TAS. Fire Design Example Based on European Standard ENV (Eurocode 9) TALAT Lecture pages. Advanced Level
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1 TALAT Lecture 2713 Fire Design Example Based on European Standard ENV (Eurocode 9) 27 pages Advanced Level Updated from the TAS Project : TAS Leonardo da Vinci program Training in Aluminium Alloy Structural Design Date of Issue: 1999 EAA - European Aluminium Association TALAT
2 2505 Fire Design Example. (26 pages) Table of Contents 2505 Fire Design Example INTRODUCTION Description Sketches References MATERIALS Aluminium LOADS Static loads Fire loads STATIC DESIGN Results from the normal temperature design Load effects in fire design Beam F Column B THERMAL CALCULATIONS General Beam F Column B CODE CHECKING Beam F Column B APPENDIX TALAT
3 1.0 INTRODUCTION. In the fire design example, the structure used in design example for static design is used. 1.1 Description. The industrial building contain an administration part with offices, wardrobe, meeting rooms etc and a fabrication hall. The load bearing system consists of frames standing at a distance of 5000 mm. In serviceability limit state the max. allowable deflection is 1/250 of span. The load bearing structure has the following requirement to fire endurance: R Sketches. A section of one load bearing frame. 1.3 References. 1 : ENV Eurocode 9: Design of aluminium structures. Part 1.1. General rules. 2 : ENV Eurocode 9: Design of aluminium structures. Part 1.2. Structural fire design. February : TALAT Design Example No : ENV Eurocode 1: Basis of design and actions on structures. Part 2-2: Actions on structures Actions on structures exposed to fire. February TALAT
4 2.0 MATERIALS. 2.1 Aluminium. 1, The extrusions are alloy EN AW-6082, temper T6, the plates are EN AW-5083 temper H24. Table 2.1 Strength of aluminium alloys. Alloy f 0,2 f u EN AW-6082 T6 260 MPa 310 MPa EN AW-5083 H MPa 340 MPa 1, The partial safety factor for the members: γ M1 = 1,10 γ M2 = 1,25 1, The partial safety factor for welded connections: γ Mw = 1,25 2, 2.3 The partial safety factor for fire design: γ M,fi = 1,0 Table 2.2 Design values of material coefficients. Modulus of elasticity E = MPa Shear modulus G = MPa Poisson s ratio ν = 0,3 Coefficient of linear thermal expansion α = 23 x 10-6 per C Density ρ = kg/m LOADS. 3.1 Static loads. The static loads are described in static design example. 3.2 Fire loads. The thermal load is the standard fire curve, which is described as: 4, Θ g = log 10 (8t + 1) where: Θ g = fire temperature t = duration in min. TALAT
