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The Inter-relation between Analytical and Experimental Methods of Structural FireEngineering Design

Pettersson, Ove

1979

Link to publication

Citation for published version (APA):Pettersson, O. (1979). The Inter-relation between Analytical and Experimental Methods of Structural FireEngineering Design. (Report / Lund Institute of Technology, Lund, Sweden, Department of Structural Mechanics;Vol. R79-6). Lund Institute of Technology.

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LUND INSTITUTE OF TECHNOLOGY· LUND . SWEDENDEPARTMENT OF STRUCTURAL MECHANICSREPORT NO. R79 - 6

OVE PETTERSSON

THE INTER-RELATION BETWEENANALYTICAL AND EXPERIMENTALMETHODS OF STRUCTURAL FIREENGINEERING DESIGN

LUND INSTITUTE OF TECHNOLOGY . LUND . SWEDENDEPARTMENT OF STRUCTURAL MECHANICSREPORT NO, R79-6

OVE PETTERSSON

THE INTER-RELATION BETWEEN ANALYTICAL AND EXPERIMENTALMETHODS OF STRUCTURAL FIRE ENGINEERING DESIGN

Reprinted from Studies on Concrete Technology, dedicated to

Professor Sven G Bergström on his 60th anniversary,

December 14, 1979

LUND 1979

THE INTE R-RELATION BETWEEN ANALYTICAL AND EXPERIMENTAL METHODSOF STRUCTURAL FIRE ENGINEERING DESIGN

Ove Pettersson

ABSTRACT

During the last ten years a rapid progress has been made in thedevelopment of analytical methods for a fire engineering designof load-bearing structures or structural members. In spite ofthis, the standard fire resistance test still is internationallypredominant as a basis for a fire classification and design.The analytical methods can be categorized as (l) an interpola­tion or extrapolation of the results of fire resistance tests,(2) a theoretical determination of the fire resistance, (3)an analytical design, directly based on differentiated gas­temperature-time curves of natural fires, and (4) an analyticaldesign, indirectly based on natural fire characteristics overan equivalent time of fire duration, connecting natural firesand the thermal exposure according to the standard fire re­sistance test.

The paper briefly describes the different approaches and demon­strates how useful input information for the analytical designmethods can be derived from the results of standard fire re­sistance tests. The consistency between the various methodsis critically reviewed and, by exemplifying for fire exposedsteel structures, one way is indicated for improving thisconsistency.

Although, the different analytical and experimental designmethods have been developed mainly independently and ratherfrequently have been discussed as contradictory to each other,it is quite clear, that the methods in a long-term perspectivewill form a well coherent pattern.

1

Ove Pettersson is Professor inStructural Mechanics at Lund University.His research contributions mainly havereference to instability problems andstructural fire engineering design. Hehas many international commitments withinCIB, ECCS, FIP and ISO.

INTRODUCTION. GENERAL BACKGROUND

The international ly predominant fire engineering designof load-bearing structures and structural members is char­acterized by aschematic procedure, based on results ofstandard fire resistance tests and connected systems ofclassification. FIG l describes the procedure. The designcomprises a proof that the structure has a fire resistanoetime tfr, determined in a standard fire resistance test,which exceeds the required time of fire duration tfd, speci­fied in building codes and regulations for different appli­cations. The fire resistance and required fire duration con­cepts, tfr and tfd, are connected to a thermal exposure,which shallvary with time within specified limits accordingto the relationship:

2

T - To = 345 loglO (8t + l)

where

(l)

= time, in minutes= temperature at time= temperature at time

. ot, ln Ct = O, in

During the last ten years important progress can be notedin the development of computation methods for an analyticalstructural fire engineering design. For steel structures,this development has arrived at aleveI which enables ananalytical fire engineering design to be carried out inmost practical applications (l). Validated material models

-~-

3

[OCCUPANCY H,

~IB=u=ll=D=IN=G=H=E='G=H=T=~Hc-'_B_U_'l_DI_N_G_C_O_D_E_--i1 REQUIRED FIRE

H:,', ..[DURATION t fdIBUilDING VOlUME ,"--------IMPORTANCE OFSTRUCTURE

,.j" PROPOSED STRUCTURE H" rr---,S-eTA-eN-,D-eA-eRDe-F-eIRccE,---+{ FIRE RESISTANCE r----<- t fr>t fd YES END

DESIGN lOAD AT RESISTANCE TEST L.t_f_r ---'

SERVICE STATE

..jNO

I

FIG l. Internationally conventionaI fire engin­eering design of load-bearing structures, basedon classification and results of standard fireresistance tests.

for the mechanical behaviour of concrete under transient high­temperature conditions (2), (3) and thermal models for "acalculation of the time variation of the charring rate inwood at a fire exposure (4), (5), derived during the lastyears, now are opening the door for an essentially enlargedapplication of an analytical approach also for fire exposedconcrete and wooden structures. (6) gives a rough idea ofthe present state of knowledge, as far as a systemized de­sign basis is concerned.

