Question

A slender pin-ended aluminium column 1.8 m long and of circular cross-section is to have an outside diameter of 50 mm. Calculate the necessary internal diameter to prevent failure by buckling if the actual load applied is 13.6 kN and the critical load applied is twice the actual load. Take \( E \) for aluminium as \( 70 \) GN/m\(^2\).

• A. 39.4 mm
• B. 47.2 mm
• C. 43.7 mm
• D. 42.8 mm

Hint:

- Hollow columns provide higher strength with less material. - Use Euler’s formula for buckling loads.

Answer 1

The Correct Option is C

- Use Euler's buckling formula: \[ P_{cr} = \frac{\pi^2 E I}{(L_{eff})^2} \] - Given \( P_{cr} = 2 \times 13.6 \) kN, solving for internal diameter: \[ d_i = 43.7 \text{ mm} \]