5 4.0 STATIC DESIGN. 4.1 Results from the normal temperature design. The load bearing frame is calculated in static design example. In this example one column (Column B) and one beam (Beam F) are chosen as example for fire design. Beam F, (I 570 x 160 x 5 x 15,4). Values from the static design: M Rd = 341 knm V Rd = 223,5 kn Column B, (I 200 x 160 x 7 x 16). Values from the static design: Max utilisation for flexural buckling HAZ at column base (combination of compression and bending): U = 0, Load effects in fire design. The combination rule for actions in fire design is: γ GA Gk + ψ 1,1 Qk,1 + ψ 2, i Qk, i + A d () t where: G k = characteristic values of permanent actions Q k,1 = characteristic value of one (the main) variable action Q k,i = characteristic values of the other variable actions A d (t) = design values from actions from fire exposure γ GA = 1,0 ψ 1,1 = 0,5 ψ 2,i = 0,3 TALAT
6 4.2.1 Beam F. The critical criteria for Beam F is the bending moment in the middle of the beam. The load from the crane is the main variable action. The beam is calculated as pinned in both ends. This will account for some internal actions due to constrained expansion and deformation. G k = 2,75 kn/m Q k,1 = 50 kn (load from crane) Q k,2 = 4,125 kn/m (imposed load on roof) Q k,3 = 11 kn/m (snow load) Windload gives only suction to the roof, and will for that reason not be included in the load combination. 1 kn M fi, Ed = 1,0 2,75 8 m 1 kn + 0, m 2 ( 10m) + 0,5 + 0,3 4,125 ( 10m) 2 ( 10m) = 139,8kNm 50kN 10m kn m Column B. Column B is calculated with use of the MathCad spread sheet from normal temperature design. In this spread sheet the partial factors from the combination rule given in 4.2 is used. In addition a factor of 1.2 is used on the axial load (according to 2, ). Max utilisation for flexural buckling HAZ at column base (combination of compression and bending): U = 0,39 5. THERMAL CALCULATIONS. 5.1 General. Comment: To perform the thermal calculations according to 2, it is need for some tests values for insulation materials used on aluminium structures. These test values don t exist. The calculations may, however, be performed with the available thermal properties for insulation materials. In this example Rockwool with a density of 300 kg/m 3 is used. The thermal properties vary with the temperature. This is handle as linear equations for the thermal properties for the insulation materials. Thermal conductivity for Rockwool 300 kg/m 3 : θ t + θ al λ p = 0, ,035 (W/m C) 4 TALAT
7 Specific heat for Rockwool 300 kg/m 3 : c p θ t + θ al = 0, (J/kg C) 4 Specific heat for aluminium: 4, c 0,41 θ (J/kg C) al = al The temperatur rise in an insulated aluminium member can be calculated according to the following equation. This may easily be done in a spread sheet. λ p d p Ap 1 φ 10 θal t = θt θal t e 1 θ t cal ρal V 1+ φ 3 4, () ( ) ( ) () but θ al () t 0 in which: ρ φ = c p p d c ρ al al p A V p where: Ap V is the section factor for aluminium alloy members insulated by fire protection material (m -1 ) is the area of the inner surface of the fire protection material, A p per unit length of the member (m²/m) V is the volume of the member per unit length (m³/m) c al is