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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

A1

B2

C4

D8

Answer:

C. 4

Read Explanation:

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 isPcr=π2EILeff2 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, Pcr,1=πEI(L/2)2P_{cr},1= \frac{\pi ΕΙ}{ (L/2)2} and for both ends hinged, Pcr,2=π2EIL2,P_{cr}, 2 =\frac{ \pi^ 2 EI}{L^ 2},The required ratio is Pcr,1Pcr,2\frac{P_{cr},1}{P_{cr},2} =π2EI(L/2)2×L2π2EI=4\frac{\pi^ 2 EI}{ (L/2)^ 2}\times \frac{L^2}{\pi^2EI}=4


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