Tensile Membrane Action of Composite Slabs in Fire. Are the current methods really OK? Ian Burgess University of Sheffield, UK

Transcription

1 Tensile Membrane Action of Composite Slabs in Fire Are the current methods reall OK? Ian Burgess Universit of Sheffield, UK

2 Cardington Max beam temperature ~1150 C cf. Code critical temperature ~ 680 C 2

3 The basis of all current simplified methods: Haes (1968) 3

4 Small-deflection ield-line mechanism slab onl L=al nl Hogging rotations about edges of panel g Sagging rotations about internal ield lines l Large-deflection failure crack sometimes observed in tests and used b Haes. Yield-line pattern is optimized for minimum concrete slab failure load. 4

5 Equilibrium 1 no through-depth YL cracks - Haes kbkt 0 T 0 l/2 E Compression bkt 0 Tension Criterion: Cracks from intersection. Moment equilibrium about E. Finds b and k. Rationale: Superposition of rebar tension and concrete compression force/unit length. 5

6 Equilibrium 2 some through-depth YL cracks - Haes kkt 0 KT 0 Compression Both b and k are constant for each of the 2 cases. No variation with deflection. Tension Rationale: Superposition of rebar tension and concrete compression force/unit length. 6

7 Partial enhancement factors both cases - Haes Membrane force enhancements: e 1m e 2m Moment of membrane forces about 11/total resistance moment about x-axis at initial YL. Moment of membrane forces about 22/total resistance moment about -axis at initial YL. These start at zero for zero deflection Resistance moment enhancement (reduction) e 1b e 2b Proportional change of resistance moment about x-axis due to membrane compression. Proportional change of resistance moment about -axis due to membrane compression. 2 7

8 Bending enhancements - Haes Wood s equation for reduction of moment capacit of a rectangular RC crosssection due to axial compression: 1. Long-span reinforcement: M = 1+ A N B N M T T T 0 T 0 T 0 N T 0 2. Short-span reinforcement: M = 1 + A' N B' N M KT KT These are integrated in x- and - directions respectivel for the bending moments across the ield lines for Portions 1 and 2. 8

9 Forming an overall enhancement factor - Haes! " =! "$ +! "&! ' =! '$ +! '& These are nearl alwas unequal (WHY?). Put together as Overall enhancement factor! =! "! "! ' , ' V z x These don t include an vertical shear between the facets. If these are included there is onl one enhancement factor. (Ton Gillies 2015) Vertical shear resultants across ield lines V New enhancement Factor equivalent to! =! "! "! ' n, ' 9

10 An problems so far? The membrane traction distribution is an assumption. It corresponds to unfractured mesh and either: No through-depth cracks along ield lines. Partial through-depth cracks along ield lines. Both of these distributions appl onl to the case where a lateral through-depth crack has formed across the short span through the YL intersection. Distribution is fixed for each case. Enhancement factor starts below 1.0 actuall at zero. Internal forces don t depend on deflection. 10

11 Structural fire resistance methods for composite floors BRE Method (Baile 2000) Amended version of Haes s method. Fire Safe Design (SCI P288) checked using BRE-Baile design method. New Zealand SPM (Clifton 2006) FRACOF (2011) Based on a European project. Almost identical to BRE method. A few changes to safet factors, extra deflection check. 11

12 Tpical design strateg for TMA Protect members on column gridlines. Leave intermediate secondar beams unprotected. Design individual panels without continuit. 12

13 BRE/FRACOF method Unprotected composite beams at high temperature carr some of the load as simpl supported. + Concrete slab carries remaining load in tensile membrane action. Needs enough deflection. 13

14 Small-deflection ield-line mechanism slab onl BRE/FRACOF L=al nl Hogging rotations about edges of panel Tensile crack across short mid-span g Sagging rotations about internal ield lines l Large-deflection failure crack observed in tests and used in Baile/BRE, FRACOF and NZ SPM. The analsis is based on the optimal ield-line pattern for the concrete slab without considering the steel beams. 14

