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Shear modulus in terms of 2 Young's moduli and Poisson ratio

Engineering Asked by Mikeb on October 14, 2020

I have two moduli, EY and EZ, and the poisson ratio NUYZ, and the equation for the shear modulus that I am using is

$G = frac{EY*EZ}{EY+EZ+2*EY*NUYZ}$
but I am not sure where it comes from.

I tried seeing if I could somehow rearrange the shear modulus from wikipedia: $G = frac{E}{2(1+nu)}$ but did not have any luck, so I was wondering if there was something obvious I am missing. Apologies if this is an easy problem, I am new to shears/Young’s moduli, but if anyone could explain where my equation comes from it would be super helpful! Thank you!

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