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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.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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 ↑
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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