|Real Life Parabolas|
Real Life Parabolas
- Parabolas are very well-known and are seen frequently in the field of mathematics. Their applications are varied and are apparent in our every day lives. For example, the main image on the right is of the Golden Gate Bridge in San Francisco, California. It has main suspension cables in the shape of a parabola.
For a detailed overview of parabolas, see the page, Parabola. However, we will provide a brief summary and description of parabolas below before explaining its applications to suspension bridges.
You may informally know parabolas as curves in the shape of a "u" which can be oriented to open upwards, downwards, sideways, or diagonally. But to be a little more mathematical, a parabola is a conic section formed by the intersection of a cone and a plane. Below is an image illustrating this.
When you were first introduced to parabolas, you learned that the quadratic equation, is its algebraic representation (where and are the coordinates of the vertex and and are the coordinates of an arbitrary point on the parabola.
Suspension Bridges are the most commonly built bridges. Known for their long spans, these bridges feature a deck with vertical supports, from which long wire cables hang above. These cables are made up of hangers that run vertically downwards to hold the cable up. The suspension cables hang over the towers until they are anchored on land by the ends of the bridges. Notably, the way these cables are hung resemble the shape of a parabola.
Usefulness of Suspension Bridges
Because of their elegant structure, suspension bridges are used to transport loads over long distances, whether it be between two distant cities or between two ends of a river. Suspension bridges are able to work efficiently because of their cables, which are interesting from a mathematical perspective.
Since the bridge’s deck spans a long distance, it must be very heavy in weight by its own, not to mention all the weight of the heavy load of traffic that it must carry. Because of all this weight, this results in two active forces: compression and tension. The cable’s parabolic shape results in order for it to effectively address these forces acting upon the bridge. For instance, the deck sags from all the weight of the traffic because of compression forces, which travels upwards the cables. The cables then transfer those compression forces downwards the vertical towers, down into the foundations buried deep within the earth. However, the cables receive the brunt of the tension forces, as they are being stretched from supporting the bridge’s weight and its load of traffic.
Overall, the suspension bridge does its job with minimal material (as most of the work is accomplished by the suspension cables), which means that it is economical from a construction cost perspective.
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