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8 Audit Task 'd'. Establishment of acceptable reliability levels for the structure
The objective of this task is to consider whether the assessed current and projected Factors of Safety are reasonable. The stated Factors of Safety combine the assessed loads in the cable with the assessed strength of the cable and provide an estimate of the overall level of reliability for the structure. The audit has reviewed the derivation of both the assessed load (Audit Task 'a') and the assessed current strength of the main cable (Audit Task 'b') and has reviewed the method for presenting the assessed Factor of Safety of the bridge in its assessed condition. The audit has also considered the projected future reductions in strength based on the deterioration model which was considered under Audit Task 'c'.
American design practice uses the working stress method of design for cables. The design capacity is commonly defined in terms of a "safety factor," being simply ultimate strength divided by the unfactored working load (Fu/T). For comparison purposes, if we apply standard AASHTO load factors to a cable designed for 690 MPa (100 ksi) working stress, the factored stress may exceed the proportional limit but will remain below yield point stress. In general, cable stresses reach their maximum value when the bridge is fully loaded and AASHTO load factors may be considered unrealistic for such a long loaded length. To illustrate the equivalency of the two methods, we can "back out" the load factors that will keep the factored stress below the proportional limit. Two examples would be: 1.3(D +L) or (1.1D +2.17L). Present day European designers use the semi-probabilistic limit state design approach. For example, the cables of the Storebaelt Suspension Bridge were designed such that stresses due to factored loads of D + 1.3L + 0.5W + 0.5T are less than or equal to Fu/2.
A discussion on the derivation of appropriate safety margins for the main cable of the Forth Bridge is included as Appendix C.
In the United States, a safety factor below two is deemed unacceptable and would lead to traffic limitations or closing of a bridge. In the UK, a reliability based approach would show that the factor should be a function of the bridge specific parameters, thus a safety factor of two on a suspension bridge with a high live load to dead load ratio will not necessarily provide the same overall reliability (and thus safety) as a bridge with a lower ratio. Whereas we would support a factor of safety of two as being acceptable, it is recommended that the factor of safety for the main cables is determined for the bridge specific conditions using reliability analysis at the Forth Road Bridge to facilitate longer term planning issues.
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