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Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?
- a)6.32 mm, 56.6 mm
- b)6.32 mm, 50.6 mm
- c)7.32 mm, 50.6 mm
- d)9.32 mm, 56.6 mm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Determine the wire diameter (d) and mean diameter (D) for a helical s...
Step 1: As there is dynamic loading, calculate the Bergstrӓsser factor (KB)
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Using eq.:
KB = (4C + 2)/ (4C – 3)
= (4(8) + 2)/(4(8) – 3)
= 34/29 = 1.172
Step 2: Substitute the Bergstrӓsser factor (KB) found in step 1 and the other given information
In eq.:
τmax = KB 8CF/πd2
3.55 × 108 N/m2 = (1.172) (8) (8) (595 N)/ πd2
Step 3: Solve for the wire diameter (d) from step 2
d2 = (1.172) (8) (8) (595 N)/ {π (3.55 × 108 N/m2)}
= 0.00004 m2
d = 0.00632 m = 6.32 mm Ans.
Step 4: Using the definition of the spring from eq.: C = D/d and the wire diameter (d) found in step 3, calculate the mean spring diameter (D).
C = D/d
8 = D/6.32 mm
D = (8) (6.32 mm)
= 50.6 mm = 5.06 cm
Most Upvoted Answer
Determine the wire diameter (d) and mean diameter (D) for a helical s...
Given data:
F = 595 N
C = 8
τmax = 355 MPa = 355 × 10^6 N/m^2
Calculations:
1. Calculate the Bergstrӓsser factor (KB):
KB = F / (π * d * τmax * C)
KB = 595 / (π * d * 355 × 10^6 * 8)
KB ≈ 3.55 × 10^8 / (d * 8.89 × 10^6)
KB ≈ 39.83 / d
2. Calculate wire diameter (d):
Given KB = 39.83 / d
Since KB is given as 3.55 × 10^8 N/m^2, substitute the value:
3.55 × 10^8 = 39.83 / d
d = 39.83 / 3.55 × 10^8
d ≈ 0.0001123 m = 0.1123 mm
d ≈ 6.32 mm
3. Calculate mean diameter (D):
D = d + d = 2d
D = 2 * 6.32
D ≈ 12.64 mm
Therefore, the wire diameter (d) is approximately 6.32 mm and the mean diameter (D) is approximately 12.64 mm. The correct answer is option B: 6.32 mm, 50.6 mm.
F = 595 N
C = 8
τmax = 355 MPa = 355 × 10^6 N/m^2
Calculations:
1. Calculate the Bergstrӓsser factor (KB):
KB = F / (π * d * τmax * C)
KB = 595 / (π * d * 355 × 10^6 * 8)
KB ≈ 3.55 × 10^8 / (d * 8.89 × 10^6)
KB ≈ 39.83 / d
2. Calculate wire diameter (d):
Given KB = 39.83 / d
Since KB is given as 3.55 × 10^8 N/m^2, substitute the value:
3.55 × 10^8 = 39.83 / d
d = 39.83 / 3.55 × 10^8
d ≈ 0.0001123 m = 0.1123 mm
d ≈ 6.32 mm
3. Calculate mean diameter (D):
D = d + d = 2d
D = 2 * 6.32
D ≈ 12.64 mm
Therefore, the wire diameter (d) is approximately 6.32 mm and the mean diameter (D) is approximately 12.64 mm. The correct answer is option B: 6.32 mm, 50.6 mm.
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Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer?
Question Description
Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer?.
Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Determine the wire diameter (d) and mean diameter (D) for a helical spring using the Bergstrӓsser factor (KB), where: F = 595 N; C = 8; τmax = 355 MPa; = 3.55 × 108 N/m2 ?a)6.32 mm, 56.6 mmb)6.32 mm, 50.6 mmc)7.32 mm, 50.6 mmd)9.32 mm, 56.6 mmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
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