Fire resistance assessment of Composite structures

Transcription

1 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Fire resistance assessment of Composite structures Basic design methods Worked examples CAJOT Louis-Guy Chairman of CEN/TC50/SC4/EG - Fire Part ArcelorMittal

2 The Building (R+5) Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 0mm slab COFRAPLUS 60 Composite beams IPE450 Partially encased composite columns HE60A Bracing system

3 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Composite slab, composite beams, composite columns S m 6 m 6 m 6 m 6 m m m m m m m m m m m A Bracing system B 4 m 7 m Bracing system 7 m Bracing system S S C Bracing system S S - S

4 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Actions (for all floor levels) Self weight G Composite slab unit weight :. kn/m² Steel structural members Permanent load G Finishing, embedded services, partitions :.50 kn/m² Façade G : kn/m Characteristic values of variable loads and ψ factors Type q k ψ ψ Live load on floors 4.0 kn/m² Snow on roof.7 kn/m²

5 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Structural members Composite slab Total thickness: cm Steel deck: COFRAPLUS60 Thickness of steel deck: 0.75 mm Continuous slab over spans Secondary beams IPE450 linked with headed studs to the composite slab; fire protected steel sections Alternative : Partially encased composite beams IPE450; fire protection obtained through partial encasement Columns for ground level Facade columns: Partially encased HEA60 Alternative: Fully encased HEB60

6 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Composite slab, composite beams, composite columns S m 6 m 6 m 6 m 6 m m m m m m m m m m m A Bracing system B 4 m 7 m Bracing system 7 m Bracing system S S C Bracing system S S - S

7 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 7 Composite slab continuous on supports S m 6 m 6 m 6 m 6 m m m m m m m m m m m A Bracing system B 4 m 7 m Bracing system 7 m Bracing system S S C Bracing system S S - S

8 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 8 Summary of data m m Slab thickness cm Required fire resistance : R60

9 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 9 Material characteristics Steel decking : Concrete : Rebars : f y 50 N/mm² C5/0 ; f c 5 N/mm² f y 500 N/mm² Mesh ST5 ; A,57 cm²/m Loads Ribs : φ8 /rib Permanent loads: Steel decking : Concrete : Permanent load : Variable load: Variable load : g t,k 0,085 kn/m² g b,k,0 kn/m² g c,k,5 kn/m² q k 4,0 kn/m²

10 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 0 Geometric parameters l COFRAPLUS60 m l φ8 per rib,5 cm²/m h 6 mm h 58 mm h 0 l 0 mm l 6 mm l 06 mm Application field Trapezoidal steel decking profiles [mm] 80 l 55 l 40 l 5 50 h 5 50 h 00 Existing geometric parameters [mm] l 0 l 6 l 06 h 6 h 58 Condition fulfilled? OK OK OK OK OK

11 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Fire resistance according to thermal insulation t i a 0 + a h ' + a Φ + a A L r + a 4 l + a 5 A L r l t i ( 8,8) +,55 h ' A + (,6) Φ + 0, L r + ( 75) l A + 48 L r l For Normal Weight Concrete a 0 [min] a [min/mm] a [min] a [min/mm] a 4 mm min a 5 [min] -8,8,55 -,6 0,

12 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Fire resistance according to thermal insulation t i a 0 + a h ' + a Φ + a A L r + a 4 l + a 5 A L r l t i A ( 8,8) +, (,6) Φ + 0, L r + ( 75) 06 A + 48 L r 06 l l 0 ½l ½ 5 h 0 h 6 h 58 Exposed Surface l 6 ' h h + h 6mm (h thickness of the screed)

13 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Fire resistance according to thermal insulation t i a 0 + a h ' + a Φ + a A L r + a 4 l + a 5 A L r l t i ( 8,8) +, (,6) Φ + 0, 5,6 + ( 75) ,6 06 h 0 ½ l l 0 ½l 5 Rib geometry factor h 6 h 58 A L r l h + l + l h + l l 5,6 mm Exposed Surface l 6

