### 3. Strain

- When a body is under a system of forces or couples in equilibrium then a change is produced in the dimensions of the body.

- This fractional change or deformation produced in the body is called strain.

- Strain is a dimensionless quantity.

- Strain is of three types

**(a) Longitudinal strain:-** It is defined as the ratio of the change in length to the original length. If l is the original length and Δl is the change in length then,

**(b) Volume strain:-**It is defined as the ratio of change in volume to the original volume

**(c) Shearing strain:-** If the deforming forces produce change in shape of the body then the strain is called shear strain. Considering Figure 2. it can also be defined as the ratio of displacement x of corner b to the transverse dimension l. Thus

or,

*Shear strain = tanθ*

In practice since x is much smaller than l so, tanθ ≅ θ and the strain is simply the angle θ(measured in radians). Thus, shear strain is pure number without units as it is ratio of two lengths.

*What is elastic limit>*
*Elastic limit is the upper limit of deforming force up to which , if deforming force is removed, the body regains its original form completely
beyond which if deforming force is increased, the body looses its property of elasticity and gets permanently deformed.
*

### 4. Hook's Law

- Hook's law is the fundamental law of elasticity and is stated as " for small deformations stress is proportional to strain".

Thus,

*stress ∝ strain*

or,

$\frac{stress}{strain}=constant$

This constant is known as modulus of elasticity of a given material, which depends upon the nature of the material of the body and the manner
in which body is deformed.

- Hook's law is not valid for plastic materials.

- Units and dimension of the modulus of elasticity are same as those of stress.

This mobile-friendly simulation allows students to stretch and compress springs to explore relationships among force, spring constant,
displacement, and potential energy in a spring.
You can use it to promote understanding of the predictable mathematical relationships that underlie Hooke's Law. Playing around with this simulation
you can get an understanding of

**restoring forces**.

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