$24$ points: You are building a bridge across a ${40}^{\text{'}}$ low water crossing to serve a client. The bridge is to be $16$ feet wide, and must be able to support a full, $10-$yard concrete truck $(72$ kips $).$ The bridge will be made of four, parallel, thick$-$walled, A$441$ steel pipes supported by four$-$foot thick, $16\text{'}$ wide and $6-$foot tall reinforced, concrete abutments at each end of the bridge. Assume uniform distribution of load$/$stress over the four pipes. Also assume the pipes will undergo only pure bending $($no torsion$)$ and the working stress of each pipe is $30$ ksi $.$ No middle support is desired. The bridge will be planked with ${16}^{\text{'}}-4^{\text{'}\text{'}}{4}^{\text{'}\text{'}}$ treated posts and $28$ treated lumber. Show all work.

a$.$ Design the pipe size for this bridge $($exclude the contributions of planking.$)$ Note, you should use the attached Round HSS look$-$up Tables.