exemple calcul foc

7/25/2019 Exemple Calcul Foc

1/36

EXAMPLE 1

FIRE DESIGN OF AN UNPROTECTED BEAM USING GRAPHS

This worked example covers the fire design of a hot-rolled IPE section forming part of

floor structure of an office building. The beam is uniformly loaded and restrained against

lateral torsional buckling by the presents of a concrete slab supported on the top flange.

The beam is to be designed to achieve R! fire resistance without the use of fire

protection material. In this worked example thermal actions are determined using "#$$%.

Mechanical actions at normal temperature

The characteristic value of the load is&

The design value of the load is&

The applied bending moment and shear force are given by&

Design at normal temperature

The IPE '$$ section is a (lass section in bending.

Basic data

Material properties"teel grade& " %)!

*ield stress&fy + %)!

,mm

#ensity&a + )/!$kgm0

Loads

Permanent action&gk +

12/ k,m

3ariable action& qk + )2/k,m


2/36

The section is checked at 45" at normal temperature. The concrete slab is assumed to

provide full lateral restraint to the beam6 therefore2 lateral-torsional instability does notneed to be taken into account.

7ending moment resistance&

"hear resistance&

"erviceability 5imit "tate&

Design in the fire situation

Mechanical actions for the fire design situation

The reduction factor for the design load level is e8ual to&


3/36

9here the : factor is taken as :2 + $2' for office buildings

The section factor for the hot-rolled section is taken from "#$$1. The box section factor

for an unprotected beam exposed on three sides is e8ual to&

The exposed perimeter is indicated by the dashed line on Figure 3.

The shadow effect is considered by modifying the section factor as follows&

Verification in the time domain

The adaptation factor + $2) is used for an unprotected beam exposed to fire on three

sides. The adaptation factor %+ 2$ is used for simply supported beam.

The fire resistance can be checked using the design data reproduced in Figure 4.

The degree of utili;ation for the beam is given by&

The critical temperature is given by&

The fire resistance period predicted using


4/36


5/36

EXAMPLE 2

FIRE DESI! "F A! #!PR"$E%$ED IPE SE%$I"! &EAM EXP"SED

$" $'E S$A!DARD $IME $EMPERA$#RE %#RVE

The worked example illustrates the fire design of a simply supported non-

composite beam. The transfer of heat into the beam is evaluated using a step-by-

step calculation procedure. The structural resistance of the member at elevated

temperature is evaluated using the simple calculation model for members sub=ect

to bending given in E,>>'--%.

? beam made of hot-rolled IPE section is a part of the floor structure of an office

building. The beam is loaded uniformly and restrained against lateral torsional

buckling by a concrete slab. The beam is design to achieve a fire resistance rating

of R!.

Partial safety factor @

A2fi

+ 2$$

The design of the beam cross section and verifications at normal temperature is run inExample .

E(aluation of gas temperature

The standard temperature-time curve is used for the gas temperature&

E(aluation of )eam temperature

The dotted line on Figure 3 indicates the perimeter that is assumed to be exposed to

fire. The section factor is calculated as follows&

The correction factor for the shadow effect ksh

for IPE-sections is given as&


6/36

where the BAmVCb is calculated from the box surrounding the section as

indicated by dashed line on Figure 3.

The increase of temperature of the steel section is calculated using an

incremental calculation procedure to determine the increase in steel temperature

given in E,>>'--% by the following e8uation&

Time interval Dt + ! sec is used in the temperature calculation.

The net heat flux is&

m is the emissivity of the carbon steel BFm + $2) - E,>>'--% G%.%C

Fr r is the emissivity of the fire BFr + 2$ H E,>>--% G'.C

is the configuration factor B + 2$ H E,>>--% G'.C

Jcc is the coefficient of the heat transfer for use with the standard temperature

time curve Bgiven in E,>>--% G'.%. as Jc + %!2$ 9BmKCC

L is the "tephan 7olt;mann constant BL + !2M) $-/ 9BmK1CC

The steel temperature-time curve of the section is shown in Table and


7/36

,ote&

The temperature of the steel beam can be evaluated from "#$$1.


8/36

(lassification of the section at elevated temperature&


9/36

The slenderness of the flange in compression is&

The limit for (lass is >F.


10/36

The adaptation factor + $2) is used for an unprotected beam exposed to fire on

three sides2 and the adaptation factor % + 2$ is used for a simply supported beam.

The design moment resistance at temperature a + M1O( is given by&

The design shear resistance is given by&

The section is satisfactory in the fire design situation.


11/36

EXAMPLE *

FIRE DESI! "F PR"$E%$ED IPE SE%$I"! &EAM

EXP"SED $" PARAME$RI% FIRE %#RVE

This worked illustrates the fire design of a simply supported non-composite beam. eat

transfer into the section is calculated using the e8uation for protected members given in

E,>>'--%2 which is evaluated using an iterative calculation procedure. The structural

resistance is calculated using the simple calculation model for members in bending2given in E,>>'--%.

