(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For a plane stress condition (stress z-axis = 0 ), prove the following relations if strain x-axis and strain y-axis are determined by experiments.

σ_x=(∈_x+v∈_y/1-v^2)E

&

σ_y=(∈_y+v∈_x/1-v^2)E

where:

σ_x = stress in x-axis

σ_y = stress in y-axis

∈_x = strain in x-axis

∈_x = strain in y-axis

E = modulus of elasticity

2. Relevant equations

∈_z=-(∈_x+∈_y)(v/1-v)

Poission's ratio

∈_x=σ_x/E

∈_y=∈_z=-vσ_x/E

v=-lateral strain/axial strain

v=-∈_y/∈_x=-∈_z/∈_x

3. The attempt at a solution

I'm not sure which equations I should be using to solve the problem. Can I use Hooke's Law for multi-axial loading since it is a plane stress condition?

I have tried rearranging Poisson's ratio equation with no luck.

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# Homework Help: Proving equations for a plane stress condition

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