FIRE RESISTANCE OF STEEL STRUCTURES (BASED ON EN1993 PART 1-2 “DESIGN OF STEEL STRUCTURES – STRUCTURAL FIRE DESIGN) JAN 2006

Abstract: This tool provides a first estimation of the ISO fire resistance of steel beams and columns, both protected and unprotected. The approach is based on EN 1993-1-2, the European Research project “Buckling curves of hot rolled H sections submitted to fire” as well as the former Nomogram of the ECCS document N°89. The method used for beams is based on the definition of the degree of utilisation and provides the critical temperature. The method for columns is a new simplified approach based on the European research project that provides as well the critical steel temperature. For unprotected members a new section factor, including the shadow affect was defined and according to the required fire resistance class, a steel temperature is obtained that should remain below the critical one. For protected members, a set of protection materials is given with their fire properties. In combination with the section factor this allows one by the same to calculate the maximum steel temperature.

HALLER Mike CAJOT Louis-Guy Arcelor LCS Research Centre Page 1 of 21

Table of contents 1.

Introduction...................................................................................................................3

2.

Principles of calculation ................................................................................................3 2.1

Steel temperature .............................................................................................................3

2.2

Mechanical properties of steel at elevated temperatures....................................................4

3.

Calculation procedure for beams and members in tension..............................................4 3.1

Temperature distribution ..................................................................................................4

3.2

General assumptions ........................................................................................................5

3.3

Calculation procedure ......................................................................................................6

4.

Calculation procedure for columns ................................................................................7 4.1

Introduction of simplified method ....................................................................................7

4.2

Design procedure .............................................................................................................7

4.3

Design tables for S235, S355 and S460 steel grades .........................................................8

5.

Nomogram for unprotected members...........................................................................11 5.1

5.1.1

Section factor including shadow effect for European sections .................................12

5.1.2

Section factor including shadow effect for British sections .....................................13

5.2 6.

Nomogram for unprotected steel members .....................................................................14 Nomogram for protected members ..............................................................................15

6.1

7.

Section factor for unprotected steel members .................................................................11

Section factor for protected steel members .....................................................................15

6.1.1

Section factor for European sections.......................................................................17

6.1.2

Section factor for British sections ...........................................................................18

6.2

Properties of fire protection material ..............................................................................19

6.3

Nomogram for protected steel members .........................................................................20 References...................................................................................................................21

Page 2 of 21

1.

Introduction

The required fire resistance of steel structures – in terms of fire resistance classes R30/R60/R90 etc. – is given by national regulations. These requirements depend on the number of floors, the use and the type of building and, in some countries, on the fire load, the number of people and the favourable effect of active measures, such as sprinklers. The assessment of the fire resistance of structural elements is based either on standard fire tests in furnaces or on calculation. This Technical Note describes calculation methods for unprotected and protected internal steelwork based on the European standard EN 1993-1-2 [1]. Hence, partially encased sections as well as integrated and slim floor beams are not covered by this approach.

2.

Principles of calculation

2.1

Steel temperature

The increase in steel temperature is influenced by the following factors: The section factor: i.e. the relation between the surface area exposed to the heat flux and the volume of the member per unit length. Calculation methods and values of section factors for common sections are given in section 5 and 6. In case of unprotected steel profiles, a section factor including the shadow effect, with (Am/V)sh = 0.9·(Am/V)b or (Am/V)sh = 1.0·(Am/V)b, is to be considered. In case of protected members the section factor Ap/V is multiplied by a factor, staying for the thermal conductivity of the protection material, divided by its thickness λp/dp. The thermal properties of a fire protection material: i.e. thermal conductivity λp, its specific heat cp and its thickness dp. Thermal properties for various types of protection materials are given in section 6.2. Product specifications can also be obtained in each country from approved testing laboratories, or other expert institutes on condition that they are based on officially approved tests. Herein it is important to consider that in reality, the thermal properties with the temperature, in order that the use of values at room temperatures are not acceptable. Consequently, the thermal characteristics, given in 6.2 are only valid for a first approach. The final design should take into account the tables established by tests for the selected protection product. In case that no data are available the procedures given in EN 13381 part 1 to 4 [2], has to be used. Test series have to be conducted that aim in proving the stickability of the protection material to the steel support, under maximum deflection and temperature. For fire protection material containing water, the evaporation of the water causes a delay of the temperature increase of the steel when the temperature of the steel reaches 100°C.

Page 3 of 21

2.2

Mechanical properties of steel at elevated temperatures

Steel properties change with temperature (Figure 2-1). For a member at a nearly uniform temperature, the critical steel temperature θa,cr, in defined as the temperature for which, the load bearing capacity becomes equal to the effect of the applied loads. Failure will then occur.

kθ

1.00

Effective yield strength ky,θ = fy,θ / fy 0.80

Slope of linear elastic range kE,θ = Ea,θ / Ea

0.60

0.40

Proportional limit kp,θ = fp,θ / fy

0.20

0.00 0

200

400

600

800

1000

1200

temperature [°C] Figure 2-1 : Reduction factors for steel strength and stiffness at elevated temperatures

3. Calculation procedure for beams and members in tension 3.1

Temperature distribution

For the fire design of beam, adaptation factors κ1 and κ2 may be introduced to take account of a non-uniform temperature distribution over the height and alongside the steel section near statically indeterminate support. The value of the adaptation factors κ1 and κ2 should be taken as follows, whereas the product of both is to be used with κ=κ1· κ2: •

κ1 for a non-uniform temperature distribution across a cross-section :

o for a beam exposed on all four sides : κ1=1.0 o for an unprotected beam exposed on three sides, with a composite or concrete slab on side four : κ1=0.70

Page 4 of 21

o for a protected beam exposed on three sides, with a composite or concrete slab on side four : κ1=0.85 •

κ2 for a non-uniform temperature along a beam:

o at the supports of a statically indeterminate beam : κ2=0.85 o in all other cases : κ2=1.0

3.2

General assumptions

The critical temperature is determined by the level of the applied load (action), expressed as the degree of utilisation in fire, given by: E fi ,d µ0 = R fi , d ,t Efi,d : the design effect of actions in fire Rfi,d,t : the design resistance in fire, for time t=0 (i.e. room temperature and with γM,fi = 1.0) The calculation of the fire resistance is based on the following assumptions: •

the method is only valid when LTB is prevented

•

the temperature increase follows the standard fire curve (ISO 834, EN1364-1)

•

uniform heating of the steel member. A non-uniform heat distribution is considered by the factor κ = κ1 · κ2 (Section 3.1)

•

steel grades according to EN 10025 parts 1 to 6 (S235, S355, S460) [3]

•

for non protected members the shadow effect is taken into account through (Am/V)sh that is equal to 0.9 · (Am/V)b for I-sections and 1.0· (Am/V)b for all other cases, with (Am/V)b as the boxed section factor (see section 5.

