Introduction to structural integrity
Introduction to structural integrity

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Introduction to structural integrity

3.5 Design of the bridge

The design of the original structure was governed by applicable standards in 1926. The official inquiry found that the design and build fell within those limits, the most important being the allowable stress in the eye-bar chain of 345 MPa. The steel was to be made with a maximum elastic limit of 520 MPa, with a safety factor on the strength of the steel of 2.75. It was argued at the time that over 70 per cent of the load was from the self-weight of the structure. Other suspension bridges of the same time were built with higher safety factors, however. A similar design of eye-bar chain in a larger bridge at Florianopolis in Brazil was given a safety factor of 4.61 using an allowable stress of 320 MPa. The bridge used four eye bars rather than two, so had greater redundancy. Safety factors (see Box 7) of 4.6 to 4.7 based on yield stress were usual in wire suspension bridges (such as the Golden Gate bridge in San Francisco).

Box 7: Safety factors

The safety factor chosen for any structure is simply an expression of the state of knowledge (or lack thereof) at the time, and should allow for any future uncertainties as well as present uncertainties, such as quality of the parts used in the structure. So the safety factor might be termed an uncertainty factor. When knowledge of strength and quality is poor, then the safety factor is high. Thus at the time of building railway bridges in Britain in the 1850s, cast iron was widely used as a principal structural material. Steel was not available until much later. It was known that cast iron was brittle in tension, and following early tragedies, it was specified that a safety factor of 6 should be used for railway bridge design. This safety factor allowed for stress concentrations such as blow holes and sharp corners in beams, although it could be exceeded if such defects were close to one another, when the effect of one is multiplied by the effect of the other. Thus a spherical blow hole (Kt ≈ 2) next to a circular hole (Kt ≈ 3) gives a net effect of Kt ≈ 6.

The safety factor is most critical and important for the most highly loaded parts of a structure, simply because they will be closest to failure if, for whatever reason, the maximum permissible load is somehow exceeded. Nowadays, structures are designed for maximum loading from a variety of sources that are often difficult to predict with high confidence. Those factors include:

  • wind loading

  • earthquake loading

  • precipitation such as snow and rain.

Some are created by the weather, a notoriously difficult area to predict, and others by movements in the earth's crust (also difficult to predict). However, hurricanes and earthquakes do tend to occur in well-defined areas of the world, and so structures built in those zones will have a higher safety factor than elsewhere to allow for the extra risk there. All these natural phenomena will produce extra loads on a structure, and frequently cause catastrophic failure. Thus a double-deck highway collapsed on itself during the San Francisco earthquake of 1989 (killing 23 drivers on the lower deck at the time). Several stadiums in Europe collapsed with heavy casualties during the winter of 2005/6 owing to high snow loading.

However, little was apparently known then about the problem of stress corrosion cracking, although the type of strengthened steel used in the eye bars had been tested before use for its fatigue properties. It was known that the material would be subject to rusting, but it was thought that painting would prevent the problem becoming serious. Unfortunately the design of the pin joints left them completely exposed to the weather, and water could gather at the lowest points within the joint. Such hidden parts of the joint could not be painted owing to their inaccessibility, so were left unprotected. Moreover, the eye-bar joint could not be inspected without disassembly, an impractical solution for a suspension bridge.

SAQ 7

  • (a) Describe the known problems of stress corrosion cracking that had occurred historically at the time of the design of the Silver Bridge, and their known solutions.

  • (b) What other problems, apart from stress corrosion, could have been foreseen at the critical eye-bar joints? Suggest measures that could have been taken to prevent the problem.

Answer

  • (a) Stress corrosion cracking was known to occur in high-pressure boilers: many examples had occurred on the railways from the 1840s onwards, especially in Britain, but also elsewhere as the railway networks expanded worldwide. The first study of the problem showed that boiler walls tended to crack at grooves or corners in the shell, often from the overlapping longitudinal joint in the boiler. The inner corner represented not only a serious stress concentrator but also a zone where liquid water collected, encouraging rusting. With daily pressurisation, crack growth was encouraged by fatigue. The problem of groove cracking was removed only by changing the design of boilers to use a riveted butt joint, thus eliminating the corner at the heart of the problem.

    The problem of SCC was also encountered in India in the 1920s, in the premature detonation of rifle shells. It was caused by attack on the copper content of the brass shell case by traces of ammonia in the air. The gas, which is produced during rotting of animal wastes, attacked cases that had been deformed during manufacture, leaving high levels of residual stress in the upper edges of the cases, where cracks were initiated. The problem was eliminated by annealing the shell cases to lower the residual stress, and storing the shells well away from sources of ammonia.

  • (b) The other problem in the joints was fretting corrosion caused by small rotary movements between the pin and the eye-bar inner surface. At high imposed stress at the bearing surface, Hertzian loading creates a local compressive zone surrounded by a tensile zone. Rusting produces hard particles of hydrated iron oxide of greater volume than the original iron. The particles abrade the bearing surfaces, creating surface pits and grooves that can act as nuclei for fatigue cracks. With the joints being totally exposed to the environment, rusting in the joint (followed by fretting wear) was foreseeable. The protective action of the silver paint was completely ineffective because the inner parts of the joint could not be reached by the paint. A protective bearing surface should have been incorporated onto the pin and eye-bar inner surfaces.

Cable suspension bridges are also corrosion-sensitive, the most recent example being the corrosion at the base of the main hangers of the first Severn suspension bridge. Although the high-tensile steel wires had been galvanised, salt water collected in the joints at the road decks and penetrated to the interior of the joints, causing breakage of the seal. The zinc coating corrodes preferentially, but once this is consumed then rusting of the core will occur. All had to be replaced at high cost during the 1990s.

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