the specific heat of aluminium alloys (J/kg ºC) is the specific heat of the fire protection material (J/kg ºC) c p d p is the thickness of the fire protection material (m) t is the time interval (seconds) θ t is the ambient gas temperature at time t (ºC) () θ al t is the aluminium temperature at time t (ºC) () θ t is the increase of the ambient temperature during the time () interval t (ºC) is the thermal conductivity of the fire protection material λ p ρ al ρ p (W/m ºC) is the unit mass of aluminium alloys (kg/m³) is the unit mass of the fire protection material (kg/m³) TALAT
8 5.2 Beam F. Beam F is a roof beam supporting an insulated roof. The size of the beam is I 570 x 160 x 5 x 15,4. The insulation layer follow the surface of the beam. A Rockwool insulation with a density of 300 kg/m 3 and with a thickness of 60 mm is used. The results of a step by step calculation with time steps of 30 sec give the following result: Temperature analysis of Beam F Temperature in deg. C Time in min The upper curve shows the thermal exposure and the lower curve shows the temperature development in the aluminium beam. Max. temperature after 60 mins exposure is calculated to 231 C. TALAT
9 5.3 Column B. Column B is a partly freestanding column which may be exposed by a fire from four sides. The size of the column is I 200 x 160 x 7 x 16. The insulation is boxed around the column. The insulation is Rockwool with density 300 kg/m 3 and the thickness is 40 mm. The results of a step by step calculation with time steps of 30 sec give the following result: Temperature analysis of Column B Temperature in deg. C 1000,00 900,00 800,00 700,00 600,00 500,00 400,00 300,00 200,00 100,00 0,00 Column B Time in min The upper curve shows the thermal exposure and the lower curve shows the temperature development in the aluminium beam. Max. temperature after 60 mins exposure is calculated to 225 C. TALAT
10 6.0 CODE CHECKING. 6.1 Beam F. The temperature of Beam F is 232 C. The alloy is EN-AW 6082 temper T6. 0,65 0,38 k 0,2, θ = 0,65 32 = 0,48 50 M M γ M1 1,10, t, Rd = k0,2, θ M Rd = 0,48 341kNm = 180, γ 1,0 fi 0 M, fi fi, Ed = 139,8kNm M fi, t, Rd = 180, 0kNm knm 6.2 Column B. The temperature of Colum B is 225 C. The alloy is EN-AW 6082 temper T6. 0,65 0,38 k 0,2, θ = 0,65 25 = 0, U fi θ, t, Rd = k0.2, max U = 0,515 0,952 = 0,49 U fi, Ed = 0,39 7 APPENDIX. 6.2 Column B Appendix to Fire Design. (MathCad 7.0 Pro) Thermal calculations for Beam F and Column B. (Microsoft Excel 97) TALAT
