A compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze [G = 6,500 ksi] tubes, which have an outside diameter of 1.55 in. and a wall thickness of 0.1975 in. Segments (3) and (4) are solid 1.10-in.-diameter steel [G = 11,500 ksi] shafts. The shaft lengths are L1 = 78 in., L2 = 8 in., L3 = 25 in., and L4 = 25 in. The torques applied to the shafts have magnitudes of TB = 940 lb·ft, TD = 500 lb·ft, and TE = 100 lb·ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign convention presented in Section 6.6., calculate: (a) the magnitude of 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.
A compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze [G = 6,500 ksi] tubes, which have an outside diameter of 1.55 in. and a wall thickness of 0.1975 in. Segments (3) and (4) are solid 1.10-in.-diameter steel [G = 11,500 ksi] shafts. The shaft lengths are L1 = 78 in., L2 = 8 in., L3 = 25 in., and L4 = 25 in. The torques applied to the shafts have magnitudes of TB = 940 lb·ft, TD = 500 lb·ft, and TE = 100 lb·ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign convention presented in Section 6.6., calculate: (a) the magnitude of 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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze [G = 6,500 ksi] tubes, which have an outside diameter of 1.55 in. and a wall thickness of 0.1975 in. Segments (3) and (4) are solid 1.10-in.-diameter steel [G = 11,500 ksi] shafts. The shaft lengths are L1 = 78 in., L2 = 8 in., L3 = 25 in., and L4 = 25 in. The torques applied to the shafts have magnitudes of TB = 940 lb·ft, TD = 500 lb·ft, and TE = 100 lb·ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign convention presented in Section 6.6., calculate:
(a) the magnitude of 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.
![A compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze
[G = 6,500 ksi] tubes, which have an outside diameter of 1.55 in. and a wall thickness of 0.1975 in. Segments (3)
and (4) are solid 1.10-in-diameter steel [G= 11,500 ksi] shafts. The shaft lengths are L₁ = 78 in., L₂ = 8 in., L3=
25 in., and L4 = 25 in. The torques applied to the shafts have magnitudes of TB = 940 lb·ft, Tp = 500 lb-ft, and TE
= 100 lb-ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign
convention presented in Section 6.6., calculate:
(a) the magnitude of 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.
TB
TD
(1)
TE
(3)
Answer:
(a) Tmax=
(b) OC/A=
(c) ΦΕΙΑ =
A
L₁
(2)
B
L2₂
psi
rad
rad
C
L3
D
(4)
L4
E
-X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F749be18b-22f2-4fe5-9f05-6fa35acbb4d0%2F11237695-558b-4f3c-b062-6c5323336f77%2Fqeee1zll_processed.png&w=3840&q=75)
Transcribed Image Text:A compound shaft drives three gears, as shown. Segments (1) and (2) of the compound shaft are hollow bronze
[G = 6,500 ksi] tubes, which have an outside diameter of 1.55 in. and a wall thickness of 0.1975 in. Segments (3)
and (4) are solid 1.10-in-diameter steel [G= 11,500 ksi] shafts. The shaft lengths are L₁ = 78 in., L₂ = 8 in., L3=
25 in., and L4 = 25 in. The torques applied to the shafts have magnitudes of TB = 940 lb·ft, Tp = 500 lb-ft, and TE
= 100 lb-ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. Using the sign
convention presented in Section 6.6., calculate:
(a) the magnitude of 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.
TB
TD
(1)
TE
(3)
Answer:
(a) Tmax=
(b) OC/A=
(c) ΦΕΙΑ =
A
L₁
(2)
B
L2₂
psi
rad
rad
C
L3
D
(4)
L4
E
-X
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