What will be the effect on Euler’s crippling load for a column wi

SOLUTION

The maximum load at which the column tends to have lateral displacement or tends to buckle is known as buckling or crippling load. Load columns can be analysed with the Euler’s column formulas can be given as

\(P = \frac{{{n}{\pi ^2}EI_{min}}}{{{L^2}}}\)

• For both end hinged, n = 1
• For one end fixed and other free, n=1/4
• For both end fixed, n = 4
• For one end fixed and other hinged, n = 2

For both end hinged (Where length of column is halved):

Here, L' = L/2 

\(P = \frac{{{}{\pi ^2}EI_{min}}}{{{L^2}}} \Rightarrow P = \frac{1}{L^2}\)

Therefore, \(\frac{P'}{P}=(\frac{L}{L'})^2\)

\(\frac{P'}{P}=(\frac{L}{L/2})^2=4\)

Therefore, P' = 4P