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Proceedings of the Institution of

Civil EngineersStructures & Buildings 161December 2008 Issue SB6

Pages 311323doi: 10.1680/stbu.2008.161.6.311

Paper 800040Received 13/05/2008

Accepted 19/08/2008

Keywords:slabs & fire/platesengineering

Ehab A. M. EllobodyAssociate Professor, Depart-

ment of Structural Engineering,

Tanta University, Egypt

Colin G. BaileyProfessor and Head of School

of Mechanical, Aerospace and

Civil Engineering, The University

of Manchester, UK

Modelling of bonded post-tensioned concrete slabs in fire

E. A. M. Ellobody PhD, CEngand C. G. Bailey PhD, CEng, FICE, MIStructE, MIFireE

This paper presents a finite element model highlighting

the behaviour of bonded post-tensioned one-way

spanning concrete slabs in fire conditions. The model

was verified against ten fire tests on bonded post-

tensioned concrete slabs at ambient and elevated

temperatures. The slabs were simply supported andpost-tensioned with 15.7 mm nominal diameter seven-

wire mono-strand tendons. The mechanical and thermal

material non-linearities of the entire slabs components,

consisting of the concrete, plastic and galvanised steel

ducts, prestressing tendon and the anchorages, have

been carefully inserted into the model. The interface

between the tendon and surrounding grout was also

considered, allowing the bond behaviour to be modelled

and the tendon to retain its profile shape during the

deformation of the slab. The temperature distributions

throughout the slab, together with the slabs

development of displacement and stress, as it was

heated, were predicted by the model and verified against

test data. A parametric study was conducted to

investigate the effects on the global structural behaviour

owing to the change in the aggregate type, duct type,

load ratio, boundary conditions and different fire

scenarios. The study has shown that the bonded post-

tensioned concrete slabs investigated in this study are

capable of achieving the designed 90 min fire resistance.

It is also shown that the fire resistance given by BS

8110-2 and BS EN 1992-1-2 are acceptable for the design

of bonded post-tensioned one-way spanning concrete

slabs under fire conditions.

NOTATION

CS cold surface

e concrete emissivity

f stress

fc compressive stress of concrete

fco proportional limit stress of concrete

fcu compressive cube strength of concrete

ft tensile stress of concrete

Gf fracture energy

HS hot surface

h slab height

LC long cool fire curveLS limestone

LT left tendon

M metallic duct

MS middle surface

MT middle tendon

PL plastic duct

RT right tendon

SH short hot fire curve

ST standard fire curveT tendon level

TG Thames Gravel

c convective coefficient

strain

cu ultimate strain of concrete in compression

tu ultimate strain of concrete in tension

1. INTRODUCTION

Post-tensioned floor slabs can be bonded or unbonded. For

bonded post-tensioned floor slabs the transfer of the force from

the tendon to the concrete is by way of the end anchors, the

bond between the tendons and concrete which is maintainedby grouting and the curvature of the tendons. For unbonded

systems the transfer of force from the tendon to the concrete is

only by way of the end anchors and the tendons curvature. To

date, there has been no detailed information regarding the

structural behaviour of bonded post-tensioned concrete slabs

under fire conditions with only a few fire tests, recently

conducted by Bailey and Ellobody1,2 reported on this form of

construction. Current design rules specified in BS 8110-23 and

BS EN 1992-1-24 provide guidance on the fire resistance of

post-tensioned floor slabs, but these have been derived based

on tests carried out on pre-tensioned and non-tensioned

concrete members. In terms of post-tensioned construction the

limited previous fire tests were only conducted on unbondedpost-tensioned slabs as reported in references[5 7]. An

extensive review of these tests, together with evidence of fires

in actual buildings constructed using post-tensioned floor

slabs, was provided by Lee and Bailey8 who concluded that

further investigation into the behaviour of post-tensioned floor

slabs in fire is required. This conclusion, of the need for further

investigation, is also shared by the latest Federation

Internationale de la Precontrainte (FIB) design guide on post-

tensioned slabs.9 The existing limited test data on unbonded

slabs were augmented by Bailey and Ellobody,10 where the

effect of different aggregate type and restraint conditions was

highlighted.

Recently, Bailey and Ellobody1 have conducted ten tests on

bonded post-tensioned one-way concrete slabs at ambient and

Structures & Buildings 161 Issue SB6 Modelling of bonded post-tensioned concrete slabs in fire Ellobody Bailey 311


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elevated temperatures. Eight

slabs were subjected to a fire

under a static load

representing a load ratio of

0.6, where the load ratio is

defined as the applied load

divided by the design

capacity. In addition to the

fire tests two additional tests

were conducted in the cold

condition to define the

capacity of the slabs. The

tests highlighted the different

structural response between

using limestone and Thames

Gravel aggregates, different

duct material types (plastic

and metallic), and different longitudinal restraint conditions.

The temperature distribution through the slabs, the strains in

the tendons, and the horizontal and vertical displacements

were measured in each test. The fire resistance of the bonded

post-tensioned concrete slabs were compared with specifiedvalues in BS 8110-23 and BS EN 1992-1-2,4 which were shown

to be acceptable for design purposes. Although it is known11

that the use of Thames Gravel aggregate and restraint to

thermal expansion can contribute to spalling, there was no

observation of any significant spalling in the tests, as presented

in Refs1 and 2, primarily owing to the moisture content being

below 2.5% by weight.

