# when a circular shaft is subjected to torque, the torsional shear stress is

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## When a shaft is subjected to torsion the shear stress induced

When a shaft, is subjected to torsion, the shear stress induced in the shaft varies from a) Minimum at the center to maximum at the circumference b) Maximum at the center to minimum at the circumference c) Zero at the center to maximum at the circumference d) Maximum at the center to zero at the circumference

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## When a shaft, is subjected to torsion, the shear stress induced in the shaft varies from

A. Minimum at the center to maximum at the circumference

B. Maximum at the center to minimum at the circumference

C. Zero at the center to maximum at the circumference

D. Maximum at the center to zero at the circumference

**Answer: Option C**

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## [Solved] A circular shaft is subjected to torque. The torsional rigid

Explanation: \( \frac{T}{J} = \frac{\tau }{r} = \frac{{G\theta }}{L}\) Torque per radian twist is known as torsional stiffness (k) \(k=\frac{T

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## Question

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A circular shaft is subjected to torque. The torsional rigidity is defined as:

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UPRVUNL JE ME 2016 Official Paper Shift 2

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product of polar moment of inertia and modulus of rigidity

ratio of torque and polar moment of inertia

product of torque and length

sum of polar moment of inertia and modulus of rigidity

## Answer (Detailed Solution Below)

Option 1 : product of polar moment of inertia and modulus of rigidity

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## Detailed Solution

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Explanation: TJ=τr=GθL

Torque per radian twist is known as torsional stiffness (k)

k=Tθ=GJL

The parameter GJ is called torsional rigidity of the shaft.

Torsional rigidity is also defined as torque per unit angular twist per unit length

GJ=Tθ/L

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## More Torsion of Shaft Questions

**Q1.**The ratio of strengths of solid to hollow shafts, both having outside diameter D and hollow shaft having inside diameter D / 2, in torsion, is

**Q2.**Three rolled steel beam ISWB 300 as shown in the figure are used as built-up sections for columns having Ixx = 9821.6 × 104 mm4 and Iyy = 990 × 104 mm4. The moment of inertia of the combined section Ixx is given as:

**Q3.**Strain energy stored in a hollow shaft of external diameter (D) and internal diameter (d) when subjected to shear stress (

τ ) is equal to

**Q4.**Power transmitted by a shaft is given by expression in watts -

**Q5.**A long shaft of diameter d is subjected to twisting moment T at its ends. The maximum normal stress acting at its cross–section is equal to

**Q6.**Which one of the given statement is WRONG about torsion?

**Q7.**For pure bending, identify the WRONG statement.

**Q8.**The maximum torque that can be safely applied to a shaft of 100 mm diameter if the permissible angle of twist is 1 degree in a length of 3 m and the permissible shear stress is 30 N/mm2. Take G = 0.8 × 105 N/mm2.

**Q9.**In the bending stress equation M/I = f/y = E/R, which of the following is INCORRECT?

**Q10.**Shear stress at the centre of Shaft is:

## Torsion of Shafts

The torsion of solid or hollow shafts - Polar Moment of Inertia of Area.

## Torsion of Shafts

Torsion of Shafts The torsion of solid or hollow shafts - Polar Moment of Inertia of Area.

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### Shear Stress in the Shaft

When a shaft is subjected to a torque or twisting a shearing stress is produced in the shaft. The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft.

The shear stress in a solid circular shaft in a given position can be expressed as:

Note

the "" is a measure of a shaft's ability to resist torsion. The " of Inertia" is defined with respect to an axis perpendicular to the area considered. It is analogous to the "Area Moment of Inertia" - which characterizes a beam's ability to resist bending - required to predict deflection and stress in a beam.

1 ft = 12 in 1 ft4 = 20736 in4

1 psf (lbf/ft2) = 1/144 psi (lbf/in2)

"Polar Moment of Inertia of an Area" is also called "Polar Moment of Inertia", "Second Moment of Area", "Area Moment of Inertia", "Polar Moment of Area" or "Second Area Moment".

### Polar Moment of Inertia vs. Area Moment of Inertia

"Polar Moment of Inertia" - a measure of a beam's ability to resist torsion - which is required to calculate the twist of a beam subjected to torque

"Area Moment of Inertia" - a property of shape that is used to predict deflection, bending and stress in beams

### Circular Shaft and Maximum Moment or Torque

Maximum moment in a circular shaft can be expressed as:

Combining (2) and (3) for a **solid shaft**

Combining (2) and (3b) for a **hollow shaft**

### Circular Shaft and Polar Moment of Inertia

Polar Moment of Inertia of a circular solid shaft can be expressed as

Polar Moment of Inertia of a circular hollow shaft can be expressed as

### Diameter of a Solid Shaft

Diameter of a solid shaft can calculated by the formula

### Torsional Deflection of Shaft

The angular deflection of a torsion shaft can be expressed as

The angular deflection of a torsion solid shaft can be expressed as

The angular deflection of a torsion hollow shaft can be expressed as

The angle in degrees can be achieved by multiplying the angle in radians with

olid shaft ( replaced)

### Torsion Resisting Moments from Shafts of Various Cross Sections

Shaft Cross Section Area Maximum Torsional

Resisting Moment - Nomenclature

Solid Cylinder Shaft

Hollow Cylinder Shaft

Ellipse Shaft h = "height" of shaft

b = "width" of shaft

h > b

Rectangle Shaft h > b

Square Shaft

Triangle Shaft b = length of triangle side

Hexagon Shaft

### Example - Shear Stress and Angular Deflection in a Solid Cylinder

A moment of is acting on a solid cylinder shaft with diameter (0.05 m) and length . The shaft is made in steel with modulus of rigidity .

Maximum shear stress can be calculated as

The angular deflection of the shaft can be calculated as

### Example - Shear Stress and Angular Deflection in a Hollow Cylinder

A moment of is acting on a hollow cylinder shaft with outer diameter , inner diameter (0.03 m) and length . The shaft is made in steel with modulus of rigidity .

Maximum shear stress can be calculated as

The angular deflection of the shaft can be calculated as

### Example - Required Shaft Diameter to Transmit Power

A 15 kW electric motor shall be used to transmit power through a connected solid shaft. The motor and the shaft rotates with 2000 rpm. The maximum allowable shear stress - - in the shaft is 100 MPa.

The connection between power and torque can be expressed

Re-arranged and with values - the torque can be calculated

T = (15 103 W) / (0.105 (2000 rpm))

= 71 Nm

Minimum diameter of the shaft can be calculated with eq. 4

D = 1.72 ((71 Nm) / (100 106 Pa))1/3

= 0.0153 m = 15.3 mm Sponsored Links

## Related Topics

**Mechanics**- Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

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