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  • Writer's pictureSi Shen

Partial factors

We often hear about ‘partial factors’. They appear everywhere in Eurocode. But what are they really? Why are they used? What do they represent? This blog post hopes to dig down to the nature of partial factors.

Reliability is the word

Contrary to popular belief, an engineer does not design a structure to be ‘safe’. He/she can never guarantee its safety, even if the works have been executed by perfectly competent contractor, exactly to specification with perfect quality and precision, and is used exactly as anticipated. We can never say a structure is ‘safe’, regardless how well the design is done, because there are simply too many things that could happen in life and it is impossible to design against them all. An engineer can only take it ‘as far as reasonably practicable’ to design a structure to survive the vast majority of disasters that might land on the structure.

In fact, Eurocode does not require structures designed to be safe, but designed to be ‘reliable’. ‘Reliability’ is the key word and the most fundamental underlying approach for Eurocode. Being ‘reliable’ as a structure means that the risk of failure is minimal and within tolerable range. The Eurocode requires engineers to design structures in such an approach that their reliability is verified and demonstrated by analysis and calculations with one of the defined approaches suitable for the situation given.

How to achieve reliability

How is reliability demonstrated? It is all founded on statistics. Statistics is the cornerstone to the most fundamental approach of Eurocode. Eurocode specifies two ways of verifying reliability, depending on the soundness of existing statistics:

1) when the design is innovative or for whatever reasons there is a lack of existing data, Eurocode allows us to collect data by doing testings. It has defined and controlled approaches to ensure the testings give us the same level of reliability as other more conventional projects.

2) when there is a lot of data available, e.g. from precedent similar projects, reliability can be verified by ‘partial factors’, which means the nominal (i.e. ‘on paper’) values from the design is multiplied by a factor, either up or down, towards the more conservative direction, so that the structure has sufficient capability to survive the majority of unfavourable events in real life, even if they go over and above the nominal value. Eurocodes call the nominal values ‘characteristic values’ and the after-factor values ‘design values’.

The partial factor verification method

There are 3 things partial factors are applied to, using the language of Eurocodes:

· Actions. These are either 1) direct impact on the structure, such as traffic, self-weight, wind, etc. or 2) imposed deformation effects such as temperature and shrinkage. Unfavourable actions are always factored up and favourable actions are always factored down. Eurocodes have 2 sets of factors for actions, one is partial factor for the magnitude of the action itself, the other is ‘combination factor’, which means when there are multiple actions going on at the same time, it is very unlikely that the peak values from all of them will happen at the exact same time. There is a ‘leading action’ and the rest are factored down by combination factors.

· Effects. These are the results of actions. They represent the design value that the structures need to survive. These take the form of cross-sectional bending moment, axial force, shear, etc

· Resistance. These are always factored down, when factors do apply. Resistance partial factors apply in the situation where the resistance is unreliable, e.g. something that provided by mother nature. For example, resistance of friction piles are factored down, as frictional resistance with the ground is relatively less predictable by calculations.

In summary, from another perspective, the partial factor verification method essentially follows 3 steps:

1. A characteristic value is either defined by codes based on readily available statistics, or determined by statistics generated by testing (in which case partial factors could already be built into the characteristic values).

2. A characteristic value after multiplication with a partial factor becomes a design value. This applies to actions, effects and resistance.

3. Design resistance is then compared with design effects to ensure the latter is smaller, in which case the design has adequate reliability.

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