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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/mm^{2}
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/mm^{2}
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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