When finding the Von Mises of given a stress tensor who's only element is a single shear component (τ):(adsbygoogle = window.adsbygoogle || []).push({});

\begin{bmatrix}

0 & τ & 0\\

τ & 0 & 0\\

0 & 0 & 0

\end{bmatrix}

the result is simply √3×τ. Is the Von Mises criterion not valid when considering a single component as in this example? I can't seem to reconcile that a calculated shear stress (say by a simple shaft twisting where τ=Tc/J) should be multiplied by √3. I understand that when using the Von Mises yield criterion, it is to be compared to the uniaxial yield allowable, not the shear allowable. However, the yield allowable is not √3 greater than the shear allowable.

In the example I am actually considering there is also normal component, but I want to see the effect of the two components in isolation as well as combined

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# Single shear element in stress tensor: Finding Von Mises

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