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Questions and Answers
What material is the entire shaft made of?
What material is the entire shaft made of?
- Aluminum
- Brass
- Steel (correct)
- Copper
What is the diameter of the hole drilled into portion CD of the shaft?
What is the diameter of the hole drilled into portion CD of the shaft?
- 50 mm
- 44 mm (correct)
- 40 mm
- 60 mm
What is the allowable stress for the aluminum tube?
What is the allowable stress for the aluminum tube?
- 70 MPa (correct)
- 80 MPa
- 90 MPa
- 50 MPa
What is the correct equation for angular velocity in terms of frequency?
What is the correct equation for angular velocity in terms of frequency?
What is the required tube thickness for a steel tube transmitting 100 kW at 20 Hz to prevent shearing stress from exceeding 60 MPa?
What is the required tube thickness for a steel tube transmitting 100 kW at 20 Hz to prevent shearing stress from exceeding 60 MPa?
What is the shear modulus G value for steel mentioned?
What is the shear modulus G value for steel mentioned?
In the context provided, what is the role of the free-body diagrams?
In the context provided, what is the role of the free-body diagrams?
What is the maximum allowable stress in the steel shaft?
What is the maximum allowable stress in the steel shaft?
What happens to every cross section of a circular shaft when subjected to torsion?
What happens to every cross section of a circular shaft when subjected to torsion?
What do the torques exerted on the turbine and generator represent?
What do the torques exerted on the turbine and generator represent?
What is the perpendicular distance (ρ) in the context of torsion?
What is the perpendicular distance (ρ) in the context of torsion?
Which of the following conditions must be satisfied by the shearing stresses in any given cross section of the shaft?
Which of the following conditions must be satisfied by the shearing stresses in any given cross section of the shaft?
What is the result of applying a torque to a circular shaft?
What is the result of applying a torque to a circular shaft?
How is the torque T′ related to torque T in the system involving the turbine and generator?
How is the torque T′ related to torque T in the system involving the turbine and generator?
In a beam experiencing torsion, how do different cross sections behave?
In a beam experiencing torsion, how do different cross sections behave?
What does the sum of the moments of the shearing forces about the axis of the shaft equal?
What does the sum of the moments of the shearing forces about the axis of the shaft equal?
What is the maximum torque that can be applied to the hollow cylindrical steel shaft without exceeding a shearing stress of 120 MPa?
What is the maximum torque that can be applied to the hollow cylindrical steel shaft without exceeding a shearing stress of 120 MPa?
What is the formula used to relate torque and shearing stress in a hollow cylindrical shaft?
What is the formula used to relate torque and shearing stress in a hollow cylindrical shaft?
Given the modulus of rigidity for steel is 77 GPa, how does this affect the angle of twist in the shaft?
Given the modulus of rigidity for steel is 77 GPa, how does this affect the angle of twist in the shaft?
What is the resulting shearing stress at the inner surface of the hollow cylinder if the angle of twist is known?
What is the resulting shearing stress at the inner surface of the hollow cylinder if the angle of twist is known?
To produce a twist of 2°, what type of torque must be applied to the shaft?
To produce a twist of 2°, what type of torque must be applied to the shaft?
How does a hole drilled into the shaft affect the overall torque capacity?
How does a hole drilled into the shaft affect the overall torque capacity?
What unit is used to measure the modulus of rigidity (G) in the given content?
What unit is used to measure the modulus of rigidity (G) in the given content?
What happens to the angle of twist when a higher torque is applied to the shaft?
What happens to the angle of twist when a higher torque is applied to the shaft?
What happens to the angle of twist ϕ for a shaft that is twice as long under the same torque T?
What happens to the angle of twist ϕ for a shaft that is twice as long under the same torque T?
How does the shearing strain γ change in relation to the distance ρ from the axis of the shaft?
How does the shearing strain γ change in relation to the distance ρ from the axis of the shaft?
What is the relationship between the shearing stress in the shaft and distance ρ within the yield limit?
What is the relationship between the shearing stress in the shaft and distance ρ within the yield limit?
What does Hooke’s law apply to in the context of torsion in the shaft?
What does Hooke’s law apply to in the context of torsion in the shaft?
