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Critical load Fcr or buckling load is the value of load that causes the phenomenon of change from stable to unstable equilibrium state.
With that beign said, first it is neessary to calculate the moment of inercia about the x-axis:
[tex]Ix= \frac{db^3}{12}\\ Ix = \frac{2.(4)^3}{12} = 10.667in[/tex]
Then it is necessary to calculate the moment of inercia about the y-axis:
[tex]Iy = \frac{db^3}{12}\\ Iy = \frac{4.(2)^3}{12} = 2.662in[/tex]
Comparing both moments of inercia it is possible to assume that the minimun moment of inercia is the y-axis, so the minimun moment of inercia is 2662in.
And so, it is possible to calculate the critical load:
[tex]Pc\gamma = \frac{2046\pi ^2E.I}{L^2} \\Pc\gamma= \frac{2046.\pi ^2.(1,6.10^3.10^3).2662}{(10.12)^2} \\Pc\gamma= 5983,9db[/tex]
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