14 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Fire resistance according to thermal insulation t i a 0 + a h ' + a Φ + a A L r + a 4 l + a 5 A L r l t i ( 8,8) +, (,6) 0,77 + 0, 5,6 + ( 75) ,6 06 t i 7min ½ l l 0 ½l 5 h 0 View factor h 6 h 58 Φ l l l l h + l + h + l 0,77 Exposed Surface l 6

15 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Simplified method (EN994--/Annex D/ D.4) For h /h,5 and h > 40mm l + l 0+ 6 heff h + 0,5 h 6 + 0,5 58 l + l mm h eff l l l h h h h 6 mm h 58 mm l 0 mm l 6 mm l 06 mm Minimal effective thickness of the slab h eff to satisfy the thermal insulation criteria Standard fire resistance h eff [mm] I 0 I 60 I 90 I 0 I 80 I h 80-h 00-h 0-h 50-h 75-h h 0 ; h eff 85mm I 60

16 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Temperature evolution in the section as a function of the time

17 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November Calculation of the sagging moment resistance M fi,t,rd Temperature distribution in the steel decking : Concrete Fire resistance [min] Part of the Steel decking b 0 [ C] θ b [ C mm] a b 0 + b b [ C/mm] l + b b [ C] A L r + b b 4 [ C] Φ + b 4 Φ ½ l l 0 ½l 5 Lower flange h 0 60 Web Upper flange h 6 Normal Concrete 90 Lower flange Web Upper flange Lower flange h 58 0 Web Upper flange l 6 For the different parts of the steel decking, the temperatures at 60 minutes are : Upper Flange Web Lower Flange θa 95 97, 5,6 + 86,4 0,77 50,7 0,77 86 C 06 θa 66 8,96 5,6 + 57,7 0,77 5,9 0,77 78 C 06 θa 40 69,6 5,6 + 48,4 0,77 679,8 0,77 78 C 06

18 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 8 Temperature of the reinforcing bar in the rib : θ s c 0 + c u h + c z + c A L r + c 4 α + c 5 l ½l 5 l 0 ½l h 6 with z u + u + u 5,8 + 5,8 + 0 z,79 mm 0,5 h 58 u u u α 70 Concrete Fire resistance [min] c 0 [ C] c [ C] c [ C/mm 0.5 ] c [ C/mm] c 4 [ C/ ] c 5 [ C] l 6 u 5,8mm u 5,8mm u 0mm (axis distances) Normal Concrete θs ,79 5,0 5,6 +,04 7, C

19 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 9 Bearing capacity of the different parts of the steel decking and the reinforcing bar : Temperature θ i [ C] Reduction factor k y,i [-] Partial area A i [cm²] f y,i,θ [kn/cm²] F i [kn] Lower flange 86 0,078 0,465,74,74 Web 78 0, 0,98 4,60 4, Upper flange 78 0,09 0,795 7, 5,8 Rebar in the rib 6 0,67 0,50 8,4 9, k y θ [ C]

20 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 0 Positive moment of the composite slab Determination of the plastic neutral axis : zpl Z Equilibrium of the horizontal forces F i α slab ( l + l ) zpl fc ½l 5 l 0 ½l F,74 + 4,+ 5,8 + 9, i zpl αslab ( l + l ) fc 0,85 (0+ 06) 5 0 4,7mm Determination of the positive moment resistance of the composite slab : F i [kn] z i [cm] M i [kncm] for a rib width of 07mm, Lower flange Web,74 4,,96 9,0 5,45 8,40 M i 76,9 kncm Upper flange 5,8 6,6 5,80 Than, for a slab width equal to m, Reinforcing bar in the rib Concrete 9, -0,57 0,0 0, 9,96-4,79 M Mi rib width,769 0,07 + fi,rd 8,5kNm / m

