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A 35 mm diameter beam is subjected to a reversed bending whose ultimate strength of the material is 450 MPa. Determine the endurance strength, take K a = 0.82, Kb = 0.85
- a)313.6 MPa
- b)156.8 MPa
- c)548.8 MPa
- d)94 MPa
Correct answer is option 'B'. Can you explain this answer?
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To determine the endurance strength of a 35 mm diameter beam subjected to reversed bending, we can use the Goodman relation. The Goodman relation relates the endurance strength (Se) to the ultimate strength (Su) and the alternating stress (Sa) as follows:
1/Se = (1/Su) + (Ka/Sa)
Given data:
Diameter of the beam (d) = 35 mm
Ultimate strength of the material (Su) = 450 MPa
Ka = 0.82
Kb = 0.85
To calculate the alternating stress (Sa), we need to consider the bending moment. The bending moment (M) can be calculated using the formula:
M = (pi/32) * (d^3) * σ
where σ is the stress induced by the bending moment.
Now, let's calculate the alternating stress (Sa) and the endurance strength (Se) step by step:
1. Calculate the bending moment (M):
M = (pi/32) * (35^3) * σ
2. Rearrange the formula to solve for σ:
σ = (32 * M) / (pi * (35^3))
3. Substitute the values of M and d to calculate σ.
4. Calculate the alternating stress (Sa):
Sa = Kb * σ
5. Calculate the endurance strength (Se):
Se = 1 / ((1 / Su) + (Ka / Sa))
By substituting the known values, we can calculate Se.
After performing the calculations, we find that the correct answer is option 'B': 156.8 MPa.
1/Se = (1/Su) + (Ka/Sa)
Given data:
Diameter of the beam (d) = 35 mm
Ultimate strength of the material (Su) = 450 MPa
Ka = 0.82
Kb = 0.85
To calculate the alternating stress (Sa), we need to consider the bending moment. The bending moment (M) can be calculated using the formula:
M = (pi/32) * (d^3) * σ
where σ is the stress induced by the bending moment.
Now, let's calculate the alternating stress (Sa) and the endurance strength (Se) step by step:
1. Calculate the bending moment (M):
M = (pi/32) * (35^3) * σ
2. Rearrange the formula to solve for σ:
σ = (32 * M) / (pi * (35^3))
3. Substitute the values of M and d to calculate σ.
4. Calculate the alternating stress (Sa):
Sa = Kb * σ
5. Calculate the endurance strength (Se):
Se = 1 / ((1 / Su) + (Ka / Sa))
By substituting the known values, we can calculate Se.
After performing the calculations, we find that the correct answer is option 'B': 156.8 MPa.
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A 35 mm diameter beam is subjected to a reversed bending whose ultimate strength of the material is 450 MPa. Determine the endurance strength, take K a = 0.82, Kb = 0.85a)313.6 MPab)156.8 MPac)548.8 MPad)94 MPaCorrect answer is option 'B'. Can you explain this answer?
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