Fire resistant steel
• Fire proof steel
– For industrial structures (furnaces, etc.) exposed to 600 °C to 1200 °C
• Fire resistant steel
– Fine crystal structure(reduced sulfur content)
– Addition of molybdenum andniobium
Used at EXPO 2000 in Hannover -The Christ Pavilion
9
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Fire resistant steel FRS275N
Increased yield limit at temperature 600˚C
10
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0100 200 300 400 500 600 700 800 900 1000 1100 12000
standard steelky,
standard steelkE,
Temperature, °C
steel FRS275Nky,
steel FRS275NkE,
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Critical temperature
11
8006004002000
Stress, MPaResistance of element
Load at fire situation
Critical temperature
Temperature, °C700500300100 8006004002000
Utilization factor,
Critical temperature
Temperature, °C700500300100
μ0
Surplus resistance
Collapse
1,0
0,8
0,6
0,4
0,2
0,0
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Critical temperature
• Attention!
• The formula is applicable only to elements whose resistance depends on the yield limit only (no stability effects)
12
Utilization factor μ0
482196740
11939 8333
,
0cr,a
μ,ln,θ
fi,d,0
fi,d0 R
Eμ
Load at fire
Resistance at fire at temperature 20˚C
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Classification at normal temperature
… at normal temperature
where
13
yf235
Element Class 1 Class 2 Class 3
Flange c/tf=10
Web in bending
Web in compression
c/tf=11 c/tf=15
d/tw=72
d/tw=33
d/tw=83
d/tw=38
d/tw=124
d/tw=42
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Classification
The slenderness
The general formula
after simplification
14
kt4,28b
p
k123512E
tb
2
2p
k
fE904,0
tb
kfE
112
tb
kf
235123512E
tb
yy2
2
y2
2p
t
c
d
rw
tf
both values depend on the temperature
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Classification
The factor ε is used at normal temperature
It needs to be modified at high temperature
Simplified approach is used in standards
15
yf235
yf23585,0
y,y
,E
y,y
,E
,y fE
kk
fkEk
fE
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Classification at high temperature
… at high temperature
reduced ε
16
Element Class 1 Class 2 Class 3
Flange c/tf=10
Web in bending
Web in compression
c/tf=11 c/tf=15
d/tw=72
d/tw=33
d/tw=83
d/tw=38
d/tw=124
d/tw=42
yf23585,0
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Elements in tension
Elements with uniform temperature distribution in the cross-section
Non-uniform temperature distribution
17
fi,M
y,yRd,t,fi
fkAN
fi,M
n
iyi,,yi
Rd,t,fi
fkAN
1
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Laterally restrained beams, Class 1 and 2
Uniform temperature distribution (constant temperature)
Non-uniform temperature distribution (general method)
– neutral axis
– bending moment resistance
18
fi,M
y,yy,plRd,t,fi
fkWM
NN
fi,M
n
iyii,,yi
Rd,t,fi
fzkAM
1
temperature stress
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Laterally restrained beams, Class 1 and 2
Non-uniform temperature distribution (alternative method)
Adaptation factors– Factor κ1 to take into account non-uniform temperature of
the cross-section• κ1 = 1,00 for beams exposed on four sides
• κ1 = 0,70 for beams exposed on three sides with concrete slab on the fourth side
– Factor κ2 to take into account non-uniform temperature of the beam
• κ2 = 0,85 for intermediate supports of statically indetermined beams
• κ2 = 1,00 in other cases19
fi,M
y,yy,pl
21Rd,t,fi
fkWκκ
M
1
= 0,701
= 0,852
= 1,002
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Laterally restrained beams, Class 3
Uniform temperature distribution (constant temperature)
Non-uniform temperature distribution
the maximum temperature of the cross-section should be used for evaluation of moment resistance
20
fi,M
y,yy,elRd,t,fi
fkWM
fi,M
ymax,,yy,pl
21Rd,t,fi
fkWκκ
M
1
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Beams (shear resistance)
All sections
21
fi,M
yz,Vweb,,yRd,t,fi
fAkV
3
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Buckling resistance
For sections of class 1, 2 and 3– the maximum temperature should be used for non-uniform
temperature
– only one buckling curve with the imperfection factor α
Slenderness
Buckling reduction factor
where
22
fi,M
ymax,,yfiRd,t,fi,b
fkAN
yf, 235650
21 2
22
1
fi
,E
,y
kk
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Buckling reduction factors
23
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,0 0,4 1,0 1,4 2,0
0,2 0,6 0,8 1,2 1,6 1,8
0,21 - curve a0,34 - curve b0,49 - curve c0,76 - curve dfire - 500°Cfire - 700°C
0,13 - curve a 0
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Buckling resistance of element
24
0 50 100 150 2000
500
1000
1500
2500
2000
100×100×3,5steel S235
Slenderness
Resistance , kNNb,fi,t,Rd
25 75 125 175
20°C
300°C400°C
500°C
600°C
700°C800°C
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Reduction of buckling length of columns
• Generally, the buckling lengths at fire are the same as those at normal temperature
• The buckling lengths for multi-storey buildings can be reduced, when– it is non-sway structure
– there are separate fire compartments in each storey
– the floors have the same or higher fire resistance than the columns
25
0,7 L
0,5 L
0,7 L
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Unrestrained beams
• Beams with class 1 and class 2 sections– reduction of the yield limit is based on the temperature of
the compressed flange– the maximum temperature can be also used (conservative
approach)
• Beams with class 3 sections
Slenderness
Buckling reduction factor where
26
fi,M
ycom,,yy,plfi,LTRd,t,fi,b
fkWM
fi,M
ycom,,yy,elfi,LTRd,t,fi,b
fkWM
21 2
,LT,LT
,LT
22
1
,LT,LT,LT
fi,LT
,E
,yLT,LT k
k
yf, 235650
Imperfection factor
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Buckling reduction factor (lateral torsional instability)