•

for member analysis, the effects of thermal expansion of the member may be neglected

•

steel sections of classes at elevated temperatures 1, 2 or 3 (with Am/V > 10 m-1). For members of class 4 cross sections other than tension members the steel temperature at all cross-sections is to be limited to θcrit = 350°C if not defined differently in the national annexes. The cross-sections may be classified at elevated temperature as for ambient temperature design according to EN 1993-1-1 [5], with a reduced value for factor ε = 0.85 235 / f y

•

temperature increase curves for insulated steel calculated with φ=0 (modification factors for other values see section 6).

Page 5 of 21

3.3

Calculation procedure

•

Choose the appropriate value of the adaptation factor κ = κ1 · κ2 (see section 3.1).

•

Calculate the degree of utilisation in fire µ0.

•

Define the critical temperature for the steel beam according to Figure 0-1.

•

Determine the section factor including shadow effect (Am/V)sh for unprotected steel members (see section 6) and Ap/V for steel members insulated by fire protection material with the thermal section factor [(Ap/V) · (λp/dp)] (see section 6).

•

Making use of the Nomogram to deduce, from the critical temperature, the fire resistance time, and to check whether with fulfils the requirement. 900 850

750 700 650 600 κ = 0.6

550

κ = 0.7 κ = 0.85

500

κ = 1.0

450 400

0.75

0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

Load ratio µ0 Figure 0-1 : Critical Temperature in function of the load ratio for different adaptation factors

Page 6 of 21

Critical temperature (°C)

800

4.

Calculation procedure for columns

4.1

Introduction of simplified method

The design buckling resistance Nb,fi,Rd of a compression member with a Class 1, Class 2 or Class 3 cross-section with a uniform temperature θa , can be rewritten as follows:

N b , fi ,Rd = χ fi ⋅ A ⋅ k y ,θ ⋅ f y = f y' ,θ ,λ ⋅ A where A is the area of the cross section and f y' ,θ,λ = χ fi ⋅ k y ,θ ⋅ f y is the critical compression stress for a given temperature θ and a given slenderness ratio λ (based on ECSC project [4]).

4.2 •

Design procedure Definition of the critical compression stress, for which the load bearing capacity becomes equal to the effect of the applied loads. f y' ,θ ,λ =

•

N b, fi ,Rd A

Definition of the slenderness ratio:

λ ( 20°C ) =

λ λE ( 20°C )

with λ1 = 93.9 ⋅

=

L fi i ⋅ λ1

235 fy

In the case of a braced frame in which each storey comprises a separate fire compartment with sufficient fire resistance, in an intermediate storey the buckling length Lfi of a continuous column may be taken as Lfi = 0.5·L and in the top storey the buckling length may be taken as Lfi = 0.7·L , where L is the system length in the relevant storey. •

Defining the critical temperature according to the Table 4.1 for S235, Table 4.2 for S355 and Table 4.3 for S460 steel grades by interpolation.

•

Determine the section factor including shadow effect (Am/V)sh for unprotected steel members (see section 6) and Ap/V for steel members insulated by fire protection material with the thermal section factor [(Ap/V) · (λp/dp)] (see section 6).

•

Making use of the Nomogram to deduce, from the critical temperature, the fire resistance time, and to check whether with fulfils the requirement.

Page 7 of 21

4.3

Design tables for S235, S355 and S460 steel grades

Table 4.1 : Critical compression stress f y' ,θ,λ for S235 steel 400°C

500°C

800°C

900°C

26 24 22 21 19 18 16 15 13 12 11 9 8 8 7 6 6 5 5 4 4

14 13 13 12 11 10 10 9 8 7 7 6 6 5 5 4 4 4 3 3 3

f y' ,θ,λ [N/mm²]

λ (20°C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Temperature θa 600°C 700°C

235 218 202 187 171 156 140 126 112 99 88 78 70 62 56 50 45 41 37 34 31

183 171 159 147 136 124 113 102 91 81 73 65 58 52 47 42 38 35 31 29 26

110 102 94 87 80 72 65 58 51 45 40 35 31 28 25 22 20 18 17 15 14

Page 8 of 21

54 50 46 42 38 34 30 26 23 20 18 16 14 12 11 10 9 8 7 7 6

Table 4.2 : Critical compression stress f y' ,θ,λ for S355 steel 400°C

500°C

800°C

900°C

39 37 35 33 31 28 26 24 21 19 17 15 14 12 11 10 9 8 7 7 6

21 20 19 18 17 16 15 14 13 12 11 10 9 8 8 7 6 6 5 5 4

f y' ,θ,λ [N/mm²]

λ (20°C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Temperature θa 600°C 700°C

355 334 313 293 272 250 227 204 182 161 143 126 112 100 89 80 72 65 59 54 49

277 261 246 231 215 199 182 165 148 132 118 105 93 83 75 67 61 55 50 46 42

167 157 147 137 126 116 105 94 83 73 65 57 51 45 40 36 32 29 26 24 22

Page 9 of 21

82 76 71 66 60 54 49 43 38 33 29 25 22 19 17 15 14 13 11 10 9

Table 4.3 : Critical compression stress f y' ,θ,λ for S460 steel 400°C

500°C

800°C

900°C

51 48 46 43 41 38 35 32 29 26 23 21 19 17 15 13 12 11 10 9 8

28 26 25 24 23 22 21 19 18 16 15 14 12 11 10 9 8 8 7 6 6

f y' ,θ,λ [N/mm²]

λ (20°C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Temperature θa 600°C 700°C

460 435 412 388 362 335 305 276 246 218 193 170 151 134 119 107 96 87 79 72 66

359 341 323 305 286 266 245 222 200 179 159 142 126 112 100 90 81 73 67 61 56

216 204 193 181 169 155 141 127 112 99 87 77 68 60 54 48 43 39 35 32 29

Page 10 of 21

106 100 93 87 80 73 66 58 51 44 39 34 30 26 23 21 18 17 15 14 12

5.

