Question

I-section of a beam is formed by gluing wooden planks as shown is the figure below. If this beam transmits a constant vertical shear force of 3000N, the glue at any of the four joints will be subjected to a shear force (in kN per meter length ) of

• A. 3.0
• B. 4.0
• C. 8.0
• D. 10.7

Answer 1

The correct option is B 4.0

$\overline{y}=150-\frac{50}{2}=125mm$
Shear force,
$V=3000N$
$I_{NA}=\frac{200\times {300}^3}{12}-\frac{150\times {200}^3}{12}$
$=350\times {10}^{6}m{m}^4$
Shear flow $=\frac{VA\overline{y}}{I}$
$=\frac{3000\times (75\times 50)\times 125}{350\times {10}^6}$
$=4.018N/mm$
$=4kN/m$