Titel_SS06

strengthening is given by:

(/*ˆ) T

FsAf@@ y Pf (12.9)

or

*

(^1) ()T ˆ
f y
s
A
FPf



@@

(12.10)

The consequences associated with testing and strengthening i.e. the total costs comprise

the costs of testing and the costs of required strengthening

CT

Ctest Cstrengt. The total costs can

be written as:

CT

*

*

T test strength test test AA i

CC C Nc EIA c

& A



  @ 8



9 (12.11)

where IAA*& is an indicator function equal to 1 only if the required cross sectional area is larger

than the original area and zero otherwise. is the initial manufacturing cost for the steel bar.

The expectation operator

ci

E@ indicates that the expectation operation is performed over the

prior probabilistic model of the steel yield stress. The formulation of the expected value in
Equation (12.11) is suited for a solution by simulation. It has been assumed that the
experiment costs vary linear in the number of costs. This may not always be the case as a
certain mobilisation cost is required disregarding the number of tests to be performed.

Equation (12.11) is now solved corresponding to different numbers of experiments. In Figure
12.9 the relation between the total reassessment costs to the initial manufacturing costs and
the costs of testing to the initial costs of manufacturing is shown.

0.10

Number of tests

0.12

0.14

0.16

0.18

0.20

0.22

2 3 4 5 6 7 8 9 10 1112 13 14 15

CT/CI

0.24

C_ Test/C_I = 1/400

C_ Test/C_I = 1/300

C_ Test/C_I = 1/200

C_ Test/C_I = 1/100

/1/40

/ 1/ 300

/1/20

/1/10









TI

TI

TI

TI

CC

CC

CC

CC

0

0

0

Figure 12.9: Illustration of the optimal planning of experiments for structural reassessment.

The figure is entered with known ratio between the costs of performing one test and the costs
of manufacturing the steel bar originally. It is also assumed that the absolute manufacturing
costs are known. Then the optimal number of tests can be found as the value for which the