Question

A circular column of external diameter $D$, and internal diameter d, carries an eccentric load such that tension is developed nowhere. What shall be the diameter of the core ?

• A. $\frac{D^2+d^2}{8D}$
• B. $\frac{D^2-d^2}{8D}$
• C. $\frac{D^2+d^2}{4D}$
• D. $\frac{D^2-d^2}{4D}$

Answer 1

The correct option is C $\frac{D^2+d^2}{4D}$

For no tension, ${\sigma }_{min}\le 0$
$\frac{P}{A}-\frac{My}{I}\ge 0$
$\frac{P}{\frac{\pi }{4}(D^2-d^2)}-\frac{Pe\frac{D}{2}}{\frac{\pi }{64}(D^4-d^4)}\le 0$
$e\le \frac{(D^2-d^2)}{8D}$
$Diameterofcore=2e=\frac{D^2+d^2}{4D}$