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Problem on Poisson's ratio, Young's modulus, Bulk modulus, and modulus of rigidity

A bar subjected to a tensile load 55 KN. Bar diameter=31 mm; Gauge length=300mm; extension=.115mm; change in diameter= 0.00367mm. Find: Poisson’s ratio, Young’s modulus, Bulk modulus, and modulus of rigidity.

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Given data:

Tensile load(F)=55KN

Diameter(d)=31mm

Gauge Length (L)=300mm

Extension (ΔL)=0.115mm

ΔdChange in diameter=0.00567 mm

i) Poisson's ratio μ=lateralstrainlongitudinalstrain

μ=0.00367310.115300

μ=0.308

2) Young's modulus=stressstrain

E=55103/π/43120.115/300

E=190.09103N/mm2

3)E=3K(12μ)

190.09103=3K(120.308)

Bulkmodulus(K)=165103N/mm2

4)E=2G(1+μ)

190.09103=2G(1+0.308)

Modulus of rigidity G=72.664103N/mm2

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