Relating Radial Strain to Circumferential

[Conorfell]

Hi,

I have a solid cylinder to which I have strain gauges attached to measure axial and circumferential strains. My goal is to relate the circumferential strain to radial strain and then to calculate possion's ratio. Every time I try to work out the geometry of the problem I end up saying that circumferential strain is equal to axial strain, can this be true?

Terms:
Ec = Circumferential Strain = dC/C
dC = change in length of circumference
C = circumference
Er = Radial Strain = dR/R
dR = change in length of radius
R = radius


Here is my logic:
Strain Circumferential (Ec) is equal to the strain is see in one single strain gauge attached along circumference. dC = 2*PI*dR. Then dR can be expressed as dR = C*Ec/(2*PI). Which means Er= dR/R = C*Ec/(2*PI*R) = Ec. Can that be right?

Then is my possion's ratio radial/axial or axial/radial?

Thanks.

 

[timthereaper]

You're right about the radial strain being equal to the circumferential strain. Since circumference changes proportionally with radius, the strains will be the same since strain is really just a proportion.

However, you're not taking axial strain into consideration. Your axial strain will be dL/L. The Poisson's ratio is v=-Er/Ea = -(dR/R)/(dL/L) or -(dC/C)/(dL/L) if you prefer.