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7/28/2019 Composite Floors Part 1
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P A P E R : B a i l e v / M o o r e
Paper
C. G.Bailey,BEng, hD,
Building Research
Establishment
D. B. Moore,
BTech, PhD, CEng,MIStructE
Building Research
Establishment
Keywords:
steel frames,
floors, composite
construction,
fire resistance
behaviour,
fire tests, reinforced
concrete slabs
The structural behaviour of steel
frames with composite floorslabssubject t o fire: Par t 7: Theory
Synopsis
This paper presents the development o f a new
design method for calculati nghe performance of
steel framed buildings, wi th composite flooring
systems, subject to fire. This design ethod is based
on the results from a series of full-s caleire tests on
an eight-storey steel framed building, together with
associated theoretical and further xperimentalinvestigations. The results from thiswork show
that the performance fcomposite steel deck
flooring systems in fire is under-utilised n current
design procedures. This iswing mainly to the
ability ofightly reinforced omposite slabs to
bridge over the supporting fire-damagedsteel
beams and t ransfer load, using membrane action,
to the undamaged art s ofhe steel structure. From
these observations a simple designmethod is
developed that isbased on a holistic, rather than
an elemental, approach. This allows thearious
interactions between the components ofa
composite slab, supported by a grillage of teel
beams, to be taken into ccount, producing cheaper
and more innovative, site-specific, fire-engineeringsolutions. A companion paper shows how this
design method can be applied to practical
buildings.
Notation
Volume 78/No 7 7 6 un e 2000
is theaspect ratio(LIZ)
is theparameter-defining the magnitude of
membrane force
is theeffective depth of reinforcement
is theenhancement of yieldline load due to
membrane action
is theenhancement of element 1due to
membrane forces
is the enhancement of element 2 duet o
membrane forces
is theenhancement of element 1due to bending
action
is the enhancement of element 2 due t o bending
action
is theyield stress
is theparameter-fixing depthof the compressive
stress block when no membrane force is present
is theparameter-defining the magnitude of
membrane force
is the shortest spanf the rectangular slab
is the largest spanf the rectangular slab
is themoment capacityof the composite slab at
the fire limit sta te
is the esistance momentlunit width t ayieldline when membraneorces are present
is themoment about he support due o
membrane forces for element 1is themoment about the support due o
membrane forces for element 2
is the moment capacity f the composite beamat
the fire limit sta te
MO is the moment capacity of the composite slab
n is he parameter-defining the yieldline pattern
p is he loadcarryingcapacity of the composite slab
U is he maximum vertical displacementof a
W is he deflectionof
yieldlinetup0 is the loadcarrying capacity of the composite floor
and grillage of composite beamsat a temperature8
wbeame is the loadcarrying capacity f the grillage of
composite beams a t a given tempera ture 8
x is he parameter-defining the intersection of
yieldlines
E is the train in the reinforcement
y is the parameter-defining the loaded area
when no membrane force is present
at the ire limit stat e
parabolic curve
supported by a composite beam
is the oad levelo r load ratio
Introduction
The traditional method of ensuring tha t a steel frame
building, with a composite flooring system, satisfies the
regulatory requirementsor fire resistance iso protect all
the columns and all the exposed surfaces of the downstand
supporting steel beams with a proprietary nsulating
material. Although this approach has proved to be satis-
factory, the current method1 for specifying the required
thickness of the insulating material s extremely conser-
vative, since t ignores the inherent fire resistance of the
structure. Furthermore, the prescriptive nature of this
approach can mpose unnecessary costs and stifle innova-
tion. The developmentof structural fire design Codes, (e.g.
BS 5950:Part 8 2 and the European prestandardsurocode
3:Part 1.23 and Eurocode4: art 1.24)provide a more solid
scientific foundation for the provision of fire resistance.
However, these design Codes were developed from s tan-
dard fire tests5 on isolated beams and columns and typi-cally ignore significant struc tural behaviour by disre -
garding the interaction between members.
It has become increasingly clear, in recent years, that
continued research into the performanceof individualcom-
ponents should not e a highpriority. Better understand-
ing of the interactions etween different components, ead-
ing t o an appreciation of the way in which complete
struc tural systems function, when subjecto fire, is likely
to prove more cost-effective. urthermore, there is gener-
al agreement that the struc tural ontribution of compos-
ite flooring systems, comprising teel deckkoncrete com-
posite floorslabs supported y a grillage of steel beams, is
under-utilised in current fire design procedures. This,
togetherwith nvestigations rom eal fires, such as
occurred a t Broadgates, suggests hat theperformance ofcomplete structures is s ignificantly better than thatf the
single element from which fire resistance is currently
assessed.
