PART 2 THERMAL RESPONSE. DIF SEK Part 2: Thermal Response 0/ 44

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1 DIF SEK PART 2 THERMAL RESPONSE DIF SEK Part 2: Thermal Response 0/ 44

2 Resistance to fire - Chain of events Θ Loads 1: Ignition Steel columns time 2: Thermal action 3: Mechanical actions R 4: Thermal response time 5: Mechanical response 6: Possible collapse DIF SEK Part 2: Thermal Response 1/ 45

3 Contents 1. Introduction 2. Basics & illustrations ti 3. Calculation rules for steel elements 4. Calculation rules for composite elements Annexes Fourier s differential equation Thermal response of steel elements Tabulated data & simple models according to ČSN EN EC rules for FR w.r.t. insulation of composite slabs EC rules for temperature sagging reinforcement in composite slabs DIF SEK Part 2: Thermal Response 2/ 45

4 Thermal response Basics Thermal conduction (= λ) Thermal capacity (= ρ cc p ) z q q + Δq DV: (shown for 1direction only) ( ρ cpθ) t Θ ( λ ) + x = 0 x boundary condition: incoming/outgoing flux at surface: h net,tot initial condition: room temperature conditions y x heat balance Δq/ Δx + Δ(ρc p Θ) / Δt = 0 Fourier s law q = λδθ / Δx DIF SEK Part 2: Thermal Response 3/ 45

5 Thermal conductivity Concrete vs. steel 60 Thermal Conductiv vity λ [W W/mK] steel concrete temperature [ C] DIF SEK Part 2: Thermal Response 4/ 45

6 Thermal capacity Concrete vs. steel phase transition 9 ty [MJ/m 3 K] Therma al capaci moisture concrete steel temperature [ o C] DIF SEK Part 2: Thermal Response 5/ 45

7 Thermal response Steel beam/concrete slab (2D) tempera ature [ o C] ] time [min] DIF SEK Part 2: Thermal Response 6/ 45

8 Thermal response Composite slab (2D) C] ] ==> Tempera temp atuur erature [ 0 C [ G F E D C B A A B C D E F Tijd [min] ==> time [min] G computer simulation test vs. simulation DIF SEK Part 2: Thermal Response 7/ 45

9 Thermal response Composite edge beam (3D) DIF SEK Part 2: Thermal Response 8/ 45

10 Calculation rules for steel elements Scope Bare steelwork Insulated steelwork Design parameters for the temperature development General Section Factor Characteristics fire protection Non-standard fire conditions DIF SEK Part 2: Thermal Response 9/ 45

11 Resistance-to-Fire of Steel Elements Principles Load bearing function only Load bearing capacity Uniform temperature distribution Critical steel temperature concept Note: refer to ČSN EN (simple calculation models) DIF SEK Part 2: Thermal Response 10 / 45

12 Resistance-to-Fire Steel elements Calculation procedure Step 1: determine mechanical response μ a Θ crit Step 2:determine thermal response Θ a Step 3: determine fire resistance fire res. Θ, Θ a Standard Fire curve Θ a steel temp. step 2 Θ crit step 1 step 3 fire res. time utilisation factor μ 0 DIF SEK Part 2: Thermal Response 11 / 45

13 Thermal actions Heat transfer exposed side Radiative heat transfer: Convective heat transfer:. h h 4 4 [( r 273 ) ( Θ 273) ] net,r= Φ εm σ Θ + m +. net,c = α ( Θ g Θ with: Θ radis radiation temperature [ C] Θ rad Θ g fire curve Θ m is surface temperature [ C] thermal response ε m is surface emissivity [-] steel: 0.7 α c is coefficient convection W/m 2 K (depending on fire model) Φ is configuration factor [-] 1.0 safe: 1.0 ρ is Stephan Boltzmann constant = W/m 2 K 4 Note: simplified!; for details: see ČSN EN m m ) DIF SEK Part 2: Thermal Response 12 / 45

14 Thermal response Steel profiles Θ ( λ ) ( ρ cθ ) + x = 0 t x boundary & initial conditions d = dt h a & tot ρ a Am cav with A m is exposed surface area member [m 2 /m] V is volume member [m 3 /m] Note: key is uniform temperature distribution DIF SEK Part 2: Thermal Response 13 / 45

15 Temperature rise bare steelwork Basic equation d Θ d t Δ Θ a a = = k k sh sh Am / V ρ ca a h& K bare Am ρ c a a V net,tot Θ Θ ( g a ) Δ t (1) (2) Legend: ΔΘ a : increase steel temp. Δt : time step A m /V section factor K bare : heat transfer coef. k sh : corr. coef. shadow effect with K bare ε = α c + m σ ( ) ( ) Θ g Θ g Θ Θa a 4 (3) DIF SEK Part 2: Thermal Response 14 / 45

