Fire resistance assessment of composite steel-concrete structures

Transcription

1 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Fire resistance assessment of composite steelconcrete structures Basic design methods Worked examples CAJOT LouisGuy CEN/TC50 EGEN994 Convenor ArcelorMittal lg.cajot@arcelormittal.com

2 Fire resistance assessment of composite steelconcrete structures Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Basic design methods of EN994 Fire part of Eurocode 4

3 Fire parts of Eurocodes to 6 and 9 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 3 Following common layout to provide design rules for fire resistance of various types of structures: General Scope, application field, definitions, symbols and units Basic principles Performances requirements, design values of material properties and assessment approaches Material properties Mechanical and thermal properties at elevated temperatures Assessment methods for fire resistance Constructional details Annexes Additional information: common case more detailed design rules

4 Scope of fire part of Eurocode 4 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 4 Load bearing function R of composite structures is covered by the design rules of the fire part of Eurocode 4 Load bearing function of a structure is satisfied only if during the relevant of fire exposure t E fi,d,t R fi,d,t where E fi,d,t : design effect of actions (Eurocodes 0 and ) R fi,d,t : corresponding design resistance of the structure at instant t In addition, for elements ensuring compartmentation, the separating function has to be maintained during the relevant fire exposure t Integrity E Thermal insulation I

5 Scope of fire part of Eurocode 4 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 5 E Integrity separating function I Thermal insulation separating function I : Calculated temperature rise under standard fire 40 K heat hot gas E assumed to be satisfied for composite slabs

6 Scope of fire part of Eurocode 4 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 6 Covered field Composite elements designed according to EN994 Longitudinal shear connection between steel and concrete in accordance with EN994 or verified by tests Typical elements Steel grades S35, S75, S355, S40 & S460 of EN005, EN00 and EN09 Profiled steel sheeting following 3.5 of EN994 Rebars in accordance with EN0080 Concrete in accordance with EN994 except < C0/5 and LC0/ and > C50/60 and LC50/55

7 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 7 Actions on structures exposed to fire Thermal actions Mechanical actions Eurocodes 0 and Load level in fire situation Design approaches Member analysis Analysis of parts of the structure Global structural analysis global structural analysis analysis of parts of the structure member analysis Material properties at elevated temperatures Thermal properties of steel and concrete Mechanical properties of steel (sections, rebars) and concrete Partial factors for fire design of steel structures

8 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 8 Application domain of different design methods for composite structures under fire situation Thermal action defined under standard fire Type of analysis Tabulated Data Simple calculation methods Critical temperature Advanced calculation models Member analysis YES YES YES YES Analysis of parts of the structure NOT applicable Applicable in some cases NOT applicable YES Global structural analysis NOT applicable NOT applicable NOT applicable YES

9 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 9 Application domain of different design methods for composite structures under fire situation Thermal action defined under natural fire Type of analysis Tabulated Data Simple calculation methods Critical temperature Advanced calculation models Member analysis Analysis of parts of the structure Global structural analysis NOT applicable YES YES Applicable with some specific conditions NOT applicable NOT applicable YES NOT applicable NOT applicable NOT applicable YES

10 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 0 Thermal properties of steel and concrete at elevated temperatures Thermal conductivity [W/m K] steel concrete (lower/upper limits) Temperature [ C] Thermal capacity (ρc) [MJ/m 3 K] steel concrete (NC) Temperature [ C] Density of steel: 7850 kg/m 3 ; Density of normal weight concrete: 300 kg/m3 Thermal properties of concrete ONLY used in Advanced Calculation Models

11 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Temperature field after 90 minutes of ISOfire θ max = 003 C θ max = 003 C STEEL HE300A CONCRETE HE300A θ max = 535 C θ max = 50 C STEEL CONCRETE column CONCRETE column

12 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Thermal properties of steel and concrete at elevated temperatures 0 Thermal expansion of steel L/L (x0 3 ) 5 concrete 0 steel Temperature [ C]