21 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 - Calculation of the hogging moment resistance M fi,t,rd Y The hogging moment resistance of the slab is calculated by considering a reduced cross section established on the basis of the isotherm for the limit temperature θ lim schematised by means of 4 characteristic points. ½ l I III II h IV X l θ lim d 0 + d N s + d A L r + d Φ + d 4 l (N s 6,6 kn is the normal force in the upper reinforcing bar ) Fire resistance [min] d 0 [ C] d [ C].N d [ C].mm d [ C] d 4 [ C].mm Normal weight concrete , ,.0-4 -, ,75-9,9-9, θlim 867, ,75 5,6 0, C 06

22 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Determination of the points of the isotherm : Y III IV ½ l I II h X l The parameter z of the formula D.9 is obtained from the equation for the determination of the temperature of the reinforcing bar, assuming that u /h 0,75 and θ s θ lim θ lim c 0 + c u h + c z + c A L r + c 4 α + c 5 l θlim c0 0,75 c 5,6 c 7,4 c4 c , ,6 5,0 7,4, z 06 06,69mm c ( 40) 0,5

23 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Coordinates of the points of the isotherm : The coordinates of the 4 characteristic points are determined by the following formulae : Y I Y II Y III h Y h IV + z b l 4 + l Points I II III IV Coordinates [mm] X 0,0,7 4, 0,5 Y 0, 0, 58,0 66,0 with b l sinα a l sinα z h a 4a + c a X I 0 X II l XIII l X IV YI + sinα b sinα ( l + l ) ( cos α ) ½ l Y I l III II h IV X c 8 h α arctan l l ( + + a ) si a 8 ( + + a ) si a 8 c + 8 <

24 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Determination of the plastic neutral axis : Y III IV ½ l I II h X l Temperature θ i [ C] Reduction factor k y,i [-] Partial area A i [cm²] f y,i,θ [kn/cm²] F i [kn] Mesh ST5 θ < θ lim,0 0,5 50 6,60 tgβ The horizontal equilibrium gives : F z + 47,4 z 0,85 i pl pl fc > z pl,5mm

25 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Moment resistance of each part of the rib : F i [kn] z i [cm] M i [kncm] Mesh ST5 6,60 8,9 9,0 Concrete rib -6,60 4,5-0, The negative moment resistance of the composite slab, for a rib width of 07mm is given by : M i 8,7 kncm Than, for a slab width equal to m, M Mi rib width,87 0,07 fi,rd 5,74 knm / m

26 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Bearing capacity of the continuous slab The applied load is : E fi,d G k + ψ, Q k, p fi,d,0 * (0,085 +,0 +,5) + 0,6 * 4 6,0 kn/m² For a slab width equal to m, the bearing capacity may be deduced from the sagging and hogging moment by the following relation : p p fi,rd fi,rd + M fi,rd + 4Mfi,Rd + l l 5, ,5 + + ( M + M ) fi,rd fi,rd p fi,rd 9,98 kn/m² > p fi,d 6,0 kn/m² fi,rd ( 5,74 + 8,5 ) 5,74 M The continuous slab has a fire resistance of 60 minutes

27 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 7 Bearing capacity of the continuous slab : Simplified formula p fi,d 6, kn/m²,4 knm 8,4 knm p fi,rd 7, kn/m² p fi,d 6, kn/m²

28 Verification of the composite slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 8 Evolution du moment fléchissant en fonction du temps

29 Verification of the composite slabv Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 9 Evolution de la déformée en fonction du temps

30 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 0 Secondary composite beams S m 6 m 6 m 6 m 6 m m m m m m m m m m m A Bracing system B 4 m 7 m Bracing system 7 m Bracing system S S C Bracing system S S - S

31 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Data Composite beam on supports Continuous slab on supports Beam span 4m Distance between beams m Required fire resistance R m G k + Q k l m l m L 4m (IPE450) S55

