A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column, if the free end is replaced with a pinned end then the critical bucking load will be N

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Solution

For a given matertial in 0.1 and length,
$P e \propto \frac{1}{α^{2}}$
$α = length fixity coefficient$
$P e = Bulking of critical load$
$\frac{(P e) 11}{(P e) 1} = {(\frac{α_{1}}{α_{11}})}^{2} = {(\frac{2 L}{1 / \sqrt{2}})}^{2} = 8$
$(P_{θ})_{11} = 8 (P_{θ})_{1} = 800 N$

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A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column, if the free end is replaced with a pinned end then the critical bucking load will be N

For a given matertial in 0.1 and length, Pe∝1α2 α=length fixity coefficient Pe=Bulking of critical load (Pe)11(Pe)1=(α1α11)2=(2L1/√2)2=8 (Pθ)11=8(Pθ)1=800N

For a given matertial in 0.1 and length,
$P e \propto \frac{1}{α^{2}}$
$α = length fixity coefficient$
$P e = Bulking of critical load$
$\frac{(P e) 11}{(P e) 1} = {(\frac{α_{1}}{α_{11}})}^{2} = {(\frac{2 L}{1 / \sqrt{2}})}^{2} = 8$
$(P_{θ})_{11} = 8 (P_{θ})_{1} = 800 N$