Mechanical Properties of Solids

Topic-by-topic explanations

1. Introduction

Solids resist changes of shape and size. Elastic deformation recovers after unloading within the elastic limit; plastic deformation leaves a permanent change.

2. Stress and strain

Stress is internal restoring force per unit area. Tensile/compressive stress is normal to a cross-section; shear stress is tangential. SI unit: pascal.

3. Hooke's law

Hooke's law states stress is proportional to strain only within the proportional limit. The slope of the linear stress-strain graph is the relevant elastic modulus.

4. Stress-strain curve

A stress-strain curve for a ductile material can show proportional and elastic limits, yielding, ultimate stress and fracture. Brittle material fractures with little plastic deformation.

5. Elastic moduli

Young's modulus Y=longitudinal stress/longitudinal strain; bulk modulus B=−Δp/(ΔV/V); shear modulus is shear stress/shear strain. A larger modulus means greater stiffness.

6. Applications of elastic behaviour of materials

Elastic behaviour is important in bridges, beams, springs and building frames. Design must keep stress and deflection within safe limits and use suitable safety factors.

Formula sheet

Use consistent SI units, identify the system and assumptions, and show the steps of each calculation. Check units and whether the result is physically reasonable.

Worked example

Common errors and revision checklist

Stress is in pascals but strain is dimensionless. Use original length and cross-sectional area; Hooke's law is not valid beyond its linear range.

• Write the relevant law or relation before substituting values.
• Show units, signs and directions.
• Check assumptions and round only the final result.