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Bridge supports

Bridge loads and reactions

Bridge loads and reactions

The Sydney Harbour Bridge is a two-pin arch construction, made up of two arches side by side, joined by horizontal cross-members. In this sort of arch, the vertical loads (the Bridge’s own weight plus the weight of trains, cars etc) tend to flatten the arch and push out against the abutments, creating both vertical and horizontal reaction forces. A beam bridge, by comparison, exerts only vertical forces at its supports. Why is the Bridge an arch?

The Bridge structure is supported on four horizontal, cylindrical forged steel pins in the main bearings, one at each end of the two arches. This allows the movement in the arch caused by temperature variations and dynamic loading to be accounted for. The arch may rise up to 180 mm due to heating during the day and cooling at night.

In his paper, the Director of Construction, Lawrence Ennis, notes that ‘… the total thrust to be sustained by the four bearings under live load conditions is no less than 78 800 tons [80 064 tonnes].’
(Ennis, 1932, p 39)

He also notes that ‘… the thrust of the main arch below the main bearings [is] at an angle of 45˚.’
(ibid, p 38)

Problem 1

The problem of the arch bridge is shown below again. Determine the position of the total weight force of the bridge using graphical means and then graphically determine the value of the reaction if the angle of the reaction is found to be 45°.

What is the load of the Bridge on each of the four main bearing pins, for the total load of 80064 tonnes, as shown in the diagram?

diagram

Click to show a graphical and an analytical solution (toggle between show or hide solution)

JJC Bradfield standing on one of the bearing pins
JJC Bradfield standing on one of the bearing pins. Harold Cazneaux, 21 February 1931. Courtesy the Cazneaux family and the National Library of Australia

Problem 2

Each bearing pin is 14·5 inches (368 mm) in diameter and 13 ft 8 in (~4·27 m) long. (a) What maximum compressive stress is set up in the pin if the applied force on each bearing is 277·4 MN as calculated in Problem 1? (b) How does this stress compare to the yield stress of the structural nickel steel of 345 MPa?

Note: The actual load is distributed over the surface of the cylindrical pin and so the actual stress is likely to be less than that calculated here.

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Problem 3

Each of the main bearing castings is mounted on a concrete ‘skewback’ on which the main bearing casting is fixed. Use the following information to calculate the maximum load that each skewback can support. Is the design adequate?

  • The area of each bearing casting is 46·8 m².
  • The upper surface of the skewbacks makes an angle of 45° to the horizontal.
  • The maximum allowable compressive stress in the skewback is 50% of the concrete’s maximum compressive strength.
  • The maximum compressive strength of the concrete is 41 MPa.

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Sydney Harbour Bridge triangulation
Diagram of a creeper crane from Sydney Harbour Bridge: Report on Tenders. Alfred James Kent, Government Printer, 1924.
State Records NSW.

Problem 4

The Director of Construction, Lawrence Ennis, noted that ‘… the heaviest lift made during the erection of the half arches was 110 tons [1096 kN], occurring in the bottom chord of the sixth panel …’ and that ‘… the lifting capacity of the creeper crane was 122 tons [1215 kN] with its main hoist.’

The diagram of the creeper crane (right) shows that the main jib had a block and tackle with three pulleys top and bottom, to increase the mechanical advantage over the load.

If the maximum capacity of the crane (ie the safe working load, SWL) was 1215 kN, what was the load in the crane lifting cable?

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Problem 5

The load in the hoisting cable is 203 kN as above, and cable diameter is 35 mm (assume a solid cable). Determine the stress in the cable.

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