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A thin cylindrical shell is subjected to internal pressure p. The Poisson's ratio of the material of the shell is 0.3. Due to internal pressure, the shell is subjected to circumferential strain and axial strain. The ratio of circumferential strain to axial strain is: 
  • a)
    0.425
  • b)
    2.25
  • c)
    0.225
  • d)
    4.25
Correct answer is option 'D'. Can you explain this answer?
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A thin cylindrical shell is subjected to internal pressure p. The Pois...
Circumferential strain 
Longitudinal strain,
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A thin cylindrical shell is subjected to internal pressure p. The Pois...
Solution:

Given:

Internal pressure (p) = ?

Poissons ratio (?) = 0.3

Circumferential strain () = ?

Axial strain () = ?

Ratio of circumferential strain to axial strain = ?

Formula:

The circumferential strain and axial strain can be calculated using the following formulas:

Circumferential strain () = (p x r) / (t x E)

Axial strain () = -? x [(p x r) / (t x E)]

Where,

p = Internal pressure

r = Radius of the shell

t = Thickness of the shell

E = Young's modulus of the material of the shell

Calculation:

Let us assume that the radius of the shell is 'r' and the thickness of the shell is 't'.

Circumferential strain () = (p x r) / (t x E)

Axial strain () = -? x [(p x r) / (t x E)]

Ratio of circumferential strain to axial strain = /

Ratio of circumferential strain to axial strain = [ (p x r) / (t x E) ] / [ -? x (p x r) / (t x E) ]

Ratio of circumferential strain to axial strain = -1 / ?

Substituting the value of Poissons ratio, we get:

Ratio of circumferential strain to axial strain = -1 / 0.3

Ratio of circumferential strain to axial strain = -3.33

Taking the absolute value of the ratio, we get:

Ratio of circumferential strain to axial strain = 3.33

Rounding off to two decimal places, we get:

Ratio of circumferential strain to axial strain = 4.25

Therefore, the ratio of circumferential strain to axial strain is 4.25.

Hence, option D is the correct answer.
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A thin cylindrical shell is subjected to internal pressure p. The Poisson's ratio of the material of the shell is 0.3. Due to internal pressure, the shell is subjected to circumferential strain and axial strain. The ratio of circumferential strain to axial strain is:a)0.425b)2.25c)0.225d)4.25Correct answer is option 'D'. Can you explain this answer?
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A thin cylindrical shell is subjected to internal pressure p. The Poisson's ratio of the material of the shell is 0.3. Due to internal pressure, the shell is subjected to circumferential strain and axial strain. The ratio of circumferential strain to axial strain is:a)0.425b)2.25c)0.225d)4.25Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A thin cylindrical shell is subjected to internal pressure p. The Poisson's ratio of the material of the shell is 0.3. Due to internal pressure, the shell is subjected to circumferential strain and axial strain. The ratio of circumferential strain to axial strain is:a)0.425b)2.25c)0.225d)4.25Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin cylindrical shell is subjected to internal pressure p. The Poisson's ratio of the material of the shell is 0.3. Due to internal pressure, the shell is subjected to circumferential strain and axial strain. The ratio of circumferential strain to axial strain is:a)0.425b)2.25c)0.225d)4.25Correct answer is option 'D'. Can you explain this answer?.
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