Stress, Strain and Hooke's Law
Stress is restoring force per unit area and strain is fractional deformation; within the elastic limit stress is proportional to strain.
What is Stress, Strain and Hooke's Law?
The maximum stress that a material can withstand without undergoing permanent deformation.
Key formula / rule: Stress
Key points
- Distinguish between various types of stress and strain.
- Apply Hooke's Law to determine the Modulus of Elasticity.
- Analyze stress-strain graphs for different materials.
- Calculate work done in stretching a wire.
Common exam trap
Assuming Hooke's law is valid up to the breaking point.
Definitions
- Term
Elastic Limit
- Meaning
The maximum stress that a material can withstand without undergoing permanent deformation.
- Term
Young's Modulus
- Meaning
The ratio of longitudinal stress to longitudinal strain.
Learning objectives
Distinguish between various types of stress and strain.
Apply Hooke's Law to determine the Modulus of Elasticity.
Analyze stress-strain graphs for different materials.
Calculate work done in stretching a wire.
Formulae
- Name
Stress
- Note
F is the restoring force proportional to the external force in equilibrium.
- Expression
σ = F / A
- Name
Longitudinal Strain
- Note
Ratio of change in length to original length.
- Expression
ε = ΔL / L
- Name
Hooke's Law
- Note
E is the Modulus of Elasticity for the material.
- Expression
σ = E × ε
Prerequisites
Basic Mechanics (Force and Equilibrium)
Dimensions and Measurements
Common mistakes
Assuming Hooke's law is valid up to the breaking point.
Using external force instead of internal restoring force for stress calculation in non-equilibrium cases.
Confusing 'Elasticity' with 'Plasticity' (Rubber is less elastic than Steel in physics terms).
Keywords
Elasticity
Restoring Force
Proportional Limit
Modulus
Pascal
Practice preview
Which of the following statements regarding the Stress-Strain relationship is correct within the elastic limit?…
easy
Two wires A and B are of the same material and have the same length. Wire A has twice the diameter of wire B. If they are pulled by the same force, the ratio of elongation of A to B is:…
medium
A wire is suspended from a ceiling and a load W is attached to its lower end. Which of the following describes the potential energy stored per unit volume of the wire?…
hard