Finite element models of post-tensioned concrete slabs under

fire conditions have previously been used to investigate the

behaviour of unbonded slabs as presented by Lee and Bailey8,12

and Ellobody and Bailey.13,14 Compared with the modelling of

unbonded slabs, the behaviour of bonded post-tensioned

concrete slabs is more complicated owing to the presence of

ducts, the bond between the tendons and grout, the bond

between the grout and ducts, and the bond between the ducts

and concrete, as well as the fact that the bond between any two

components may not be maintained at elevated temperatures.

The current paper highlights the behaviour of post-tensioned

bonded one-way spanning concrete slabs in fire conditions

through non-linear numerical modelling. A detailed thermo-

mechanical three-dimensional (3D) finite element model was

developed using Abaqus15 and verified against the tests

conducted by Bailey and Ellobody.1,2 A parametric study has

been conducted to study the effects of the change in theaggregate type, duct type, load ratio, fire scenarios and

boundary conditions on the behaviour of bonded post-

tensioned one-way concrete slabs at elevated temperatures. The

results of the numerical investigation have been compared with

the design values specified in BS 8110-2,3 and BS EN 1992-1-

2,4 with detailed discussions and conclusions presented.

2. SUMMARY OF EXPERIMENTAL INVESTIGATION

As shown in Table1, ten teststwo at ambient temperature

(TB1 and TB2) and eight at elevated temperature (TB3TB10)

were carried out on bonded post-tensioned one-way spanning

concrete slabs. The main variable parameters in the tests werethe boundary conditions (free and restrained longitudinal

expansion), the aggregate type (limestone and Thames Gravel)

and the duct type used within the bonded slabs (plastic and

steel). The slabs were designed according to BS 8110-116 and

the Concrete Society technical report 43.17 The slabs were

4.3 m long, 1.6 m wide and 160 mm deep. Each slab had three

longitudinal parabolic tendons with a nominal diameter of

15.7 mm and an area of 150 mm2. The tendon was a mono-strand with seven high-strength steel wires, with an average

measured tensile strength of 1846 MPa. Plastic ducts, 23 mm

internal diameter, were used with slabs TB3, TB4, TB5 and TB6.

Galvanised steel ducts with 40 mm internal diameter were used

with slabs TB7, TB8, TB9 and TB10. The ducts were positioned

in a second degree parabolic shape before casting the concrete.

Steel chairs were used to create the parabolic shape for the

ducts to ensure that the distance between the bottom surface of

the slab to the centre of the tendon was 42 mm. Each slab had

three longitudinal ducts, where one duct was positioned in the

middle of the slab with the other two positioned either side, at

a spacing of 530 mm, as shown in Fig.1. The duct ends were

positioned exactly at the mid-height of the slab, where the

dead and live anchorages were located. One tendon was

threaded through each duct before casting the concrete.

Bursting reinforcement was designed according to BS 8110-116

to resist tensile bursting forces around individual anchorages.

No other non-tensioned reinforcement was included.

The concrete cube strength at 4, 14 and 28 days after casting, as

well as at the time of testing, is shown in Table2 together with

the measured moisture content for the slabs which were tested

Test specimen Fire Longitudinal expansion Duct Coarse aggregate

Free Restrained Plastic Metallic Limestone ThamesGravel

Slab TB1 X X XSlab TB2 X X XSlab TB3 X X X XSlab TB4 X X X XSlab TB5 X X X X

Slab TB6 X X X XSlab TB7 X X X XSlab TB8 X X X XSlab TB9 X X X XSlab TB10 X X X X

Table 1. Tests on bonded post-tensioned concrete slabs

Fig. 1. Mould used for casting the bonded test specimens

312 Structures & Buildings 161 Issue SB6 Modelling of bonded post-tensioned concrete slabs in fire Ellobody Bailey


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under fire conditions. Grouting followed BS EN 44718 using a

mixing ratio of ordinary Portland cement to water of 2 .5:1.

Grouting was conducted immediately after the post-tensioning

of the tendons. The measured grout strength was 47 MPa at 28

days. The full applied design prestressing force to the slabs was

195 kN, with the average measured force in the three tendons

being 169 kN, equating to 13% losses. Further details of the

post-tensioning process, and measurements obtained during

this process, are presented in Ellobody and Bailey.19

The slabs were tested over a span of 4.0 m. The test set-up,

loading positions and instrumentation are shown in Fig. 2. In

the ambient tests, the slabs were loaded to failure, while in the

fire tests, the slabs were subjected to a static load equal to

78.3 kN representing a load ratio of 0.6. The slabs were loaded

at four locations using spreader plates 1600 3 350 3 40 mm,

as shown in Fig.3. The applied load, the strains in the tendons,

and the vertical deflections were measured in all tests. In the

fire tests, temperatures through the slab were also measured

together with longitudinal displacements in the unrestrained

slabs, at the locations shown in Fig. 2, with the middle 3.2 m of

the slab heated. The strains in the tendons were measured nearthe ends of the tendons (Fig. 2), ensuring that gauges remained

at ambient temperature. As the tendons were bonded these

gauges should give a good indication of the strains at their

location near the dead ends. The slabs were heated in the fire

tests using two burners following the standard time

temperature curve specified in BS EN 1991-1-2.20 Further

details of the tests and results obtained are given in Ref. 1.

