Using the AISC equations, select from Appendix B the lightest-weight structural A992 steel column that is 30 ft long and supports an axial load of 200 kip. The ends are fixed.

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[latex] ext { Try } \mathrm{W} 8 imes 40 \quad r_{y}=2.04 ext { in. } \quad A=11.7 \mathrm{in}^{2} \\left(\frac{K L}{r} ight)_{c}=\sqrt{\frac{2 \pi^{2} E}{\sigma_{Y}}}=\sqrt{\frac{2 \pi^{2}(29)\left(10^{3} ight)}{50}}=107 \\frac{K L}{r_{y}}=\frac{0.5(30)(12)}{2.04}=88.24[/latex]

[latex]\left(\frac{K L}{r_{y}} ight)<\left(\frac{K L}{r} ight)_{c}[/latex] intermediate column.

[latex]\sigma_{ ext {allow }}=\frac{\left\{1-\frac{1}{2}\left[\frac{\frac{K L}{r}}{\left(\frac{K L}{r} ight)_{c}} ight]^{2} ight\} \sigma_{Y}}{\left.\left\{\frac{5}{3}+\frac{3}{8}\left[\frac{\frac{K L}{r}}{\left(\frac{K L}{r} ight)_{c}} ight]-\frac{1}{8}\left[\frac{\frac{K L}{r}}{\left(\frac{K L}{r} ight)_{c}} ight] ight\}^{3} ight\}} \=\frac{\left\{1-\frac{1}{2}\left[\frac{86.54}{107} ight]^{2} ight\} 50}{\left\{\frac{5}{3}+\frac{3}{8}\left[\frac{86.54}{107} ight]-\frac{1}{8}\left[\frac{86.54}{107} ight]^{3} ight\}}=17.315 \mathrm{ksi}[/latex]

[latex]P_{ ext {allow }}=\sigma_{ ext {allow }} A=17.315(11.7)=203 \mathrm{kip}>P=200 \mathrm{kip} \quad OK[/latex]

Use [latex]W 8 imes 40[/latex]

Question 13.84: Using the AISC equations, select from Appendix B the lighte...

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