European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
2
Objectives of the lecture
• Summary of structural aluminium and steel design
at ambient temperature
• Properties of structural aluminium
• Particularities of aluminium fire design
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
3
Outline of the lecture
� Introduction� Thermal properties� Mechanical properties� Transfer of heat
� Unprotected elements� Protected elements
� Elemental analyses� Classification of sections� Columns� Beams� Critical temperature
� Summary� Worked example
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Structural aluminium/steel behaviour?
Ambient temperature
• Stress-strain diagram
– No yield stress
– Modulus of elasticity 1/3 of steel
– Lower ductility
• Different production of sections
– Majority wrought aluminium
– Buckling curves more favourable
• Heat affected zones HAZ
• Reduction of material properties
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Structural aluminium/steel design?
Ambient temperature
• Diferent procedures
– HAZ for resistance
– HAZ for stability
– Lugs for stiffening
– Material model
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Structural aluminium/steel design?
Ambient temperature
• Standards different structure
• EN 1999 Design of Aluminium Structures:
– EN 1999-1-1 General structural rules
– EN 1999-1-2 Structural fire design
– EN 1999-1-3 Structures susceptible to fatigue
– EN 1999-1-4 Cold-formed structural sheeting.
– EN 1999-1-5 Shell structures
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
7
Relative thermal elongation
� As a function of the temperature
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
8
Relative thermal elongation
� Mathematical model
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
9
Specific heat of aluminium
0
200
400
600
800
1000
1200
1400
0 200 400 600 800 Teplota, °C
prEN 1999-1-2
Měrné teplo, J/ (kg K)
Tavenina
� As a function of the temperature
Liquid alloy
Temperature, °C
Specific heat J/kg K
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
10
Specific heat of aluminium
200
600
800
1000
1200
0
400
5004003002001000
θal
/ °C
cal
/ (J/kg°C)
alc
� Mathematical model
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
11
Thermal conductivity
of aluminium alloy λal
�The thermal conductivity for 0 ºC < θal
< 500 ºC
0
50
100
150
200
250
0 100 200 300 400
Tepelná vodivost, W m K
Teplota, °C
5000 a 7000
-1 -1
Řada 1000, 3000 a 6000
Řada 2000, 4000,
Series
Temperature, °C
Thermal conductivity, W/m K
Series
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
12
Thermal conductivity
� Mathematical model
50
150
200
250
0
100
5004003002001000
θal
/ °C
λal
/ (W/m°C) A
B
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
13
Mechanical properties
of aluminium alloys
� At 20 °C should be taken as those given
in EN 1999-1-1 for normal temperature design
� For up to 2 hours thermal exposure period
� 0,2 % proof strength at elevated temperature
fo,θ = ko,θ ⋅ fo
where
fo,θ is 0,2 proof strength at elevated temperature
fo is 0,2 proof strength at room temperature
according to EN 1999-1-1
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
14
0,2 % proof strength
at elevated temperature
� 0,2% proof strength ratios ko,θ
� Two tables
� Lower limits
Aluminium alloy temperature °C
20 100 150 200 250 300 350 550
Lower limit values 1,00 0,90 0,75 0,50 0,23 0,11 0,06 0
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
15
0,2 % proof strength
at elevated temperature
� 0,2% proof strength ratios ko,θ
� Two tables for different alloys and tempers
0
0,1
0,3
0,4
0,5
0,6
0,7
0
0,2
0,8
1,0
0,9
500400300200100
6061-T66063-T5
E
6063-T6
6082-T6
6082-T4
θal
/ °C
ko,θ
Eal,θ
Eal
3004-H34
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
16
0,2 % proof strength
at elevated temperature
� 0,2 % proof strength ratios ko,θ
� Two tables for different alloys and tempers
0
0,1
0,3
0,4
0,5
0,6
0,7
0
0,2
0,8
1,0
0,9
500400300200100
5454-O
E
5005-O
5005-H14
5083-H12
5052-H34
θal
/ °C
ko,θ
Eal,θ
Eal
5454-H34
5083-O
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
17
Exposure period
300
200
400
100
015 30 60 3600
log min.
