Presentation for Dissertation - EuroCode 3

Department ofCivil and Structural Engineering

HEAT TRANSFER TO EXTERNAL STEELWORK

Eurocode 3BS EN 1993 Part 1-2:2005 General rules – Structural fire design

Design of Steel Structures

Content of BS EN 1993-1-2CO

NTE

NT

Heat transfer to structural elementsH

EAT

TRAN

SFER

Column not engulfed in flame Column engulfed in flame

Beam not engulfed in flame Beam fully or partially engulfed in flame

AssumptionsAS

SUM

PTIO

NS

The size of fire compartment is considered to be single storey.

All openings in the fire compartment are assumed to be rectangular.

Determination of parameters such as compartment fire temperature, size and temperature of flames projecting out of the window, convection and radiation characteristics as per Annex B in EN 1991-1-2.

Elements distinguished as member engulfed or not engulfed in flame depending on the relative position with respect to the openings

Radiative heat transfer for an element which is not engulfed with flame projecting out from the windows.

Convective heat transfer when element is engulfed with flame and also heat transfer by radiation of flame engulfing it and also from compartment opening.

Heat BalanceH

EAT

BALA

NCE

Member not engulfed in flame

Average steel temperature Tm [K] is found by iterative solution of the

σ Tm4 + α Tm = Iz + If + 293α

Where,σ Stefan Boltzmann constant taken as 56.7x10-12 kW/m2K4

α Coefficient for heat transfer by convection [kW/m2K]Iz Heat flux by radiation from the flames [kW/m2]

If Heat flux by radiation from the opening [kW/m2]

Heat BalanceH

EAT

BALA

NCE

Member engulfed in flame

Average steel temperature Tm [K] is found by iterative solution of

σ Tm4 + α Tm = Iz + If + α Tz

Where,Tz Temperature of flame [K]

Iz Heat flux by radiation from the flames [kW/m2]

If Heat flux by radiation from the opening [kW/m2]

Heat balanceH

EAT

BALA

NCE

Relative heat flux Iz

Calculated depending on the type of member and situation as below.

Column not engulfed in flameBeam not engulfed in flameColumn engulfed in flameBeam fully or partially engulfed in flame

Heat transferH

EAT

TRAN

SFER

If = ϕf εf (1- az) σ Tf4

Where,Φf Overall configuration factor for heat transfer by radiation from

the opening for that memberεf Opening emissivityaz Flame absorptivityTf Fire temperature [K]

Opening Emissivity εf must be taken as 1.

Flame absorptivity az is calculated depending on the type of the

member and the situation.

Radiative heat flux If

Configuration factorsCO

NFI

GU

RATI

ON

FAC

TORS

To find temperatures of external members, all radiating surfaces are assumed to be rectangular in shape.

A rectangular envelope is drawn outer to the member cross-section receiving the heat transferred by radiation

The ϕ value must be determined at the midpoint P at each and every face.

P

P

P P

P

P

P

Envelope


NFI

GU

RATI

ON

FAC

TORS

X

a

bP

X

a

1

4 3

2 Keya) Radiating surfaceb) Receiving surface ϕ = ϕ + ϕ + ϕ + ϕ

1 2 3 4

S

a = h/s;b = w/ss distance between P and Xh Radiating surface zone

heightw zone width

1. Receiving surface in a plane parallel to the radiating surface


NFI

GU

RATI

ON

FAC

TORS

2. Receiving surface in a plane perpendicular to radiating surface


NFI

GU

RATI

ON

FAC

TORS

3. Receiving surface in a plane at an angle θ to the

radiating surface

X

1

2

P

X

a

1

2

Key1) Radiating surface2) Receiving surface ϕ = ϕ + ϕ

1 2

S

w

h

θ

Overall configuration factorsO

VERA

LL C

ON

FIG

URA

TIO

N F

ACTO

RS Overall configuration factor for an opening

di cross section dimension of member face i

Ci Coefficient for protection for member with face i

Ci = 0 for a protected face

Ci = 1 for an unprotected face

Configuration factor ϕf,i for a member with face i must be taken zero

when the opening is not visible.

Overall configuration factorsO

VERA

LL C

ON

FIG

URA

TIO

N F

ACTO

RS Overall configuration factor for flame

Configuration factor becomes zero when the flame is not visible to the member face taken into consideration.

Heat screen can be used to protect the member face. When a member face is immediately near to wall of the compartment, then it is considered as protected when there is no gap in that part of wall. Rest of the member faces are considered to be unprotected.

