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‌A hollow shaft whose internal diameter is half of the external diameter is subjected to maximum bending moment of 2KN -m at a section and constant torque of 4KM-m all along its length. If yield stress of the material is 280 MPa and factor of safety is 3.0, what should be minimum safe diameter of shaft?
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‌A hollow shaft whose internal diameter is half of the external diamet...
Solution:

Given data:

Maximum bending moment, M = 2KN-m

Torque, T = 4KM-m

Yield stress, σ_y = 280 MPa

Factor of safety, n = 3.0

Internal diameter, d_i = d/2

We know that the maximum shear stress (τ_max) and maximum bending stress (σ_b) in the shaft can be calculated as follows:

τ_max = T/(π/16*d^3)

σ_b = M*c/I

where,

c = distance from the neutral axis to the outermost fiber

I = moment of inertia

For a hollow shaft, the moment of inertia can be given as:

I = π/64*(d^4 - d_i^4)

Calculating maximum shear stress:

τ_max = T/(π/16*d^3)

4*10^3*10^3/(π/16*d^3) = 15.9 MPa

Calculating maximum bending stress:

We know that the bending stress is maximum at the outermost fiber of the shaft. Therefore, c = d/2.

σ_b = M*c/I

σ_b = 2*10^3*1000*(d/2)/[π/64*(d^4 - (d/2)^4)]

σ_b = 15.7*d^3/(d^4 - (d/2)^4)

Calculating allowable stress:

The allowable stress can be calculated as:

σ_allowable = σ_y/n

σ_allowable = 280/3 = 93.3 MPa

Calculating the minimum safe diameter:

The minimum safe diameter of the shaft can be obtained by equating the maximum shear stress and maximum bending stress to the allowable stress.

τ_max = σ_allowable

15.9 MPa = 93.3 MPa

σ_b = σ_allowable

15.7*d^3/(d^4 - (d/2)^4) = 93.3 MPa

Solving the above equation, we get,

d = 46.8 mm

Therefore, the minimum safe diameter of the shaft should be 46.8 mm.
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‌A hollow shaft whose internal diameter is half of the external diameter is subjected to maximum bending moment of 2KN -m at a section and constant torque of 4KM-m all along its length. If yield stress of the material is 280 MPa and factor of safety is 3.0, what should be minimum safe diameter of shaft?
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‌A hollow shaft whose internal diameter is half of the external diameter is subjected to maximum bending moment of 2KN -m at a section and constant torque of 4KM-m all along its length. If yield stress of the material is 280 MPa and factor of safety is 3.0, what should be minimum safe diameter of shaft? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about ‌A hollow shaft whose internal diameter is half of the external diameter is subjected to maximum bending moment of 2KN -m at a section and constant torque of 4KM-m all along its length. If yield stress of the material is 280 MPa and factor of safety is 3.0, what should be minimum safe diameter of shaft? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ‌A hollow shaft whose internal diameter is half of the external diameter is subjected to maximum bending moment of 2KN -m at a section and constant torque of 4KM-m all along its length. If yield stress of the material is 280 MPa and factor of safety is 3.0, what should be minimum safe diameter of shaft?.
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