? steel beam forms part of a floor structure of an office building. The beam is uniformly

load and restrained against lateral torsional buckling by a concrete slab. The beam is

re8uired to achieve M$ minutes fire resistance and will be fire protected using sprayed

vermiculite cement. The thermal actions will be determined using the parametric

temperature - time curve.

Data for fire calculation

#ata for parametric fire curve&

+ !2)>1

tmax + %% minutes

x +

Properties of fire protection material

"prayed vermiculite cement

thickness dp + $ mm

densityp + !!$ kgm'

specific heat cp + $$ QkgK

thermal conductivityp + $2% 9mK

The section is satisfactory at normal temperature Bsee Ex and %C.

Design for the fire situation

Mechanical actions for fire design situation

4sing the simplified rule in E, >>-%2 actions in the fire situation may be


12/36

determined from actions in normal design. Bsee Ex. %C


The full calculation of a parametric fire curve is illustrated by worked example"$1%. The curve used in this example is based on the following parameters

+ !2)>12 tmax + %% min B$2'M) hourC andx + should be used. The modified

time t* Bin hoursC is used in the parametric curve&

The maximum gas temperature is reached at time t*max

The heating part of the temperature curve is given&

The maximal gas temperature in the fire compartment

is&

9hen t*max S %2 the curve in the cooling phase is given by&

E(aluation of )eam temperatureThe section factor can be calculated as follows Bsee


13/36

The increase of temperature of the steel section is calculated using step-by-step

procedure using the following formula&

Time interval Dt + '$ sec is used in the temperature calculation.

The maximum temperature reached due to exposure to the parametric fire is

a2max + !/%O(. The steel


14/36


15/36

Verification in the resistance domain

%lassification of the section at ele(ated temperature




16/36

The design moment resistance during fire exposure is givenby&

The adaptation factor + $2/! is used for an unprotected beam exposed to fire on

three sides.

The adaptation factor % + 2$ is used for simply supported beam.

The design moment resistance at the temperature

a

+ !/%O( is&

The design shear resistance is given by&

The section is satisfactory in the at fire design situation.

%omparison +ith design for standard fire resistance


17/36

EXAMPLE 4

FIRE DESIGN OF A PROTECTED HEB SECTION COLUMNEXPOSED TO THE STANDARD TEMPERATURE TIME CURVE

This worked example illustrates the fire design of a column that is continuous over

two storeys. eat transfer into the section is evaluated using the E,>>'--%

calculation procedure. The resistance of the column is evaluated using the simple

calculation model for compression members given in E,>>'--%.


18/36

Data for fire calculation

Aaterial properties of fire protectionH sprayed vermiculite cement

- thickness dp + %$ mm

- thermal conductivityp + $2% 9m-K-

- densityp + !!$ kgm-'

- specific heat cp + $$ Qkg-K-


The design value of the load in lower part of the column is&


"ection E /$ 7 is designed to resist the applied load2 classified as (lass section.

The buckling length of the column is e8ual to&

7uckling perpendicular to ;-axis is critical.

The elastic critical force for normal design is&


19/36

The non-dimensional slenderness at normal temperature is&

The buckling reduction factor for hot-rolled I sections with hb ratio Y 2% is

evaluated on curve c Bthe imperfection factor J + $21>C.

7uckling resistance at 4ltimate 5imit "tate.

The section is satisfactory at normal temperature.



4sing the simplified rule in E, >>-%2 actions in the fire situation may be determinedfrom actions in normal design.

The accidental situation is used for the combination of mechanical actions during fire

exposure2 where the : factor is taken as :%2 + $2' for office buildings. The reduction

factor for the design load level is e8ual to&

!&, The : factor is a nationally determined parameter. The value used in this example is

the value recommended in E, >>--%


20/36


The standard temperature-time curve is used for the gas temperature.

E(aluation of column temperature

The dotted line in Figure 3 indicates the perimeter of the section exposed to fire. The

section factor is calculated as follows&

The increase of temperature of the steel section is calculated by step-by-step procedure

using&

where&

Time interval Dt + '$ sec is used in the temperature calculation.

The steel and gas temperatures are shown in Table and Figure 4.


21/36


22/36

$ minutes

is a + !!1O(.

,ote&

?s an alternative2 the temperature of the steel column could be evaluated from "#$$!.

m- and taking into account the properties of the fire

protection material2 as follows.

The steel temperature at t + >$ minutes2 is a + M$%O(

The difference between the steel temperature calculated by the E,>>'--% step-by-step

calculation and the steel temperature determined from "#$$! is caused by the assumption

that $+Z

Bi.e. neglecting the thermal capacity of the fire protection materialC in the design data givenin "#$$!. 4sing a design temperature from "#$$! will therefore lead to a conservative

evaluation of the member resistance in fire.


(lassification of the section at elevated temperature




23/36

The limit is not exceeded. Therefore2 the flange is (lass .

The slenderness of the web in compression is&

The limit for (lass is ''F.


