Question

A cylinder 10 mm in diameter is pulled with a stress of 150 MPa. The diameter elastically decreased by 0.007 mm. Determine Poisson's ratio if the material has a elastic modulus of 100 GPa.

Answer 1

Answer:Poisson's Ratio,μ = 0.46

Step-by-step explanation:

Poisson's Ratio is calculate as

μ = transverse/ longitudinal strain

μ = - εt / εl

where

μ = Poisson's ratio

εt = transverse strain

εl = longitudinal strain

Transverse strain can be expressed as

εt = change in diameter / initial diameter

where

εt =transverse strain

change in diameter=0.007mm

initial diameter = 10mm

εt =0.007mm/ 10mm= 0.0007

Longitudinal strain can be expressed as

εl=Stress/ elastic modulus = σ/ E

= Stress = 150 MPa , converting to GPa becomes 150/1000 = 0.15 GPa

εl= 0.15 GPa / 100 GPa= 0.0015

Poisson's Ratio,μ = transverse/ longitudinal strain

( 0.0007 /0.0015) = 0.46 =0.46