The steel pipe is fixed supported at its ends. If it is 4 m long and has an outer diameter of 50 mm, determine its required thickness so that it can support an axial load of P=100 kN without buckling. E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=250 \mathrm{MPa}
Critical Load:
P_{\mathrm{cr}}=\frac{\pi^{2} E I}{(K L)^{2}} ; \quad K=0.5 \\100\left(10^{3}\right)=\frac{\pi^{2}(200)\left(10^{9}\right)\left[\frac{\pi}{4}\left(0.025^{4}-r_{i}^{4}\right)\right]}{[0.5(4)]^{2}} \\r_{i}=0.01908 \mathrm{~m}=19.1 \mathrm{~mm} \\t=25 \mathrm{~mm}-19.1 \mathrm{~mm}=5.92 \mathrm{~mm}Check Stress:
\sigma=\frac{P_{\mathrm{cr}}}{A}=\frac{100\left(10^{3}\right)}{\pi\left(0.025^{2}-0.0191^{2}\right)}=122 \mathrm{MPa}<\sigma_{Y}=345 \mathrm{MPa}