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7/30/2019 05a CAJOT Theory EC FireDesign WS
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 1
Fire resistance assessment of composite
steel-concrete structures
Basic design methodsWorked examples
CAJ OT Louis-Guy
CEN/TC250 EG-EN1994-1-2 ConvenorArcelorMittal
email: [email protected]
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 2
Fire resistance assessment ofcomposite steel-concrete structures
Basic design methods of EN1994-1-2
Fire part of Eurocode 4
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 3
Fire parts of Eurocodes 2 to 6 and 9
Following common layout to provide design rules for fire
resistance of various types of structures:
General Scope, application field, definitions, symbols and units
Basic principles
Performances requirements, design values of material propertiesand assessment approaches
Material properties Mechanical and thermal properties at elevated temperatures
Assessment methods for fire resistance
Constructional details
Annexes Additional information: common case - more detailed design rules
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 4
Scope of fire part of Eurocode 4
Load bearing function R of composite structures is covered by the designrules of the fire part of Eurocode 4
Load bearing function of a structure is satisfied only if during the relevant offire exposure t
Efi,d,t Rfi,d,twhere
Efi,d,t: design effect of actions (Eurocodes 0 and 1)
Rfi,d,t: corresponding design resistance of the structure at instant t
In addition, for elements ensuring compartmentation, the separatingfunction has to be maintained during the relevant fire exposure t
IntegrityEThermal insulation I
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 5
hot gas
heat
E - Integrity separating function
I -Thermal insulation separating function I :Calculated temperature
rise under standard fire
140 K
E assumed to be satisfied for composite slabs
Scope of fire part of Eurocode 4
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 6
Scope of fire part of Eurocode 4
Covered field
Composite elements designed according to EN1994-1-1
Longitudinal shear connection between steel and concrete in accordancewith EN1994-1-1 or verified by tests
Typical elements
Steel grades S235, S275, S355, S420 & S460 of EN10025, EN10210-1
and EN10219-1
Profiled steel sheeting following 3.5 of EN1994-1-1
Rebars in accordance with EN10080
Concrete in accordance with EN1994-1-1 except < C20/25 and LC20/22
and > C50/60 and LC50/55
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 7
Application of EC4 for fire resistanceassessment basic knowledge
Actions on structures exposed to fire
Thermal actions
Mechanical actions
Load level in fire situation
Design approaches Member analysis
Analysis of parts of the structure
Global structural analysis
Material properties at elevated temperatures
Thermal properties of steel and concrete
Mechanical properties of steel (sections, rebars)and concrete
Partial factors for fire design of steel structures
Eurocodes 0 and 1
global structural
analysis
member
analysis
analysis of
parts of the
structure
global structural
analysis
member
analysis
analysis of
parts of the
structure
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 8
Application domain of different design methods for composite
structures under fire situation
Thermal action defined under standard fire
Application of EC4 for fire resistanceassessment basic knowledge
Type ofanalysis
Tabulated Data
Simple calculation methods
Critical
temperature
Advanced
calculation
models
Member
analysisYES YES YES YES
Analysis of
parts of the
structureNOT appl icable
Appl icable in
some casesNOT appl icable YES
Global
structural
analysis
NOT applicable NOT applicable NOT applicable YES
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 9
Thermal action defined under natural fire
Application of EC4 for fire resistanceassessment basic knowledge
Application domain of different design methods for composite
structures under fire situation
Type ofanalysis
Tabulated Data
Simple calculation methods
Critical
temperature
Advanced
calculation
models
Member
analysisNOT appl icable
Appl icable with
some specificconditions
YES YES
Analysis of
parts of the
structureNOT applicable NOT applicable YES
Global
structural
analysis
NOT applicable NOT applicable NOT applicable YES
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 10
Thermal properties of steel and concrete at elevated temperatures
Density of steel:7850 kg/m3 ; Density of normal weight concrete:2300 kg/m3
Application of EC4 for fire resistanceassessment basic knowledge
Thermal conductivity[W/mK]
Temperature [C]
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200
steel
concrete (lower/upper limits)0
1