The developmentof BRE's Large Building Tests Facility
(LBTF)at Cardington provided the construction industry
with a unique opportunityo carry out ull-scale fire tests
on a complete building designed and built t o current prac-
19
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P A P E R : Ba i l e v /Moo r e
tice. Consequently, in the 1990s a series of six compart-
ment fire tests were conducted ona full-scale steel framed
building a t Cardington. The test building was eight storeys
high and covered a plan areaof 21m x 45m. The compos-
ite flooring system comprised steel downstand beams act-
ing compositely with a floorslab, constructed using a trape-
zoidal steel deck, lightweight concrete, and an anticrack
A142 steel mesh. The overall depth of the slabwas 130mm
thick, with the mesh placed 15mm above the steel deck.
Bailey e t aZ7 and Martin e t U P give a detailed account of
these t ests, which confirmed tha t th e performance of a
steel frame, with a composite flooring system, is signifi-
cantly bet ter than that suggested by current fire design
methods.
Observations from these ests uggested hat he
improved performance of composite flooring systems is
due to th e ability of lightly reinforced composite slabs to
bridge over the supporting ire-damaged steel beams and
transfer load, using membrane action, to theundamaged
parts of the steel structure. The enhanced loadcarrying
capacity of lightly reinforced concrete labs has been inves-
tigated by a number of authorsg-13 but , because of the very
large displacementsassociated with this mode of behav-iour, it was previously considered o have no application in
the design of buildings. Although this is true for normal
temperature design, at elevated temperatures large dis-
placements are acceptable provided that structural col-
lapse or breach of compartmentation is avoided. This
prompted Bailey14 to inves tigate theoadcarrying capaci-
ty of lightly reinforced concrete slabs a t large displace-
ments. Based on observations from the Cardington fire
tests, together with a full-scale composite floor t est a t
BREI5 and a number of small-scale tests9,10,13,16,17,18,
Bailey developed simple method for alculating the load-
carrying capacity of lightly reinforced concrete slabs a t
largedisplacements. However, thi s method ha s been
applied only to square or rectangular concrete slabs at
ambient temperature.Logically, th e nex t step is to extend this work t o com-
posite flooring systems, subject to fire, that incorporate
both the composite slab and suppor ting grillage of steel
beams, with the im of developing a design method based
on a holistic, rather than an eleme ntal, approach. This
would permit the various intera ctions etween the com-
posite slab and its supportingmembers t o be taken into
account, allowing cheaper and more innovative, site-spe-
cific, fire engineer ing olutions to be adopted. This paper
develops a simple but conservative design method for
steeVconcrete composite flooring systems based on the
work on membrane action put forward by Bailey14 and
the experimental ork undertaken as partf the Carding-
ton fire tes t programme. A companion paper19 shows how
this method can be applied to practical buildings.
The behaviour of composi te loo ring systems in
fire
At normal temperature theoadcarrying capacity f a com-
posite flooring system is estimatedby considering, n iso-
lation, the lexural strength of the composite slab and the
supporting composite beams.The strength of the compos-
ite slab isypically based on the steel deck and concrete,
with any anticrack mesh ignored. Current fire design
methods follow a simi lar approach, except tha t the heo-
retical design method for composite slabs in fire ignores
any contribution from the steel eck. This was considered
necessary following observations fromctual fires, such s
the Broadgate6 and Basingstokezo fires, which showedha t
the steel eck had debonded, owing tohe release of steam
from the concrete, during he fire. Since th e deck is
ignored, the theoretical flexural strength of the slab in
fire is based on the mesh reinforcement and the concrete.
Therefore, the struc tural omponents tha t are ssumed to
contribute to theoadcarrying capacity of the flooring sys-
tem in a fire a re the concrete, mesh reinforcement, and
supporting composite beams. n the esign methods, hese
components are reduced in strengthor the fire resistance
period considered.Observations from full-scale ire tests7 have shown tha t
the current fire design methods for composite floor sys-
tems ar e very conservative. This is due to currentdesign
being based on the load path mechanisms that are
assumed a t th e ultimate and serviceability limit states .
These assumptions are adequate for the small, vertical
displacements experienced by the flooring system at nor-
mal temperature.However, they do not consider the true
load-path mechanism experienced by the flooring system
at large, vertical displacements, which are typically expe-
rienced during a fire.
