��� ��� PART 5a WORKED EXAMPLES ��� ��� Part 5a: Worked examples 0 / 62
Resistance to fire - Chain of events Resistance to fire - Chain of events Loads Θ Θ Θ Θ Steel columns time 1: Ignition 2: Thermal action 3: Mechanical actions R time 6: Possible 4: Thermal 5: Mechanical collapse response response ��� ��� ��� ��� Part 5a: Worked examples 1 / 62
Used standards Used standards Ambient temperature design � EN 1990 Basis of structural design � EN 1993-1-1 Design of steel structures � EN 1994-1-1 Design of composite structures Fire design � EN 1990 Basis of structural design � EN 1991-1-2 Thermal actions � EN 1993-1-2 Fire design of steel structures � EN 1994-1-2 Fire design of composite structures ��� ��� ��� ��� Part 5a: Worked examples 2 / 62
Worked examples – Overview Worked examples – Overview Number of examples � EN 1991: Actions on structures 2 Part 1-2: General actions – Actions on structures exposed to fire � EN 1993: Design of steel structures 3 Part 1-2: General rules – Structural fire design � EN 1994: Design of composite steel and 4 concrete structures Part 1-2: General rules – Structural fire design ��� ��� Part 5a: Worked examples 3 / 62
Worked examples - Overview Worked examples - Overview � Actions � Compartment fire � Localised fire � Steel � Steel column � Steel beam (N + M) � Steel beam (hollow section) � Composite � Composite slab � Composite beam (steel beam) � Composite beam (partially encased beam) � Composite column ��� ��� Part 5a: Worked examples 4 / 62
Compartment Fire Compartment Fire Task Task Determination of the gas temperature of a fully engulfed fire ⇒ Natural fire model for compartment fires ⇒ Parametric temperature – time curve θ g = f (q f,d , O, b) EN 1991-1-2: Annex A ��� ��� Part 5a: Worked examples 5 / 62
Compartment Fire Compartment Fire Parameters Parameters Building: Cardington test facility Type: Office Fire load: q f,d = 483 MJ/m² Floor area: A f = 135 m² Height: H = 4.0 m Average window height: h eq = 1.8 m Area of vertical openings: A v = 27 m² Vertical opening factor: O = 0.076 m 1/2 Material of boundaries: Lightweight concrete b = 1263.3 J/(m 2 s 1/2 K) ��� ��� Part 5a: Worked examples 6 / 62
Compartment Fire Compartment Fire Fuel or ventilation controlled? Fuel or ventilation controlled? − 3 0.2 10 ⋅ ⋅ q O = 0.363 h t,d 0.363 h < t = 0.333 h fuel controlled lim 0.363 h > t = 0.333 h ventilation controlled lim where q = q ⋅ A A t,d f,d f t ��� ��� Part 5a: Worked examples 7 / 62
Compartment Fire Compartment Fire Heating curve Heating curve Calculation of the heating curve: ( ) − 0.2 t* ⋅ − 1.7 t* ⋅ − 19 t* ⋅ θ = 20 + 1325 ⋅ 1 − 0.324 e ⋅ − 0.204 e ⋅ − 0.472 e ⋅ g where: t* = ⋅ Γ t 2 ( ) O b Γ = 2 ( ) 0.04 1160 ��� ��� Part 5a: Worked examples 8 / 62
Compartment Fire Compartment Fire Maximum temperature Maximum temperature Equal to the calculation of the heating curve, except: − 3 0.2 10 ⋅ ⋅ q O t,d t = t = max max t lim The maximum temperature is needed to determine the cooling curve. ��� ��� Part 5a: Worked examples 9 / 62
Compartment Fire Compartment Fire Cooling curve Cooling curve Calculation of the cooling curve: ( ) θ = θ − 625 ⋅ t * t * − ⋅ x g max max where ( ) − 3 t * = 0.2 10 ⋅ ⋅ q O ⋅ Γ max t,d t* = ⋅ Γ t If fire is ventilation controlled: x = 1.0 If fire is fuel controlled: x = t lim · Γ / t* max ��� ��� Part 5a: Worked examples 10 / 62
Compartment Fire Compartment Fire Final curve and comparison Final curve and comparison Parametric temperature-time curve Comparison calculation – measurement (Factors of q fi,d : δ q1 =1.0, δ q2 = 1.0, δ n = 1.0 ��� ��� Part 5a: Worked examples 11 / 62
Worked examples - Overview Worked examples - Overview � Actions � Compartment fire � Localised fire � Steel � Steel column � Steel beam (N + M) � Steel beam (hollow section) � Composite � Composite slab � Composite beam (steel beam) � Composite beam (partially encased beam) � Composite column ��� ��� Part 5a: Worked examples 12 / 62
Localised fire Localised fire Task Task Determination of the steel temperatures of a steel beam exposed to fire by a burning car. ⇒ Natural fire model for localised fires EN 1991-1-2: Annex C ��� ��� Part 5a: Worked examples 13 / 62
