Question: A short column of external dia 40 cm and internal diameter 20 cm carries an eccentric load of 80 kN.Find greatest eccentricity which the load can have without producing tension on the cross-section.
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somd-2 • 18 views
 modified 8 days ago  • written 8 days ago by
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Given:

For short circular (hollow) column

D = 40 cm = 400 mm

d = 20 cm = 200 mm

Criteria - no tensional base

Solution:

C/S Area = $A = \frac{\pi}{4}(D^{2} - d^{2}) = \frac{\pi}{4}(400^{2} - 200^{2}) = 94.25 \times 10^{3} mm^{2}$

M I = $I = \frac{\pi}{64}(D^{4} - d^{4}) = \frac{\pi}{64}(400^{4} - 200^{4}) = 11.78 \times 10^{8} mm^{4}$

$y_{max} = \frac{D}{2} = \frac{400}{2} = 200 mm$

For no tension Condition,

$\sigma_{o} = \sigma_{b}$

$\therefore \frac{P}{A} = \frac{P.e.y_{max}}{I}$

$\therefore e = \frac{I}{A \times y_{max}} = \frac{11.78 \times 10^{8}}{94.25 \times 10^{3} \times 200}$

$e = 62.49 mm$