The bracket shown in the figure has the same circular cross$-$section along the

entire length. External force is $200$ kN and it acts in y $-$direction. Shear failure

stress is $80$ MPa $.$ The factor of safety is $2\mathrm{.}5$

Hint: This is not a bending problem, but a simple shear problem $($at point A$).$

Write the final solution in the box for this question.

$($a$)$ What is the amplitude of the force reaction at the support A$?$

$($b$)$ What is the allowable shear stress?

$($c$)$ Determine the diameter $(4$ decimal places$)$ of the circular cross$-$

section, in meters, at which the shear stress will be equal to the

allowable shear stress.

Please answer all parts of the question with solution.