ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE

Transcription

1 ANALYSIS OF REINFORCED CONCRETE BUILDINGS IN FIRE Dr Zhaohui Huang Universiy of Sheffield 6 May

2 VULCAN layered slab elemens: connecion o beam elemens Plae Elemen Slab nodes y x Reference Plane h z Disribued Seel Layers Beam node offse Concree Layers Connecor node 2 Beam Elemens

3 Developmen of VULCAN slab elemens: Maerial Nonlinear Slab Elemen Layered elemen. Temperaure disribuions Geomeric hrough non-lineariy of slab hicness of slab. elemens: Models hermal bowing of slab. Allows invesigaion of ensile membrane acion a high Thermal degradaion of maerial for emperaures/deflecions. each layer. Also predics hermal bucling Biaxial failure surface for concree. (compressive membrane acion) a Failure layer-by-layer based lower on principal emperaures. sress levels a Gauss poins. Cracing perpendicular o principal ensile sress, crushing removes all srengh of layer for elemen. Uniaxial seel reinforcemen layers. 3

4 Concree sress-srain curves a high emperaures Concree also loses srengh and siffness from 100 C upwards. Does no regain srengh on cooling. Sress raio ( σ c / f c '(20 C )) C C 600 C 400 C 800 C 1000 C Srain (%) 4

5 Seel sress-srain curves a high emperaures Seel sofens progressively from C up. Only 23% of ambienemperaure srengh remains a 700 C. A 800 C srengh reduced o 11% and a 900 C o 6%. Mels a abou 1500 C. Sress raio( σ / f (20 C)) s y 1.0 < 100 C C 400 C C C 1000 C Srain (%) 5

6 Concree biaxial failure envelopes: solid slabs σ c2 f c ' A Cracing O B σ c1 f c ' Cracing Increasing emperaure α = C Crushing 6 E Crushing -1.0 D σ c1 α = > σ σ c2 c1 σ c2

7 Concree ension curve used in VULCAN Sress σ f Cracing A f = f c 0.33f B 0 ε cr 4.44ε cr 20ε cr ε c Srain C 7

8 Membrane acions in slabs A low deflecions slabs may show: compressive arching agains boundaries hermal bucling A high deflecions: 8 biaxial ension in mesh a cenre compressive ring in concree around periphery Boundary Condiions o mobilise his effec?

9 A square plae simply suppored on four edges Uniform loading (q) y h = mm E = MPa ν = x Quarer-plae analysed a =15240 mm 9

10 10 Normalised plo of cenral deflecion of square plae 3 v/h Geomerically linear Geomerically non-linear Chia (1980) (qa 4 ) / (Eh 4 )

11 11 Disribuion of principal membrane racions for he quarer-plae modelled q = 0.24 MPa

12 12 Prediced cracing paern for reinforced concree slabs (specimen B1) q = 8.4 N/m 2

13 13 Disribuion of principal membrane racions for reinforced concree slabs (specimen B1) q = 45.5 N/m 2

14 14 Prediced cracing paern for reinforced concree slabs (specimen C1) q = 12 N/m 2

15 15 Disribuion of principal membrane racions for reinforced concree slabs (specimen B1) q = 85 N/m 2

16 16 Three-dimensional hree-noded beamcolumn elemen configuraion Reference axis 2 Segmens 3 z' x' V V r V s 1 y' r Beam neural axis s s a z b y x

17 17 The main assumpions of he model: Plane secions originally normal o he reference axis remain plane and undisored under deformaion, bu are no necessarily normal o his axis. The displacemens and roaions of he elemen can be arbirarily large bu he elemen srains are sill assumed o be small. Each segmen wihin he cross-secion can have a differen emperaure, bu his is uniform along he elemen.

18 18 The main assumpions of he model: The iniial maerial properies of each segmen may be differen, and he sress-srain relaionships may change independenly for each segmen. For each segmen only he longiudinal sress and wo shear sresses are non-zero.

19 19 19 The Caresian coordinaes of a poin in an elemen wih N node poins a ime The Caresian coordinaes of a poin in an The Caresian coordinaes of a poin in an elemen wih elemen wih N node poins a ime node poins a ime ( ) ( ) ( ) = = = = = = = = = = = = N sz N z N N sy N y N N sx N x N V h s s b V h a z h s r z V h s s b V h a y h s r y V h s s b V h a x h s r x ,, 2 2,, 2 2,,

20 20 20 The oal displacemens of a poin in an elemen wih N node poins a ime The oal displacemens of a poin in an The oal displacemens of a poin in an elemen wih elemen wih N node poins a ime node poins a ime ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = = = = = = = = = = = N sz sz N z z N N sy sy N y y N N sx sx N x x N V V h s s b V V h a w h s w r V V h s s b V V h a v h s r v V V h s s b V V h a u h s r u ,, 2 2,, 2 2,,

