Titel_SS06

In this example this acceptance criteria is fulfilled for yield strength larger than 434MPa see

Figure 13.10, C). This corresponds to a probability of failure of Pf3.675 10^5.

For the considered structural member yield strengths larger than 434MPaare acceptable. But

the question remains: which one is the optimal decision? The optimal point can be determined
by maximizing the objective function.

The objective function is given by:

Z




pBpCpmpCpkNSVSLC yyPE (^) U (13.18)
Herein all expected costs and benefits are taken into account. B
p denotes the benefit of the
structural member and CU are the expected clean up costs after a failure occurs:



10.000

100.000





CCHFU

B pCHF

In the objective function the fatalities are taken into account by the societal value of a
statistical life according to Equation (13.18).

In Figure 13.10 (D) the objective function for this example is illustrated. The maximum
benefit is reached with a yield strength of 441 MPa and a corresponding probability of failure

of. Since the optimum yield strength is larger than the one required by the

LQI criterion, the optimum is acceptable. If the optimal decision is not acceptable the
maximum in the acceptable region has to be found.

2.595 10^5

Pf

In many situations the benefit of a structure or a part of the structure is unknown and not
determinable. For the most problems in the field of civil engineering the benefit of the
member is independent of the design value p. By taking the derivative of the objective

function to find the maximum the benefit vanishes and the optimal solution is independent
from the benefit B.