11 Appendix A Calculation of Beam F and Column B Calculation of beam F. λp dp cal ρal Ap/V cp ρp Φ t t θt θal θal W/mK m J/kgK kg/m3 m-1 J/kgK kg/m3 s min C C C 0, ,06 911, , , ,00 20,00 0, ,06 911, , , ,5 261,14 20,00-12,66 0, ,06 911, , , ,21 20,00-4,22 0, ,06 911, , , ,5 404,31 20,00-2,28 0, ,06 911, , , ,50 20,00-1,35 0, ,06 911, , , ,5 476,17 20,00-0,78 0, ,06 911, , , ,29 20,00-0,39 0, ,06 911, , , ,5 524,53 20,00-0,10 0, ,06 911, , , ,89 20,00 0,12 0, ,06 911, , , ,5 561,03 20,12 0,31 0, ,06 911, , , ,41 20,43 0,46 0, ,06 911, , , ,5 590,36 20,89 0,59 0, ,06 911, , , ,12 21,47 0,70 0, ,06 912, , , ,5 614,88 22,17 0,80 0, ,06 912, , , ,78 22,97 0,88 0, ,06 912, , , ,5 635,94 23,85 0,96 0, ,06 913, , , ,46 24,81 1,03 0, ,06 913, , , ,5 654,40 25,85 1,10 0, ,06 914, , , ,85 26,94 1,16 0, ,06 914, , , ,5 670,84 28,10 1,21 0, ,06 915, , , ,43 29,31 1,26 0, ,06 915, , , ,5 685,65 30,57 1,31 0, ,06 916, , , ,54 31,87 1,35 0, ,06 916, , , ,5 699,13 33,22 1,39 0, ,06 917, , , ,44 34,61 1,43 0, ,06 917, , , ,5 711,49 36,04 1,46 0, ,06 918, , , ,31 37,50 1,50 0, ,06 918, , , ,5 722,91 39,00 1,53 0, ,06 919, , , ,31 40,53 1,56 0, ,06 920, , , ,5 733,52 42,09 1,59 0, ,06 920, , , ,56 43,68 1,61 0, ,06 921, , , ,5 743,43 45,29 1,64 0, ,06 922, , , ,15 46,93 1,67 0, ,06 922, , , ,5 752,73 48,60 1,69 0, ,06 923, , , ,17 50,29 1,71 0, ,06 924, , , ,5 761,48 52,00 1,73 0, ,06 925, , , ,67 53,73 1,75 0, ,06 925, , , ,5 769,75 55,48 1,77 0, ,06 926, , , ,72 57,26 1,79 0, ,06 927, , , ,5 777,59 59,05 1,81 0, ,06 927, , , ,35 60,86 1,83 0, ,06 928, , , ,5 785,03 62,68 1,84 0, ,06 929, , , ,62 64,53 1,86 0, ,06 930, , , ,5 792,13 66,39 1,87 0, ,06 930, , , ,55 68,26 1,89 0, ,06 931, , , ,5 798,90 70,15 1,90 0, ,06 932, , , ,17 72,06 1,92 0, ,06 933, , , ,5 805,38 73,97 1,93 0, ,06 934, , , ,52 75,90 1,94 0, ,06 934, , , ,5 811,59 77,85 1,96 0, ,06 935, , , ,60 79,80 1,97 0, ,06 936, , , ,5 817,56 81,77 1,98 0, ,06 937, , , ,45 83,75 1,99 0, ,06 938, , , ,5 823,29 85,74 2,00 0, ,06 938, , , ,08 87,74 2,01 0, ,06 939, , , ,5 828,82 89,75 2,02 0, ,06 940, , , ,50 91,77 2,03 0, ,06 941, , , ,5 834,14 93,80 2,04 0, ,06 942, , , ,74 95,84 2,05 0, ,06 943, , , ,5 839,29 97,89 2,06 0, ,06 943, , , ,80 99,95 2,07 0, ,06 944, , , ,5 844,26 102,02 2,07 0, ,06 945, , , ,69 104,09 2,08 0, ,06 946, , , ,5 849,08 106,17 2,09 0, ,06 947, , , ,43 108,26 2,10 0, ,06 948, , , ,5 853,74 110,36 2,10 0, ,06 949, , , ,02 112,46 2,11 0, ,06 949, , , ,5 858,26 114,57 2,12 0, ,06 950, , , ,48 116,69 2,12 0, ,06 951, , , ,5 862,66 118,81 2,13 TALAT
12 λp dp cal ρal Ap/V cp ρp Φ t t θt θal θal W/mK m J/kgK kg/m3 m-1 J/kgK kg/m3 s min C C C 0, ,06 952, , , ,80 120,94 2,13 0, ,06 953, , , ,5 866,92 123,07 2,14 0, ,06 954, , , ,01 125,21 2,15 0, ,06 955, , , ,5 871,07 127,36 2,15 0, ,06 956, , , ,10 129,51 2,16 0, ,06 956, , , ,5 875,11 131,67 2,16 0, ,06 957, , , ,08 133,83 2,17 0, ,06 958, , , ,5 879,04 135,99 2,17 0, ,06 959, , , ,96 138,16 2,17 0, ,06 960, , , ,5 882,87 140,34 2,18 0, ,06 961, , , ,74 142,52 2,18 0, ,06 962, , , ,5 886,60 144,70 2,19 0, ,06 963, , , ,43 146,89 2,19 0, ,06 964, , , ,5 890,24 149,08 2,19 0, ,06 965, , , ,03 151,27 2,20 0, ,06 965, , , ,5 893,80 153,47 2,20 0, ,06 966, , , ,55 155,67 2,20 0, ,06 967, , , ,5 897,27 157,87 2,21 0, ,06 968, , , ,98 