A column of length 8m with both ends fixed may be considered as e

SOLUTION

Concept:

 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 analyzed with the Euler’s column formulas can be given as

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

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

Effective Length:

\(L_{eq}=\frac{L}{n}\)

Calculation:

Given, for both ends fixed columns L = 8 m.

that is n = 2 and critical load \(P = \frac{{{4}{\pi ^2}EI}}{{{8^2}}}\)

and for both end hinged, n = 1 and critical load \(P = \frac{{{}{\pi ^2}EI}}{{{L^2}}}\)

for an equivalent column, E and I will be same as well as P will be same

so, \(\frac{{{4}{\pi ^2}EI}}{{{8^2}}} = \frac{{{}{\pi ^2}EI}}{{{L^2}}}\)

⇒ Length of the column \(L^2=\frac{8^2}{4}=16\)

⇒ L = 4 m