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GATE 2024 CE (CE1) – Question 14

Solid Mechanics · Transformation of stress, Mohr circle · 1 mark · Multiple choice

The three-dimensional state of stress at a point is given by $\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix}$ MPa. The maximum shear stress at the point is

  1. 20 MPa
  2. 15 MPa
  3. 5 MPa
  4. 25 MPa

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Correct answer: (A) 20 MPa

Explanation

The matrix is diagonal, so the principal stresses are 40, 10 and 0 MPa. The maximum shear stress is half the difference between the largest and the smallest principal stress: $\frac{40 - 0}{2} = 20$ MPa.