For a beam of circular cross-section, analysis from elementary strength of materials theory yields the following stresses:

where R is the section radius, I = πR⁴/4, M is the bending moment, V is the shear force, and dM/dx = V. Assuming zero body forces, show that these stresses do not satisfy the equilibrium equations. This result is one of many that indicate the approximate nature of strength of materials theory.

Transcribed Image Text:

ox My Txy V (R - y) 31 ay 0 txz = Tyz = 0