Part 3: Mechanical response. DIF SEK Part 3: Mechanical response 0/ 43

Transcription

1 DIF SEK Part 3: Mechanical response DIF SEK Part 3: Mechanical response 0/ 43

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 3: Mechanical response 1/ 44

3 How structures react to fire Temperature rise thermal expansion + loss of both stiffness and resistance additional deformation eventual collapse t = 0 θ = 20 C 16 min θ = 620 C 22 min θ = 720 C 31 min θ = 850 C DIF SEK Part 3: Mechanical response 2/ 44

4 Assessment of mechanical response of structures in fire Purpose to describe structural behaviour under any type of fire condition Means P P Fire tests Design Deflection Load-bearing resistance Standard Fire Time P Time DIF SEK Part 3: Mechanical response 3/ 44

5 Basic features related to assessment of mechanical response of steel structures t in fire Mechanical loadings under fire situation specific load combination Mechanical properties of relevant materials at elevated temperatures stiffness and resistance varying with temperatures Assessment methods for structural analysis in fire different approaches application domain Specific consideration in fire design of steel and composite structures connections, joints, etc DIF SEK Part 3: Mechanical response 4/ 44

6 Mechanical loading combination according to Eurocode (ČSN EN 1990 and ČSN EN ) 1 G k,j +(Ψ 1,1 or Ψ 2,1 ) Q k,1 + Ψ 2,i Q k,i j 1 i 2 G kj k,j : characteristic values of permanent actions Q k,1 : characteristic leading variable action Q ki k,i : characteristic values of accompanying variable actions ψ 1,1 : factor for frequent value of a leading variable action ψ 2,i : factor for quasi-permanent values of accompaning variable actions Load level: η fi,t (see presentation of WP1) DIF SEK Part 3: Mechanical response 5/ 44

7 Mechanical properties of structural steel at elevated temperatures (ČSN EN ) Strength % of normal value Elastic modulus Effective yield strength Temperature ( C) Normalised stress 20 C 200 C 400 C C C 700 C 800 C Strain (%) Elastic modulus at 600 C reduced by about 70% Yield strength at 600 C reduced by over 50% DIF SEK Part 3: Mechanical response 6/ 44

8 Mechanical properties of concrete at elevated temperatures (ČSN EN ) 1 Strength % of normal value Strain (%) 6 Strain ε cu at 100 maximum 5 strength 4 50 Normalweight Concrete Normalised stress C C 400 C 800 C 600 C Temperature ( C) Strain (%) ε c Compressive strength at 600 C reduced by about 50% u DIF SEK Part 3: Mechanical response 7/ 44

9 Thermal expansion of steel and concrete (ČSN EN and ČSN EN ) 1 20 ΔL/L (x10 3 ) normal concrete steel temperature ( C) DIF SEK Part 3: Mechanical response 8/ 44

10 Different design approaches for mechanical response of structure in fire Three different approaches according to Eurocodes global structural analysis analysis of parts of the structure member analysis (mainly when verifying standard fire resistance requirements) DIF SEK Part 3: Mechanical response 9/ 44

11 Different design approaches for mechanical response of structure t in fire Member analysis Global structural analysis independent structural element analysis simple p to apply generally for nominal fire condition interaction effects between different parts of the structure role of compartment global stability DIF SEK Part 3: Mechanical response 10 / 44

12 Three types of design methods for assessing mechannical response of structures t in fire Tabulated data composite structural members Simple calculation models critical temperature steel and composite structural members Advanced calculation models all types of structures numerical models based on: finite element method finite difference method Classic and traditional application Advanced and specific fire design DIF SEK Part 3: Mechanical response 11 / 44

13 Application domain of different design methods under fire situation ti Thermal action defined with nominal fires Type of analysis Tabulated data Simple calculation models Advanced calculation models Member analysis Yes ISO-834 standard fire Yes Yes Analysis of a part of the structure Not applicable Yes (if available) Yes Global structural analysis Not applicable Not applicable Yes DIF SEK Part 3: Mechanical response 12 / 44

14 Application domain of different design methods under fire situation ti Thermal action defined with natural fires Type of analysis Tabulated data Simple calculation models Member Not Yes analysis applicable (if available) Analysis of a part of the Not Not structure applicable applicable Global structural analysis Not applicable Not applicable Advanced calculation models Yes Yes Yes DIF SEK Part 3: Mechanical response 13 / 44

15 Tabulated data (steel and concrete composite members) Composite Composite columns beams Slab Concrete for insulation DIF SEK Part 3: Mechanical response 14 / 44

