Question

Find the correct match between the plane stress states and the Mohr’s circles. \includegraphics[width=0.5\linewidth]{55image.png}

• A. (P)-(III); (Q)-(IV); (R)-(I); (S)-(II)
• B. (P)-(III); (Q)-(II); (R)-(I); (S)-(IV)
• C. (P)-(I); (Q)-(IV); (R)-(III); (S)-(II)
• D. (P)-(I); (Q)-(II); (R)-(III); (S)-(IV)

Hint:

When matching stress states to Mohr's circles, focus on the principal stress values and whether shear stress is present.

Answer 1

The Correct Option is A

Step 1: Understanding the plane stress states Each stress state corresponds to a Mohr’s circle representation. We analyze the stress components and match them accordingly: - Case (P): Pure axial stress with equal normal forces in the horizontal direction corresponds to the Mohr's circle with a center at \(\sigma = 10\) and no shear stress.\ \( \Rightarrow \) Matches with (III) - Case (Q): Equal biaxial stress in both directions should result in a Mohr’s circle symmetric about the origin with radius equal to the stress magnitude.\ \( \Rightarrow \) Matches with (IV) - Case (R): Uniaxial stress in the vertical direction with no shear stress corresponds to the Mohr's circle with the center at \(\sigma = 10\) and no shear.\ \( \Rightarrow \) Matches with (I) - Case (S): Equal biaxial stress in both horizontal and vertical directions results in a Mohr’s circle symmetric about the origin.\ \( \Rightarrow \) Matches with (II)