Transcript Eurocode 1: Actions on structures

EN1994-1-2:2003
Eurocode 4: Design of composite
steel and concrete structures–
Part 1–2: General rules –
Structural fire design
Annex F [informative]:
Calculation of moment
resistances of partially
encased steel beams
connected to concrete
slabs
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Content
General
Basis of Design
Material Properties
Basic requirements
Actions
Material design values
Verification methods
Structural steel
Concrete
Reinforcing steel
Tabulated data
Annex B
Stress-strain relationships
for siliceous concrete
Mechanical &
thermal properties
Partially encased beams
Composite columns
Unprotected / protected
composite slabs
Design Procedures
Simple Models
Composite beams
Composite columns
Constructional Details
Composite beams
Composite columns
Connections
Advanced Models
Annex I
Planning & evaluation of
experimental models
Annex A
Stress-strain relationships
for structural steel
General aspects
Thermal response
Mechanical response
Validation
Annex C
Stress-strain relationships
for concrete adapted to
natural fires
Annex D
Fire resistance of
unprotected slabs
Annex E
Moment resistance of
unprotected beams
Annex F
Moment resistance of
partially encased beams
Annex G
Simple models for partially
encased columns
Annex H
Simple models for
concrete filled columns
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F.1(1) Flat slab system
The section of concrete slab
is reduced as follows:
regardless
fire classes
fc/γM,fi,c
beff
Compressive
stress in
concrete
Tensile
stress in
steel
-
ef
+
hc,h
hc,fi
hc
h
ew
bc
fay/γM,fi,a
fay,x/γM,fi,a
x
krfry/γM,fi,s
b
kafay/γM,fi,a
Table F.1
Standard fire resistance
Slab reduction hc,fi (mm)
R30
10
R60
20
R90
30
R120 R180
40
55
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F.1(2-3) Other slab systems
trapezoidal profiles
transverse to beam
re-entrant profiles
transverse to beam
hc,fi
hc,fi
hc,fi,min
hc,fi ≥ hc,fi,min
prefabricated
concrete planks
Table F.1
applies
trapezoidal profiles
parallel to beam
hc,fi
hc,fi,min
hc,fi ≥ hc,fi,min
Joint between precast
elements which is unable to
transmit compression stress
hc,fi
heff
For calculation
Annex D
refer to
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F.1(4) Active width of upper flange (b - 2bfi)
(b – 2bfi) varies with fire classes.
Yield strength of steel is taken
equal to fay/γM,fi,a.
fay/γM,fi,a
ef
bfi
bfi
ew
bc
b
Table F.2
Standard fire
resistance
R30
R60
R90
R120
R180
Width reduction bfi of
upper flange
(ef / 2) + (b – bc) / 2
(ef / 2) + (b – bc) / 2 + 10
(ef / 2) + (b – bc) / 2 + 30
(ef / 2) + (b – bc) / 2 + 40
(ef / 2) + (b – bc) / 2 + 60
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F.1(5) Web division
Web is divided into two parts:
h
ew
bc
x
hh
Top part
hl
Bottom part
b
hl are given for different fire classes:
For h/bc ≤ 1 or h/bc ≥ 2
For 1< h/bc < 2
a1 a2ew
hl 

bc
bc h
hl is given directly
in Table F.3
Parameters a1
& a2 are given
in Table F.3
 Next
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Table F.3 Bottom part of web: hl
Standard fire
resistance
a1
[mm2]
3 600
9 500
14 000
23 000
35 000
R30
R60
R90
R120
R180
ef
h
h/bc ≤ 1
a2
[mm2]
0
20 000
160 000
180 000
400 000
hl,min
[mm]
20
30
40
45
55
a1
[mm2]
3 600
9 500
14 000
23 000
35 000
h/bc ≥ 2
a2
[mm2]
0
0
75 000
110 000
250 000
hl,min
[mm]
20
30
40
45
55
a1 a2ew
hl 

bc
bc h
ew
bc
hh
x
hl
b
hl,min ≤ hl ≤ hl,max
= h – 2ef
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Table F.3 Bottom part of web: hl
Standard fire
resistance
1< h/bc < 2
hl,min
[mm]
R30
3600
bc
20
R60
e 
9500
h

