Why is that the main suspension cables hang in a shape of a parabola, and not in a catenary, a similar ‘u-shaped’ curve? But we shall explain the differences between parabola and catenary with more emphasis on the parabola. 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. However, the cables receive the brunt of the tension forces, as they are supporting the bridge’s weight and its load of traffic, being stretched by the anchors' ends on-land. The cables then transfer those compression forces downwards the vertical towers, down into the foundations buried deep within the earth. For instance, the deck sags from all the weight of the traffic because of compression forces, which travels upwards the cables. The cable’s parabolic shape results in order for it to effectively address these forces acting upon the bridge. Because of all this weight, this results in two active forces: compression and tension.
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. Suspension bridges are able to work efficiently because of their cables, which are interesting from a mathematical perspective. Notably, the way these cables are hung resemble the shape of a parabola.ĭue to 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. The suspension cables hang over the towers until they are anchored on land by the ends of the bridges. These cables are made up of hangers that run vertically downwards to hold the cable up. Known for their long spans, these bridges feature a deck with vertical supports, from which long wire cables hang above. Suspension Bridges are the most commonly built bridges.
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.
But to be more mathematical, a parabola is a conic section formed by the intersection of a cone and a plane. You may informally know parabolas as curves in the shape of a "u" which can be oriented to open upwards, downwards, sideways, or diagonally. However, we will provide a brief summary and description of parabolas below before explaining its applications to suspension bridges. For a detailed overview of parabolas, see the page, Parabola.