Question

A structural steel beam has an unsymmetrical I-cross-section. The overall depth of the beam is 200 mm. The flange stresses at the top and bottom are 120 N/mm${}^2$ and 80 N/mm${}^2$, respectively. The depth of the neutral axis from the top of the beam will be

• A. 120 mm
• B. 100 mm
• C. 80 mm
• D. 60 mm

Answer 1

The correct option is A 120 mm


${\sigma }_1={\sigma }_{top}=120Mpa$

${\sigma }_1={\sigma }_{bottom}=80Mpa$

${\sigma }_{top}>{\sigma }_{bottom}$

So, $y_q>y_2$

$\frac{{\sigma }_1}{y_1}=\frac{{\sigma }_2}{y_2}$

$\frac{120}{y_1}=\frac{80}{y_2}$

So, $y_1+y_2=200$ .....(ii)

So, $y_1=120mm$