# Combined shear stress due to shear force and torsion

Let's assume I have a rotating shaft supported with bearings at both ends. This shaft is exposed to a point load (by means of another bearing) at some point and a torque. I want to calculate shear stress so as to find plane stresses at some infinitesimal part. I'm confused about how to combine the shear stresses due to torque and transverse shear. Should I just sum them, or calculate the square root of the sum of the square of them? I'm perplexed by some figures I saw that illustrate the transverse shear downward but torsional shear in a tangential direction. I would be grateful if you explain it for me.

The shear stresses due to torque will point in a direction which is tangential to the radial coordinate. This means that depending on which point you pick, the direction of the shear will change. In design considerations, you want the maximum net shear stress, because the failure criterion will be applied to the that critical case. Thus you have two shear vectors $$\tau_{torsion}$$ and $$\tau_{transverse}$$. $$\tau_{transverse}$$ always points in the same direction (direction of point load), whereas $$\tau_{torsion}$$ can be in any orientation with respect to $$\tau_{transverse}$$. Thus the maximum net shear happens at the point where they point in the same direction and therefore simply add up.