Name: Practical Applications of Elasticity
Uploaded: 2019-07-19
Duration: 5 min 6 s
Description: How do you think the concept of elasticity of materials is used in different applications? Let’s learn why some materials have a specific shape or size for v...

Question

Define stress and explain the types of stress.

Accepted Answer

When forces are applied on a body such that the body is still in static equilibrium, it is deformed to a small or large extent depending upon the nature of the material and the magnitude of the deforming force. When a body is subjected to a deforming force, a restoring force is developed in the body. This restoring force is equal in magnitude but opposite in direction to the applied force. The restoring force per unit area is known as stress. The SI unit of stress is $N m^{- 2}$ or pascal $(Pa)$ and its dimensional formula is $[{ML}^{- 1} T^{- 2}]$ .

We can classify the stress into three based on the nature of force causing the dimensional change. They are:

$(1)$ Longitudinal stress:- Consider the following figure.

In the figure, a cylinder is stretched by two equal forces applied normal to its cross-sectional area. The restoring force per unit area in this case is called tensile stress. If the cylinder is compressed under the action of applied forces, the restoring force per unit area is known as compressive stress. Tensile or compressive stress can also be termed as longitudinal stress.

$(2)$ Tangential stress or shear stress:-

Consider the following figure.

If two equal and opposite deforming forces are applied parallel to the cross-sectional area of a cube, as shown in figure, there is relative displacement between the opposite faces of the cylinder. The restoring force per unit area developed due to the applied tangential force is known as tangential or shearing stress.

$(3)$ Hydraulic stress:

Consider a body with a random shape placed in a fluid as shown in the figure. We know that the body will be under pressure and as a result, it is compressed uniformly on all sides. Also, we know that the force applied by the fluid acts in perpendicular direction at each point of the surface and the body is said to be under hydraulic compression. This leads to decrease in its volume without any change of its geometrical shape as shown in the figure. As a result, The body develops internal restoring forces that are equal and opposite to the forces applied by the fluid. The internal restoring force per unit area in this case is known as hydraulic stress and in magnitude is equal to the hydraulic pressure.

Define stress and explain the types of stress.

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