Internationally, the analytical approach in connection witha structural fire engineering design can be categorized withreference to the following leveIs:

(l) A theoretical interpolation or extrapolation of theresults of a standard fire resistance test for a classifica­tion of a structure with a modified design in relation tothe test specimen,

(2) a theoretical determination of the fire resistance of aload-bearing structure, based on a thermal exposure accordingto the standard fire resistance test, Eq (l),

(3) an analytical design, directly based on differentiatedgastemperature-time curves of a real fire development, speci­fied in detail with regard to the influence of the fire loaddensity and the geometrical, ventilation and thermal proper-

4

> 750

liI

Q ;:.> 5 mm

)'- ~___"2___"O___"O___'_O_m_m___'_" __Jv

1IIV

~~~~Z~'L.-:.~u~(.LZ{LL.[L..'L.-:.~~::z~~ TOPPI NG

~--·~--STEEL BEAMS

-jzs====zm:=============~i5iil5i!~_-=S~USPEN DEDCEI LlNG

I C

L~k_...a---\-

MINERAL OR CERAMIC FIBRE PLATES,DENSITY 125 ~ 25 kg m- 3

C ;:.>2d + MAX ALLOWED DEFLECTION

FIG 2. Test assembly for a determination according to draftproposal ISO DP 6167 "Fire resistance test - suspended ceilin~s"(9), (10) of the contribution of a suspended ceiling to thefire resistance of an unventilated load-bearing floer er roefstructure.

ties of the fire compartment (l), (6),

(4) an analytical design, based on differentiated gas tempera­ture-time curves of a real fire development but taken intoaccount indirectly over an eguivalent time of fire duration,connected to the heating according to the standard fire resis­tance test, Eg (l), (l), (6), (7), (8).

The described pattern of methods of structural fire enginee­ring design gives the standard fire resistance test an essen­tiaI role to produce information which can be used as a basisor as input data for different types of analytical approach.The importance of this role is further supported by the factthat fire resistance tests of load-bearing structures andstructural elements have been carried out freguently for morethan half a century, having given a very large volume ofknowledge and experience.

The present paper exemplifies how results of standard fireresistance tests can be used as basic or input informationin different analytical methods of a structural fire engin­eering design. The exemplification applies to an unventilated,load-bearing floor or roof assembly, composed of a supportingstructure of steel beams, a slab of normal or aerated concreteand a suspended ceiling, as shown in FIG 2.

BASIC QUANTITIES, TO BE DERIVED FROM A STANDARD FIRERESISTANCE TEST

In a fire resistance test of a load-bearing floor or roofassembly according to FIG 2, the time curve of the maximumsteel beam temperature Ts is recorded - the das hed anddotted line curve in FIG 3 and 4. The collapse of the sup­porting structure - normally defined by a deflection or arate of deflection criterion - determines the critical steelbeam temperature Ts crit and the corresponding collapse timets,crit. If the suspended ceiling is damaged in the test,the time of this damage ti,crit is noted.

From the recorded time curve of the maximum steel beamtemperature Ts ' a derived value (di/Ai)der of the testedsuspended ceiling can be determined - di is a thicknessmeasure and Ai a thermal conductivity measure for theceiling. The determination is based on a reguirement thatthe agreement between the maximum steel beam temperature,measured in the test, and the corresponding calculatedtime curve shall be as close as possible. Such a determina­tion is rendered easily feasible by using sets of diagramsof the type shown by the full line curves in FIG 3 or 4as presented in (Il) for floar or roof assemblies with aslab of alternatively normal concrete or aerated concreteand supporting steel beams with varying U/F values - U is

5

di i/\i = 0025 m2 °C W-l

0.050

o 100

0.200

t h

6

t s, cri t

FIG 3. Calculated time curves of the steeltemperature Ts of the supporting beams of afloor or roof assembly, as shown in FIG 2,with a suspended ceiling, having differentvalues of di/Ai (full line curves), and ameasured time curve of the maximum steel beamtemperature, determined in a fire resistancetest according to ISO DP 6167 (dashed anddotted line curve).

