Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
DESIGN REPORT
MECHANICAL DESIGN CALCULATIONS
FOR
GNL-LINE-3 EPCS SILOS
CAPACITY - 150MT
TAG NOS.
L3-S-101/102/103/104/105
1
0
Rev
Design Code
: IS: 9178, PART-I,II,III, IS:875, IS:1893 , Pressure Vessel
Handbook by Dennis R Moss, Pressure Vessels Hand Book
By Eugene F. Megesy (Buthod)
Client
: JPFL (Div. :- Global Nonwovens)
Consultant
: Mott Macdonald
22.06.21
16.06.21
Date
LM
LM
Prepd. By
Page 1 of 45
SB
SB
Chkd. By
JIT
JIT
Appd. By
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
NOTATIONS
bo
=
Minor Dimension of the Outlet, m
do
=
Diameter of the Opening of Hopper, m
lo
d
=
=
=
Diameter of a Circular Cylinder, that is, dia. of Vertical Portion of Storage System,
Width of Rectangular or Square Cylinder, m
Height of Cylinder, m
Coefficient,
m = 0 for Wedge Hopper
m = 1 for Conical Hopper
Distance from the axis of symmetry, m
Bulk Density of the Soild, kg/m3
Area of horizontal section of a cylinder, m2
Diameter of hopper, width of a hopper, m
Unconfined yield force of bulk solid, kgf
Hydraulic Radius = A/U
Perimeter of the Cross-Section of the Stored Material, m
Shearing Force, kgf
Janssen's Pressure Line
Depth of the Fill in the Cylinder, m
Frictional stress on the bin wall, kgf/m2
=
Shear Cell Area (Cross Sectional area of the Test Sample), m
h
m
=
=
r
w
A
B
F
R
U
S
J
Z1
=
=
=
=
=
=
=
=
=
=
th
=
tw
As
Rt
ƒƒ, ƒƒ1
=
=
Pn
=
P ntr
Pt
Pr
=
Flow Factor of a Channel (Hopper)
Initial pressure on a hopper wall at the vertex, kgf/m2
=
P nt1
V
=
FF O
P nt
Radius of Curvature at Transition
=
=
=
=
P n1
Frictional stress on the hopper wall, kgf/m2
V
Major Consolidating force, kgf
Major Force in a dome or a pipe (bulk Material under flow), kgf
V
=
Flow Function of Bulk Material
F
Instantaneous flow function of bulk solid
Time Flow Function of Bulk solid stored for a period ' t ' before delivery starts
V
V
FF
FF t
Major Dimension of the Outlet or Length of the Opening (Slot Length), m
=
=
=
=
=
Pressure normal to hopper or cylinder wall, kgf/m2
Peak Pressure at the Transition, kgf/m2
Initial pressure on a hopper wall at the Transition, kgf/m2
Radial pressure on a hopper wall at the Transition, kgf/m2
Peak Pressure at an Effective Transition, kgf/m2
Non-dimensional vertical force acting within a bulk solid at the level of the
=
transition due to radial stresses in the hopper
Vertical force developed in cylinder walls due to wall friction, kgf
Pressure normal to cylinder wall, kgf/m2
EUL
WUL
θ
θc
=
=
=
=
due to stresses in the cylinder, kgf
Effective Yield locus of the flow of bulk solid
Wall Yield locus of the flow of bulk soilds for a particular hopper wall
Hopper Slope measured from Vertical, Deg (°)
Conical Hopper slope measured from Vertical, Deg (°)
θ'
H (θ)
f
G (f)
=
=
=
=
=
Slope of Flow Channel with respect to vertical, Deg (°)
A Function depending on θ
Kinematic angle of Internal friction of Bulk Solid, Deg (°)
A Function depending on f
Effective angle of Wall Friction of Bulk Soild on the walls of the bin, Deg (°)
Pw
=
Qc
=
Ph
θp
d
=
Total Vertical force acting within the Bulk Solid at the level of transition
Plane flow Hopper slope measured from vertical, Deg (°)
Page 2 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
d'
dh
=
=
Kinematic angle of wall friction between bulk solid and wall of bin, Deg (°)
Angle of Friction between bulk soild and hopper wall, Deg (°)
A
Ar
=
=
Cross-Section area of Bin, ft2
Area of Reinforcement required, in.2
As
C.A.
E
F
Fa
ƒ
hi
=
=
=
=
=
=
=
Cross-Section area of Strut, in.2
pv
=
G ( d ')
μ
λ
σ
Aa
K1, K2
M
N
P
pn
ph
Q
Rh
S
T 1 ,T 1s
T 2 ,T 2s
G
θ
φ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Area of Reinforcement available, in.2
Corrosion Allowance, in.
