Titel_SS06

subject to tension loading.

The problem is as before that the loading of the steel bar is to be increased by 10 % and the
problem is to identify means to prove that the safety of the steel bar is sufficient.

In this case the situation is that a similar steel bar has been in operation and due to an error in
the operational procedures this other steel bar has been subjected to a loading which was equal
to l without failing or showing signs of excessive loading. It is suspected that the steel used to
manufacture the other steel bar does not originate from the same batch as the steel used to
manufacture the steel bar of interest but it is known that the steel originates from the same
manufacturer. Based on extensive experimental data it is known that the correlation between
the uncertain mean value of the yield strength of the steel from the two batches is correlated
with a coefficient of correlation 1 0.8.

On this basis it is possible to update the probabilistic model of the yield stress can be updated
as:

12

12

2

(0

(0)

()

PR s R l

PR s R l

PR l



&

 & 

&

)

(12.22)

where R 1 and R 2 both are normal distributed with uncertain mean values as in the examples

before. However, it is now assumed that the uncertain mean values are two different but
correlated random variables.

In Figure 12.13 it is shown how the failure probability of the considered steel bar subject to a
loading of 3041.5 KN is changed by updating on the basis of the indirect information obtained
from a “proof load” test of an other similar steel bar.

2800 3000 3200 3400

Updated failure

probability

Proof load intensity

Probability of failure

1.20E-02

1.00E-02

6.00E-03

4.00E-03

2.00E-03

0.00E+00

3600

8.00E-03

Updated failure probability

Figure 12.13: Updated probability of failure using indirect information.

From Figure 12.13 it is seen that the value or the strength of the likelihood of the indirect
information is rather weak. Even for relatively significant load intensities l the decrease in the
failure probability is quite moderate. However this should not lead to discourage. In many
cases indirect information is the main source of information in the reassessment and it can