Baileyl4J5 has shown tha t lightly reinforced, square or
rectangular concrete slabs, which are vertically supported
around the perimeter nd are subjected to significant ver-
tical displacements, have the ability t o support loads inexcess of the estimatesobtained considering basic flexur-
al behaviour. This is due to th e development of membrane
forces within the slab. It is thisoadcarrying mechanism,
which is different t o that assumed at ambient tempera-
ture, th at enhances the oadcarrying capacity of the com-
posite flooring ystem above that calculated using current
fire design methods. To utilise the enhanced loadcarrying
capacity identified by Bailey, the entire floor plate of the
building must be divided into square or rectangular slab
panels, with each panel incorporating a number of unpro-
tected beams. The edges of each panel must be vertically
supported, for the dura tion f the fire, using either:
-protected beams
-unprotected beams or slabs that are outside the firecompartment area
Floor plate divided into Denotes protectedslab panels that incorporate beams (or beams
unprotected beams designed to support
the applied loadduring the fire)
Denotes unprotected beams
I
Fig '. possible slab panels that incorporateFloorplate divided into
options for dividing unprotected beams
LDenotes protectedbeams (or beamsdesigned to support
the floor plate into the applied load
slab panels Denotes unprotected beamsduring the fire)
20The Structural Engineer
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P A P E R : B a i l e y I M o o r eI
-beams, within the fire compartment a rea, tha t are
designed to support he applied load for the dura tion
of the fire
Two examples are shown in Fig 1. n each example, the
fire compartment is assumed to be the whole floor plate
and the edges of each slab panelare vertically supported
using protected composite beams. Each slab panel ncor-
porates a number of unprotected composite beams. The
size of the panel depends n the stren gth f the compositeslab (which ncludes membrane action), the strengthf the
composite beams, the fire resistanceeriod, and the llow-
able vertical displacement,hich is based on the ultimate
structural collapse of the system.
The question now arises as t o whether these heated
slab panels can be considered unrestrained or restrained
against horizontalmovement. If the edge of the slab coin-
cides with the dge of a building ora service duct, it is obvi-
ously unrestrained along th at edge. However, f the slab is
in the centre of the floor plate, the reinforcement will be
continuous over it s boundaries. However, the test s at
Cardington7.8 on the two larger and more realistic sized .compartments showed tha t a large crack occurred in the
heated slab aroundhe perimeter of the fire compartment.
This resulted inhe reinforcement fracturing in this area
(Fig2). I t is believed that the rack occurred during the fire
because of large hogging moments over the partially pro-
tected beams which, together withhe membrane forces in
the heated slab, ed t o fracture of the reinforcement. This
suggests that the eated slab panelsre unrestrained dur-
ing the ire.
Simplified fire design method, including
membrane action
Considering a simply supported rectangular or square
floor slab, supportedn a grillage of steel composite beams,
the loadcarrying capacityt a particular emperature can
be calculated using he following energy equation:
Internal work doneby the
composite slab in bending
External work done by the[pe=e
floor systemfunit load l+ ....1)Internal work done by the
beam(s) in bending
External work done by the
floor systemfunit load
where e is the enhancement due to membranection in th e
composite slab. To simplify the above design equation,
catenaryaction of thesteel beams is conservatively
ignored.
For a composite floor ystem subjectedo fire, the shape
of the yieldline pattern will be dependent on the behaviour
of the supporting steel composite beams, which are con-
tinually reducing in strength. This is best explained by
considering a simple example. Consider the BRE corner
fire test7, which consisted of heating a 9.0m x 6.0m area
of slab with one secondary beam. The mode of behaviour
of the system, which is continually changing ith increas-
ing temperature, is shown in Fig 3. The change rom one
mode to the next is dependent on the stren gth f the steel
composite beam, which is continually reducing. The final
mode of behaviour, as the apacity of the composite beam
tends towardszero, is due to the .0m x 6.0m simply sup-
ported two-way spanningslabsupporting heentire
applied load.For the yieldline patterns shown in Fig 3, membrane
action can occur. It has been shown from ambient tem-
perature tests n unrestrained slabs that,nce membrane
action occurs, the shapeof the yieldline pat tern does not
change with increasing vertical displacement. However,
this is not true in a fire situation, since the supporting
steel beam,which controls the shapeof the yieldline pat-
Volume 78/No l l 6 une 2000
Fig 2. Crack through
the concrete slab
around the heated
perimeter (arrows,
from to p to bottom,
show shear stud nd
fracture of mesh
reinforcement)
Fig 3. Slab and beam
behaviour with
increase in
temperature
tern, is continually reducing in strength. Thisill result
in a change inhe mode ofbehaviour with increasing tem-
perature (Fig 3). With continual changes in the mode of
behaviour and continual changes in membrane action
(which is dependent on the mode of behaviour), it can be
seen that applying eqn (l), even to the simple example
described above, can be complicated and time-consuming.