Joint Efficiency, 0.35-1.0
Summation of all vertical downward forces, lb
Allowable Compressive Stress, psi
Vertical Reaction at Support Points, lb
depth of Contents to point of evaluation, ft
Rankines Factors, ratio of Lateral to vertical pressure
Overturning Moment, ft-lb
No. of Supports
Internal Pressure, psi
Pressure normal to surface of Cone, psf
Vertical Pressure of Contents, psf
Horizontal Pressure on Bin Walls, psf
Total Circumferential force, lb
Hydraulic Radius of Bin, ft
Allowable Tension Stress, psi
Longitudinal Force, lb/ft
=
=
=
=
=
Circumferential Force, lb/ft
Specific Gravity of Contents
Angle of Repose of Contents, Degrees (°)
Angle of Filling, Angle of Surcharge, Friction Angle.
Equal to θ for free filling or 0 if filled flush, Degree
Angle of Rupture, Degree
Friction Coefficient, material on material
Friction Coefficient, material on bin wall
Height of filling peak, depth of emptying crater, ft
a function of the area of shell that acts with strut to As
W
w
WT
=
=
=
Total Weight of Bin Contents, lb
Density of Contents, lb/ft3
Total Weight of Bin & Contents, lb
WR
=
=
D.L. + L.L. of roof plus applied loads, lb
(include weight of any installed plant equipment)
Weight of Shell and Lining (Cylindrical portion only), lb
W + WC
=
Load caused by Vertical Pressure of Contents, lb, = pvπR2
β
μ
μ'
Δh
Cs
=
=
=
=
A Function depending on d'
Coefficient of Friction between the bulk solid and the cylinder wall
Pressure Ratio, that is, Horizontal to Vertical Pressure
Pressure, kgf/m2
Weights
WC
=
WS
=
W2
=
W1
W3
W4
W5
W6
W7
W C1
=
=
=
=
=
Weight of Cone & Lining below Elevation under Consideration, lb
Weight of Contents in cylindrical portion of bin, lb, = πR2HW
Portion of Bin Contents carried by Bin Walls due to friction, lb, = W 2 - W 3
W 4+W R+W s
W T - W C - W C1
Weight of Bin below point of supports plus total weight of contents, lb
Weight of Contents in bottom, lb
Page 3 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
DESIGN DATA
1 Design Code
:
2 Material Stored
:
IS: 9178 (Part-I, II & III), IS:875-2002, IS:1893-2002,
Pressure Vessel Design Manual by Dennis R Moss
Pressure Vessel Hand Book By Eugene F. Megesy (Buthod)
PP Granules
3 Type of Silo
:
Cylindrical,Top Conical, Bottom Conical Outlet
4 Material Storage Capacity
:
150 T
5 Volumetric Capacity of Silo
:
278.93 m^3
4 Inside Diameter,
d
:
5 Height of Cylindrical Shell
h
:
6 Height of Top Cone
h3
7 Height of Bottom Circular Cone
4500 mm
=
4.5 m
16000 mm
=
16.0 m
:
395 mm
=
0.395 m
h1
:
3900 mm
=
3.900 m
8 Height of Bottom Transition Cone
h2
:
NA
=
NA
9 Bottom Circular Cone Smaller Dia
do
:
312 mm
=
0.312 m
:
10.0°
10 Top Cone Slope Angle
11 Bottom Circular Cone Angle
θc
:
30.0°
(Conical Hopper slope measured from Vertical, Deg (°) )
12 Density of Material Stored
w
:
530
Kg/m3
13 Corrosion Allowance
:
0.00 mm
14 Design Pressure
:
(+/-) 1500mmWC
15 Design Temperature
:
16 Radiography
:
Nil
16 Joint Efficiency
:
0.7
17 Maximum Wind Speed
:
140 Km/Hr
18 Seismic Zone
:
III
19 Material of Construction
a) Shell
b) Bottom Cone
c) Top Cone
d) Nozzle Necks(Fabricated)
e) Nozzle Necks (pipes)
f) Nozzle Flanges (From Plate)
g) Reinforcements
h) Couplings (forged)
i) Stiffeners
j) Structutarls (Inside)
k) Structutarls (Outside)
l) Gaskets
m) Fasteners
:
:
:
:
:
:
:
:
:
:
:
:
:
SA-240 Gr.304
SA-240 Gr.304
SA-240 Gr.304
SA-240 Gr.304
SA-312 TP 304 (SMLS)
SA-240 Gr.304
SA-240 Gr.304
