The steel pipe is fixed supported at its ends. If it is \(4 \mathrm{~m}\) long and has an outer diameter of \(50 \mathrm{~mm}\), determine its required thickness so that it can support an axial force of \(P=100 \mathrm{kN}\) without buckling. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=250 \mathrm{MPa}\).

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4 m P P