Question

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends closed to the case with both ends hinged is

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

Answer:

C. 4

The critical buckling load of a slender column with both ends closed to both ends hinged is in the ratio of 4:1. The theoretical critical buckling load formula is$P_{cr} = \frac{\pi^ 2 EI}{ L_{eff} ^ 2}$ where L is the effective length of the column depends on the end condition. For both ends fixed, $P_{cr},1= \frac{\pi ΕΙ}{ (L/2)2}$ and for both ends hinged, $P_{cr}, 2 =\frac{ \pi^ 2 EI}{L^ 2},$The required ratio is $\frac{P_{cr},1}{P_{cr},2}$ =$\frac{\pi^ 2 EI}{ (L/2)^ 2}\times \frac{L^2}{\pi^2EI}=4$