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Engineering background

The Sydney Harbour Bridge was not originally designed to be an arch bridge. Bradfield initially had a cantilever bridge in mind to span the harbour. However on a trip to New York he was inspired by the Hell’s Gate Bridge and he realised the cantilever bridge was inferior to an arch bridge for his proposed bridge.

The Cantilever bridge functions quite differently to an arch bridge. Being a beam bridge, a cantilever relies on the supports to carry only vertical reactions to vertical loads. The bridge transmits these loads to the supports and the supports react with vertical reactions. This is different to an arch where vertical loads will create horizontal reactions, because an arch bridge will try to flatten the arch and push out horizontally against the abutments. This means that an arch must have significantly stronger abutments than a beam bridge.

For Bradfield the arch was the better system, it was a more efficient structure which meant it would carry the same load as the cantilever but require less steel.

SHB is not the longest span steel arch bridge, but it is the widest and heaviest.

At the time the bridge was designed and built, riveting was the normal method of joining steel members as electric arc welding of steel was still a developing technology and its use on load-bearing structures was rare. Consequently, the components of the Bridge were joined by riveting and because of the Bridge's size, riveting was on a much greater scale than any previous structure. The use of rivets is now an oddity.

The Impact

All engineering projects have some impact on the environment and the people living around the project. For Sydney as a whole, the bridge opened up the northern side of the harbour and allowed the city to expand north. However to achieve this, parts of the Rocks had to be demolished as did the Dawes Pt battery, which was designed by Francis Greenway.

The Sydney Harbour Bridge would have improved safety, because, prior to its opening, there were 75 ferries per hour between the north and south sides of the harbour. The bridge would have replaced much of this traffic and heightened safety for commuters.

In terms of morale the Bridge’s value is immeasurable. Built during the Great Depression, it was the lifeblood of the floundering NSW economy. It was not the first large engineering venture in Australia, but it certainly was one of the most recognised and it showed Sydney, like other great cities around the world, could build a large bridge that symbolically was so much more than a road/rail link north.

It has, ever since its opening, become an icon for Sydney and Australia, and due to its dramatic placement, it has become the centre piece for many celebrations around the harbour.

It is arguably one of the most dramatically placed bridges in the world.

Graphical Solution

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

Solution (graphical)

From the free body diagram given above, the total mass for the bridge is given as 80064 tonne. First we need to convert this to a force. 1 tonne = 1000 kg, and g = 9.8 m/sec².

80064 × 1000 × 9.8 = 784.6 MN.

Next we need to draw the force polygon.

On a piece of paper draw a vertical line to a suitable scale for this force (say 100 mm = 1000 MN). The line will be 78.4 mm long. Place an arrow on the lower end of the line to indicate the force direction. The line now represents the direction and magnitude of the total weight of the bridge.

From the free body diagram it can be seen that each reaction (RA and RB) acts upward at 45° but we do not know the magnitude of these reactions. Therefore we need to add the reactions to our force polygon.

From the arrowhead, draw a line at 45° up and to the right to represent the reaction on the southern shore (assume we are looking at the bridge from the east).

Draw a line from the other end of the vertical line at 45°, down and to the right to intersect the first line. This line represents the reaction on the northern shore. Add arrowheads to the end of each new line to represent the direction of each reaction.

Label each reaction. The lower line would be R_A and the upper line R_B.

To find the magnitude of the reactions we need to scale their length from the force polygon. My lines each measure 55.5 mm, and from our scale the reaction forces would be;

R_A = R_B = 555 MN.

Now there are two main bearings on the southern shore and two on the northern. Therefore each main bearing supports half of the reaction:

The maximum force at each main bearing will be 277.4 MN. How accurate was your answer? Remember that better accuracy comes from using a larger scale to solve the problem.

Note how simple this solution is when compared with the analytical solution below.

Solution (analytical)

The distance between the bearings is 1650 feet (503 m) and the height from the bearings to the crown is approximately 400 feet (122 m).

Using this information we are able to calculate the reaction at each shore, and from this the reaction at each bearing.

equation

As the thrust (reaction) angle is known to be 45°, the horizontal component of the reaction is equal to the vertical component. That is,

equation

The total reaction loads R_A, R_B on each shore are given by

equation

Since this load is shared equally between the two bearings on each shore, the total load (live and dead) on each bearing is given by:

equation

Dr. Bradfield indicates that '... the thrust of 44 000 000 lb (approximately 20 000 tons [20 320 tonnes]) from each truss is transferred from the lower chord to the concrete skewbacks.'
(Bradfield, 1932, p 3)

Sydney Harbour Bridge

Board of Studies NSW

Engineering Studies

Engineering background

The Impact

Graphical Solution