Design of Tall Vessels (Distillation columns) stress relations

1. Malaviya National Institute of Technology
मालवीय राष्ट्रीय प्रौद्यौगिकी संस्थान
DESIGNS OF TALL VESSELS
SESSION 2014-15
APRIL 20, 2015
Presented by,
Pulkit M Singh Mayank Mehta

2. INTRODUCTION
Self supporting tall equipment's are widely employed in
Chemical Process Industries. Due to their large height
these equipment's are erected in open space. Special
consideration is necessary to predict the stress induced
due to Dead Weight, Action of Wind and Seismic
Forces.
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3. STRESSES IN THE SHELL
• Circumferential, Axial and Radial : Due to pressure or
vacuum in vessel.
• The compressive stresses caused by DEAD LOADS.
• Tensile and Compressive stresses due to BENDING
MOMENTUM.
• Due to eccentricity of IRREGULAR LOAD DISTRIBUTION.
• Shearing stresses caused by a torque about the
longitudinal axis.

4. DETERMINATION OF EQUIVALENT STRESS UNDER
COMBINED LOADING
 Maximum principal stress theory.
 Maximum shear energy theory
 Maximum strain energy theory
 Modified shear strain energy theory
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5. The equivalent stress applying MAX. STRESS THEORY gives: σϴ = σz
The stress equivalent to membrane stress on SHEAR STRAIN
ENERGY criterion is given by: σϴ = (σϴ
2 - σϴ * σz + σz
2 + 3τ2)^0.5
where
σz :longitudinal stress comprising axial tensile or compressive
stress due to pressure
σϴ :hoop stress
τ :shearing stress
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6. TEST PRESSURE
Test Pressure = 1.3*Design Pressure*(Stress at Test temp./Stress at
design temp.) IS : 2825-1969
The loads acting on a tall vessel will depend upon the condition
under which the vessel exits:
Case 1 Vessel under construction
Case 2 Vessel completed but not under operation
Case 3 Vessel under test condition
Case 4 Vessel in operation
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7. DETERMINATION OF LONGITUDINAL/AXIAL STRESSES
1. The axial stress due to dead loads
The major sources of the load acting over tall vertical vessel are the weight of the
vessel shell and weight of the vessel fittings which includes the internal, external
and auxiliary attachments.
Stresses caused by dead loads may be considered in three groups for convenience:
(a) stress induced by shell and insulation
(b) stress induced by liquid hold-up in vessel
(c) stress induced by the attached equipment.
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8. a. Stress induced by shell and insulation
The stress induced by shell weight at a distance X meters
from the top is:
σzs = Ws+Wi/ᴨ t (di+t)
Where , Ws = weight of the shell for a length X meter (N)
Wi = weight of installation upto a distance X from the
top (N)
t = shell thickness (m)
b. Stress induced by liquid hold-up in vessel
σzl= Wl / ᴨ t (di+t)
Where, Wl = weight of liquid hold-up upto a distance X from the
top.
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9. c. Stress induced by the attached equipment
Stress induced by the attachment, like trays, over head
condenser, instruments, platform, ladders etc is given by-
σza = Wa / ᴨ t (di+t)
Where , Wa = weight of all attachments upto a distance X from
top.
The TOTAL DEAD LOAD STRESS (σzw), acting along the axial
direction of shell at a point is given by:
σzw = σzs + σzl + σza
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10. 2. The axial stress due to pressure-
Where,
d = Di for internal pressure (m)
= Do for vacuum (m)
P = design pressure (MN/m^2)
t = thickness of vessel (m)
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11. 3. The axial bending stress due to dynamic loads
while designing the vessel stresses induced due to different
parameters have to be considered such as
a) compressive and tensile stress induced due to bending moment
caused by wind load acting on the vessel and its attachments
b) stress resulting from seismic forces.
c) stress induced due to eccentric and irregular load distributions
from piping, platforms etc.
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12. a). The axial stresses (tensile and compressive) due to wind
loads on self supporting tall vertical vessel-
The stress due to wind load may be calculated by treating the
vessel as uniformly loaded cantilever beam. The wind loading
is a function of wind velocity, air density and shape of tower.
wind load on the vessel can be given by-
where, CD = drag coefficient
ρ = density of air
Vw = wind velocity
A = projected area normal to the direction of wind
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13. • If wind velocity is known approximate wind pressure can be
computed from the following simplified relationship
• Wind velocity varies with height. it is suggested that the wind
load may be determined separately for the bottom part of the
vessel having height equal to 20 m, and then for rest of the
upper part.
Load due to wind acting in the bottom portion of the vessel
Pbw = K1 K2 p1 h1 Do
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14. Pbw = total force due to wind
load acting
p1 = wind pressure for bottom
part
Do = outer diameter of the
vessel including the
insulation thickness
h1 = height of the bottom part
of the vessel equal to or less
than 20 m
K1 = coefficient depending
upon the shape factor
= 1.4 for flat plate
= 0.7 for cylindrical surface
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15. Load due to wind acting in the upper portion of the vessel
Puw = K1 K2 p2 h2 Do
Where,
Puw = total force due to wind load acting on the upper part above 20 m.
p2 = wind pressure for upper part
Do = outer diameter of the vessel including the insulation thickness
h2 = height of the upper part of the vessel above 20 m
K2 = coefficient depending upon the period of one cycle of vibration of
the vessel
= 1 if period of vibration is 0.5 seconds or less
= 2 if period exceeds 0.5 seconds
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16. Bending moment is determined from the following equations.
(i) For the vessel with H<=20 m
Mw = Pbw*H/2
(ii) For the vessel with H > 20 m
Mw = Pbw*h1/2 + Puw(h1 + h2/2)
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17. THE STRESS RESULTING FROM SEISMIC LOADS
• it produces horizontal shear in self supported
tall vertical vessel
• This produce bending moment at the base.
• Seismic load is minimum at the base of the
column and maximum at the top of the
column.
• It is a vibrational load.
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18. Cont.
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19. Cont.
The load may, therefore be considered as acting at a distance
2/3 from the bottom of the vessel.
Load, F = m*a = (W/g) * a = Cs W
Where, W = weight of the vessel ,
Cs = seismic coefficient = (a/g)
Seismic coefficient depends on the intensity and period of
vibrations.
Seismic zone T<0.4 0.4<T<1 T>1
Mild 0.05 0.02/T 0.02
Medium 0.1 0.04/T 0.04
Severe 0.2 0.08/T 0.08
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20. Cont.
Stress induced due to bending moment up to height
X from the top of the column is given by:
MS =
𝐶 𝑆 𝑊 𝐻2 (3𝐻−𝑋)
3𝐻2
Where X = H, maximum bending moment is at the base of
column
MS = 2/3 CS W H
The resulting bending stress due to seismic bending
moment is given by:
𝜎 𝑧 𝑠𝑚 =
4 𝑀 𝑆
𝜋𝑡 𝐷 𝑖+𝑡 𝐷𝑡
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21. PERIOD OF VIBRATION OF THE VESSEL
Study of vibration of the vessel should be made to understand
• Vibration induced by the earthquake
• Vibration induced by the wind
For seismic force, natural frequency of vessel calculated for
magnitude of earthquake
At a particular wind velocity , the vessel starts vibrating in the
direction right angles to the direction of wind due to vortex
shedding.
At the critical wind velocity the frequency of vortex shedding
coincides with the natural frequency of the vessel and resonant
oscillation begins.
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22. Cont.
the frequency of vortex shedding is given by :
F =
𝑆 𝑉 𝑤
𝐷 𝑂
Where S = characteristic number = 0.2 for circular cynlinder
𝑉𝑤 = wind velocity
𝐷 𝑜 = outsides diameter of vessel including insulation
If the natural frequency , N , of the vessel is equated to vortex shedding
frequency , f , the critical wind velocity for the vessel will be obtained
as :-
N =
𝑆 𝑉𝑐
𝐷 𝑜
Where 𝑉𝐶 = 5 N Do
= critical wind velocity
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23. Cont.
To avoid the resonate oscillation the vessel should be designed , as far
as possible to avoid critical wind velocity.
So, the relationship for natural frequency and weight of vessel can be
derived as
T =
2 𝜋
3.53
𝑊 𝐻3
𝐸 𝐼 𝑔
Where T = period of vibration
W = total weight of the tower
H = total height of tower
E = modulus of elasticity
I = moment of inertia of the shell cross section =
𝜋 𝐷3
8
𝑡
D = Di + t
g = gravitational constatnts
N=1/T 23Department of Chemical Engineering

