The GATE Grind

GATE 2016 ME (ME1) – Question 48

Machine Design · Design for static and dynamic loading, failure theories · 2 marks · Multiple choice

The principal stresses at a point inside a solid object are σ1 = 100 MPa, σ2 = 100 MPa and σ3 = 0 MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca (maximum shear stress) theory is nT and the factor of safety calculated using von Mises (maximum distortional energy) theory is nV. Which one of the following relations is TRUE?

  1. $n_T=(\sqrt3/2)n_V$
  2. $n_T=\sqrt3n_V$
  3. $n_T=n_V$
  4. $n_V=\sqrt3n_T$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $n_T=n_V$

Explanation

Tresca equivalent stress is the largest principal-stress difference:100MPa. Von Mises equivalent stress is sqrt[((100−100)²+(100−0)²+(0−100)²)/2]=100MPa. Both safety factors are200/100=2. Hence **nT=nV, C**.