byfield ise gamma m
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bhjkTRANSCRIPT
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Eurocodes – failing to standardise safety
Mike Byfield, Cranfield University
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The Eurocode approach to partial safety factors
• The structural Eurocodes aim to restrict the probability of the actual resistance of structural components falling below the design resistance to 1 in 845 (approximately 10-3).
•Each member state selects its own M values, which are applied to a whole range of different resistance functions.
• Advantage – Political: It retains the authority of member states to set the safety levels achieved by the codes.
• Disadvantage – structural reliability: The system cannot account for variations in the quality of the design expressions
•CEN have adopted what is known as a “boxed values” approach to M-factors.
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The probability of the resistance falling below the design resistance is influenced by 3 factors:Reliability of material and geometric properties
Design expression accuracy
The value of partial safety factor, M
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Comparison between poor and high quality design expressions
00
Experimental strength
Pred
icte
d st
reng
th
Series1
Series2
Design expression accuracy
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Three different resistance functions have been investigated:
• Tensile resistance of bolts (based on 135 direct tensile tests on 20mm diameter grade 8.8 ordinary bolts)
• Bending resistance of restrained beams (based on 20 tests with restraints selected to produce a worst-case scenario)
• The shear buckling resistance of plate girders (based on 35 plate girder tests)
Examples of variations in design expression accuracy
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Design task Probability of actual strength falling below
the design strength
R* Safety factor to achieve the
“target reliability”, existing M
factor in bracketsTensile resistance of
ordinary bolts<10-8 0.95 (1.25)
Bending resistance of restrained beams
4.6x10-6 0.95 (1.10)
Shear buckling resistance of plate
girders
1.0x10-2 1.33 (1.10)
Results from reliability analysis
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Conclusions from the reliability analysis
• The most complex design task requires the highest safety factor.
•Reliability variations can reduce safety by leading to over-strength components, transferring failure to connections or columns
•Increasing the boxed value to improve the reliability of plate girder design would not necessarily solve all the reliability problems.
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Solution 1
•Determine a M factor for each resistance function. The factor could take the form of a numerical constant incorporated into the design expression
•Designer being largely unaware of the origin of the factor.
•No other safety factors on resistance.
•Problem – politically unacceptable
A practical solution to variable safety levels
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•Retain the boxed value system
•Embed a supplementary safety factor into each resistance function.
•The boxed values selected by nation states would merely adjust design economy and target reliability.
Supplementary factor, k =
Where:
M is the boxed value
is the safety factor output from reliability analysis
Thus the design resistance, rd = k rn / M
Solution 2
*R
M
*R
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Example
In the case of the plastic moment capacity of restrained beamsk = 1.10 / 0.94 = 1.17The modified design expression would take the form:
0MyplRd.pl /fW17.1M
This would offer a 17% increase in the design moment, whilst still achieving the target reliability.
During the calibration of k factors it may be desirable to adjust the target reliability depending on the consequences of failure.
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Variations in reliability using the supplementary safety factors
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
Individual design expressions
Rel
iabi
lity,
Pr(
r<r d
)
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
Individual design expressions
Rel
iabi
lity,
Pr(
r<r d
)
Current variations in reliability