# Elastic Behaviour Of Materials

What happens to a slingshot when you stretch it? It deforms but regains its original shape when you stop applying a force. But let us say that you take a thin steel rod and try to bend it. You manage to bend it a little and then stop applying force. Does the rod regain its original shape? No, it doesn’t. This difference in the behaviour of the material is based on their elastic and plastic nature which is explained using Hooke’s law.

The rubber strip of the slingshot has high elasticity. Elasticity is the ability of a body to resist any permanent change to it when stress is applied. When stress application ceases, the body regains its original shape and size. Different materials show different elastic behaviour. The study of the elastic behaviour of a material is of much importance. Almost every engineering design requires knowledge of the elastic behaviour of materials. In the construction of various structures like bridges, columns, pillars, beams, etc. knowledge of the strength of the materials used in the construction is of prime importance.

For example: while constructing a bridge, the load of traffic that it can withstand should be adequately measured beforehand. Or while constructing a crane used to lift loads, it is kept in mind that the extension of the rope does not exceed the elastic limit of the rope. To overcome the problem of bending under force the elastic behaviour of the material used must be considered primarily.

To study the elastic behaviour of materials let us consider a beam of length l, breadth b and depth d supported at the ends and loaded at the centre by load W.

In this case, it is given as;

$$\begin{array}{l}\delta = \frac{Wl^{3}}{4bd^{3}Y}\end{array}$$

Where,
δ is the sag
Y is Young’s modulus of elasticity

Using the above equation we can easily say that to reduce the amount of bending for a certain load, Young’s modulus of elasticity of the material used must be large. Also, depth d must be considered since sag is inversely proportional to the cube of depth. But the problem faced with increasing the depth is that bending increases and this is known as buckling. Therefore, a compromise is made between the different cross-sectional shapes.

## Frequently Asked Questions – FAQs

Q1

### What is elasticity?

Elasticity is the capacity of a deformed body to return to its original size and shape when the forces creating the deformation are withdrawn.
Q2

### What is stress?

If a force F is exerted uniformly over a body of surface area A, then the stress can be defined as the force applied per unit area.
Q3

### What are the three main types of stress?

Longitudinal stress, volume stress or bulk stress, and tangential stress (or) shear stress are the three main types of stress.
Q4

### What is a strain?

A body under the influence of stress normally gets deformed if there is enough force to counter the structural strength of the body. The fractional variation in the size of a body generated by the outside stress acting on is known as strain.
Q5

### What are the main three types of strain?

Longitudinal strain, volume strain, and shearing strain or tangential strain are the main three types of strain.
Q6

### Does Hooke’s Law apply to all materials?

Hooke’s spring law applies to any elastic object of arbitrary complexity, as long as a single number can express the deformation and the stress.
Q7

### How are we able to break the wire due to repeated bending?

When the substance is subjected to repeated strain, the elastic properties of the material get greatly impaired. This property is called elastic fatigue. Thus, we are able to break the wire by repeated bending.
Q8

### When does Hooke’s Law fail?

Hooke’s law applies to a perfectly elastic material and does not apply beyond the elastic limit of any material.
Q9

### What is the difference between an elastic body and a plastic body?

• An elastic body is one that regains its original shape and size when deforming forces are removed.
• A plastic body is one that succumbs to deforming forces (however small) and cannot return to its original shape and size.
Q10

### Why are the bridges declared unsafe after long use?

Due to repeated stress and strain, the materials used in the bridge lose elastic strength and ultimately may collapse. Hence, bridges are declared unsafe after long use.
Test Your Knowledge On Elastic Behaviour Of Materials!