Nomogram for unprotected members

5.1

Section factor for unprotected steel members

A  A  Section factor including shadow effect for I-sections:  m  = 0.9 ·  m   V  sh  V b A  with  m  =  V b

 box surface area per unit length   volume of the member per unit length   

Figure 5-1 : Section factor for I-sections

box surface are cross-section area of steel profile

A  A  For any sections else then I-sections, the section factor is to be taken as  m  = 1.0 ·  m   V  sh  V b Figure 5-2 : Approximated section factor for different shapes

Description

[Am/V]sh

Flat bar

exposed to fire on all sides : ≈ 2/t exposed to fire on one sides : ≈ 1/t

t b

Open section with uniform thickness exposed to fire on all sides : ≈ 2/t (the calculation of the boxed value would give more accurate value)

t

t

Hollow section with uniform thickness exposed to fire from outside : ≈ 1/ t (for width >> t and the assumption of no radiation between the internal surfaces)

t

t

Solid section d

d

exposed to fire on all sides : = 4/d

Page 11 of 21

5.1.1 Section factor including shadow effect for European sections HE

-1

[Am/V]sh [m ] IPE IPE 80 A IPE 80 IPE A 100 IPE 100 IPE A 120 IPE 120 IPE A 140 IPE 140 IPE A 160 IPE 160 IPE A 180 IPE 180 IPE O 180 IPE A 200 IPE 200 IPE O 200 IPE A 220 IPE 220 IPE O 220 IPE A 240 IPE 240 IPE O 240 IPE A 270 IPE 270 IPE O 270 IPE A 300 IPE 300 IPE O 300 IPE A 330 IPE 330 IPE O 330 IPE A 360 IPE 360 IPE O 360 IPE A 400 IPE 400 IPE O 400 IPE A 450 IPE 450 IPE O 450 IPE A 500 IPE 500 IPE O 500 IPE A 550 IPE 550 IPE O 550 IPE A 600 IPE 600 IPE O 600 750 x 137 750 x 147 750 x 173 750 x 196

HP 285 243 257 222 244 207 234 194 221 180 204 169 151 189 158 142 174 149 134 160 138 125 154 132 114 144 125 109 134 118 103 124 110 96 120 104 93 114 99 85 106 94 80 100 87 77 93 82 66 91 85 73 65

350 297 314 270 296 251 283 233 266 217 247 203 182 228 190 171 208 178 161 193 166 150 185 158 137 173 150 131 160 141 123 149 131 114 142 123 110 134 117 99 124 109 94 116 102 88 107 95 77 104 98 84 75

186 185 174 167 160 154 148 139 134 126 123 119 98 103 107 99

227 222 206 196 188 179 171 160 154 145 141 136 111 116 120 111

UPN UPN 80 UPN 100 UPN 120 UPN 140 UPN 160 UPN 180 UPN 200 UPN 220 UPN 240 UPN 260 UPN 280 UPN 300 UPN 320 UPN 350 UPN 380 UPN 400

Table 5.1

HP 200 x 43 HP 200 x 53 HP 220 x 57 HP 260 x 75 HP 260 x 87 HP 305 x 79 HP 305 x 88 HP 305 x 95 HP 305 x 110 HP 305 x 126 HP 305 x 149 HP 305 x 180 HP 305 x 186 HP 305 x 223 HP 320 x 88 HP 320 x 103 HP 320 x 117 HP 320 x 147 HP 320 x 184 HP 360 x 84 HP 360 x 109 HP 360 x 133 HP 360 x 152 HP 360 x 174 HP 360 x 180 HP 400 x 122 HP 400 x 140 HP 400 x 158 HP 400 x 176 HP 400 x 194 HP 400 x 213 HP 400 x 231

101 81 79 72 63 82 73 68 59 52 45 38 37 32 73 63 56 46 38 88 69 58 50 45 43 63 55 50 45 41 38 35

135 109 107 97 85 109 98 91 79 70 60 50 50 42 97 85 75 61 50 119 93 77 68 60 59 86 75 67 60 56 51 48

97 79 59 50 41 35 86 67 52 43 35 30 25 57 52 48 44 41 42 38 34 32 29 27 25 23 21 20 18 17 16 15 14 14 13 12 11 10

131 105 79 66 54 46 114 88 69 57 46 39 32 77 70 64 59 54 58 50 47 42 39 36 33 31 28 26 24 23 21 20 19 18 16 15 14 14

HD HD 260 x 54,1 HD 260 x 68,2 HD 260 x 93,0 HD 260 x 114 HD 260 x 142 HD 260 x 172 HD 320 x 74,2 HD 320 x 97,6 HD 320 x 127 HD 320 x 158 HD 320 x 198 HD 320 x 245 HD 320 x 300 HD 360 x 134 HD 360 x 147 HD 360 x 162 HD 360 x 179 HD 360 x 196 HD 400 x 187 HD 400 x 216 HD 400 x 237 HD 400 x 262 HD 400 x 287 HD 400 x 314 HD 400 x 347 HD 400 x 382 HD 400 x 421 HD 400 x 463 HD 400 x 509 HD 400 x 551 HD 400 x 592 HD 400 x 634 HD 400 x 677 HD 400 x 744 HD 400 x 818 HD 400 x 900 HD 400 x 990 HD 400 x 1086

