Strain and Hooke's Law<

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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