In the restrained fire tests, two restraining beams were designed

and positioned against both ends of the slab to prevent

horizontal displacement and end rotation of the slab. The

beams were bolted to the loading frame, which allowed an

initial expansion (approximately 4.5 mm) to occur until the

slab became in full contact with the restraining beams and

until the bolts fixing the restrained beams became intact with

the edges of the holes. Further details for the test set-up of the

restrained fire tests is given in Ref. 1.

3. FINITE ELEMENT MODEL

The bonded post-tensioned concrete slab components were

modelled using a combination of 3D solid elements (C3D8 and

C3D6) available within the Abaqus15 element library. The

elements have three degrees of freedom per node. Owing to

symmetry, only one quarter of the bonded slab was modelled

(Fig.4), with 6894 elements, including interface elements, used.

The boundary conditions and load application were identical to

that used in the tests. The measured post-tensioning stress in

the tendons (169 kN) was initially applied in a separate step.

The dead load representing the weight of the slab was applied

as a static uniformly distributed load on the top surface of the

slab and the dead load representing the weight of the loading

tree (Fig.3) was applied as a static distributed load over the

area of the spreader plates. For the ambient tests the jack load

was applied in increments as a static distributed load over the

area of the spreader plates. For the fire tests the applied load

remained constant and the temperature within the slab

increased.

For the modelling of the fire tests a thermal analysis was

conducted, using the heat transfer option available within

Abaqus,15 to calculate the temperature distribution throughout

the slabs, based on the measured furnace temperature from the

test. A constant convective coefficient (c) of 25 W/m2K was

assumed for the exposed surface and 9 W/m2K was assumedfor the unexposed surface. The radiative heat flux was

calculated using a concrete emissivity (e) value of 0.7.

Concrete was modelled using the damaged plasticity model

implemented within Abaqus.15 Under uniaxial compression the

response is linear until the value of the proportional limit

stress, (fco) is reached, which is assumed to equal 0.33 times

the compressive strength (fc), as shown in Fig.5(a). Under

uniaxial tension the stressstrain response follows a linear

elastic relationship until the value of the failure stress. The

tensile failure stress is taken as 0.1 times the compressive

strength of concretefc, which is assumed to be equal to 0.67

times the measured concrete cube strength ( fcu). The softening

stressstrain response, past the maximum tensile stress, was

represented by a linear line defined by the fracture energy and

crack band width. The fracture energyGf (energy required to

open a unit area of crack) was taken as 0.217 N/mm.19 The

fracture energy divided by the crack band width was used to

define the area under the softening branch of the tension part

of the stressstrain curve, as shown in Fig. 5(b). The crack

band width was assumed as the cubic root of the volume

between integration points for a solid element, as

recommended by Comite

Europeen du Beton (CEB).21

The measured stressstraincurve of the tendon at

ambient temperature, as

shown in Fig.6, was used in

modelling the tendons. Based

on experimental

observations,1 there was no

slip at the ductgrout

interface as well as at the

ductconcrete interface.

Hence only the contact

between the tendon and

grout was modelled, utilisinginterface elements (using the

contact pair option) available

within the Abaqus15 element

Slab Aggregate type Measured concrete strength at different days aftercasting: MPa

Moisturecontent: %

4 days 14 days 28 days At testing

TB1 Limestone 32.3 39.2 40.0 41.2 TB2 Limestone 22.1 30.3 31.7 30.3 TB3 Limestone 25.2 36.4 39.4 36.6 1.19TB4 Limestone 32.9 41.5 43.9 40.9 1.93TB5 Thames Gravel 24.0 35.0 35.3 35.5 1.07TB6 Thames Gravel 30.8 37.2 39.3 38.6 2.50TB7 Limestone 29.2 36.0 39.1 40.4 2.43TB8 Limestone 29.0 37.4 40.0 42.3 1.84TB9 Thames Gravel 26.5 35.3 38.9 36.9 2.27

TB10 Thames Gravel 32.0 35.1 38.6 39.3 2.18

Table 2. Measured concrete cube strength and moisture content



4/13

library. The interface elements consisted of two matching

contact faces from the tendon elements and surrounding grout

elements. As observed experimentally, and discussed later in

the paper, there was a significant decrease in the strains of the

tendons in most of the fire tests. The decrease initiated at a

tendon temperature of 1008C owing to water migration from

the grout, suggesting a possible loss of bond at this

temperature. Within the model a friction coefficient of 0.25

was therefore considered between the two faces until the

(a)

Tendon

Furnace

Position of thermal couples

Position of strain gauges

Position of displacement transducers

3200 400400150150

160

500 10001000500 500

150150

500

Duct

(b)

Tendon

Furnace

Quarter (1)

Quarter (2)

Quarter (3)

Quarter (4)

Centre (5)

270

270

530

530

10001000 11501150

Duct

Fig. 2. Test set-up and positions of instrumentation and loading: (a) section elevation; (b) plan (dimensions in mm)

Fig. 3. Picture of test showing loading positions

Duct

Tendon

Grout

Symmetry surface (1)

Edge linesupport


Concrete

Fig. 4. Finite element mesh for quarter of the bonded slab



5/13

tendon temperature reached 1008C and was then taken as zero

after this temperature. The interface element allowed the

surfaces to displace relative to each other, based on the friction

coefficients, but ensured that the contact elements could not

penetrate each other when there was no friction.