HE 100 AA HE 100 A HE 100 B HE 100 M HE 120 AA HE 120 A HE 120 B HE 120 M HE 140 AA HE 140 A HE 140 B HE 140 M HE 160 AA HE 160 A HE 160 B HE 160 M HE 180 AA HE 180 A HE 180 B HE 180 M HE 200 AA HE 200 A HE 200 B HE 200 M HE 220 AA HE 220 A HE 220 B HE 220 M HE 240 AA HE 240 A HE 240 B HE 240 M HE 260 AA HE 260 A HE 260 B HE 260 M HE 280 AA HE 280 A HE 280 B HE 280 M HE 300 AA HE 300 A HE 300 B HE 300 M HE 320 AA HE 320 A HE 320 B HE 320 M HE 340 AA HE 340 A HE 340 B HE 340 M HE 360 AA HE 360 A HE 360 B HE 360 M HE 400 AA HE 400 A HE 400 B HE 400 M HE 450 AA HE 450 A HE 450 B HE 450 M HE 500 AA HE 500 A HE 500 B HE 500 M HE 550 AA HE 550 A HE 550 B HE 550 M HE 600 AA HE 600 A HE 600 B HE 600 M HE 600 x 337 HE 600 x 399 HE 650 AA HE 650 A HE 650 B HE 650 M HE 650 x 343 HE 650 x 407 HE 700 AA

163 124 104 59 164 123 95 55 155 116 88 52 135 108 79 49 127 104 75 47 117 97 69 44 110 89 65 42 103 82 61 35 97 79 59 35 94 76 58 34 87 70 54 30 86 67 52 30 85 65 51 31 83 63 50 31 81 61 50 32 82 59 50 34 82 59 49 35 79 59 50 37 79 59 50 38 33 29 79 59 50 40 34 30 77

221 167 139 77 222 167 127 72 210 157 117 68 183 145 106 64 171 140 99 61 158 131 92 59 149 121 87 56 139 110 82 47 131 105 79 46 125 102 77 45 118 95 72 39 114 88 69 39 111 85 68 39 108 82 66 40 104 78 64 41 103 75 62 42 102 72 60 43 97 71 60 45 95 71 60 46 40 34 95 70 59 47 41 35 92

HE 700 A HE 700 B HE 700 M HE 700 x 352 HE 700 x 418 HE 800 AA HE 800 A HE 800 B HE 800 M HE 800 x 373 HE 800 x 444 HE 900 AA HE 900 A HE 900 B HE 900 M HE 900 x 391 HE 900 x 466 HE 1000 AA HE 1000 x 249 HE 1000 A HE 1000 B HE 1000 M HE 1000 x 393 HE 1000 x 415 HE 1000 x 438 HE 1000 x 494 HE 1000 x 584 HL 920 x 345 HL 920 x 368 HL 920 x 390 HL 920 x 420 HL 920 x 449 HL 920 x 491 HL 920 x 537 HL 920 x 588 HL 920 x 656 HL 920 x 725 HL 920 x 787 HL 920 x 970 HL 1000 AA HL 1000 A HL 1000 B HL 1000 M HL 1000 x 443 HL 1000 x 483 HL 1000 x 539 HL 1000 x 554 HL 1000 x 591 HL 1000 x 642 HL 1000 x 748 HL 1000 x 883 HL 1100 A HL 1100 B HL 1100 M HL 1100 R

68 59 48 41 36 88 68 59 50 43 37 84 67 59 51 44 38 81 73 67 59 53 48 45 43 39 33 56 52 50 46 43 40 37 33 31 28 26 22 66 61 53 49 45 41 38 37 35 32 28 24 61 54 50 43

209 204 195 187 180 173 165 155 148 142 124 113 107 100

258 248 233 223 212 203 193 180 171 163 141 128 121 112

UPE UPE 80 UPE 100 UPE 120 UPE 140 UPE 160 UPE 180 UPE 200 UPE 220 UPE 240 UPE 270 UPE 300 UPE 330 UPE 360 UPE 400

Section factors for unprotected steel members - European sections

Page 12 of 21

58 50 41 35 31 76 59 51 43 37 32 73 59 51 45 39 33 71 64 59 51 47 42 40 38 34 30 47 44 41 39 37 33 32 29 26 23 23 18 57 52 46 41 39 36 32 32 30 28 24 21 53 47 42 38

5.1.2 Section factor including shadow effect for British sections UB UB 127 x 76 x 13 UB 152 x 89 x 16 UB 178 x 102 x 19 UB 203 x 102 x 23 UB 203 x 133 x 25 UB 203 x 133 x 30 UB 254 x 102 x 22 UB 254 x 102 x 25 UB 254 x 102 x 28 UB 254 x 146 x 31 UB 254 x 146 x 37 UB 254 x 146 x 43 UB 305 x 102 x 25 UB 305 x 102 x 28 UB 305 x 102 x 33 UB 305 x 127 x 37 UB 305 x 127 x 42 UB 305 x 127 x 48 UB 305 x 165 x 40 UB 305 x 165 x 46 UB 305 x 165 x 54 UB 356 x 127 x 33 UB 356 x 127 x 39 UB 356 x 171 x 45 UB 356 x 171 x 51 UB 356 x 171 x 57 UB 356 x 171 x 67 UB 406 x 140 x 39 UB 406 x 140 x 46 UB 406 x 178 x 54 UB 406 x 178 x 60 UB 406 x 178 x 67 UB 406 x 178 x 74 UB 457 x 152 x 52 UB 457 x 152 x 60 UB 457 x 152 x 67 UB 457 x 152 x 74 UB 457 x 152 x 82 UB 457 x 191 x 67 UB 457 x 191 x 74 UB 457 x 191 x 82 UB 457 x 191 x 89 UB 457 x 191 x 98 UB 533 x 210 x 82 UB 533 x 210 x 92 UB 533 x 210 x 101 UB 533 x 210 x 109 UB 533 x 210 x 122 UB 610 x 229 x 101 UB 610 x 229 x 113 UB 610 x 229 x 125 UB 610 x 229 x 140 UB 610 x 305 x 149 UB 610 x 305 x 179 UB 610 x 305 x 238 UB 686 x 254 x 125 UB 686 x 254 x 140 UB 686 x 254 x 152 UB 686 x 254 x 170 UB 762 x 267 x 147 UB 762 x 267 x 173 UB 762 x 267 x 197 UB 838 x 292 x 176 UB 838 x 292 x 194 UB 838 x 292 x 226 UB 914 x 305 x 201 UB 914 x 305 x 224 UB 914 x 305 x 253 UB 914 x 305 x 289 UB 914 x 419 x 343 UB 914 x 419 x 388 UB 1016 x 305 x 222 UB 1016 x 305 x 249 UB 1016 x 305 x 272 UB 1016 x 305 x 314 UB 1016 x 305 x 349 UB 1016 x 305 x 393 UB 1016 x 305 x 415 UB 1016 x 305 x 438 UB 1016 x 305 x 494 UB 1016 x 305 x 584

