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6.5 Hooke's Law

The statement regarding strain & stress being proportional to each other in the elastic region is known as Hooke's law. "Within Elastic limit stress and strain are directly proportional to each other".

i.e., Stress a Strain within elastic limit.

The constant ratio of stress to strain within elastic limit is called elastic modules.

Note : Unit of Elastic modules is same as that of stress (as strain has no limit) viz. n/m2.

The behavior of an elastic object, with increasing stress is represented in the Stress - Strain Curve shown below.

OP = Linear Elastic region

PQ = Rising Fatigue region

QR = Total Yield, with breaking into pieces

P = Elastic limit

Q = Yield Point

Linear Elastic region

In this region if stress is increased from O to A & is decreased back from A to O then, the strain increases in direct proportion from, O to C and decreases from C to O in the same proportion. In this region the object retain its elasticity, strain is the directly proportional to strain. The limit point 'P' of this region is called elastic limit.

Rising Fatigue region

In this strain region increases with the same amount as, the increase in stress; eventually the substance looses its elasticity partially, and therefore becomes partially plastic. This deformation remains permanent, even if the stress is reduced back from B to A and then from A to O. The end point of this region 'Q' is called the Yield Point.

The total yield region

The region QR, represents infinitely large increase in strain produced when stress is increased even by small amount; the substance has completely lost its elasticity & has become completely plastic; hence it yields completely to deforming forces. The substance in this region can be broken into pieces.

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6.1 Definition of Elasticity
6.2 Types Of Deformations
6.3 Deforming and Restoring Forces
6.4 Strain and Stress
6.5 Hooke's Law
6.6 Elastic Modules
6.7 Strain Energy

Chapter 7

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