This document discusses the design of pressure vessels subjected to external pressure. It covers pressure vessel codes and standards, fundamental design principles, and considerations for thin-walled vessels under internal and external pressure. Key points include that external pressure induces higher hoop stresses, vessels can fail through elastic or plastic buckling, and stiffening rings can increase rigidity to prevent collapse. The design procedure involves determining safe pressures based on elastic or plastic failure theories and selecting appropriate circumferential stiffeners.

1. Chemical Engineering Plant Design
CHE 435
Dr. Azeem Mushtaq
Email: azeemmushtaq@ciitlahore.edu.pk
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Lecture 17 -18

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Course learning outcomes (CLOs)
◼ Apply process design consideration and cost analysis on a
chemical engineering plant.
◼ Design Unit operation equipment.
◼ Apply optimization techniques on chemical engineering
equipment/plant.

3. Design of Pressure Vessels
-Under external pressure
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4. Design of Pressure Vessels
◼ Pressure vessel codes and standards
◼ Fundamental principles and equations
◼ General design considerations
◼ Design of thin-walled vessels under internal pressure
◼ Related examples and problems
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5. • Many of the chemical process equipment are operated
under conditions when inside pressure < outside
pressure.
Internal Pressure
vs
External Pressure
• Inside vacuum
• Outside High pressure
• Combination of both
External pressure
condition
• Multiple effect evaporator – usually operated below atm
pressure
• Due to vacuum it takes the feed on its own
• Vacuum distillation column
• Crystallizer
• Jacketed Vessels
Examples
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Design of Vessels Subject to External Pressure

6. ◼ Because of external pressure effects the cylindrical vessels
experience an induced circumferential compressive stress
(hoop stress) that is equal to twice the longitudinal compressive
stress.
◼ Under external pressure the vessels are subjected to two kind
of failure; these are due to:
1. Elastic instability (or buckling)
❑ Stress < proportional limit
◼ Geometrical irregularities like lobes (dents) in shell cause
buckling at lower pressure.
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Design of Vessels Subject to External Pressure

7. 2. Plastic Instability
 Yield point > Stress > Proportional limit
 Proportional limit is defined as the greatest stress which a material can
sustain without deviating from the law of stress-strain proportionality (i.e.,
Hooke’s Law)
◼ Out of roundness may cause failure at lower critical
pressure
 Out of roundness → When geometry is not regular
 Out of roundness results in increased stress concentration under external
pressure
 As a result, a shell of elliptical shape, or a circular shell, either dented or
with flat spots, is less strong under external pressure than a vessel
having a true cylindrical shape.
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Design of Vessels Subject to External Pressure

8. Internal Pressure Failure vs External Pressure Failure
◼ The mechanism of external pressure failure is different from internal pressure
failure.
◼ Internal pressure failure can be understood as a vessel failing after stresses in part
or a large portion exceeds the materials strength – results in “Bursting”
◼ In contrast, during external pressure failure the vessel can no longer support its
shape and suddenly, takes on a new lower volume shapes and undergoes
implosion – results in “Buckling” , it occurs in seconds.
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Design of Vessels Subject to External Pressure

9. ◼ Because of external pressure effect the cylindrical vessels, experience
an induced circumferential compressive stress equal to twice the
longitudinal compressive stress.
◼ As a result, the vessel is apt to fail because of elastic instability caused
by the circumferential compressive stress.
How the rigidity of the vessel can be increased to avoid buckling?
◼ The rigidity of the vessels under such condition may be increased
using uniformly spaced, internal or external circumferential stiffening
rings (structural support provided to support the cylindrical vessel). This reduces the effective
length of the vessels to the center-to-center distance of the stiffeners.
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Design of Vessels Subject to External Pressure

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Design of Vessels Subject to External Pressure
Stiffening rings

11. Critical length between Stiffeners
◼ If the stiffeners are spaced with in critical length, they offer
restraint to collapsing of the vessels under external pressure.
◼ Under these conditions the vessel with same thickness can
sustain higher external pressure.
Critical length (Lc) is the distance after which elastic instability
may occur
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Design of Vessels Subject to External Pressure

12. Out of roundness (Geometrical Irregularity)
◼ Out of roundness in any form is very much detrimental to the vessel strength
under external pressure.
◼ As a result, a shell of elliptical shape, or a circular shell, either dented or with flat
spots, is less strong under external pressure than a vessel having a true
cylindrical shape.
◼ Out of roundness factor, U, is
For oval or cylindrical shape: For dent:
◼ For older vessels (cylindrical vessels with dents), larger value from above
expressions is to be selected
◼ For new vessels, where U is not known, U = 1.5% (minimum) is taken
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Design of Vessels Subject to External Pressure
Where a = depth of dent
(maximum value is to be taken)

13. Design Procedure for Pressure Vessels
-Under external pressure
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14. Determination of Safe Pressure
1. Elastic failure
◼ Safe external pressure, p, against elastic failure is found
from
Where,
E = modulus of elasticity
t = thickness of the vessel
Do = outer diameter of the shell
K and m = constants = f (Do/L)
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15. Determination of Safe Pressure
2. Plastic failure
◼ Safe external pressure
◼ safe external pressure
◼ Where, t = shell thickness
U = out of roundness (%)
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16. ◼ Circumferential stiffeners are used in external pressure
vessels to improve the rigidity against collapsing. For that
purpose, the stiffeners themselves should be rigid enough.
◼ The value of moment of inertia is the measure of such
rigidity.
◼ The moments of inertia of the stiffening ring and the shell act
together to resist collapse of the vessel under external
pressure.
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What should be the circumferential stiffeners?
I = required moment of inertia of structure
t = shell thickness
Do = outer diameter of the shell
L = distance between stiffeners
As = cross-sectional area of one circumferential stiffeners
f = allowable stress
If Moment of inertia of the
stiffener > Required moment of
inertia of the structure (Correct)

17. Circumferential Stiffeners
◼ Any external metal welded or rigidly held along the circumference can
be considered as stiffener provided it satisfies above equation.
◼ In determining end side effective length, 1/3 depth (inside) of formed
end is to be added to the cylindrical length. Fig 8.1 shows stiffener
cross-section and effective length.
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18. I Beam Column
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19. I Beam Column
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20. Channel Column
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21. Example 1
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26. = No. of Stiffeners × Periphery × Weight of unit length

27. Example 2
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32. Summary
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33. ◼ Chapter 8, Introduction to CHEMICAL EQUIPMBJT DESIGN Mechanical Aspects by B. C.
BHATTACHARYYA
◼ Analysis, Synthesis, and Design of Chemical Processes (International Series in the Physical
and Chemical Engineering Sciences) 5th Edition by Richard Turton and Debangsu
Bhattacharyya
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References

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