Question

Polar moment of inertia is used primarily for calculating the stresses in

• A. Bending
• B. Torsion
• C. Shear
• D. Compression

Hint:

Moment of Inertia Applications. Area Moment of Inertia (I): Used for bending stress (\(\sigma = My/I\)) and deflection. Polar Moment of Inertia (J): Used for torsional shear stress (\(\tau = Tr/J\)) and angle of twist.

Answer 1

The Correct Option is B

The Polar Moment of Inertia (\(J\)) of a cross-sectional area is a geometric property that measures its resistance to twisting or torsion.
It is analogous to how the area moment of inertia (I) measures resistance to bending.
The formula for shear stress (\(\tau\)) due to torsion (T) in a circular shaft involves the polar moment of inertia: $$ \tau = \frac{T r}{J} $$ where \(r\) is the radial distance from the center.
Similarly, the angle of twist (\(\theta\)) is related to J by \( \theta = \frac{TL}{GJ} \), where G is the shear modulus and L is the length.
Stresses in bending are calculated using the area moment of inertia (I), while shear stresses due to transverse loads relate to the first moment of area (Q) and area moment of inertia (I).
Compression stresses relate directly to area (A).
Therefore, the polar moment of inertia is primarily used in torsion calculations.