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GATE 2024 CE (CE1) – Question 38

Solid Mechanics · Transformation of stress, Mohr circle · 2 marks · Multiple choice

Find the correct match between the plane stress states and the Mohr's circles.

four stress elements P, Q, R, S: (P) a tension of 10 on two opposite faces (horizontal), (Q) a pure shear of 10 on all four faces, (R) a compression of 10 on two opposite faces (vertical) and (S) a compression of 10 on all four faces. The four Mohr's circles are: (I) a circle from −10 to 0 on the σ-axis, (II) a single point at σ = −10, (III) a circle from 0 to 10, (IV) a circle centred at the origin from −10 to 10.
  1. (P)-(III); (Q)-(IV); (R)-(I); (S)-(II)
  2. (P)-(III); (Q)-(II); (R)-(I); (S)-(IV)
  3. (P)-(I); (Q)-(IV); (R)-(III); (S)-(II)
  4. (P)-(I); (Q)-(II); (R)-(III); (S)-(IV)

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Show answer and explanation

Correct answer: (A) (P)-(III); (Q)-(IV); (R)-(I); (S)-(II)

Explanation

(P) is a uniaxial tension of 10, so the principal stresses are 10 and 0, which is the circle from 0 to 10 (III). (Q) is pure shear of 10, so the principal stresses are ±10 and the circle is centred at the origin (IV). (R) is a uniaxial compression, the principal stresses are 0 and −10, which is the circle from −10 to 0 (I). (S) is equal compression of 10 in both directions, so the circle shrinks to the point at −10 (II).