The maximum shear stress theory for the failure of a material at the elastic limit is known as:
Try it first: pick an option, then read the explanation.
Correct answer: A. Guest's or Tresca's theory
Asked in SSC JE 22/01/2018 (Morning)
Detailed Explanation
The maximum shear stress theory says yielding starts when the maximum shear stress at a point reaches the maximum shear stress at yield in a simple tension test, σy/2.
\[ \tau_{max} = \frac{\sigma_1 - \sigma_3}{2} = \frac{\sigma_y}{2} \Rightarrow \sigma_1 - \sigma_3 = \sigma_y \]
Why “Guest's or Tresca's theory” Is Correct
This is Guest's or Tresca's theory. It works well for ductile materials and is slightly conservative compared with von Mises.
Why the Other Options Are Wrong
- B. St. Venant's theory: St. Venant: maximum principal strain theory.
- C. Rankine's theory: Rankine: maximum principal stress theory.
- D. Haigh's theory: Haigh: total strain energy theory.
Key Point
Tresca/Guest: σ₁ − σ₃ = σy; hexagonal yield locus.
Key Concepts for Students
- In pure shear Tresca predicts yield at τ = 0.5σy (von Mises: 0.577σy).
- Widely used in shaft design.
- Hexagon lies inside the von Mises ellipse.
Practice more: this is question 22 in Principal Stress and Principal Planes MCQs – Part 2. Try the whole set and check every answer instantly.