24/36

The buckling reduction factor is&

The design resistance at temperature a + !!1O( is given by&


25/36

The elastic critical force at normal temperature is given as follows&

In this case2 the calculation of2 [ should be based on the elastic critical load for a

column buckling length of $.)L. The non-dimensional slenderness at normal

temperature is given as follows&

,on-dimensional slenderness at temperature a is&

The factor J is e8ual to&

and the buckling reduction factor is&

The design resistance at temperature a + M$%O( is calculated as&


26/36

Therefore2 the section is satisfactory for the fire design situation.

!&, The conservative approximation of the steel temperature obtained from "#$$! hasresulted in a %!\ reduction in compressive resistance.

%omparison +ith design using standard fire resistance and manufacturers/ data

$ minutes exposure to the standard time temperature curve2 the thickness ofprotection re8uired can be determined using manufacturers design tables for

vermiculite spray2 published in


27/36

EXAMPLE .

FIRE DESI! "F A PR"$E%$ED 'E& SE%$I"! %"L#M! EXP"SED

$" $'E PARAME$RI% FIRE %#RVE

This worked example illustrates the fire design of a column that is continuous over

two storeys. Transfer of heat into the section is calculated using the e8uation given in

E,>>--%2 evaluated by step-by-step calculation procedure. The load bearing

capacity of the column is calculated using the simple calculation model for

compression members given in E,>>'--%.

? column made of hot-rolled E7 section supports two floors and is fire protected with

gypsum boards. The column is re8uired to achieve M$ minutes fire resistance.

Properties of fire protection material

Wypsum board&

- Total thickness dp + % mm6

- thermal conductivityp + $2%$ 9m-K-

- densityp + /$$ kgm'

- specific heat cp + )$$ Qkg-K-


The design value of the load in the lower part of the column is


"ection E /$ 7 is designed to resist the applied load2 classified as (lass section.


28/36

The buckling length of the column is e8ual to&

7uckling perpendicular to ;-axis is critical.The elastic critical force for normal design is&

The non-dimensional slenderness at normal temperature is&

The buckling reduction factor for hot-rolled I sections with hb ratio Y 2% is

evaluated on curve c Bthe imperfection factor J + $21>C.

7uckling resistance at 4ltimate 5imit "tate.

The section is satisfactory at normal temperature.


29/36



4sing the simplified rule in E, >>-%2 actions in the fire situation may be determined

from actions in normal design.

The accidental situation is used for the combination of mechanical actions during fire

exposure2 where the : factor is taken as :%2 + $2' for office buildings. The reduction

factor for the design load level is e8ual to&

!&, The : factor is a nationally determined parameter. The value used in this example is

the value recommended in E, >>--%


The gas temperature is calculated on parametric temperature-time curve. The

parameters of the curve in this example have been calculated as + 2')%2 tmax+ ''2M minutes B$2!M hourC andx + . ? full illustration of the calculation method

for parametric fire curves is given in "$1%.

The modified time t* Bin hoursC is used in the parametric curve

The maximum gas temperature is reached at time t*max

The heating part of the temperature curve is given by&

The maximum gas temperature reached in the fire compartment is


30/36

9hen $2!Y t*max Y % the curve in the cooling phase is given by&

E(aluation of column temperature

The section factor is calculated as follows Bsee Figure 32 where the dotted line

indicates the section perimeter exposed to fireC&

The increase of temperature of the steel section is calculated by step-by-stepprocedure using&

Time interval Dt + '$ seconds is used in the temperature calculation.

The maximum steel temperature attained during this design fire occurs after ))

minutes&


31/36


32/36


%lassification of the section at ele(ated temperature




33/36

The limit is not exceeded. Therefore2 the flange is (lass .

The slenderness of the web in compression is&

The limit for (lass is ''F.


34/36

The design resistance at temperature a2max + 1%)O( is given by&

!&, #ue to relatively low design temperature and the reduction in effective

length the buckling resistance is higher than the room temperature capacity.


35/36

Exemplul 2.

Etapa II. Verifcarea la cald a stalpului

Clasa de rezistenta R90: protectie cu mortar torcretat cu adaos de vermiculite de

grosime di= cm.

Caracteristicile stratului protector :

i= !"0 #g$m! % i=0.0 &$m20C% pi= '% Ci= 200 ()$#g0C*

+olicitarile pe setiune din grupare si din com,inatia la actiunea -ocului se vor

considera: = /000 si respectiv = 9" #m

1entru sectiunea de otel a stalpului : $3=40./ m5 % cs= "20 )$#g0C

a6 +e determina : =7!"0x2006$72x"20x8"06=0.0"

,6 +e determina : $3=40./$70.0"x0.0/x40./6=".9c6 ;emperatura la -ata elementului din otel tre,uie sa corespunda clasei de

rezistenta R90 :

d??

e?c?

%

%

s

+

+=

7 6

unde :

g?

4

c

?

red

=

7 6

fd

$?

i

'

% +=

7 6

3=7$.06".952.44="4.2/

32= 70!0.0/6$0.".4/=/".4/

s= 7"4.2/x29/".4/x0./"6$"4.2//".4/x0.46=!".20

C


36/36

exemple calcul foc

Documents