Question

Define stress and strain. Write their SI units and dimensions.

Answer 1

Hint: Stress is the force acting on the unit area of a material. The effect of stress on a body is called strain. Stress can result in deformation of the body. Strain is the measurement of how much an object is stretched or deformed due to the stress developed in the object. Strain occurs when external force is applied to an object.

Complete step by step answer:
When the deforming force is applied to an object, the object changes its shape. In order to bring the object back to its original shape and size, there will be an opposing force developed inside the object. This restoring force is equal in magnitude and opposite in direction to the applied deforming force. The measurement of value of this restoring force generated per unit area of the material is known as stress.
Thus, Stress is defined as the restoring force per unit area of the material. Stress is a tensor quantity. It is denoted by the symbol $\sigma$.
Mathematical expression for stress is given as:
$\sigma ={\displaystyle \frac{F}{A}}$
Where,
$\sigma$ is the stress generated inside the object
$F$ is the restoring force measured in Newton
$A$ is the area of cross-section measured in square meter
Units of stress:
Fundamental Unit - $Kg{m}^{-1}{s}^{-2}$
SI unit - $N{m}^2$or Pascal $\left(Pa\right)$
Dimension of stress:
$\begin{array}{rl}& \text{Stress = }{\displaystyle \frac{\text{Force}}{\text{Area}}}={\displaystyle \frac{ML{T}^{-2}}{L^2}}\\ & \text{Stress}=M{L}^{-1}{T}^{-2}\end{array}$
Strain is defined as the response of a system to an applied stress. When a substance or a material is loaded with a force, it produces a stress, which then causes that material to deform. Strain is defined as the amount of deformation of a material in the direction of the applied force divided by the initial length of the material.
Types of Strain in a material:
Longitudinal strain: If the deforming force produces a change in length alone, the strain produced in the body is known as the longitudinal strain or the tensile strain.
It is given as:
$\epsilon ={\displaystyle \frac{\mathrm{\Delta }l}{l}}$
Where,
$\epsilon$ is the longitudinal strain due to stress applied
$\mathrm{\Delta }l$ is the change in length
$l$ is the original length of the material.
Volumetric strain: If the deforming force produces a change in volume alone, the strain produced in the body is known as the volumetric strain.
It is given as:
$${\epsilon }_V={\displaystyle \frac{\mathrm{\Delta }V}{V}}$$
Where,
${\epsilon }_V$ is the volumetric strain due to stress applied
$\mathrm{\Delta }V$ is the change in volume
$V$ is the original volume of the material.
Shear strain: The angle tilt caused in the body due to tangential stress expressed is known as the shear strain.
It is given as:
$$\gamma ={\displaystyle \frac{\mathrm{\Delta }x}{l}}$$
Where,
$\gamma$ is the shear strain due to stress applied
$\mathrm{\Delta }x$ is the change in angle
$l$ is the length of the material.
Unit of strain:
The unit of strain is one, as Strain is the ratio of similar quantities.
Dimension of strain:
The strain is a dimensionless quantity as it only defines the relative change in shape of an object.

Note:
Students should not get confused between the terms Stress and Pressure. Stress is not physically the same as pressure. In pressure, external force per unit area is considered, but in case of stress, it is the internal force per unit area. Strain is the relative change in the shape and size of a body due to the applied force.