Problem $1(40$ points$)$:

Shaft $BC$ is hollow with inner and outer diameters of $80$ mm and $110$ mm $,$ respectively. Shafts $AB$ and $CD$ are solid and of diameter $d.$ For the loading shown, determine $($a$)$ the minimum and maximum shearing stress in shaft $BC,(b)$ the required diameter $d$ of shafts $AB$ and $CD$ if the allowable shearing stress in these shafts is $70$ MPa $.$