Resistance to Accidental and Catastrophic Fires

Transcription

1 Resistance to Accidental and Catastrophic Fires General principles 1

2 Fire and Explosion Integrated Analysis of Fire Combustion Process (CFD) Transient temperature development (FEM) Mechanical response (NLFEA) 2

3 Transient temperature analysis Radiation Conduction Convection 3

4 Heat conduction T x Q cond = k T x Steady-state k = 45 W/mK, dq cond dx T T = k = ρc p Transient conduction x x t the change dq/dx used to heat/cool material cp= 600 J/kgK 4

5 Temperature development due to heat conduction in a semi-infinite slab. z Heat exposure Constant temperature x x Insulation y T t 2 T = α 2 x Conduction is a slow process!! α = k ρc p thermal diffusivity 5

6 Temperature profile after 2 hours for axisymmetric conduction in a 2m x 2 m steel plate (Red colour: T C left, T C right) Note the steep radial gradient 6

7 Convection and radiation - fundamental laws ( ) Q = c T T c 0 e Q r = εσt 4 Convection coeff. Emissivity coeff. Radiation predominates for high temperatures 7

8 The effect of emissivity and convection coefficient on a plate subjected to unilateral heating emissivity The rate of heat transfer is affected by emissivity convection emissivity heating 8

9 Conduction in a semi-infinite slab with radiation/irradiation and convection z Heat exposure Constant temperature x x irradiation Convection /radiation 9

10 Two-dimensional heat transfer- Finite element formulation T T T ρc = kx + ky + q t x x y y mt& + kt = Q + Q = Q surf edge MT & + KT = Q Heat capacity matrix i i i Conductivity matrix Differential equation Finite element relation System equation 10

11 From beam elements to 2D heat transfer elements Structural beam elements represented by 2D elemnst for heat transfer analysis Internal radiation to be included for hollow sections Different exposure for different surfaces 2D element temperature profiles to be interpreted/transferred to beam elements 11

12 Temperature profile in stiffener exposed to radiation on plate flange Temperature field for shell plating and stiffener 150kW/m 2 for 10 minutes. Temperature field for shell plating and stiffener 250kW/m 2 for

13 Temperature analysis of double bottom exposed to constant radiation on cellar deck ~150 kw/m 2 Q , Temperature 0 C Bottom 8 mm 25 mm 40 mm Cellar deck 8 mm Web 20 mm bottom 8 mm 25mm 40mm 20 25, Q Fire exposure [min.] After 10 minutes.cellar deck temperature 830 o C Bottom plating temperature < 600 o C after 1 hour 13

14 Heat transfer analysis of members with passive fire protection (PFP) Analysis of PFP numerically ill-conditioned because of widely different thermal diffusivity property (than steel) Heat transfer in PFP is 1-dimensional (through thickness) Typical PFP has low conductivity and low mass Analysis significantly eased if PFP represented by its resultant thermal conductivity or: Effective Heat Transfer Coefficient (EHTC) 14

15 Passive fire protection- Effective Heat Transfer Coefficient- K(T) K(T) T Temperature profile 1 T = Ts + T 2 ( ) ( ) E = K T T T ins ins s e ( ) e EHTC, K [W/(m 2 K)], is time dependent. EHTC is large during activation phase, remains virtually constant during fire, until it starts eroding 15

16 Passive fire protection- required effective heat transfer coefficient (EHTC) Structural members requiring PFP should have PFP with EHTC of at least 5 [W/m 2 /K] fire duration min 10 [W/m 2 /K] fire duration < 30 min EHTC product dependent Typical epoxy products: 5 [W/m 2 /K] ~ 4 mm PFP 10 [W/m 2 /K] ~ 6 mm PFP 16

17 Mechanical response - global structural analysis Uncertainties Strategy: Increase functional loads at maximum fire effect /Resistance R fi, d, t E fi, d, t 17

18 Structural integrity verification 1. Apply functional loads 2. Simulate degradation of resistance as temperatures are applied 3. Increase functional load in worst state to check margin, 10% reserve desired (100 year acc. ~ 20%) Resistance/Loads Resistance Functional load Structure survives Structure fails Check margin at critical state t cr Fire time t 18

19 NORSOK STANDARD Mechanical response calculation Simple calculation models - Eurocode 3/1.2 -Individual members General calculation methods - NLFEM -Sub-systems/Systems Analysis shall comply with Eurocode 3/1.2/Sect. 4.3 Assessment of ultimate strength not needed if T < C (but deformation criteria for impairment of main safety function may have to be checked) 19

20 Eurocode 3 (Steel) / Eurocode 9 (Alu.) Section 4.3:General calculation methods: Failure modes not covered by general calculation method to be eliminated by appropriate means (e.g. local buckling, shear..) Thermally induced strains and stresses to be considered Transient thermal creep neglected if using standard material stress-strain relationships Where relevant take account of combined effect of mechanical actions, geometrical imperfections and thermal actions temperature dependent mechanical properties of material nonlinear geometry non-linear material properties (loading/unloading of yielding fibers/sections) ) 20

21 NORSOK N-004 Appendix A Guidance on nonlinear FE analysis of fire exposed steel structures: Material modeling Equivalent imperfections Local cross-sectional buckling Ductility limits Capacity of connections but information is limited! 21

22 DESIGN AGAINST FIRE Mechanical effects Degradation of yield stress Degradation of elastic modulus Creep (disregarded if standard material stress-strain properties) Thermal expansion 22

