Example 8⁸

Problem: The allowable stress in the machine element shown is 90 MPa. Determine the allowable bending moment when the radius r of the semicircular portions of the grooves is

a) 10 mm
b) 15 mm

This is the same for both parts since its width (50 mm) does not change.

a) D/d = 100/50 = 2 and r/d = 10/50 = 0.2. From 4.32 on page 234 (of the third edition), K = 1.77. The stress is

where the factor of 10⁹ has been added to make the units work out.

b) For this case, r/d = 15/50 = 0.3. D/d is still the same. K = 1.55. The stress is

⁸ This is Problem 4.64 in Beer & Johnston's Mechanics of Materials, 2^nd Edition, McGraw-Hill.