16 Shadow effect Basics Shadow effect caused by local shielding of radiative heat transfer, due to shape of steel profile, i.e.: profiles, shadow effect: yes profiles, shadow effect: no Without thermal radiation, no shadow effect; hence: bare members, shadow effect: yes insulated members, shadow effect: no DIF SEK Part 2: Thermal Response 15 / 45

17 Shadow effect Consequences Unprotected members: Am V ΔΘ =. Δ a k sh hnet caρ with: for I sections: a t k sh = 0.9 [A m /V] box /[A m /V] for all other sections: k sh = [A m /V] box /[A m /V] Protected members: no effect DIF SEK Part 2: Thermal Response 16 / 45

18 Temperature rise insulated steelwork Basic equations insulation steel strip Δ Θ a = K ins ρ c a a A V m Θ Θ ( g a ) Δt (a) Θ g Θ m with K ins = K ins λ (, ρ,,, d p c p ρ a c a ) (b) Notes: (a) Θ g - Θ m << Θ m - Θ a (b) for light weight insulation: K ins λ/d Θ a temperature distribution effect thermal thermal capacity insulation DIF SEK Part 2: Thermal Response 17 / 45

19 Temperature development in steel profiles [ o C] perature tem Standard curve 800 A/V= 50 [m-1] A/V = 100 [m-1] Series1 500 Series6 400 Series7 A/V = 250 [m-1] Series8 300 Series Poly. (Series5) A/V = 100 [m-1] + insulation time [min] DIF SEK Part 2: Thermal Response 18 / 45

20 Steel temperature as function of Section Sector Bare steel profiles temperature [ C] minutes minutes A m /V (m -1 ) DIF SEK Part 2: Thermal Response 19 / 45

21 Steel temperature as function of Section Factor Insulated steel profiles standard fire duration: 90 min mm 20 mm 25 mm tem mperature e [C] mm mm mm section factor [m -1 ] DIF SEK Part 2: Thermal Response 20 / 45

22 Section Factor steel profile Concept bare steel members insulated steel members Definition: ratio between surface area through which heat is transferred to steel and steel volume DIF SEK Part 2: Thermal Response 21 / 45

23 Section Factor (A/V) Numerical values IPE HE280A HE320B Note: range: [m -1 ] DIF SEK Part 2: Thermal Response 22 / 45

24 Heat transfer coefficient Insulated steel members Approximation: K ins λ/d (for light weight insulation) with: d is thickness insulation material λ is coefficient of thermal insulation Determination: ti semi-empirical ii approach ENV 13381, p. 4 Note: Do not use room temperature handbook values for λ in fire design calculations! DIF SEK Part 2: Thermal Response 23 / 45

25 Characterisation tests Fire insulation steel elements Aim: insulation characteristics fire protection steelwork Complication: Stickability Methodology: loaded & unloaded beam (2 pairs) unloaded columns (10 x) Ref.: EN beam before fire test beam after fire test DIF SEK Part 2: Thermal Response 24 / 45

26 Fire insulation systems Options Boards Sprays Intumescents Screens to protect horizontal elements ( floor construction) (EN ) to protect vertical elements ( partitions) (EN ) Note: for details on insulation characteristics refer to: (a) test reports fire labs (b) information manufacturers DIF SEK Part 2: Thermal Response 25 / 45

27 Euronomograms for insulated steelwork; to be used as first approximation DIF SEK Part 2: Thermal Response 26 / 45

28 Calculation rules for composite elements Scope Thermal response steel columns with concrete between flanges Verification of the insulation criterion for composite slabs Temperature in additional reinforcement in composite slabs Thermal response of concrete filled SHS columns Evaluation DIF SEK Part 2: Thermal Response 27 / 45

29 Composite slabs & beams Options Shear connectors Flat concrete slab or composite slab with profiled steel sheeting Profiles with or without Fire protection material slabs Reinforcing bar Shear connectors beams Optional slab Stirrups welded to web of profile Reinforcing bar DIF SEK Part 2: Thermal Response 28 / 45

30 Composite columns Options (a) (b) (c) a: steel embedded in concrete (traditional approach) b: concrete between flanges (f.r. dependent d on reinforcement) c: concrete filled SHS - without reinforcement (f.r. ca. 30 minutes or less) -with reinforcement (f.r. dependent d on reinforcement) DIF SEK Part 2: Thermal Response 29 / 45

31 Calculation procedure thermal response Composite elements Non-uniform temperature distribution Load bearing and (possibly) separating function Load bearing capacity Thermal insulation Integrity Options tabulated data simple calculation model advanced calculation model Note: Reference: ČSN EN DIF SEK Part 2: Thermal Response 30 / 45

32 Composite elements Calculation rules thermal response Similar to concrete elements Complications due to shape Simple calculation rules available variety of backgrounds see ČSN EN DIF SEK Part 2: Thermal Response 31 / 45

