On the ‘Proof’ of Assumptions in the Basic Theories of Bending and Torsion

In the theory of beam bending, transverse sections of a beam are assumed to remain plane during bending. In torsion analysis, the radii of shafts of circular cross-sections are assumed to remain straight during twisting. Some popular textbooks present mathematical proofs for these statements. This article shows that these proofs are incorrect and that these statements should be treated as assumptions.