Sign issue with the skew bending formula

[Amaelle]

Good day !
I have an issue with the sign minus inside the skew bending (unsymmetric) formula
First we all know that the stress generated by the bending moment is the following:

and then after we have the formula

I really don't understand why we don t have the sign minus in all the formula, because of the superposition principle? I'm really confused regarding that point
Many thanks in advance

 

[haruspex]

I am not certain of the topic ... I assume it is the beam that's asymmetric rather than the bending. E.g. as at http://courses.washington.edu/me354a/Unsym.pdf.
What looks like the same equation appears there on page 3. In that case it arises from the sign convention that happens to have been used for the axes and the bending moment. The bending moment vector is taken to be in the first quadrant between the X and Y principal axes. The cross product of that with the axis vectors will be into the page for one axis and out of the page for the other, i.e. opposite signs in the z direction.

 

[Amaelle]

thanks a lot!