Factor of safety
In engineering, a ‘factor of safety’ is applied in the design of objects or structures in various ways. It is essentially a comparison between the strength of the material or structure and the stress we wish to apply to it — ensuring that the design is ‘safe’ for that material or that object or structure.
For ductile steel as used in the Sydney Harbour Bridge, the factor of safety is the ratio of the stress at the yield point to the applied or working stress:
F of S = yield point/working stress.
The following table provides a list of mechanical properties for a range of steels available at the time of building the Sydney Harbour Bridge: ultimate tensile strength (UTS), the yield point, and percentage elongation as determined from tensile testing suitable samples. Also see the Engineering Materials section for more about steel.
It also gives an indication of the maximum allowable stress (working stress) for these steels when used in certain Bridge applications.
| Material | UTS | Yield Point | Elongation Min. | Working stress direct tension | Working stress direct compression | Working stress direct shear | Rivets in shear. Shear stress |
|---|---|---|---|---|---|---|---|
| MPa | MPa | % | MPa | MPa | MPa | MPa | |
| STRUCTURAL MILD STEEL | 386-455 | 193-248 | 20 | 110-124 | 94-105 | 69-76 | – |
| STRUCTURAL RIVET STEEL | 345-413 | – | 25 | – | – | – | 83 |
| ADMIRALTY STEEL | 510-593 | 234 | 17 | 145 | 124 | 89 | – |
| STRUCTURAL NICKEL STEEL | 524-607 | 303-345 | 20 | 165 | 141 | 103 | – |
| NICKEL RIVET STEEL | 427-483 | 276 min. | 25 | – | – | – | 110 |
| SILICON STEEL | 483-579 | 276-303 | 17-20 | 145 | 124 | 89 | – |
| CHROMADOR STEEL | 510-579 | 303-358 | 17 | 158-172 | 135-146 | 96-103 | – |
| CHROMADOR RIVET STEEL | 413-496 | – | – | – | – | – | 103-110 |
Table adapted from EH Salmon, 1938, Materials and Structures, Volume 2.
The steel chosen by Dorman, Long & Co. Ltd. for the main beams of the arch was silicon steel with a composition of 0.38% C, 0.2% Si and 0.9% Mn, and for the deck hangers it was chromador steel with a composition of 0.22% C, 0.9% Cr, 0.8% Mn and 0.3% Cu.
Using the data from the table we can get an idea of the factor of safety that was being applied to steel used in these applications.
For the silicon steel beams in compression:
F of S = from 276/124 to 303/124
= from 2·2 to 2·4.
For the chromador steel in tension:
F of S = from 303/158 to 358/172
= from 1·9 to 2·0.
For the rivets in shear, using the figures for nickel rivet steel, we get:
F of S = 276/110
= 2·5.
Problem 1
Dr Bradfield is trying to plan the size of the chromador steel hangers used in the Bridge. If the yield strength of the steel is 325 MPa, the length of the longest hanger is 192 ft (58·5 m) and constructed as a box section of dimensions 3 ft - 0½ in (927 mm) x 2 ft (609·6 mm), calculate the maximum load one hanger can support if the steel is 12·5 mm thick. The factor of safety is to be 2·5.
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Problem 2
What maximum load can the 42 hangers support?
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