21 21 21 The incremenal displacemens of a poin in an elemen wih N node poins a ime The incremenal displacemens of a poin in The incremenal displacemens of a poin in an elemen wih an elemen wih N node poins a ime node poins a ime ( ) ( ) ( ) = = = = = = = = = = = = N sz N z N N sy N y N N sx N x N V h s s b V h a w h s w r V h s s b V h a v h s r v V h s s b V h a u h s r u ,, 2 2,, 2 2,,

22 22 Using he second-order order approximaions for he vecor of nodal roaional degrees of freedom V V s = = θ θ V V s θ θ ( ) θ V ( ) θ V s

23 23 The consiuive marix of a craced concree segmen D ' c = µ 0 G c µ 0 G 0 c

24 24 Canilever beam subjeced o concenraed end momen: canilever beam and is finie elemen model z y Fixed end L = 304.8mm x M = f m E = MPa ν = 0.0 b = h = 25.4 mm M = f m m = πei/l = N-m z b h y δ z β x δ x Four hree-node parabolic elemens

25 Canilever beam subjeced o concenraed end momen: Load-deflecion deflecion behaviour Normalized displacemens and roaions δ x /L (Curren model) δ z /L (Curren model) β/2π (Curren model) δ x /L (Surana e al 1989) δ z /L (Surana e al 1989) β/2π (Surana e al 1989) Load facor f

26 26 A full-scale ISO384 sandard fire es on a Slimflor beam: deails of he Silimflor beam esed P = 84.6N P P P P ISO384 Fire A142 mesh Seel 80 Concree: f c = 45MPa Seel: f y = 402 MPa Reinforcemen: f y = 460 MPa Concree Cross-secion of he beam (All in mm)

27 27 A full-scale ISO384 sandard fire es on a Slimflor beam: elemen segmenaion mesh adoped 950 P P5 P4 P3 P2 P ISO384 Fire (All in mm)

28 A full-scale ISO384 sandard fire es on a Slimflor beam: emperaures a seelwor Temperaure ( C) 1200 Tesed P1 Prediced P2 900 P3 600 P4 P5 300 P Time (min)

29 A full-scale ISO384 sandard fire es on a Slimflor beam: deflecions a mid-span Mid-span deflecion (mm) Tesed Prediced Time (min)

30 A full-scale ISO384 sandard fire es on a Slimflor beam: deflecions a mid-span for differen end suppor condiions Mid-span deflecion (mm) Tesed Simply suppored Acual column siffness -750 Fully braced column siffness Time (min)

31 31 A generic 37.5 x 37.5 m reinforced concree srucure (whole floor heaed using ISO384 fire ) A B C D E F 6 Nominal cover for 2 hours fire resisance (BS8110) 5 Beam: 30mm Column: 25mm 4 Slab: 25mm C 3 Design load a fire limi sae: N/m 2 B 7.5m A 7.5m Quarer srucure analysed Axis of symmery 2 1 Concree: f c = 45 MPa Reinforcemen: f y = 460 MPa

32 32 Cross-secions secions of beam and column 2T12 6T T Bar 1 Bar 2 Cross-secion of beam Bar 1 Bar 2 Cross-secion of column (All dimensions in mm)

33 Temperaure ( C) 800 Temperaures of reinforcemen wihin cross- secions of members (whole floor heaed) 2T12 6T T Bar 1 Bar 2 Bar 1 Bar 2 Cross-secion of column Cross-secion of beam (All dimensions in mm) Beam bar 1 Beam bar Column bar 1 Column bar 2 Slab mash Time (min)

