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Applications of Elastic Behaviour of Materials

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Applications of Elastic Behaviour of Materials - Lesson Summary

Man has made structures such as skyscrapers and over bridges to make life convenient.
For example of a crane used to lift heavy loads. The highest value of stress the crane’s rope can be subjected to must be lower than the breaking stress value of its material. 
In practice, a large margin of safety is provided and thus a thicker rope about, 8 millimetres, is recommended.
A collection of thinner wire strands when compacted together make the rope stronger than a solid rope of the same cross-section. That is why crane ropes are made of several strands instead of one.
Structures such as bridges and tall buildings that have to support static or dynamic loads are generally constructed using pillars and beams to support them.
The beams used in buildings and bridges have to be carefully designed so that they do not bend excessively and break under the stress of the load on them.
As the deflection of the beam is inversely proportional to just the single power of the thickness of the beam compared to the cube of width, the thickness of the beam does not have as great an effect on the maximum load that can be supported as the width.
But on increasing the width, unless the load is placed at the right place, there is every chance that the beam will bend as shown. Such bending is called ‘buckling’. Thus the beam can buckle under asymmetric loading, which is the case in bridges that carry differently distributed traffic at different times.
To avoid this, the cross-section of the beam is chosen to be an I-shape This shape provides a large load-bearing surface and enough depth to prevent bending. It also reduces the weight of the beam without compromising on its strength to bear loads.
The pillars used in buildings and bridges are also modified to be able to support greater loads by making the ends distributed. The elastic properties of rocks can help calculate the maximum height of mountains on the earth.
The stress due to the mountain’s weight can be equated with the yield stress, the stress at the elastic limit. The value of yield stress for rocks is typically in the range of three times ten to the power eight pascal.
Taking an average density of rocks as about 3,000 kg per metre cubed, and solving for h, we get h as approximately 10 kilometres.


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