Problem Statement: Plot the column curve, as defined in AISC Specification Section E$3,$ two ways for each of the cases listed below. The first plot should have $P_n$ on the vertical axis and $L_c$ on the horizontal axis $($show $L_c$ from $0$ to $70ft.).$ The second plot should have $F_n$ on the vertical axis and $\frac{L_c}{r}$ on the horizontal axis $($show $\frac{L_c}{r}$ from $0$ to $250).$ All six cases should be plotted on each of the two figures $($some lines will overlap$).$ Prepare the plots with a computer $($hand$-$drawn figures are not acceptable$).$

$($a$)W14159,F_y=50$ksi, major$-$axis

$($b$)$ W$14$x$159,F_y=65$ksi, major$-$axis

$($c$)W14159,F_y=50$ksi, minor$-$axis

$($d$)$ W$14$x$159,F_y=65$ksi, minor$-$axis

$($e$)W18158,F_y=50$ksi, major$-$axis

$($f$)W18158,F_y=50$ksi, minor$-$axis

On the $P_n$ vs$.L_c$ plot, why do cases $($a$),($c$),($e$),$ and $($f$)$ converge at $L_c=0ft.?$

On the $P_n$ vs$.L_c$ plot, why do cases $($a$)$ and $($b$)$ converge at large values of $L_c?$

On the $F_n$ vs$.\frac{L_c}{r}$ plot, why do only two distinct lines appear?