$8\mathrm{.}7$ and $8\mathrm{.}8($a$)$ Knowing that ${}_{\text{a}\text{l}\text{l}}=165$MPa and ${}_{\text{a}\text{l}\text{l}}=100$MPa, select the most economical wide$-$flange shape that should be used to support the loading shown. $($b$)$ Determine the values to be expected for ${}_m,{}_m,$ and the principal stress ${}_{\text{m}\text{a}\text{x}}$ at the junction of a flange and the web of the selected beam.

Fig. P$8\mathrm{.}7$