Context

There are many different types of bridge designs used throughout the world, such as: arch, beam, truss, cantilever and suspension bridges 

This photo shows an arched bridge going over a roadway consisting of a dual carriageway with two lanes in each direction.

Task

Your task is to design the cross-section for the arch of the bridge that supports an overpass that is approximately 11m high, similar to that in the photographed scenario above, and calculate an estimation for the volume of concrete required to build the solid arch using the information in the stimulus section

Stimulus

• The ends of each arch support are located at different heights, h1 and h2. and distance d apart. The width of the upper roadway, supported by the arch, is T. All measurements are provided in metres. These values will be assigned to you by your teacher.

• The arch needs a minimum clearance that suits Australian road vehicles.

• To retain the structural integrity of the bridge the distance between the lower and upper outlines of the arch need to be between 1 and 2m.

• Two models are required: one for the upper outline and one for the lower outline of the arch. These models must consist of two polynomial functions.

• The area of the cross-section of the arch is to be calculated using the formula: A= w/2 (E+2M), where w is the constant width of each segment, E is the sum of the end segment lengths and M is the sum of the middle segment lengths.

Stage