The chapter Mechanical Properties of Solids deals with how solid materials respond when external forces are applied. It explains concepts like stress, strain, elasticity, and deformation, which are essential in engineering and real-life structures.
👉 Core Idea: Solids can resist deformation, but beyond a limit, they permanently change shape.
1. Elasticity and Plasticity
Elasticity
Definition
Elasticity is the property of a material by which it regains its original shape and size after the removal of external force.
Plasticity
Definition
Plasticity is the property of a material by which it undergoes permanent deformation when force is applied.
Examples
- Rubber → highly elastic
- Clay → plastic
Concept Clarity
👉 WHY materials return to original shape?
Due to restoring forces between molecules.
2. Stress
Definition
Stress is the internal restoring force per unit area developed inside a body when external force is applied.
Formula
Stress = Force / Area
Types of Stress
1. Longitudinal Stress
Force applied along length
2. Shear Stress
Force applied tangentially
3. Bulk Stress
Force applied equally in all directions
3. Strain
Definition
Strain is the measure of deformation produced in a body due to stress.
Formula
Strain = Change in dimension / Original dimension
Types of Strain
- Longitudinal strain
- Shear strain
- Volume strain
Concept Clarity
👉 Strain has no unit because it is a ratio.
4. Hooke’s Law (Very Important)
Statement
Within elastic limit, stress is directly proportional to strain.
Formula
Stress ∝ Strain
or
Stress = k × Strain
Graph
Stress vs strain graph is a straight line in elastic region.
5. Elastic Moduli
Definition
Ratio of stress to strain.
(A) Young’s Modulus (Y)
Formula
Y = (Longitudinal Stress) / (Longitudinal Strain)
(B) Bulk Modulus (K)
Formula
K = Pressure / Volume strain
(C) Shear Modulus (G)
Formula
G = Shear stress / Shear strain
Concept Clarity
👉 Higher modulus → more rigid material
6. Stress-Strain Curve
Important Points
Proportional Limit
Hooke’s law valid
Elastic Limit
Body returns to original shape
Yield Point
Permanent deformation begins
Ultimate Strength
Maximum stress
Breaking Point
Material breaks
Concept Clarity
👉 WHY materials break?
Because intermolecular forces are exceeded.
7. Energy Stored in Stretched Wire
Elastic Potential Energy
Energy stored when a material is stretched.
Formula
U = (1/2) × Stress × Strain × Volume
8. Poisson’s Ratio
Definition
Ratio of lateral strain to longitudinal strain.
Formula
Poisson’s ratio = Lateral strain / Longitudinal strain
Concept Clarity
👉 When stretched, a body becomes thinner.
9. Applications of Elasticity
- Bridge construction
- Buildings
- Springs
- Measuring instruments
Important Numericals
Numerical 1
Find stress if force = 100 N, area = 2 m²
Stress = 100 / 2 = 50 Pa
Numerical 2
Find strain if change in length = 0.01 m, original = 1 m
Strain = 0.01
Numerical 3
Find Young’s modulus if stress = 200 Pa, strain = 0.02
Y = 200 / 0.02 = 10000 Pa
Numerical 4
Find energy stored using formula
Important Formula Sheet
- Stress = F/A
- Strain = ΔL/L
- Y = Stress/Strain
- K = Pressure/Volume strain
- G = Shear stress/strain
Concept Clarity (Important)
👉 WHY solids resist deformation?
Because of strong intermolecular forces.
👉 WHY metals are elastic?
Because they return to original shape after deformation.
👉 WHY glass breaks easily?
Because it has low elasticity and high brittleness.
Common Mistakes
- Confusing stress and pressure
- Ignoring elastic limit
- Wrong formula usage
Conclusion
Mechanical Properties of Solids explains how materials behave under force. Understanding stress, strain, and elasticity is essential for solving real-world engineering problems.
👉 Focus on concept clarity + formulas + practice numericals.