fire design of hollow core slabs ipha seminar · ha12 self weight kn/m² vtestvtest/dalle kn test...
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11
FIRE DESIGN OF HOLLOW CORE SLABS
IPHA SeminarGothenburg, 6-7 November 2007
André de ChefdebienCERIBConstruction Products Division
Yahia MsaadCERIBConstruction Products DivisionFire section
22
Plan
calculation of the temperature field on supports and at mid-span
shear resistance modelo Interaction model
o Simplified shear-flexure model
o Validation and results
33
Temperature along the strand: midspan and support
Fire - ISO 834
Air circulation 20°C
Fire test in CERIB(up side down)
FEM thermal model
44
Boundary conditions for thermal model derived from EC2-1-2
The heat capacity of air is neglected
The convective heattransfer coefficient in the cavity is the same that for non exposed surface
55
Thermal calculation
3D-temperature (°K) after 2h of Iso-834 fire curve
660
100
200
300
400
500
600
700
0 20 40 60 80 100 120 140 160 180 200
Voie n°6
Voie n°15
M03_C2
M14_C2
num
Strands temperatures
77
After 1h
0
50
100
150
200
250
300
350
-200 -150 -100 -50 0 50 100 150 200
numexpexp2
Temperature along the strandOn supportFar from support
88
Calculation method
for shear strength at high temperature
99
Interaction model
∫∫= cvdR fV max,
Calculation of a « upper bound » value of the shear strength :Integration of the shear strength along the assumed failure surface
Shear strength –normal stress interaction curvegiven by EC2-1-1 §12
)(2
2
lim,
2lim,2
lim,
2lim,
cdctdctdcdc
ccpctdcpctdcvdccp
ctdcpctdcvdccp
ffff
fffif
fffif
+−=
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−+=⇒>
+=⇒≤
σ
σσσσσ
σσσ
1010
Interaction model
•Assume a 45° failure surface•Calculate the bond/anchorage capacity of reinforcement•Calculate the longitudinal stress field equilibrating MEd
and thermal strain (1st step with a reduced load, include shift rule)•Calculate VR,fi by integration of the interaction curve•Adjustment of the load level: VEdfi = VR,fi
•Iterations until convergence
l
d a laVEd = p (l/2 - la/2 - a - d)MEd = p (la/2 + a + d)(l/2 - la/4 - a/2- d/2)
1111
Compatibility of shear strain : Kinematic factor
glissement γ
τ (M
pa)
50°C
300°C
500°C
Interaction model
∫∫= iicvd
icvdR ds
kf
V,
,max,
min
,
min, γγ
γi
icvd
Gf
iicvdk ==
∫∫= iicvd
R dsf
V5.1
,max,
Assumption: shear stress / shear strain relationship at high temperature proportional to axial stress / strain relationship
1212
yksfibpdfibpd
p
fiyksfirap
sfiaRpfiaRfiaR
fAfxfl
A
fAA
FFF
+⎟⎟⎠
⎞⎜⎜⎝
⎛+=
+=
+=
φαφα
σ
2
,
2
,
,,
,,,,,,,,
.''.
φ12 fully anchoredand Ks(θ)=1
fic
CCtcCctm
pfibpd
TTkff
,
2560,50,
12,2
7,0'
γηη
⎟⎠⎞
⎜⎝⎛ +
= ( )fic
CtcCctmpfibpd
Tkff
,
25,25,12,
7,0γ
ηη=
Interaction model
Bond and achorage of reinforcement
1313
A proposal of simplified
calculation method
for shear strength
1414
Shear flexure simplified model
( )( ) dbkfkCV wficpficfilcRdficRd ,1
3/1
,,,,, 100( σρ +=
dbF
w
fiaRfil
1500
,,,
∑=ρ wb web minimal width
ratio of longitudinal reinforcements brought back to the minimal section
ficf ,mean compressive concrete strength on the total section, i.e. temperature at mid heigth of the slab
average concrete stress due to prestressing on the considered section
);)(min( ,,,20,,
c
fipaRCcppficp A
Fk °= σθσ
1515
Comparison between shear-flexure simplified model and interaction model
0
5
10
15
20
25
0 5 10 15 20 25
Vr-simplified(kN/cell)
Vr-intrinsic curve(kN/cell)
y=x
1616
comparison between shear load and shear strength given by simplified method
0
5
10
15
20
25
0 5 10 15 20 25
shear load applied (kN/cell)
shear strength(kN/cell)
shear failure observedno failure observedy=x
NO SHEAR FAILURELINE OF SHEAR FAILURE VEd,fi = VRd,fi
Data base (shear failure tests):-Arnold Van Acker: 5-Tauno Hietanen: 4
Comparison with available test results
1717
Test report.Test report. YearYear OriginOrigin Slab Slab heightheight