13 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 3 Mechanical properties of steel at elevated temperatures Reduction factors Elastic modulus k E,θ Effective yield strength k y,θ obtained with % strain Temperature ( C) Elastic modulus at 600 C reduced by about 70% Normalised stress 0 C 00 C 400 C 500 C 600 C 700 C 800 C % Strain (%) Yield strength at 600 C reduced by over 50%

14 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 4 Mechanical properties of concrete at elevated temperatures Strength % of normal value Strain (%) 6 Strain ε cu at 00 maximum 5 strength Normalweight Concrete Temperature ( C) 3 Normalised stress.0 0 C C 800 C 400 C 600 C 3 4 Strain (%) ε cu Compressive strength at 600 C reduced by about 50% 0

15 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 5 Mechanical properties of concrete and steel at elevated temperatures Strength % of normal value Normalweight Concrete Effective yield strength k y,θ obtained with % strain Temperature ( C)

16 Application of EC4 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 6 Partial safety factors of steel/composite at elevated temperatures Material Structural steel Resistance of cross section Ambient temperature design Fire design γ M0 =.00 γ M,fi,a =.0 Stability of members γ M =.00 γ M,fi,a =.0 Resistance of cross section In tension to fracture γ M =.5 γ M,fi,a =.0 Stud connectors γ v =.5 γ M,fi,v =.0 Steel reinforcing bars γ s =.5 γ M,fi,s =.0 Concrete γ c =.50 γ M,fi,c =.0

17 Application of EC4 for fire resistance assessment Tabulated Data Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 7 Thermal action defined under standard fire Type of analysis Tabulated Data Simple calculation methods Critical temperature Advanced calculation models Member analysis YES YES YES YES Analysis of parts of the structure NOT applicable Applicable in some cases NOT applicable YES Global structural analysis NOT applicable NOT applicable NOT applicable YES

18 Application of EC4 for fire resistance assessment Tabulated Data Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 8 Tabulated data (steel/concrete composite members) Composite beams Composite columns Slab Concrete for insulation

19 Application of EC4 for fire resistance assessment Tabulated Data Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 9 Design load in fire situation E fi,d,t = G k,j Ψ, Q k, Ψ,i Q k,i j i Recommended, for practical application refer to each National Annex Load level η fi,t = E fi,d,t R d relative to room temperature design resistance

20 Application of EC4 for fire resistance assessment Tabulated Data Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 0 Tabulated data and relevant parameters (composite partially encased columns) A c e w b e f A s u s u s h Standard Fire Resistance R30 R60 R90 R0 Minimum ratio of web to flange thickness e w /e f 0,5 Minimum crosssectional dimensions for load level η fi,t 0,8...3 minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c A s ) in % Minimum crosssectional dimensions for load level η fi,t 0, minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c A s ) in % 3 Minimum crosssectional dimensions for load level η fi,t 0, minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c A s ) in % Standard fire rating Load level η fi,t = E fi.d / R d Section dimension Reinforcing steel Rebars cover

21 Application of EC4 for fire resistance assessment Tabulated Data Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Tabulated data and relevant parameters (composite encased columns) Load level η fi,t = E fi.d / R d c c u s h c Standard Fire Resistance Standard fire rating b c u s R30 R60 R90 R0 R80 R Minimum dimensions h c and b c [mm] minimum concrete cover of steel section c [mm] minimum axis distance of reinforcing bars u s [mm] * or Minimum dimensions h c and b c [mm] minimum concrete cover of steel section c [mm] minimum axis distance of reinforcing bars u s [mm] * * Section dimension NOTE : *) These values have to be checked according to of EN 99 Section and rebars Cover

22 Establishing fire resistance of composite structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Thermal action defined under standard fire Type of analysis Tabulated Data Simple calculation methods Critical temperature Advanced calculation models Member analysis YES YES YES YES Analysis of parts of the structure NOT applicable Applicable in some cases NOT applicable YES Global structural analysis NOT applicable NOT applicable NOT applicable YES

