A cylindrical specimen of a metal alloy is stressed elastically in tension. The original diameter was 8 mm and a force of 15,700 N produces a reduction in diameter of 5x10-3 mm (magnitude). Compute Poisson's ratio for this alloy if its modulus of elasticity is 140 GPa.

The value of poisson's ratio of the material = 0.28

Explanation:

Given data

Force F = 15700 N

Diameter D = 8 mm

Change in diameter ΔD = 0.005 mm

Modulus of elasticity E = 140 × M Pa.

Stress induced in the shaft due to applied force

Area  A =

⇒ A = = 50.24

Now stress

⇒ Stress = 312.5 M pa ------  (1)

Now strain in the element is given by

∈

⇒ ∈ =

⇒ Strain ∈ = 2.232 ×

We know that poisson's ratio is given by

⇒

Change in diameter ΔD = 0.005 mm

Diameter D = 8 mm

Strain ∈ = 2.232 ×

⇒

⇒ 0.28

This is the value of poisson's ratio of the material.

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