PROBLEM 3.3-20

The shaft in Figure below consists of a 3-in. -diameter aluminum segment that is rigidly joined to a 2-in. -diameter steel segment. The ends of the shaft are attached to rigid supports, Calculate the maximum shear stress developed in each segment when the torque T= 10 kip.in is applied. Use G = 4×106 psi for aluminum and G = 12×106 psi for steel. Aluminum 3-in. diameter 6 ft T Steel 2-in. diameter 3 ft

A circular steel tube of length L = 1.1 m is loaded in torsion by torques T (see figure). T T r2 (a) If the inner radius of the tube is r, = 51 mm and the measured angle of twist between the ends is 0.5°, what is the shear strain y, (in radians) at the inner surface? (Enter the magnitude.) rad (b) If the maximum allowable shear strain is 0.00043 rad and the angle of twist is to be kept at 0.45° by adjusting the torque T, what is the maximum permissible outer radius (r,)may (in mm)? mm

A circular hollow shaft is subjected to a torsional moment T = 30 kNm and a compressiveload P = 80 kN, as shown. The shaft has an outer diameter D = 120 mmand inner diameter d = 100 mm. Points A and B are on the surface of the shaft. (a)Calculate the direct and shear stress at point A. (b)Calculate the maximum,minimum and oriention of the max and min principal stresses at point A. (c)Calculate the maximum in-plane shear stress at point A and the orientation.

A = Tab Problem 1. An ellipse with semi-major axis a = 150 mm and semi-minor axis b = 100 mm is etched on a brass plate. The plate has dimensions 400 x 400 × 20 mm. Uniformly distributed normal stresses ox = -25 MPa and o, = 50 Mpa are applied to the plate. The Young's modulus E = 100 GPa, and Poisson's ratio v = 0.34. (Note: The ellipse remains an ellipse after stretching, but with different semi-major and semi-minor axes.) Find: a) The change in the area of the ellipse. Oy The in the thickness of the plate. b) c) The change AV in the volume of the plate. Ox a. -b- Ox a d) The strain energy, U, stored in the plate. Ty