the heat exposed surface and F the volume of the steel beamper unit length. By this procedure, the suspended ceilingtested is characterized in an integrated way with regardtaken to the· real structural design and behaviour atafire exposure, including the influence of initial moisturecontent, crack formations, dis integration of materials, andpartiaI failure of the ceiling and its fastening devices.

The referenCe diagrams presented in (Il), are based onheat transfer eguations, which neglect the influence ofthe heat stored in the suspended ceiling. If such diagramsare used for a determination of a derived value (di/Ai)derof the suspended ceiling tested, the influence of this storedheat will be included in away which has to be describedmore as a trick of calculation than as a functionally basedprocedure. For ordinary types of suspended ceilings, theapproximation is reasonable. For suspended ceilings with alarge thickness and made of materials of high density, itis recommended in (IV to use a presented and listed computerprogram for a direct and more accurate characterization of

the suspended ceiling.

For some types of suspended ceilings, the measured timecurve of the maximum steel beam temperature can have a formwhich deviates considerably from the calculated time curves ­FIG 4. The criterion for the determination of the value(di/Ai)der of the suspended ceiling then' should be that thecalculated curve and the curve measured in the test give thesame steel temperature Ts crit at the time t s crit. For the

'. ' . ,example, shown ln FIG 4, thls leads to a (di/Ai)der == 0.05 m2 0C w-l. By applying such a criterion, a (di/Äi)deris obtained, from which test results can be extrapolatedwithout giving values of the fire resistance on the unsafeside.

7

T °cs

•Ts, crit

- ---""----

di n\j:; 0.025 m2 °c W-1

0.050

0.100

0.200

t h

FIG 4. Criterion for the determination of(di/Äi)der of a suspended ceiling, if the formsof the measured and calculated time curves ofthe steel beam temperature deviate. Notationaccording to FIG 3.

If the suspended ceiling is damaged in the test, the timefor this damage t i crit can be transferred to a criticaltemperature at the' centre level of the ceiling Ti,crit byusing design diagrams, presented in (11) and exemplifiedin FIG 5.

--------_..

Tt °C

tI

Tj,crit ,-

I

II

t i, cri t

0.050

0.100

0.200

t h

8

FIG 5. Ca1culated time curves of the temperatureat the centre level of the suspended ceiling Tiin a floor or roof assernbly, according to FIG 2,for different values of dilAi of the ceiling.Dashed and dotted line curve applies to a derivedvalue (di/Ai)der of an assembly tested and usedfor transferring the time for damage of the suspend­ed ceiling ti crit to a corresponding criticaltemperature of the ceiling Ti/crit.

DIRECT INTERPOLATION OR EXTRAPOLATION OF RESULTS OF FIRERESISTANCE TESTS FOR CLASSIFICATION PURPOSES

Knowing the following quantities of a floor or roof assernblyaccording to FIG 2

(l) the critical steel bearn temperature Ts/crit at the collapseof the supporting structure/

(2) the derived value (di/Ai)der of thesuspended ceiling/characterizing in an integrated way the real structural de­sign and behaviour of the ceiling and its fastening devicesat a fire exposure ,

(3) the critical temperature at the centre level of the sus­pended ceiling Ti/crit f corresponding to a fai1ure of the

9

ceiling, if any,

the results of the fire resistance test can be directly inter­polated or extrapolated for a determination of the fire resis­tance tfr for structural modifications of the tested floar orroof assembly, having a suspended ceiling which is identicalwith the one tested. The modification then relates to the slaband the supporting steel beams.

A guick carrying through of the interpolation or extrapolationreguires that a design basis is available which directly givesthe time curves of the steel beam temperature Ts and the temp~

erature at the centre level of the suspended ceiling Ti forvarying slab material, steel beam characteristics and (di/Ai)derfor the suspended ceiling at a fire exposure according toEq (l). Such a design basis is presented in (Il) togetherwith some examples, illustrating the practical application ofthe interpolation or extrapolation procedure.

