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A uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factor
- a)48
- b)50
Correct answer is option ''. Can you explain this answer?
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Verified Answer
A uniform bar having a machined surface is subjected to an axial load...
Using Goodman’s equation with
Kc = 0.7, Kf = 1.42
Su = 630 MPa and Se = 315 MPa
Thus,
∴d = 48.69 mm
d ≈ 49 mm
Question_type5
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A uniform bar having a machined surface is subjected to an axial load...
To determine the diameter of the rod using Goodman's Criteria, we can follow these steps:
1. Identify the given values:
- Ultimate tensile strength (Su) = 630 MPa
- Surface finish factor (kc) = 0.7
- Fatigue stress concentration factor (kf) = 1.42
2. Calculate the alternating stress (Sa):
The alternating stress is the difference between the maximum and minimum axial loads applied to the bar.
Sa = (Maximum load - Minimum load) / 2
= (400 kN - 150 kN) / 2
= 250 kN / 2
= 125 kN
3. Calculate the allowable alternating stress (Sa_allow):
The allowable alternating stress is determined using Goodman's Criteria:
Sa_allow = Su / (kf * (1 + kc))
= 630 MPa / (1.42 * (1 + 0.7))
= 630 MPa / (1.42 * 1.7)
= 630 MPa / 2.414
= 260.6 MPa
4. Calculate the diameter of the rod:
The diameter of the rod can be determined using the formula for axial stress:
σ = P / (π * d^2 / 4)
where σ is the axial stress, P is the axial load, and d is the diameter of the rod.
Since we know that the factor of safety (FS) is 1.5, we can write:
Sa_allow / FS = σ_allow = P / (π * d^2 / 4)
Solving for d:
d^2 = 4 * P / (π * σ_allow)
d = √(4 * P / (π * σ_allow))
Substituting the given values:
d = √(4 * 150 kN / (π * 260.6 MPa))
= √(600 kN / (π * 260.6 MPa))
= √(600 kN / (3.14159 * 260.6 N/mm^2))
= √(600 / (3.14159 * 260.6))
= √(600 / 819.948)
= √0.73171
≈ 0.8557
Converting the diameter to mm:
d_mm ≈ 0.8557 * 1000
≈ 855.7 mm
Rounding off to the nearest whole number, the diameter of the rod is approximately 856 mm.
1. Identify the given values:
- Ultimate tensile strength (Su) = 630 MPa
- Surface finish factor (kc) = 0.7
- Fatigue stress concentration factor (kf) = 1.42
2. Calculate the alternating stress (Sa):
The alternating stress is the difference between the maximum and minimum axial loads applied to the bar.
Sa = (Maximum load - Minimum load) / 2
= (400 kN - 150 kN) / 2
= 250 kN / 2
= 125 kN
3. Calculate the allowable alternating stress (Sa_allow):
The allowable alternating stress is determined using Goodman's Criteria:
Sa_allow = Su / (kf * (1 + kc))
= 630 MPa / (1.42 * (1 + 0.7))
= 630 MPa / (1.42 * 1.7)
= 630 MPa / 2.414
= 260.6 MPa
4. Calculate the diameter of the rod:
The diameter of the rod can be determined using the formula for axial stress:
σ = P / (π * d^2 / 4)
where σ is the axial stress, P is the axial load, and d is the diameter of the rod.
Since we know that the factor of safety (FS) is 1.5, we can write:
Sa_allow / FS = σ_allow = P / (π * d^2 / 4)
Solving for d:
d^2 = 4 * P / (π * σ_allow)
d = √(4 * P / (π * σ_allow))
Substituting the given values:
d = √(4 * 150 kN / (π * 260.6 MPa))
= √(600 kN / (π * 260.6 MPa))
= √(600 kN / (3.14159 * 260.6 N/mm^2))
= √(600 / (3.14159 * 260.6))
= √(600 / 819.948)
= √0.73171
≈ 0.8557
Converting the diameter to mm:
d_mm ≈ 0.8557 * 1000
≈ 855.7 mm
Rounding off to the nearest whole number, the diameter of the rod is approximately 856 mm.
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A uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. Can you explain this answer?
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A uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. 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 uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. 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 uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. Can you explain this answer?.
A uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. 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 uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. 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 uniform bar having a machined surface is subjected to an axial load varying from 400 kN to 150 kN. The material of the bar has Su= 630 MPa,kc = 0.7 and kf= 1.42 Using Goodman’s Criteria and factor of safety 1.5, The diameter of the rod is __________ mm, Where, Su = ultimate tensile strength,kc = surface finish factor, kf = fatigue st!ess concentration factora) 48b) 50Correct answer is option ''. Can you explain this answer?.
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