Question

Arrange the following steps in correct sequence to construct Mohr’s circle for a given plane stress \((\sigma_x, \sigma_y, \tau_{xy})\): A. Plot center at \(\left(\frac{\sigma_x+\sigma_y}{2}, 0\right)\)
B. Identify principal stresses as horizontal intercepts
C. Plot points \(X(\sigma_x,-\tau_{xy})\) and \(Y(\sigma_y,\tau_{xy})\)
D. Connect points X and Y and draw a circle

• A. C, A, D, B
• B. A, D, B, C
• C. C, A, B, D
• D. A, C, D, B

Hint:

Always plot stress points first, then center, then circle, then read results.

Answer 1

The Correct Option is A

Concept: Mohr’s circle is a graphical representation of stress transformation.

Step 1: Plot stress points.
First plot: \[ X(\sigma_x,-\tau_{xy}), \quad Y(\sigma_y,\tau_{xy}) \]

Step 2: Find center.
Center is midpoint: \[ \left(\frac{\sigma_x+\sigma_y}{2},0\right) \]

Step 3: Draw circle.
Join X and Y and draw circle with center as midpoint.

Step 4: Identify principal stresses.
Principal stresses occur where circle intersects horizontal axis.

Step 5: Correct sequence.
\[ C \rightarrow A \rightarrow D \rightarrow B \] Final Answer: \[ \boxed{C, A, D, B} \]