mmmm
Prestressing Prestressing strandsstrands
SpanSpanx widthx width
mm²²
HA12HA12 Self Self WeightWeightkN/mkN/m²²
VtestVtest//dalledallekNkN
Test Test durationduration
VrVr/dalle /dalle kNkN
DkDk--BetonelemBetonelem
ententforeningenforeningen 20052005 DenmarkDenmark 265265
2T12.5 2T12.5 a=40a=40
2,94 x 2,94 x 2,42,4 yesyes 3,653,65 89.4889.48 45'45' 90.5590.55
FEBEFEBE--RUG RUG 91589158--aa 19981998 BelgiumBelgium
265265+30+30
2T12.5 2T12.5 a=50a=50 2,9 x 2,42,9 x 2,4 yesyes 4,554,55 85.5485.54 120'120' 83.183.1
BelgiumBelgium19711971 19711971 BelgiumBelgium 265265 T12.5 a=31T12.5 a=31 2,9 x 1,22,9 x 1,2 nono 3,863,86 54.7254.72 33'33' 52.1652.16
DenmarkDenmark19981998 19981998 DenmarkDenmark 185185 T9.3 a=31T9.3 a=31 6,2 x 2,46,2 x 2,4 nono 2,622,62 43.543.5 22'22' 47.847.8
VTT/PAL VTT/PAL 43504350 19841984 FinlandFinland 265265 T9.3 a=60T9.3 a=60
5,08 x 5,08 x 2,42,4 nono 3,863,86 25.1125.11 130'130' 27.4327.43
VTT/PAL VTT/PAL 2480/822480/82 19821982 FinlandFinland 265265 T12.5 a=65T12.5 a=65 3,9 x 2,43,9 x 2,4 nono 3,63,6 44.2844.28 63'63' 43.6843.68
VTT/PAL VTT/PAL 4248/844248/84 19841984 FinlandFinland 265265 T12.5 a=64T12.5 a=64
5,185 x 5,185 x 2,42,4 nono 3,63,6 48.6548.65 49'49' 48.5448.54
VTT/PAL VTT/PAL 566d/85566d/85 19851985 FinlandFinland 265265 T12.5 a=57T12.5 a=57
5,165 x 5,165 x 2,42,4 yesyes 3,63,6 55.5655.56 77'77' 54.8654.86
VTT/PAL VTT/PAL 90228/8990228/89 19891989 FinlandFinland 265265
T9.3 a=62 T9.3 a=62 T12.5 a=92T12.5 a=92
5,165 x 5,165 x 2,42,4 yesyes 3,63,6 77.4477.44 27'27' 79.3279.32
Characteristics of tests with shear failure
1818
Influence of longitudinal bars and protruding strands
ConfigurationConfiguration VrVr ((kNkN//cellcell) ) intrinsicintrinsiccurvecurve
VrVr((kNkN//cellcell))SimplifiedSimplified methodmethod
No No φφ1212L=0 L=0
11.211.2 12.112.1
φφ1212L=0L=0
16.716.7 15.115.1
φφ1212L=0.1L=0.1
19.819.8 17.817.8
l=0.07l=0.07
HC : 270 mm
Span : 12.5 m
R120
1919
Concluding remarks on the shear resistance models
Both formulas seems to give a correct answer compared to test results of HC slabs
The “interaction method” allows to take into account the inter-action between the slabs ant supports (compression for floors with low slenderness ratio –tension for floors with cable effect), this approach could be developed for a global study (fire development, behaviour of the structure)
It is obvious that “shear flexure” simplified method is too conservative for short time fire exposure, and probably for thick HC
2020
Tentative review of of tabulated dataShear capacityVRd,fi/VRd,cold
( %)Slab thickness (mm)
Standard fire resistance
160 200 265 320 400
R30
73 70 71 76R60
66 68 56 / 62 55 / 63 52 / 70R90
60* 63 53 50 48 / 68R120
55* * 50 47 46R180
44* * * 42
* Does not satisfy the insulation criterion
In blue : « shear-flexure » in red : « interaction »
2121
Shear by prestressing Shear by thermal strain
2222
Dk-Betonelement (Denmark)
cellkNVmkNV cellfiEdfiEd /56.16/3.73 /,, =⇒=⇒
fiyksfibpdfibpd
p
fiyksfirapsfiaRpfiaRfiaR
fAfxfl
A
fAAFFF
,2
,
2
,
,,,,,,,,,,
.''.+⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
+=+=
φαφα
σ
7.0)(25011070
40;0'4.460
=⇒°==+=
===⇒=
scts
ctmck
TkCTmmammx
mmalMPafMPaf
MPafTkff
MPa
Tkff
ykfis
sykfiyk
fic
stcctmpfibpd
500)()12(
59.21
7.04.47.02.1
)(7,0
,
12,
,
,12,
==×
=
=××
=
=
γφ
γηη
φ
kNFmmA
mmATfira
s
p 5.67²4.90
²186;19.0 ;5.122,
2 =⇒⎭⎬⎫
⎩⎨⎧
=
==× α
Effort anchored by reinforcement
2323
Dk-Betonelement (Denmark)
%46.122540
41 500,
,
==⇒⎭⎬⎫
⎩⎨⎧
=−==
dbmmhdmmb firaF
filω
ω ρ
MPaA
dxF
c
pfiaRficp 2.2
)(,,,, =
+=σ
( )( ) kNdbkfkCV wficpficfilcRdficRd 77.16100( ,1
3/1
,,,,, =+= σρ
MPakfffic
cckfic 8.5898.060)(
,, =×==
γθ
94.12001 =+=d
k18.0, =cRdC 15.01 =k
ratio of longitudinal reinforcements brought back to the minimal section
average concrete stress at x+d (shift rule):
Mean compressive concrete strength