200 °C
160 °C
250 °C
300 °C Doba vystavení prvku
Mez úměrnosti, MPa
zvýšené teplotě,
prEN 1999-1-2: 2004
Time of
exposure
log min
0,2 proof strength fo,θ N/mm2
Time
of
exposure
log min
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
18
Modulus of elasticity Eal,θ
� Ratio E = Eal,θ/Eal for aluminium alloys
at elevated temperature θal °C Aluminium alloy
temperature,θ
(°C)
Modulus of elasticity,
Eal,θ
(N/mm²)
20 70 000
50 69 300
100 67 900
150 65 100
200 60 200
250 54 600
300 47 600
350 37 800
400 28 000
550 0
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
19
Modulus of elasticity Eal,θ
� Ratio E = Eal,θ/Eal for aluminium alloys
at elevated temperature θal °C
0
0,1
0,3
0,4
0,5
0,6
0,7
0
0,2
0,8
1,0
0,9
500400300200100
5454-O
E
5005-O
5005-H14
5083-H12
5052-H34
θal
/ °C
ko,θ
Eal,θ
Eal
5454-H34
5083-O
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Assessment 1
• What thermal exposure is expected for
aluminium alloys during fire?
• When starts at elevated temperature the
reduction of 0,2 % proof strength?
20
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
21
Unprotected aluminium
temperature development
� Simple analytical model
� Step by step procedure (the lumped mass method)
∆t should not be taken as more than 5 s
Am/V the section factor should not be taken as less than 10 m-1
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
22
Section factor
for unprotected aluminium members
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
23
Section factor
for unprotected aluminium members
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
24
Section factor
for unprotected aluminium members
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
25
Grooves with gap in the surface
� The calculation of the exposed surface area
� Grooves with gap in the surface less than 20 mm
should not be included in the exposed surface
area.
� Grooves with gap in the surface > 20 mm,
the area of the groove should be included
in the area of the exposed area
< 20 mm > 20 mm
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
26
Surface emissivity ����m
� The values of net,d
should be obtained from EN 1991-1-2 using
�m = 0,3 for clean uncovered surfaces
�m = 0,7 for painted and covered
(e.g. sooted) surfaces
hɺ
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
27
Surface emissivity ����m
100
200
300
400
5 10 15 20 25
Teplota prvku , °C
25A / V =m355075150200300 100125
150200300 125 3550100 25A / V =m
εm = 0,7
00
εm = 0,3
Čas, min.
Součinitel průřezu
Time, min
Element
temparature, °CSection factor
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Aluminium element
insulated by fire protection
materialFor a uniform temperature distribution
in a cross-section, the temperature increase
28
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Section factor Ap/V
for insulated members
29
Sketch Description Section factor (Ap/V)
Contour encasement of uniform thickness, exposed to fire on four sides.
area section-cross aluminium
perimeter aluminium
b
h
Hollow encasement of uniform thickness, exposed to fire on four sides.
area section-cross aluminium
) + ( 2 hb
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Section factor Ap/V
for insulated members
30
b
Contour encasement of uniform thickness, exposed to fire on three sides.
area section-cross aluminium
- perimeter aluminium b
b
h
Hollow encasement of uniform thickness, exposed to fire on three sides.
area section-cross aluminium
+ 2 bh
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
31
Design tools TALAT
� Reference thickness of fire protection
dp = k dp,ref (k based on material form 0,4 to 1,4)
V
Ap
0
200
300
400
500
0 5 10 15 20 25 30
Teplota, °C
=
= 25 m
100
200 300
150
200
300
-1
V
Ap
10025
50
100
150
Tloušťka pož. ochr., ,mm
R 30
Požární
PožárníodolnostR 15 50
odolnost
dp
m-1
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Assessment 2
• What differences are for step by step procedure
of aluminium compare to steel?
• Desribe the section factor Ap/V
for insulated member by bords?
• What surface emissivity �m is expected for
clean uncovered surface?
