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.
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.
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= 25mm
gear radii R₁-200mm ; R₂=40mm
Torque T=4KN-m
Li
B
C
(2)
L2
* assume the gears to be rigid
↑
Expert Solution
Step 1
Given data:
Torque applied, T=4 kN-m
Shaft-1:
Material-steel
Length, L1=1.5 m
Radius, r1=50 mm
Gear radius, R1=200 mm
Shear modulus, G=85 MPa
Shaft-2:
Material-Aluminium
Length, L1=1.0 m
Radius, r1=25 mm
Gear radius, R2=25 mm
Shear modulus, G=28 MPa
It is asked to determine the angular rotation at point D relative to that of point A.
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