$(10$ pts$)$ Problem $4$:

A structural steel built$-$up section is fabricated as shown $($two W$1022$ rolled section welded together$).$ Calculate the least radius of gyration for the built$-$up section.

Given: Cross$-$section geometric properties of the built$-$up section

$Ix=571\mathrm{.}63i{n}^4$

$ly=22\mathrm{.}80i{n}^4$

Area $=12\mathrm{.}98i{n}^2$