"4₂ A two celled tube with wall thickness 0.5 mm is subjected to a torque of 10 N.m as shown in Fig.(4). The resulting shear flows in two shells are shown below

(30%) A circular aluminum tube subjected to T pure torsion by torques T has an outer radius r2 equal to 2 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 500x10-6 rad, what is the shear strain y1 at the inner surface? (b) If the maximum allowable rate of twist (0) is 0.15°/m and the maximum shear strain is to be kept at 500x10-6 rad by adjusting the torque T, what is the minimum required outer radius (r2 )min?

Q2(c) The steel alloy shaft having a diameter of 38 mm is used to transmit torque, T as shown in Figure Q2(c). If the allowable shear stress of the shaft is 80kPa, i)Determine the maximum torque T that can be transmitted by the shaft. ii)What would be the maximum torque T' if a 25 mm diameter hole is bored through the shaft? Figure Q2(c.) |Q2 c) (i) T c The torsion formula :7 = J Т (0.019) T (0.019)^4 ; Therefore, the max torque T = x10 Nm 80 2 Q2 c) (ii) For point lying on the outside suurface of the shaft: x10 ="(0.019) * (0.019*-0.0125 ) ; Therefore the max torque T' Nm 80 2 Q2 c) (iii) The shear stress at point located at inner surface of shaft, T'c T = -= J ) (0.0125) = 7 (0.019*-0.01254) T'c kPa 4. 2 2.

1) A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending moment that results in a variable stress (M=60 MPa) due to loads by bearings and gears, and a steady torque (T-80 MPa). However, these stress values do not take into account stress concentration factors. The shaft has a D=45 mm, d=30 mm, and r=6 mm, resulting in kr,bend=1.34, Kr,axial=1.48, and kf,tor 1.2. The shaft is made of steel with S₁=1006 MPa, S,=648 MPa, and H₂=229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 90% reliability is required. Verify the stress concentration factors are correct for this shaft geometry. Calculate the safety factor relative to infinite life (105 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure. (60) M