15 Force equilibrium no through-depth YL cracks BRE etc kbkt 0 This is the onl mechanism no separation of concrete along the ield lines. bkt 0 (Ultimate strength of reinforcement across Fracture) 1.1T 0 l/2 E Criterion: Crack across mid-long-span. Moment equilibrium about E. Finds b and k. 15

16 TMA enhancement calculations BRE/FRACOF Similarl to Haes: Horizontal force equilibrium assuming mid-span crack. (But onl the linear membrane traction distribution). Separate membrane enhancements e 1m and e 2m b moments about long and short edges. Add bending enhancements e 1b and e 2b to make e 1 and e 2. Overall enhancement factor! =! ". /0. 1 "2'34 1 or Gillies! =! ". /0. 1 "2'364 1 Cutoff at enhancement 1.0 for aspect ratios > 1.0. Enhancement factor BRE 1.0 Gillies 1.0 BRE 1.5 Gillies 1.5 BRE 2.0 Gillies 2.0 BRE 3.0 Gillies d/d 1 16

17 Limiting deflection (central cracking) criterion 7 8 = 9.;< 1? = B + 7 D = E F ' F " G ' 16h w E w q 17

18 Back to basics 18

19 Increasing deflection of ield-line mechanism Yield-line mechanism is a plastic bending mechanism at small deflections. Yield lines are essentiall discrete cracks. Mechanism B As deflections start to increase the ield-line pattern increases the rotations of its flat facets, with the rebar ielding until it fractures. So the initial large-deflection mechanism is this one. 19

20 Geometr of ield-line crack opening D x z f x s h µt q t Dx x x CRACK OPENING AT REBAR LEVEL TOP SURFACE OF SLAB As deflections start to increase the ield-line pattern increases the rotations of its flat facets, and rebar ields across cracks until it fractures. 20

21 Force equilibrium of Mechanism B M 1 M 2 S C 1 T 2 C 2 T 1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks M 3 21

22 Change of stress blocks ductile -reinforcement z x Compression a1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 22

23 Change of stress blocks ductile -reinforcement z x Compression a1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 23

24 Change of stress blocks ductile -reinforcement z x Compression a1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 24

25 Change of stress blocks ductile -reinforcement z x Compression b1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 25

26 Change of stress blocks ductile -reinforcement z x Compression b1 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 26

27 Change of stress blocks ductile -reinforcement z x Compression b2 Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 27

28 Change of stress blocks ductile -reinforcement z x Compression c Shape of concrete compression blocks is dictated b compatibilit and equilibrium: Initiall tension and compression at ever point of ieldlines. As deflection increases concrete compression blocks concentrate towards slab corners, rebar fractures when its strain exceeds its ductilit. No tension within compression blocks Tension 28

29 Change of stress blocks possibilities with less ductilit z x With different rebar ductilit, mesh can either fracture abruptl or progressivel at an stage. Unfractured Mid YL fractured Diagonals unzipping Tension 29

30 Change of stress blocks possibilities with less ductilit z x With different rebar ductilit, mesh can either fracture abruptl or progressivel at an stage. Unfractured Mid YL fractured Diagonals unzipping Tension 30

31 Change of stress blocks possibilities with less ductilit z x With different rebar ductilit, mesh can either fracture abruptl or progressivel at an stage. Unfractured Mid YL fractured Diagonals unzipping Tension 31

32 Garston test comparison Enhancement factor 1.5 b1x' b1x** b1x*** 1.0 b1x a1x Slab aspect ratio (6.360m x 9.353). 120mm thick, 52MPa concrete; Edges verticall supported. d/d 1 A142 mesh (142 mm 2 per metre, 580MPa steel at 200mm spacing in x and directions) at 69mm effective depth; Mesh ductilit 12%. 32

33 Garston comparison for different aspect ratios Enhancement factor BRE BRE BRE BRE d/d 1 33

34 Garston appl tensile strength to change mechanism Stress Q Stress R Stress S EC2 tensile strength for C52 [0.3f c 0.67 ] Bending stress (MPa) 4 3 Q R 2 1 S d/d 1 34