33 Thermal response composite elements Advanced model (illustration) Te emperatu temper rature uur [ 0 C] [ C C] ==> G F E D C B A A B Tijd [min] ==> time [min] C D E F G computer simulation test vs. simulation DIF SEK Part 2: Thermal Response 32 / 45

34 Composite elements Simple calculation models thermal response Semi-empirical empirical approach Parameter study based on systematic calculation with advanced calculation model Direct application of advanced calculation model DIF SEK Part 2: Thermal Response 33 / 45

35 Simple calculation models Semi-empirical approach b c,fi u 1 b Z e f Y h Components cross section: - flanges steel section - web steel section - concrete - re-bars h w,fi b c,fi u2 e w Reduced cross section For each component: -reduced strength and/or -reduced area For details: see ČSN EN DIF SEK Part 2: Thermal Response 34 / 45

36 Simple calculation models Parameter study approach Composite slabs with profiled steel sheet Decking type Concrete depth Concrete type H B [mm] re-entrant (6x) 50, 60, 70, 80, NCW and LWC trapezoidal (49x) 90, 100, 110, 120 ČSN EN standard fire conditions - profiled shape deckings taken into account - thermal properties according to EC - average moisture content: 4% (NWC) and 5% (LWC) Note: total number of simulations: 880 DIF SEK Part 2: Thermal Response 35 / 45

37 Typical temperature distribution at the unexposed side of a composite slab temperature [ C] average Insulation criterion: -ΔΘ av 140 ºC -ΔΘ max 180 ºC DIF SEK Part 2: Thermal Response 36 / 45

38 Composite slabs Thermal insulation (illustration) Issues: h 1 t f = t f (l 1, l 2,, A/L r, φ) h 2 l 2 l 1 l 3 A L r with: l 1, l 2,.. geometry slab A volume rib L r exposed surface rib φ configuration factor t f = a 0 + a 1 h 1 + a 2 φ + a 3 A/L r + a 4 1/L 3 + a 5 A/L r 1/l 3 [min] with: a i coefficients, depending on duration of s.f.c. exposure DIF SEK Part 2: Thermal Response 37 / 45

39 Thermal insulation composite slabs Verification simple calculation rule Fire resistance (Eurocode 4). Fire resistance (adv. model) [-] == => Fire resistance (new rule). Fire resistance (adv. model) [-] = => Unsafe Safe μ σ Unsafe Safe μ σ Fire resistance (adv. model) [min] ==> Fire resistance (adv. model) [min] ==> (a) ČSN P ENV rule (b) new rule DIF SEK Part 2: Thermal Response 38 / 45

40 Composite slabs Thermal response positive reinforcement z compression zone concrete (20 C) u 2 u 1 u 3 Temperature reinforcement has significant impact on M + p,θ Θ r = Θ r (u 1, A/O, l 3, z..) z = z(u 1, u 2,u 3 ) Note: steel sheet may significantly contribute to the load bearing capacity! DIF SEK Part 2: Thermal Response 39 / 45

41 Thermal response positive reinforcement Simple calculation rule. [-] ==> perature (EC 4) rature (adv. model) Tem Tempe safe unsafe O A u 1 1 / 2 L 3 α μ σ Temperature (adv. model) [ 0 C] ==> (a) ČSN P ENV rule 0 H ==> w rule).. model) [-] perature (new erature (adv. Temp Tempe safe unsafe O A μ u 1 1 / 2 L 3 α σ Temperature (adv. model) [ 0 C] ==> (b) new rule H DIF SEK Part 2: Thermal Response 40 / 45

42 Concrete filled SHS columns Resistance to fire (traditional approach) Design charts available Unpractical Need for user friendly design tool e.g. POTFIRE no. concrete rebar quality % 1 C C C C C C C C C DIF SEK Part 2: Thermal Response 41 / 45

43 POTFIRE In- & output input output DIF SEK Part 2: Thermal Response 42 / 45

44 Validation POTFIRE ature tes st temper assumptions: - α conv = 25 W/m 2 k - ε res = 0.7 Concrete Filled Steel Hollow Section temperature t (Potfire) DIF SEK Part 2: Thermal Response 43 / 45

45 Composite elements Evaluation thermal response Thermal response is relative complicated Simple verification rules are available*): tabulated data design graphs special purpose computer programmes (e.g. POTFIRE) Alternative: advanced calculation models; feasible for NFSC *) Simple rules have a limited field of application! DIF SEK Part 2: Thermal Response 44 / 45

46 National Annex to ČSN EN and ČSN EN ČSN EN (steel structures) Allows to choose parameters in 6 paragraphs The values from EN accepted without modification The only change is the critical temperature of thin-walled elements (see Part 3 for details) ČSN EN (composite structures) Allows to choose parameters in 8 paragraphs The original values are accepted Allows to use European software without modifications DIF SEK Part 2: Thermal Response 45 / 45

47 Thank you for your attention DIF SEK Part 2: Thermal Response