The stress straintemperature curves for concrete in

compression and tension are shown in Fig. 5. The curves were

based on the reduction factors given in BS EN 1992-1-24 for

calcareous aggregate, which were adopted for the limestone

aggregate used in this study, and siliceous aggregate, which

were adopted for Thames Gravel. The specific heat and thermal

conductivity were also calculated according to BS EN 1992-1-

2,4 with the measured moisture content (see Table 2)

considered in the calculation of the specific heat of concrete.

The measured stressstrain curve for the tendon at ambient

temperature was used to calculate the stressstrain curves at

elevated temperatures following the reduction factors given in

BS EN 1992-1-2,4 as shown in Fig.6. Similar curves were used

for the anchorages, with material properties at ambient

temperature conforming to BS 4447.22 The stress strain curves

of the plastic and steel ducts were predicted based on data

provided by the manufacturers.

Recent finite element modelling presented in Ref. 14

recommended the use of measured values of thermal expansion

coefficients for concrete with limestone and Thames Gravel

aggregates available in the literature, 23,24 instead of the values

given in the code.4 A linear thermal expansion coefficient of

8.1310

6 per8C was used for the concrete with limestoneaggregate based on measurements by Ndon and Bergeson23 For

the concrete with Thames Gravel a linear thermal expansion

coefficient of 13.23106 per8C was used based on measured

values given by the Building Research Board.24 The same

values were used to model the thermal expansion of the

bonded concrete slabs with limestone and Thames Gravel

investigated in this study.

For the modelling of the restrained fire tests, detailed in Ref. 1,

interface elements, similar to that used between the tendons

and grout, were used between the slab ends and the restraining

beams. The interface elements allowed the initial thermal

expansion and rotation of the slab observed in the tests to

occur until the slab was fully in contact with the restraining

beams. After this stage, the longitudinal expansion was

prevented. The faces of the interface elements were the slab

end (the slave surface) and a rigid plate representing the flange

of the restraining beam (the master surface). The initial

clearance between the two faces was taken as 4.5 mm based on

the average initial expansions observed in the tests. 1 Only

horizontal restraint to expansion of the slab was provided. The

slab was free to contract, corresponding to the test conditions.

4. VERIFICATION OF THE FINITE ELEMENT MODEL

4.1. Verification of the ambient tests

The results obtained from the finite element model in terms of

the ultimate loads, load-central deflection curves, failure modes

and stresses in the tendons were compared against the test

results. The loadcentral deflection relationship obtained from

slab TB1, in comparison with that obtained from the model, is

shown in Fig.7. Good agreement was achieved between

numerical and experimental results. The failure load observed

experimentally was 215.4 kN, at a central deflection of

112 mm, compared with 212.5 kN and 105 mm obtained from

the model. The failure load predicted using the model was 1.3%

lower than that observed from the test. The deformed shape atfailure for slab TB1, obtained from the model, is shown in Fig.

8,which is in good agreement with that observed in the test

TB1.1,2 Fig.8 also shows the stress distribution in the concrete

20C

100C

200C

300C

400C

500C

(b)

20C

100C

200C

300C

400C

500C

600C

700C

800C

900C

(a)

f

f

fc

ft

fco

cu

tu

Fig. 5. Stressstrain curves of concrete at elevatedtemperatures: (a) compression; (b) tension

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 40000 80000 120000 160000Micro strain

Stress:MPa

20C

100C

200C

300C

400C

500C

600C

700C

800C

900C

Fig. 6. Stressstrain curves of the tendon at elevatedtemperatures



6/13

elements at failure. It can be seen that the concrete element

stresses in the compression zone of the maximum bending

moment region under the middle spreader plates approachedthe maximum compressive stresses. The mode of failure of

concrete crushing in the model therefore corresponded to the

mode of failure observed experimentally and reported in Refs1

and2. The loadstrain curves of the tendons obtained

experimentally and numerically are presented in Fig.9. The

strains were recorded by the three strain gauges fitted on the

left tendon (LT), middle tendon (MT) and right tendon (RT) of

the bonded slab TB1, as shown in Fig. 9. It should be noted

that the strains observed experimentally remained constant

from the start of loading until the end of the test, while that

predicted numerically had an increase of 560 microstrain from

a load 183.1 to 212.5 kN. The strains recorded from the finite

element model were averaged over the full cross-sectional area

of the bar whereas in the test the strains in the individual wires

were measured. The absolute average value used in the model

was close to the maximum stressed wire, as shown in Fig. 9. At

higher loads, the strains recorded in the tendon from the finite

element model slightly exceeded the elastic strains. Similar

conclusions could be drawn from the comparison of load-strain

curves of the tendons for the bonded slab TB2, as shown in

Fig.10.