Member face numberingM

embe

r fac

e nu

mbe

ring

Column

Beam

Column

1

2

34

1 and 2 are perpendicular to radiator3 and 4 are parallel to radiator4 out of sight to radiator

Envelope

Beam2

1

43

Envelope

Column face numbering - Plan Beam face numbering - Section

Member dimensions - ColumnM

embe

r dim

ensi

ons

- Co

lum

n

Column opposite opening

Column

d

d2

1

(2)

(3)

s

Column

d

d 2

1

(4)

(3)

s

Column between opening

Member dimensions - BeamM

embe

r dim

ensi

ons

- Be

am

Beam parallel to wall

Beam perpendicular to wall

Beam

d

d 2

1

(3)

(4)

s

Beam

d

d 2

1

(3)

(4)(2)

Colu

mn

not e

ngul

fed

in fl

ame

Column not engulfed in flame

Column not engulfed in flame

Column not engulfed in flameCo

lum

n no

t eng

ulfe

d in

flam

e

Radiative heat transfer - Column opposite opening

Openings

Flames

No forced Draught: Column placed opposite an opening

Openings

Flames

Forced Draught: Column placed opposite an opening


lum

n no

t eng

ulfe

d in

flam

e


Heat flux due to radiation when the column is placed opposite to a window opening

Iz = ϕz εz σ Tz4

Where,ϕz Overall configuration factor for flame heat of columnεz Flame emissivityTz Temperature of flame [K]


lum

n no

t eng

ulfe

d in

flam

e


No forced draught: Wall above and h < 1.25w

Column

z

2h/3

Equivalent front rectangle 2h/3

Column

Section Plan


lum

n no

t eng

ulfe

d in

flam

e


No forced draught: Wall above and h > 1.25w or no wall above

Column

z

2h/3

Equivalent front rectangle 2h/3

Column

Section Plan

x

x


lum

n no

t eng

ulfe

d in

flam

e


Forced draught

Column

z

xEquivalent front

rectanglex

Column

h

w +

0.4

x


lum

n no

t eng

ulfe

d in

flam

e

Radiative heat transfer - Column between opening

No forced Draught: Column placed opposite an opening

Forced Draught: Column placed opposite an opening

n openingsm openings

Flame side m Flame side n

n openingsm openings

Flame side m Flame side n


lum

n no

t eng

ulfe

d in

flam

e


Heat flux due to radiation when the column is placed between window openings

Iz = (ϕz,m εz,m + ϕz,n εz,n) σ Tz4

Where,ϕz,m Overall configuration factor for flame heat of column on side mϕz,n Overall configuration factor for flame heat of column on side nεz,m Total flame emissivity on side mεz,m Total flame emissivity on side n


lum

n no

t eng

ulfe

d in

flam

e


No forced draught: Wall above and h < 1.25w

Column

z

2h/3

Equivalent side rectangle 2h/3

Column

Section Plan


lum

n no

t eng

ulfe

d in

flam

e


No forced draught: Wall above and h > 1.25w or no wall above

Column

z

2h/3

Equivalent side rectangle

Section Plan

x

2h/3

Column


lum

n no

t eng

ulfe

d in

flam

e


Forced draught

Column

x


x

Column

Section Plan

h

w +

0.4

s

s

s


lum

n no

t eng

ulfe

d in

flam

e Flame Emissivity - Column opposite an opening

Emissivity of flame εz when a column is placed opposite an opening is given by using the flame thickness λ at the top of opening. In case when there is no balcony or awning, flame thickness is given as

‘No forced draught’ λ = 2h/3‘forced draught’ λ = x but λ hx/z

h, x and z are taken as per Annex B of EN 1991-1-2


lum

n no

t eng

ulfe

d in

flam

e Flame Emissivity - Column between two openings

Total emissivities εz,m and εz,n when a column is placed between two openings is given by using the flame thickness λ as follows

For side m:

For side n:

Where, m number of openings on side mn number of openings on side nλi flame thickness for opening i, which is taken as equal to the

width of the opening or window, wi in ‘no forced draught’ condition.


lum

n no

t eng

ulfe

d in

flam

e Flame thickness

‘No forced draught’ λ = wi

‘forced draught’ λ = wi + 0.4s

Where, wi Opening widths horizontal distance taken perpendicular from wall of the compartment to the centreline of the column


lum

n no

t eng

ulfe

d in

flam

e

Temperature of flame, Tz

‘No forced draught’ l = h/2

‘Forced draught’ l = 0 column opposite an openingl = sX/x column between openings, where l is

distance on the flame axis to distance s measured from the wall of compartment.

