The maximum strain 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: B. St. Venant's theory
Asked in SSC JE 25/01/2018 (Morning)
Detailed Explanation
The maximum principal strain theory says failure occurs when the largest principal strain reaches the strain at yield in simple tension, σy/E.
\[ \frac{1}{E}\left(\sigma_1 - \mu\sigma_2 - \mu\sigma_3\right) = \frac{\sigma_y}{E} \Rightarrow \sigma_1 - \mu(\sigma_2 + \sigma_3) = \sigma_y \]
Why “St. Venant's theory” Is Correct
This is St. Venant's theory.
| Theory of failure | Due to | Failure when | Yield locus (2-D) | Suited to |
|---|---|---|---|---|
| Maximum principal stress | Rankine | σ₁ = σy | Square | Brittle materials |
| Maximum principal strain | St. Venant | σ₁ − μσ₂ = σy | Rhombus | Rarely used |
| Maximum shear stress | Guest / Tresca | σ₁ − σ₃ = σy | Hexagon | Ductile (conservative) |
| Total strain energy | Haigh (Beltrami) | σ₁² + σ₂² − 2μσ₁σ₂ = σy² | Ellipse | Ductile |
| Shear strain (distortion) energy | von Mises (Hencky) | σ₁² + σ₂² − σ₁σ₂ = σy² | Ellipse | Ductile (best fit) |
Why the Other Options Are Wrong
- A. Guest's or Tresca's theory: Guest/Tresca: maximum shear stress.
- C. Rankine's theory: Rankine: maximum principal stress.
- D. Haigh's theory: Haigh: total strain energy.
Key Point
St. Venant → maximum principal strain.
Key Concepts for Students
- Its 2-D locus is a rhombus.
- Not reliable for most materials; rarely used.
- Gives results between Rankine and Tresca for some cases.
Practice more: this is question 25 in Principal Stress and Principal Planes MCQs – Part 2. Try the whole set and check every answer instantly.