Eurocodes – failing to standardise safety Mike Byfield, Cranfield University

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

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

Design expression accuracy Comparison between poor and high quality design expressions

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)

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)

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.

A practical solution to variable safety levels 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

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

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

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