The loadcentral deflection curves obtained experimentally

and numerically for slab TB2 are compared in Fig. 11. Once

again the experimental and numerical curves are in good

agreement. The failure load observed experimentally was

187.9 kN at a central deflection of 107 mm compared with

203.9 kN and 108 mm obtained from the model. The failure

0

50

100

150

200

250

0 40 80 120 160Central deflection: mm

Load:kN

Test TB1

FE TB1

Fig. 7. Comparison of loadcentral deflection curves forbonded slab TB1

Concrete

Duct

Tendon

Grout



Edge line

support

Stress units: N/m2

1

2

3

1151 109

3000 106

2500 105

2500 106

5250 106

8000 106

1075 107

1350 107

1625 107

1900 107

2175 107

2450 107

2725 107

3000 107

3547 108

S, S22

(Avg: 75%)

Fig. 8. Deflected shape and stress contours for bonded slab TB1

0

50

100

150

200

250

0 2000 4000 6000 8000Micro strain

Load:kN

FE

RT3

RT2

RT1

MT3

MT2

MT1LT3

LT2

LT1

Fig. 9. Comparison of loadstrain curves of the tendons forbonded slab TB1

0

50

100

150

200

250

0 2000 4000 6000 8000Micro strain

Load:kN

FE

RT3

RT2

RT1

MT2

MT1

LT3

LT2

LT1

Fig. 10. Comparison of loadstrain curves of the tendons forbonded slab TB2



7/13

load predicted using the model was 8.5% higher than that

observed in the test. Slab TB2 had a metallic duct of 40 mm

internal diameter while slab TB1 had a plastic duct with 23 mm

internal diameter. The difference in the failure loads is

attributed to the unexpected lower concrete strength of slabTB2 (30.3 MPa) compared to slab TB1 (41.2 MPa) as reported in

Refs1 and 2. Interestingly, as the post-tensioning of the slabs

took place before grouting, the axis of the tendon might have

shifted upwards away from the centre of the duct, especially at

the centre span of the slab. The effect of the movement of the

tendon is particularly prominent in slab TB2 owing to the

greater diameter (40 mm) of the metallic duct used. This was

highlighted using the model by moving the tendon inside the

metallic duct by a nominal 2 mm upwards at the centre span of

slab TB2, which reduced the failure load to 176.6 kN at a

central deflection of 94 mm, as shown in Fig. 11. As the

movement of the tendon inside the duct cannot be controlled,

and is dependent on the diameter of duct used, the designed

tendon axis distance (i.e. at the centre of the duct) will be used

in the finite element analysis for all the slabs investigated in

this study. The deflected shape, stress contours and failure

modes predicted for slab TB2 were similar to that of slab TB1

shown in Fig.8.

4.2. Verification of the fire tests

To indicate the accuracy of the thermal modelling, the

temperature distribution throughout the bonded post-tensioned

concrete slabs was plotted and compared against the tests. As

an example, the predicted and recorded test temperatures at the

hot surface (HS), the tendon (T), the mid-surface (MS) and thecold surface (CS) at the centre of slab TB3 is shown in Fig. 12.

Similar accuracy was obtained when the model was compared

against the other fire tests.

The timecentral deflection curves obtained from the

unrestrained tests and the finite element analysis were

compared and good agreement was achieved. As an example,

Fig.13shows the central deflectiontime relationships plotted

for the unrestrained slabs TB3 (having plastic ducts and

limestone aggregate) and TB5 (having plastic ducts and Thames

Gravel aggregate). The central deflections observed

experimentally for slabs TB3 and TB5 were 59 mm at 94.5 min

and 82 mm at 88 min, respectively, compared with 66 mm at

94.5 min and 95 mm at 86 min numerically. The axial

movements for slabs TB3 and TB5 were also compared

experimentally and numerically, as shown in Fig. 14. The

maximum axial movements were 4.2 and 7.2 mm at the

mid-height of the slab, recorded in the slabs TB3 and TB5

respectively, compared with 4.1 and 7.5 mm from the model.

Considering Figs13and14, it can be seen that both the test

and finite element results show that the slab TB5, which had

Thames Gravel, had significant higher vertical and horizontal

0

50

100

150

200

250

0 20 40 60 80 100 120Central deflection: mm

Load:kN

FE TB2

Test TB2

FE TB2 (shifted tendon)

Fig. 11. Comparison of load central deflection curves forbonded slab TB2

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120Time: min

Temperature:C

Test: HS

Test: T

Test: MS Test: CS

FE: HS

FE: T

FE: MS

FE: CS

Fig. 12. Measured and predicted temperatures throughout thedepth of the slab TB3

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100 110Time: min

Centraldeflection:mm

FE TB5

Test TB5

FE TB3

Test TB3

Fig. 13. Comparison of timecentral deflection curves forbonded slabs TB3 and TB5

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120Time: min

Expansion:mm

Test TB5

FE TB5

Test TB3

FE TB3

Fig. 14. Comparison of timelongitudinal expansion curves forbonded slabs TB3 and TB5



8/13

displacements compared with slab TB3 having limestone

aggregate owing to the higher thermal expansion of the

Thames Gravel.

Figures15and16 show the central deflectiontime curves

plotted for the restrained fire slabs TB8 (having metallic ducts

and limestone aggregate) and TB10 (having metallic ducts and

Thames Gravel aggregate), respectively. For slab TB8, the

maximum central deflection observed experimentally was

35 mm at 55.5 min from the start of heating, compared with

37 mm at 48.4 min from the model. For slab TB10, the

maximum central deflection observed experimentally was

39 mm, recorded at 39 min from the start of heating, compared

with 40 mm predicted at 43 min from the model. In both tests

it can be seen (Figs15and16)that there is an excellent

agreement between test results and the model. The finite

element model was able to accurately follow the test from the

start of heating, where the slab is not fully restrained,1 until it

became in full contact with the restraining beam.

