Fire Design of Aluminium Structures - Aluminium structures.pdfStructural aluminium/steel design?...

Fire Design

of Aluminium Structures

František Wald

Czech Technical University in Prague

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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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



Master Course




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


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes

12

Thermal conductivity


50

150

200

250

0

100

5004003002001000

θal

/ °C

λal

/ (W/m°C) A

B


Master Course




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


Master Course




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


Master Course




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 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


Master Course




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 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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes

23

Section factor



Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes

24

Section factor



Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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.


) + ( 2 hb


Master Course




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.


- perimeter aluminium b

b

h

Hollow encasement of uniform thickness, exposed to fire on three sides.


+ 2 bh


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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



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


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


for structural steel

38

b

σk




Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


for steel

39

b

σk



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


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


for aluminium


40

b

σk



0f

250θ= αε

oo,

alal,,

/

/

ff

EE

θ

θ

θ

θθ =

o,

alE,

k

kα


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


for aluminium

41

b

σk



0f

250θ= αε


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


for aluminium

42

b

σk



0f

250θ= αε


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


Master Course




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


� Buckling length od rectangular hollow section 60x60x4

Slenderness

Buckling resistance

Alloy EN AW 6082

Temper T6

Steel S235


Master Course




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


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

Unprotected

Protected

Elemental analyses

Classification

Beams

Columns

Critical temp.

Summary

Worked example

Notes


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


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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


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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


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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


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Transfer of heat

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Elemental analyses

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Critical temp.

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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

×= = =

× ++


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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


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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

Thank you

for your attention

František WALD

[email protected]


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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,


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Introduction

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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.


Master Course




Introduction

Properties

Thermal

Mechanical

Transfer of heat

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Elemental analyses

Classification

Beams

Columns

Critical temp.

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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

Fire Design of Aluminium Structures - Aluminium structures.pdfStructural aluminium/steel design?...

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