If the modified floor or roof assembly is to be classifiedfor the same ratio between the design load Q and the ultimateload at ordinary room temperature Qu as applied in the test,the critical steel bearn temperature Ts crit obtained in thefire resistance test directly constitutes the limiting valuefor the interpolation or extrapolation. If the classificationrelates to another ratio Q/Qu than used in the test, the limit­ing steel bearn temperature of the supporting structure Ts critmust be corrected, for instance, by way of FIG 6 (12) .. '

cc700 Ts,crit600500400300200100o

------- I-~ I

I ~'"- ~ i

~ I

- I I ~,'"

"- "! I I ! Io

0.2

0.4

0.6

0.8

FIG 6. Limiting steel temperature Ts crit as functionof ratio between design load Q and uitimate load atordinary room temperature Qu.

10

THEORETICAL DETERMINATION OF FIRE RESISTANCE

More and more countries now are permitting a determinationof the fire resistance of load-bearing structures or structuralmembers to be done analytically all through. The Europeanrecommendations for the design of fire exposed steel structures,recently drawn up by the European Convention for ConstructionalSteelwork (13), certainly will stimulate still more countriesto approve officially this way of classification as an alterna­tive to the standard fire resistance test.

The components of the design procedure are outlined in FIG 7.The thermal exposure is specified by Eg (l).

END

: NOI

TIME OF FAILURE =FIRE RESISTANCE t fr

GASTEMPERATURE-TIMECURVE ACCORDI NG TOSTANDARD FIRERESISTANCE TEST

..

RESTRAINT FORCES ANDMOMENTS, THERMALSTRESSES IN STRUC­TURAL ELEMENTS

PROPOSED STRUCTURE

THERMAL PROPERTlES OFSTRUCTURAL MATERIALS

MECHANICAL PROPERTfESOF STRUCTURAL MATERIALS

DESIGN LOAD ATSERVICE STATE

. COEFFICIENT OF HEATTRANSFER

LIo_c_cu_p_Ä_N_Cy ---'hI

I_B_U_IL_DI_NG_H_E_IG_H_T__--'Hf-I__-=B,O...UI-=LO=-''-'-.NG=---'C:.::.O=..;DE=-- ...r REQUIRED FIRE

I Hi," DURATION t IdBUILDING VOLUME .

ILIM-P-O-R-TA-N-C-E-O-F----'LJ

ISTRUCTURE I

FIG 7. Analytical fire engineering design ofload-bearing structures, based on classificationand thermal exposure according to Eg (l).

It could be seen as quite natural to base a theoreticaldetermination of the fire resistance of a floor or roofassembly according to FIG 2 on the following assumptions:

(l) Characteristic values of the rnechanical properties ofthe material of the steel beams at elevated temperatures,

(2) characteristic values of the geometrical imperfectionsand residual stresses of the steel beams,

.(3) a uniform temperature distribution across the steel beams,

(4) a uniform temperature distribution along the steel beams.

Fire resistancetests of load-bearing structures or structuralmembers are veryexpensive and consequently, the number oftests on each prototype ordinarily is limited to only onetest - in a few countries, two tests. Hence, there are nopossibilities to evaluate the test results statistically.

The actual quaIity of the structural material in a singletest specimen can be considered as a random sample from awide variety. Therefore, the material quaIity of a structuralelement, used in a fire resistance test, will generally behigher than the quaIity guaranteed by the manufacturer andconsequently the mechanical properties of the material betterthan the characteristic values.

1 1

Analogously, the realleveI Qf the influence of imperfectionsfor a single test specimen can be considered as a random sample.Hence, a steel beam member generally has a lower level ofimperfections than the characteristic level specified in codesand regulations.

Finally, in a fire resistance test, the steel beams in a flooror roof assembly according to FIG 2 will get a considerabletemperature variation over the cross section as weIl as inthe longitudinal direction.

These circumstances indicate that considerable discrepancieswill arise when the fire resistance of a floor or roof assembly,as shown in FIG 2, is determined on one hand by a standardfire resistance test, on the other by a calculation based onthe assumptions, listed above. Generally, then the analyticalmethod gives a lower - frequently essentially lower - valueof the fire resistance than the test.

