Answer:
The Poisson's ratio for the material is 0.0134.
Step-by-step explanation:
The Poisson's ratio (
), no unit, is the ratio of transversal strain (
), in inches, to axial strain (
), in inches:
(1)
(2)
(3)
Where:
- Initial axial length, in inches.
- Final axial length, in inches.
- Initial transversal length, in inches.
- Final transversal length, in inches.
If we know that
,
,
and
, then the Poisson's ratio is:
![\epsilon_{a} = 61.235\,in - 61.2\,in](https://tex.z-dn.net/?f=%5Cepsilon_%7Ba%7D%20%3D%2061.235%5C%2Cin%20-%2061.2%5C%2Cin)
![\epsilon_{a} = 0.035\,in](https://tex.z-dn.net/?f=%5Cepsilon_%7Ba%7D%20%3D%200.035%5C%2Cin)
![\epsilon_{t} = 2.69953\,in - 2.7\,in](https://tex.z-dn.net/?f=%5Cepsilon_%7Bt%7D%20%3D%202.69953%5C%2Cin%20-%202.7%5C%2Cin)
![\epsilon_{t} = -4.7\times 10^{-4}\,in](https://tex.z-dn.net/?f=%5Cepsilon_%7Bt%7D%20%3D%20-4.7%5Ctimes%2010%5E%7B-4%7D%5C%2Cin)
![\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}](https://tex.z-dn.net/?f=%5Cnu%20%3D%20-%20%5Cfrac%7B%28-4.7%5Ctimes%2010%5E%7B-4%7D%5C%2Cin%29%7D%7B0.035%5C%2Cin%7D)
![\nu = 0.0134](https://tex.z-dn.net/?f=%5Cnu%20%3D%200.0134)
The Poisson's ratio for the material is 0.0134.