Question

Explain Poisson's ratio. Discuss its limiting values.

Answer 1

Poisson's ratio is the ratio of transversal strain. to the corresponding longitudinal strain.

e.g., Poisson's ratio = transversal strain/longitudinal strain

actually, Poisson's ratio is the material constant which is need to quantity elasticity in mathematical terms.

The range of poisson's Ratio is empirically found to be in range of 0–0.5.

for example : Poisson's ratio of gold is 0.42 which lies in interval [0, 0.5]

Answer 2

Poisson's ratio:-

When a deforming force is applied at the free end of a suspended wire of length l and diameter D, then its length increases by ∆l but its diameter decreases by ∆D.

Now two types of strains are produced by a single force:-

(i) Longitudinal strain = ∆l / l

(ii) Lateral strain = −∆ D/ D

∴ Poisson’s Ratio (σ)

= Longitudinal strain / Lateral strain

= (−∆ D / D) / (∆ l / l )

= −l ∆ D / D ∆ l

→The negative sign shows that longitudinal and lateral strains are in opposite sense.

→As Poisson’s ratio is the ratio of two strains, it has no units and dimensions.

→The theoretical value of Poisson’s ratio lies between – 1 and 0.5. Its practical value lies between 0 and 0.5.

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