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# TALAT Lecture 2704: Member with Requirement to Fire Resistance

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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.

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### TALAT Lecture 2704: Member with Requirement to Fire Resistance

1. 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. 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. 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. 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. 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. 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. 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. 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