Question

A circular column of diameter 'd' carries an axial compressive load P at an eccentricity equal to one fourth of radius of column. The ratio between maximum compressive stress and maximum tensile stress is

• A. 2
• B. 2.5
• C. 3
• D. None of these

Answer 1

The correct option is D None of these

The normal stress, $\sigma =\frac{P}{A}\pm \frac{M}{Z}$
$=\frac{P}{A}\pm \frac{Pe}{\frac{\left(\frac{\pi d^4}{64}\right)}{\frac{d}{2}}}$
$=\frac{P}{A}\pm \frac{Pe}{A\left(\frac{d}{8}\right)}$
$=\frac{P}{8}(1\pm \frac{e}{\frac{d}{8}})$
Maximum compressive stress, ${\sigma }_c=\frac{P}{A}(1+\frac{e}{\frac{d}{8}})$
$\left(\begin{array}{c}\text{Sign convection used}\\ \text{Compression}\to +ve\\ \text{Tension}\to \to ve\end{array}\right)$
Maximum tensile stress, ${\sigma }_t=\frac{P}{A}(1-\frac{e}{\frac{d}{8}})$
$\frac{{\sigma }_c}{{\sigma }_t}=\left(\frac{1+8e/d}{1-8e/d}\right)=\left(\frac{1+\frac{8\times d/8}{d}}{1-\frac{8\times d/8}{d}}\right)=\frac{2}{0}[\text{Given}:e=\frac{d}{8}]$
This implies that tension does not occur anywhere in the column. Hence, option(d) is correct.