Torsion stress and twist criterion

[xJJx]

Hi, below i have attached a exercise sheet question with the solution, however i don't quite understand it. In torsion, the maximum shear stress of a shaft is determined using the max radius of the shaft. Also, when comparing two sections, the one with the larger radius gives a higher shear stress value. After rewatching the lecture, the professor said that a larger radius decreases the shear stress. I find this contradicting & now I am confused as to why the maximum diameter in the solution below gives a lower shear stress.

 

[Chestermiller]

I can’t read some key features of this because of your poor handwriting. Please use LaTex to display your equations.