Question

A steel section shown in figure is subjected to a shear force of 200 kN. The maximum shear stress developed is __________ MPa

• A. $4.31N/m{m}^2$
• B. $5.081N/m{m}^2$
• C. $1.34N/m{m}^2$
• D. $2.09N/m{m}^2$

Answer 1

The correct option is B $5.081N/m{m}^2$


$S=200\times {10}^{3}N$

Side $=a=300mm$

Diameter $d=200mm$

$I_{N.A}=I_{Square}-I_{circle}$

$=\frac{a^4}{12}-\frac{\pi }{64}(d{)}^4$

$=\frac{{300}^4}{12}-\frac{\pi }{64}(200{)}^4=596.46\times {10}^{6}m{m}^4$

$b_{N.A}=300-200=100mm$

${\tau }_{N.A}={\tau }_{max}=\frac{SA\overline{y}}{I_{N.A}.b}=\frac{S(A_1{\overline{y}}_2-A_2\overline{y_2})}{I_{N.A}.b_{N.A}}$

$=\frac{200\times {10}^3\left[\right(300\times 150\times 75)-\frac{\pi }{2}(100{)}^2\times \frac{4}{3\pi }\times 400]}{596.46\times {10}^6\times 100}$

$=5.081MPa$