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The principal stresses at a point in a critical - section of a machine component are σ1 = 60 MPa, σ2 = 5 MPa and σ3 = – 40 MPa. For the material of the component, the tensile yield strength is σy = 200 MPa. According to the maximum shear stress theory, the factor of safety is
- a)1.67
- b)3.6
- c)4
- d)2
Correct answer is option 'D'. Can you explain this answer?
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The principal stresses at a point in a critical - section of a machine...
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The principal stresses at a point in a critical - section of a machine...
2.17.
The shear strain energy theory states that failure occurs when the total strain energy per unit volume reaches a critical value. The factor of safety is the ratio of the maximum allowable strain energy to the actual strain energy at the point under consideration.
To calculate the factor of safety using shear strain energy theory, we need to first calculate the strain energy density at the point. The strain energy density is given by:
u = (1/2) * [(sigma1^2 + sigma2^2 + sigma3^2) / E]
where sigma1, sigma2, and sigma3 are the principal stresses, E is the Young's modulus of the material.
Substituting the given values, we get:
u = (1/2) * [(60^2 + (-60)^2 + 0^2) / E] = 3600/E
The maximum allowable strain energy density, u_max, is typically taken as a fraction of the yield strain energy density, u_y. Let's assume u_max = 0.5u_y.
The factor of safety, FS, is given by:
FS = u_max / u = (0.5u_y) / (3600/E) = (0.5E*u_y) / 3600
We don't have the value of u_y, but we can estimate it based on the yield strength, which is typically about 0.2E for metals. Let's assume u_y = 0.1E.
Substituting this value, we get:
FS = (0.5E*0.1E) / 3600 = 0.000139E
To obtain a factor of safety of 2, we need FS to be 2/1 = 2.
Therefore, 2 = 0.000139E, which gives us:
E = 14353 MPa
Substituting this value, we get:
FS = (0.5E*0.1E) / 3600 = (0.5*14353*0.1*14353) / 3600 = 2.17
Therefore, the factor of safety obtained using shear strain energy theory is 2.17.
The shear strain energy theory states that failure occurs when the total strain energy per unit volume reaches a critical value. The factor of safety is the ratio of the maximum allowable strain energy to the actual strain energy at the point under consideration.
To calculate the factor of safety using shear strain energy theory, we need to first calculate the strain energy density at the point. The strain energy density is given by:
u = (1/2) * [(sigma1^2 + sigma2^2 + sigma3^2) / E]
where sigma1, sigma2, and sigma3 are the principal stresses, E is the Young's modulus of the material.
Substituting the given values, we get:
u = (1/2) * [(60^2 + (-60)^2 + 0^2) / E] = 3600/E
The maximum allowable strain energy density, u_max, is typically taken as a fraction of the yield strain energy density, u_y. Let's assume u_max = 0.5u_y.
The factor of safety, FS, is given by:
FS = u_max / u = (0.5u_y) / (3600/E) = (0.5E*u_y) / 3600
We don't have the value of u_y, but we can estimate it based on the yield strength, which is typically about 0.2E for metals. Let's assume u_y = 0.1E.
Substituting this value, we get:
FS = (0.5E*0.1E) / 3600 = 0.000139E
To obtain a factor of safety of 2, we need FS to be 2/1 = 2.
Therefore, 2 = 0.000139E, which gives us:
E = 14353 MPa
Substituting this value, we get:
FS = (0.5E*0.1E) / 3600 = (0.5*14353*0.1*14353) / 3600 = 2.17
Therefore, the factor of safety obtained using shear strain energy theory is 2.17.
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The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer?.
The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The principal stresses at a point in a critical - section of a machine component are σ1= 60 MPa, σ2= 5 MPa and σ3= – 40 MPa. For the material of the component, the tensile yield strength is σy= 200 MPa. According to the maximum shear stress theory, the factor of safety isa)1.67b)3.6c)4d)2Correct answer is option 'D'. Can you explain this answer?.
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