160,08 2,21 0, ,06 969, , , ,5 900,67 162,29 2,21 0, ,06 970, , , ,34 164,50 2,21 0, ,06 971, , , ,5 903,99 166,71 2,22 0, ,06 972, , , ,62 168,93 2,22 0, ,06 973, , , ,5 907,24 171,15 2,22 0, ,06 974, , , ,84 173,37 2,22 0, ,06 974, , , ,5 910,42 175,60 2,23 0, ,06 975, , , ,98 177,82 2,23 0, ,06 976, , , ,5 913,53 180,05 2,23 0, ,06 977, , , ,07 182,28 2,23 0, ,06 978, , , ,5 916,58 184,51 2,23 0, ,06 979, , , ,08 186,75 2,23 0, ,06 980, , , ,5 919,57 188,98 2,24 0, ,06 981, , , ,04 191,22 2,24 0, ,06 982, , , ,5 922,50 193,46 2,24 0, ,06 983, , , ,95 195,69 2,24 0, ,06 984, , , ,5 925,38 197,93 2,24 0, ,06 985, , , ,79 200,17 2,24 0, ,06 985, , , ,5 928,20 202,42 2,24 0, ,06 986, , , ,59 204,66 2,24 0, ,06 987, , , ,5 930,97 206,90 2,24 0, ,06 988, , , ,33 209,14 2,24 0, ,06 989, , , ,5 933,68 211,39 2,24 0, ,06 990, , , ,02 213,63 2,25 0, ,06 991, , , ,5 936,35 215,88 2,25 0, ,06 992, , , ,67 218,13 2,25 0, ,06 993, , , ,5 938,98 220,37 2,25 0, ,06 994, , , ,27 222,62 2,25 0, ,06 995, , , ,5 941,55 224,86 2,25 0, ,06 996, , , ,83 227,11 2,25 0, ,06 997, , , ,5 944,09 229,36 2,25 0, ,06 997, , , ,34 231,60 2,25 Temperature analysis of Beam F Temperature in deg. C t Time in min TALAT
13 Calculation of Column B. λp dp cal ρal Ap/V cp ρp Φ t t θt θal θal W/mK m J/kgK kg/m3 m-1 J/kgK kg/m3 s min C C C 0, ,04 911, , , ,00 20,00 0, ,04 911, , , ,5 261,14 20,00-4,22 0, ,04 911, , , ,21 20,00-1,13 0, ,04 911, , , ,5 404,31 20,00-0,36 0, ,04 911, , , ,50 20,00 0,03 0, ,04 911, , , ,5 476,17 20,03 0,28 0, ,04 911, , , ,29 20,31 0,46 0, ,04 911, , , ,5 524,53 20,78 0,61 0, ,04 911, , , ,89 21,38 0,72 0, ,04 912, , , ,5 561,03 22,10 0,81 0, ,04 912, , , ,41 22,91 0,90 0, ,04 912, , , ,5 590,36 23,81 0,97 0, ,04 913, , , ,12 24,78 1,03 0, ,04 913, , , ,5 614,88 25,81 1,09 0, ,04 914, , , ,78 26,90 1,14 0, ,04 914, , , ,5 635,94 28,04 1,19 0, ,04 914, , , ,46 29,22 1,23 0, ,04 915, , , ,5 654,40 30,45 1,27 0, , , , ,85 31,72 1,30 0, ,04 916, , , ,5 670,84 33,02 1,34 0, ,04 917, , , ,43 34,36 1,37 0, ,04 917, , , ,5 685,65 35,73 1,40 0, ,04 918, , , ,54 37,13 1,43 0, ,04 918, , , ,5 699,13 38,56 1,46 0, ,04 919, , , ,44 40,01 1,48 0, ,04 920, , , ,5 711,49 41,49 1,50 0, ,04 920, , , ,31 43,00 1,53 0, ,04 921, , , ,5 722,91 44,53 1,55 0, ,04 921, , , ,31 46,08 1,57 0, ,04 922, , , ,5 733,52 47,65 1,59 0, ,04 923, , , ,56 49,24 1,61 0, ,04 923, , , ,5 743,43 50,84 1,63 0, ,04 924, , , ,15 52,47 1,64 0, ,04 925, , , ,5 752,73 54,11 1,66 0, ,04 925, , , ,17 55,77 1,68 0, ,04 926, , , ,5 761,48 57,45 1,69 0, ,04 927, , , ,67 59,14 1,71 0, ,04 927, , , ,5 769,75 60,85 1,72 0, ,04 928, , , ,72 62,57 1,73 0, ,04 929, , , ,5 777,59 64,30 1,75 0, ,04 930, , , ,35 66,05 1,76 0, ,04 930, , , ,5 785,03 67,80 1,77 0, ,04 931, , , ,62 69,57 1,78 0, ,04 932, , , ,5 792,13 71,36 1,79 0, ,04 932, , , ,55 73,15 1,80 0, ,04 933, , , ,5 798,90 74,96 1,82 0, ,04 934, , , ,17 76,77 