27
LT,
LT,
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,0 0,4 1,0 1,4 2,0
0,2 0,6 0,8 1,2 1,6 1,8
0,21 - curve a 0,34 - curve b0,49 - curve c0,76 - curve d
fire - 500°Cfire - 700°C
hot-rolled H sections
hot-rolled I sections
welded H sections
welded I sections
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Bending and compression
• For class 1 and class 2 sections
– restrained elements (no lateral torsional instability)
– unrestrained elements (with lateral torsional instability)
• For class 3 sections
– similarly, but elastic section modulus is used
28
1
fi,M
y,yz,pl
Ed,zz
fi,M
y,yy,plfi,LT
Ed,yLT
fi,M
y,yfi,z
EdfkW
MkfkW
MkfkA
N
1
fi,M
y,yz,pl
Ed,zz
fi,M
y,yy,pl
Ed,yy
fi,M
y,yfimin,
EdfkW
MkfkW
MkfkA
N
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Class 4 sections
29
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,90
200
100
300
400
500
600
700
800Critical temperature ,°C
μ0
Utilisation factor,
a,cr
Elements with class1, 2 and 3 sections
Thin walled elements in tension
Beams with class 4 sectionsColumns with class 4 sections
1,0
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Class 4 sections
• As an alternative method, the resistance of thin-walled elements can be evaluated the same way as for class 3 sections, but effective section properties should be used
• The effective section properties can be evaluated at normal temperature
• The reduction factor for thin-walled sections (both, hot-rolled and cold-formed) is different from the factor for hot-rolled sections
30
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Reduction factors for thin-walled sections
• The reduction factors are used for thin-walled sections – cold-formed– hot-rolled, welded
31
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0100 200 300 400 500 600 700 800 900 1000 1100 12000
Reduction factor
for yield limit of hot-rolled sectionsky,
for yield limitky,
for modulus of elasticitykE,
Temperature, °C
of thin-walled sections
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Joints
• The joints are usually not the critical part of the structure, as the temperature is lower than the temperature of the connected elements
• There are requirements for structural integrity
To check resistance of the joints:• The temperature is the most important• The methods:
– simplified models for temperature– calculation using step by step method
with A/V ratio for the joint• The resistance calculation
can be based on component method adopted for high temperatures
32
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Temperature of the joints
Pictures from thermo cameras used to measure the beam to beam and beam to column connectionsa) Heating phase (30 min) b) The maximum temperature (54 min)
c) Cooling phase (69 min) d) The end (240 min)
33
31,5°C
945,9°C
200
400
600
800
SP01SP02SP03
430,0°C
750,0°C
500
600
700
SP01
SP02SP03
25,0°C
250,0°C
50
100
150
200
250
SP01SP02SP03
20,0°C
635,0°C
200
400
600
SP01SP02SP03
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Simplified model for temperature
Temperature of the beam supporting the concrete slab is based on beam temperature in the mid spanh < 400 mm
h > 400 mm
34
hh
,, k0h 301880
2pro21201880
2pro880
hhhh
,,
hh,
kk
0h
k0h
Concrete slab
h
400 mm0,62
0,75
0,88
> 400 mm
0,70
0,88
0,88
hk
0
0
0
h h0
0
0
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Temperature of the joint
Temperature of the joint depends on the location of the elements (bolts, weld, etc.)
35
hhk
720°C664°C
425°CIPE 360460°C
300
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Temperature by step by step method
Splice connection of the lower chord of the truss, R45 required
Unprotected connection
the fire resistance is 44 min 45 sec (standard curve)
Protected connection (protection thickness 15 mm)
the fire resistance is 112 min (standard curve)
36
4 × M24
P 28
85 125 40 45
150500 kN 500 kN
1m1843241
054 ,,
,VAm
13KWm288015010
241054
,,
,,
dVA
p
pp
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Reduction factors
EN 1993-1-2 gives the reduction factors for• bolts• welds
37
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0100 200 300 400 500 600 700 800 900 1000 1100 12000
Reduction factor
for yield limitky,
for weldskw,
for boltskb,
Temperature, °C
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Component method
Components– Resistance
– Stiffness
– Deformation
Joint– Resistance
– Stiffness
38
i,y,i FkF
i,E,i kkk
i,E
,y
,i
,i,i k
kkF
Rd,j,yRd,,j MkM
i ,i
,ini,j
k
zES
1
2
, mrad
M, kNm 20 ºC
800ºC
500ºC100ºC
50
0200 10040 60 80
600ºC
700ºC
M z
6070
203040
10
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Structural integrity
Axial force in the joint for various fire scenarios
39
Heating Cooling 720°C
I. Part of the beam (localised fire)II. Single beamIII. The whole floor
Axial force, kN
Time, min
The frame 60 80
300
200
100
0
-100
-200
- 300
20
100
40
4 × 6,0 m
The analysed joint 6 × 3,75 m
I. II. III.
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Comparison of different joints
40
Heating Cooling
Axial force, kN
100
-120-100-80-60-40-20
020406080
0
10 20 30 40 50 60 70 80 90Time, min
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Conclusion
41
• Simple design models for steel structures• Based on design at ambient temperature• Knowledge of material behaviour at high
temperature is necessary
• Joints usually do not represent critical part of the structure, no specialised check is necessary
• Simple temperature model for joints is available
• Proper detailing of joints ensuring structural integrity is very important
Introduction
Properties of steel at high
temperatures
Design models for structural
elements
Design models for joints
Conclusion
Thank you for your attention
Zdeněk SokolFrantišek Wald
České vysoké učení technické v Praze
URL: www.ocel-drevo.fsv.cvut.cz