 20000 w  2 
bc
bc h 
bc 
30
R90
e
e 
14000
h

 75000 w  85000 w  2 
bc
bc h
bc h 
bc 
40
R120
R180
e
e 
23000
h

 110000 w  70000 w  2 
bc
bc h
bc h 
bc 
e
e 
35000
h

 250000 w  150000 w  2 
bc
bc h
bc h 
bc 
45
55
hl,min ≤ hl ≤ hl,max
= h – 2ef
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F.1(7-8) Section yield strength
fay/γM,fi,a
Top web
h
ef e
w
bc
hh
x
Bottom flange
Standard fire
resistance
R30
R60
R90
R120
R180
Bottom web
hl
f ay, x
kafay/γM,fi,a
The reduced yield
strength depends
on distance x:

x
 f ay 1  (1  k a ) 
hl 

a0 = 0.018 ef + 0.7
Reduction factor ka
ka,min
ka,max
[1.12 – 84 / bc + h / 22bc] a0
[0.21 – 26 / bc + h / 24bc] a0
[0.12 – 17 / bc + h / 38bc] a0
[0.1 – 15 / bc + h / 40bc] a0
[0.03 – 3 / bc + h / 50bc] a0
0.5
0.12
0.06
0.05
0.03
0.8
0.4
0.12
0.10
0.06
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F.1(9) Yield strength of rebars
Yield strength decreases with temperature.
Reduction factor kr depends on fire class & position of
rebar:
kr  (u a3  a4 ) a5 / Am / V
h bc
2h + bc
1
u
1 / ui  1 / usi  1 /(bc  ew  usi )
ew
us
h
bc
3
12
u2
u1,3
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Standard fire
resistance
R30
R60
R90
R120
R180
a3
a4
a5
kr,min
kr,max
0.062
0.034
0.026
0.026
0.024
0.16
-0.04
-0.154
-0.284
-0.562
0.126
0.101
0.090
0.082
0.076
0.1
1
F.1(11) Shear resistance of web
May be verified using the
distribution of the design yield
strength according to (7)
If Vfi,d ≥ 0.5Vfi,pl,Rd
Resistance of reinforced
concrete may be
considered
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Stress in
concrete
F.2 Yield strength of rebars
3b
uh
ul
+
ef
-
bc
h
Stress
in steel
Reduction factor
ks depends on:
Fire classes
Position of rebars
Table F.6
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hc
Bottom bars
u = ui
Top bars
u = hc - uh
hfi
b
Standard fire
resistance
R30
R60
R90
R120
R180
Reduction factor
ks
1
0.022 u + 0.34
0.0275 u – 0.1
0.022 u – 0.2
0.018 u – 0.26
ks,min
ks,max
0
1
F.2(2) Upper flange
F.1(4) applies
as follows:
fay/γM,fi,a
ef
bc
h
hfi
b
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
R30
R60
R90
R120
R180
Width reduction bfi of
upper flange
(ef / 2) + (b – bc) / 2
(ef / 2) + (b – bc) / 2 + 10
(ef / 2) + (b – bc) / 2 + 30
(ef / 2) + (b – bc) / 2 + 40
(ef / 2) + (b – bc) / 2 + 60
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F.2(3) Reduced concrete section
3b
Section is reduced as shown.
Compressive strength:
bc
h bc,fi
hfi
bc,fi
fc/γM,fi,c
b
Standard fire
resistance
R30
R60
R90
R120
R180
hfi
[mm]
≥ 25
165 – 0.4bc – 8(h / bc) ≥ 25
220 – 0.5bc – 8(h / bc) ≥ 45
290 – 0.6bc – 10(h / bc) ≥ 55
360 – 0.7bc – 10(h / bc) ≥ 65
not varying with
fire classes
Table F.7
bc,fi
[mm]
≥ 25
60 – 0.15bc ≥ 30
70 – 0.1bc ≥ 35
75 – 0.1bc ≥ 45
85 – 0.1bc ≥ 55
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F.2(4-5) Yield strength of rebars
F.1(9) applies
as follows:
Reduction factor kr depends on fire
class & position of rebar:
kr  (u a3  a4 ) a5 / Am / V
2h + bc
3b
h
3
12
u2
1
u
1 / ui  1 / usi  1 /(bc  ew  usi )
bc
ew
us
u1,3
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b
h bc
Standard fire
resistance
R30
R60
R90
R120
R180
a3
a4
a5
kr,min
kr,max
0.062
0.034
0.026
0.026
0.024
0.16
-0.04
-0.154
-0.284
-0.562
0.126
0.101
0.090
0.082
0.076
0.1
1
F.2(6-7) Shear resistance
Assumptions:
Shear force is transmitted by
steel web, which is neglected
when calculating the hogging
bending moment resistance.
If Vfi,d ≥ 0.5Vfi,pl,Rd
Resistance of reinforced
concrete may be
considered
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