Maximum strain ory for failure of material at elastic limit is known as ............

1. Solution to Provided MCQ

Question: Maximum strain theory for the failure of material at the elastic limit is known as ............ A) Guest or Trecas theory B) St. Venant theory C) Rankine theory D) Haig theory

• Correct Option: B) St. Venant theory
• Justification: The Maximum Principal Strain Theory postulates that a material fails when the maximum principal strain in a complex stress system reaches the value of the strain at the yield point in a simple tensile test. This theory is historically attributed to St. Venant.

2. & 3. Additional High-Yield MCQs

1. Maximum shear stress theory for the failure of a material at the elastic limit is known as ............ A) Guest or Tresca’s theory B) St. Venant theory C) Rankine theory D) Haig theory

• Correct Answer: A) Guest or Tresca’s theory

2. Maximum principal stress theory for the failure of a material at the elastic point is known as ............ A) Guest or Tresca theory B) St. Venant theory C) Rankine theory D) Haig theory

• Correct Answer: C) Rankine theory

3. Total strain energy theory for the failure of a material at the elastic limit is known as ............ A) Guest or Tresca theory B) St. Venant theory C) Rankine theory D) Haig theory

• Correct Answer: D) Haig theory

4. Shear strain energy theory (or Distortion Energy Theory) for the failure of a material at the elastic limit is due to ............ A) Rankine B) Guest or Tresca C) St. Venant D) Von Mises

• Correct Answer: D) Von Mises

5. For ductile materials, the most appropriate failure theory is ............ A) maximum shear stress theory B) maximum principal stress theory C) maximum principal strain theory D) shear strain theory

• Correct Answer: A) maximum shear stress theory

4. Core Theoretical Concepts: Theories of Failure

• Maximum Principal Stress Theory (Rankine’s Theory):
  • States failure occurs when the maximum principal stress reaches the yield stress (or ultimate stress) from a simple tension test.
  • Best suited for brittle materials (like cast iron) which are weak in tension.
• Maximum Shear Stress Theory (Guest & Tresca’s Theory):
  • States failure occurs when the maximum shear stress equals the shear stress at yield in simple tension.
  • Best suited for ductile materials. It is often used in design because it is safe and simple to apply.
• Maximum Principal Strain Theory (St. Venant’s Theory):
  • States failure occurs when the maximum principal strain reaches the yield strain.
  • Generally not used for ductile materials as it can overestimate strength; occasionally applied to brittle materials or in specific thick-cylinder problems.
• Total Strain Energy Theory (Haigh’s Theory):
  • States failure occurs when the total strain energy per unit volume reaches the strain energy density at yield.
  • Historically used for ductile materials but largely superseded by Von Mises.
• Shear Strain Energy / Distortion Energy Theory (Von Mises & Hencky):
  • States failure occurs when the distortion energy (energy associated with change in shape, not volume) reaches a critical limit.
  • Considered the most accurate theory for ductile materials.