What is the expected shape change of a square element under torsion loading?
What is the expected shape change of a square element under torsion loading?
Which statement is true regarding the stress distribution within a circular shaft?
Which statement is true regarding the stress distribution within a circular shaft?
In torsion, which statement is applicable when two adjacent cross sections are analyzed?
In torsion, which statement is applicable when two adjacent cross sections are analyzed?
What is the relationship between torque T and angle of twist ϕ within the elastic range?
What is the relationship between torque T and angle of twist ϕ within the elastic range?
For a hollow cylindrical steel shaft, which characteristics are important for determining the angle of twist?
For a hollow cylindrical steel shaft, which characteristics are important for determining the angle of twist?
Flashcards
Torsion in a shaft
Torsion in a shaft
The twisting of a circular shaft due to applied torques.
Torque (T)
Torque (T)
A twisting force applied to a shaft.
Cross-section plane in torsion
Cross-section plane in torsion
Cross-sections of a shaft under torsion remain plane and undistorted.
Shearing stress(τ)
Shearing stress(τ)
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Shaft cross-section rotation in torsion
Shaft cross-section rotation in torsion
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Torque and cross-section
Torque and cross-section
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Equilibrium of torques
Equilibrium of torques
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Condition of shearing stress.
Condition of shearing stress.
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Torsion angle (ϕ)
Torsion angle (ϕ)
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Constant shearing strain (γ)
Constant shearing strain (γ)
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Shaft cross-section
Shaft cross-section
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Shearing Stress Variation
Shearing Stress Variation
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Shaft material behavior
Shaft material behavior
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Angle of Twist (ϕ) proportionality
Angle of Twist (ϕ) proportionality
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Torque (T)
Torque (T)
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Relationship between angle of twist and length
Relationship between angle of twist and length
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Deforming Element in Torsion
Deforming Element in Torsion
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Shearing strain variation
Shearing strain variation
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Maximum allowable torque
Maximum allowable torque
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Minimum shearing stress
Minimum shearing stress
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Hollow cylindrical shaft
Hollow cylindrical shaft
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Polar moment of inertia
Polar moment of inertia
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Angle of twist
Angle of twist
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Modulus of rigidity (G)
Modulus of rigidity (G)
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Torsional stress
Torsional stress
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Torque in shaft segments
Torque in shaft segments
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Torque in shaft segments
Torque in shaft segments
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Angle of twist (shaft)
Angle of twist (shaft)
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Transmission shaft power
Transmission shaft power
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Angular velocity
Angular velocity
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Allowable stress
Allowable stress
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Power Transmission
Power Transmission
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Shaft tube thickness
Shaft tube thickness
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Material property G (Torsion)
Material property G (Torsion)
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Study Notes
Torsion
- Torsion is a twisting force applied to a shaft.
- When a circular shaft is subjected to torsion, every cross-section remains plane and undistorted.
- Various cross sections along the shaft rotate through different angles.
- Each cross section rotates as a solid rigid slab.
- All equally spaced circles rotate by the same amount relative to their neighbors.
- Each straight line transforms into a curve (helix).
- The shearing strain at a given point of a shaft in torsion is proportional to the angle of twist and the distance p from the axis of the shaft.
- The shearing strain in a circular shaft is zero at the axis of the shaft and varies linearly with the distance from the axis of the shaft.
- The stresses in the shaft will remain below both the proportional limit and the elastic limit - Hooke's law will apply.
- τ = Gy/c
- Gy = Gγmax
- τ = ρτmax /c
- Within the yield limit - the shearing stress in the shaft varies linearly with the distance p from the axis of the shaft.
- Minimun shear stress is given by τmin = τmax * c1/c2
- The angle of twist is proportional to the torque and the length of the shaft.
- Angle of twist is given by φ = (TL)/(JG)
- The largest torque T that can be applied is given by T=(τmax *J)/c
- The torque in each segment of a shaft is found using free-body diagrams and the equation: φ = Σ (TᵢLᵢ)/(JᵢGᵢ)
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Description
This quiz covers the fundamental concepts of torsion as applied to circular shafts. It explores twisting forces, shear strain, and the properties of materials under torsional stress. Test your understanding of how these principles apply to engineering and mechanics.