However, by assuming tha t the dominant loadcarrying
capacity of the system is due to the composite slab, the fol-lowing assumptions can be applied t o obtain a conserva-
tive estimate.
(1)The load carried by the flexural behaviourof the gril-lage of composite beams, within the fire compartment, s
based on the lower-bound mechanism for the beam with
the highest load ratio2 (i.e. the beam th at will ‘fail’ irst in
the fire). The beams are assumed to be simply supported
Behaviour mode i)Composite slab is one-way
spanning onto he beam
Behaviour mode ii)
centre of steel compositePlastic hinge forms at
beam and a fan yieldpattern forms n the slab
Behaviour mode (iii)
composite beam reduces n
Plastic hinge nsteel
strength with increase ntemperature resulting n the
yield pattern shown
Behaviour mode iv)With increasing os s ofstrength for he compositebeam, the slab yieldline
pattern tends towardshe
slab acting without he beamlower bound patternor a
=nL forlower-bound pattern
21
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P A P E R : B a i l e v / M o o r e
TABLE 1 -Critical temperatures for unprotected steel composite beams
supporting a floor slab
LoadLevel 0.01.02.04.06.08.1.23.4.5.6 0.7
526 558 590 629 1150 11000000060 8202571Temp. (“C)
Note: Interpolation can be used
Fig 4. Assumedloaded area
supported by beams
and support a loaded area calculated assuming tha t the
slab is simply supported (i.e. typical assumptions taken for
normal design).
(2)The load supported owing t o the flexural behaviourof
the composite slab is calculated based n th e lower-bound
yieldline mechanism, assuminghat the eams have ero
resistance.
(3)The enhancement due o membrane action in the om-
posite slab (e) s based on th e lower-bound yieldline mech-
anism of the slab.
(4) The loadcarrying capacity f the composite beams an d
slab (enhanced owing to membrane action) are added
together, as shown in eqn( l ) .
By assuming a ower-bound mechanism, togetherwithmembrane action based on this mechanism, conservative
estimates will always be obtained for the loadcarrying
capacity of the composite floorslab. The amount of load
tha t the composite beams support is calculated using a
simple area model. Since this can lead to n error in the
external work done by the loads, further investigation is
needed t o determine the accuracy of the method.
Consider the simple example hown in Fig 4, consisting
of a rectangular slab and two composite beams. Using
assumption (1) the load carried by the beams (Wbeame) is
based on the lower-bound mechanism of one beam given
by:
....2)
where y defines the width of slab supportedby one beam,
and using assumption (1) y =113. The accuracy of thi s
assumption is considered by comparing eqn (1)with the
proper mechanism fo r the complete beam nd slab system,
assuming tha t a diagonalyieldline forms (modes (iii) and
(iv), Fig3).Using eqn (1) the load supported by the two
composite beams, shown in Fig4, is given by:
Internal work done
by beams -Wbeame =External work done by th e
- .... 3)x
floor s ys ted un it load
wherex defines the position of the intersection f the yield-lines, as shown in Fig 3. The value f x varies between L/2
and nL, as the beams continueo lose strength. From eqn
(3) the lowest value of Wb em e is obtained when x =L/2.
Therefore, taking this value, equating eqns (2) and (3) and
solving fo r y results in y =113, which i s the exact value
taken in the simplified approach (assumption (l)) . y
using the above procedure it can be shown, for various
2
Fig 5. Failure of BRE
membrane test
structural beam layouts, that the simplificationof assump-
tion (1) s always conservativerovided that there isore
than one beamwithin the system.For the case where there
is only one beam within the heated area (i.e. the BRE cor-
ner fire est7) the error, when calculatinghe load carried
by the beam, can be as high as 33% at the oint at which
x =L/2 (mode iii),Fig 3). However,as the eam continues
to rise in temperature the imension x reduces and the
error tends towardszero. It should also be noted that , at
the point a t which the maximum error occurs, the com-
posite beam has nominal strength, with the slab (inem-
brane action) supportingmost of the load. Therefore, the
actual error inerms of loadcarrying capacityf the whole
flooring system, which the designer is concerned with, issmall. It can also be shown tha t, if catenary action of the
steel beam s considered, the unconservatism for the case
where only one beam is within the heated system is
removed. It can therefore be argued that the ssumptions
will result in conservative estimatesor all structural sys-
tems. It is worth mentioning th at including catenary
action of the beam will influence the calculation of th e
membrane action in the composite slab. This results in a
complicated design method tha t can be used practically
only as a pecification for computer software.or this rea-son th e conservative assumption of ignoring catenary
action in the steel beams was adopted in this implified
design approach.
