$7\mathrm{.}4-15$ A sign is supported by a pipe $($see figure$)$ having outer diameter $110$ mm and inner diameter $90$ mm $.$ The dimensions of the sign are $\backslash (2\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash$times $1\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash ),$ and its lower edge is $3\mathrm{.}0$ m above the base. Note that the center of gravity of the sign is $1\mathrm{.}05$ m from the axis of the pipe. The wind pressure against the sign is $1\mathrm{.}5$ kPa $.$

Determine the maximum in$-$plane shear stresses due to the wind pressure on the sign at points $\backslash ($ A$,$ B $\backslash ),$ and $\backslash ($ C $\backslash ),$ located on the outer surface at the base of the pipe.

PROB. $7\mathrm{.}4-15$