Question

What is the nature of distribution of shear stress in a rectangular beam?

• A. Linear
• B. Parabolic
• C. Hyperbolic
• D. Elliptical

Hint:

In rectangular beams, shear stress follows a parabolic distribution — highest at the center and zero at the top/bottom.

Answer 1

The Correct Option is B

In a rectangular beam under transverse loading, the shear stress distribution across the cross-section is parabolic.
The shear stress is maximum at the neutral axis (center of the height of the beam) and zero at the top and bottom surfaces.
Mathematically, shear stress at a distance \( y \) from the neutral axis is given by: \[ \tau = \frac{3V}{2A} \left(1 - \left(\frac{2y}{d}\right)^2\right) \] Where:
- \( \tau \) = shear stress,
- \( V \) = shear force,
- \( A \) = cross-sectional area,
- \( d \) = total depth of the beam,
- \( y \) = distance from the neutral axis.
This equation clearly shows a parabolic variation.