Question

A beam with the cross-section given below is subjected to a positive bending moment (causing compression at the top) of 16-kN-m acting around the horizontal axis. The tensile force acting on the hatched area of the cross-section is

• A. Zero
• B. 5.9 kN
• C. 8.9 kN
• D. 17.8 kN

Answer 1

The correct option is C 8.9 kN


Given data,

$M=16kNm$
$=16\times {10}^{6}Nmm$

Stress at a distance 25 mm below neutral axis using flexure formula

$f=\frac{My}{I_{NA}}=\frac{16\times {10}^6\times 25}{100\times \frac{{150}^3}{12}}$

$=14.22N/m{m}^2$

Force acting on hatched area,
F = hatched area x average stress

$=25\times 50\times \frac{14.22}{2}$

$=8888.88N$

$=8.89kN$