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A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.
Correct answer is '6'. Can you explain this answer?
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A helical compression spring made of wire of circular cross-section is...
P1=P2 , d2 = 2d1 , D2 =2D1
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A helical compression spring made of wire of circular cross-section is...
Given:
- A helical compression spring made of wire of circular cross-section is subjected to a compressive load.
- The maximum shear stress induced in the cross-section of the wire is 24 MPa.
To Find:
- The maximum shear stress induced in the cross-section of the wire when both the wire diameter and the mean coil diameter are doubled.
Solution:
Let's assume the original wire diameter is 'd' and the original mean coil diameter is 'D'.
Step 1: Calculate the original shear stress induced in the wire.
The shear stress in a helical compression spring can be calculated using the formula:
Shear Stress (τ) = (16 * W * R) / (π * d^3)
Where:
W = Load applied on the spring
R = Mean coil radius (D/2)
d = Diameter of the wire
Given that the maximum shear stress induced in the wire is 24 MPa, we can rewrite the formula as:
24 MPa = (16 * W * R) / (π * d^3)
Simplifying the equation, we get:
W * R = (π * d^3 * 24 MPa) / 16
Step 2: Calculate the new shear stress when both the wire diameter and the mean coil diameter are doubled.
Let the new wire diameter be '2d' and the new mean coil diameter be '2D'.
Using the same formula as before:
Shear Stress (τ') = (16 * W' * R') / (π * (2d)^3)
Where:
W' = Load applied on the spring (same as before)
R' = Mean coil radius (2D/2)
(2d)^3 = (2^3 * d^3) = 8 * d^3
Simplifying the equation, we get:
τ' = (16 * W' * R') / (π * 8 * d^3)
τ' = (2 * W' * R') / (π * d^3)
Comparing this equation with the original equation, we can see that the new shear stress (τ') is half of the original shear stress (τ).
Conclusion:
When both the wire diameter and the mean coil diameter are doubled, the maximum shear stress induced in the cross-section of the wire is reduced to half. Therefore, the maximum shear stress induced in the wire is 6 MPa.
- A helical compression spring made of wire of circular cross-section is subjected to a compressive load.
- The maximum shear stress induced in the cross-section of the wire is 24 MPa.
To Find:
- The maximum shear stress induced in the cross-section of the wire when both the wire diameter and the mean coil diameter are doubled.
Solution:
Let's assume the original wire diameter is 'd' and the original mean coil diameter is 'D'.
Step 1: Calculate the original shear stress induced in the wire.
The shear stress in a helical compression spring can be calculated using the formula:
Shear Stress (τ) = (16 * W * R) / (π * d^3)
Where:
W = Load applied on the spring
R = Mean coil radius (D/2)
d = Diameter of the wire
Given that the maximum shear stress induced in the wire is 24 MPa, we can rewrite the formula as:
24 MPa = (16 * W * R) / (π * d^3)
Simplifying the equation, we get:
W * R = (π * d^3 * 24 MPa) / 16
Step 2: Calculate the new shear stress when both the wire diameter and the mean coil diameter are doubled.
Let the new wire diameter be '2d' and the new mean coil diameter be '2D'.
Using the same formula as before:
Shear Stress (τ') = (16 * W' * R') / (π * (2d)^3)
Where:
W' = Load applied on the spring (same as before)
R' = Mean coil radius (2D/2)
(2d)^3 = (2^3 * d^3) = 8 * d^3
Simplifying the equation, we get:
τ' = (16 * W' * R') / (π * 8 * d^3)
τ' = (2 * W' * R') / (π * d^3)
Comparing this equation with the original equation, we can see that the new shear stress (τ') is half of the original shear stress (τ).
Conclusion:
When both the wire diameter and the mean coil diameter are doubled, the maximum shear stress induced in the cross-section of the wire is reduced to half. Therefore, the maximum shear stress induced in the wire is 6 MPa.
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A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer?
Question Description
A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer? 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 helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer?.
A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer? 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 helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.Correct answer is '6'. Can you explain this answer?.
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