Eurocode 4: Design of composite steel and concrete structures– EN1994-1-2:2003 Part 1–2: General rules – Structural fire design.

Eurocode 4: Design of composite steel and concrete structures–

EN1994-1-2:2003

www.structuralfiresafety.orgwww.structuralfiresafety.org

Part 1–2: General rules –

Structural fire design

Annex F [informative]:

Calculation of moment resistances of partially encased steel beams connected to concrete slabs

Content

Design Procedures

Annex AStress-strain relationships

for structural steel

Basis of Design

Basic requirementsActionsMaterial design valuesVerification methods

Simple Models

General aspectsThermal responseMechanical responseValidation

Tabulated dataPartially encased beams

Composite columns

Material Properties Mechanical & thermal properties

Structural steel Concrete

Reinforcing steel

General

Advanced ModelsConstructional Details

Composite beamsComposite columns

Connections


Annex BStress-strain relationships

for siliceous concrete

Annex CStress-strain relationships

for concrete adapted to natural fires

Unprotected / protected composite slabs

Composite beams

Composite columns

Annex EMoment resistance of unprotected beams

Annex DFire resistance of unprotected slabs

Annex FMoment resistance of

partially encased beams

Annex GSimple models for partially

encased columns

Annex HSimple models for

concrete filled columnsAnnex I

Planning & evaluation of experimental models


F.1(1) Flat slab system


h

hc

ew

bc

b

ef

beff

+

-

x

Compressive stress in concrete

Tensile stress in

steel

hc,h

hc,fi

fc/γM,fi,c

fay/γM,fi,a

fay,x/γM,fi,a

krfry/γM,fi,s

kafay/γM,fi,a

The section of concrete slab is reduced as follows: regardless

fire classes

Standard fire resistance R30 R60 R90 R120 R180

Slab reduction hc,fi (mm) 10 20 30 40 55

Table F.1

F.1(2-3) Other slab systems


applies

Joint between precast elements which is unable to transmit compression stress

trapezoidal profiles transverse

to beam

Table F.1

re-entrant profiles transverse to

beam

hc,fi hc,fi,min

hc,fi ≥ hc,fi,minprefabricated concrete planks

hc,fihc,fi,min

hc,fi ≥ hc,fi,min

hc,fi

hc,fi

trapezoidal profiles parallel to

beam

heff

Annex DFor calculation

refer to

F.1(4) Active width of upper flange (b - 2bfi)


ew

bc

b

ef

fay/γM,fi,a

(b – 2bfi) varies with fire classes.

Yield strength of steel is taken equal to fay/γM,fi,a.

Standard fire resistance

Width reduction bfi ofupper flange

R30 (ef / 2) + (b – bc) / 2

R60 (ef / 2) + (b – bc) / 2 + 10

R90 (ef / 2) + (b – bc) / 2 + 30

R120 (ef / 2) + (b – bc) / 2 + 40

R180 (ef / 2) + (b – bc) / 2 + 60Table F.2

bfibfi

F.1(5) Web division


ewbc

b

Web is divided into two parts:

hh

x

Top part

Bottom parthl

hbea

ba

hc

w

cl

21

h

hl are given for different fire classes:

For h/bc ≤ 1 or h/bc ≥ 2

For 1< h/bc < 2 hl is given directly in Table F.3

Parameters a1 & a2 are given in Table F.3

Next Next

Table F.3 Bottom part of web: hl



h/bc ≤ 1 h/bc ≥ 2

a1

[mm2]a2

[mm2]hl,min

[mm]a1

[mm2]a2

[mm2]hl,min

[mm]

R30 3 600 0 20 3 600 0 20

R60 9 500 20 000 30 9 500 0 30

R90 14 000 160 000 40 14 000 75 000 40

R120 23 000 180 000 45 23 000 110 000 45

R180 35 000 400 000 55 35 000 250 000 55

= h – 2ef

hl,min ≤ hl ≤ hl,max

ewbc

b

hh

x hl

h

efhbea

ba

hc

w

cl

21

Table F.3 Bottom part of web: hl



1< h/bc < 2hl,min

[mm]