32 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Geometrical characteristics and material properties Beam : IPE450 h 450 mm b eff b b b 90 mm e w 9,4 mm h c b e e f e e 4,6 mm f y 55 N/mm² h e w h w Steel decking : f y 50 N/mm² b e Concrete : h c 0 mm b eff 000 mm C5/0 h h f c 5 N/mm² l l l Connectors : f u 450 N/mm² Number 6 Diameter 9 mm h 6 mm h 58 mm l 0 mm l 6 mm l 06 mm

33 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 Geometrical characteristics and material properties Fire protection (use of sprayed protection) High density spray (vermiculite) IPE450 Fire protection material characteristics : Thickness : d p 5 mm Thermal conductivity : λ p 0, W/(m K) Specific heat : c p 00 J/(kg K) Density: ρ p 550 kg/m³

34 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Loads Permanents loads: Steel decking : Concrete : Permanent load : Self weight of the profile : g t,k 0,085 kn/m² g b,k,0 kn/m² g c,k,5 kn/m² G a,k 0,776 kn/ml Variable load: Variable load : q k 4,0 kn/m²

35 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Determination of the load level in fire situation Efi,d,t η fi,t R d M M fi,ed Rd k,j d,, Qk,+ ψ j if Combination of the mechanical actions: E E G + P+ A + ( ψ ou ψ ) System considered: Central support : reaction,5 P. l d,i Q k,i l m l m L 4m (IPE450) S55 [(g + ψ q ) ] + G,5 [(,6 + 0,6 4) ] + 0,776, kn/m Ffi,d,5 k,, k, l a, k Calculated moment: M M fi,ed Rd Ffi,dL, 4 57,6 knm , knm (see Calculation Note) 57,6 065, η fi, t 0,57

36 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Critical temperature method Determination of the critical T For R60 η f fi, t ay,θ cr ay,θ cr / f θ cr 578 C Resistance % of the nominal value f ay f ay 0,57 Table.: Reduction factors k θ for stress-strain relationships of structural steel at elevated temperatures. Steel Temperature θ a [ C] k E,θ,00,00 0,90 0,80 0,70 k p,θ,00,00 0,807 0,6 0,40 k y,θ,00,00,00,00,00 k u,θ,5,5,5, Effective resistance k y,θ ,60 0, 0, 0,60 0,80 0,075 0,78 0,47 0, ,09 0,050 0, 40 0 Elastic modulus k E,θ ,0675 0,0450 0,05 0,075 0,050 0,05 0,06 0,04 0, Temperature [ C]

37 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 7 Temperature calculation in the protected steel cross section The increase of temperature of the various parts of the protected steel beam during the time interval may be determined by the following equation : Δθ a,t λ c p a /d ρ p a A V p,i i + w/ w/0 ( θ θ ) Δt [( e ) Δθ ] with : C a specific heat of the steel ; varying according to the steel temperature [J/(kg.K)] (..(4)) ρ a density of the steel [kg/m ] (.4()) λ p thermal conductivity of the fire protection material [W/m K] d p thickness of the fire protection material [m] A p,i is the area of the inner surface of the fire protection material per unit length of the part i of the steel member [m²/m] V i volume of the part i of the steel cross section per unit length [m /m] A p,i /V i section factor of the part i of the insulated steel cross-section [m - ] Δt time interval (less than 5sec) [s] c pρp A p,i w dp c aρa V where c i p specific heat of the fire protection material [J/kg K] ρ p density of the fire protection material [kg/m ] t a,t t

38 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 8 Temperature calculation in the protected steel cross section T lower flange T upper flange Upper flange Web Lower flange A m /V [m - ] 47,5,8 47,5 Steel temperature after 60 [ C]

39 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 9 Determination of the failure time Steel temperature [ C] θ cr 578 C Protected IPE t 88min time [min]

40 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 40 Verification of the resistance by the moment resistance method θ a,max,0 [ C] k y,θ [-] f ay,θ [N/mm²] Upper flange 480 0,84 9,5 Web 588 0,507 79,9 Lower flange 480 0,84 9,5 k y,θ θ [ C]

