- #1

AnotherParadox

- 35

- 3

## Homework Statement

"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"

## Homework 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

## 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