Eurocode 4: Design of composite steel and concrete structures– EN1994-1-2:2003 Part 1–2:...
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Transcript of Eurocode 4: Design of composite steel and concrete structures– EN1994-1-2:2003 Part 1–2:...
Eurocode 4: Design of composite steel and concrete structures–
EN1994-1-2:2003
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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
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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
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F.1(1) Flat slab system
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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
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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)
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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
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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
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Standard fire resistance
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
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Standard fire resistance
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
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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
Standard fire resistance
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
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ew
bch
Standard fire resistance
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
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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
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Fire classes
Position of rebars
F.2 Yield strength of rebars
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Reduction factor ks depends on:
hbc
b
ef
3 b
+
Stress in concrete
Stress in steel
hfi
-
-
-
uhul
hc
Standard fire resistance
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
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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.
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 + 60
F.1(4) applies as follows:
hbc
b
ef
hfi
F.2(3) Reduced concrete section
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fc/γM,fi,c
Section is reduced as shown. Compressive strength:
Standard fire resistance
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
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Standard fire resistance
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
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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
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