under research contract GR/L98619. This sup-port is gratefully acknowledged.

Appendix A. Mathematical modelclassical beam theory

The bending moment expressions in the three zones moving from left to rightacross the T-stub are:

EIv00 Qx wkx Fx

2 0 x nEIv00 Qx wx n

2

2 wkx Fx

2 wx n

2

2n x n k

EIv00 Qx wkx n k=2 wkx Fx2

wkx n k=2n k x n km

Integration of these equations gives

EIv0 wkx2

2 Fx2

4 C1

EIv0 wkx2

2 Fx

2

4 wx n

3

6 C2

EIv0 wkx2

2 Fx

2

4 wkx n k=2

2

2 C3

Performing a second integration the deflection equations become:

EIv wkx3

6 Fx

3

12 C1x C4

EIv wkx3

6 Fx

3

12 w x n

4

24 C2x C5

EIv wkx3

6 Fx

3

12 wkx n k=2

3

6 C3x C6

The six constants of integration appearing in the preceding equations can befound from the following boundary conditions:

. at x 0 the deflection is zero;

.

at x n and x n k the slope and deflection for the two parts of the beammust be equal;. at x n k m the slope is zero.


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Using the above boundary conditions the constants can be found and the deflec-tion dcl at x n km can be determined.

dcl FL3e48EI

wk

EI

L3e24

m

k=2

3

6 m

k=2

2Le

4 k2

n

k=2

24 A1Failure Mode I

The bending moment expressions are:

EIv00 Dwx2

20 x k=2

EIv00 Dwx k=42

k=2 x k=2 m

Integration of these equations gives

EIv0 Dwx3

6 C1

EIv0 Dwx k=42

4 C2

Performing a second integration the deflection equations become

EIv Dwx4

24 C1x C3

EIv Dwx k=43

12 C2x C4

The four constants of integration appearing in the preceding equations can befound from the following boundary conditions:

. At x 0 the deflection v DwkLb=EbAs,

. At x k=2 the slope and deflection for the two parts of the beam must be equal,

. At x m k=2 the slope is zero.

Using the above boundary conditions the constants can be found and theincremental displacement Dd Icl at x m k=2 determined as

DdIcl DF

EI

m k=42m k=28

m k=43

24 k

3

1536 EILb2EtbAs

A2

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