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00, ........ 12) and where ro maximizes the function r(1- FR (r». 12]). 3. 4 kN. 6 kN. In a real structure with a low degree of redundancy it is likely that brittle failure of one structural element will result in subsequent failure of other elements. The structural system will therefore in such cases with good accuracy be modelled by a series system.

Such dominant (with regard to failure) failure elements are called critical failure elements. The notation )>critical» is used here to indicate that they are critical or significant to include when an estimate of the systems probability of failure is performed. 4. 14. This column has two potential yield hinges, namely the failure elements 7 and 8 at each end of the column. 4. 04746. 18. 19 Systems modelling at level 2. For some structures it is acceptable that failure takes place in one failure element but when failure takes place in two failure elements the structure is considered in a state of failure.

4) has been used. 2. 2 with n = 2, but with a stochastic loading S. 11. Calculate the probability of failure Pf and the formal reliability index ~S for the system. 11 not always result in failure of the total system. The reason for this is that the remaining structural elements may by redistribution of the load effects be able to sustain the external loading. For statically indeterminate structures total failure will usually require that failure takes place in more than one structural element. It is of course necessary to define what is understood by total failure of a structural system.

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Application of Structural Systems Reliability Theory by Palle Thoft-Christensen

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