Question
Download Solution PDFIf a column is fixed at one end and free at the other end, the effective length is ______ the original length.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Buckling load:
The load at which column buckle is termed as buckling load. Buckling load is given by:
\({P_b} = \frac{{{\pi ^2}EI}}{{L_e^2}}\)
where E = Young's modulus of elasticity, Imin = Minimum moment of inertia, and Le = Effective length
End conditions | Le | Buckling load |
Both ends hinged | Le = L | \({P_b} = \frac{{{\pi ^2}EI}}{{L_e^2}}\) |
Both ends fixed | Le = L/2 | \({P_b} = \frac{{{4\pi ^2}EI}}{{L_e^2}}\) |
One end fixed and another end is free | Le = 2L | \({P_b} = \frac{{{\pi ^2}EI}}{{4L_e^2}}\) |
One end fixed and another end is hinged | \({L_e} = \frac{L}{{\sqrt 2 }}\) | \({P_b} = \frac{{{\pi ^2}EI}}{{2L_e^2}}\) |
Last updated on May 12, 2025
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