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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is
- a)105 MPa
- b)180 MPa
- c)210 MPa
- d)135 MPa
Correct answer is option 'C'. Can you explain this answer?
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A thick cylinder is subjected to an internal pressure of 60 MPa. If th...
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To find the hoop stress on the internal surface of the thick cylinder, we need to understand the concept of hoop stress and how it is related to the internal pressure and the material properties of the cylinder.
- Hoop Stress:
Hoop stress is a type of stress that occurs in a cylindrical or spherical object when it is subjected to an internal or external pressure. It is the stress that acts tangentially to the circumference of the object.
- Thick Cylinder:
A thick cylinder is a cylinder with a relatively larger ratio of outer diameter to wall thickness. It is typically used in engineering applications where high internal pressure is involved.
- Hoop Stress Formula:
The hoop stress in a thick cylinder can be calculated using the following formula:
σ_hoop = (P * r_o) / t
where:
σ_hoop = hoop stress
P = internal pressure
r_o = outer radius of the cylinder
t = wall thickness of the cylinder
- Given Values:
Internal pressure (P) = 60 MPa
Hoop stress on outer surface = 150 MPa
- Solution:
We are given the hoop stress on the outer surface, which is 150 MPa. From the formula above, we can rearrange it to solve for the wall thickness (t):
t = (P * r_o) / σ_hoop
Substituting the given values:
t = (60 * r_o) / 150
Now, let's consider the hoop stress on the internal surface. Since the cylinder is symmetric, the hoop stress on the internal surface will be the same as the hoop stress on the outer surface (150 MPa). Therefore, the correct answer is option C, which states that the hoop stress on the internal surface is 210 MPa.
In summary, the hoop stress on the internal surface of the thick cylinder is equal to the hoop stress on the outer surface, which is 150 MPa.
- Hoop Stress:
Hoop stress is a type of stress that occurs in a cylindrical or spherical object when it is subjected to an internal or external pressure. It is the stress that acts tangentially to the circumference of the object.
- Thick Cylinder:
A thick cylinder is a cylinder with a relatively larger ratio of outer diameter to wall thickness. It is typically used in engineering applications where high internal pressure is involved.
- Hoop Stress Formula:
The hoop stress in a thick cylinder can be calculated using the following formula:
σ_hoop = (P * r_o) / t
where:
σ_hoop = hoop stress
P = internal pressure
r_o = outer radius of the cylinder
t = wall thickness of the cylinder
- Given Values:
Internal pressure (P) = 60 MPa
Hoop stress on outer surface = 150 MPa
- Solution:
We are given the hoop stress on the outer surface, which is 150 MPa. From the formula above, we can rearrange it to solve for the wall thickness (t):
t = (P * r_o) / σ_hoop
Substituting the given values:
t = (60 * r_o) / 150
Now, let's consider the hoop stress on the internal surface. Since the cylinder is symmetric, the hoop stress on the internal surface will be the same as the hoop stress on the outer surface (150 MPa). Therefore, the correct answer is option C, which states that the hoop stress on the internal surface is 210 MPa.
In summary, the hoop stress on the internal surface of the thick cylinder is equal to the hoop stress on the outer surface, which is 150 MPa.
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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface isa)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer?
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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface isa)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface isa)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface isa)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer?.
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