The stresses in the tendons were predicted from the finite

element analysis for all the bonded slabs. The measured strainsrecorded by the strain gauges fitted on the middle tendon

(MT1, MT2 and MT3), left tendon (LT1, LT2 and LT3) and right

tendon (RT1 and RT2) were used to predict the stresses in the

tendons adopting the reduction factors given in BS EN 1992-1-

2.4 As an example, the stresses predicted numerically were

compared with those obtained experimentally for slab TB3, as

shown in Fig.17. Generally good agreement was achieved

between experimental and numerical results. It can be seen that

the prestress force in the tendon started to decrease

significantly after 35 min as observed experimentally and

confirmed numerically. As explained previously, the strains

recorded from the finite element model were averaged over the

full cross-sectional area of the bar whereas in the test the

strains in the individual wires were measured. This caused the

prestress force predicted numerically to decrease gradually as

shown in Fig.17. Similar behaviour was observed for the other

bonded fire tests.

Taking the restrained slab TB4 as an example, the stresses at

the maximum temperature are shown in Fig. 18. As slab TB4

was restrained, the strains in the concrete elements at the

restraint position approached the maximum compressive

strains. Hence local concrete crushing was predicted using the

finite element model, which compares well with the behaviour

observed experimentally in the restrained tests.1 Fig.19 shows

the cracks and spalling of the restrained slabs TB4 and TB6

observed in the tests. Fig.18 also shows that tensile stresses areconcentrated at the tendon position and extend towards the top

surface in the longitudinal direction of the slab.

Similar to the fire tests conducted on unbonded post-tensioned

concrete slabs,10 longitudinal cracks directly above and in line

with the tendons were observed in all the bonded slabs .1,2 The

cracks appeared on the unexposed surface of the bonded slabs

between 15 and 19 min, corresponding to a tendon temperature

of approximately 1108C. The cracks are caused by tensile

stresses being induced perpendicular to the trajectory of the

tendons owing to lateral thermal expansion at elevated

temperatures. Detailed explanation of the cause of the cracks,

when investigating unbonded slabs, was previously provided

using finite element modelling conducted by the authors.14

5. PARAMETRIC STUDIES AND DISCUSSIONS

The verified finite element model was used to investigate the

effects of the change in aggregate type, duct type, load ratio,

boundary conditions and different fire scenarios, on the global

structural behaviour of bonded post-tensioned one-way

concrete slabs in fire. The different parameters considered are

summarised in Table3.

0

10

20

30

40

0 20 40 60 80 100 120

Time: min

Centraldefle

ction:mm

Test TB8 FE TB8

Fig. 15. Comparison of timecentral deflection curves forrestrained slab TB8

0

10

20

30

40

50

0 20 40 60 80 100 120Time: min


Test TB10

FE TB10

Fig. 16. Comparison of timecentral deflection curves forrestrained slab TB10

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120Time: min

Stress:MPa

Test: MT1

Test: MT2Test: MT3

FE analysis

Test: RT2Test: RT1

Test: LT3

Test: LT1

Test: LT2

Fig. 17. Comparison of tendons stress time curves forunrestrained slab TB3



9/13

Group G1 included three slabs S1S3 that had plastic ducts

(PL), limestone aggregate (LS) and load ratios of 0.3, 0.5 and

0.7 respectively for slabs S1, S2 and S3. Group G2 (slabs

S4S6) was identical with G1 except the type of aggregate

used was changed to Thames Gravel (TG). Groups G3 (slabs S7

S9) and G4 (slabs S10S12) were identical with G1 and G2

respectively, except the slabs had metallic ducts (M). All the

four groups (G1G4) were allowed free longitudinal expansion.

Groups G5 (slabs S13S15), G6 (slabs S17S18), G7 (slabs S19S21) and G8 (slabs S22S24) were identical with G1, G2, G3

and G4 respectively, except the slabs were restrained against

longitudinal thermal expansion. All the slabs in the eight

groups (G1G8) were subjected to the standard fire curve,20 as

shown in Fig.20. Group G9 (slabs S25S27) had limestone

aggregate, plastic ducts, a load ratio of 0.7, were allowed free

longitudinal expansion, and were subjected to different fire

curves. The fire curves used represent the standard (ST), short

hot (SH) and long cool (LC) fires shown in Fig.20for slabs

S25, S26 and S27 respectively. More details regarding the

short hot and long cool fires can be found in Lamont et al.25

The fire resistance and maximum central deflections for all the

slabs investigated in the parametric study are summarised in

Table3. The timecentral deflection relationships for all the

slabs are plotted in Figs2126.

Similar to the tested slabs, the tendon had a cover of 30 mm at

the central span of the slab, which according to BS 8110-23

should achieve 90 min fire resistance. BS EN 1992-1-24

specifies fire resistance in terms of the distance from the

bottom of the slab to the centre of the tendon (denoted axis

distance), which in this case is 42 mm. For 90 min fire

resistance BS EN 1992-1-2 specifies an axis distance of 45 mm

and for 60 min an axis distance of 35 mm. The slab should

therefore have at least 60 min fire resistance (as shown in Table3).It can be seen that all the bonded post-tensioned one-way

spanning concrete slabs investigated in the parametric study

had a fire resistance of approximately 105 min with slabs S26

and S27 surviving the full duration of the natural fire. This

indicates that the codified values in BS 8110-23 and BS EN

1992-1-24 are conservative, however the fire resistance

specified in BS 8110 were more closely aligned with the finite

element analysis predictions.

