Mechanical Engineering - Strength of Materials - Thin and Thick Cylinders

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Question - 1

Longitudinal stresses act - to the longitudinal axis of the shell

  • A perpendicular
  • B parallel
  • C either of the above
  • D None of these

Question - 2

In case of seamless shell, the change in volume (dv) is given by

  • A \(\delta V=\frac { pdV }{ 2tE } \left( \frac { 5 }{ 2 } -\frac { 2 }{ m } \right) \)
  • B \(\delta V=\frac { pdV }{ 4tE } \left( \frac { 5 }{ 2 } -\frac { 2 }{ m } \right) \)
  • C \(\delta V=\frac { p{ d }^{ 2 }V }{ 2tE } \left( \frac { 7 }{ 2 } -2\mu \right) \)
  • D \(\delta V=\frac { p{ d }^{ 2 }V }{ 2tE } \left( \frac { 5 }{ 2 } -2\mu \right) \)

Question - 3

In a thin shell, circumferential stress (\({ \sigma }_{ c }\))is given by

  • A \({ \sigma }_{ c }=\frac { pd }{ 2t{ \eta }_{ l } } \)
  • B \({ \sigma }_{ c }=\frac { pd }{ 2t{ \eta }_{ c } } \)
  • C \({ \sigma }_{ c }=\frac { pd^2 }{ 2t{ \eta }_{ c } } \)
  • D \({ \sigma }_{ c }=\frac { pd }{ t{ \eta }_{ l } } \)

Question - 4

In thin cylinders, the radial stress in the wall thickness is

  • A zero
  • B negligibly small
  • C not negligible
  • D Any of these

Question - 5

In thick cylinders, the radial stress in the wall thickness

  • A is zero
  • B negligibly small
  • C not negligible and varies from the inner surface to the outer surface
  • D None of the above

Question - 6

Which of the following assumptions are made while solving problems on thick cylinders using Lame's theory?

  • A The material is homogeneous and isotropic
  • B Plane sections perpendicular to the longitudinal axis of the cylinder remains plane after the application of internal pressure
  • C Both (a) and (b)
  • D None of the above

Question - 7

Consider the following statements:
In a thick walled cylindrical pressure vessel subjected to internal pressure, the tangential and radial stresses are
1. minimum at outer side.
2. minimum at inner side.
3. maximum at inner side and both reduce to zero at outer wall.
4. maximum at inner wall but the radial stress reduces to zero at outer wall.
Which of the statements given above is/are correct?

  • A 1 and 2
  • B 1 and 3
  • C 1 and 4
  • D Only 4

Question - 8

In case of a column

  • A one end is hinged and other end fixed
  • B one end is fixed and other end free
  • C both ends are fixed rigid1y
  • D both ends are hinged

Question - 9

Match List I with List II and select the correct answer using the code given below the lists.

List I
(Long column)		 List II
(Critical load)
P. Both ends hinged.
Q. One end fixed and other end free.
R. Both ends fixed.
S. One end fixed and othe rend hinged.		 \(1.\quad { \pi }^{ 2 }\frac { El }{ { 4l }^{ 2 } } \)
\(2.\quad { 4\pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \)
\(3.\quad { 2\pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \)
\(4.\quad { \pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \)

Codes

  • A P Q R S 1 2 3 4
  • B P Q R S 3 2 1 4
  • C P Q R S 2 4 1 3
  • D P Q R S 4 1 2 3

Question - 10

The buckling, in case of a column, takes place about the axis having

  • A minimum radius of gyration
  • B maximum radius of gyration
  • C does not depend upon k
  • D None of the above
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