Eurocodes – failing to standardise safety Mike Byfield, Cranfield University

1. Eurocodes – failing to standardise safetyMike Byfield, Cranfield University

2. 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). • CEN have adopted what is known as a “boxed values” approach to gM-factors. • 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

3. 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, gM

4. Design expression accuracy Comparison between poor and high quality design expressions

10. Examples of variations in design expression accuracy • 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)

11. Results from reliability analysis Design task Probability of actual strength falling below the design strength gR* Safety factor to achieve the “target reliability”, existing gM factor in brackets Tensile 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)

12. 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.

13. A practical solution to variable safety levels • Solution 1 • Determine a gM 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

14. Solution 2 • 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: • gM is the boxed value • is the safety factor output from reliability analysis • Thus the design resistance, rd = k rn / gM

15. In the case of the plastic moment capacity of restrained beamsk = 1.10 / 0.94 = 1.17The modified design expression would take the form: Example 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.

16. Current variations in reliability Variations in reliability using the supplementary safety factors