_______________________________________________________________________ PROBLEM (*9.36) The shaft ABC shown in Fig. P9.36 is driven by a motor, which delivers through the gears 30 kW at a speed of n = 500 rpm to a machine connected to the shaft DE. Calculate the required diameter d of shaft ABC if the allowable shear stress is not to exceed τ all . Given: a = 120 mm, r = 100 mm. τ all = 50 MPa, n = 600 rpm *SOLUTION 9550 P 9550(30) = = 477.5 N ⋅ m 12 600 Tangential force F at gear A: T 477.5 F= = = 4775 N r 0.1 Bending moment at B: M B = Fa = 4775(0.12) = 573 N ⋅ m Mc M (d 2) 32 M 16T σ= = = τ= 3 4 3 I π d 64 π d πd Hence 16 τ max = τ all = 3 M 2 + T 2 πd or 16 d all = 3 πτ all M 2 + T 2 T= 16 5732 + 477.52 6 π (50 ×10 ) = 0.042.4 m = 42.4 mm = 3 Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.