Theories of Failure MCQ with answer and solution

Concept

Tresca failure theory for ductile transmission shafts

Formula

τ_max = σ_y / (2 × FOS)

Step-by-step solution

1. Transmission shafts are made of ductile structural steel and resist combined axial loads and torsional shear stresses. 2. For ductile materials subjected to multi-axial stresses, yielding is governed by shear slip along crystal planes. 3. Maximum Shear Stress Theory (Tresca theory) and Distortion Energy Theory (von Mises) predict ductile yielding accurately. 4. Among the given options, Tresca is the established failure theory for ductile shaft design. Answer: B

Explanation

For ductile metal components such as steel transmission shafts subjected to combined axial tension and torsional shear loading, yield failure is governed by shear deformation. Consequently, the Maximum Shear Stress Theory (Tresca theory) or the Distortion Energy Theory (von Mises) is recommended for conservative mechanical design.

Why the other options are wrong

A) Rankine theory applies to brittle materials prone to tensile cleavage fracture. C) St. Venant maximum principal strain theory is obsolete and inaccurate for ductile metals. D) Castigliano formulated strain energy deflection theorems, not a yield failure criterion.

Shortcut

Ductile shaft under torsion + axial = Tresca (Max Shear Stress) or von Mises.

Common mistake

Selecting Rankine's maximum principal stress theory, which is strictly for brittle materials like cast iron.