23 Establishing fire resistance of composite structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 3 Simple calculation models and critical temperature for composite members Beams (steel or composite) Columns

24 Establishing fire resistance of composite structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 4 Critical temperature method for composite beams Simply determined composite beam h h h c > 0mm h < 500mm

25 Establishing fire resistance of composite structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 5 FIRE RESISTANCE Action in fire situation E fi.d.t Classify member Composite Steel/Concrete Temperature (UNPROTECTED Steel) Find Section Factor A m /V and k sh Building regulations t fi,requ Resistance at 0 C by fire rules R fi,d,0 θ t,fi,requ Load level for fire design ηµ 0 fi,t Critical temperature θ cr η fi,t = k y,θcr Is θ cr θ t,fi,requ??

26 Establishing fire resistance of composite structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 6 FIRE RESISTANCE Action in fire situation E fi.d.t Classify member Steel Temperature (PROTECTED) Find Section Factor A m /V and k sh Building regulations t fi,requ Resistance at 0 C by fire rules R fi.d.0 θ t,fi,requ Load level for fire design η fi,t Critical temperature θ cr η fi,t = k y,θcr Is θ cr θ t,fi,requ??

27 Establishing fire resistance of composite structures using composite process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 7 Critical temperature of steel members Steel member temperature (assumed to be uniform and equal to bottom flange temperature) Degree of utilisation η fi,t Stable structure Temperature Strength reduction of steel member θ cr Collapse

28 Establishing fire resistance of composite structures using composite process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 8 Simple Calculation Models Steel elements (sections, Steel Sheet, Rebars) θ k y,θ f y,θ k s,θ f s,θ Concrete θ

29 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 9 Composite slab fire design No tabulated data Simplified calculation ( 4.3) Only for use with ISO fire Integrity criteria E is assumed always satisfied Thermal insulation I Criteria: T max 80 K T average 40 K

30 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 30 Simple Calculation Models The fire resistance t i [min] corresponding to criteria I is given by with exposed perimeter: L r area: A h h ½ 3 3 r r 3 0 i L A a a L A a a h a a t Φ = r h h L A = 3 3 h h Φ = Table D.: Coefficients for determination of the fire resistance with respect to thermal insulation a 0 [min] a [min/mm] a [min] a 3 [min/mm] a 4 [mm min] a 5 [min] Normal weight concrete 8,8,55,6 0, ,0 Lightweight concrete 79,,8,44 0, ,3

31 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 3 Φ = h 3 h 3 area: A area: A ½ 3 3 Φ is the view factor F A,B calculated by the rule of Hottel h h A exposed perimeter: L r B exposed perimeter: L r

32 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 3 Alternative method : minimum effective thickness () The effective h eff is given by the formula : h eff = h 0,5 h 3 for h / h,5 and h > 40mm h eff h = h 0, eff 75 3 for h / h >,5 and h > 40mm Table D.6: Minimum effective thickness as a function of the standard fire resistance. Standard Fire Resistance Minimum effective thickness h eff [mm] I 30 I 60 I 90 I 0 I 80 I h 3 h 3 h 3 h 3 h 3 h 3

33 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November I [min] h eff h 3 [mm]

34 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 34 Composite slab fire design No tabulated data Simplified calculation ( 4.3) Only for use with ISO fire Integrity criteria E is assumed always satisfied Thermal insulation I Load bearing capacity R If the design conforms to EN 994, R 30 minutes. For composite slabs, the bending capacity has to be determined by a plastic design.

