Problem $1$

A built$-$up beam section is formed by welding $2L861$ angles to the bottom flange of

W$36$x$210$ as shown in Fig. $1.$

Determine the following section properties of the built$-$up cross section:

Cross sectional area, $A(i{n}^2)$

The location of the centroids CG$-$X and CG$-$Y id of the built up section from the

bottom of angle $($this value is given, so you need to check that you get this value$)$

Moments of inertia ICG.X $($in ${?}^4)$ and ICG$-$Y $($in ${?}^4)$

Section modulus $Sx($bot$)(i{n}^3)$ and $Sx(top)(i{n}^3)$

Radius of gyration $rx($in$)$ and $ry($in$)$

Weight of the built up section, $w(1\frac{b}{f}t)($use density of steel $=490pcf)$

Surface area of the built$-$up section, $S(f\frac{t^2}{f}t)$

W $36210$

$d=36\mathrm{.}7$ in $,A=61\mathrm{.}9i{n}^2$

$I_x=13200i{n}^4,l_y=411i{n}^4$

bf $=12\mathrm{.}2$ in$,$ tf $=1\mathrm{.}36$ in$,$ tw $=0\mathrm{.}83$ in

L $861$

$A=13\mathrm{.}1i{n}^2$

$I_x=80\mathrm{.}9i{n}^4,I_y=38\mathrm{.}8i{n}^4$

Ybar $=2\mathrm{.}65$ in$,$ xbar $=1\mathrm{.}65$ in

Fig. $1$