Flame absorptivity, az

‘No forced draught’ - taken as zero.

‘Forced draught’ - equal to the emissivity of flame εz.

Beam

not

eng

ulfe

d in

flam

e

Beam not engulfed in flame


Beam not engulfed in flameBe

am n

ot e

ngul

fed

in fl

ame

Heat transfer by radiation

Bottom of beam does not go below the top level of the opening

The two ways of beam orientation with respect to the external - Beam parallel to compartment wall- Beam perpendicular to compartment wall


am n

ot e

ngul

fed

in fl

ame

Average steel temperature, Tm – Beam parallel to wall

Is calculated at a point on the beam directly above the centre of the opening.

Iz = ϕz εz σ Tz4

Where, ϕz Overall configuration factor of flame opposite to the beamεz Emissivity of flameTz Temperature of flame


am n

ot e

ngul

fed

in fl

ame

Average steel temperature, Tm – Beam perpendicular to wall

Is calculated at every 100mm distance along the length of the beam.

Iz = (ϕz,m εz,m + ϕz,n εz,n ) σ Tz4

Where,ϕz,m Overall configuration factor of beam heated by flames on side mϕz,n Overall configuration factor of beam heated by flames on side nεz,m Emissivity of flames on side mεz,n Emissivity of flames on side nTz Temperature of flame


am n

ot e

ngul

fed

in fl

ame

Emissivity of flame, εz - Beam parallel to wall

In case when there is no balcony or awning, flame thickness is given as

‘No forced draught’ λ = 2h/3‘Forced draught’ λ = x but λ hx/z

h, x and z are taken as per Annex B of EN1991-1-2


am n

ot e

ngul

fed

in fl

ame

Emissivity of flame, εz,m and εz,n - Beam perpendicular to wall

For side m:

For side n:

Where, m number of openings on side mn number of openings on side nλi opening width


am n

ot e

ngul

fed

in fl

ame

Flame thickness - λi

‘No forced draught’ λi = wi

‘Forced draught’ λi = wi + 0.4s

Where, wi Opening widths horizontal distance taken to the point on beam from wall of the

compartment


am n

ot e

ngul

fed

in fl

ame


z

2h/3

Equivalent front rectangle

2h/3

Section Plan


Beam

Beam


No forced draught: Wall above and h<1.25w


am n

ot e

ngul

fed

in fl

ame


No forced draught: Wall above and h>1.25w or no wall above

z

2h/3


2h/3

Section Plan


Beam

Beam


x


am n

ot e

ngul

fed

in fl

ame


Forced draught

h


s

Section Plan


Beam

Beam


x

z

x

w +

0.4

s


am n

ot e

ngul

fed

in fl

ame

Flame temperature, Tz

‘No forced draught’ l = h/2

‘Forced draught’ l = 0 beam parallel to external wall on top of opening

l = sX/x beam perpendicular to external wall with no awning on top of opening, where l is distance along the flame axis to distance s measured from the wall of compartment.

Flame absorptivity, az

‘No forced draught’ - is taken as zero.

‘Forced draught’ - equal to the emissivity of flame εz.

Colu

mn

engu

lfed

in fl

ame

Column engulfed in flame


Column engulfed in flameCo

lum

n en

gulfe

d in

flam

e

Radiative heat flux Iz

with,Iz,1 = C1 εz,1 σ Tz

4

Iz,2 = C2 εz,2 σ Tz4

Iz,3 = C3εz,3 σ To4

Iz,4 = C4 εz,4 σ Tz4

where, Iz,i Heat flux due to radiation on column due to flameεz,1 Flame emissivity with respect to face i of the columni indicator for column faceCi Coefficient of protection for face iTz Temperature of flameTo Temperature of flame at opening


lum

n en

gulfe

d in

flam

e


Forced draught

Column

λ

FlameColumn

Section

d λ4 31

Plan

λ d λ4 31

Flame

λ1

λ2

d2


lum

n en

gulfe

d in

flam

e


No forced draught condition

Column

λ

FlameColumn

Section

d λ4 31

Plan

λ

d λ

4

31

Flame

λ1

λ2

d2 FlameAxis


lum

n en

gulfe

d in

flam

e


Forced draught: Flame axis intersects column axis above top of opening

Column

λ

FlameColumn

Section

d λ4 31

Plan

λ

d λ

4

31

Flame

λ1

λ2

d2 FlameAxis


lum

n en

gulfe

d in

flam

e

Emissivity of flames εz,i for each face of column is found from ε stated in Annex B, EN 1991-1-2, replacing flame thickness λ with dimension λi

Temperature of flame Tz

No forced draught’ l = h/2

Forced draught’ l = (λ3 + 0.5 d1) X/x but l 0.5hX/z, where l is

distance along the flame axis to the level where λ1 is measured with

condition that there is no balcony or awning above the opening.

