Problem $4.$ A two$-$bar truss ABC supports a sign weighing $5\mathrm{.}4$ kN $.$ Supports at A and $C$ are pinned and $B$ is connected in double shear. The length of bar $BC$ is $3\mathrm{.}00$ m with the $5\mathrm{.}4$ kN load supported equally between $D$ and $E.$ The weight of the bars $AB$ and $BC$ can be neglected.

a$.$ What would be the minimum cross$-$sectional area for $AB$ if the allowable tensile stress is $125$ MPa $?$ Round your answer up to the nearest mm $.$

b$.$ Calculate the minimum diameter of the pin at $B$ if the allowable shear stress is $45$ MPa $.$ Round up to the nearest mm $.$