reliability-based assessment of system effect for timber...
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COST Action E24, 6th working group meeting, Florence, 27-28 May, 200411
Reliability-based assessment of system effect for timber floors
Alaa Mohamed
French Institute for Advanced Mechanics, LaMI - IFMA & UBP, France
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Coupled joist behavior due to sheathing stiffness
Floor slab configuration
Joists
Sheathing (polywood/RC)
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Redistribution of loading between joists
System behavior under loading
Additional safety margin due to load reduction
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Outline of the presentation
• Reliability analysis
• Mechanical model for timber floors
• Reliability assessment of the system effect
• parametric analysis of the floor
• Conclusion
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Reliability analysis
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SollicitationRésistance "R"
"S"f (s),f (r)R S
s, rx
Action Strength
mS mRsk rk
S*=r*
Fundamental case of safety
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Structural reliability formulation
fX1,X2(x1,x2)
X2
X1
{ } in XXXX =,,, 21 K• Random variables:• Limit state function:• Failure probability:
)( ixG[ ] 1( ) 0
P ( ) 0 ( ,..., ) ( )i
ii X nG x
G X f x x dx β≤
≤ = =Φ −∫
2X
1X
Safetydomain
Failuredomain
G( X )= 0
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2X
1X
Safetydom ain
F ailuredom ain
G ( X )= 0
2U
1U H(U) = 0
βP*
0
Reliability index methods (FORM/SORM)
• Reliability index• Importance factors• Design point
FORM/SORM
Transformation into the standard space
Approximations
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Mechanical model
and
reliability computation
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Finite element model
• Shell
• Beam
• Links
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Deformed shape
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Coupled Reliability and Mechanical model
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Reliability computation tool
Reliability combination
under PHIMECA©
Mechanical model
FEA analysis(ABAQUS, ANSYS, …)
Interface files
Reliability results :Probability, sensitivities, influence, …
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Reliability assessment
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System modification factor
Single beam
Beam span
Ben
ding
mom
ent
Beam in system
8
2LPM uu = βsamethefor
LLK
B
Ss
2
=
Single beam
Beam spanR
elia
bilit
y in
dex
Beam in system
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2
=
B
SsK
ββ
Single beam
Beam span
Rel
iabi
lity
inde
x
Beam in system
Other definition of the System modification factor
Sβ
Bβ
2
=
fS
fBs P
PKor
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Random variables in the floor design
Variable Description Distribution Mean COVfm Timber strength Lognormal 36 MPa 25%G Dead load Lognormal 1 kN/m2 10%Q Live load Gumbel 2 kN/m2 30%
b = 0.06m
h = 0.18 m
Lx*Ly = 4 x 4 m
Number of beams = 9 (i.e. spacing a = 0.5 m)
Timber class: C24
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Reliability sensitivities
G = 0.8 fm - σ(G,Q,b,h,…)
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Effect of sheathing thickness and Length
L
eSlab
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eSlab
RC sheathing
L
5 cm7.5 cm
10 cm
12.5 cm
15 cm
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Effect of MOE variability
E1 / E0E0E1E0
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Parametric studies
Variable Description Distribution Mean COVfm Timber strength Lognormal 36 MPa 25%G Dead load Lognormal 1 kN/m2 10%Q Live load Gumbel 2 kN/m2 30%
b = 0.06m
h = 0.18 m
Lx*Ly = 4 x 4 m
Number of beams = 9 (i.e. spacing a = 0.5 m)
Timber class: C24
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Mean strength - Mean Live load
Mean(fm)
COV(Q)
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COV and mean of stength
COV(fm)
mean(fm)
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Mean and COV of Live load
COV(Q)
Mean(Q)
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Mean stength - COV of Live load
COV(Q)
Mean(fm)
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COV of stength - mean of Live load
COV(fm)
Mean(Q)
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COV of stength - COV of Live load
COV(fm)
COV(Q)
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Conclusion
Large effect of system when RC slabs are involved.
Significant effects of uncertainties on moment redistribution.
Further works:Post-failure system combination
Fastners (nonlinear) rigidity
Correlation of Ei’s