Question

A beam of square cross-section of side 500 mm is placed horizontally with one diagonal horizontal. It is subjected to a vertical shear force of 100 kN acting along the depth of cross section. The maximum shear stress and position of maximum shear stress from the neutral axis are respectively ?

• A. $400kN/m^2;88mm$
• B. $450kN/m^2;88mm$
• C. $400kN/m^2;44mm$
• D. $450kN/m^2;84mm$

Answer 1

The correct option is B $450kN/m^2;88mm$

$\because {\tau }_{avg}=\frac{P}{A}$

$=\frac{100}{0.5\times 0.5}$

$=400kN/m^2$


The maximum shear stress

$\because {\tau }_{max}=\frac{9}{8}{\tau }_{avg}$

$=\frac{9}{8}\times 400=450kN/m^2$

From figure

$CD=0.5\sqrt{2}m$

$h=\frac{CD}{2}=\frac{0.5\sqrt{2}}{2}=0.35m$

So position of maximum shear stress from neutral axis

$=\frac{h}{4}=0.088m=88mm$