Question

A structural beam subjected to sagging bending has a cross-section which is an unsymmetrical I-section. The overall depth of the beam is 300 mm. The flange stresses in the beam are:
${\sigma }_{top}=200N/m{m}^2$
${\sigma }_{bottom}=50N/m{m}^2$

What is the height in mm of the neutral axis above the bottom flange?

• A. 240 mm
• B. 60 mm
• C. 180 mm
• D. 120 mm

Answer 1

The correct option is B 60 mm

The sagging moment will cause compressive stresses above the neutral axis and tensile stresses below the neutral axis. The variation of stresses is linear in pure bending.

$\frac{x}{50}=\frac{300-x}{200}$

$\Rightarrow 200x=15000-50x$

$\Rightarrow x=\frac{15000}{250}=60mm$