Principles of Dairy Machine Design

Module 3. Stress

Lesson10
HOOKE’S LAW

10.1 Introduction

In mechanics Hooke's law of elasticity is an approximation which states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.

10.2 Hook's Law:

It states that, ‘when a material is loaded, within its elastic limit, the stress is proportional to the strain’. Mathematically,

Stress / Strain = E,

which is a constant known as Young’s Modulus or elasticity

It may be noted that Hooke’s law equally holds good for tension as well as compression.

Where G is known as shear modulus of elasticity or modulus of rigidity.

10.3 Stress - Strain Diagram

Fig. 10.1 Stress and strain

When stresses for a specimen are plotted along ordinates and strains along the abscissa, we get stress strain diagram. The shape of the diagram remains the same for tensile as well as compressive stresses.

10.3.1 Ultimate stress

10.3.2 Factor of safety

(for Brittle material)

10.3.3 Factor of safety:

(for Ductile material)

*Working Stress: Stress developed in the material during working.