Can Bending Stress on Curved Beams Be Calculated Using a Simple Formula?

[gomerpyle]

I have a problem where I'm considering a curved member of circular cross section bent in the shape of a half circle and fixed at the base. A force is applied perpendicular to it (so in the picture, the dot is the force going 'into' the screen at the top view) and I'm trying to find the bending stress at the base. Can I approach this as a simple Mc/I situation with c being half the diameter of the rod, and M being the distance of F to the base? I'm confused, though, on what I would use for the area moment of Inertia.

Any assistance would be appreciated. Thank you.

 

[SteamKing]

I have a problem where I'm considering a curved member of circular cross section bent in the shape of a half circle and fixed at the base. A force is applied perpendicular to it (so in the picture, the dot is the force going 'into' the screen at the top view) and I'm trying to find the bending stress at the base. Can I approach this as a simple Mc/I situation with c being half the diameter of the rod, and M being the distance of F to the base? I'm confused, though, on what I would use for the area moment of Inertia.

Any assistance would be appreciated. Thank you.

You can't treat the bending of curved beams in the same manner as you do the bending of straight, prismatic beams.

The bending of curved beams is usually treated in courses on advanced strength of materials.