32
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Structural fire design
– Simple calculation models
Efi,d ≤ Rfi,d,t
Efi,d is the design effect of actions for the fire design situation
Rfi,d,t is the design resistance of the aluminium structure or
structural member, for the fire design situation
– Advanced calculation models
• The development and distribution of the temperature
within structural members (thermal response model);
• The mechanical behaviour of the structure or of any part
of it (mechanical response model).
• Validation of advanced calculation models
33
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Effect of actions
• For time t = 0
• Using combination factors ψ1,1 or ψ2,1 according to
EN1991-1-2
Efi,d = ηfi Ed
Where Ed is the design value of the corresponding
force or moment for normal temperature design
• As a simplification the recommended value
of ηηηηfi = 0,65 may be used
(Except areas susceptible to accumulation of goods,
including access areas.)
34
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Classification of cross-sections
• Classified as for normal temperature design
• Based on the same relative drop in the 0,2 %
proof strength and modulus of elasticity
• Actual drop in modulus of elasticity
– Classification of the section changes
– Larger capacity value of the section
35
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
εεεε coefficient
• To introduce different materials
• Plate slenderness
36
of/250=ε
=
−⋅⋅
==
σσ
kEf
t
b
kt
b
o
p
εµ
πελ
)2
2
1(12
4,28
σσσ
==
−⋅⋅
=
kf
Et
b
kf
Et
b
kEf
t
b
ooo
950,0235
0620,0)1(12 2
2
εµ
π
b
σk
kde t je tloušťka této části,
t is plate thickness
b is width,
µ is Poisson ratio
E is modulus od elasticity
fo is 0,2 % proof strength
součinitel napětí
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
• At elevated temperature
37
b
σk
kde t je tloušťka této části,
součinitel napětí
oo
E
o
E
o, f
E
k
k
fk
Ek
f
E
o θ
θ
θ
θ
θ
θ ==,
,
,
,
yyy,
E,
f
E
f
E
k
k00,1≅
θ
θ
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
for structural steel
38
b
σk
kde t je tloušťka této části,
součinitel napětí
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
for steel
39
b
σk
kde t je tloušťka této části,
součinitel napětí
yyy,
E,,
f
E
f
E
k
k850≅
θ
θ• Currently for steel
, °C0
0,2
0,4
0,6
0,8
1
1,2
0 200 400 600 800
θθ ,y,E k/k
θθ ,y,E k/k
539 °C
766 °C
0,85
368 °C
436 °C
θ1000
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
for aluminium
at elevated temperature
40
b
σk
kde t je tloušťka této části,
součinitel napětí
0f
250θ= αε
oo,
alal,,
/
/
ff
EE
θ
θ
θ
θθ =
o,
alE,
k
kα
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
for aluminium
41
b
σk
kde t je tloušťka této části,
součinitel napětí
0f
250θ= αε
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Reduction of εεεε coefficient
for aluminium
42
b
σk
kde t je tloušťka této části,
součinitel napětí
0f
250θ= αε
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Tension members
• The design resistance
Nfi,t,Rd = ∑ Ai ko,θ,i fo / γM,fi
where
Ai is an elemental area of the net cross-section
with a temperature θi , including a deduction if
required to allow for the effect of HAZ
softening.
The deduction is based on the reduced thickness
of ρo,HAZ⋅ t
ko,θ,i is the reduction factor for the effective 0,2 %
proof strength at temperature θi.
θ is the temperature in the elemental area A43
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Beams
The design Mfi,t,Rd of a cross-section
in class 1, 2, 3 or 4
with a uniform temperature distribution at time t
Mfi,t,Rd = ko,θ MRd (γMx/γM,fi)
where
MRd is the moment resistance of the cross-section for
normal temperature design. MRd is either Mc,Rd or Mu,Rd
γMx is the material coefficient according to EN 1999-1-1. γM1
is used in combination with Mc,Rd and γM2 is used in
combination with Mu,Rd
The design resistance Mfi,t,Rd is given by the combination of
MRd and γMx which gives the lowest capacity.
