Answered: A compound shaft drives three gears, as…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A compound shaft drives three gears, as shown in Figure
P6.14. Segments (1) and (2) of the shaft are hollow bronze [G =
6,500 ksi] tubes with an outside diameter of 1.75 in. and a wall
thickness of 0.1875 in. Segments (3) and (4) are solid 1.00 in. diameter
steel [G = 11,500 ksi] shafts. The shaft lengths are L1 = 60 in.,
L2 = 14 in., L3 = 20 in., and L4 = 26 in. The torques applied to the
shafts have magnitudes TB = 960 lb ⋅ ft, TD = 450 lb ⋅ ft, and TE =
130 lb ⋅ ft, acting in the directions shown. The bearings shown allow
the shaft to turn freely. Calculate
(a) the maximum shear stress in the compound shaft.
(b) the rotation angle of flange C with respect to flange A.
(c) the rotation angle of gear E with respect to flange A.

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Follow-up Question

For T_max=TC/J in the first part why is 16 in the numerator

a.
The value of maximum torque,
Tax = 640 lb.ft
16ta d₂
r(d + = G+)
16x640×12×1.75
(1.75 -1.375*)
Tmax=11792.58 psi

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