The state of stress in 3-dimension is given by the following determinant, the coefficient of σ2 is an invariant quantity which is equal to ________

Question

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$\begin{vmatrix}\sigma-\sigma x & -\tau yx & -\tau zx\ -\tau xy & \sigma-\sigma y & -\tau zy\ -\tau xz & -\tau yz & \sigma-\sigma z\end{vmatrix}$

TuteeHUB · Answer

σx+σy+σz

TuteeHUB · Answer

σxσy+σyσz+σzσx-τxy2- τyz2- τzx2

TuteeHUB · Answer

σxσyσz+2τxyτyzτzx-σxτxy2 -σyτyz2 -σzτzx2

TuteeHUB · Answer

1

1.	The state of stress in 3-dimension is given by the following determinant, the coefficient of σ2 is an invariant quantity which is equal to ________
A.	\(\begin{vmatrix}\sigma-\sigma x & -\tau yx & -\tau zx\\ -\tau xy & \sigma-\sigma y & -\tau zy\\ -\tau xz & -\tau yz & \sigma-\sigma z\end{vmatrix}\)
B.	σx+σy+σz
C.	σxσy+σyσz+σzσx-τxy2- τyz2- τzx2
D.	σxσyσz+2τxyτyzτzx-σxτxy2 -σyτyz2 -σzτzx2
E.	1
Answer» B.

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