The equivalent length of the column when both the ends are fixed
| The equivalent length of the column when both the ends are fixed is ________.
A. L
B. L/2
C. L/4
D. 2L
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
Buckling load: the load at which column buckle is termed as Buckling load.
Buckling load is given by:
\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{L_e^2}}\)
where
E = Young’s modulus of elasticity
Imin = Minimum moment of inertia
Le = Effective length
|
End conditions |
Le |
Buckling load |
|
Both ends hinged |
Le = L |
\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{L^2}}\) |
|
Both ends fixed |
\({L_e} = \frac{L}{2}\) |
\({P_b} = \frac{{{4\pi ^2}E{I_{}}}}{{L^2}}\) |
|
One end fixed and another end is free |
Le = 2L |
\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{4L^2}}\) |
|
One end fixed and another end is hinged |
\({L_e} = \frac{L}{{\sqrt 2 }}\) |
\({P_b} = \frac{{{2\pi ^2}E{I_{}}}}{{L^2}}\) |