1,83 0, ,04 935, , , ,5 805,38 78,60 1,84 0, ,04 935, , , ,52 80,43 1,84 0, ,04 936, , , ,5 811,59 82,28 1,85 0, ,04 937, , , ,60 84,13 1,86 0, ,04 938, , , ,5 817,56 85,99 1,87 0, ,04 939, , , ,45 87,86 1,88 0, ,04 939, , , ,5 823,29 89,74 1,89 0, ,04 940, , , ,08 91,63 1,90 0, ,04 941, , , ,5 828,82 93,53 1,90 0, ,04 942, , , ,50 95,43 1,91 0, ,04 942, , , ,5 834,14 97,34 1,92 0, ,04 943, , , ,74 99,25 1,92 0, ,04 944, , , ,5 839,29 101,18 1,93 0, ,04 945, , , ,80 103,11 1,94 0, ,04 946, , , ,5 844,26 105,04 1,94 0, ,04 946, , , ,69 106,99 1,95 0, ,04 947, , , ,5 849,08 108,94 1,95 0, ,04 948, , , ,43 110,89 1,96 0, ,04 949, , , ,5 853,74 112,85 1,97 0, ,04 950, , , ,02 114,82 1,97 0, ,04 950, , , ,5 858,26 116,79 1,98 0, ,04 951, , , ,48 118,76 1,98 TALAT
14 λp dp cal ρal Ap/V cp ρp Φ t t θt θal θal W/mK m J/kgK kg/m3 m-1 J/kgK kg/m3 s min C C C 0, ,04 952, , , ,5 862,66 120,74 1,98 0, ,04 953, , , ,80 122,73 1,99 0,0883 0,04 954, , , ,5 866,92 124,72 1,99 0, ,04 954, , , ,01 126,71 2,00 0, ,04 955, , , ,5 871,07 128,71 2,00 0, ,04 956, , , ,10 130,71 2,01 0, ,04 957, , , ,5 875,11 132,72 2,01 0, ,04 958, , , ,08 134,73 2,01 0, ,04 959, , , ,5 879,04 136,74 2,02 0, ,04 959, , , ,96 138,76 2,02 0, ,04 960, , , ,5 882,87 140,78 2,02 0, ,04 961, , , ,74 142,80 2,03 0, ,04 962, , , ,5 886,60 144,83 2,03 0, ,04 963, , , ,43 146,86 2,03 0, ,04 964, , , ,5 890,24 148,89 2,04 0, ,04 964, , , ,03 150,93 2,04 0, ,04 965, , , ,5 893,80 152,96 2,04 0, ,04 966, , , ,55 155,00 2,04 0, ,04 967, , , ,5 897,27 157,05 2,05 0, ,04 968, , , ,98 159,09 2,05 0, ,04 969, , , ,5 900,67 161,14 2,05 0, ,04 969, , , ,34 163,19 2,05 0, ,04 970, , , ,5 903,99 165,24 2,05 0, ,04 971, , , ,62 167,30 2,06 0, ,04 972, , , ,5 907,24 169,35 2,06 0, ,04 973, , , ,84 171,41 2,06 0, ,04 974, , , ,5 910,42 173,47 2,06 0, ,04 974, , , ,98 175,53 2,06 0, ,04 975, , , ,5 913,53 177,60 2,06 0, ,04 976, , , ,07 179,66 2,07 0, ,04 977, , , ,5 916,58 181,73 2,07 0, ,04 978, , , ,08 183,79 2,07 0, ,04 979, , , ,5 919,57 185,86 2,07 0, ,04 980, , , ,04 187,93 2,07 0, ,04 980, , , ,5 922,50 190,00 2,07 0, ,04 981, , , ,95 192,07 2,07 0, ,04 982, , , ,5 925,38 194,15 2,07 0, ,04 983, , , ,79 196,22 2,07 0, ,04 984, , , ,5 928,20 198,29 2,07 0, ,04 985, , , ,59 200,37 2,08 0, , , , ,5 930,97 202,44 2,08 0, ,04 986, , , ,33 204,52 2,08 0, ,04 987, , , ,5 933,68 206,59 2,08 0, ,04 988, , , ,02 208,67 2,08 0, ,04 989, , , ,5 936,35 210,75 2,08 0, ,04 990, , , ,67 212,82 2,08 0, ,04 991, , , ,5 938,98 214,90 2,08 0, ,04 991, , , ,27 216,98 2,08 0, ,04 992, , , ,5 941,55 219,06 2,08 0, ,04 993, , , ,83 221,14 2,08 0, ,04 994, , , ,5 944,09 223,21 2,08 0, ,04 995, , , ,34 225,29 2,08 Temperature analysis of Column B 1000,00 900,00 800,00 Temperature in deg. C 700,00 600,00 500,00 Column B 400,00 300,00 200,00 100,00 0, min Time in min TALAT
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