Torsion in Circular Shafts

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Questions and Answers

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?

50 mm

44 mm (correct)

40 mm

60 mm

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?

ω = 2πf Signup and view all the answers

What is the required tube thickness for a steel tube transmitting 100 kW at 20 Hz to prevent shearing stress from exceeding 60 MPa?

5 mm Signup and view all the answers

What is the shear modulus G value for steel mentioned?

77 GPa Signup and view all the answers

In the context provided, what is the role of the free-body diagrams?

To determine the torque in each shaft segment Signup and view all the answers

What is the maximum allowable stress in the steel shaft?

120 MPa Signup and view all the answers

What happens to every cross section of a circular shaft when subjected to torsion?

Each cross section rotates as a solid rigid slab. Signup and view all the answers

What do the torques exerted on the turbine and generator represent?

The turbine and generator exert opposite torques of equal magnitude. Signup and view all the answers

What is the perpendicular distance (ρ) in the context of torsion?

The distance from the force dF to the axis of the shaft. Signup and view all the answers

Which of the following conditions must be satisfied by the shearing stresses in any given cross section of the shaft?

They must counteract the applied torque. Signup and view all the answers

What is the result of applying a torque to a circular shaft?

It produces shearing stresses on the faces perpendicular to the axis of the shaft. Signup and view all the answers

How is the torque T′ related to torque T in the system involving the turbine and generator?

T′ equals T in magnitude but is opposite in direction. Signup and view all the answers

In a beam experiencing torsion, how do different cross sections behave?

Each cross section rotates through different angles. Signup and view all the answers

What does the sum of the moments of the shearing forces about the axis of the shaft equal?

The applied torque. Signup and view all the answers

What is the maximum torque that can be applied to the hollow cylindrical steel shaft without exceeding a shearing stress of 120 MPa?

750 Nm Signup and view all the answers

What is the formula used to relate torque and shearing stress in a hollow cylindrical shaft?

$T = \frac{\pi}{32} \cdot (D^4 - d^4) \cdot \tau$ Signup and view all the answers

Given the modulus of rigidity for steel is 77 GPa, how does this affect the angle of twist in the shaft?

Higher modulus results in a lesser angle of twist. Signup and view all the answers

What is the resulting shearing stress at the inner surface of the hollow cylinder if the angle of twist is known?

It is directly proportional to the angle of twist. Signup and view all the answers

To produce a twist of 2°, what type of torque must be applied to the shaft?

A constant torque Signup and view all the answers

How does a hole drilled into the shaft affect the overall torque capacity?

Decreases torque capacity due to stress concentration. Signup and view all the answers

What unit is used to measure the modulus of rigidity (G) in the given content?

GPa (Gigapascals) Signup and view all the answers

What happens to the angle of twist when a higher torque is applied to the shaft?

The angle of twist increases. Signup and view all the answers

What happens to the angle of twist ϕ for a shaft that is twice as long under the same torque T?

It is twice as large. Signup and view all the answers

How does the shearing strain γ change in relation to the distance ρ from the axis of the shaft?

It varies linearly. Signup and view all the answers

What is the relationship between the shearing stress in the shaft and distance ρ within the yield limit?

It varies linearly with ρ. Signup and view all the answers

What does Hooke’s law apply to in the context of torsion in the shaft?

Both shearing stress and strain. Signup and view all the answers

What is the expected shape change of a square element under torsion loading?

It deforms into a rhombus. Signup and view all the answers

Which statement is true regarding the stress distribution within a circular shaft?

Stress is maximum at the outer surface and zero at the axis. Signup and view all the answers

In torsion, which statement is applicable when two adjacent cross sections are analyzed?

They rotate as a solid rigid slab. Signup and view all the answers

What is the relationship between torque T and angle of twist ϕ within the elastic range?

They are directly proportional. Signup and view all the answers

For a hollow cylindrical steel shaft, which characteristics are important for determining the angle of twist?

Length L and shear modulus G. Signup and view all the answers

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.