To calculate the loadcarrying capacity f the composite
flooring system, using eqn (1) and the assumptions dis-
cussed above, the designer needs o calculate the flexural
stren gth of the supporting beams and the membrane
strength of the composite slab. The procedure is discussed
below.
Calculation of moment capacityof composite beams n
fireTo determine the moment capacity of composite beams
during a fire, amodified form of the critical temperaturemodel given n EC 4:Part 1.24 is used. he equation inEC
4 uses an adaptation factorof 0.9 to take intoccount the
top flangeypically being at lower temperature compared
with the rest of the steel beam. However, the Code state s
tha t the quation can e used provided tha t theibs of the
composite slab are insulated above the beam. Previous
research21, albeit on protected sections,has shown that, for
composite beams with full shear onnection and ‘unfilled
voids’, the adaptation factor shoulde increased t o 1.0 fo r6Omin fire resistance.Therefore, using the same symbols
given in EC 4:Part 1.2 :
....4)
Using eqn (4), together with able 3.2 n EC 4: Part 1.2,he
critical temperatures (termed ‘limiting temperatures’ in
BS 5950Part 8) an be calculated for a given load level
(term ed ‘load ratio’ in BS 5950: Part 8), s shown in
Table 1.
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P A P E R : B a i l e y l M o o r e
k b K T
DA
lbKT0 i'
t
ICalculation of the membrane strength of a lightly
reinforced composite lab
Bailey14 has developed a theoretical design method th at
estimates theoadcarrying capacity of a lightly reinforcedconcrete slab, for a given vertical displacement, based on
the in-plane stresses (membrane ction) in the lab. These
in-plane stresses ar e governed by the mode of failure
shown in Fig 5. (A full deviation of the method is given in
refs 14 and 22.) The basic equations required to use he
design methodand develop design har ts are hown below.
The in-plane stress distribution is hown in Fig 6. The
values ofk and b t ha t define the magnitude of the in-plane
stress can be calculated by considering equilibrium and
taking moments about E , assuming fracture of th e rein-
forcement along the lineEF. These values are iven by:
4na2(1- 2n)+k =
4n2a2+1
and
1.112b =
8(A+B+C-D)
where
B=1(""I$-+ k -&[ +
. . (5)
.... 6)
Fig 6. In-plane stress
distribution
Fig 7. Enhancement
factors for composite
slab used on the
Cardington frame
0 1 2 3 4 5 6 7 8 9 1012 13 145 167 18
Displacement/effectivedepth
The loadcarrying apacity of the slab can ow be esti-
mated by considering the membrane forces and the ffect
of these forces on the bending resistanceof the slab. By
relating theffect of the membrane forces to the ieldline
load, a simple enhancement actor can be obtained. Each
of the elements1and 2 (Fig 6) re considered separate-
ly, with the contr ibution of in-plane or vertical shear,
along the yieldlines, initially ignored. The loads dete r-
mined by considering elements 1and 2 will generally beunequal, and an average value,considering the contri-
bution of she ar forces (as suggested by Hayesls), can be
calculated.
For element 1 he enhancement factor for membrane
action is given by:
Similarly, for element 2 the enhancement factor for
membrane action is given by:
2+3k2m= =L()[--1 k3 ....(8)
Mol 3+ g o dl 6(l+ 6(1+ k)2
The effect of the membrane forceon the bending
moment will result in annhancement factor forelement
1 f:
and similarly for element 2:
e2b=-=M l+-(k-1)--(K2-k+1)b p b 2 ....10)MO1 2 3
The net enhancement is obtained by combining these
effects foreach element, i.e.
el =elm +elb
e2 =e2m +e2b
Typically el and 2 are not qual. Hayes13 suggests that,
if the difference can be explained by the effects of vertical
shear or th e in-plane shear, the verall enhancement may
be shown o be given by:
The above method as been shown o give excellent sti-mates of the loadcarrying capacity of the slab, for a given
displacement, for the large-scale test conducted by BREI5
and a large number of small-scale tests conducted by other
authorsl4. The method has also been shown to give accu-
ra te resu lts, irrespective of the aspect rat io (a=L/Z) of the
slab.
