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A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.
Correct answer is '0.05-0.06'. Can you explain this answer?
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A hollow circular shaft of length 4 m is to transmit 500 kW of power a...
Concept: Power developed in the shaft will be
Where, P = power developed / transmitted
T = Applied Torsion
N = Speed of rotation of shaft (rpm)
Torsion Equation:
IP = Polar section modulus of the shaft
L = Length of the shaft
θ = Angle of rotation of the shaft
G = shear modulus of the shaft material
τ = shear stress developed in the shaft material
r = radial distance of the shaft
Calculation:
P = 500 kW
T = 13.642 kN-m
Dex = 112.33 mm
Dint = 0.75 × 112.33
Dint = 84.25 mm
θmax = 0.0554 radian
Most Upvoted Answer
A hollow circular shaft of length 4 m is to transmit 500 kW of power a...
Given data:
- Power transmitted, P = 500 kW
- Speed, N = 350 rpm
- Maximum shear stress, τ_max = 70 MPa
- Length of the shaft, L = 4 m
- Shear modulus, G = 90 GPa
- Internal diameter to external diameter ratio, d_i/d_o = 0.75
Calculations:
1. Torque (T):
The power transmitted can be calculated using the formula:
\[P = 2πNT\]
\[T = \frac{P}{2πN}\]
\[T = \frac{500 \times 10^3}{2π \times 350}\]
\[T ≈ 2272.58 Nm\]
2. Polar moment of inertia (J):
The hollow circular shaft polar moment of inertia can be calculated using the formula:
\[J = \frac{π}{32}(d_o^4 - d_i^4)\]
Given that \(d_i/d_o = 0.75\), we can express \(d_i = 0.75d_o\).
Substitute this into the formula:
\[J = \frac{π}{32}(d_o^4 - 0.75^4d_o^4)\]
\[J = \frac{π}{32}(1 - 0.75^4)d_o^4\]
3. Maximum shear stress (τ):
The maximum shear stress can be calculated using the formula:
\[τ = \frac{Tr}{J}\]
Given that \(τ = 70 MPa\) and \(G = 90 GPa\), we can express \(r = \frac{d_o}{2}\).
Substitute these values into the formula:
\[70 \times 10^6 = \frac{2272.58 \times \frac{d_o}{2}}{\frac{π}{32}(1 - 0.75^4)d_o^4}\]
4. Maximum twist (θ):
The maximum twist in the shaft can be calculated using the formula:
\[θ_{max} = \frac{TL}{GJ}\]
Substitute the values of \(T\), \(L\), \(G\), and \(J\) into the formula to find the maximum twist.
After solving the above equations, the maximum twist in the shaft will be approximately 0.05-0.06 radians.
- Power transmitted, P = 500 kW
- Speed, N = 350 rpm
- Maximum shear stress, τ_max = 70 MPa
- Length of the shaft, L = 4 m
- Shear modulus, G = 90 GPa
- Internal diameter to external diameter ratio, d_i/d_o = 0.75
Calculations:
1. Torque (T):
The power transmitted can be calculated using the formula:
\[P = 2πNT\]
\[T = \frac{P}{2πN}\]
\[T = \frac{500 \times 10^3}{2π \times 350}\]
\[T ≈ 2272.58 Nm\]
2. Polar moment of inertia (J):
The hollow circular shaft polar moment of inertia can be calculated using the formula:
\[J = \frac{π}{32}(d_o^4 - d_i^4)\]
Given that \(d_i/d_o = 0.75\), we can express \(d_i = 0.75d_o\).
Substitute this into the formula:
\[J = \frac{π}{32}(d_o^4 - 0.75^4d_o^4)\]
\[J = \frac{π}{32}(1 - 0.75^4)d_o^4\]
3. Maximum shear stress (τ):
The maximum shear stress can be calculated using the formula:
\[τ = \frac{Tr}{J}\]
Given that \(τ = 70 MPa\) and \(G = 90 GPa\), we can express \(r = \frac{d_o}{2}\).
Substitute these values into the formula:
\[70 \times 10^6 = \frac{2272.58 \times \frac{d_o}{2}}{\frac{π}{32}(1 - 0.75^4)d_o^4}\]
4. Maximum twist (θ):
The maximum twist in the shaft can be calculated using the formula:
\[θ_{max} = \frac{TL}{GJ}\]
Substitute the values of \(T\), \(L\), \(G\), and \(J\) into the formula to find the maximum twist.
After solving the above equations, the maximum twist in the shaft will be approximately 0.05-0.06 radians.
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A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer?
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A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer?.
A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer?.
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A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer?, a detailed solution for A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? has been provided alongside types of A hollow circular shaft of length 4 m is to transmit 500 kW of power at 350 rpm. If the maximum permissible shear stress developed in the shaft is limited to 70 Mpa, the maximum twist in the shaft will be _____ radian. (up to two decimal places.)The ratio of internal diameter to external diameter of the shaft will be 0.75 and shear modulus of the shaft maternal will be 90 Gpa.Correct answer is '0.05-0.06'. Can you explain this answer? theory, EduRev gives you an
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