Table 5.2

UC 180 175 169 156 152 129 196 173 156 148 126 110 203 180 157 140 124 110 135 120 104 176 150 137 122 110 95 170 146 129 116 105 95 142 125 113 103 94 115 105 95 88 81 109 98 90 84 76 100 90 82 74 72 61 47 91 82 76 68 86 73 65 79 72 62 74 67 59 53 46 41 71 64 59 52 47 42 40 38 34 30

221 213 207 186 189 160 229 202 181 180 154 134 231 206 178 163 146 129 165 145 125 203 174 164 146 131 113 195 167 151 138 124 113 163 143 129 117 107 135 123 113 104 95 127 113 104 97 87 116 104 95 86 87 73 56 105 95 87 79 98 84 75 91 83 71 85 77 68 60 55 49 81 73 67 59 53 48 45 43 39 33

UC 152 x 152 x 23 UC 152 x 152 x 30 UC 152 x 152 x 37 UC 203 x 203 x 46 UC 203 x 203 x 52 UC 203 x 203 x 60 UC 203 x 203 x 71 UC 203 x 203 x 86 UC 254 x 254 x 73 UC 254 x 254 x 89 UC 254 x 254 x 107 UC 254 x 254 x 132 UC 254 x 254 x 167 UC 305 x 305 x 97 UC 305 x 305 x 118 UC 305 x 305 x 137 UC 305 x 305 x 158 UC 305 x 305 x 198 UC 305 x 305 x 240 UC 305 x 305 x 283 UC 356 x 368 x 129 UC 356 x 368 x 153 UC 356 x 368 x 177 UC 356 x 368 x 202 UC 356 x 406 x 235 UC 356 x 406 x 287 UC 356 x 406 x 340 UC 356 x 406 x 393 UC 356 x 406 x 467 UC 356 x 406 x 551 UC 356 x 406 x 634

140 110 91 94 84 74 64 54 74 62 52 43 36 68 56 49 43 35 30 26 59 50 44 40 35 29 25 23 20 17 15

187 146 121 125 112 98 84 71 98 82 69 58 47 89 75 65 57 47 40 34 79 68 59 52 47 39 33 30 26 23 20

[Am/V]sh [m-1]

Section factors for unprotected steel members - British sections

Page 13 of 21

Nomogram for unprotected steel members 10

105

[Am/V]sh

90

15

75

20

30

60

40 50

Critical Steel temperature [°C] Page 14 of 21

0

100

200

300

400

500

600

700

800

900

0

15

30

45

75 125 200 350

Fire Resistance [min]

120

5.2

6.

Nomogram for protected members

6.1

Section factor for protected steel members

Section factor :

Ap V

=

inner contour of encasement steel cross sec tion area

inner contour of encasement 1)

dp

h

cross-section area of steel profile

c1

dp c2

b

Description

Ap/V 1)

Contour encasement of uniform thickness

Hollow encasement of uniform thickness

Contour encasement : steel perimeter steel cross-section area h

Hollow encasement 1): 2(b+h)

c1

b

c2

Contour encasement of uniform thickness, exposed to fire on three sides

steel cross-section area b

Hollow encasement 1) of uniform thickness, exposed to fire on three sides

Contour encasement 1): steel perimeter - b steel cross-section area

h

Hollow encasement : (2h+b)

c1

b

1)

c2

b

The clearance dimensions c1 and c2 should normally not exceed h/4 Legend :

insulation (with thickness dp) steel cross-section inner contour Ap

Page 15 of 21

steel cross-section area

For any sections else then I-sections, the section factor could be estimated as shown in Figure 6-1. Figure 6-1 : Approximated section factor for different shapes

Description

Ap/V

Flat bar

exposed to fire on all sides : ≈ 2/t exposed to fire on one sides : ≈ 1/t

t b

Open section with uniform thickness exposed to fire on all sides : ≈ 2/t

t

t

Hollow section with uniform thickness exposed to fire from outside : ≈ 1/ t (for width >> t and the assumption of no radiation between the internal surfaces)

t

t

Solid section d

d

exposed to fire on all sides : = 4/d

Page 16 of 21

6.1.1 Section factor for European sections -1

Ap/V [m ]

HE

IPE IPE 80 A IPE 80 IPE A 100 IPE 100 IPE A 120 IPE 120 IPE A 140 IPE 140 IPE A 160 IPE 160 IPE A 180 IPE 180 IPE O 180 IPE A 200 IPE 200 IPE O 200 IPE A 220 IPE 220 IPE O 220 IPE A 240 IPE 240 IPE O 240 IPE A 270 IPE 270 IPE O 270 IPE A 300 IPE 300 IPE O 300 IPE A 330 IPE 330 IPE O 330 IPE A 360 IPE 360 IPE O 360 IPE A 400 IPE 400 IPE O 400 IPE A 450 IPE 450 IPE O 450 IPE A 500 IPE 500 IPE O 500 IPE A 550 IPE 550 IPE O 550 IPE A 600 IPE 600 IPE O 600 750 x 137 750 x 147 750 x 173 750 x 196

HP 437 369 389 334 370 311 354 291 332 269 308 253 226 283 235 212 260 221 200 240 205 185 230 197 170 216 188 163 199 175 152 185 163 142 176 152 135 165 143 122 152 134 114 142 124 108 131 115 93 128 120 102 91

509 429 452 387 428 360 409 335 382 310 354 291 260 326 270 244 298 254 230 276 236 213 265 227 195 248 216 187 228 200 175 211 186 162 200 174 154 187 162 138 172 151 129 160 140 121 147 129 104 144 134 114 102

317 270 286 247 271 230 260 215 245 200 227 188 168 210 176 158 193 165 149 178 153 139 171 147 127 160 139 121 149 131 114 138 122 107 133 116 103 127 110 94 118 104 89 111 97 85 103 91 73 101 94 81 72

