Question

Four columns of the same material and having identical geometric properties are supported in different ways as shown below



It is required to order these four beams inthe increasing order of their respective first buckling loads. The correct order is given by

• A. I, II, III, IV
• B. III, IV, II, I
• C. II, I, IV, III
• D. I, II, IV, III

Answer 1

The correct option is D I, II, IV, III

In case I, $l_{eff}=2l$
In caseII, $l_{eff}=l$
In case III,$l_{eff}=\frac{l}{2}=0.5l$
In case IV,$l_{eff}=\frac{l}{\sqrt{2}}=0.707l$

$\therefore$ We know that other condition remaining same if effective length is increased, bunkling load will decrease.
Hence in the order of increasing buckling load we will have I, II, IV, III