Q.1 [14 marks]

=

Figure Q1 shows a vertical pressure vessel consisting of a cylindrical shell (radius

r = 0.50 m, and length, L 20 m) and two hemispherical heads with the same

radius as the shell. The vessel is pressurised to 125 bar. It is constructed of carbon

steel with a density of p = 8000 kg m-³ and a yield strength of Oy = 800 MPa.

support

Part A

head

B

shell

CP303 Materials, Processing, Applications

—A-

head

L

Figure Q1: Vertical Pressure Vessel

(a) Calculate the thickness, t, of the cylindrical shell and hemispherical heads

required to withstand the internal pressure if the maximum allowable stress,

Gallow, is one-half of gy.

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[2 marks]

Page 2 of 9 [Q1. continued]

(b) Calculate the mass (in kg) of the cylindrical section and hemispherical

heads. Express the combined head and shell mass as a weight (in N) and

calculate the resulting stress, ow, produced in the vessel wall at the point

where the lower head and shell meet (position A in the figure).

[4 marks]

(c) Using the thickness calculated in (a), calculate the hoop and longitudinal

stress in the cylindrical shell arising from the internal pressure. Then

calculate the combined (total) longitudinal stresses due to the internal

pressure and the weight of the shell and upper head at the position A. Also,

calculate the total combined stresses in the hoop direction at this position.

[4 marks]

(d) Similarly, consider position B at the junction between the upper head and

shell. Determine the combined longitudinal and hoop stresses at this point.

[4 marks]

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CP303 Materials, Processing, Applications

Page 3 of 9 Q.2 [11 marks]

Consider a pressure vessel with identical dimensions and materials of construction

to that in Figure Q1 above but operating at a higher pressure of 180 bar and with

an increased shell thickness of t = 2.25 cm.

(a) Calculate the hoop and longitudinal stress in the cylindrical section of the

revised vessel.

[2 marks]

(b) Assume that there was uniform internal corrosion in the cylindrical section

of the vessel at a rate of 0.8 mmpy. How many years would it take the vessel

to become unsafe - i.e. the point at which the hoop stress exceeds the yield

strength?

(c) The vessel develops a semi-circular crack in the cylindrical shell (size, 2a =

0.2 cm, Y = 0.70) oriented in the hoop (circumferential) direction. Determine

whether this crack is stable if the fracture toughness of the carbon steel is

KIC = 15 MPa m

[3 marks]

112.

[2 marks]

(d) Demonstrate that for the situation in (c) above, this vessel is not a 'leak

before break' design. Hence, calculate the value of Kic that would be

required to make this vessel leak before break.

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CP303 Materials, Processing, Applications

[4 marks]

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