Question

A T beam-section as shown below is subjected to a vertical shear force of magnitude 100 kN. If the moment of inertia about horizontal axis is $314.2\times {10}^4$ $m{m}^4$, the shear stress induced at the junction of flange and web is ___________N/$m{m}^2$.

• A. $27.7$
• B. $37.0$
• C. $52.5$
• D. $70.7$

Answer 1

The correct option is D $70.7$

Position of N.A. from top of flange

$y=\frac{A_1{y}_1+A_2{y}_2}{A_1+A_2}$

$=\frac{(100\times 20\times 10)+(80\times 20\times 60)}{100\times 20+80\times 20}=32.22mm$

Shear stress in web at junction

$\tau =\frac{VA\overline{y}}{Ib}$

$\frac{(100\times 1000)(100\times 20)\times (32.22-\frac{20}{2})}{314.2\times {10}^4\times 20}=70.72N/m{m}^2$