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

"In a component under multi-axial state of stress, the ratio of shear stress to normal stress along principle places is _____.

A) 0.0 B) 0.5 C) 1.0 D) 1.5 E)2.0"

2. Relevant equations

σ_{x'}= (σ_{x}+σ_{y})/2 + ((σ_{x}-σ_{y})/2)*cos(2θ) + τ_{xy}*sin(2θ)

σ_{y'}= (σ_{x}+σ_{y})/2 - ((σ_{x}-σ_{y})/2)*cos(2θ) - τ_{xy}*sin(2θ)

τ_{max,in plane}= √[((σ_{x}-σ_{y})/2)^{2}+ τ_{xy}^{2}]

σ_{1,2}= (σ_{x}+σ_{y})/2) ± [((σ_{x}-σ_{y})/2)^{2}+ τ_{xy}^{2}]

τ_{max,absolute}= σ_{1}/2

3. The attempt at a solution

Ratio of shear stress to normal stress?? ->

τ_{max,in plane}/σ_{x'}->

[τ_{max,in plane}= √[((σ_{x}-σ_{y})/2)^{2}+ τ_{xy}^{2}]] / [σ_{x'}= (σ_{x}+σ_{y})/2 + ((σ_{x}-σ_{y})/2)*cos(2θ) + τ_{xy}*sin(2θ)]

Impossible to simplify? Wrong ratio equations?

I don't know what to do. Please help. I have heard from different sources that it is either 0 or 0.5 neither with explanations or work shown.

Thank you

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# Homework Help: Ratio of shear stress to normal stress along principle place

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