389 330 349 300 329 279 314 259 295 241 274 226 202 253 211 190 231 198 179 214 184 167 205 176 152 192 167 145 178 157 137 165 146 127 158 137 122 149 130 110 138 121 104 129 113 98 119 105 85 116 109 93 83

250 239 223 210 200 193 182 171 163 154 149 145 116 123 125 117

291 276 255 240 228 218 205 192 183 173 167 162 130 135 138 129

186 185 174 167 160 154 148 139 134 126 123 119 98 103 107 99

227 222 206 196 188 179 171 160 154 145 141 136 111 116 120 111

UPN UPN 80 UPN 100 UPN 120 UPN 140 UPN 160 UPN 180 UPN 200 UPN 220 UPN 240 UPN 260 UPN 280 UPN 300 UPN 320 UPN 350 UPN 380 UPN 400

Table 6.1

HP 200 x 43 HP 200 x 53 HP 220 x 57 HP 260 x 75 HP 260 x 87 HP 305 x 79 HP 305 x 88 HP 305 x 95 HP 305 x 110 HP 305 x 126 HP 305 x 149 HP 305 x 180 HP 305 x 186 HP 305 x 223 HP 320 x 88 HP 320 x 103 HP 320 x 117 HP 320 x 147 HP 320 x 184 HP 360 x 84 HP 360 x 109 HP 360 x 133 HP 360 x 152 HP 360 x 174 HP 360 x 180 HP 400 x 122 HP 400 x 140 HP 400 x 158 HP 400 x 176 HP 400 x 194 HP 400 x 213 HP 400 x 231

181 145 143 129 111 147 132 122 106 94 80 67 65 55 128 111 98 80 65 162 126 104 92 81 78 116 102 91 82 75 69 64

219 176 174 156 135 178 159 148 129 113 97 81 79 67 155 135 119 96 78 196 153 126 111 98 95 141 124 111 100 91 84 77

112 90 88 80 70 91 81 76 66 58 50 42 41 35 81 70 62 51 42 98 77 64 56 50 48 70 61 55 50 46 42 39

150 121 119 108 94 121 109 101 88 78 67 56 55 47 108 94 83 68 55 132 103 86 76 67 65 95 83 74 67 62 57 53

176 141 105 86 71 59 152 117 91 74 60 50 42 104 95 87 79 72 78 68 63 57 52 48 44 40 37 34 31 29 28 26 25 23 21 19 18 17

214 171 127 104 86 72 184 141 110 89 72 60 50 125 114 105 95 87 94 82 76 69 63 58 53 49 45 41 38 35 33 31 30 27 25 23 22 20

108 88 66 55 46 39 95 74 58 48 39 33 28 63 58 53 49 45 47 42 38 35 32 30 28 25 23 22 20 19 18 17 16 15 14 13 12 11

146 117 88 73 60 51 127 98 77 63 51 43 36 85 78 71 65 60 64 56 52 47 43 40 37 34 31 29 27 25 23 22 21 20 18 17 16 15

HD HD 260 x 54,1 HD 260 x 68,2 HD 260 x 93,0 HD 260 x 114 HD 260 x 142 HD 260 x 172 HD 320 x 74,2 HD 320 x 97,6 HD 320 x 127 HD 320 x 158 HD 320 x 198 HD 320 x 245 HD 320 x 300 HD 360 x 134 HD 360 x 147 HD 360 x 162 HD 360 x 179 HD 360 x 196 HD 400 x 187 HD 400 x 216 HD 400 x 237 HD 400 x 262 HD 400 x 287 HD 400 x 314 HD 400 x 347 HD 400 x 382 HD 400 x 421 HD 400 x 463 HD 400 x 509 HD 400 x 551 HD 400 x 592 HD 400 x 634 HD 400 x 677 HD 400 x 744 HD 400 x 818 HD 400 x 900 HD 400 x 990 HD 400 x 1086

HE 100 AA HE 100 A HE 100 B HE 100 M HE 120 AA HE 120 A HE 120 B HE 120 M HE 140 AA HE 140 A HE 140 B HE 140 M HE 160 AA HE 160 A HE 160 B HE 160 M HE 180 AA HE 180 A HE 180 B HE 180 M HE 200 AA HE 200 A HE 200 B HE 200 M HE 220 AA HE 220 A HE 220 B HE 220 M HE 240 AA HE 240 A HE 240 B HE 240 M HE 260 AA HE 260 A HE 260 B HE 260 M HE 280 AA HE 280 A HE 280 B HE 280 M HE 300 AA HE 300 A HE 300 B HE 300 M HE 320 AA HE 320 A HE 320 B HE 320 M HE 340 AA HE 340 A HE 340 B HE 340 M HE 360 AA HE 360 A HE 360 B HE 360 M HE 400 AA HE 400 A HE 400 B HE 400 M HE 450 AA HE 450 A HE 450 B HE 450 M HE 500 AA HE 500 A HE 500 B HE 500 M HE 550 AA HE 550 A HE 550 B HE 550 M HE 600 AA HE 600 A HE 600 B HE 600 M HE 600 x 337 HE 600 x 399 HE 650 AA HE 650 A HE 650 B HE 650 M HE 650 x 343 HE 650 x 407 HE 700 AA

290 217 180 96 296 220 167 92 281 208 155 88 244 192 140 83 229 187 131 80 211 174 122 76 200 161 115 73 185 147 108 61 176 141 105 59 168 136 102 59 158 126 96 50 152 117 91 50 147 112 88 50 142 107 86 51 135 101 82 52 133 96 79 53 130 92 76 55 123 90 76 56 120 89 75 57 49 42 118 87 74 58 50 43 114

355 264 218 116 361 267 202 111 342 253 187 106 297 234 169 100 279 226 159 96 256 211 147 92 242 195 140 88 225 178 131 73 214 171 127 72 204 165 123 71 192 153 116 60 184 141 110 60 177 134 106 60 170 128 102 61 161 120 97 62 156 113 93 62 152 107 89 63 142 104 88 64 138 102 86 65 56 48 135 100 85 66 57 49 129