R30 20

R60 30

R90 40

R120 45

R180 55

cc

w

c

w

c bh

hbe

hbe

b270000110000

23000

cc

w

c

w

c bh

hbe

hbe

b2150000250000

35000

cc

w

c

w

c bh

hbe

hbe

b28500075000

14000

cc

w

c bh

hbe

b220000

9500

cb3600

= h – 2ef

hl,min ≤ hl ≤ hl,max

F.1(7-8) Section yield strength


ewbc

hh

x hl

h The reduced

yield strength depends on distance x:

laayxay h

xkff )1(1,

Bottom web

Top web fay/γM,fi,a


Reduction factor ka ka,min ka,max

R30 [1.12 – 84 / bc + h / 22bc] a0 0.5 0.8

R60 [0.21 – 26 / bc + h / 24bc] a0 0.12 0.4

R90 [0.12 – 17 / bc + h / 38bc] a0 0.06 0.12

R120 [0.1 – 15 / bc + h / 40bc] a0 0.05 0.10

R180 [0.03 – 3 / bc + h / 50bc] a0 0.03 0.06

a0 = 0.018 ef + 0.7

ef

kafay/γM,fi,aBottom flange

F.1(9) Yield strength of rebars


ew

bch


a3 a4 a5 kr,min kr,max

R30 0.062 0.16 0.126

0.1 1

R60 0.034 -0.04 0.101

R90 0.026 -0.154 0.090

R120 0.026 -0.284 0.082

R180 0.024 -0.562 0.076

u1,3

VAaaauk mr //)( 543

Yield strength decreases with temperature. Reduction factor kr depends on fire class & position

of rebar:h bc

2h + bc

)/(1/1/11

siwcsii uebuuu

1 2u2

3

us

F.1(11) Shear resistance of web


May be verified using the distribution of the design yield

strength according to (7)

Resistance of reinforced concrete may be

consideredIf Vfi,d ≥ 0.5Vfi,pl,Rd


Fire classes

Position of rebars

F.2 Yield strength of rebars


Reduction factor ks depends on:

hbc

b

ef

3 b

+

Stress in concrete

Stress in steel

hfi

-

-

-

uhul

hc


Reduction factorks

ks,min ks,max

R30 1

0 1

R60 0.022 u + 0.34

R90 0.0275 u – 0.1

R120 0.022 u – 0.2

R180 0.018 u – 0.26

u = uiBottom bars

Top bars u = hc - uh

Table F.6

F.2(2) Upper flange


fay/γM,fi,a

Active width of upper flange: (b – 2bfi) varies with fire classes.

Yield strength of steel is taken equal to fay/γM,fi,a.


Width reduction bfi ofupper flange

R30 (ef / 2) + (b – bc) / 2

R60 (ef / 2) + (b – bc) / 2 + 10

R90 (ef / 2) + (b – bc) / 2 + 30

R120 (ef / 2) + (b – bc) / 2 + 40

R180 (ef / 2) + (b – bc) / 2 + 60

F.1(4) applies as follows:

hbc

b

ef

hfi

F.2(3) Reduced concrete section


fc/γM,fi,c

Section is reduced as shown. Compressive strength:


hfi

[mm]bc,fi

[mm]

R30 ≥ 25 ≥ 25

R60 165 – 0.4bc – 8(h / bc) ≥ 25 60 – 0.15bc ≥ 30

R90 220 – 0.5bc – 8(h / bc) ≥ 45 70 – 0.1bc ≥ 35

R120 290 – 0.6bc – 10(h / bc) ≥ 55 75 – 0.1bc ≥ 45

R180 360 – 0.7bc – 10(h / bc) ≥ 65 85 – 0.1bc ≥ 55

hbc

b

hfi

3 b

bc,fi bc,fi not varying with fire classes

Table F.7

F.2(4-5) Yield strength of rebars



a3 a4 a5 kr,min kr,max

R30 0.062 0.16 0.126

0.1 1

R60 0.034 -0.04 0.101

R90 0.026 -0.154 0.090

R120 0.026 -0.284 0.082

R180 0.024 -0.562 0.076

VAaaauk mr //)( 543

Reduction factor kr depends on fire class & position of rebar:

h bc

2h + bc

)/(1/1/11

siwcsii uebuuu

F.1(9) applies as follows:

h

bc

b

3 b

u1,3

1u2

3

us

2

ew

F.2(6-7) Shear resistance


Assumptions:Shear force is transmitted by steel web, which is neglected when calculating the hogging bending moment resistance.

Resistance of reinforced concrete may be

consideredIf Vfi,d ≥ 0.5Vfi,pl,Rd


Eurocode 4: Design of composite steel and concrete structures– EN1994-1-2:2003 Part 1–2: General rules – Structural fire design.

Documents

fi mm1020304055f

b bc 2r60ef

concrete structuresen1994

section of concrete

concrete tensile stress

encased steel beams

yield strength of steel

hbc 2a1mm2a2mm2hl