A pinned-pinned column has $E=29,000\text{ ksi}$, $I_y=93.4\text{ in}^4$, and $L=15\text{ ft}=180\text{ in}$. Determine the ideal elastic weak-axis buckling load.

An A992 W14x90 has $F_y=50\text{ ksi}$, $A_g=26.5\text{ in}^2$, $r_x=6.14\text{ in}$, $r_y=3.70\text{ in}$, and $KL=180\text{ in}$ about both axes. Assume the section elements are nonslender and flexural buckling governs.

A W12x50 has $r_x=5.18\text{ in}$ and $r_y=1.96\text{ in}$. The x-axis unbraced length is 24 ft while a valid mid-height brace reduces the y-axis unbraced length to 12 ft. For this idealized example use $K_x=K_y=1.0$.

A W8x24 has $A_g=7.08\text{ in}^2$, $r_y=1.61\text{ in}$, $F_y=50\text{ ksi}$, and $KL=300\text{ in}$.

A built-up box column has one or more plate elements that exceed the compression width-to-thickness limit.

A single angle is proposed as an 8 ft compression brace.

A frame analysis uses Direct Analysis assumptions, but the member calculation later substitutes an arbitrary alignment-chart $K$ value greater than 1 because the frame is unbraced.