2
3
4
5
6
7
8
9
0 200 400 600 800 1000 1200
steel
concrete (NC)
Thermal capacity (c)[MJ /m3K]
Temperature [C]
Thermal properties of concrete ONLY used in Advanced Calculation Models
li i f f fi i
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 11
Application of EC4 for fire resistanceassessment basic knowledge
Temperature field after 90 minutes of ISO-fire
CONCRETE HE300A
max = 1003C
STEEL CONCRETE column
max = 535C
max = 1003C
STEEL HE300A
CONCRETE column
max = 50C
li i f C f fi i
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 12
Thermal expansion of steel
0
5
10
15
20
0 200 400 600 800 1000 1200
L/L (x103)
Thermal properties of steel and concrete at elevated temperatures
Application of EC4 for fire resistanceassessment basic knowledge
Temperature [C]
steel
concrete
A li i f EC4 f fi i
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 13
Mechanical properties of steel at elevated temperatures
Elastic modulus at 600C
reduced by about 70%
Yield strength at 600C
reduced by over 50%
0 300 600 900 1200
1.0
0.8
0.6
0.4
0.2
Reduction factors
Temperature (C)
Effective yield
strength ky,obtained with
2% strainElastic
modulus
kE,
Normalised stress
Strain (%)
20C 200C 400C
500C
600C
700C
800C
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
2%
Application of EC4 for fire resistanceassessment basic knowledge
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 14
Mechanical properties of concrete at elevated temperatures
Application of EC4 for fire resistanceassessment basic knowledge
Compressive strength at 600C reduced by about 50%
600C
20C
Strain (%)
Normalised stress
cu
200C
400C
800C
1 2 3 4
1.0
0.8
0.6
0.4
0.2
0
Temperature (C)
Strain (%)% of normal value
Strain cu atmaximum
strength
Normal-weightConcrete
Strength
6
5
4
3
2
1
100
50
0400 800 1200
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 15
Mechanical properties of concrete and steel at elevated
temperatures
Application of EC4 for fire resistanceassessment basic knowledge
Temperature (C)
% of normal value
Normal-weightConcrete
Strength
100
50
0400 800 1200
Effective yield
strength ky,obtained with
2% strain
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 16
Partial safety factors of steel/composite at elevated temperatures
MaterialAmbient temperature
designFire
design
Structural steelResistance of cross section
M0 = 1.00 M,fi,a = 1.0
Stability of members M1 = 1.00 M,fi,a = 1.0
Resistance of cross sectionIn tension to fracture
M2 = 1.25 M,fi,a = 1.0
Stud connectors v = 1.25 M,fi,v = 1.0
Steel reinforcing bars s = 1.15 M,fi,s = 1.0
Concrete c = 1.50 M,fi,c = 1.0
Application of EC4 for fire resistanceassessment basic knowledge
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 17
Thermal action defined under standard fire
Application of EC4 for fire resistanceassessment Tabulated Data
Type ofanalysis
Tabulated Data
Simple calculation methods
Critical
temperature
Advancedcalculation
models
Member
analysisYES YES YES YES
Analysis of
parts of the
structureNOT appl icable
Appl icab le in
some casesNOT applicable YES
Global
structural
analysis
NOT applicable NOT applicable NOT applicable YES
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 18
Application of EC4 for fire resistanceassessment Tabulated Data
Tabulated data (steel/concrete composite members)
Composite beams Composite columns
Concretefor insulation
Slab
A li ti f EC4 f fi i t
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 19
Design load in fire situation
Gk,j + 2,1Qk,1 + 2,iQk,ij 1 i 2
Efi,d,t=
Recommended, for practical
application refer to eachNational Annex
relative to roomtemperature design
resistanced
t,d,fi
t,fiR
E=Load level
Application of EC4 for fire resistanceassessment Tabulated Data
Application of EC4 for fire resistance
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 20
Tabulated data and relevant parameters
(composite partially encased columns)
Standard FireResistance
c As
us
us
w
ef
e
b
A h
R30 R60 R90 R120
Minimum ratio of web to flange thickness ew/ef 0,5
1 Minimum cross-sectional dimensions for load level fi,t 0,281.11.21.3
minimum dimensions h and b [mm]minimum axis distance of reinforcing b ars us [mm]
minimum ratio of reinforcement As/(Ac+As) in %
160
-
-
200
50
4
300
50
3
400
70
4
2 Minimum cross-sectional dimensions for load level fi,t 0,472.12.22.3
minimum dimensions h and b [mm]minimum axis distance of reinforcing b ars us [mm]
minimum ratio of reinforcement As/(Ac+As) in %
160
-
-
300
50
4
400
70
4
-
-
-
3 Minimum cross-sectional dimensions for load level fi,t 0,663.13.23.3
minimum dimensions h and b [mm]minimum axis distance of reinforcing b ars us [mm]
minimum ratio of reinforcement As/(Ac+As) in %
160
40
1
400
70
4
-
-
-
-
-
-
Standard
fire rating
Section
dimension
Rebars
cover
Reinforcing
