Stress generated by a bending moment

[Amaelle]

Good day all,
I have an issue regarding the theoretical concept regarding the stress generated by the skew bending
in a rectangular cross section for example

the formula used to calculated the stress is

while when it is a circular cross section we have the following formula

I really can't understand why we use different formulas in the second case (I couldn't understand the given explanations)
many thanks in advance

 

[haruspex]

In the case of the rectangle, there is a natural direction for the coordinate axes. You do not have to use those, but if you choose something else then the calculations of the moments get messy.

For the circle, it is clear that you can choose any pair of orthogonal axes. The moments will be the same. So it is convenient to choose axes that are orthogonal to / parallel to the bending moment. That gives the simpler equation found.
You could, again, choose arbitrary axes and use the same equation as for the rectangle, but numerically the answer will be the same.

 

[Amaelle]

In the case of the rectangle, there is a natural direction for the coordinate axes. You do not have to use those, but if you choose something else then the calculations of the moments get messy.

For the circle, it is clear that you can choose any pair of orthogonal axes. The moments will be the same. So it is convenient to choose axes that are orthogonal to / parallel to the bending moment. That gives the simpler equation found.
You could, again, choose arbitrary axes and use the same equation as for the rectangle, but numerically the answer will be the same.

Thanks a lot for your answer, but this point still confuses me, could you please point me out a link where i can study more this particular issue?
many thanks in advance

 

[haruspex]

Thanks a lot for your answer, but this point still confuses me, could you please point me out a link where i can study more this particular issue?
many thanks in advance

I do not know any links to recommend. There must be lots out there, but you can search them as easily as I can.