44
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Columns
The design buckling resistance Nb,fi,t,Rd of a
compression member at time t
Nb,fi,t,Rd = ko,θ,max Nb,Rd (γM1/1,2 γM,fi)
where
Nb,Rd is the buckling resistance for normal
temperature design according to EN 1999-1-1
1,2 is a reduction factor of the design resistance
due to the temperature dependent creep
of aluminium alloys
45
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Buckling length
of a column in intermediate storey
Braced frame in which each storey comprises
a separate fire compartment
with sufficient fire resistance
46
A: Shear wall or other bracing system
B: Separate fire compartments in each storey
C: Column buckling length
D: Deformation mode in fire
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Relative slenderness
• The same relative drop in the 0,2 % proof
strength and modulus of elasticity.
• If the actual drop in modulus of elasticity is
taken into account, a larger capacity value can
be obtained.
47
θ
=αλ
λθoo,
alal,,
/
/
ff
EE
θ
θ
θ
θθ =
o,
alE,
k
kα
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
48
Buckling curves
• Buckling classes: A
• 1,2 is a reduction factor of the design resistance due to the
temperature dependent creep of aluminium alloys
λλλλ
χχχχ
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,0 0,5 1,0 1,5 2,0
α
hliník
ocel
0,20 - tepelně upravené0,32 - tepelně neupravené
0,20 - tepelně upravené
0,32 - tepelně neupravené
0,21 - křivka a
0,76 - křivka dZa požáru
Poměrná štíhlost
Součinitel vzpěrnosti
redukce 1,2
Relative slenderness
Reduction factor for buckling
Aluminíum
Steel
Class A
Class B
Class A
Class B
Curve a
Curve d1,2
reduction
for fire
design
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
49
Únosnost, kN
60 x 60 x 4
0,0
20,0
40,0
60,0
80,0
100,0
120,0
140,0
160,0
180,0
200,0
0 20 40 60 80 100 120 140 160 180 200 λλλλ
Štíhlost
f0 = 250 MPa ,
α = 0,20; 00 =λ
Ocel S235
Slitina EN AW-6082
20 °C
300°C
T6, tepelně upravená;
200 °C
fy = 235 MPa ; α = (křivka a)0,21
Buckling resistance
at elevated temperature
� Buckling length od rectangular hollow section 60x60x4
Slenderness
Buckling resistance
Alloy EN AW 6082
Temper T6
Steel S235
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
The critical temperature
of aluminium alloys
50
0
100
200
300
400
500
600
700
800
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
ocel
EN AW-5454
EN AW-5086
EN AW-5083
EN AW-6082
EN AW-3003
Kritická teplota prvku , °C
Stupeň využití průřezu, µ0
170
Slitiny hliníku
Degree of utilisation µ0
Critical temperature °C
Steel
Aluminium
Simplified value 170 °C
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
The critical temperature
of aluminium alloys
• where the degree of utilisation µ0 = Efi,d / Rfi,d,0
may not be taken lass than 0,015
• Efi,d is the design effect of actions for the fire
design situation according to EN 1991-1-2 and
• Rfi,d,0 is the corresponding design resistance of
the steel member for fire design situation at
time t.
• The accuracy of the prediction varies is limited.
• The prediction of critical temperature of steel
shows a deviation 3,73%. 51
BA
lnCDcr,a +
−= 1
1
0µθ
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
The critical temperature
of aluminium alloys
Constants for calculation of critical temperature
of aluminium alloys
52
Alloy Thermaltreatment
Constants Maximal deviationA B C D
EN AW-5052 O 0,9905 428 74,88 0,2063 14,7 %
EN AW-5052 H34 0,9797 420 90,06 0,1273 27,0 %
EN AW-5083 O 0,9942 430 62,53 0,1485 10,5 %EN AW-5083 H113 0,9843 424 89,97 0,2711 0,9 %EN AW-5454 O 0,9885 424 74,01 0,1519 15,7 %
EN AW-5454 H32 0,9806 422 85,83 0,1427 15,6 %
EN AW-6061 T6 0,9957 427 65,38 0,1169 1,8 %EN AW-6063 T6 0,9902 422 74,06 0,1048 8,7 %EN AW-6082 T6 0,9826 420 89,37 0,1377 4,6 %EN AW-3003 O 0,9806 424 95,59 0,3199 4,5 %EN AW-3003 H14 0,9753 412 95,87 0,1263 9,4 %EN AW-5086 O 0,9843 424 89,97 0,2711 0,8 %EN AW-5086 H112 0,9826 428 78,80 0,2438 19,6 %
EN AW-7075 T6 0,9763 412 94,12 0,1143 12,0 %
53
ECCS nomogram for aluminium
50125 3575
-1
100150200300
200
250
300
350
400
450
500
150
100
Kritická teplota, ,°Cal,crθ mAm / V
100
200
150
250
300400
500
600
700
800
900
1000
1200
1500
2000
5 10 15 20 250,0
50
0,10,20,30,40,50,60,70,8
µ0
)(Ap / V /(λp / dp ) W K m -3
25EN AW -3003
EN AW -5083EN AW -6061
EN AW -6082EN AW -7075
EN AW -5086
EN AW -5454
-1
170
Čas, min.
