Question

A beam of rectangular cross-section (b$\times$d) is subjected to a torque T. What is the maximum torsional stress induced in the beam (b < d and $\alpha$ is a constant)?

• A. $\frac{T}{\alpha b^{2}d}$
• B. $\frac{T}{\alpha b{d}^2}$
• C. $\frac{T}{\alpha bd}$
• D. $\frac{T}{bd}$

Answer 1

The correct option is A $\frac{T}{\alpha b^{2}d}$

Torsional constant of a rectangular,section of width b and depth d (b < d) may be expressed as
$J=b^{3}d$
For T, L and I sections torsion,canstant,
$J=\sum \frac{1}{3}{b}_i^3{d}_i$

where $b_i$ and $d_i$ are the-dimensions of e.ach of the component rectangles into which the:s.ection may be divided.
Torsional shear stress for rectangular section
$\tau =\frac{T}{\alpha b^{2}d}$
For T, L and.J,sections torsional shear stress may be calculated for each component rectangle by considering them subjected to torsional moment

$T_i^{\prime }=T\left[\frac{b_i^3{d}_i}{\sum b_i^3{d}_i}\right]$