This lecture gives an example calculation of the fire resistance of a thermally insulated aluminium I-beam loaded in bending on the basis of a simplified calculation method and of a computer analysis. Basic knowledge of structural engineering is assumed.

1. TALAT Lectures 2704
Member with Requirements to Fire Resistance
8 pages, 6 figures
Basic Level
prepared by Steinar Lundberg, Hydro Aluminium Structures, Karmoy
Objectives:
− to give an example calculation of the fire resistance of a thermally insulated
aluminium I-beam loaded in bending on the basis of a simplified calculation method
and of a computer analysis
Prerequisites:
− basic knowledge of structural engineering
− TALAT Lectures no. 2501 - 2504
Date of Issue: 1994
 EAA - European Aluminium Association

2. 2704 Member with Requirement to Fire Resistance
Contents
2704 Member with Requirement to Fire Resistance ..................................2
2704.01 Description of the Problem ........................................................................ 2
2704.02 Simplified Method..................................................................................... 3
2704.03 Computer Analysis...................................................................................... 5
Conclusion: ................................................................................................................ 8
Reference: .................................................................................................................. 8
List of figures............................................................................................................. 8
2704.01 Description of the Problem
In this example the method described in TALAT Lecture 2503 ("Design of Aluminium
Alloy Structures Exposed to Fire") shall be used together with a more exact computer
analysis for comparing the results of the problem: will the beam shown in Figure
2704.01.01 have a fire resistance of 60 minutes?
The floor beam has a span of 8000 mm and a load of 20 kN/m. The floor itself is
insulated with 100 mm Rockwool 110. The beam is insulated with 30 mm Rockwool
with density 300 kg/m³ (Conlit 300). The beam is an I 450 x 200 x 10 x 25, the alloy is
6082-T6.
the moment of inertia I = 515,8 x 106 mm4
the elastic section modulus W = 2,29 x 106 mm4
the yield strength σ0,2 = 250 Mpa
TALAT 2704 2

3. Vertical Cross-Section of the Test Model
q = 20 kN/m
Floor plate
8000
100
Conlit 300
Rockwool 110 295
Aluminium beam
30 + 25 + 30
Vertical section
alu
Vertical Cross-Section of the Test Model 2704.01.01
Training in Aluminium Application Technologies
2704.02 Simplified Method
Finding the metal temperature of the beam:
Insulation: 30 mm Rockwool 300 kg/m³
Insulation correction factor: C = 1,5
Equivalent insulation thickness: tequ = 1,5 • 30 mm = 45 mm
Section factor Fi/V:
0,35 x 2 + 0,2 x 2 - 0,01
Fi/V = ———————————————— = 78
0,2 x 0,025 x 2 + 0,4 x 0,01
With this Fi/V value the metal temperature is found from Figure 2704.02.01.
TALAT 2704 3

4. Equivalent Insulation Thickness Versus Metal
Temperature for 60 Min Fire Resistance
600
Metal temperature in degree Celsius
550
500
450 300
150
400
350 100 200
300
125
75
240
200 37 50
150
25
100
50
0
0 12,5 25 37,5 50 62,5 75 87,5 100 112,5 125
45 Equivalent insulation thickness in mm
alu Equivalent Insulation Thickness Versus Metal
Training in Aluminium Application Technologies Temperature for 60 Min Fire Resistance 2704.02.01
The relative strength is obtained from Figure 2704.02.02.
The strength after 60 minutes of exposure to a standard fire is
σ f = 0,59 x σ 0,2 = 0,59 x 250 MPa = 148 MPa
Fire is an accidental loadcase. In most design codes both the material factors and the
load factors are equal to 1,0 for this loadcase.
TALAT 2704 4

5. Relative Strength for Various Aluminium Alloys
at High Temperatures
100 6082
2014
6005,
6060
80
Relative strength in %
7005
5083,
5454
59 60 5052
40
20
0
0 100 200 300 400 500
Temperature in deg. Celsius
alu Relative Strength for Various Aluminium Alloys
Training in Aluminium Application Technologies at High Temperatures
2704.02.02
The bending stress in the beam is
M 1/8 x 20 N/mm x (8000 mm)²
σ b = —— = ————————————— = 70 Mpa
W 2,29 x 106 mm³
Conclusion: The beam has a fire resistance of at least 60 minutes which was required.
(σ f = 148 Mpa > σ b = 70 Mpa).
2704.03 Computer Analysis
To determine the metal temperature of the beam with the aid of a computer programme
called TASEF v.3.0 PC, the following procedure was followed:
The cross section of the beam has to be modelled for the analysis (see Figure
2704.03.01):
After one hour of exposure the obtained temperature distribution over the cross-section
is shown in Figure 2704.03.02. The average temperature of the lower flange is 240 °C
which will be the critical part of the member (maximum bending stress).
TALAT 2704 5

6. The average temperature rise in the lower flange during the one hour fire exposure is
shown in Figure 2704.03.03.
0.005
0.015
0.025
0.035
0.125
0.03
0.11
0.12
0.13
0.1
0.3
0
1 2 3 4 5 6 7 8 9 10 11 12
0
0.025 13 24
y
0.05 25 2 1 36
0.075 37 48
0.09 49 60
0.1 61 72
- Conlit 300 (rockwool 300 kg/m3)
3
7
- Rockwool 110 (rockwool 120 kg/m3)
0.395 73 84
0.4 85 96
0.405 97 4
108
0.415 109 8 120
0.425 121 5
132
0.45 133 144
0.46 145
- Aluminium (main region)
156
0.47 157 6 168
0.475 169 180
0.48 181 192
182
183
184
185
186
187
188
189
190
191
x
alu
Model of the Beam for a Computer Analysis 2704.03.01
Training in Aluminium Application Technologies
TALAT 2704 6

7. Temperature Distribution after One Hour of Exposure
Temperature in deg. celsius
100
100
200
300
Temperature in deg. Celsius
100
200
300
Temperature in deg. Celsius
alu
Training in Aluminium Application Technologies
Temperature Distribution after One Hour of Exposure 2704.03.02
Temperature Rise during the Exposure to Fire
Temperature in
deg. Celsius
250
200
150
100
50
0
0 15 30 45 60
Time in min.
alu
Training in Aluminium Application Technologies
Temperature Rise during the Exposure to Fire 2704.03.03
TALAT 2704 7

8. Conclusion:
Compared to the simplified method, the computer analysis gave exactly the same
average temperature in the lower flange of the beam. The rest of this calculation will be
the same as for the simplified method.
The output file of this computer run is called TASEF U02. The computer listing is
available on request.
Reference:
[1] TALAT Lectures 2501 to 2504
[2] Ulf Wickström, TASEF (Temperature Analysis of Structures Exposed to Fire),
V. 3.0 PC, Computer Programme for the determination of fire resistance of
structural elements with or without insulation. Swedish National Testing
Institute
List of figures
Figure No. Figure Title (Overhead)
2704.01.01 Vertical Cross-Section of the Test Model
2704.02.01 Equivalent Insulation Thickness Versus Metal Temperature for 60 Min. Fire
Resistance
2704.02.02 Relative Strength for Various Aluminium Alloys at High Temperatures
2704.03.01 Model of the Beam for a Computer Analysis
2704.03.02 Temperature Distribution after One Hour of Exposure
2704.03.03 Temperature Rise during the Exposure to Fire
TALAT 2704 8