0
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.
somd-2 • 214  views
0  upvotes
0

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,

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

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

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

$e = 62.49 mm$

0  upvotes
Please log in to add an answer.

Next up

Read More Questions

If you are looking for answer to specific questions, you can search them here. We'll find the best answer for you.

Search

Study Full Subject

If you are looking for good study material, you can checkout our subjects. Hundreds of important topics are covered in them.

Know More