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A close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearly
- a)20 N/mm2
- b)33.3 N/mm2
- c)55.6 N/mm2
- d)92.6 N/mm2
Correct answer is option 'C'. Can you explain this answer?
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A close-coiled helical spring is made of 5 mm diameter wire coiled to...
Given Data:
- Diameter of wire (d1) = 5 mm
- Mean diameter of coil (D1) = 50 mm
- Maximum shear stress in the spring = 20 N/mm2
Calculations:
- Diameter of wire (d2) = 3 mm
- Mean diameter of coil (D2) = 30 mm
Formula:
The maximum shear stress in a close-coiled helical spring is given by the formula:
\[\tau_{max} = \frac{16F}{\pi d^3 D}\]
Where:
- \(\tau_{max}\) = Maximum shear stress
- F = Axial force
- d = Diameter of wire
- D = Mean diameter of coil
Using the formula for both springs:
For the first spring:
\[\tau_{max1} = \frac{16F}{\pi (5)^3 (50)} = 20 N/mm^2\]
For the second spring:
\[\tau_{max2} = \frac{16F}{\pi (3)^3 (30)}\]
Calculating the maximum shear stress for the second spring:
\[\tau_{max2} = \frac{16F}{\pi (27) (30)} = \frac{16F}{\pi 810} = \frac{F}{50.96}\]
Comparing the maximum shear stresses:
Since maximum shear stress is directly proportional to the force and inversely proportional to the cube of the wire diameter and mean coil diameter, the maximum shear stress in the second spring will be higher than the first spring. Therefore, the maximum shear stress in the second spring will be nearly 55.6 N/mm2 (option c).
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A close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. Can you explain this answer?
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A close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. 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 close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. 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 close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. Can you explain this answer?.
A close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. 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 close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. 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 close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice A close-coiled helical spring is made of 5 mm diameter wire coiled to 50 mm mean diameter. Maximum shear stress in the spring under the action of an axial force is 20 N/mm2. The maximum shear stress in a spring made of 3 mm diameter wire coiled to 30 mm mean diameter, under the action of the same force will be nearlya) 20 N/mm2b) 33.3 N/mm2c) 55.6 N/mm2d) 92.6 N/mm2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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