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GATE 2023 ME – Question 27

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 1 mark · Multiple select

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

four Mohr's circle plots on $\sigma$-$\tau$ axes. M1 is a circle centred at the origin. M2 is a circle with its centre above the $\sigma$-axis, entirely in the first quadrant. M3 is a circle centred on the $\sigma$-axis, to the right of the origin, crossing the $\tau$-axis. M4 is a circle whose centre is on the $\tau$-axis, above the origin, so that it touches the $\sigma$-axis at the origin.
  1. M1
  2. M2
  3. M3
  4. M4

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Show answer and explanation

Correct answer: (A) M1; (C) M3

Explanation

In Mohr's circle the horizontal axis is the normal stress and the vertical axis is the shear stress. The centre of the circle is at $\left(\frac{\sigma_x + \sigma_y}{2}, 0\right)$, so it must lie on the $\sigma$-axis. M1 (centre at the origin, pure shear) and M3 (centre on the $\sigma$-axis) are valid. In M2 and M4 the centre is above the $\sigma$-axis, which is not possible.