181 138 115 65 182 137 106 61 172 129 98 58 150 120 88 54 141 115 83 52 130 108 77 49 122 99 72 47 114 91 68 39 108 88 66 39 104 84 64 38 97 78 60 33 95 74 58 33 94 72 57 34 92 70 56 34 90 68 56 36 91 66 55 38 91 65 54 39 88 65 55 41 88 65 56 42 37 32 88 65 56 44 38 33 86

245 185 154 85 247 185 141 80 233 174 130 76 203 161 118 71 190 155 110 68 175 145 102 65 165 134 97 62 154 122 91 52 146 117 88 51 139 113 85 50 131 105 80 43 127 98 77 43 123 94 75 43 120 91 73 44 115 87 71 45 114 83 69 47 113 80 67 48 108 79 67 50 106 79 67 51 44 38 105 78 66 52 45 39 102

HE 700 A HE 700 B HE 700 M HE 700 x 352 HE 700 x 418 HE 800 AA HE 800 A HE 800 B HE 800 M HE 800 x 373 HE 800 x 444 HE 900 AA HE 900 A HE 900 B HE 900 M HE 900 x 391 HE 900 x 466 HE 1000 AA HE 1000 x 249 HE 1000 A HE 1000 B HE 1000 M HE 1000 x 393 HE 1000 x 415 HE 1000 x 438 HE 1000 x 494 HE 1000 x 584 HL 920 x 345 HL 920 x 368 HL 920 x 390 HL 920 x 420 HL 920 x 449 HL 920 x 491 HL 920 x 537 HL 920 x 588 HL 920 x 656 HL 920 x 725 HL 920 x 787 HL 920 x 970 HL 1000 AA HL 1000 A HL 1000 B HL 1000 M HL 1000 x 443 HL 1000 x 483 HL 1000 x 539 HL 1000 x 554 HL 1000 x 591 HL 1000 x 642 HL 1000 x 748 HL 1000 x 883 HL 1100 A HL 1100 B HL 1100 M HL 1100 R

Section factors for protected steel members - European sections

Page 17 of 21

85 72 59 51 44 108 84 72 60 52 44 101 81 70 62 54 45 98 88 81 70 64 57 54 51 46 39 69 65 62 58 54 50 46 42 38 35 32 27 82 76 66 60 55 51 46 45 42 39 34 29 76 67 61 53

96 82 67 58 50 122 94 81 68 59 50 113 90 78 69 60 51 108 97 89 78 70 63 60 57 51 44 79 74 70 66 61 56 52 48 43 39 37 30 92 85 74 67 63 58 52 51 48 44 38 33 85 75 68 59

64 55 45 39 34 84 66 57 48 41 35 81 65 57 50 43 37 79 71 66 57 52 47 44 42 38 33 52 49 46 43 41 37 35 32 29 26 25 20 63 58 51 46 43 40 36 35 33 31 27 23 59 52 47 42

76 65 53 46 40 98 76 66 55 48 41 93 74 65 57 49 42 90 81 74 65 59 53 50 48 43 37 62 58 55 51 48 44 41 37 34 31 29 24 73 68 59 54 50 46 42 41 39 36 31 27 68 60 55 48

291 278 259 247 235 225 213 198 188 178 153 138 130 120

341 322 298 282 267 254 240 223 211 199 171 153 144 133

209 204 195 187 180 173 165 155 148 142 124 113 107 100

258 248 233 223 212 203 193 180 171 163 141 128 121 112

UPE UPE 80 UPE 100 UPE 120 UPE 140 UPE 160 UPE 180 UPE 200 UPE 220 UPE 240 UPE 270 UPE 300 UPE 330 UPE 360 UPE 400

6.1.2 Section factor for British sections UB UB 127 x 76 x 13 UB 152 x 89 x 16 UB 178 x 102 x 19 UB 203 x 102 x 23 UB 203 x 133 x 25 UB 203 x 133 x 30 UB 254 x 102 x 22 UB 254 x 102 x 25 UB 254 x 102 x 28 UB 254 x 146 x 31 UB 254 x 146 x 37 UB 254 x 146 x 43 UB 305 x 102 x 25 UB 305 x 102 x 28 UB 305 x 102 x 33 UB 305 x 127 x 37 UB 305 x 127 x 42 UB 305 x 127 x 48 UB 305 x 165 x 40 UB 305 x 165 x 46 UB 305 x 165 x 54 UB 356 x 127 x 33 UB 356 x 127 x 39 UB 356 x 171 x 45 UB 356 x 171 x 51 UB 356 x 171 x 57 UB 356 x 171 x 67 UB 406 x 140 x 39 UB 406 x 140 x 46 UB 406 x 178 x 54 UB 406 x 178 x 60 UB 406 x 178 x 67 UB 406 x 178 x 74 UB 457 x 152 x 52 UB 457 x 152 x 60 UB 457 x 152 x 67 UB 457 x 152 x 74 UB 457 x 152 x 82 UB 457 x 191 x 67 UB 457 x 191 x 74 UB 457 x 191 x 82 UB 457 x 191 x 89 UB 457 x 191 x 98 UB 533 x 210 x 82 UB 533 x 210 x 92 UB 533 x 210 x 101 UB 533 x 210 x 109 UB 533 x 210 x 122 UB 610 x 229 x 101 UB 610 x 229 x 113 UB 610 x 229 x 125 UB 610 x 229 x 140 UB 610 x 305 x 149 UB 610 x 305 x 179 UB 610 x 305 x 238 UB 686 x 254 x 125 UB 686 x 254 x 140 UB 686 x 254 x 152 UB 686 x 254 x 170 UB 762 x 267 x 147 UB 762 x 267 x 173 UB 762 x 267 x 197 UB 838 x 292 x 176 UB 838 x 292 x 194 UB 838 x 292 x 226 UB 914 x 305 x 201 UB 914 x 305 x 224 UB 914 x 305 x 253 UB 914 x 305 x 289 UB 914 x 419 x 343 UB 914 x 419 x 388 UB 1016 x 305 x 222 UB 1016 x 305 x 249 UB 1016 x 305 x 272 UB 1016 x 305 x 314 UB 1016 x 305 x 349 UB 1016 x 305 x 393 UB 1016 x 305 x 415 UB 1016 x 305 x 438 UB 1016 x 305 x 494 UB 1016 x 305 x 584