The effect of the load ratio, defined as the applied load divided

by the design capacity, was investigated by modelling the three

slabs in each group, except group G9, for different load ratios of0.3, 0.5 and 0.7 (Table3and Figs2124).It can be seen that the

greater the load ratio the greater the vertical deflection of the

slab for a given time. For the restrained slabs, however, the final

Compressive stressconcentration near the

restraining beam

Tensile stress

progress at the

tendons

Concrete

Stress units: N/m2

2

1

3

6350 108

2000 106

1667 105

1667 106

3500 106

5333 106

7167 106

9000 106

1083 107

1267 107

1450 10

7

1633 107

1817 107

2000 107

4189 108

S, S22

(Avg: 75%)

Fig. 18. Failure mode from the FE model for restrained bonded test TB4

(a)

(b)

Fig. 19. Position of cracks and spalling observed in the tests(a) TB4 and (b) TB6



10/13

deflections were limited by the restraining force created by the

restraining beams. Of interest is the fact that all the slabs failed

at the same time (105 min) irrespective of the load ratio.

Previous experience has shown that the increase in the load

ratio generally results in a decrease in the fire resistance. For the

bonded post-tensioned concrete slabs investigated in this study,

however, failure in the model was initiated owing to a crack

occurring directly in line and parallel to the tendons. Similar

observations were previously reported in Ref. 14. When the

temperature of the tendons increases the tendon starts to expand

longitudinally causing partial relief of the compressive stresses,which then allows the lateral expansion to cause splitting at the

weaker sections of the slab. The same failure mode has also been

observed in an independent study conducted by Herberghen and

Damme.7 From the study presented here it can be concluded

that the splitting mode of failure is not affected by the applied

static load. As shown in Table3,all the slabs failed at 105 min,

which is higher than the 90 min specified in BS 8110- 23 and the

60 min specified in BS EN1992-1-2.4

As shown in Table3 and Figs2124,the slabs with Thames

Gravel aggregate have a significantly higher vertical deflection

compared with the equivalent slab with limestone, owing to thegreater thermal expansion of Thames Gravel. For the restrained

slabs, the final deflections were limited by the restraining force

created by the restraining beams. Owing to the variation of

Group Slab Coarseagg.

Duct Fire curve Long.exp.

Loadratio

Present study BS EC

Max. def.:mm

Fire res.:min

Fire res.:min

Fire res.:min

S1 LS PL ST Free 0.3 53 105.3 90 60G1 S2 LS PL ST Free 0.5 71 105.4 90 60

S3 LS PL ST Free 0.7 106 105.3 90 60S4 TG PL ST Free 0.3 79 105.4 90 60

G2 S5 TG PL ST Free 0.5 94 105.3 90 60S6 TG PL ST Free 0.7 114 105.3 90 60S7 LS M ST Free 0.3 55 107.3 90 60

G3 S8 LS M ST Free 0.5 74 107.2 90 60S9 LS M ST Free 0.7 106 107.2 90 60

S10 TG M ST Free 0.3 80 107.1 90 60G4 S11 TG M ST Free 0.5 96 107.2 90 60

S12 TG M ST Free 0.7 116 107.1 90 60S13 LS PL ST Rest. 0.3 32 105.2 90 60

G5 S14 LS PL ST Rest. 0.5 38 105.4 90 60S15 LS PL ST Rest. 0.7 47 105.4 90 60S16 TG PL ST Rest. 0.3 35 105.4 90 60

G6 S17 TG PL ST Rest. 0.5 40 105.4 90 60S18 TG PL ST Rest. 0.7 52 105.3 90 60S19 LS M ST Rest. 0.3 26 107.4 90 60

G7 S20 LS M ST Rest. 0.5 30 107.3 90 60S21 LS M ST Rest. 0.7 34 107.3 90 60S22 TG M ST Rest. 0.3 27 107.3 90 60

G8 S23 TG M ST Rest. 0.5 30 107.2 90 60S24 TG M ST Rest. 0.7 34 107.4 90 60S25 LS PL ST Free 0.7 106 105.3 90 60

G9 S26 LS PL SH Free 0.7 52 328.0 90 60S27 LS PL LC Free 0.7 118 540.0 90 60

Table 3. Summary of parametric study results

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600Time: min

Temperature:C

Standard

Long cool

Short hot

Fig. 20. Standard, short hot and long cool fire curves

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120Time: min


PL, TG, Free, 07

PL, TG, Free, 05

PL, TG, Free, 03

PL, LS, Free, 03

PL, LS, Free, 05

PL, LS, Free, 07

Fig. 21. Effect of load ratio and different aggregate types(LS limestone, TG Thames Gravel) on free bonded testswith plastic ducts (groups G1 and G2)



11/13

temperature through the depth of the slab, thermal curvature

contributes to the vertical deflection (with the bottom part ofthe slab expanding greater than the top part), together will loss

of strength of the tendon and concrete, with the Thames Gravel

slabs having the greater displacement.

