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UPRVUNL JE ME 2016 Official Paper Shift 1

Option 1 : Both the ends are hinged

__Explanation:__

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, I = Minimum Moment of Inertia, and 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 |
\({L_e} = \frac{L}{{\sqrt 2 }}\) |
\({P_b} = \frac{{{2\pi ^2}E{I_{}}}}{{L^2}}\) |