The two$-$bar truss ABC shown in figure

has pin supports at points A and $C,$

which are $2\mathrm{.}0m$ apart. Members $AB$

and $BC$ are steel bars, pin connected at

joint B$.$ The length of bar BC is $3\mathrm{.}0m.$

A sign weighing $5\mathrm{.}4kN$ is suspended

from bar BC at points $D$ and $E,$ which

are located $0\mathrm{.}8m$ and $0\mathrm{.}4m,$

respectively, from the ends of the bar.

Determine the required diameter of the

pin at support $C$ if the allowable shear

stress is $45$MPa. $($Note: The pins at the

supports are in double shear. Also,

disregard the weights of members $AB$

and $BC.)$