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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