Out of plane forces acting on a bicycle frame can be large and must be taken into account in frame design. The diagram represents the seat tube and bottom bracket with a force of 150 lbf being applied to the pedal. The line of action of this force is 5" out of the plane of the frame. Assuming that the moment is supported by the seat tube, the maximum stress due to the pedaling force can be estimated. The bending moment in the tube, M = (150 x 5) in-lbf, and if the geometric moment of inertia of the tube is computed the stress in the tube wall can be estimated.

Taking a circular steel tube of diameter, D = 1.125", and a wall thickness of 0.05", gives an inner tube diameter, d, of 1.025".
The geometric moment of inertia:
I = (p/64){D⁴ - d⁴} = (0.049){0.498} = 0.0244.
The maximum wall stress:
s = [M D/2 I] = [750 x 1.125/ 2 x 0.0244] = 17.290 ksi.
This is much larger than the compressive stress in the tube due to the static load on the frame of 160 psi but much less than the yield stress of the material (circa 50 ksi).

From: McMahon & Graham,
"The Bicycle & the Walkman,"
Merion (1992)