35 New mechanism central through-depth crack D x D x D x b u 3 = 2 v3 = rl + z 2 2 x Gap = 2 2 x u 2 2 = v = + x z 2 2 u' = x u 4 4 = 2 l v = + x z 2l 4 x Gap = Gap = x + z+ x+ z+ 2x Gap = 2 2 x+ 2 z + 2l 2 u 1 v = 0 1 = x z 2x 2 35

36 Change of stress blocks ductile -reinforcement z x 36

37 Change of stress blocks ductile -reinforcement z x 37

38 Change of stress blocks ductile -reinforcement z x 38

39 From basic mechanism to centrall cracked Enhancement factor d/d 1 39

40 With attached steel beams the ield-line mechanism changes. 40

41 Forces on the x-aligned mechanism rl n x l g x C 2 C 1 S T b, t T x1 l A B T 1 T b, t T 2 Unprotected beams at high temperature 41

42 Forces on the -aligned mechanism rl T 1 g n l T b, t T x1 S T b, t B C 1 l T x2 A C x2 Unprotected beams at high temperature 42

43 Combinations of compression block and rebar fracture x Compression block Reinforcement mesh fracture level (x-aligned mechanism) None Central Diag. x Central + Diag. Central + Diag. x Central + Diag. x, Full above mesh a1 a1 a1* a1** a1* a1*** below mesh a2 a2 a2* a2** a2* a2*** Triangular above mesh b1 b1 b1* b1** b1* b1*** below mesh b2 b2 b2* b2** b2* b2*** Trapezoidal c1 c1 c1* c1** c1* c1*** 43

44 Example of application: 9m x 6m composite slab 9m 130mm thick slab, 30MPa concrete; A142 mesh (142 mm 2 per metre, 500MPa steel at 200mm spacing in x and directions) at 60mm effective depth; 6m Mesh effective ductilit (over 200mm length) 1%: fracture crack-width 2mm; One central downstand steel beam, 305x165UKB40, Grade S275 - unprotected against fire; Edges verticall supported

45 Initial ield-line parameter for different load capacities 0.8 n x n x 0.6 n n x or n n Load capacit (kn/m 2 ) 45

46 Critical temperature variation with load capacit 1200 Critical temperature ( C) x-mechanism x -mechanism Load capacit (kn/m 2 ) 46

47 Enhancement of critical steel temperature with deflection 1400 Unprotected beam temperature ( C) (No failure of non-composite slab) (Ambient-temperature failure of composite slab) x Slab deflection (mm) 47

48 Enhancement of critical steel temperature with deflection Unprotected beam temperature ( C) a1 b1 b1 * b1 3kN/m 2 b1*** Slab deflection (mm) 48

49 Maximum steel temperature enhancements 160 B1x** b1 * Temperature enhancement ( C) b1x b1 b1 * B1* x-mechanism -mechanism Load capacit (kn/m 2 ) 49

50 5 Maximum tensile stress at section A B A Stress (MPa) kn/m 2 A Slab deflection (mm) 50

51 In summar Existing simplified methods: For concrete slabs: Fixed membrane traction distribution independent of slab deflection. Membrane traction distribution onl valid while concrete has compression along whole ield lines. Assumes central crack full formed. Rebar at ultimate strength (+10%) Enhancement factor starts below 1.0. For composite slabs in fire: Yield-line pattern based on non-composite slab. Superposes high-temperature composite beam capacit and deflection-controlled slab enhancement. Criterion for mid-span through-depth crack is meaningless. 51

52 In summar The new approach: For all slabs: Based on the kinematics of deflecting flat facets of the small-deflection ield line mechanism, together with in-plane equilibrium of the concrete and steel forces. Allows concrete stress blocks to move and mesh to fracture across ield lines. For composite slabs in fire: Keeps load constant, allows beams temperature to increase until ield line mechanism forms. Enhancement of steel beam temperature with deflection. Biggest problems to be solved: Fracture ductilit of rebar across discrete cracks - ield lines or through-depth mid-span crack. Concrete tensile stress to initiate the mid-span (or intersection) crack. 52

53 Thank ou 53