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If the above equation is true then the insulation can be considered ‘light’ and the heavy insulation term in brackets, {}, can be omitted to simplify the equation. To see the effect of this omission, refer to Section 5.3.1. 2.2 ALTERNATIVE FORMULATIONS OF THE SPREADSHEET METHOD: There are alternatives to the spreadsheet method as primarily used in this report. The method used in this report and described in Section 2.1, based on the principles of heat transfer, was developed by the European Convention for Constructional Steelwork (ECCS, 1983). The formula for protected steel, with heavy insulation is as below: ∆ T s H = p A ( k d ρ c ) i i s s ρ sc s ρ c ( T − T ) ∆t f s s s 1 H 2 d A ρic p + i i For light, dry, or relatively thin insulation, the middle term in {} brackets can be negligible and therefore ignored. Another method as recommended by ECCS in earlier work gave the following two formulas for light and heavy insulation. The heat flow to insulated steelwork was divided into these classes because the formulas used for heavy insulation gave unstable results when the insulation was termed ‘light’ from equation 2.4. The method for heavy insulation can not be justified on theoretical grounds, but the formulas have been included here for completeness, (Purkiss, 1996). The light insulation equation is the same as stated above with the heat capacity term neglected. Light insulation: ∆T s k H i p = dic s s A ρ ( T − T ) ∆t f s 2.5 and for heavy insulation: 23
( T − T ) k H p f s ∆t ∆T i f ∆T s = − 2.6 dics ρ s A 1 + φ 1 + 2 2 φ c H i ρi p where φ = d i 2.7 cs ρ s A The formula for heavy protection is the same as the spreadsheet used in this report, expect for the final term accounting for the change in temperature of the fire over the time period. The time step ∆t can be defined as: 25000 ∆t ≤ H p A By rearranging this equation, H p /A must be greater than 416 m -1 with a time step of 60 seconds, which covers most beam sizes. 1200 Temperature ( o C) 1000 800 600 400 200 0 -200 ECCS Spreadsheet 0 20 40 60 80 100 120 140 Time (min) ECCS spreadsheet Figure 2.2: Comparison between the ECCS formula, equation 2.6, and the spreadsheet method for heavy insulation Figure 2.2 above shows that there is quite a substantial difference in the estimated steel temperature from the ECCS and spreadsheet methods. The ECCS formula shows unstable behaviour at the start of the test, and the results are significantly higher than the results found from the spreadsheet method used throughout this report. The equation for light insulation with this method is the same as that given by the spreadsheet method with the heat capacity of the steel neglected. Eurocode 3, ENV 1993-1-2 gives the following method, which was derived by Wickstrom: 24
Page 1 and 2: Fire Design of Steel Members K R Le
Page 4: ABSTRACT: The New Zealand Steel Cod
Page 8 and 9: TABLE OF CONTENTS: ABSTRACT:.......
Page 10 and 11: 5.4 RESULTS FOR FOUR SIDED EXPOSURE
Page 12 and 13: LIST OF FIGURES: FIGURE 1.1: VARIAT
Page 14: FIGURE 5.11: TEMPERATURE CONTOUR LI
Page 17 and 18: designed with confidence. Full scal
Page 19 and 20: eams and struts when subjected to a
Page 21 and 22: Gilvery and Dexter, (1997), prepare
Page 23 and 24: with conditions specified to ensure
Page 25 and 26: 1.6 BACKGROUND INFORMATION: 1.6.1 F
Page 27 and 28: experienced in fire situations, but
Page 29 and 30: The thermal conductivity is not imp
Page 31 and 32: [ The heated perimeter of the steel
Page 33 and 34: The advantages of board systems are
Page 35 and 36: The values for the thermal properti
Page 37: insulation has on the rise of the s
Page 41 and 42: spreadsheet method very closely, wi
Page 43 and 44: protection, and for user defined fi
Page 45 and 46: This equation originates from the y
Page 47 and 48: 1400 1200 1000 800 600 400 200 0 0.
Page 49 and 50: time. The value of the wall lining
Page 51 and 52: The Eurocode does not define a meth
Page 53 and 54: f f y y ( T ) (20) = 1.0 0 < T < 21
Page 55 and 56: temperature is chosen because it is
Page 57 and 58: The variation of yield stress data
Page 59 and 60: 15 m -1 < H p /A < 275 m -1 in NZS
Page 61 and 62: = H p A (m -1 ) 7.85 The cons
Page 63 and 64: Connections: NZS 3404 requires that
Page 66 and 67: 4 CALCULATION OF STEEL TEMPERATURES
Page 68 and 69: 4.1.2 Analysis Between Methods of T
Page 70 and 71: Figure 4.2 shows the variation of t
Page 72 and 73: Minimum temperatures Maximum temper
Page 74 and 75: For all three sizes of beam, the sp
Page 76 and 77: Temperature ( o C) 1200 1000 800 60
Page 78 and 79: The ECCS equation has a time period
Page 80 and 81: 4.3.1 Results from simulations with
Page 82 and 83: From Figure 4.5 a-c, the formula ra
Page 84 and 85: Temperature ( o C) 1000 800 600 400
Page 86 and 87: average temperature of the beam, be
Page 88 and 89:
Temperature ( o C) 1400 1200 1000 8
Page 90 and 91:
significantly decreased from a cool
Page 92 and 93:
Since both programmes use the same
Page 94 and 95:
Therefore, the ECCS equations provi
Page 96 and 97:
5 CALCULATION OF STEEL TEMPERATURES
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calculations made by the spreadshee
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susceptible to heating, heat up mor
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Figure 5.3 a-c show the results fro
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7850*600*10500 > 2*775*1100*(1869*2
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As can be seen from Figure 5.4 a-c,
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310 UB 40.4 beam H p /A = 241 m -1
Page 110 and 111:
The SAFIR results fit between the t
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constant specific heat being used i
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From Figure 5.7 a-c, it appears tha
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800 Temperature ( o C) 600 400 200
Page 118 and 119:
To examine the limits of the thickn
Page 120 and 121:
1000 Temperature ( o C) 800 600 400
Page 122 and 123:
Thermal conductivity, k i = 0.19 W/
Page 124 and 125:
1000 Temperature ( o C) 800 600 400
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the slab except to reduce the secti
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Figure 5.14 shows the correlation b
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5.8 CONCLUSIONS: The thermal behavi
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6 COMPARISON OF METHODS USING OTHER
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Temperature ( o C) 1200 1000 800 60
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6.2.4 Results for protected steel:
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Figures 6.2 b shows the comparison
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Figure 6.3 a shows that the average
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The fire that the test beams were e
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7 ADDITIONAL MATERIAL IN EUROCODE 3
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For thermal analysis in Eurocode 3,
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To determine the performance of a s
Page 150 and 151:
The plastic neutral axis is located
Page 152 and 153:
It is therefore recommended that th
Page 154 and 155:
These methods may be used to provid
Page 156:
Eurocode has a large annex with gui
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8.3 CHANGES TO NZS 3404: The follow
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H v height of the ventilation (m) I
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EC3, 1995. Eurocode 3: Design of St
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Temperature Conditions. National Re
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APPENDIX A - SPREADSHEET METHOD: Be
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APPENDIX B - SAFIR: In Figure B.2 i
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*.str file developed by the pre pro
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22 FISO 23 FISO FISO 24 FISO FISO 2
Page 176:
APPENDIX C - FIRECALC Below in Figu
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