The described discrepancies between an analytical and experi­mental determination of the fire resistance are discussed andanalysed more'in detail in (14) for different types of load­bearing steel structures. Alternative methods of correctionare briefly outlined for getting an improved consistencybetween the analytical and experimental approaches and oneof these methods is further developed to a design basis,which can easily be applied in practice.

Principally, the method is characterized by a correction ofthe analytically determined load-bearing capacity R, basedon the characteristic values of the mechanical properties ofthe structural material, the characteristic value of theinitial imperfections of the structure and a uniformly distri­buted steel temperature across and along the structure. FIG 8reproduces a recommended correction factor f, by which theload-bearing capacity R is to be multiplied in order to getthe corrected load-bearing capacity Re, i.e.

R = fRc (2 )

12

The correction factor f then depends on the tyPe of steelstructure and on the steel temperature Ts ' calculated on theassumption of a uniform distribution across and along thestructure.

T 5

700 °C6005001.00300200100o

,

l , i ,

iiI

" i , I, I

,

HYPERSTATIC IBEAMS ...,j

. ,il

"i il

• i /,

1, • ,

•

, /,

,i :/ ISOSTATIC

• BEAMS ..J,.<:::

•

i • Y ~,COlUMNS

~ ~, i

•

,

•

J.,.--t::: :+ , I : I: , ! I I i, ' I ,, , ,1.0

1.5

2.0

FIG 8. Correction factor f as a function of uhi­formly distributed steel temperature Ts for columns,isostatic beams and hyperstatic beams with tworedundancies. For hyperstatic beams with only oneredundancy, f roughly can be taken as the averageof the values for isostatic beams and hyperstaticbeams with two redundancies.

Applied to a floor or roof assembly with load-beari~g steelbeams and a suspended ceiling, as shown in FIG 2, an analyti­cal determination of the fire resistance according to FIG 7normal ly reguires a support from results of a standard fireresistance test, specifying the integrated behaviour of thesuspended ceiling, for instance, by the derived value(di/Ai)der and the critical temperature at the centre levelof the ceiling Ti crit. In (l), these guantities are put downfor a large number of types of suspended ceilings, obtainedin fire resistance tests performed at the National SwedishInstitute for Testing and Meteorology in Stockholm.

ANALYTICAL DESIGN, DIRECTLY BASED ON REAL FIRE CHARACTERISTICS

An input information in the form of the guantities (di/Ai)derand Ti,crit or other eguivalentguantities for the suspendedceiling, determined in a standard fire resistance test orin some other test, ordinarily is reguired also in an analyti­cal design for a real fire exposure, when applied to a floor

--'w

DESIGN RESIDUAL LOAD­CARRYING CAPACITY Rrd

ENDYES

NO

DESIGN LOAD-CARRYINGCAPACITY R

d

INTEROEPENDENCEON NON-FIRE DESIGNPROCEDURE

TEMPERATURE- TIME FIELD-SL_OF STRUCTURAL ELEMENT~

RESTRAINT FORCES AND MO­MENTS,THERMAL STRE5SESIN STRUCTURAL ELEMENTS

DESIGN GASTEMPERATURE.::iTIME CURVE OF FIRE PR~

RATE OF BURNING AND ~HEAT RELEASE'---------.------

NOMINAL LOADS AND LDAD DESIGN LOAD EFFECT- FACTORS FOR DEAD, LIVE f-- AT SERVICE STATE -

LOAD ETC AT SERVICE STATE Srd

NOMINAL LOADS AND LOAO.- FACTORS FOR DEAD, LIVE f---___. DESIGN LOAD

LOAD ETC AT FIRE EFFECT AT FIRE Sd

PROBAB1USTICINFLUENCES

THERMAL PROPERTlES OFSTRUCTURAL MATERIALS

._-----'

PROBABILlsnclNFLUENCES

PROBABIllSTIC INFlUENCES

COEFFIC1ENT OF HEATTRANSFER

fiRE LQAD COMBUSTlONCHARACTER1STICS

MECHANICAL PROPERTlES OFSTRUCTURAL MATERIALS

VENTILATION CHARACTERISTlCSOF FIRE COMPARTMENT

SIZE AND GEOMETRY OFFIRE COMPARTMENT

NOMINAL LOAD AND lOADFACTOR FOR FIRE LOAD DENSITY

THERMAL PROPERTlES OFENCLOSING STRUCTURES

------~"--~ ---,._---- ..,,~--- ..~----~,~~------_., ...._--_.-._.~ ._------,~,-------_._ .._-.--~,---

LIL~O_A_D_C_H_AR_A_C_T_E_R_rS_T_'C_S__~_.

L..... --'

--I PROPOSEn STRUCTURE

or roof assembly, as shown in FIG 2.

The procedure of an analytical structural fire engineeringdesign, directly based on differentiated gastemperature ­time curves of a real fire development, is shown in FIG 9(l), (6). Decisive quantities for the fire exposure are

(l) the design fire load density and its combustion characte­ristics,

(2) the size and geometry of the fire compartment,