23 Degradation of material properties at elevated temperatures (Eurocode 3) Proportional limit Effective yield strength Elastic modulus 23

24 Difference in EC3 and BS compensated by 1.2 factor 24

25 Reduction factors for yield strength, proportional limit and elastic modulus according to Eurocode 3 25

26 The effect of thermal elongation 26

27 Collapse of axially free beam and column 27

28 Comment on non-redundant members Thermal expansion does not influence the resistance of non-redundant members The capacity is exhausted once the yield stress has degraded to a level corresponding to the ULS utilization If the fire resistance is insufficient PFP must be applied 28

29 Collapse of beam with axially fixed ends 1.00 M-N Interaction history 0.75 Normalised axial force M-N trajectory Yield 500C Plastic 500C Yield 20C Plastic 20C Plastic 865C M-N trajectory M-N trajectory Normalised moment 29

30 Collapse of beam with axially fixed ends Note: Plastic displacement/axial strain is small until final collapse of the beam at ~ 700 deg C 30

31 Comments on fire resistant design of beams Beams typically carry equipment ULS design based on resistance in bending, hence axial support not considered From accidental fire design point of view axial fixity beneficial The beam may buckle due to thermal expansion but displacements are controlled Lateral displacements in post-buckled state induce load-carrying by membrane action Thermal expansion contributes favorably to membrane action little plastic straining until yield stress starts to degrade significantly The beam may undergo large lateral displacements, but it will maintain its load-carrying function for a longer time/higher temperature 31

32 P Collapse of X-brace subjected to uniform heating Illustration of redundancy in statically indeterminate system P 32

33 Comment on statically indeterminate systems Thermal expansion creates a very complex history in statically indeterminate systems Due to the indeterminacy, buckling may occur for very moderate temperature (e.g < 200 deg C) but buckling is displacement controlled Apparently, the load-carrying is changed significantly during moderate temperature stages As the temperature increases the load-carrying virtually returns to its original state Final collapse very much governed by reduction in yield strength 33

34 Comment on statically indeterminate systems Thermal expansion cause internal, self-equilibrating forces and is of no concern for ductile plastic collapse (load-path more flexible but ultimate resistance unaffected) refer welding residual stresses Thermal expansion creates additional lateral displacements, which influences the buckling load of compression members (but less influence on resistance in post-buckled state) Practical remedy: Increase initial displacement for fire analysis? 34

35 Analysis of statically indeterminate systems Because thermal expansion causes 80-90% of the events during fire, it is suggested to do initial analysis neglecting it. For a given temperature history of the structure check the worst temperature state(s) (given time instant) Use reduced yield stress and elastic modulus according to member temperature Perform static nonlinear analysis of degraded structure by incrementing functional loads up to required level The above procedure removes the complexity and disguising effect of thermal expansion Once the design is completed, perform complete analysis 35

36 Deformation criteria The validity of the mechanical response model, and also the transient temperature calculation depends on the fulfillment of the deformation criteria with respect to: Maximum average strain for members in tension and bending Maximum deformation w.r.t. local buckling Maximum local deformation of connections Maximum local strain in Passive Fire Protection. 36

37 Passive Fire Protection Testing of Passive Fire Protection When does the protection fail mechanically? For a given deformation, the PFP cracks and does not longer work as intended. This angle is measured in laboratory tests. Crack Angle. Typical Crack Angles: - Reinforced epoxy: No reinforced : 1-3 Cracks occur on worst possible location. Tore Holmås, Oct

38 Passive Fire Protection Testing in SINTEF Fire Lab. Unprotected Attachments Protected Main Steel Hydro Carbon Fire (standardized 200 kw/m 2 ) Failure after ~60 min Heat leakage through unprotected Attachments into the Main Steel Web Extreme Deformations 38

39 Behaviour of girders with attachments during fire Girder with PFP Unprotected sec. stiffeners Heat through PFP Key issues: Heat conducted from sec. stiffeners into web Temperature development in girder Girder connection Degradation of shear and bending resistance 39

40 Test specimen 40

41 Test specimen Hydraulic acutator Protected Main Steel Hydro Carbon Fire (standardized 200 kw/m 2 ) 41

42 Specimen after testing Failure after ~60 min Large deformations Crack in PFP 42

43 The effect of coat-back on bending and shear resistance for I-girder 250 0,40 Moment KNm Resistance - no coat back Resistance - full coat back Time [minutes] Shear force [MN] 0,30 0,20 0,10 0,00 Resistance - no coat back Resistance - full coat back Time [minutes] Note: Critical time difference small 43

44 The effect of axial restraint and internal stress redistribution on the capacity of I-girder with attachment 0,50 0,40 Tension-compression field in girder at ultimate resistance Force [MN] 0,30 0,20 Fixed Spring1 Spring2 Free 0,10 Shear yield 0,00 0,00 0,05 0,10 0,15 0,20 Displacement [m] Collapse deformation mode strain distribution at 0.15 m deformation Shear resistance versus displacement 44

45 PFP - CONCLUSIONS PFP on members undergoing large deformations must be reinforced Reduced need for coat-back on secondary members because: Heat conduction is a slow process Redistribution of stresses in cross-section Membrane forces may develop if connections are carefully designed 45

46 Tension test T-joint Uniform temperature 46

47 Tension test skew axial force 47

48 Resistance vs. temperature 48