Calculation of flexural s trength of composite slab
Wood9 has shown tha t, for rectangular or square simply
supported slabs,
Using eqn (12) the value of p12/m can be calculated for
various aspect ratios, leading to an assessment of the load-
caring capacity<p).The moment capacity of the slab (m)s
dependent on the position of the reinforcement, the
streng th of the materials used, and the temperature
through the cross-section. The calculation is simple and i s
shown in curren t esign Codes24 and guides23.
Volume 78 /No 7 7 6 l une 200023
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P A P E R : B a i l e y / M o o r e
A B C D E F
9000000 -L 9000 -- 9000 9000W -
Fire I! compartment
v -
. I
0
0
3
2 #
1
Assumed yieldline pattern
Fig 8. Assumed simplified yieldline pattern for Cardington ests 1, 2, and 4
A B C D E F
9000 9000000000 9000
FireI compartment I 8I
4
0
3- I1
Assumed yieldline
Load ratioof beams were low,
such that they provide vertical
support during the fire test
Column ignored
for simplification
Fig9.Assumed simplified yieldline pattern for Cardington ests 3, 5, and 6
Calculation of the enhancement factor (e) owing to tensile
membrane action
The enhancement factor due to membrane action can be
calculated from first principles using theequations sum-
marised earlier. However, these equations can be repre-
sented as simple design charts, based on th e effective
depth of the reinforcement (represented by the value g,,).
For the composite floorslab used at Cardington, Fig 7
shows the enhancement due to membrane action.
Validation of the simple design method
The simple design method was compared agains t the six
fire tests onducted on the Card ington rame. The follow-
ing assumptions were taken:
(1)A yield strength of 600N/mm2was used for the A142
mesh reinforcement. In all the tests the reinforcement
remained below 4OO0C, and therefore did not significant-
ly reduce in strength.
(2) An averagemeasured concrete cube streng th of
47N/mm2 was used.
(3)The measured yield stres s of 308N/mm2 forgrade 43
steel and390N/mm2 for rade 50 steel wassed.
(4) The moment capacity of the slab, ignoring the stee ldeck, was 4.2kNm7based on a n effective depth of 51mm.
(5) The total applied load (including the self-weight) was
4.9kN/m2.
(6) Since no struc tural collapse occurred in the tests, no
limits were imposed to define fracture of the reinforce-
ment.
(7)All beams were assumed toe pin-ended.
24
Fig 10. Comparisonbetween the simple
design method and
test 1
To allow the simple design method to be compared
aga ins t th e test results the ollowing procedure was fol-
lowed. For ach tes t the oadcarrying capacity of the gril-
lage of composite beams was calculated, for a given tem-
perature.This was based on the composite beamwith the
highest load ratio2, within the heated area i.e. the beam
in thegrillage tha t fails first). If the loadcarrying capaci-
ty of the beams was lower than he applied load of
4.9kN/m2, the load that must be carried by the slab was
calculated. This allowed the enhancement factor to be cal-
culated and thus theequired displacement (Fig 7) to be
defined. This displacement for a given steel temperature
could then be compared against the test results. In ach
test a lower-bound yieldline pat tern was considered, as
shown in Figs 8 and 9, and th e comparisons between the
simplified method and the test resu lts arehown in Figs
10-15. These comparisons indicate th at th e simplified
method providesan accurate estimate f the loadcarrying
capacity of the struc ture infire. For full calculations,he
reader is irected towards ref. 22. However, there are ome
interesting test observations and comparisons with the
design method that are worth mentioning.
In the British Steel corner test (test 3, Fig 9) straingauges placed, at the centreof slab, on the surface of the
concrete in the direction of the long span recorded high val-
ues of tens ile strain. Thisorresponds to he mode of fail-
ure of a crack forming across the shor ter spant the cen-
tre of the slab, as shown in the BRE membrane test (Fig
5).Following he fire, it was found th at a crack did formn
the slab, as shown in Fig 16. This provides confidence ha t
the correct mode of behaviour is considered in the impli-
fied design method.
In the British Steel emonstration test (test 6, Fig 91,
the test results howed that thecomposite floor was up-
ported, during the ire test, by the loadbearing blockwork,
which formed the compartment wall. Unfortunately, the
extent of the support rovided by the wall cannot be deter-
mined from the tes t results. Fig 9 shows a ‘guess’ at the
behaviour and load paths of the structure, assuming that
it is supported by a large extentof the wall. However, in
the absence of tes t data, o firm conclusions can be drawn
from this comparison.
