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QUESTION: 1

The area for circumferential stress calculation for the thin cylinder subjected to internal pressure is taken as

Solution:

Circumferential stress x resisting area = Pressure x projected area

QUESTION: 2

A shell may be termed as thin if the ratio of thickness of the wall to the diameter of the shell is less than one to

Solution:

**Correct Answer :- C**

**Explanation : **T < Di/10 - Di/15 = Thin shell.

T > Di/10 - Di/15 = Thick shell.

i.e. 1/20

QUESTION: 3

A cast-iron pipe of 750 mm diameter is used to carry water under a head of 60 m. Water is the thickness of pipe if the permissible stress is to be 20 MPa?

Solution:

Pressure = ρgH = 1000 x 9,81 x 60

= 588.6 kPa

∴ P = 0.5886 MPa

QUESTION: 4

The initial hoop stress in a thin cylinder when it is wound with a wire under tension is

Solution:

A tube can be strengthened against the internal pressure by winding it with wire under tension and putting the tube wall in compression. As the pressure is applied, the resultant hoop stress produced is much less as it would have been in the absence of wire.

QUESTION: 5

The analysis of thick cylinders is usually based on Lame’s theory and for which assumptions are made as under:

1. The material of the cylinder is homogeneous and isotropic.

2. The material is stressed beyond elastic limits.

3. Yong’s modulus is the same in tension and compression.

4. Plane sections normal to the longitudinal axis of the cylinder remain plane after the application of pressure.

Which of the above assumptions are valid?

Solution:

The material is stressed within elastic limits.

QUESTION: 6

Hoop strain in case of thick cylinder subjected to internal pressure is given by

Solution:

QUESTION: 7

The error in calculation of hoop stress for a thin cylinder subjected to internal pressure if the ratio of internal diameter and thickness is 20

Solution:

Given

Hoop stress at inner surface of thick cylinder

QUESTION: 8

Variation of difference of radial and circumferential stress for a thick cylinder subjected to internal pressure follows:

Solution:

QUESTION: 9

What is the increase of volume per unit volume of a thin-walled steel circular cylinder closed at both ends and subjected to a uniform internal pressure of 0.5 MPa? The wall thickness is 1.5 mm, the. radius 300 mm, and Poissson’s ratio = 0.33. Consider E - 200 GPa.

Solution:

Longitudinal strain

Hoop strain

Volumetric strain

= (0 .486 x 2 + 0.097) x 10^{-3}

= 1.069x10^{-3}

QUESTION: 10

In thick spherical pressure vessels, the variation of the stresses is

Solution:

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