SA-182 F304
SA-240 Gr.304
SA-240 Gr.304 / SS304
M.S. to IS:2062 Gr.A E250 BR
PTFE
SS-304
5 °C
Page 4 of 45
to
=
65 °C
39.0 m/s
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
ASSUMPTIONS
a)
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
Bulk Material :
Material to be Stored
:
Particle Size
:
Shape of Particles
:
Condition
:
Average Bulk Density
:
Moisture Content
:
Temperature
:
Period of Storage
:
Classification of Material as per IS-9178(Part-1)
- Size-Fine 3mm & Under
:
- Flowability (Free Flowing)
:
- Abrasiveness (Non Abrasive)
:
-Other Characteristics
:
-Angle of Internal Friction
f
:
- Angle of Wall Friction
d
:
d
(While Filling)
:
- Angle of Wall Friction
d
:
d
(While Emptying)
:
PP Granules
3 mm to 5 mm
Rounded
Non Abrasive
Kg/m3
530
5%
65 °C
7 Days
C
2
6
Not Known
60°
0.75φ
45°
0.60φ
36°
(Assumed)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
- Angle of friction between bulk soild & Hopper Wall Friction
dh
(While Filling)
:
34°
dh
(While Emptying)
:
22°
- Pressure Ratio
l
:
(While Filling)
- Pressure Ratio
l
:
(While Emptying)
-Coeff. of Friction Between the bulk solid & cylinder Wall
m
:
m
:
b)
Silo Wall
i) Material of Construction
ii) Finish of Wall
:
:
:
0.50
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
1.00
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
tan(d) =Pw/Ph
1.0
SA-240 Gr.304
Smooth & Passivated
Page 5 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
VOLUMETRIC & STORAGE CAPACITY CALCULATIONS
1 Material Storage Capacity
:
150 T
=
150000 Kg
2 Inside Diameter,
d
:
4500 mm
=
4.5
m
3 Height of Cylindrical Shell
h
:
16000 mm
=
16
m
4 Height of Top Cone
h3
:
395 mm
=
0.395
m
5 Height of Bottom Circular Cone
h1
3900 mm
=
3.9
m
6 Bottom Circular Cone Smaller Dia
do
:
312 mm
=
0.312
m
7 Top Cone Nozzle ID
d1
:
312 mm
=
0.31
m
:
10.0°
8 Top Cone Slope Angle
:
9 Bottom Circular Cone Angle
θc
:
30.0°
(Conical Hopper slope measured from Vertical, Deg (°) )
10 Density of Material Stored
w
:
530
Kg/m3
a) Shell Volume , V1
=
=
=
0.7854 x d^2 x h
0.7854x 4.5^2 x 16
254.47 m^3
b) Bottom Circular Cone Volume,V2
=
=
=
p h1(d2+ ddo+do2) / 12
3.1416x 3.9 x (4.5^2 + 4.5 x 0.312 + 0.312^2) / 12
22.21 m^3
c) Top Circular Cone Volume, V3
=
=
=
p h3(d2+ dd1+d122) / 12
3.1416 x 0.395 x (4.5^2 + 4.5 x 0.312 + 0.312^2) / 12
2.25 m^3
Total Volume of Silo
=
Total Volume of Silo
Volume of Shell & Bottom Cone
=
=
=
=
V1 + V2 + V3
254.47+ 22.21+ 2.25
278.93 m^3
254.47+ 22.21
= 276.68 m^3
Density of Material Stored , w
=
530
Filling Percentage
=
97.59%
=
=
Vol. Capacity of Silo x Density of Material Stored x Filling Percentage
276.68 x 530 x 0.9759
143106 Kg
=
143.11 T
Nominal Capacity
=
143 T
(Rounded off)
Nominal Capacity Considered
=
143 T
- For Design Purpose
A) VOLUMETRIC CALCULATIONS
Shell Volume + Bottom Circular Cone Volume + Top Circular Cone Volume
B) STORAGE CAPACITY CALCULATIONS
Total Weight of Material to be Stored
=
Kg/m3
Page 6 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
CHECKING ASSUMED DIMENSIONS OF SILO AS PER CODE REQUIREMENT
1 Inside Diameter,
d
:
4500 mm
=
4.5 m
2 Height of Cylindrical Shell
h
:
16000 mm
=
16 m
3 Height of Top Cone
h3
:
395 mm
=
0.395 m
4 Height of Bottom Circular Cone
h1
:
3900 mm
=
3.9 m
5 Bottom Circular Cone Smaller Dia
do
:
312 mm
=
0.312 m
6 Top Cone Nozzle ID
d1
312 mm
=
0.312 m
:
7 Top Cone Slope Angle
:
10.0°
8 Bottom Circular Cone Angle
θc :
30.0°
