Project ForgeStrength of Materials
Bending of Beams
GATE 2012
Easy
For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is
- A1
- B2
- 4
- D8
Explanation
Euler's critical load Pcr=π²EI/Le². For both-ends-hinged, Le=L, so Pcr=π²EI/L². For both-ends-clamped (fixed-fixed), Le=L/2, so Pcr=π²EI/(L/2)²=4π²EI/L². Ratio (clamped/hinged) = 4.
Source: GATE ME 2012 (Booklet Code A) (2012)
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