16 Tabulated data and relevant parameters (composite columns ČSN EN ) 1 A c ew b e f As u s us h Standard Fire Resistance R30 R60 R90 R120 Minimum ratio of web to flange thickness e w /e f 0,5 1 Minimum cross-sectional 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 % 2 Minimum cross-sectional 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 Section dimensioni Reinforcing steel 3 Minimum cross-sectional dimensions for load level η fi,t 0, minimum i dimensions i h and db[ [mm] Concrete 3.2 minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c +A s ) in % cover DIF SEK Part 3: Mechanical response 15 / 44

17 How to apply tabulated data in fire design (two different situations) VERIFICATION PRE-DESIGN R d of θ 20 C E fi.d and E d E fi.d η fi,t = E fi.d / E d η fi,t =E fi.d /R d Section dimension reinforcing steel concrete cover Standard fire rating Section dimension reinforcing steel concrete cover Standard fire rating R d E d DIF SEK Part 3: Mechanical response 16 / 44

18 Simple calculation model (steel and composite members) Beams (steel or composite) Columns DIF SEK Part 3: Mechanical response 17 / 44

19 Simple calculation model (composite beam) -plastic resistance theory S 1 Concrete slab Connector Steel section S 1 Section S F c D + + F t Section geometry Temperature distibution Stress distribution Moment resistance M fi,rd + = F + t D + DIF SEK Part 3: Mechanical response 18 / 44

20 Simple calculation model (composite column) - buckling curve P A Z A ai χ(λ θ ) L fi A cj Y Effective section A sk 0 Appropriate buckling curve λ θ Load capacity: N fi.rd = χ(λ θ ) N fi.pl.rd χ(λ θ ) strength and rigidity of effective section + column buckling length L fi DIF SEK Part 3: Mechanical response 19 / 44

21 Critical temperature method (only steel members and certain composite beams) Beams (steel and composite) Columns DIF SEK Part 3: Mechanical response 20 / 44

22 Critical temperature method According to simple calculation models, for uniformly heated steel members: R fi,d,t = k y,θ R fi,d,0 On the other hand, fire resistance should satisfy: R fi,d,t E fi,d = E fi,d R fi,d,0 = μ 0 R fi,d,0 k y,θ μ 0 Rfi,d,0 In particular, when k y,θθ = μ 0 the corresponding temperature is defined as critical temperature θ cr In ČSN EN , a simple formula is given to determine critical temperature θ cr 1 θ cr =3919ln μ DIF SEK Part 3: Mechanical response 21 / 44

23 How to apply critical temperature method Action in fire E fi.d Design resistance at 20 C: R d or design action at 20 C: E d Load level in fire: η fi,t = η fi,t E fi,d R d γ M,fi Utilisation level: μ 0 = η fi,t γm Critical temperature: θ cr direct method iterative method DIF SEK Part 3: Mechanical response 22 / 44

24 Why direct and iterative critical temperature method (case of steel column) Short column without instability N b,fi,t,rd =Ak y,θmax f y 1 γm,fi Strength reduction factor k y.θ.max at θ a,max Column with risk of buckling N b,fi,t,rd =χ(λ θ )Ak y,θmax f y 1 γm,fi Reduction factor of buckling χ(λ θ ) depends on: strength stiffness As a consequence, simple iterative procedure is needed to find the accurate θ a,max in case of instability problem DIF SEK Part 3: Mechanical response 23 / 44

25 Advanced calculation model for any case (steel and concrete composite cellular beam) 300 Tested failure mode Deflecti ion (mm) test calculation time (min) Calculation vs test Simulated failure mode DIF SEK Part 3: Mechanical response 24 / 44

26 Fire design by global structural analysis General rules necessary to use advanced calculation model choice of appropriate structural modeling existing boundary conditions loading conditions appropriate material models restrained condition in relation with unmodeled parts of the structure analysis of results and check on failure criteria review i of untreated t features in direct analysis (consistency between numerical model and constructional details) DIF SEK Part 3: Mechanical response 25 / 44

27 Fire design by global structural analysis Application requirement of advanced calculation models requirement on material models strain composition kinematical material model strength during cooling phase step by step iterative solution procedure check of possible failure untreated in direct analysis rupture due to excessive steel elongation cracking and crushing of concrete DIF SEK Part 3: Mechanical response 26 / 44

28 Requirement on material model Strain composition ε t = ε th + (ε σ + ε c )+ ε r ε t : total strain ε t : strain due to thermal elongation ε σ : strain due to stress tensor ε r : strain due to residual stress (if appropriate) ε c : strain due to creep y z G θ ε th ε t ε σ ε r ε c Section Temperature distribution z = constant Unitary strain DIF SEK Part 3: Mechanical response 27 / 44

29 Requirement on material model kinematical material model Steel (isotropic material) Concrete (compression-tension anisotropic material) dσ parallel to (θ 1, ε = 0) dε θ 1 = θ (t) σ Compression θ 1 = θ (t) θ 2 = θ (t+δt) θ 2 = θ (t+δt) dσ parallel to (θ 2, ε = 0) dε ε ε Tension DIF SEK Part 3: Mechanical response 28 / 44

