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The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is
- a)15.0 MPa
- b)7.5 MPa
- c)30 MPa
- d)22.5 MPa
Correct answer is option 'B'. Can you explain this answer?
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The hoop stress at a point on the surface of a thin cylindrical pressu...
Analysis:
To find the value of maximum shear stress at a point on the surface of a thin cylindrical pressure vessel, we need to use the relationship between hoop stress and shear stress.
Hoop Stress:
The hoop stress, denoted by σ_h, is the stress that acts circumferentially around the cylinder. It can be computed using the formula:
σ_h = P * d / (2 * t)
where:
- σ_h is the hoop stress in MPa
- P is the internal pressure in MPa
- d is the diameter of the cylinder in mm
- t is the thickness of the cylinder in mm
In this case, the hoop stress is given as 30.0 MPa.
Shear Stress:
The shear stress, denoted by τ, is the stress that acts tangentially to the surface of the cylinder. It can be related to the hoop stress using the formula:
τ = σ_h / 2
In other words, the maximum shear stress is half of the hoop stress.
Calculation:
Given that the hoop stress is 30.0 MPa, we can calculate the maximum shear stress as follows:
τ = 30.0 / 2 = 15.0 MPa
Therefore, the value of the maximum shear stress at this point is 15.0 MPa, which corresponds to option B.
To find the value of maximum shear stress at a point on the surface of a thin cylindrical pressure vessel, we need to use the relationship between hoop stress and shear stress.
Hoop Stress:
The hoop stress, denoted by σ_h, is the stress that acts circumferentially around the cylinder. It can be computed using the formula:
σ_h = P * d / (2 * t)
where:
- σ_h is the hoop stress in MPa
- P is the internal pressure in MPa
- d is the diameter of the cylinder in mm
- t is the thickness of the cylinder in mm
In this case, the hoop stress is given as 30.0 MPa.
Shear Stress:
The shear stress, denoted by τ, is the stress that acts tangentially to the surface of the cylinder. It can be related to the hoop stress using the formula:
τ = σ_h / 2
In other words, the maximum shear stress is half of the hoop stress.
Calculation:
Given that the hoop stress is 30.0 MPa, we can calculate the maximum shear stress as follows:
τ = 30.0 / 2 = 15.0 MPa
Therefore, the value of the maximum shear stress at this point is 15.0 MPa, which corresponds to option B.
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The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point isa)15.0 MPab)7.5 MPac)30 MPad)22.5 MPaCorrect answer is option 'B'. Can you explain this answer?
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