34 Deflecion (mm) Deflecions a ey Posiion A, B and C (whole floor heaed) 0 Posiion A -100 Posiion B Posiion C Time (min)

35 Deflecion (mm) Verical deflecions of columns (whole floor heaed) Column A1 Column B Column C Time (min)

36 36 Deflecion profile (whole floor heaed) 0 min

37 37 Deflecion profile (whole floor heaed) 15 min

38 38 Deflecion profile (whole floor heaed) 30 min

39 39 Deflecion profile (whole floor heaed) 45 min

40 40 Deflecion profile (whole floor heaed) 60 min

41 41 Deflecion profile (whole floor heaed) 75 min

42 42 Deflecion profile (whole floor heaed) 90 min

43 43 Deflecion profile (whole floor heaed) 105 min

44 44 Deflecion profile (whole floor heaed) 120 min

45 45 Deflecion profile (whole floor heaed) 135 min

46 46 Deflecion profile (whole floor heaed) 150 min

47 0 min Slab principal force vecors (whole floor heaed) P3 P2 47 P1

48 15 min Slab principal force vecors (whole floor heaed) P3 P2 48 P1

49 30 min Slab principal force vecors (whole floor heaed) P3 P2 49 P1

50 45 min Slab principal force vecors (whole floor heaed) P3 P2 50 P1

51 60 min Slab principal force vecors (whole floor heaed) P3 P2 51 P1

52 75 min Slab principal force vecors (whole floor heaed) P3 P2 52 P1

53 90 min Slab principal force vecors (whole floor heaed) P3 P2 53 P1

54 105 min Slab principal force vecors (whole floor heaed) P3 P2 54 P1

55 120 min Slab principal force vecors (whole floor heaed) P3 P2 55 P1

56 135 min Slab principal force vecors (whole floor heaed) P3 P2 56 P1

57 150 min Slab principal force vecors (whole floor heaed) P3 P2 57 P1

58 Axial forces of beams a ey Posiion P1, P2 and P3 (whole floor heaed) Axial force of beam (N) 1200 Force a P1 900 Force a P2 Force a P Time (min)

59 A generic 37.5 x 37.5 m reinforced concree srucure (comparmen fire) A B C D E F Case III 3 Case II 2 7.5m Case I 7.5m Quarer srucure analysed Axis of symmery 1 59

60 Deflecion (mm) Comparison of cenral deflecions wih differen fire comparmen posiions Case-I -300 Case-II Case-III Time (min)

61 61 0 min Slab principal force vecors (comparmen fire case-i)

62 62 15 min Slab principal force vecors (comparmen fire case-i)

63 63 30 min Slab principal force vecors (comparmen fire case-i)

64 64 45 min Slab principal force vecors (comparmen fire case-i)

65 65 60 min Slab principal force vecors (comparmen fire case-i)

66 66 75 min Slab principal force vecors (comparmen fire case-i)

67 67 90 min Slab principal force vecors (comparmen fire case-i)

68 min Slab principal force vecors (comparmen fire case-i)

69 min Slab principal force vecors (comparmen fire case-i)

70 min Slab principal force vecors (comparmen fire case-i)

71 min Slab principal force vecors (comparmen fire case-i)

72 min Slab principal force vecors (comparmen fire case-i)

73 min Slab principal force vecors (comparmen fire case-i)

74 74 0 min Slab principal force vecors (comparmen fire case-ii)

75 75 15 min Slab principal force vecors (comparmen fire case-ii)

76 76 30 min Slab principal force vecors (comparmen fire case-ii)

77 77 45 min Slab principal force vecors (comparmen fire case-ii)

78 78 60 min Slab principal force vecors (comparmen fire case-ii)

79 79 75 min Slab principal force vecors (comparmen fire case-ii)

80 80 90 min Slab principal force vecors (comparmen fire case-ii)

81 min Slab principal force vecors (comparmen fire case-ii)

82 min Slab principal force vecors (comparmen fire case-ii)

83 min Slab principal force vecors (comparmen fire case-ii)

84 min Slab principal force vecors (comparmen fire case-ii)

85 min Slab principal force vecors (comparmen fire case-ii)

86 86 0 min Slab principal force vecors (comparmen fire case-iii)

87 87 15 min Slab principal force vecors (comparmen fire case-iii)

88 88 30 min Slab principal force vecors (comparmen fire case-iii)

89 89 45 min Slab principal force vecors (comparmen fire case-iii)

90 90 60 min Slab principal force vecors (comparmen fire case-iii)

91 91 75 min Slab principal force vecors (comparmen fire case-iii)

92 92 90 min Slab principal force vecors (comparmen fire case-iii)

93 min Slab principal force vecors (comparmen fire case-iii)

94 min Slab principal force vecors (comparmen fire case-iii)

95 min Slab principal force vecors (comparmen fire case-iii)

96 min Slab principal force vecors (comparmen fire case-iii)

97 min Slab principal force vecors (comparmen fire case-iii)

98 98 Conclusions I is clear from his sudy ha relaively small areas of ensile membrane force were formed wihin he concree slabs, and large areas of he slabs were subjec o compressive membrane force during he fire. As a resul he downsand concree beams were subjeced o enhanced ension during he fire, especially in he iniial sages, and hese ensions were mainly carried by heir ensile reinforcemen. I is herefore very imporan o eep he emperaure of he reinforcemen wihin cerain limis.

99 99 The covers o reinforcemen specified in curren design codes are reasonable provided ha concree spalling does no occur during he fire. Designers should herefore pay aenion o measures o preven concree spalling, in order o enable srucures o saisfy heir fire resisance requiremens. I is eviden ha adjacen cool srucure provides resrain and coninuiy, increasing he fire resisance of he srucure wihin he fire comparmen. As for composie srucures, he fire resisance of columns is vially imporan for reinforced concree buildings. In all cases analysed in his sudy he evenual srucural failures were due o bucling of he heaed columns.