Relating Radial Strain to Circumferential

  1. 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?

    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?

  2. jcsd
  3. 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.
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