Using the AISC equations, select from Appendix B the lightest-weight structural A992 steel column that is 12 ft long and supports an axial load of 40 kip. The ends are fixed.

Question

Accepted Answer

Try [latex]W6 imes 9 \quad A=2.68 \mathrm{in}^{2} \quad r_{y}=0.905 \mathrm{in}[/latex]

[latex]\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(12)(12)}{0.905}=79.56 \\frac{K L}{r_{y}}<\left(\frac{K L}{r} ight)_{c}[/latex]

Intermediate column

[latex]\sigma_{ ext {allow }} =\frac{\left[1-\frac{1}{2}\left(\frac{K L / r}{(K L / r)} ight)^{2} ight] \sigma_{y}}{\left[\frac{5}{3}+\frac{3}{8}\left(\frac{K L / r}{(K L / r)_{c}} ight)-\frac{1}{8}\left(\frac{K L / r}{(K L / r)_{c}} ight)^{3} ight]}=\frac{\left[1-\frac{1}{2}\left(\frac{79.56}{107} ight)^{2} ight] 50}{\left[\frac{5}{3}+\frac{3}{8}\left(\frac{79.56}{107} ight)-\frac{1}{8}\left(\frac{79.56}{107} ight)^{3} ight]}=15.40 \mathrm{ksi} \P_{ ext {allow }} =\sigma_{ ext {allow }} A \=19.10(2.68) \=51.2 \mathrm{kip}>40 \mathrm{kip} \quad \mathrm{OK}[/latex]

Use [latex]W6 imes 9[/latex]

Question 13.86: Using the AISC equations, select from Appendix B the lightes...

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