Localised fire Localised fire Parameters Parameters Building: Car park Auchan, Luxembourg Type: Underground car park Height: H = 2.7 m Horizontal distance from flame axis to beam: r = 0.0 m Diameter of flame: D = 2.0 m Steel Beam: IPE 550 ��� ��� Part 5a: Worked examples 14 / 62
Localised fire Localised fire Rate of Heat Release Rate of Heat Release Curve of the rate of heat release of one car From ECSC project:Development of design rules for steel structures subjected to natural fires in closed car parks. ��� ��� Part 5a: Worked examples 15 / 62
Localised fire Localised fire Flame Length Flame Length if L r ≥ H ⇒ Model A has to be used if L r < H ⇒ Model B has to be used ��� ��� Part 5a: Worked examples 16 / 62
Localised fire Localised fire Steel temperatures Steel temperatures Temperature-time curve for the unprotected steel beam: A / V p & θ = θ + k ⋅ ⋅ h ⋅ ∆ t a,r m sh net c ⋅ρ a a θ = 770 ° C a,max at t = 31.07 min θ ,max ��� ��� Part 5a: Worked examples 17 / 62
Worked examples - Overview Worked examples - Overview � Actions � Compartment fire � Localised fire � Steel � Steel column � Steel beam (N + M) � Steel beam (hollow section) � Composite � Composite slab � Composite beam (steel beam) � Composite beam (partially encased beam) � Composite column ��� ��� Part 5a: Worked examples 18 / 62
Steel column Steel column Task Task Determination of the design axial resistance for a steel column. ⇒ Simple calculation model for compression members EN 1993-1-2: Section 4.2.3.2 ��� ��� Part 5a: Worked examples 19 / 62
Steel column Steel column Parameters Parameters Building: Department store Fire resistance class: R 90 Loads: G k = 1200 kN P k = 600 kN Profile: Rolled section HE 300 B Fire protection: Hollow encasement of gypsum board (d p = 3 cm) Steel grade: S 235 ��� ��� Part 5a: Worked examples 20 / 62
Steel column Steel column Mechanical actions during fire exposure Mechanical actions during fire exposure Accidental situation: ( ) ∑ ∑ E = E ⋅ G + A + ψ ⋅ Q dA k d 2,i k,i Combination factor for shopping areas: ⇒ ψ 2,1 = 0.6 ⇒ N = 1560 kN fi,d ��� ��� Part 5a: Worked examples 21 / 62
Steel column Steel column Maximum steel temperature Maximum steel temperature A λ ⋅ p p V d λ p 2 (b ⋅ + h) W p ⋅ = 540 3 A d m ⋅ K a p Euro-Nomogram: ⇒ θ a,max,90 ≈ 445 ° C Reduction factors: ⇒ k y, θ = 0.901 k E, θ = 0.655 ��� ��� Part 5a: Worked examples 22 / 62
Steel column Steel column Reduction factor and verification Reduction factor and verification � Reduction factor χ fi : for: θ a = 445 ° C S 235 k y, θ λ = λ ⋅ = 0.25 fi, θ k E, θ ⇒ χ = 0.86 fi � Flexural buckling: f y N = χ ⋅ A k ⋅ ⋅ γ b,fi,t,Rd fi y, ,max θ M,fi N N = 0.58 < 1 fi,d b,fi,t,Rd ��� ��� Part 5a: Worked examples 23 / 62
Worked examples - Overview Worked examples - Overview � Actions � Compartment fire � Localised fire � Steel � Steel column � Steel beam (N + M) � Steel beam (hollow section) � Composite � Composite slab � Composite beam (steel beam) � Composite beam (partially encased beam) � Composite column ��� ��� Part 5a: Worked examples 24 / 62
Steel beam (N + M) Steel beam (N + M) Task Task Verification of a steel beam subjected to bending and compression loads. ⇒ Simple calculation model for members subjected to bending and compression loads EN 1993-1-2: Section 4.2.3.5 ��� ��� Part 5a: Worked examples 25 / 62
Steel beam (N + M) Steel beam (N + M) Parameters Parameters Building: Office building Fire resistance class: R 90 Loads: G k = 96.3 kN g k = 1.5 kN/m p k = 1.5 kN/m Profile: Rolled section HE 200 B Fire protection: Hollow encasement of gypsum board (d p = 2 cm) Steel grade: S 235 ��� ��� Part 5a: Worked examples 26 / 62
Steel beam (N + M) Steel beam (N + M) Mechanical actions during fire exposure Mechanical actions during fire exposure Accidental situation: ( ) ∑ ∑ E = E ⋅ G + A + ψ ⋅ Q dA k d 2,i k,i ⇒ ψ 2,1 = 0.3 Combination factor for office areas: ⇒ N = 96.3 kN fi,d M = 24.38 kNm fi,d ��� ��� Part 5a: Worked examples 27 / 62
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