Součinitel průřezu,
Stupeň využití průřezu,
Pokud teplota nepřekročínení třeba posuzovat
Utilisation
Section factorCritical temperature
Time, min
Critical temperature
Reduction of material Transfer of heat
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Assessment 3
• What advantage may be utilesed for
classification of aluminium cross-sections?
• How is treated the temperature dependent
creep of aluminium alloys for simple modelling
of buckling resistance?
• What is the simplified value of critical
temperature of aluminium alloys?
54
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
55
Summary
� EN1999-1-2 first standard for fire design of aluminium str.
� Based on steel knowledge
� Lower fire resistance compare to steel
� The low melting point of aluminum (590 °C až 650 °C)
� The good emisivity 0,3
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 200 400 600 800 1000 Teplota, °C
Smluvní mez kluzu oceli
Redukční součinitel
Mez úměrnosti hliníkových slitin
Reduction factor
Steel - effective yield strength ratio
ky,θ
Aluminium - 0,2 % proof strength ratios ko,θ
Temperature, °C
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Worked example – beam column
• Laterally restrained beam
• Load (gk + qk) 2 kN/m
• Load reduction factor γF = 1,45
• Alloy EN AW-5083 (material class B)
56
Section classification
Flage in compression not decide
Web in compression – stiffened plate
η is taken form diagram 6.4 in EN 1999-1-1
Web and all section Class 4
Web in bending
section asymmetry coefficient ε
varying the stress coefficient g
Web and all section Class 157
3
1800,95 34,2 18 18 1,51 27,1
5
b
tβ η β ε= = = > = ⋅ = ⋅ =
1
1800,95 0,351 12,0 13 13 1,63 21,1
5
bgt
β η β ε= ⋅ = ⋅ = < = ⋅ = ⋅ =
Effective section
Reduction factor for web in compression
material buckling class B
Effective area
Shift of the center of gravity due to buckling
58
( ) ( )1 2
c 2 2
29 1980,894
180 5 180 5
C C
b t b tρ = − = − =
( ) ( ) 2eff g c1 2 3848 1 0,894 2 180 5 3752 mmA A b tρ= − − ⋅ ⋅ ⋅ = − − ⋅ ⋅ ⋅ =
( ) ( )c
teff
1801 0,894 2 180 5 83
1 2 20,36 mm
3752
b t zz
A
ρ − − ⋅ ⋅ ⋅ ⋅ − − − − ⋅ ⋅ ⋅ ⋅ ∆ = = =
Resistance check
Section bending resistance
Section poor compression resistance
Buckling factor χ
Combination of buckling and pure bending
OK
59
( ) ( )
c 0,8
Ed Ed
Rd y,Rd
c min
27,9 15,30,895 1,0
0,483 375,2 22,8
kde max 0,8;1,3 max 0,8;1,3 0, 483 0,8
N M
N M
ψ
χ
ψ χ
+ = + = < ⋅ ⋅
= ⋅ = ⋅ =
Serviceability check
Full gross section
Due to lower stessess no local buckling
Web in compresion
Simplified
Secant modulus of eleasticity for maximal stress
Ramberg-Osgood material model
OK
3
s 53Ed,ser
Ed,ser 0
70 1061 022 MPa
70 10 55,81 0,0021 0,002
55,8 110
n
EE
E
f
σσ
×= = =
× ++
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Design et elevated temperature
61
• Hall of a train station
• Localised fire of newsstand
– The largest diameter of fire 2 m
– Fire load 4 640 MJ
– Medium speed fire development tα = 300 s
– The fastest rate of heat release
RHRf = 1250 kW/m2
Mechanical actions at fire
Reduction factor ηfi