Failure criterion
The previous simple design method, and its validation
against the Cardington fire tests , did not includea check
on the ultimate failuref the system.As shown from est s
at ambient temperature, themode of failure of a simply
supported concrete slab is dueo a full depth crack form-
ing across the shorter span (Fig 5). To predict failure at
normal temperature the mechanical stra ins in the rein-
forcement need to be considered. For concrete slabs sub-jected to fire, the prediction of ultimate failure becomes
more complicated, sinceoth the mechanical and thermal
effects of the slab eed to be considered.
Test 1 (British Steel Restrained Beam)
1000 Prediction using simple
design method
aTest results
(Maximum recorded displacementand temperature)
0.00 50.00 100.00 150.0000.0050.00 300.00~ 350.00
Displacement (mm)
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Test 2 (British Steel 2-D Test)
" " V I
800-
700-h
600-
Prediction using simple
design method2
2500-
a, Test results
400-(Maximum recorded displacement
and temperature)-
300-
200
100-
ti
O ' " " , " " , " " , " " ~ " " , " "
0.00 100.0000.0000.0000.0000.00
Displacement (mm)
Fig 11. Comparison between the simple design method and test 2
Test3 British Steel Corner Test)
1200 IPrediction using simple
1000 design method
W22 600-
2
ec, 400-
ti
a,
200
0' I I I i I I I I0.0 50.0 100.050.000.0 250.0 300.050.000.0
Prediction using simpledesign method
I I I i I I I I0.0 50.0 100.050.000.0 250.0 300.050.000.0 450.0
Displacement mm)
Fig 12. Comparison between he simple design method and test 3
Test4 (BRE Corner Fire Test)
1200
Prediction using simple
design method
/ Maximum recorded displacement
Test iesults
# and steel temperature)
1
0 50 100 150 2005050
Vertical displacement(m)
Fig 13. Comparison between the simple design method and test 4
Mechanical strains
If we consider th e longer span of the concrete slab and
assume that the slabdeflects in the form of a paraboliccurve, the str ain in the einforcement can be calculated
(approximately) by:
8v2&=-
3L2-413)
Eqn (13)assumes that the strain in the einforcement
is the same value long the length of the slab, whereas in
reality the strains concentrated at crack locations. Forhe
failure mode considered (where a full-depth crack forms
across the shorter span), the strain in theeinforcement
will increase significantly once the crack forms, resu lting
in fracture f the reinforcement. Predicting the strain ev-
els at which the crack forms is complex. Therefore, prag-
matic approach is proposed where a limit is defined for he
average strain in theeinforcement, based on maximum
stres s for the reinforcement of 0.5fy.This leads to a maxi-
mum allowable displacement of
..(14)
In addition, a geometrical limit of 1/30 is applied to the
above equation.
Thermal effects
Thermal effects can be beneficial o the membrane action
of concrete slabs, since the vertical displacements are
increased without an increase in mechanical strains. This
increase in vertical displacement is due partly o thermal
curva ture hroug h he beams and slab. In addition,depending on the restraint to therm alxpansion, the gril-
lage of composite beams can be in a post-buckled state24
during the fire, which will also increase the vertical dis-
placement of the structure,without significant increase in
mechanical strains.
Because of the difficulty of defining the rest raint to ther-
mal expansion, the effect of the grillage of beams being in
a post-buckled s tate is conservatively ignored. To include
the effects of thermal curvature, the temperaturedistri-
bution through the slab isssumed to be linear, allowing
the displacements to be estimated using:
a(T2-T1)Z2Vtherm
@hwhere
v is the vertical displacement
a is the coefficient of thermal expansion
T2 is the bottom temperature
T I is the op temperature
h is the depth of slab
1 is the length f shorter span of the slab
(conservative)
is the actor of safety
.... 15)
was considered necessary owing to he temperatureyp-
ically varying throughout thecompartment in a fire. The
required value isdifficult to define. However, if we consider
both the mechanical and thermal effects and carry out
comparison with hedisplacementsobtained n he
Cardington tests, a conservative factor of 2.4 is obtained,
as shown below. This is based on a value of 770°C for T2-
TI or all the tests.
