The shear strain energy theory for the failure of a material at the elastic limit is due to:
Try it first: pick an option, then read the explanation.
Correct answer: D. von Mises
Asked in SSC JE 29/01/2018 (Morning)
Detailed Explanation
Strain energy can be split into a part that changes volume and a part that changes shape (distortion). Only the distortion part causes yielding in ductile metals.
\[ \sigma_1^2 + \sigma_2^2 - \sigma_1\sigma_2 = \sigma_y^2 \quad (\sigma_3 = 0) \]
Why “von Mises” Is Correct
The shear strain energy (maximum distortion energy) theory is due to von Mises (with Hencky). It agrees best with tests on ductile materials.
Why the Other Options Are Wrong
- A. Rankine: Rankine: maximum principal stress.
- B. Guest or Tresca: Guest/Tresca: maximum shear stress.
- C. St. Venant: St. Venant: maximum principal strain.
Key Point
von Mises (Hencky) → shear strain / distortion energy; elliptical yield locus.
Key Concepts for Students
- Predicts yield in pure shear at τ = σy/√3 ≈ 0.577σy.
- Hydrostatic stress causes no yield under this theory.
- Basis of the 'equivalent stress' used in design software.
Practice more: this is question 28 in Principal Stress and Principal Planes MCQs – Part 2. Try the whole set and check every answer instantly.