Question

A square column section of size $400mm$ is subjected to a concentrated load of magnitude $400kN$ causing compression in member at an eccentricity of $50mm$ from centroid measured along one of its diagonal. The maximum compressive and tensile stress respectively are:

• A. $6.151MPa,2.131MPa$
• B. $5.151MPa,0.151MPa$
• C. $0.151MPa,6.263MPa$
• D. $2.629MPa,9.136MPa$

Answer 1

The correct option is B $5.151MPa,0.151MPa$


$OA=OB=\frac{\left(400\sqrt{2}\right)}{2}mm$

$=282.84mm$

$A={400}^{2}m{m}^2$

$I=\frac{{400}^4}{12}=2.133\times {10}^{9}m{m}^4$

$Z_A=\frac{2.133\times {10}^9}{282.84}=7541366.143m{m}^3$

Also, $Z_B=7541366.143m{m}^3$

$({\sigma }_C{)}_{max}=\frac{400\times {10}^3}{{400}^2}+\frac{400\times {10}^3\times 50}{7541366.143}=5.152MPa$

$\left[\begin{array}{c}\text{Sign convention:}\\ \text{Compression}\to ‘‘+"\\ \text{Tension}\to ‘‘-"\end{array}\right]$

$({\sigma }_T{)}_{max}=\frac{400\times {10}^3}{{400}^2}-\frac{400\times {10}^3\times 50}{7541366.143}=-0.152MPa$