Stress and Strain Questions

Some objects undergo deformation upon the application of force, while some objects do not undergo a change in shape. The deformation depends upon the stress and strain applied to the object. The stress-strain curve differs for each material. It is caused by the relationship between stress and strain. Using the stress and strain curve one can determine the properties of a material, like the ultimate tensile strength, Young’s modulus, and the yield strength.

According to the definition of stress, it is described as the force per unit area, and it is given by the formula:

where,

A – the area of force application

σ – the stress applied

F – the force applied

Dyne-cm² is the CGS unit of stress. N/m² is the unit of stress. ML^-1T^-2 is the dimensional formula for stress.

There are two types of stress, they are:

• Normal stress
• Tangential Stress

According to normal stress, it is the restoring force per unit area that acts perpendicular to the surface of the body. Normal stress is classified into:

• Tensile stress
• Compressive stress

Tensile stress is defined as the stress that stretches or lengthens the material, and acts normally on the stressed area. Objects under tensile stress become longer and thinner.

Compressive stress is defined as the force applied per unit area that decreases the length (or area) of a body. The object under compressive stress becomes shorter and thicker.

Tangential stress is seen when the elastic deforming or restoring force is applied parallel to the surface area.

Read more: Yield strength

Strain is defined as the ratio of the quantity of deformation the body experiences in the direction of applied force to the initial size of the body. The strain is a dimensionless quantity that defines the change in the shape of the body.

Deformation, in terms of the length of a solid, is given by the formula:

where,

ε – strain due to stress applied

ρl – change in length

L – original length of the material

There are two types of strain, they are:

• Longitudinal strain or tensile strain
• Volumetric strain or compressive strain

The strain produced in the body upon applying deforming force, where the change in length takes place, is known as tensile strain or longitudinal strain.

The strain produced in the body upon applying deforming force, where the change in the area takes place, is known as volumetric strain or compressive strain.

According to Hook’s law, the strain of the material is directly proportional to the stress applied within the elastic limit of the material. It is given by the formula: F = –k.x.

Where,

F – force

x – the extension length

k – the constant of proportionality or spring constant in N/m.

The ability of the body to regain its original shape after removing deforming force is known as elasticity.

The inability of the body to regain its original shape and size after removing deforming force is known as plasticity.

Important Stress and Strain Questions with Answers

1. What is Young’s modulus (E) in GPa for iron?
2. 12
3. 70
4. 100
5. 91

Answer: d) 91

Explanation: Young’s modulus of iron is 91 in gigapascal.

2. What is the formula to calculate the modulus of rigidity?

The modulus of rigidity is given by the formula:

G= Shearing stress / Shearing strain

3. Strain is a _____ quantity.

1. Scalar
2. Vector
3. Dimensionless
4. None of the above options

Answer: c) Dimensionless

Explanation: Since strain is the ratio of two similar quantities like length, area, or volume, it is a dimensionless or unitless quantity.

4. Upon the removal of a deforming force, the inability of the body to regain its original shape and size is known as _____.

1. Plasticity
2. Undeformation
3. Elasticity
4. Hook’s constant

Answer: a) Plasticity

Explanation: A non-reversible change of shape in response to applied forces is known as plasticity.

5. When the yield point of an object is crossed, _____ occurs.

1. Compressibility
2. Plastic deformation
3. Elastic deformation
4. None of the above options

Answer: b) Plastic deformation

Explanation: Plastic deformation takes place when the object crosses the yield point.

6. What are the two types of yield points?

Two types of yield points are the upper yield point and the lower yield point.

7. Dimensional formula of stress is _____

1. MLT^-2
2. ML^-1T^-2
3. M^-1LT^-2
4. ML^-1T

Answer: b) ML^-1T^-2

Explanation: Dimensional formula of stress is ML^-1T^-2.

8. Choose the correct answer: In the volumetric strain, the deforming force produces a change in _____.

1. Length
2. Volume

Answer: b) Volume

9. _____ is the region in the stress-strain curve that obeys Hooke’s law.

1. Yield Point
2. Elastic Limit
3. Proportional Limit
4. Breaking Point

Answer: c) Proportional Limit

Explanation: In the proportional limit, the stress-strain ratio gives us a proportionality constant known as Young’s modulus.

10. 1 GPa = ______

1. 100 Pa
2. 100,00 Pa
3. 1,00,00,000 Pa
4. 1,00,00,00,000 Pa

Answer: d) 1,00,00,00,000 Pa

Explanation: 1 gigapascal = 1,00,00,00,000 Pa

Practice Questions

1. What is meant by stress?
2. Define the stress-strain curve.
3. What is the formula to calculate the strain?
4. Define elasticity.
5. What is meant by tensile stress?

Watch the video below to learn in detail about Hooke’s law.