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Mechanics of Solids - Concepts and Definitions
By GATE Tutor - Mechanical Engineering - Examcrazy.com
Q 1. Define stress.

When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude of the resisting force is numerically equal to the applied force. This internal resisting force per unit area is called stress.
Stress = Force/Area

2. Define strain

When a body is subjected to an external force, there is some change of dimension in the body. Numerically the strain is equal to the ratio of change in length to the original length of the body.= P/A unit is N/mm2

Strain = Change in length/Original length
e = δL/L

3. State Hooke’s law.

It states that when a material is loaded, within its elastic limit, the stress is directly proportional to the strain.

Stress ∝ Strain
σ ∝ e
σ = Ee
E = σ/e unit is N/mm2

Where,
E - Young’s modulus
σ - Stress
e - Strain

4. Define shear stress and shear strain.

The two equal and opposite force act tangentially on any cross sectional plane of the body tending to slide one part of the body over the other part. The stress induced is called shear stress and the corresponding strain is known as shear strain.

5. Define Poisson’s ratio.

When a body is stressed, within its elastic limit, the ratio of lateral strain to the longitudinal strain is constant for a given material.

Poisson’ ratio (ì or 1/m) = Lateral strain /Longitudinal strain

6. State the relationship between Young’s Modulus and Modulus of Rigidity.

E = 2K (1+1/m)

Where,
E - Young’s Modulus
K - Bulk Modulus
1/m - Poisson’s ratio

7. Define strain energy

Whenever a body is strained, some amount of energy is absorbed in the body. The energy that is absorbed in the body due to straining effect is known as strain energy.

8. What is resilience?

The total strain energy stored in the body is generally known as resilience.

9. State proof resilience

The maximum strain energy that can be stored in a material within elastic limit is known as proof resilience.

10. Define modulus of resilience

It is the proof resilience of the material per unit volume Modulus of resilience = Proof resilience / Volume of the body

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