Find out change in diameter, Mechanical Engineering

Find out change in diameter:

A cylindrical shell, 0.8 m in a diameter and 3 m long is along with 10 mm wall thickness. If the shell is subjected into an internal pressure of 2.5 N/mm2, find out

(a) change in diameter,

(b) change in length, and

(c) change in volume.

Take E = 200 GPa and Poisson's ratio = 0.25.

Solution

Diameter of the shell, d = 0.8 m = 800 mm.

Thickness of the shell, t = 10 mm.

Internal pressure, p = 2.5 N/mm2.

Hoop stress,

σh  = pd/ 2t

= 2.5 × 800/(2 × 10 ) = 100 N/mm2

Longitudinal stress,

σl  =  pd /4t

 = 2.5 × 800/(4 × 10) = 50 N/mm2

Hoop strain, εn = E (σh  - ε σl ) =( 1/(2 × 105))  (100 - 0.25 × 50)

= 4.375 × 10- 4

Longitudinal strain, εl  = E (σl  - ν σh ) = 2 × 105  (50 - 0.25 × 100)

= 1.25 × 10- 4

Change in volume /Original volume = 2εh  + εl  = 2 × 4.375 × 10- 4  + 1.25 × 10- 4

= 10 × 10- 4  = 10- 3

Increase in diameter = Hoop strain × Original diameter

4.375 × 10- 4 × 800 = 0.35 mm

Enhance in length = Longitudinal strain × Original length

1.25 × 10- 4 × 3000 = 0.375 mm

Increase in internal volume = =( δv/ v )× Original length

 Original volume =( π d 2 /4 )× l = (π /4)× 8002 × 3000 = 1507 × 106  mm3

Increase in volume = 10- 3 × 1507 × 106 = 1507 × 103 mm3

Posted Date: 1/21/2013 2:21:36 AM | Location : United States







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