If one uses the Rotation matrix to do calculate the component of a Tensor (Tensor A) gets something like this: enter image description here

Now,one can get the same results for the stress tensor by means of equilibrium enter image description here

enter image description here

My question is: If one changes the sign convention for the shear stresses (negative on the positive side of the cube) (Tensor B) an does the equilibrium equation one arrives at a diferent equation for the rotated components (in the first equation above the sign of the shear stresses changes: Sigmax'=....-Tau*sin2a) and it seems that the Tensor B has a different rule of transformation than Tensor A although the coordinate system rotates the same. I don't really understand why....is this the reason for the stress convention to point in the possitive direction of the axes? or in general are the components of a tensor considert allways to be positivve in the direction of the axis.

  • $\begingroup$ I think that you would have to change the sign convention of not just the shear stresses but also all of the normal stresses in order to get another tensor which transforms properly. Look at the first three stress equations you listed above. If you flip the signs of all of the stress components in the equations, then the new equations will all be valid. But if you just flip the signs of the shear stress components, then the new equations will not in general be valid. $\endgroup$ – Samuel Weir Jul 3 at 17:55

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