Answer 1 and 2 questions  A hollow aluminum tube used is a roof structure has an outside diameter 70mm and inside diameter 50mm. The tube is 3m long and the aluminum has a shear modulus of G=28 GPa. 1.If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist in degrees when the max shear stress is 50 MPa? 2.What diameter “d” is required for a solid shaft to resist the same torque with the same maximum stress?

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A circular aluminum tube subjected to pure torsion by torque T (see figure) has an outer radius r, equal to 1.5 times the inner radius r,. T (a) If the maximum shear strain in the tube is measured as 460 x 10-° rad, what is the shear strain y, (in radians) at the inner surface? rad (b) If the maximum allowable rate of twist is 0.126°/m and the maximum shear strain is to be kept at 460 x 10-6 rad by adjusting the torque T, what is the minimum required outer radius (r..min' in mm)? mm

6- A circular shaft is composed of a steel core and a brass covering, as shown in the figure. Under the applied torque, what is the maximum shear stress in each material? The composite shaft is attached to a wall at A. B O T= 5 KN•m Steel core r=15mm G=78 GPa bross cylinder ro=20mm (outer diameter) G=39 GPa