Table 6.2

UC 279 270 262 234 244 207 281 248 222 231 196 170 282 250 217 201 179 158 209 184 159 248 212 207 184 165 142 240 205 189 172 154 140 199 175 157 143 130 169 153 139 129 118 157 141 129 120 108 143 129 117 105 110 92 71 130 116 107 97 120 103 91 111 101 87 104 93 83 73 69 61 98 88 81 70 64 57 54 51 46 39

325 314 304 269 286 242 318 280 251 268 227 197 314 279 241 227 202 178 242 212 183 278 237 236 210 189 162 268 229 215 195 175 159 222 195 175 159 145 191 173 158 146 133 177 159 145 135 122 161 145 131 118 126 106 81 145 131 121 109 134 115 102 124 113 98 116 104 93 82 78 70 108 97 89 78 70 63 60 57 51 44

200 194 188 173 169 143 218 192 173 164 140 122 225 200 174 155 138 122 150 133 115 195 167 152 136 122 105 189 162 143 129 117 106 158 139 125 114 104 128 117 106 98 90 121 109 100 93 84 111 100 91 82 80 68 52 101 91 84 76 95 81 72 88 80 69 82 74 66 59 51 46 79 71 66 58 52 47 44 42 38 33

246 237 230 207 210 178 254 224 201 200 171 149 257 229 198 181 162 143 183 161 139 225 193 182 162 146 126 217 186 168 153 138 125 181 159 143 130 119 150 137 125 115 105 141 126 116 108 97 129 116 106 95 97 81 62 117 105 97 88 109 93 83 101 92 79 94 85 76 67 61 54 90 81 74 65 59 53 50 48 43 37

UC 152 x 152 x 23 UC 152 x 152 x 30 UC 152 x 152 x 37 UC 203 x 203 x 46 UC 203 x 203 x 52 UC 203 x 203 x 60 UC 203 x 203 x 71 UC 203 x 203 x 86 UC 254 x 254 x 73 UC 254 x 254 x 89 UC 254 x 254 x 107 UC 254 x 254 x 132 UC 254 x 254 x 167 UC 305 x 305 x 97 UC 305 x 305 x 118 UC 305 x 305 x 137 UC 305 x 305 x 158 UC 305 x 305 x 198 UC 305 x 305 x 240 UC 305 x 305 x 283 UC 356 x 368 x 129 UC 356 x 368 x 153 UC 356 x 368 x 177 UC 356 x 368 x 202 UC 356 x 406 x 235 UC 356 x 406 x 287 UC 356 x 406 x 340 UC 356 x 406 x 393 UC 356 x 406 x 467 UC 356 x 406 x 551 UC 356 x 406 x 634

252 195 161 168 150 131 112 94 132 110 93 76 62 120 100 87 76 62 52 45 108 92 80 71 63 52 45 39 34 29 26

304 235 194 202 180 158 135 113 160 133 112 92 74 145 120 105 91 74 62 54 130 111 96 85 76 63 54 48 41 35 31

Ap/V [m-1]

Section factors for protected steel members - British sections

Page 18 of 21

156 122 101 104 93 82 71 60 82 69 58 48 40 75 62 54 48 39 33 29 66 56 49 44 39 32 28 25 22 19 17

208 162 134 139 124 109 93 79 109 91 77 64 52 99 83 72 63 52 44 38 88 75 66 58 52 43 37 33 29 25 22

6.2

Properties of fire protection material

For a uniform temperature distribution in a cross-section, the temperature increase ∆Θ a,t of an insulated steel member during a time interval ∆ t is given by: ∆Θ a ,t =

φ Ap λ p  (Θ g ,t − Θ a ,t )  1 . . ⋅ ⋅ ∆ t  −  e 10 − 1 ⋅ ∆Θ g ,t V d p 1 + φ / 3  ca ⋅ ρ a   

; with

φ=

c p .d p .ρ p . Ap ca .ρ a .V

As simplification φ may be taken equal to 0 (safe-sided approach), which results in a modified section factor, the thermal section factor:

Ap λ p . V dp The protection material must be fixed in such a way that it will keep its protective function during the required fire resistance time, even under huge deformations, see EN13381 [2]. The following material properties may be used as an approximation to calculate the thermal section factor. Other data may be obtained from national fire tests. Table 6.1 : General properties for preliminary design. Material Sprays - mineral fibre - vermiculite cement - perlite High-density sprays - vermiculite (or perlite) and cement - vermiculite (or perlite) and gypsum Boards - vermiculite (or perlite) and cement - fibre-silicate or fibre calcium-silicate - fibre-cement - gypsum board Compressed fibre boards - fibre-silicate, mineral-wool stone-wool Concrete Light weight concrete Concrete bricks Bricks with holes Solid bricks

Unit mass ρp [kg/m3]

Thermal conductivity λp [W/(m.K)]

Specific heat cp [J/(kg.K)]

300 350 350

0.12 0.12 0.12

1200 1200 1200

550

0.12

1100

650

0.12

1100

800

0.2

1200

600

0.15

1200

800 800

0.15 0.20

1200 1700

150

0.2

1200

2300 1600 2200 1000 2000

1.60 0.80 1.00 0.40 1.20

1000 840 1200 1200 1200

Page 19 of 21

⋅

6.3

Ap λ p

V dp 1500

1200 1000

800

Page 20 of 21

Critical Steel temperature [°C]

800 700 600

700

500

600

400 350 300

500

250 200

400

150

300 100

200 100 0 0

15

30

45

60

75

90

105

120

135

150

165

Fire Resistance [min]

180

Nomogram for protected steel members

2000

900

7.

References

[1]

EN 1993 part 1-2: “Design of steel structures – Structural fire design”

[2]

EN 13381 part 1 to 4:” Test methods for determining the contribution to the fire resistance of structural members “

[3]

EN 10025 parts 1 to 6: Hot rolled products of structural steels

[4]

ECSC project “Buckling curves of hot rolled H sections submitted to fire”; CN° 7210SA/316/515/618/931

[5]

EN 1993 part 1-1: “Design of steel structures-General rules and rules for buildings”

Page 21 of 21