24. Cont.
units must be consistent.
If w = total weight in kN,
g = 9.81 m/s2
E = 2 × 1011N/m2,
Previous equation can also be expressed as :-
T = 6.35 × 10-5 (H/D)3/2 (W/t)1/2,sec.
Where t = corroded wall thickness, m.
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25. • Distribute external attachments (ladders,
platforms, piping, etc.) all around the vessel.
• Provide helical strakes to break up the
continuity of airflow.
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26. THE LONGITUDINAL BENDING STRESSES DUE TO ECCENTRIC
LOADS
The externally attached equipment and parts usually act as
eccentric load.
The eccentricity is calculated by: e =
𝛴 𝑀𝑒
𝛴 𝑊𝑒
𝛴 𝑀𝑒 = summation of moments of eccentric loads,
𝛴 𝑊𝑒 = summation of all eccentric loads.
Again, 𝛴 𝑀𝑒 = 𝑊𝑒1 𝑒1+ 𝑊𝑒2 𝑊𝑒2 + ……..
𝛴𝑊𝑒= 𝑊𝑒1 + 𝑊𝑒2 + …………
The additional bending stress at plane X caused at this moment is :
𝜎𝑧𝑒 =
4 𝛴 𝑀𝑒
𝜋 𝐷𝑖 + 𝑡 𝐷𝑖

27. DETERMINATION OF RESULTANT LONGITUDINAL
STRESSES
The resulting longitudinal tensile stress (on upwind side) in
absence of eccentric load will be:
(1.) for internal pressure
σz = σzp – σzw + (σzsm)
(2.) for external pressure
σz = (σzsm ) – σzp - σzw
The resulting compressive stress(on downwind side) in absence
of eccentric load will be :
(1.) for internal pressure
σz = (σzsm) + σzw - σzp
(2.) for external pressure
σz = (σzsm ) + σzp + σzw
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28. THANK YOU
DESIGNS OF TALL VESSELS
APRIL 20, 2015
Presented by,
Mayank Mehta and Pulkit M Singh
Dept. of Chemical Engineering, MNIT Jaipur
28Department of Chemical Engineering