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