steel
Load level fi,t = Efi.d / Rd
Application of EC4 for fire resistanceassessment Tabulated Data
Application of EC4 for fire resistance
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 21
bc
us
us
hc
c
c
Standard Fire Resistance
R30 R60 R90 R120 R180 R240
1.1
1.2
1.3or
2.1
2.2
2.3
-
-
-
NOTE : *) These values have to be checked according to 4.4.1.2 of EN 1992-1-1
Minimum dimensions hc and bc [mm]
minimum concrete cover of steel section c [mm]
minimum axis distance of reinforcing bars us [mm]
Minimum dimensions hc and bc [mm]
minimum concrete cover of steel section c [mm]
minimum axis distance of reinforcing bars us [mm]
150
40
20*
180
50
30
220
50
30
300
75
40
350
75
50
400
75
50
200
40
20*
250
40
20*
350
50
30
400
60
40
-
-
-
Tabulated data and relevant parameters
(composite encased columns)
Standardfire rating
Section
dimension
Load level fi,t = Efi.d / Rd
Section and
Application of EC4 for fire resistanceassessment Tabulated Data
rebarsCover
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 22
Thermal action defined under standard fire
Type ofanalysis
Tabulated Data
Simple calculation methods
Critical
temperature
Advancedcalculation
models
Member
analysisYES YES YES YES
Analysis of
parts of the
structureNOT appl icable
Appl icable in
some casesNOT appl icable YES
Global
structural
analysis
NOT applicable NOT applicable NOT applicable YES
Establishing fire resistance of compositestructures using simple process
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 23
Simple calculation models and critical temperature for
composite members
Beams (steel or composite) Columns
Establishing fire resistance of compositestructures using simple process
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 24
Critical temperature method for composite beams
Simply determined composite beam
h
hc
> 120mm
Establishing fire resistance of compositestructures using simple process
h < 500mm
h
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 25
Action in fire situation Efi.d.tFIRE RESISTANCE
Buildingregulations
tfi,requClassify member
Load level for fire
design fi,t
Resistance at 20C by fire rulesRfi,d,20
Critical temperature
cr
Find Section Factor
Am/V andksh
Is
crt,fi,requ??
Composite Steel/Concrete
Temperature (UNPROTECTED Steel)
t,fi,requ
fi,t = ky,cr
Establishing fire resistance of compositestructures using simple process
0
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 26
Action in fire situation Efi.d.tFIRE RESISTANCE
Buildingregulations
tfi,requClassify member
Load level for fire
design fi,t
Resistance at 20C by fire rulesRfi.d.20
Critical temperature
cr
Find Section Factor
Am/V andksh
Is
crt,fi,requ??
Steel Temperature
(PROTECTED)
t,fi,requ
fi,t = ky,cr
Establishing fire resistance of compositestructures using simple process
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 27
Critical temperature of steel members
Steel member temperature (assumed to be uniform and equal to bottomflange temperature)
Temperature
crCollapse
Strength reduction of
steel member
Stable structure
Establishing fire resistance of compositestructures using composite process
fi,t
0.0
0.2
0.4
0.6
0.8
1.0
Degreeofutilisation
Establishing fire resistance of composite
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 28
Simple Calculation Models
Steel elements
(sections, Steel Sheet, Rebars)
Concrete
ky, fy,
Establishing fire resistance of compositestructures using composite process
ks, fs,
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 29
Simple Calculation Models
No tabulated data
Simplified calculation (4.3)
Only for use with ISO fire
Integrity criteria E is assumed always satisfiedThermal insulation I
Composite slab fire design
Criteria:Tmax 180 KTaverage 140 K
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 30
Simple Calculation Models
The fire resistance ti [min] corresponding to criteria I is given by
with
exposed perimeter: Lr
area: A1
h2
h1
3
2
3r5
34
r32110i
1
L
Aa
1a
L
Aaahaat
+++++=
221222
212
r
2h2
2h
L
A
++
+
=
3
2
2122
2
213
22
2h
2h
+
++=
Table D.1: Coefficients for determination of the fire resistance with respect to thermal insulation
a0[min]
a1[min/mm]
a2[min]
a3[min/mm]
a4[mm min]
a5[min]
Normal weight concrete -28,8 1,55 -12,6 0,33 -735 48,0
Lightweight concrete -79,2 2,18 -2,44 0,56 -542 52,3
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 31
Simple Calculation Models
exposed perimeter: Lr
area: A
13
2
exposed perimeter: Lr
area: A
1
h2
h1
3
2
3
2
2122
2
213
22
2h
2h
+
++=
is the view factor FA,Bcalculated by the rule of
Hottel
A
B
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 32
Alternative method : minimum effective thickness
Simple Calculation Models
heff
Table D.6: Minimum effective thickness as a function of the standard fire resistance.
