UPSC Exam > UPSC Questions > A solid steel shaft is to transmit a torque o...
Start Learning for Free
A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.?
Most Upvoted Answer
A solid steel shaft is to transmit a torque of 10kNm. If the shearing ...
To determine the minimum diameter of a solid steel shaft that can safely transmit a torque of 10 kNm without exceeding a shearing stress of 45 MPa, we can use the following formula:
1. Torque Formula
The relationship between torque (T), shearing stress (τ), and the diameter (d) of the shaft is given by the equation:
Where:
- T = Torque in Nm
- τ = Shearing stress in MPa
- d = Diameter in m
2. Convert Units
First, we need to convert the torque from kNm to Nm:
Next, convert the shearing stress from MPa to Pa (1 MPa = 1,000,000 Pa):
3. Rearranging the Formula
Now, we can rearrange the torque formula to solve for d:
4. Substituting Values
Now substitute the values of T and τ into the equation:
5. Calculation
Calculating the above expression:
Now take the cube root to find d:
6. Conclusion
Thus, the minimum diameter of the shaft needed to safely transmit a torque of 10 kNm without exceeding a shearing stress of 45 MPa is approximately:
1. Torque Formula
The relationship between torque (T), shearing stress (τ), and the diameter (d) of the shaft is given by the equation:
- T = (π/16) × τ × d^3
Where:
- T = Torque in Nm
- τ = Shearing stress in MPa
- d = Diameter in m
2. Convert Units
First, we need to convert the torque from kNm to Nm:
- T = 10 kNm = 10,000 Nm
Next, convert the shearing stress from MPa to Pa (1 MPa = 1,000,000 Pa):
- τ = 45 MPa = 45 × 1,000,000 Pa = 45,000,000 Pa
3. Rearranging the Formula
Now, we can rearrange the torque formula to solve for d:
- d^3 = (16 × T) / (π × τ)
4. Substituting Values
Now substitute the values of T and τ into the equation:
- d^3 = (16 × 10,000) / (π × 45,000,000)
5. Calculation
Calculating the above expression:
- d^3 = (160,000) / (141,372.6) ≈ 1.131 m^3
Now take the cube root to find d:
- d ≈ (1.131)^(1/3) ≈ 0.105 m
- d ≈ 105 mm
6. Conclusion
Thus, the minimum diameter of the shaft needed to safely transmit a torque of 10 kNm without exceeding a shearing stress of 45 MPa is approximately:
- 105 mm
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.?
Question Description
A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.?.
A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.?.
Solutions for A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? defined & explained in the simplest way possible. Besides giving the explanation of
A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.?, a detailed solution for A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? has been provided alongside types of A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? theory, EduRev gives you an
ample number of questions to practice A solid steel shaft is to transmit a torque of 10kNm. If the shearing stress is not to exceed 45MPa, find the minimum diameter of the shaft.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup