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A circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm
(A) 59
(B) 60.50
Correct answer is between ','. Can you explain this answer?
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Verified Answer
A circular bar of 500 mm length is supported by a hinge at its two en...
Given
l = 500 mm
Wmin =20 KN, Wmax =50 KN, F.S. = 1.5
Ka = 0.9, Kb = 0.85, Sut = 650 MPa,
Syt = 500 MPa, Se = 350 MPa
Let d = diameter of the bar in mm
Maximum bending moment is given by
Mmax = 6250 x 103 N-m
Mmin = 2500 x 103 N-mm
∴Mean bending moment
Variable bending moment
Section modulus of bar
∴ Mean bending stress
Variable bending stress
Corrected endurance limit
S’e = SeKaKb
= 350 x 0.9 x 0.85
Se’ = 267.75 MPa
Goodman‘s Equation
∴ d = 59.42
d ≈ 60 mm
Most Upvoted Answer
A circular bar of 500 mm length is supported by a hinge at its two en...
Given data:
- Length of bar (L) = 500 mm
- Minimum load (Pmin) = 20 kN
- Maximum load (Pmax) = 50 kN
- Ultimate strength (Su) = 650 MPa
- Yield strength (Sy) = 500 MPa
- Endurance strength (Se) = 350 MPa
- Factor of safety (N) = 1.5
- Size effect factor (Ks) = 0.85
- Surface finish factor (Kf) = 0.9
To find: Diameter of the bar as per Goodman's criteria
Formula:
Goodman's criteria states that the alternating stress (Sa) and mean stress (Sm) acting on a material should be within the endurance limit of the material. Mathematically,
Sa / Su + Sm / Sy <= 1="">
where,
Sa = (Pmax - Pmin) / 2
Sm = (Pmax + Pmin) / 2
Also, the diameter (d) of the bar can be calculated using the formula,
P / (π / 4 * d^2) <= sy="">
where,
P = Pmax
d = diameter of the bar
Calculation:
- Sa = (50 - 20) / 2 = 15 kN
- Sm = (50 + 20) / 2 = 35 kN
- Sa / Su + Sm / Sy = (15 / 650) + (35 / 500) = 0.049
- 1 / N = 1 / 1.5 = 0.67
- Sa / Su + Sm / Sy <= 1="" n="">
- Sy / N = 500 / 1.5 = 333.33 MPa
- P / (π / 4 * d^2) <= sy="">
- d = √(P / (π / 4 * Sy / N))
- d = √(50 / (π / 4 * 333.33)) = 60.50 mm (approx)
Therefore, the diameter of the bar as per Goodman's criteria is 60.50 mm (approx).
- Length of bar (L) = 500 mm
- Minimum load (Pmin) = 20 kN
- Maximum load (Pmax) = 50 kN
- Ultimate strength (Su) = 650 MPa
- Yield strength (Sy) = 500 MPa
- Endurance strength (Se) = 350 MPa
- Factor of safety (N) = 1.5
- Size effect factor (Ks) = 0.85
- Surface finish factor (Kf) = 0.9
To find: Diameter of the bar as per Goodman's criteria
Formula:
Goodman's criteria states that the alternating stress (Sa) and mean stress (Sm) acting on a material should be within the endurance limit of the material. Mathematically,
Sa / Su + Sm / Sy <= 1="">
where,
Sa = (Pmax - Pmin) / 2
Sm = (Pmax + Pmin) / 2
Also, the diameter (d) of the bar can be calculated using the formula,
P / (π / 4 * d^2) <= sy="">
where,
P = Pmax
d = diameter of the bar
Calculation:
- Sa = (50 - 20) / 2 = 15 kN
- Sm = (50 + 20) / 2 = 35 kN
- Sa / Su + Sm / Sy = (15 / 650) + (35 / 500) = 0.049
- 1 / N = 1 / 1.5 = 0.67
- Sa / Su + Sm / Sy <= 1="" n="">
- Sy / N = 500 / 1.5 = 333.33 MPa
- P / (π / 4 * d^2) <= sy="">
- d = √(P / (π / 4 * Sy / N))
- d = √(50 / (π / 4 * 333.33)) = 60.50 mm (approx)
Therefore, the diameter of the bar as per Goodman's criteria is 60.50 mm (approx).
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A circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. Can you explain this answer?
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A circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. 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 circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. 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 circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. Can you explain this answer?.
A circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. 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 circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. 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 circular bar of 500 mm length is supported by a hinge at its two ends. It is acted upon by a central cyclic load having a minimum value of 20 kN and a maximum value of 50 kN. The material properties of bar are given by: Ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. Taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9, the diameter of the bar as per Goodman’s criteria is __________ mm(A) 59(B) 60.50Correct answer is between ','. Can you explain this answer?.
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