Standard Fire Resistance Minimum effective thickness
heff [mm]
I 30
I 60
I 90
I 120
I 180
I 240
60
80
100
120
150
175
-3
h
- 3h
- 3h
- 3h
- 3h
- 3h
(1) The effective heffis given by the formula :
+
++=
31
2121eff h5,0hh
+
+
+= 3121
1eff 75,01hh
for h2 / h1 1,5 and h1 > 40mm
for h2 / h1 > 1,5 and h1 > 40mm
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 33
Simple Calculation Models
0
60
120
180
240
0 50 100 150 200heff+ h3 [mm]
I[min
]
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 34
Simple Calculation Models
No tabulated data
Simplified calculation (4.3)
Only for use with ISO fire
Integrity criteria E is assumed always satisfiedThermal insulation I
Load bearing capacity R
Composite slab fire design
If the design conforms to EN 1994-1-1, R 30
minutes.For composite slabs, the bending capacity has to bedetermined by a plastic design.
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 35
Simple Calculation Models
Composite slab fire design
Temperature field
243
r2
310a ab
L
Ab
1bb ++++=
(D.2.1)
The temperature a of the lower flange, web and upper flange of the steel decking may be given by:
Concrete
Fire
resistance
[min]
Part of the steel
sheet
b0
[oC]
b1
[oC]. mm
b2
[oC]. mm
b3
[oC]
b4
[oC]
Normal
weight
concrete
60
Lower flangeWeb
Upper flange
951661340
-1197-833-3269
-2,32-2,96-2,62
86,4537,71148,4
-150,7-351,9-679,8
90
Lower flangeWeb
Upper flange
1018816618
-839-959-2786
-1,55-2,21-1,79
65,1464,9767,9
-108,1-340,2-472,0
120
Lower flangeWeb
Upper flange
1063925770
-679-949-2460
-1,13-1,82-1,67
46,7344,2592,6
-82,8-267,4-379,0
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 36
Simple Calculation Models
Composite slab fire design
Temperature field
354
r32
2
310s
1cc
L
Aczc
h
ucc
+++++= (D.2.2)
The temperature s of the reinforcement bars in the rib, if any according to figure D.2.1, as follows:
321 u
1
u
1
u
1
z
1++=
Concrete Fire resistance [min]c0
[oC]
c1
[oC]
c2
[oC]. mm0.5
c3
[oC].mm
c4
[oC/o]
c5
[oC].mm
Normal
weight
concrete
60 1191 -250 -240 -5,01 1,04 -925
90 1342 -256 -235 -5,30 1,39 -1267
120 1387 -238 -227 -4,79 1,68 -1326
Table D.2.2 : Coefficients fo r the determination of the temperatures of the reinforcement bars in the rib.