41 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 4,096 kn γ e b f e h f e b f T M,fi,a f ay,θ w w ay,θ w f ay,θ + + Determination of the tensile force in the profile Verification of the composite beam The location of the tensile force (with regard to the bottom flange) is given by the following equation : ( ),6mm T e h ) e (b f h e e h f e b f y M,fi,a f f ay, w f w w w ay, f ay, T γ θ θ θ The steel profile is subjected to a tensile force T which could be calculated by the following way

42 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Limitation of the tensile force T N P fi,rd with N P fi,rd is the number of connectors in the critical length of the beam is the design shear resistance of one connector in fire situation P fi, Rd min P P fi, Rd, fi, Rd, 0,8 k k c,θ P u,θ ' Rd, P ' Rd, where ' fu π.d 450 π.9 PRd, 0,8 0,8 γ 4,0 4 M,fi,v 0kN and fc E ' cm PRd, 0,9 α d 0,9,0 9 γ,0 M,fi,v 9kN

43 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 4 Determination of the reduction factors θ v (connectors) 80% θ semelle 0,8 x C k u,θ,04 θ c (concrete) 40% θ semelle 0,4 x C k c,θ 0,954 k θ.,04 0,954 k c,θ k u,θ θ [ C] P fi, Rd min ' Pfi, Rd, 0,8 k u,θprd, 0,8, ,9kN ' Pfi, Rd, k c,θprd, 0, ,kN Limit of the tensile force is fulfilled : T N P fi,rd 4,096 kn< 68 84, kn OK

44 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 44 Determination of the compressive zone of the slab Determination of the effective thickness of the slab h eff 84,8 cm Determination of the critical height h 60' cr 0' h cr 50mm Determination of the thickness of the compressive zone of the concrete : h T f /γ 4, /,0 u beff c M,fi,c b eff h u,mm h eff h cr [mm] Temperature [ C]

45 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 45 Determination of the moment resistance f c,0 C / γ M,fi,c F h u h d h c h eff f ay, θ / γ M,fi,a y F h cr f ay, θw / γ M,fi,a T Location of the force F : f ay, θ / γ M,fi,a y T yf h+ hc (hu /) 5cm M Mfi,Ed 57,6 T(yF y T ) 69,4kNm Verification : 0,8 < M 69,4 fi, Rd fi,rd The stability of the beam in fire situation is fulfilled for R60

46 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 46 Verification of the shear resistance V pl,fi,rd A v f ay, θ γ M,fi,a 9,5 p l Vpl,fi,Rd ,5kN > Vfi, Ed 6, kn,0 OK

47 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 47 Alternative with reactive coating painted beam 8.00 Typical Intumescent Thickness Range Thickness (mm) R0 R60 R90 R A/V (m )

48 Verification of the composite beam Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 48 ABC calculation (Alternative AF solution without fire protection) IPE450 4φ6

49 Structure grid of the composite building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 49 Composite columns S m 6 m 6 m 6 m 6 m m m m m m m m m m m A Bracing system B 4 m 7 m Bracing system 7 m Bracing system S S C Bracing system S S - S

50 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 50 Summary of data Partially encased composite column Height,40 m Geometrical characteristics and material properties Profile : HEA 60 h 50 mm b 60 mm e w 7,5 mm e f,5 mm A a 8680 mm² f y 460 N/mm² e f Z e w u h Y Concrete : C0/7 ; f c 0 N/mm² A c 5860 mm² u Rebars : 4 ø 8 ; A s 46 mm² u 5mm ; u 60mm f s 500 N/mm² b

