📘 Mechanical Properties of Solids
Complete Chapter Notes for Students
1. Elasticity
Elasticity is the property of a material to regain its original shape and size after the removal of external force.
Elastic Body: Returns to original shape (Steel, Rubber)
Plastic Body: Does not return (Clay)
Elastic Limit: Maximum stress up to which body regains shape
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Plastic Body: Does not return (Clay)
Elastic Limit: Maximum stress up to which body regains shape
2. Stress
Stress is the internal restoring force per unit area developed in a body when external force is applied.
σ = F / A
Unit = Pascal (Pa)
Unit = Pascal (Pa)
Types of Stress
- Tensile Stress: Pulling force
- Compressive Stress: Pushing force
- Shear Stress: Force parallel to surface
3. Strain
Strain is the ratio of change in dimension to original dimension.
Strain = Change / Original (No unit)
Types of Strain
- Longitudinal Strain
- Volumetric Strain
- Shear Strain
4. Stress-Strain Curve
The stress-strain curve shows how a material deforms under stress.
- Proportional Limit: Stress ∝ Strain
- Elastic Limit: No permanent deformation
- Yield Point: Plastic deformation begins
- Ultimate Stress: Maximum stress
- Breaking Point: Failure of material
5. Hooke’s Law
Within elastic limit:
Stress ∝ Strain
σ = E × Strain
Stress ∝ Strain
σ = E × Strain
Where E is modulus of elasticity.
---6. Elastic Moduli
(A) Young’s Modulus (Y)
Y = Longitudinal Stress / Longitudinal Strain
Measures stiffness of a material.
(B) Bulk Modulus (K)
K = Pressure / Volumetric Strain
Measures resistance to change in volume.
(C) Shear Modulus (G)
G = Shear Stress / Shear Strain
Measures resistance to shape change.
---7. Poisson’s Ratio
ν = Lateral Strain / Longitudinal Strain
Range: 0 to 0.5
---8. Elastic Energy
Energy stored in a body due to deformation.
U = ½ × Stress × Strain × Volume
For spring: U = ½ F × x
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For spring: U = ½ F × x
9. Applications of Elasticity
- Design of bridges and buildings
- Springs in vehicles
- Rubber tyres and belts
- Shock absorbers
- Spring balance
10. Important Points
- Stress has unit, strain has no unit
- Hooke’s law valid only within elastic limit
- Steel is more elastic than rubber
- Elasticity is not same as flexibility