Flame absorptivity az

Where εz,1 , εz,2 and εz,3 are the emissivities of flame for column faces 1, 2 and 3.

Beam

fully

or p

artia

lly e

ngul

fed

in

flam

e

Beam fully or partially engulfed in flame

Beam fully or partially engulfed in flame

Beam

fully

or p

artia

lly e

ngul

fed

in

flam

eBeam fully or partially engulfed in flame

Radiative Heat Transfer

AssumptionsBeams bottom not going below the top level of the adjoining opening

There are two separate cases, - Beam parallel to the fire compartment wall - Beam perpendicular to the fire compartment wall

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Beam engulfed in flame – No forced draught

λ

Flame

Section

d λ3 41

Elevation

λ d λ3 41

λ

λ

d

1

2

2

Opening

Compartment wall

Beam perpendicular to wall Beam parallel to wall

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Beam engulfed in flame – No forced draught

Top of flame below top of beam Beam immediately adjacent to wall

Flame

Section

λ d3 1

λ

λ

d

1

2

2

Flame

Section

λ d λ3 41

h

λ

d

1

2 z

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Beam engulfed in flame – Forced draught

Beam not adjacent to wall Beam immediately adjacent to wall

Flame

Section

λ d3 1

λ

λ

d

1

2

2

Upper surface of

flame

Flame

Section

λ d3 1

d2λ

1

λ4

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


The average temperature Tm Found at a point along the length of beam just above the midpoint of opening when the beam is parallel to the external wall.

In the case of beam perpendicular to the external wall is found by taking maximum of calculated values at every 100mm along the length of beam.

Heat flux due to radiation Iz due to flame is found by

with, Iz,i heat flux due to radiation Iz from flame to beam face ii Indicator for face of beam

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


No forced draught

- Flame above the top of the beam and when the flame is below the top of beam.

Following equations are used when top of flame is over the upper part of beam

Iz,1 = C1 εz,1 σ To4

Iz,2 = C2 εz,2 σ Tz,24

Iz,3 = C3 εz,3 σ (Tz,14 + Tz,2

4)/2Iz,4 = C4 εz,4 σ (Tz,1

4 + Tz,24)/2

where, εz,i emissivity of flame for face i of the beamTo Temperature at openingTz,1 Temperature of flame at bottom level of beamTz,2 Temperature of flame at top level of beam

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


No forced draught

In case the beam is parallel and directly adjoining the compartment wall, C4 is taken equal to zero.

In case top of flame reaches only below the beam top,


Iz,2 = 0Iz,3 = (hz/d2) C3 εz,3 σ (Tz,1

4 + Tx4)/2

Iz,4 = (hz/d2) C4 εz,4 σ (Tz,14 + Tx

4)/2

where, Tx Temperature of flame at tip [813 K].hz Height of the flame top measure from beam bottom.

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Forced draught

In the case of forced draught condition- Beams placed directly adjoining to the external wall, or - Beam placed not directly adjoining to the external wall

When the beam is placed parallel to the wall and away from the wall or even when the beam is perpendicular to the wall following equations are used


Iz,2 = C2 εz,2 σ Tz,24

Iz,3 = C3 εz,3 σ (Tz,14 + Tz,2

4)/2Iz,4 = C4 εz,4 σ (Tz,1

4 + Tz,24)/2

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Forced draught

If a beam is positioned parallel and directly adjoining to the compartment wall, the bottom face is considered engulfed in flame, while on one side and top of beam is only exposed to radiative heat transfer from the upper portion of the frame.


Iz,2 = ϕz,2 C2 εz,2 σ Tz,24

Iz,3 = ϕz,3 C3 εz,3 σ (Tz,14 + Tz,2

4)/2Iz,4 = 0

Where ϕz,i configuration factor relative to the upper portion of the flame, for face i of the beam, from Annex G in EN 1991-1-2.

Beam

fully

or p

artia

lly e

ngul

fed

in

flam


Emissivity of flame εz,i

Flame emissivity εz,i for each face of beam if found using the formula stated in Annex B of 1991-1-2, using flame thickness λi corresponding to each face of thebeam.

Flame Absorptivity

Absorptivity of flame az is found by using the expression

az = 1 – e-0.3h

The End

Presentation for Dissertation - EuroCode 3

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