Stress And Strain - Practice Questions & MCQ

• When a force is applied on a body, it is deformed to a small or large extent depending upon the nature of the material of the body and the magnitude of the deforming force.

• The internal restoring force acting per unit area of the cross-section of the deformed body is called stress and is denoted by σ.

• - The magnitude of stress, $\sigma=\frac{F}{A}$
  - Unit of stress: $N / m^2$ or Pascal(Pa)
  - Dimension of stress: $\left[M L^{-1} T^{-2}\right]$

• Types of stress:

1. Longitudinal stress/ Normal stress: In Longitudinal stress, the force is applied normally to the surface.

• It is of two types:

1. Tensile stress: Longitudinal stress produced due to an increase in the length of a body under a deforming force is called tensile stress.

2. Compressive stress: Longitudinal stress produced due to a decrease in the length of a body under a deforming force is called compressional stress.

 Fig: Tensile Stress                                                                      Fig: Compressive Stress

2. Shearing stress/ tangential stress: if two equal and opposite deforming forces are applied parallel to the cross-sectional area of the cylinder, there is a 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.

• In this case, deforming force is applied tangentially to one of the faces.

• The area for calculation is the area of the face on which force is applied.

• It produces a change in shape, with volume remaining the same.

Fig:- Shearing stress

3. Volume stress:  

• It produces a change in volume and density, shape remaining the same.

• It occurs in solids, liquids or gases

• In the case of fluids, only bulk stress can be found.

• It is equal to a change in pressure because the change in pressure is responsible for change in volume.

Volume stress $=\frac{F}{A}=P$

• Strain is defined as the ratio of change in configuration to the original configuration.

• It has no dimensions and units as it is the ratio of two similar kind of physical quantities.

• Types of strain:-

1. Longitudinal strain:- If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain.

• If the length increases from its natural length, the longitudinal strain is called tensile strain.

• If the length decreases from its natural length, the longitudinal strain is called compressive strain. 

Longitudinal strain $=\frac{\Delta L}{L}$

   Fig: Tensile strain         

                                                                                                                                        Fig: Compressive strain

2. Shear strain:- If the deforming force produces a change in the shape of the body without changing its volume, strain produced is called shearing strain.

• It is defined as angle in radians through which a plane perpendicular to the fixed surface of the cubical body gets turned under the effect of   tangential force.                 

            Fig:- Shearing strain

Shearing stress $=\frac{\Delta X}{L}$

• Example:- when a book is pressed with the hand and pushed horizontally.

Fig:- A book subjected to a shearing stress       

3. Volume Strain:- If the deforming force produces a change in volume alone the strain produced in the body is called                                  volumetric strain.

Fig:- Volumetric strain

Volume strain $=\frac{\Delta V}{V}$