51 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Load P P TOTAL 6*P tot q l m l m P q IPE450 pp0,776kn/m q IPE450 pp0,776kn/m L 4 m.4 m HE60A pp0,68kn/m For one level : q,5 [(,6+0,6*4,0)*]+0,776,5 kn/m q 0,750 [(,6+0,6*4,0)*]+0,776 4, kn/m P tot (,5*4/)+ (4,*4/)+*6+0,776*6+,4*,4 87,66 kn P TOTAL 6 * 87,66 76 kn

52 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Inertia Profile : I z 668 cm 4 I y 0450 cm 4 Rebars : 4 π d π d b I s,z 4 + u 4,6 cm π d π d h I s,y 4 + u 8,9 cm Concrete : h.b I 4 c, z Iz Is,z 70 cm b.h I 4 c, y Iy Is,y 080 cm

53 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 5 Use of tabulated data (0,8 < η fi,t < 0,47) Allowed parameters R60 e w / e f > 0,5 h and b > 00 mm u and u > 50 mm A c A s + A s > 4% Existing parameters 7,5 /,5 0,6 h 50 mm b 60 mm u 5mm u 60mm 46 58, ,4% Fulfilled conditions? YES NO YES YES Method not applicable

54 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 54 Simplified method : Application field Allowed parameters R60 Existing parameters Fulfilled conditions? l θ,5b,5. 0,6,5m 0mm h 00mm 0mm b 500 l θz l θy 0,7.,4,8 m h 50 mm b 60 mm YES YES YES % A s /(A c + A s ) 6% 4,6/(58,6+4,6)4,4% YES max R0 R60 YES l θ limited to 0b if 0 b < 00 Weak axis : l θz,8 < 0b,6 Strong axis : l θy,8 < 0b,6 YES YES Method applicable l fi 0,7L

55 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 55 Resistance to axial compression according to weak axis Flanges of the profile Mean temperature Standard fire resistance R 0 R 60 R 90 R 0 Plastic resistance : N fi,pl,rd,f (b e f f θ o,t [ C] ay,f k y,θ )/γ k t [m C] M,fi,a 9,65 9,55 6,5 4,65 N fi,pl,rd,f (60, ,095)/,0 θ f,t θ 0,t with + k A V t A / V θf,t ,55 5,7 80 C 84,kN m (h + b) 5,7 h.b m m % of the nominal value k y,θ 0,095 k E,θ 0,08 Effective resistance k y,θ Effective stiffness : (EI) fi,f,z E a,f k E,θ (e f b )/ Elastic modulus k E,θ (EI) fi,f,z ,08 (,5 60 )/6 640,4kN. m Temperature [ C]

56 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 56 Web of the profile Reduced height of web : h w,fi 0,5 ( h e f ) ( 0,6 (H t / h) ) (50,5) ( 0,6(770/ 50) ),4mm h w,fi 0,5 h w,fi Standard fire resistance R 0 R 60 R 90 R 0 H t [mm] h w,fi Level of maximum stress : f ay,w,t f ay,w (0,6H t /h) Plastic resistance : Effective stiffness : f ay,w,t 460 (0,6 770 /50) 7,6MPa N [ e w ( h e f h w,fi ) fay,w,t ] M,fi,a fi,pl,rd,w /γ ( 7,5(50,5,4)7,6 )/,0 9,7 kn N fi,pl,rd,w (EI) [ E ( h e h ) e ]/ fi,w,z fi,w,z a,w f w,fi w ( 0000( 50,5,4 ) 7,5 )/,8kN.m (EI)

57 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 57 Concrete Reduced thickness of concrete : b c,fi b c,fi Standard fire resistance R0 R60 R90 R0 b c,fi [mm] 4,0 5,0 0,5(A m /V)+,5,0(A m /V)+4,0 b c,fi R0 R60 R90 R0 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] A m /V 5,7m - Average temperature in the concrete θ c,t 56 C

