A hollow shaft made of red-brass copper (G= 37 GPa, shear yield strength = 150 MPa) is sandwiched between two solid shafts made of the same material. End A is fixed to a rigid wall and torques are applied to the shaft as shown. 75 kNm d₂160 kNm A d₁ L₁ B Use the following values in your working out: L₂ L₁ = 1.5 m L3 = 2.2 m d₁ = 1 m d₂ = 0.7 m d3 = 1.2 m C dz L₂ 130 kNm D a) Draw a torque diagram for the entire shaft. b) Determine the maximum allowable inner diameter for the hollow section of the shaft, to the nearest mm. c) Determine the maximum length of L₂ (to the nearest mm) that will ensure the angle of twist of D relative to the wall is less than 2°. Use your value from part b for the inner diameter of the hollow shaft.
A hollow shaft made of red-brass copper (G= 37 GPa, shear yield strength = 150 MPa) is sandwiched between two solid shafts made of the same material. End A is fixed to a rigid wall and torques are applied to the shaft as shown. 75 kNm d₂160 kNm A d₁ L₁ B Use the following values in your working out: L₂ L₁ = 1.5 m L3 = 2.2 m d₁ = 1 m d₂ = 0.7 m d3 = 1.2 m C dz L₂ 130 kNm D a) Draw a torque diagram for the entire shaft. b) Determine the maximum allowable inner diameter for the hollow section of the shaft, to the nearest mm. c) Determine the maximum length of L₂ (to the nearest mm) that will ensure the angle of twist of D relative to the wall is less than 2°. Use your value from part b for the inner diameter of the hollow shaft.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A hollow shaft made of red-brass copper (G = 37 GPa, shear yield strength = 150 MPa) is sandwiched between two solid shafts
made of the same material. End A is fixed to a rigid wall and torques are applied to the shaft as shown.
75 kNm
d₂160 kNm
A
d₁
L₁
B
Use the following values in your working out:
L₂
L₁ = 1.5 m
L3 = 2.2 m
d₁ = 1 m
d₂ = 0.7 m
d3 = 1.2 m
C
d₂
3
L3
130 kNm
D
a) Draw a torque diagram for the entire shaft.
b) Determine the maximum allowable inner diameter for the hollow section of the shaft, to the nearest mm.
c) Determine the maximum length of L₂ (to the nearest mm) that will ensure the angle of twist of D relative to the wall is less
than 2°. Use your value from part b for the inner diameter of the hollow shaft.
d) By estimating relevant load(s), dimensions, and material properties, calculate the approximate angle of twist between two
(non-coincident) points on the object shown below. Clearly state all assumptions, including the location of the chosen points.
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