Si l C l l i d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 37
Simple Calculation Models
Composite slab fire design
T
fy(T)
SteelReinforcing
steelConcrete
Temperature[C]
fy(T)/fy fsy(T)/fsy fc(T)/fc
20 1.00 1.00 1.00
100 1.00 1.00 1.00
200 1.00 1.00 0.95300 1.00 1.00 0.85
400 1.00 0.94 0.75
500 0.78 0.67 0.60
600 0.47 0.40 0.45
700 0.23 0.12 0.30
800 0.11 0.11 0.15
900 0.06 0.08 0.08
1000 0.04 0.05 0.04
1100 0.02 0.03 0.01
1200 0.00 0.00 0.00
ky, fy,ks, fs,
Si l C l l i M d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 38
Simple Calculation Models
Bending capacity in sagging moment Mfi,Rd
x
Design moment resistance
The plastic neutral axis of a composite slab or composite beam may be determined from :
The design moment resistance Mfi,t,Rd may be determined from :
=
=
=
+
m
1j c,fi,M
j,cj,,cjslab
n
1i a,fi,M
i,yi,,yi 0
fkA
fkA 85,0slab =
=
=
+
=
m
1j c,fi,M
j,cj,,cjjslab
n
1i fi,M
i,yi,,yiiRd,t,fi
fkzA
fkzAM
+
Si l C l l ti M d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 39
X
Y
I II
III
IV
(0 , YI) (XII , YI)
(XIII , YIII)
(XIV, YIV)
Isotherm for =lim
Simple Calculation Models
Temperature field
3
54
r
32
2
310s
1ccL
Aczch
ucc +++++=
Xi and Yi = f(z)
343
r2s10lim
1dd
L
AdNdd
++++=with
and
Bending capacity in hogging moment Mfi,Rd-
z is obtained from the equation for the determination of s, assuming that u3/h2= 0,75 and s= lim
Si l C l l ti M d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 40
Simple Calculation Models
h2
YI
If YI> h2 Alternative procedure based on the effective thickness
Bending capacity in hogging moment Mfi,Rd-
Si l C l l ti M d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 41
Simple Calculation Models
heff
x
heff c
Heated lower side of slab
x
Depth
X[mm]
Temperature c [C] after a fire duration in min. o f30 60 90 120 180 240
510
535470
705642 738
1520
415350
581525
681627
754697
2530
300250
469421
571519
642591
738689 740
3540
210180
374327
473428
542493
635590
700670
4550
160140
289250
387345
454415
549508
645550
5560
125110
200175
294271
369342
469430
520495
80100
8060
140100
220160
270210
330260
395305
Bending capacity in hogging moment Mfi,Rd-
Si l C l l ti M d l
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Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 27-28 November 2012 42
Simple Calculation Models
Bending capacity of the composite slab
+Rd,fiM
D,Rd,fiM
G,Rd,fiM
8
p 2fi
8p
2
fi
+Rd,fiM
8
pM
2
MM 2fi
Rd,fiD,Rd,fiG,Rd,fi +
+ +
Si l C l l ti M d l
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Simple Calculation Models
Rd,fiM
8
p 2fi +Rd,fiM
8
pM
2
M 2fi
Rd,fiRd,fi + +
( ) ( ) 4MM2M4
M
2
M
8
p 5.02Rd,fi
2
Rd,fiRd,fiRd,fiRd,fi
2fi
+++=
++
Bending capacity of the composite slab
Si l C l l ti M d l
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Simple Calculation Models
Composite beam fire design
Temperature field
b1
hw
b2
beff
e2
e1
ew h
hc
thV
A
c
1k net
i
i
aashadowt,a
=
Upper flange
Lower flange
Web
1111ii,pii eb/)eb(2V/AorV/A +=
2222ii,pii eb/)e2b(V/AorV/A +=
2222ii,piieb/)eb(2V/AorV/A +=
If the beam depth h does not exceed500mm, the temperature of the web may betaken as equal to that of the lower flange.
heff c
Heated lower side of slab
x
Depth
X
[mm]
Temperature c [C] after a fire duration in min. o f30 60 90 120 180 240
510
535470
705642 738
1520
415350
581525
681627
754697
2530
300250
469421
571519
642591
738689 740
3540
210180
374327
473428
542493
635590
700670
4550
160140
289250
387345
454415
549508
645550
5560
125110
200175
294271
369342
469430
520495
80100
8060
140100
220160
270210
330260
395305
Simple Calculation Models
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Simple Calculation Models
Structural behaviour - Bending moment resistance model MRd+
Classical determination of the bending moment resistance, taking into accountthe variation of material properties with temperatures, see Annex E.
No strength reduction in concrete if T < 250C
The value of the tensile force is limited by the resistance of the shear
connectors :
Composite beam fire design
Rd,fiPNT +
Simple Calculation Models
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Simple Calculation Models
Structural behaviour - Bending moment resistance model MRd+
Composite beam fire design
Pfi,Rd = minimum of the 2 following values:
with
Verification of the stud connectors
m,fi used instead of
ku, and kc, defining the decrease of material strength
u in the stud = 0.80 upper flange
c of the concrete = 0.40 upper flange
with PRd obtained from equation 6.18 of EN1994-1-1
with PRd obtained from equation 6.19 of EN1994-1-1
Rd,uRd,fi Pk8,0P =
Rd,cRd,fi PkP =
Simple Calculation Models
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Simple Calculation Models
Composite beam fire design
Hogging moment resistance at an intermediate support
Choose the effective width of the slab to have the slab completely cracked,but beff(T) beff(20C).
