Question

An aluminum alloy rod with 10 mm diameter was subjected to a 5-kN tensile load. After the load was applied, the diameter...


An aluminum alloy rod with 10 mm diameter was subjected to a 5-kN tensile load. After the load was applied, the diameter was measured and found to be 9.997 mm.If the yield strength is 139 MPa, calculate the Poisson’s ratio of the material.

Answer

Given:

Original diameter of rod, d = 10 mm

Tensile load, P = 5 kN

Reduced diameter of rod, d’ = 9.997 mm

Yield strength = 139 MPa

The formula for lateral strain is given by,

Civil Engineering homework question answer, step 2, image 1

Where,

∆d = change in diameter

d = original diameter

 

The formula for Poisson’s ratio is given by,

Civil Engineering homework question answer, step 2, image 2

 

The formula for Young’s modulus is given by,

Civil Engineering homework question answer, step 2, image 3

 

The formula for stress is given by,

Civil Engineering homework question answer, step 2, image 4

Where,

P = Load

A = Cross-sectional area

 

Also,

Yield strength = 0.2% of Young’s modulus (E)

The lateral strain is calculated as,

Civil Engineering homework question answer, step 3, image 1

The stress is calculated as,

Civil Engineering homework question answer, step 3, image 2

The Young’s modulus will be calculated as,

Civil Engineering homework question answer, step 3, image 3

The longitudinal strain is calculated as,

Civil Engineering homework question answer, step 3, image 4

So, the Poisson’s ratio is calculated as,

Civil Engineering homework question answer, step 3, image 5

Answer:

Poisson’s ratio of the material, µ = 0.3275

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