(3) the ventilation of the fire compartment, and

(4) the thermal properties of the structures enclosing thefire compartment.

The design criterion requires that the lowest value of theload-bearing capacity R during the fire exposure - the designload-carrying capacity ~ - exceeds the design load effect atfire Sd.

For buildings containing activities, which are particularlyimportant from, for instance, an economical point of view,there may be the motive for requiring that the building canbe used again after a fire - either directly or after onlyvery limited repairs - for the current activities in a fullextent. If a fire engineering design also includes such a re­quirement on re-serviceability of the structure after fire,the residual load-carrying capacity Rrd must exceed the de­sign load effect at service, non-fire state on the structureSrd·

An analytical design according to FIG 9 is now approved inSweden for a general practical use by the National SwedishBoard of Physical Planning and Building (15). For facilitatingthe practical application, a comprehensive set of design dia­grams and tables have been systematically produced, givingdirectly, on one hand, the design temperature state of thefire exposed structure, on the other, a transfer of thisinformation to the corresponding design load-bearing capacityof the structure; cf, for instance (l), (6), (16).

Compared with the internationally predominant fire engineeringdesign, based on classification and results of standard fireresistance tests, the analytical design according to FIG 9has a more logical structure, based on well-defined functionalrequirements and performance criteria, gives a structuralfire design with improved economy, and leads to a more con­sistent fire safety level.

14

15

ANALYTICAL DESIGN, INDIRECTLY CONNECTED TO REAL FIRE EXPOSUREOVER THE CONCEPT EQUIVALENT TIME OF FIRE DURATION

In those cases, at which the present state of knowledge doesnot enable a complete analytical fire engineering designaccording to FIG 9 to be carried out, the concept eguivalenttime of fire duration can be a useful implement. The concepthas been introduced as a means for a direct translatian froma real fire exposure to a corresponding heating according to astandard fire resistance test, and vice versa.

In principle, the eguivalent time of fire duration is definedas that length of the heating period in a standard fireresistance test which gives the same, most hazardous effecton the structure as the complete fire process of a real fire- e.g., the same maximum temperature for a steel structure.Depending on the type of design problem to be deålt withand the level of accuracy intended, the character of theconcept will vary.

If the available design basis permits a theoretical determi­nation to be performed, as cancerns the transient temperaturefields but not the design load-carrying capacity of a fireexposed structure, it can be motivated to use a differentiatedform of the eguivalent time of fire duration concept. Theequivalent time of fire duration then becomes a function bothof the parameters of the fire process and of the quanti-tieswhich describe the detail design of the actual structure(l), (6).

A more rough form of the concept is necessary to use, whenthe structural fire engineering design is to be based on realfire.exposure characteristics without the prerequisites exist­ing for an analytical determination of the transient tempera­ture fields and the connected load-bearing capacity of thefire exposed· structure. Under such circumstances, the eguiva­lent time of fire duration te can be differentiated only withrespect to the detail properties of the fire process butnot with respect to the characteristics of the structuraldesign - FIG 10 (7), (8), (17). For fire exposed steel struc­tures - for instance, a floar or roof assembly according toFIG 2 - then the following approximate formula can be applied(8 )

te = 0.067 (min) (3)

in wh~~h gf is the fictitious value of the fire load density(MJ'm ) and (AIh/At)f thel!ictitious value of the opening factorof the fire compartment (m 2); cf (l), (6). Written in thisform, the formula·enables that the influence of varyingthermal properties of the structures surrounding the fire

compartment can be taken into account.