Looking at the restrained slabs in Table3 (and the predicted

response shown in Figs22and 24), it can be seen that owing

to the longitudinal restraint to thermal expansion, as the slab

tries to expand, a restraining moment at the ends was created

which together with arching action reduces the central vertical

displacement. The failure mode was attributable to tensile

splitting cracks at the tendon locations as well as localised

failure in the proximity of the restraint at the bottom of the

slab. It can also be seen that the maximum deflections were

observed generally between 40 and 60 min, after which the

deflections started to decrease or remained approximatelyconstant until the failure was observed at approximately

105 min for all the slabs. Once again, the fire resistances

predicted were higher than that specified in BS 8110-23 and

BS EN1992-1-2.4

The temperatures throughout the bonded post-tensioned slabs

S25, S26 and S27 analysed for different fire scenarios are

shown in Fig.25. The thermal analysis was conducted for slabs

S26 and S27 which were heated using the short hot and long

cool fires, respectively, during the heating and cooling stages

of the fires (a total period of 540 min). Slab S25, which was

heated using the standard fire curve, was also analysed for thesame period in the thermal analysis. Slab 25 failed in the

thermal-mechanical analysis at 106 min, however, owing to the

tensile splitting along the tendons, as shown in Fig. 26.

0

10

20

30

40

50

60

0 20 40 60 80 100 120Time: min


PL, TG, Restrained, 07PL, TG, Restrained, 05

PL, LS, Restrained, 07

PL, TG, Restrained, 03



Fig. 22. Effect of load ratio and different aggregate types(LS limestone, TG Thames Gravel) on restrained bondedtests with plastic ducts (groups G5 and G6)

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120Time: min


M, TG, Free, 07

M, TG, Free, 05

M, TG, Free, 03

M, LS, Free, 03

M, LS, Free, 05M, LS, Free, 07

Fig. 23. Effect of load ratio and different aggregate types

(LS limestone, TG Thames Gravel) on free bonded testswith metallic ducts (groups G3 and G4)

0

10

20

30

40

0 20 40 60 80 100 120Time: min


M, LS, Restrained, 07

M, TG, Restrained, 07





Fig. 24. Effect of load ratio and different aggregate types(LS limestone, TG Thames Gravel) on restrained bondedtests with metallic ducts (groups G7 and G8)

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600Time: min

Temperature:C

Long cool: HS

Short hot: HSStandard: HS

Standard: T

Long cool: T

Short hot: T

Short hot: CSStandard: CS

Long cool: CS

Fig. 25. Effect of different fire scenarios on bondedpost-tensioned slabs (group G9)

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600Time: min


Standard

Short hot

Long cool

Fig. 26. Effect of different fire scenarios on bondedpost-tensioned slabs (group G9)



12/13

Looking at Fig.25, it can be seen that the tendon temperature

predicted using the short hot fire was greater than that

predicted using the standard and long cool fires in the first

50 min, from the start of heating. After that the tendon

temperature was much higher in the slab using the standard

fire curve compared with the other two curves. Fig.26 shows

the timecentral deflection curves plotted for slabs S25, S26

and S27. The maximum deflections predicted from the finite

element model were 106 mm at 105 min, 52 mm at 55 min and

118 mm at 214 min, respectively as shown in Fig.26.

The maximum central deflections of the slabs with plastic and

metallic ducts (summarised in Table 3 and plotted in Figs21

24),show that the type of duct has a nominal effect on the

timecentral deflection behaviour owing to the fact that the

ducts are subjected to compressive stresses created by the post-

tensioning.

6. CONCLUSIONS

A detailed thermo-mechanical non-linear finite element model,

for the analysis of bonded post-tensioned concrete slabs at

elevated temperatures, has been developed and presented. Theinterface between the tendon and surrounding grout was

modelled, allowing the tendon to retain its profile shape during

the deformation of the slab and representing the bond

behaviour between the tendon and grout. The temperature

distribution throughout the slab, the timedeflection

behaviour, timelongitudinal expansion, timestress

behaviour of the tendon, and the failure modes have been

predicted by the model and verified against experimental

results. The comparison between the experimental and

numerical results has shown that the model can accurately

predict the behaviour of bonded post-tensioned one-way

concrete slabs under fire conditions. It is also shown that the

model provides excellent representation for the varying

boundary conditions at elevated temperatures.

The developed model was used to investigate the effects on the

global structural behaviour owing to the change in the

aggregate type, duct type, load ratio, boundary conditions and

different fire scenarios. It is also shown that the central

deflection is higher with an increase of the load ratio, but the

fire resistance time remains the same owing to the mode of

failure, comprising cracking (splitting) above the tendons, not

being influenced by the magnitude of load. Similarly, using

different aggregates influenced the displacementtime response

but did not significantly affect the failure fire resistance time.The numerical results were compared with values calculated

using current design codes. The comparison has shown that the

bonded post-tensioned concrete slabs investigated in this study

are capable of achieving the designed 90 min fire resistance. It

is also shown that the fire resistance given by BS 8110 and BS

EN 1992-1-2 are conservative for bonded post-tensioned one-

way spanning concrete slabs under fire conditions. It was

shown that BS 8110 predictions were more aligned with the

finite element analysis predictions.

ACKNOWLEDGEMENTS

The work in this paper was conducted at the University ofManchester and was funded by the Engineering and Physical

Sciences Research Council (EPSRC) (grant no. EP/D034477/1).

The authors are grateful to Tarmac Limited for supplying the

concrete, Bridon Limited for supplying the tendons, CCL

Limited for supplying the dead and live anchorages, General

Technologies Inc. for supplying the plastic ducts, Wells Ltd. for

supplying the metallic ducts and Pennine Grouting Limited for

supplying the grouting equipment. The authors are also

grateful to Paul Nedwell, for his continuous support and useful

discussions and the support provided by the technical staff at

The University of Manchester, headed by Paul Townsend and

Jim Gee.

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