Combining mechanical and thermal effects
Considering mechanical and therma l effects, the maxi-
mum deflection is given by:
a(T2- +/ O.Lfy) -L2V =
19.2hReinf't,,.,
8
but,
a(T2-Tl)lV <
19.2h +z30..(l61
The comparison between eqn (16)and themaximum ver-
tical displacements recorded in the Cardington tests is
shown in Table 2. The factor of safety in eqn (16)has been
calculated such that the estimated aximum vertical dis-
placement corresponds to four of the tests. In the BRE
corner test an d British Steel restrained beam test, eqn
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Test 5 (BRE Large Compartment Test)
""" I I700-
IF
Prediction using simpledesign method
LTest results
100- (Maximum slab displacement andsteel temperatureof secondary beam)
0 ' I l I I I I I I I0 100 200 300 400 500 600 700 800 900 loo0
Displacement (mm)
Fig 14. Comparison between the simple design method and test 5
Test6 (British Steel DemoTest)
Prediction using simple Idesign method
b 400 7 0
Displacement (mm)
Fig 15. Comparisonbetween the simple design method and test 6
Fi q 16. Crack at
(16)gives displacements slightly higherhan those record-
ed in the ests. However, this seems reasonable,since no
failures occurred. In addition, the above equation will
always give conservative results since
(1) he thermal curvatures calculated based n the short-
er span f the slab;
(2)any additional vertical displacements dueo the system
being in a post-buckled sta te are gnored;
(3) any contribution from the steel deck is ignored;(4)any contribution from the resistance of the steel beams
to the ultimate failure mode is ignored;
(5) the increase in ductilityf the mesh reinforcement,as
it increases in temperature,s ignored.
Furthe r research is needed t o obtain a better estimate
of the vertical displacement at which ultimate failure
occurs. Meanwhile, eqn (16)can be conservatively adopt-
ed for design purposes.
Conclusions
During the 1990sa considerable amount of workwas under-
taken to investigate the behaviour of steel framed buildings,
with composite flooringystems,subject to fi re.Observations
from this work supported the general view tha t the per-formanceof composite-steel-decking flooringystems subject
to f i e s under-utilisedin current design procedures.This is ,
due mainly to the ability of lightly reinforced concrete labs
to bridge over he fire-damaged supporting steel beams and
transfer load, using membrane action, to the undamaged
parts of the steeluilding. On the basis of these observations,
the authorshave developed a simple design method foral-
culating the erformanceof composite flooring ystems sub-
ject to fire.This method assumes that the tructural compo-
nents that contribute to the loadcafiying capacity of the
flooring system in a fire are the concrete, the mesh rein-
forcement, and the supporting steeleams.
The method uses a simple energy approacho calculate
the loadcarrying capacity of a composite flooring system.The energy of the lightly reinforced composite lab isbased
on th e yieldline approach modified to account for the
enhancement due to in-plane forces. This is added o th e
energy of the supporting composite beams, which are cal-
culated usinga modified form of the critical temperature
model given in EC 4 Part: 1.2.This approach s validated
against the resultsf six full-scale fire tests carried outn
the eight-storey steel framed uilding at Cardington. In all
but one of these comparisons the method gives accurate
predictions. In the one case where the method gives less
accurate predictions, the perimeter compartment walls
supported the composite floor during the fire. The extent
of this support to the floor was not identified inhe test,
and an estimate had toe made.
A companion paper19 shows how th e method can be
applied'to practica l composite flooring systems and com-
pares the method with the traditional approachesof pro-
viding fire resistance. n all the cases examined, the pro-
posed method. predicts behaviourhat is superior t o that
obtained using he existing design approaches.
centreGf slab acrossth e span TABLE 2 -Comparisonbetweenallowable (eqnl6)and recorded maximumdisplacement for theCardington fire tests
Test
A due to
mechanical
Maximum
test AllowableA
due to
(mm)mm)strains
AllowableAaximum
Eqn(l6) test A(mm)
L (m) 1 (m)
I 2)Britishteel 2-D test I 14.0 I 9.0 I O* I 300 I 300 I 293 I 1.02
(3) ritish Steel corner es t
0.9957 5520052.01.05)BRE €mge comDartment test
1.16 269 3112.0.04) BRE comer test
1.028 430 237 193 7.87
(6) British Steel demo. test 1.0 641311 I 333 I 644
0.0 14.6
Note: Owingto the small areafheated slab the displacement due to thermal curvature was taken asero.
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note on possible basis ora
new method of ultimate loaddesign of reinforced concrete slabs’,Magazine
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Institute, 1991
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Department of the Environment, Transport& the Regions and the Steel Construction Institute, Report No. 87475,
Carston, The Building Research Establishment, 2000
23. Newman, C.M.:. ‘The fire resistance of composite floorswith steel decking’ (2nded.), SCl Publication 056, scot, The
Steel Construction Institute, 1991
24. Rotter, J .M.: ‘Behaviour of highly redundant multistorey buildings under compartment fires’,dvances in SteelStructures,
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Structures (to be published).
under fire conditions’, Engineering Structures (to be published)
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