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If the principle stresses in a plane stress problem are s1 = 100 MPa, s2= 40 MPa, the magnitude of the maximum shear stress (in MPa) will be
- a)60
- b)40
- c)30
- d)50
Correct answer is option 'C'. Can you explain this answer?
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If the principle stresses in a plane stress problem are s1 = 100 MPa, ...
Given:
Principal stresses:
s1 = 100 MPa
s2 = 40 MPa
To Find:
Magnitude of the maximum shear stress
Solution:
Step 1: Calculate the difference between the principal stresses
The difference between the principal stresses is given by:
Δσ = s1 - s2
Substituting the given values:
Δσ = 100 MPa - 40 MPa
Δσ = 60 MPa
Step 2: Calculate the maximum shear stress
The maximum shear stress (τmax) is given by:
τmax = Δσ / 2
Substituting the value of Δσ:
τmax = 60 MPa / 2
τmax = 30 MPa
Step 3: Conclusion
Therefore, the magnitude of the maximum shear stress is 30 MPa.
Explanation:
In a plane stress problem, the principal stresses represent the maximum and minimum normal stresses acting on a plane. The maximum shear stress occurs on a plane that is oriented at a 45-degree angle to the principal stress planes.
The difference between the principal stresses (Δσ) represents the range of normal stresses acting on the plane. The maximum shear stress is half of this difference, as the shear stress is related to the difference in normal stresses.
In this problem, the difference between the principal stresses is 60 MPa, which means that the range of normal stresses acting on the plane is 60 MPa. Therefore, the maximum shear stress is half of this value, which is 30 MPa.
Principal stresses:
s1 = 100 MPa
s2 = 40 MPa
To Find:
Magnitude of the maximum shear stress
Solution:
Step 1: Calculate the difference between the principal stresses
The difference between the principal stresses is given by:
Δσ = s1 - s2
Substituting the given values:
Δσ = 100 MPa - 40 MPa
Δσ = 60 MPa
Step 2: Calculate the maximum shear stress
The maximum shear stress (τmax) is given by:
τmax = Δσ / 2
Substituting the value of Δσ:
τmax = 60 MPa / 2
τmax = 30 MPa
Step 3: Conclusion
Therefore, the magnitude of the maximum shear stress is 30 MPa.
Explanation:
In a plane stress problem, the principal stresses represent the maximum and minimum normal stresses acting on a plane. The maximum shear stress occurs on a plane that is oriented at a 45-degree angle to the principal stress planes.
The difference between the principal stresses (Δσ) represents the range of normal stresses acting on the plane. The maximum shear stress is half of this difference, as the shear stress is related to the difference in normal stresses.
In this problem, the difference between the principal stresses is 60 MPa, which means that the range of normal stresses acting on the plane is 60 MPa. Therefore, the maximum shear stress is half of this value, which is 30 MPa.
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If the principle stresses in a plane stress problem are s1 = 100 MPa, s2= 40 MPa, the magnitude of the maximum shear stress (in MPa) will bea)60b)40c)30d)50Correct answer is option 'C'. Can you explain this answer?
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