35 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 35 Composite slab fire design Temperature field The temperature θ a of the lower flange, web and upper flange of the steel decking may be given by: θ a = b 0 b 3 b A L r b 3 Φ a 4 Φ (D..) Concrete Fire resistance [min] Part of the steel sheet b 0 [ o C] b [ o C]. mm b [ o C]. mm b 3 [ o C] b 4 [ o C] Normal weight concrete 60 Lower flange Web Upper flange ,3,96,6 86,4 537,7 48,4 50,7 35,9 679,8 90 Lower flange Web Upper flange ,55,,79 65, 464,9 767,9 08, 340, 47,0 0 Lower flange Web Upper flange ,3,8,67 46,7 344, 59,6 8,8 67,4 379,0

36 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 36 Composite slab fire design Temperature field The temperature θ s of the reinforcement bars in the rib, if any according to figure D.., as follows: θ s = c 0 c u h 3 c z c 3 A L r c 4 α c 5 3 (D..) z = u u u3 Table D.. : Coefficients for the determination of the temperatures of the reinforcement bars in the rib. Concrete Fire resistance [min] c 0 [ o C] c [ o C] c [ o C]. mm 0.5 c 3 [ o C].mm c 4 [ o C/ o ] c 5 [ o C].mm Normal weight concrete ,0, ,30, ,79,68 36

37 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 37 Composite slab fire design θ k y,θ f y,θ f y (T) k s,θ f s,θ T Temperature [ C] Steel Reinforcing steel Concrete f y (T)/f y f sy (T)/f sy f c (T)/f c

38 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 38 Bending capacity in sagging moment M fi,rd The plastic neutral axis of a composite slab or composite beam may be determined from : n i= f m y,i f c,j A θ α ik y,,i θ = slab A jkc,,j 0 γm,fi, a j= γ α slab = 0, 85 M,fi, c x Design moment resistance The design moment resistance M fi,t,rd may be determined from : M fi,t,rd = n i= A z k i i y, θ,i f γ y,i M, fi α m slab j= A z k j j c, θ,j f γ c,j M,fi, c

39 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 39 Bending capacity in hogging moment M fi,rd Temperature field Y Isotherm for θ = θ lim IV (X IV, Y IV ) (X III, Y III ) III I II (0, Y I ) (X II, Y I ) X i and Y i = f(z) with and θ θ lim s = d = c 0 0 d c N s u h d 3 c A L r d 3 z c Φ 3 A L r d 4 3 z is obtained from the equation for the determination of θ s, assuming that u 3 /h = 0,75 and θ s = θ lim c 4 α c 5 3 X

40 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 40 Bending capacity in hogging moment M fi,rd h Y I If Y I > h Alternative procedure based on the effective thickness

41 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 4 Bending capacity in hogging moment M fi,rd h eff x Depth X [mm] Temperature θ c [ C] after a fire duration in min. of h eff x θ c Heated lower side of slab

42 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 4 Bending capacity of the composite slab pfi 8 M fi,rd M fi,rd,g M fi,rd,d pfi 8 M fi,rd Mfi,Rd,G Mfi,Rd,D pfi Mfi,Rd 8

43 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 43 Bending capacity of the composite slab M fi,rd pfi 8 M fi,rd Mfi,Rd M fi,rd pfi 8 pfi 8 = M fi,rd M fi,rd ( M M ) ( M ) 4 fi,rd fi,rd fi,rd

44 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 44 Composite beam fire design Temperature field b eff b h c e Upper flange Web Lower flange A / V or A / V = (b e i i A / V or A / V = (b e ) / b i i i i p,i A / V or A / V = (b e p,i p,i i i i ) / b ) / b If the beam depth h does not exceed 500mm, the temperature of the web may be taken as equal to that of the lower flange. e e e e w b θ a,t = k shadow h w e caρ a A i Vi h net t h Depth X [mm] Temperature θ c [ C] after a fire duration in min. of h eff x θ c Heated lower side of slab

45 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 45 Composite beam fire design Structural behaviour Bending moment resistance model M Rd Classical determination of the bending moment resistance, taking into account the variation of material properties with temperatures, see Annex E. No strength reduction in concrete if T < 50 C The value of the tensile force is limited by the resistance of the shear connectors : T N P fi,rd