Tension
Compression
beff
As
hc
h
b2
hw
e2
e1
ew
b1
2
w
1
fs s M fiy , ,s( ) /
fa 2 M fiy , ,a( )/
fa w M fiy , ,a( ) /
fa M fiy , ,a( ) / 1
YF
YT
T
F
If web or lower flange are Class 3, reduce its width according to EN 1993-1-5.If web or lower flange are Class 4, its resistance may be neglected.
Note: classification according to EN1993-1-2 [ ] 5,0yf/23585,0=
Simple calculation model for
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pcomposite members
Beams Columns
Simple calculation model for
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pcomposite members
Partially Encased Beam
Sagging moment Mfi,Rd+
3 b
b
h
bfi b
bc
hc
u
ef
uh
bc,fibc,fi
hfi
ew(A)
(B)
krfry M,fi,s
fc M,fi,c
fay M,fi,a
ks fsy M,fi,s
+
fi
+
-
-
-
-
Hogging moment Mfi,Rd-
Simple calculation model for
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pcomposite members
Beams Columns
Simple calculation model for
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)V/A(k mtt,0t,f +=
pcomposite members
Partially Encased Column
Z
Yh
ef
b
ewu2
u1
bc,fi
bc,fihw,fi
)h/H16,0(1ff tC20,w,ayt,wmax,a =
Table G.5: Reduction f actor ky,t
for the yield point fsy,20C
of the reinforcing bars
u[mm]StandardFire Resistance
40 45 50 55 60
R30 1 1 1 1 1
R60 0,789 0,883 0,976 1 1
R90 0,314 0,434 0,572 0,696 0,822
R120 0,170 0,223 0,288 0,367 0,436
Table G.6: Reduction f actor kE,t
for the modulus of elasticity Es,20C
of the reinforcing bars
u[mm]StandardFire Resistance
40 45 50 55 60
R30 0,830 0,865 0,888 0,914 0,935
R60 0,604 0,647 0,689 0,729 0,763
R90 0,193 0,283 0,406 0,522 0,619
R120 0,110 0,128 0,173 0,233 0,285
R30 R60 R90 R120
Am/V[m-1]
c,t[C]
Am/V[m-1]
c,t[C]
Am/V[m-1]
c,t[C]
Am/V[m-1]
c,t[C]
42346--
--
136300400
--
--
492150-
--
214300400600
-
--
46133354
--
256300400600800
--
4592338
4143
265300400600800
9001000
StandardFire
Resistance
0,t
[C]
kt
[mC]
R30 550 9,65
R60 680 9,55
R90 805 6,15
R120 900 4,65
Simple calculation model for
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pcomposite members
Partially Encased Column
)h/H(16,011)e2h(5,0h tffi,w =
where Ht is given in table G.2
Standard FireResistance
Ht[mm]
R 30 350
R 60 770
R 90 1100
R 120 1250
Z
Yh
ef
b
ewu2
u1
bc,fi
bc,fihw,fi
Standard Fire
Resistance
bc,fi[mm]
R 30 4,0
R 60 15,0
R 90 0,5 (Am/V) +22,5
R 120 2,0 (Am/V) +24,0
Simple calculation model for
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composite members
Partially Encased Column
Buckling curve "c" of EN 1993-1-1
fi,s,zs,fi,c,zc,fi,w,zw,fi,f,zf,fi,eff,z (EI)(EI)(EI)(EI)(EI) +++=
fi,pl,Rd,sfi,pl,Rd,cfi,pl,Rd,wfi,pl,Rd,ffi,pl,Rd NNNNN +++=
where i, is a reduction coefficient depending on the effect of thermal stress.
The values ofi, are given in Table G.7
Standard fi re
resistancef, w, c, s,
R30 1,0 1,0 0,8 1,0
R60 0,9 1,0 0,8 0,9
R90 0,8 1,0 0,8 0,8
R120 1,0 1,0 0,8 1,0
Table G.7
Simple calculation model fori b
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composite members
Beams Columns