The solid aluminum shaft has a diameter of 50mm and an allowable shear stress of 60 mpa. determine the largest torque t1 that can be applied to the shaft if it is also subjected to the other torsional loadings

The torque is the shear strees multiplied by radius. Radius = 50mm. We'll also have to convert mpa to Newton/mm^2. 1 mpa = 1 N/mm^2. Sowe are good to go. I. e we also have 60N/mm^2. Multiplying both gives 60 N/mm^2 * 50mm = 300N