- #1
AnotherParadox
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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
σx' = (σx+σy)/2 + ((σx-σy)/2)*cos(2θ) + τxy*sin(2θ)
σy' = (σx+σy)/2 - ((σx-σy)/2)*cos(2θ) - τxy*sin(2θ)
τmax,in plane = √[((σx-σy)/2)2 + τxy2]
σ1,2 = (σx+σy)/2) ± [((σx-σy)/2)2 + τxy2]
τmax,absolute = σ1/2
The Attempt at a Solution
Ratio of shear stress to normal stress?? ->
τmax,in plane/σx' ->
[τmax,in plane = √[((σx-σy)/2)2 + τxy2]] / [σx' = (σx+σy)/2 + ((σx-σy)/2)*cos(2θ) + τxy*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