Question

Let \(\sigma\) and \(\tau\) represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under \textit{pure bending} is/are:

Hint:

For pure bending in beams, only normal stress exists. Mohr’s circle lies on the \(\sigma\)-axis, with no shear stress (\(\tau = 0\)).

Answer 1

Correct Answer: 2 - 3

Step 1: Understand stress in pure bending.
In pure bending, the internal stress developed is purely normal stress due to bending moment, i.e., \(\tau = 0\) and \(\sigma \ne 0\).
Step 2: Analyze Mohr’s circle behavior.
Mohr’s circle for pure bending will lie completely on the \(\sigma\)-axis, centered symmetrically between the maximum tensile and compressive stresses. There should be no vertical (shear stress) component.
Step 3: Analyze options.
Option (A): Has non-zero shear (\(\tau \ne 0\)), hence not valid.
Option (B): Correct – lies on the \(\sigma\)-axis with zero shear.
Option (C): Also correct – same as (B), just a mirror image.
Option (D): Circle on \(\tau\)-axis (i.e., only shear, no normal stress) – not valid for pure bending.