46 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 46 Composite beam fire design Structural behaviour Bending moment resistance model M Rd Verification of the stud connectors P fi,rd = minimum of the following values: P P fi,rd fi,rd = 0,8 ku, θ = kc, θ P Rd P Rd with P Rd obtained from equation 6.8 of EN994 with P Rd obtained from equation 6.9 of EN994 with γ m,fi used instead of γ ν k u,θ and k c,θ defining the decrease of material strength θ u in the stud = 0.80 θ upper flange θ c of the concrete = 0.40 θ upper flange

47 Simple Calculation Models Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 47 Composite beam fire design Hogging moment resistance at an intermediate support Choose the effective width of the slab to have the slab completely cracked, but b eff (T) b eff (0 C). h c h b eff A s b b e w e h w e θ θ θ w Tension f s y ( θs ) / γ M, fi,s f a y ( )/ γm, fi,a θ f a y ( θ w ) / γm, fi,a f a y ( θ) / γ M, fi,a Y F T F Y T Compression If web or lower flange are Class 3, reduce its width according to EN If web or lower flange are Class 4, its resistance may be neglected. Note: classification according to EN993 ε = 0,85 [ 35 / ] 0, 5 f y

48 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 48 Beams Columns

49 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 49 Partially Encased Beam Sagging moment M fi,rd (B) 3 b k s f sy γ M,fi,s u h h c (A) b fi b c,fi b c h fi e w b fi f ay e f b c,fi f c γ M,fi,c k r f ry γ M,fi,a γ M,fi,s u h Hogging moment M fi,rd b

50 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 50 Beams Columns

51 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 5 u Partially Encased Column b Z e f Y h f amax,w,t = ay,w,0 C f (0,6H Table G.5: Reduction factor k y,t for the yield point f sy,0 C of the reinforcing bars u[mm] Standard Fire Resistance R30 R60 0,789 0,883 0,976 R90 0,34 0,434 0,57 0,696 0,8 R0 0,70 0,3 0,88 0,367 0,436 t / h) Table G.6: Reduction factor k E,t for the modulus of elasticity E s,0 C of the reinforcing bars b c,fi u h w,fi e w b c,fi u[mm] Standard Fire Resistance R30 0,830 0,865 0,888 0,94 0,935 R60 0,604 0,647 0,689 0,79 0,763 R90 0,93 0,83 0,406 0,5 0,69 R0 0,0 0,8 0,73 0,33 0,85 R30 R60 R90 R0 θ f,t = θ0,t k t (A m / V) A m /V [m ] θ c,t [ C] A m /V [m ] θ c,t [ C] A m /V [m ] θ c,t [ C] A m /V [m ] θ c,t [ C] Standard Fire Resistance θ 0,t [ C] k t [m C] R ,65 R ,55 R ,5 R ,65

52 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 5 Partially Encased Column b Z Standard Fire Resistance b c,fi [mm] e f R 30 4,0 u R 60 5,0 Y h R 90 0,5 (A m /V),5 R 0,0 (A m /V) 4,0 b c,fi h w,fi = 0,5(h e f ( 0,6(H t / h) ) ) h w,fi b c,fi where H t is given in table G. u e w Standard Fire Resistance H t [mm] R R R R 0 50

53 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 53 Partially Encased Column N = N N N N fi,pl,rd fi,pl,rd,f fi,pl,rd,w fi,pl,rd,c fi,pl,rd,s (EI) fi,eff,z = ϕ f,θ (EI) fi,f,z ϕ w,θ (EI) fi,w,z ϕ c,θ (EI) fi,c,z ϕ s,θ (EI) fi,s,z where ϕ i,θ is a reduction coefficient depending on the effect of thermal stress. The values of ϕ i,θ are given in Table G.7 Standard fire resistance Buckling curve "c" of EN 993 φ f,θ φ w,θ φ c,θ φ s,θ R30,0,0 0,8,0 R60 0,9,0 0,8 0,9 R90 0,8,0 0,8 0,8 R0,0,0 0,8,0 Table G.7

54 Simple calculation model for composite members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 54 Beams Columns