Chapter-3 Vessel with external pressure-For students.pdf

presser vessel iit

1. INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
Design of Vessel Exposed to
External pressure
Dr. Deepak K Ojha
Department of Chemical Engineering
IIT Roorkee
Chapter-3

2. 2
Introduction
•It experiences circumferential compressive stress converging towards the vertical axis.
•Strength of the circumferential compressive stress is twice the strength of the
longitudinal compressive stress.
•Many process vessels are operated in the conditions where the external pressure is higher
than the internal pressure.
•This may be due to: inside vacuum, outside higher pressure, both.
•Example: Vacuum distillation, Condensers, Heating & Cooling coil of internal pressure
vessels.
•Rigidity of the becomes very important in this case and it can be enhanced by stiffening
rings also known stiffeners.

3. 3
Introduction
•The rings must be used uniformly spaced(equal
distance) and can be internal or external.
•It reduces the effective length of the vessel to the
center-to-center distance of stiffeners.
•It reduces the effective length of the vessel to the
center-to-center distance of stiffeners.
l
•L/D
0 becomes an important parameter in determining
the safe pressure under external comprehensive
force.
l
l
l

4. 4
Introduction
•If the vessel is deformed to the extent that the normal operation can not be carried
out, it may be considered as failed, though no bursting occurred.
•The external pressure vessel experience two types of failure: Elastic instability or
buckling within proportional limit, and failure at stress above the proportional limit but
below the yield point.
•The first type of failure occurs with the cylindrical vessels having effective length larger
than the ‘critical length’. Geometrical irregularities like ‘lobes’ in the shell also cause
buckling at low pressure.
Critical pressure = f(t/D
0, E)
•The second type of failure occurs with the cylindrical vessels having effective length
less than the ‘critical length’. Geometrical irregularities like ‘out of roundness’ in the
shell also cause buckling at low pressure.
Critical pressure = f(L/D
0,t/D
0, E)

5. 5
Preventive measures
•Critical length between stiffeners: if the stiffeners are uniformly spaced within
critical length, the vessel with same thickness can sustain higher external
pressure. For steel vessels
??????
??????=1.11�
0Τ�
0??????
Example-1: Estimate the critical length of stiffeners for the pressure vessel of external
diameter 1.2m & thickness 15 mm.
If the critical length is greater than the effective length, stiffeners are not required.
Ans: L
c=11.91 m

6. 6
Stress-Strain diagram
Elastic region
Plastic region
•If the vessels are provided with stiffeners located at or below
the critical length, the vessel can surpass the elastic failure.
Plastic failure occurs in this case.
•If the vessels are long and without stiffeners, or the stiffeners
are located above the critical length, elastic failure occurs.

7. 7
Preventive measures
•Out-of-roundness of shell: Although it doesn't cause much worries in internal
pressure vessel, it is very much determinantal to the vessel strength under
external pressure. Out of roundness factor (U, in %) is defined as
For Oval shape
U=
2??????�????????????−??????
�??????�
??????�????????????+??????
�??????�
×100

For dent or flat spots
U=
4??????
??????0
×100
a= depth of dent or flat spots.
•In case of old vessel, the largest value from (a) and (b) is to be taken for design
calculation.
•In case of new vessel whose OoR is not known, U
min= 15% is taken.

8. 8
Preventive measures
Safe pressure against elastic failure:
??????
??????=
2�
1−??????
2
??????
�
0
3
For steel the Poisson ratio, µ=0.3
??????
??????=2.2�Τ??????�
0
3

The above equation give theoretical ‘critical’ external
pressure at which a long cylindrical vessel will buckle. In
actual investigation often the magnitude was found to be
much less than the calculated.
The above expression assume to be compressed radially
without any local distortion like lobe formation which is
not always true.
Safe pressure P = P
c /f
E = P
c /3
P=0.73�Τ??????�
0
3

9. 9
Preventive measures
Considering the effect of number of lobes formed on buckling, and factor of safety (f
E =3
as per German code)
Safe Pressure, P = KE(t/D
0)
m
Where, t= thickness (without corrosion allowance), E = modulus of elasticity at design
Temperature, K and m are function of D
0/L and obtained from Table below
D
0/L K m D
0/L K m
0 0.733 3.0 0.8 0.660 2.48
0.1 0.185 2.60 1.0 0.879 2.49
0.2 0.224 2.54 1.5 1.572 2.52
0.3 0.229 2.47 2.0 2.364 2.54
0.4 0.246 2.43 3.0 5.144 2.61
0.5 0.381 2.46 4.0 9.037 2.62
0.6 0.516 2.49 5.0 10.359 2.58

10. 10
Preventive measures
Problem-2: Estimate the safe thickness for vessel expose to the external pressure (design) of
525 kN/m
2
, considering (1) no lobe formation, (2) lobe formation. Consider the external
diameter and length as 1.2m and 2.4m. Consider modulus of elasticity E = 2*10
11
N/m
2
.

11. 11
Buckling under plastic deformation
If D
0/L>5
Safe pressure (P) estimation
If D
0/L < 5
f = allowable stress.
t= corroded thickness or thickness without corrosion allowance, U = Out-of-Roundness (%)
??????=2??????
??????
&#3627408439;
0
1
1+
1.5??????(1−0.2Τ&#3627408439;
0??????)
100Τ??????&#3627408439;
0
P =2f(t/D
0)
2/2
4/2
10/2
1/2
Making sense of D/L
Increasing
P
c =2f
c(t/D
0)
f
c = Yield stress.

12. 12
Buckling under plastic deformation
Problem-3: Estimate the safe external pressure a vessel can be expose to
considering plastic deformation. The vessel is not perfect cylinder, consider the
external diameter as 1.1 & 1.2m. Length is 2.4 m. Consider Allowable stress, f =
118*10
6
N/m
2
.

13. 13
Buckling under plastic deformation
Problem-4: Estimate the safe thickness of a pressure vessel exposed to external
pressure of 525 kN/m
2
, considering plastic deformation. The vessel is not perfect
cylinder, consider the external diameter as 1.1 & 1.2m. Length is 2.4 m. Consider
Allowable stress, f = 118*10
6
N/m
2
.

14. 14
MTE: Sept. 12 at 9:00
Remaining classes on 4,8,9 Sept.