Topic: Machine Design
Match the following: Theories of failure with Shape of region of safety. (A) Rankine Theory, (B) Tresca Theory, (C) St. Venants theory, (D) Von mises Theory. (i) Hexagon, (ii) Ellipse, (iii) Square, (iv) Rhombus.
- A. (A)-(ii), (B)-(iv), (C)-(i), (D)-(iii)
- B. (A)-(iii), (B)-(iv), (C)-(ii), (D)-(i)
- C. (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)
- D. (A)-(iv), (B)-(i), (C)-(iii), (D)-(ii)
Answer: C. (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)
Explanation: Rankine theory (Maximum Normal Stress) boundary is a Square (iii). Tresca theory (Maximum Shear Stress) boundary is a Hexagon (i). St. Venants theory (Maximum Principal Strain) boundary is a Rhombus (iv). Von Mises (Maximum Distortion Energy) boundary is an Ellipse (ii).