Skew bending in a circular cross section (proof)

[Amaelle]

Good day all
I'm looking for the proof of stress generated in case of skew bending applied in acircular cross section ( I browsed internet the whole day without finding anything convincing)

we use

with

many thanks in advance!

 

[Baluncore]

The principle of superposition says that forces due to torsion and forces due to bending of the tube should be simply added. The same goes for displacement. When many forces are applied, the order of summation of all forces is not important.

 

[PhanthomJay]

No need to break up the moment into its components, because the circle is symmetrical about all axes, and I is the same no matter which axis is chosen. Thus, bending stress at any point is M_f*r/I, where r is the perpendicular distance from the chosen point to the neutral axis, and if the radius of the section is R, then max stress is M_f*R/I, which occurs at the point on the edge of the circle which is a distance R measured perpendicular to the neutral axis.

 

[Amaelle]

Thanks a lot to both of you!