For snow loading ψ1,1 = 0,2
321051331351660
33120660,
,,,,
,,,
γQγG
QψGη
QkGk
k1,1kfi =
⋅+⋅⋅+
=+
+=
kNm9143210315 ,,,ηMM fiEdEd,fi =⋅==
kN9683210927 ,,,ηNN fiEdEd,fi =⋅==
Termal loading during fire
Annex E standard EN 1991-1-2:2004
Rate of heat release Q
35302520151050
0,5
0
1,5
1,0
2,5
2,0
3,5
3,0
4,0
Čas, min
Rychlost uvolňování tepla, MWRate of heat release, MW
Time, min
Thermal heat during fire
Flame heigt in time t
Diameter of the fire in time t
Temperature along the flame axes
Convective part of the rate of heat release Qc
353025201510500
1,0
2,0
3,0
4,0
Čas, min
Délka plamenů, m
5,0
6,0 Flame heigt, m
Time, min
Transfer of heat into structure
Step by step procedure
Surface emissivity of the member εm = 0,3
Cleen aluminium element
Coefficient of heat transfer by convection αc = 35 W/m2K
Section factor Am/V = 130 m-1
Section exposed to three sides
Transfer of heat into structure
Maximal beam temperature 272 ºC in 22 min 40 s
Reduction factor for k0,θ,max = 0,596
0
50
0
150
100
250
200
350
300
400
3530252015105
Teplota, °C
40Čas, min
teplota plynů
teplota nosníku
Temperature, °C
Time, min
Gas
Beam
Resistance at elevated temperature
Bending resistance
Buckling resistance
Buckling length as at ambint temperature
Interaction as at ambient temperature
OK
0147509514
914
099
96880
,,,
,
,
,
M
M
N
N,
Rd,t,fi
Ed,fi
Rd,t,fi,b
Ed,fi
c
<=+
=+
ψ
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
68
List of Lessons at Seminar
1. Fire safety RZ
2. Fire and mechanical loading RZ
3. Thermal response RZ
4. Steel structures RZ
5. Concrete structures JMF
6. Composite structures JMF
7. Advanced models JMF
8. Composite floors FW
9. Aluminium structures FW
10. Timber structures FW
11. After fire and Historical structures FW
12. Definitions of Design for Robustness JMD
13. Global response of structures JMD
14. Design recommendations JMD
15. Alternative load path method JMD
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
70
Notes to users of the lecture
• Further readings on the relevant documents from website of www.eaa.net/eaa/education/TALAT
• Keywords for the lecture:
fire design, aluminium structures, material properties,
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Notes to users of the lecture
• Text books
– Wang Y., Burgess I., Wald F., Gillie M.,
Performance Based Fire Engineering of Structures
CRC Press 2012, ISBN: 978-0-415-55733-7.
– Buchanan A. H.,
Structural Design for Fire Safety,
Wiley, 2001, ISBN 0471889938.
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Introduction
Properties
Thermal
Mechanical
Transfer of heat
Unprotected
Protected
Elemental analyses
Classification
Beams
Columns
Critical temp.
Summary
Worked example
Notes
Sources
• EN 1999-1-1 Design of Aluminium Structures:
General structural rules, CEN, Brussels, 2008.
• EN 1999-1-2 Design of Aluminium Structures:
Structural fire design, CEN, Brussels, 2008.
• Bulson P.S.: Aluminium structural analysis: recent
European advances, Elsevier, London, 1992,
ISBN 1-85166-660-5.
• Educational programme TALAT
www.eaa.net/eaa/education/TALAT