30 Step by step iterative solution procedure Calculation procedure must take account of temperature dependance of both stiffness and strength of the structure t 0 = 0 θ 0 = 20 C t 1 = 20 min θ 1 = 710 C t 2 = 27 min θ 2 = 760 C Loading P fi t 0 = 0 t 1 t 2 θ 1 θ θ2 θ 0 Displacement U DIF SEK Part 3: Mechanical response 29 / 44

31 Material strength during cooling phase Steel recovers its initial strength during cooling phase Concrete t during cooling phase Temperature of concrete θ max Strength 300 f c,θ max 0.9 f c,θ max 20 t max Time 0 t max Time For example if θ max 300 C max f c,θ,20 C = 0.9 f c,θ max Linear interpolation applies to f c,θ for θ between θ max and 20 C DIF SEK Part 3: Mechanical response 30 / 44

32 Global analysis of steel and concrete composite floor under localised li fire Standard part of the floor system Composite slab Steel deck: 0.75 mm 3.2 m 42m m 10 m 15 m 10 m 10 m 15 m DIF SEK Part 3: Mechanical response 31 / 44

33 Choice of structural model Two different structural models may be adopted 2D composite frame model (beam elements) membrane effect is limited to one direction due to 1D effect slab model load redistribution is not possible between parallel beams 3D composite floor model (multi-type element) membrane effect over whole floor area load redistribution becoming possible with help of shell elements More realistic to apply 3D composite floor model DIF SEK Part 3: Mechanical response 32 / 44

34 Validity of 3D composite floor model ) Vert. Dis sp. (mm Test D calculation model.disp. (mm) Hori Time (min) VTest Cal. 3D Cal. 2D Time (min) DIF SEK Part 3: Mechanical response 33 / 44

35 Strategy of 3D composite floor modelling Fire area Global structure without composite slab Detail of numerical modelling DIF SEK Part 3: Mechanical response 34 / 44

36 Mechanical loading and boundary conditions Uniformly distributed load: G + Ψ 1,1 Q θ = 0 Continuity condition of concrete slab θ = 0 Continuity condition of columns DIF SEK Part 3: Mechanical response 35 / 44

37 Mechanical response of the structure Total deflection of the floor and check of the corresponding failure criteria i 140 mm 310 mm 20 min 40 min DIF SEK Part 3: Mechanical response 36 / 44

38 Mechanical response of the structure Total deflection of the floor and check of the corresponding failure criteria i 60 min 230 mm (mm) Deflection mm L/20 = 500 mm Secondary beam Main beam Time (min) 280 mm L/20 = 750 mm DIF SEK Part 3: Mechanical response 37 / 44

39 Mechanical response of the structure Check of failure criteria: elongation of reinforcing steel 1.4 % 5 % 1.3 % 5 % Strain of reinforcing steel // slab span Strain of reinforcing steel slab span DIF SEK Part 3: Mechanical response 38 / 44

40 Construction details shall be respected in prder to consistent t with numerical models Reinforcing bars between slab and edge columns φ12 in S500 Maximum gap of 15 mm between beam and column and between lower flange of the beam gap gap 15 mm DIF SEK Part 3: Mechanical response 39 / 44

41 Real building with bare steel frames based on global structural analysis Finished During construction DIF SEK Part 3: Mechanical response 40 / 44

42 Specific consideration in fire design of steel and composite structures t Constructional details Joint details (steel and composite) Connection between steel and concrete Connectors Reinforcing steel Behaviour during cooling phase under natural fire Joint DIF SEK Part 3: Mechanical response 41 / 44

43 Construction details to get hogging moment resistance in fire situation ti (ČSN EN ) 1 Join detail - Example Continuous reinforcing bar studs Sections with infilled concrete gap A limited gap allowing to develop a hogging moment tin the fire situation DIF SEK Part 3: Mechanical response 42 / 44

44 Construction details for connection between concrete and steel (ČSN EN ) 1 Connection between steel profile and encased concrete φ r 8 mm φ s 6 mm welding a w 0,5 φ s l w 4 φ s h ν studs d 10 mm h ν 0,3b φ r 8 mm Welding of stirrups to the web b Welding of studs to the web DIF SEK Part 3: Mechanical response 43 / 44

45 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 critical temperature for Class 4 sections: elements loaded by bending moment: θ cr = 500 ºC element loaded in compression: θ cr = 450 ºC In addition: critical temperature of fire-resistant steel FRS 275 N critical temperature of cold-formed elements in tension ČSN EN (composite structures) Allows to choose parameters in 8 paragraphs p The original values are accepted Allows to use European software without modifications DIF SEK Part 3: Mechanical response 44 / 44

46 Thank you for your attention DIF SEK Part 3: Mechanical response