Titel_SS06

2700 2800 2900 3000 3100

Probability of failure

after test

Probability of failure

during test

2500

Proof load intensity

Probability of failure

2600

1.40E-02

1.20E-02

1.00E-02

8.00E-03

6.00E-03

4.00E-03

2.00E-03

0.00E+00

Figure 12.12: Probability of failure as function of the proof load intensity l.

In Figure 12.12 is also shown the probability of failure of the steel bar during the test. This is
often referred to as the test risk. It is seen that there is a close relationship between the benefit
of the proof test i.e. a decrease in the failure probability after the test and the risk of loosing
the steel bar during the test. A decision analysis as outlined in the previous where the costs of
failure during the test, costs of failure after the test and the costs of the test itself are included
can assist in deciding whether a proof load test should be performed.

The calculations necessary to perform the reliability updating may be performed using
systems reliability analysis, however, for this simple case FORM/SORM analysis can be used
most efficiently by consideration of the limit state function (Faber et al. [41]):

MrRU (12.20)

where RUis the updated capacity obtained by:

U (^1) ( ( )(1 ( ))
R FUFlRR
,  (12.21)
where U is an auxiliary standardised normally distributed variable and is the original
distribution of R.

FR

The proof load reliability updating illustrated in the above is strongly simplified, however, the
principle is the same in more rigorous analysis. In Moses et al. .(1994), Fujino and Lind
(1977), Saraf and Nowak (1998) and Faber et al. (1998) proof load testing is elaborated for
the reassessment of bridges.

Example 12.6 – Reliability updating by indirect information

An important aspect in reliability updating is the possibility to use information about the
considered structure which does not origin from the structure itself but which may be
correlated to the structure. Such correlation can origin in a number of sources such as
common loading, correlated materials and correlated degradation processes.

To illustrate the use of indirect information, consider again the example with the steel bar