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Which of the following factors does NOT affect the buckling load?


1. Modulus of Elasticity
2. Slenderness ratio
3. Area of cross-section
4. Area moment of inertia

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Correct Answer - Option 3 : Area of cross-section

Explanation:

Column:

  • If a beam element is under a compressive load and its length is an order of magnitude larger than either of its other dimensions such a beam is called a column.
  • Due to its size, its axial displacement is going to be very small compared to its lateral deflection called buckling.


Euler's Buckling Load:

\( {P_{cr}} = \frac{{{{\rm{\pi }}^2}E{I_{\min }}}}{{l_e^2}}\)

where, Pcr = crtical load for buckling; E = Young's Modulus (GPa); Imin = Area moment of inertia, l= effective length; kmin  = minimum raduis of gyration

Slenderness Ratio (S): 

The ratio between the length and least radius of gyration.

\(S = \frac{{{l_e}}}{{{k_{\min }}}}\)

Hence, buckling load does not depend on the area of the cross-section.

Buckling load for various end conditions is given in the table below.

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

\({L_e} = \frac{L}{{\sqrt 2 }}\)

\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{2L^2}}\)

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