Question
Download Solution PDFColumns of given length, cross section and material, have different values of crippling loads, for different end conditions. The strongest column is one whose:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The load at which column buckle is termed as buckling load. According to Euler, Buckling load is given as:
\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{L_e^2}}\)
where E = Young’s Modulus of Elasticity, I = Minimum Moment of Inertia, and Le = Effective length
|
End conditions |
Effective length (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 |
\({L_e} = \frac{L}{{\sqrt 2 }}\) |
\({P_b} = \frac{{{2\pi ^2}E{I_{}}}}{{L^2}}\) |
Hence, The maximum buckling load will be in Both ends fixed condition and hence fixed column will be strongest column \({P_b} = \frac{{{4\pi ^2}E{I_{}}}}{{L^2}}\)
Last updated on Jun 4, 2025
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