Part $1(40$ points$)$: A plan view of a multi$-$purpose hall for condominium development is shown on

page $2.$ The roof of the structure $($Figure $1\mathrm{.}1),$ which serves for large social gatherings, consists of a

$5-$in$.$ thick lightweight concrete $/$ metal deck system. This deck rests on roof purlins, which in turn

frame into the panel points on the top chord of simply supported steel roof trusses. An elevation

view of the trusses, which are spaced every $10ft,$ is illustrated in Fig. $1\mathrm{.}2.$

Find maximum internal axial force in tension for element L$2-$L$3.$ Solve for dead load and "partial roof

live load". Use ultimate, factored loads shown in Fig. $1\mathrm{.}2$: $F_q=20$kips,$F_{q1}=12\mathrm{.}8$kips,$F_{q2}=7\mathrm{.}2$kips.

Assume the factored load on U$1$ is also Fq$.$