58 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 58 θ c,t 56 C k c,θ 0,79 k c,θ Secant modulus of concrete : E E c,sec, θ ε c, θ cu, θ ε Plastic resistance : N Effective stiffness : f f c 8,68 0.k 0 0,79 c, θ cu, θ c,sec,θ 746,4MPa {( h ef bc,fi )( b ew bc,fi ) A s} fc,θ M,fi,c fi,pl,rd,c 0,86 /γ {( 50,5 5)( 60 7,5 5) 46} 5 0,79/,0 89 kn N fi,pl,rd,c 0,86 (EI) (EI) fi,c,z fi,c,z E c,sec,θ 746,4 [{( h e b )( ( b b ) e )/} I ] f c,fi c,fi w 4 [{( 50,5 5)( ( 60 5) 7,5 )/} 4,6 0 ] 509,5kN m s,z θ [ C] 00

59 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 59 Reinforcing bars Standard fire resistance Reduction factor for yield strength : k y,t u [mm] u R0 R60 0,789 0,88 0,976 R90 0,4 0,44 0,57 0,696 0,8 R0 0,70 0, 0,88 0,67 0,46 u Standard fire resistance R0 R60 R90 R0 Plastic resistance : Effective stiffness : Reduction factor for Young modulus : k E,t N 40 0,80 0,604 0,9 0,0 fi, pl,rd,s A sk y,t fs,y/γm,fi,s N fi, pl, Rd,s 46,0 500 /,0,5kN (EI) fi,s, z k 45 0,865 0,647 0,8 0,8 E,t E s u [mm] 0,406 0,7 I 50 0,88 0,689 s,z 0,94 0,79 0,5 0, 0,95 0,76 0,69 0,85 4 (EI) fi,s, z 0, , u 88,4 u u ,86 mm kn. m

60 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 60 Plastic resistance of the composite section N N + N + N + N fi, pl,rd fi,pl,rd,f fi,pl,rd,w fi,pl,rd,c fi,pl,rd,s N fi, pl, Rd 84, + 9, ,5 748kN Effective stiffness of the composite section (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 Standard fire resistance φ f,θ φ w,θ φ c,θ φ s,θ R0,0,0 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 (EI) 0,9 640,4 +,0,8 + 0,8 509,5 + 0,9 88,4 fi,eff, z 678,4 kn. m

61 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Determination of the axial buckling load at elevated temperatures Euler buckling load : N fi,cr,z π (EI) l fi,eff,z θz with l θz,8m π 678,4 Nfi, cr,z, kn Slenderness ratio : λ Nfi,pl,R 748 0,767 c curve z 0, 68 N 4667 χ θ fi,cr,z Axial buckling resistance : N fi, Rd,z χ z N fi,pl,rd Nfi, Rd,z 0, kn > Nfi, Rd 76kN

62 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 Resistance to axial compression according to strong axis Same method as for weak axis, excepted of the inertia! Plastic resistance of the composite section Nfi, pl,rd Nfi,pl,Rd,f + Nfi,pl,Rd,w + Nfi,pl,Rd,c + Nfi,pl, Rd,s 748 kn Effective stiffness of the composite section (EI) ϕ (EI) + ϕ (EI) + ϕ (EI) + ϕ (EI) fi,eff, y f,θ fi,f,y w,θ fi,w,y c,θ fi,c,y s,θ fi,s,y 4097,kN. m Euler buckling load π (EI) fi,eff,y Nfi, cr,y l θy 78,8kN Slenderness ratio λ N fi,pl,r θ N fi,cr,y 0,6 Axial buckling resistance Nfi, Rd,y χ y.nfi,pl,rd 4,8kN > Nfi, Rd 76kN

63 Verification of the composite column Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 7-8 November 0 6 AC calculation (Alternative solution : Fully encased HEB60) c 60 u s 4 Tabulated data c c h c Standard Fire Resistance h c 80 4φ HEB60 u s b c 80 b c u s R0 R60 R90 R0 R80 R Table 4.4: 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] Minimum cross-sectional dimensions, minimum concrete cover of the steel section and minimum axis distance of the reinforcing bars, of composite columns made of totally encased steel sections * * *