4 - Two circular shafts are connected via a gear assembly as shown in the figure. Shaft 1 is fixed to a wall at point A. Torque T is applied to shaft 2 at point D. Shaft 1 is made of steel with a shear modulus of 85 GPa; shaft 2 is made of aluminum with a shear modulus of 28 GPa. The other relevant paramters are indicated alongside the figure. The shafts are restrained by bearings such that they do not undergo bending (i.e., it is a case of pure torsion). Determine the angular rotation at point D relative to that at point A. Shafts L₁=1.5m; L₂= Im r=50mm; ₂= 25mm gear radii R₁-200mm ; R₂-40mm Torque T=4kN-m Li thes B C L2 T
4 - Two circular shafts are connected via a gear assembly as shown in the figure. Shaft 1 is fixed to a wall at point A. Torque T is applied to shaft 2 at point D. Shaft 1 is made of steel with a shear modulus of 85 GPa; shaft 2 is made of aluminum with a shear modulus of 28 GPa. The other relevant paramters are indicated alongside the figure. The shafts are restrained by bearings such that they do not undergo bending (i.e., it is a case of pure torsion). Determine the angular rotation at point D relative to that at point A. Shafts L₁=1.5m; L₂= Im r=50mm; ₂= 25mm gear radii R₁-200mm ; R₂-40mm Torque T=4kN-m Li thes B C L2 T
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:4 - Two circular shafts are connected via a
gear assembly as shown in the figure.
Shaft 1 is fixed to a wall at point A. Torque
T is applied to shaft 2 at point D. Shaft 1 is
made of steel with a shear modulus of 85
GPa; shaft 2 is made of aluminum with a
shear modulus of 28 GPa. The other
relevant paramters are indicated alongside
the figure. The shafts are restrained by
bearings such that they do not undergo
bending (i.e., it is a case of pure torsion).
Determine the angular rotation at point D
relative to that at point A.
Shafts L₁=1.5m; L₂=1m
r=50mm; ₂= 25 mm
gear radii R₁-200mm; R₂=40mm
Torque T=4KN-m
Li
C
L2
* assume the gears to be rigid
T
Expert Solution
Step 1
Given:-
The shear modulus of steel shaft 1 = 85 GPa
The shear modulus of aluminum shaft 2 = 28 GPa
The length of the shaft 1 = 1.5 m
The length of the shaft 2 = 1 m
The radius of the shaft 1 = 50 mm
The radius of the shaft 2 = 25 mm
The radius of the gear 1 = 200 mm
The radius of the gear 2 = 40 mm
The magnitude of the torque developed = 4 kN-m
To determine:-
The angular rotation at point D relative to that at point A
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