lPROBABILlSTtC INFLUENCES

NOMiNAL LOAQ AND LDADFACTOR FOR FIRE LOAD f-----,DEN$ITY

16

SIZE AND GEDMETRYOF FIRE COMPARTMENT

VENTILATION CHARACTER1S­TiCS OF FIRE COMPARTMENT

THERMAL PRDPERTIES OFENCLDSING STRUCTURES

qt = k fe (Alh)"1

,-_~ A-,t---,-f_.,EQUIVALENT TIME AT 1-'__~FIRE DURATION t e

rl PROPOSEO STRUCTURE t--DESIGN LOAD EFFECT ATFIRE

ST ~,ANDARD FIRE FIRE RESISTANCE ;F-ES

'-" -.-JL

- -/l~r>. te ENDRESISTANCE TEST t fr "'-

NO

NOMINAL lOADS AND LDADFACTORS FOR DEAD, LIVELQAD ETC AT FIRE

IPRDBABILlSTIC INFLUENCES I

INTERDEPENDENCE ONY NON-FIRE DESIGN

!PROCEDURE I

FIG 10. Procedure for a structural fire engineeringdesign,based on a simplified expression for theequivalent time of fire duration te and on an experi­mental ly determined fire resistance of the structuretfr'

REFERENCES

(l) Pettersson, O., Magnusson, S.E. and Thor, J., "Fireengineering design of steel structures", Publication 50,Swedish Institute of Steel Construction, Stockholm, 1976(Swedish Edition 1974) .

(2) Anderberg, Y. and Thelandersson, S., "Stress and deforma­tion characteristics of concrete at high temperatures.2.Experimental investigation and material behaviour model",Bulletin 54, Division of Structural Mechanics and Con­crete Construction, Lund Institute of Technology, Lund,1976.

(3) Schneider, U. and Kordina, K., "Ueber das Vorhalten vonNormalbeton unter stationärer und instationärer Tempera­turbeanspruchung", 3rd International Conference on Struc­tural Mechanics in Reactor Technology, Vol. 3, Part H,M 1/6, London, 1975.

17

(4) Hadvig, s. and Paulsen, O.R., "one-dimensional charringrates in wood" , Journal of Fire & Flammability, Vol. 7,October 1976.

(5) Fredlund, B., "Modell för beräkning av temperaturer ochfuktfördelning samt reducerat tvärsnitt i brandpåverkadeträkonstruktioner (Analytical model for a determinationof temperature and moisture distribution and reducedcross section in fire exposed wooden structures)",Internal Report IR 79-2, Division of Structural Mechanics,Lund Institute of Technology, Lund, 1979.

(6) Pettersson, O. and Ödeen, K., "Brandteknisk dimensionering­principer, underlag, exempel (Fire engineering design ofbuilding structures - principles, design basis, examples)",Liber Förlag, stockholm, 1978.

(7) Law, M. and Arnault, P., "Fire loads, natural fires andstandard fires", ASCE-IABSE International Conference onPlanning and Design of Tall Buildings, Lehigh University,Bethlehem, Pennsylvania, August 21-26, 1972.

(8) Pettersson, O., "The connection between a real fireexposure and the heating conditions according to standardfire resistance tests," European Convention for Construc­tional Steelwork, Chapter II, CECM-III-74-2E.

(9) ISO/TC92, DP 6167 "Fire resistance test - suspendedceilings", Document ISO/TC92 N494, October 1978.

(10) ISO, "Fire resistance tests - elements of buildingconstruction" , International Standard 834, 1975-11-01.

(Il) Sandberg, B. och Pettersson, O., "Theoretical evaluationof fire resistance tests of floor and roof assemblieswith suspended ceiling", Bulletin 58, Division of Struc­tural Mechanics and Concrete Construction, Lund Instituteof Technology, Lund, 1978.

(12) Witteveen, J., "Brandveilighed staalconstructies (Fireresistance of steel structures)", Centrum Bouwen inStaal, Rotterdam, 1966.

(13) European Convention for Constructional Steelwork,Committee 3, "European recommendations for the designof steel structures exposed to the standard fire", FinalDraft, July 1979.

(14) Pettersson, o. and Witteveen, J., "On the fire resistanceof structural steel elements, derived from standard firetests or by calculation", to be published in the Journalof Fire Safety, 1979.

(15) National Swedish Board of Physical Planning and Building,"Brandteknisk dimensionering (Fire engineering design)",Comments on SBN (Swedish Building Code), No. 1976:1.

(16) Pettersson,. O.,"Calcul theorique des structures exposeesau feu", Securite de la Construction Face ii l'Incendie,Seminaire tenu ii Saint-Remy-les Chevreuse (France) du18 au 20 Novembre 1975, Editions Eyrolles, Paris, 1977.

(17) Pettersson, O. and Magnusson, S.E., "Fire test methods ­background, philosophy, development trends and futureneeds", Nordtest Doc Gen 011, Stockholm, 1977.

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