Based on this problem as an example, only that instead of C$12$ x $30$ it was C$10$ x $20$ and what it entails in data in your diagram, please

The two C$1020$s shown in Fig. $4\mathrm{.}2$ have been selected to support a dead tensile working load of $120k$ and a $240-k$ live tensile working load. The member is $30ft$ long. consists of A$36$ steel, and has one line of three $7/8-$in bolts in each channel flange $3$ in on center. Using the AISC Specification, determine whether the member is satisfactory and design the necessary tie plates. Assume centers of bolt holes are $1\mathrm{.}75$ in from the backs of the channels.

Solution. Using each, $t_f=0\mathrm{.}501in,I_x=162i{n}^4$ each, $I_y=5\mathrm{.}12i{n}^4$ each, $y$ axis $0\mathrm{.}674$ in from back of $C,r_y=0\mathrm{.}762$ in$)$

FIGURE $4\mathrm{.}2$ as reference

Built$-$up section for Example $4-3.$