00.1
0.2
0.3
0.4
0.5
0.6
0.7
2500.8
0.9
1.0
Predictive
300 350 400 450OriginalFigure 12.11: Illustration of original and predictive probability distribution functions for the steel yield
stress.
The 5% percentile value, which is a typical characteristic value for the steel yield stress is
changed from 317 MPa to 322 MPa as a result of the test results.
In practical applications the scheme illustrated in the simple example above may be used to
update e.g. the probability distribution of material characteristics such as the concrete
compressive strength or the fracture toughness of steel materials. During manufacturing and
execution of structures testing of material characteristics is normally inexpensive but for
existing structures material testing can be extremely expensive as it may require that the
operation of the structure to be discontinued. In such cases then it must be evaluated whether
or not it is cost effective to perform the tests.
Example 12.5 – Reliability updating by proof load testing
The steel bar subject to tension loading is considered. Due to changed operational conditions
of the component it is necessary to prove that the steel bar can sustain an increased loading
with sufficient safety. In order to prove that the component has the required capacity a load
test is planned. The intensity of the load test shall be such that the capacity of the component
after the test is sufficient in regard to the required safety. In order to assess the required
intensity of the test load the updated capacity for a range of different test loads may be
evaluated. Assuming that the steel bar is subjected to a proof load l the probability distribution
function of the updated capacity RUof the steel bar after the load test with intensity l may be
evaluated by:
()(
()PRU r PR r R l
PR l&
&
) (12.19)
The probability distribution function is illustrated in Figure 12.12.