(Conical Hopper slope measured from Vertical, Deg (°) )
9 Density of Material Stored
w
530
Kg/m3
:
10 Classification of Material as per IS-9178(Part-1)
a) Size-Fine 3mm to 5mm
:
C
b) Flowability (Sluggish)
:
Free Flowing
c) Abrasiveness
:
Non Abrasive
d) Other Characteristics
:
Not Known
f
e) Angle of Internal Friction
:
60°
d
f) Angle of Wall Friction
:
0.75f
(While Filling)
d
:
45°
Angle of Wall Friction
d
:
0.60φ
d
(While Emptying)
:
36°
g) Angle of friction between bulk soild & Hopper Wall Friction
dh
(While Filling)
:
34°
dh
(While Emptying)
:
22°
h) Pressure Ratio
l
:
0.50
(While Filling)
Pressure Ratio
l
:
1.00
(While Emptying)
i) Coeff. of Friction Between the bulk solid & cylinder Wall
tan(d) =Pw/Ph
m
:
m
:
1.0
(Assumed)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
(From Table-3 of IS:9178, Part-1 for Granular material >=0.2mm)
Determimnation of Type of Material Flow pattern in Hoppers (Mass Flow or Funnel Flow )
In Bottom Circular Cone:
a) Bottom Circular Cone Angle
θc :
30.0°
(Hopper Slope Angle)
b) Angle of friction between bulk soild & Hopper Wall Friction
dh :
(While Filling)
34°
dh :
(While Emptying)
22°
Refer Fig.C-7 of IS:9178 (Part-III)
The Intersection of q & dh falls in Funnel Flow Region.
Hence the Material Flow Pattern in Bottom Circular Cone is Funnel Flow & all the clauses, formulae for funnel flow shall be
refered.
Range of Conical & Plane Flow
Refer Clause No.5.4 (a) & (b), Section-2 of IS:9178 (Part-III),
The Silo Bottom Cone-Hopper Shape falls in two distinct group.
a) Hopper having Circular outlet will have Conical Channel
- Applies to Bottom Circular Cone in our case
Hence, the Bottom Circular Cone, with Circular Outlet will have Conical Flow.
Refer & apply all the formulae & figures in IS:9178(Part-III) with respect to Conical Flow on Bottom Circular Cone .
Page 7 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Calculate Flow Factor ff :
Refer Fig.No.C-9 from IS:9178 (Part-III)) for Flow Factor for No Piping
Kinematic Angle of Friction of Bulk Solid f
=
60°
Effective Angle of friction of Bulk Solid on the Wall =
of the Bin, d
45°
The Intersection of Kinematic Angle of Friction of Bulk Solid f & Effective Angle of friction of Bulk Solid on the Wall of the Bin, d is at
friction Factor Value ff of 4.7
Therefore,
ff
=
4.7
>1.7
Since the Friction Flow Factor ff is greater than 1.7, the assumed values of Kinematic Angle of Friction of Bulk Solid f & Effective Angle
of friction of Bulk Solid on the Wall of the Bin, d are OK
a)
b)
Estimated Hopper Slope Angle qc
For Bottom Circular Cone - with Conical Channel, d' =45° & d =45°
i) Estimated ƒƒ
(from Fig.C-13 of IS:9178 (Part-III))
:
2
ii) Estimated qc
(from Fig.C-10 of IS:9178 (Part-III))
:
30°
Estimation of Outlet Dimensions:
°
°
I) For Bottom Circular Cone - with Conical Channel, d' =45 , d =45° & f =60
(Circular Outlet)
i) Function G(f)
:
7.5
(from Fig.C-11 of IS:9178 (Part-III))
i) H (q)
(from Fig.C-12 of IS:9178 (Part-III))
:
2.45
ii) Estimated ƒƒ
:
2
iii) Major Force in a dome or Pipe V
:
315 Kg
iv) Cross Sectonal Area at the level under consideration
As
=
=
As
=
v) Minimum Outlet Dimensions (Dia),
0.7854*d^2
0.7854 x 4.5 ^2
15.91
m^2
do
=
V . G (f)
do
=
315 x 7.5 / (15.91 x 530 )
do
=
290.00
do
=
As . w
0.290
Provided Outlet Dia of Bottom Circular Cone =
Hence OK
d)
m
mm
0.312m
=
312 mm
>
290 mm
Adopted Values for Design
i) Bottom Circular Cone Smaller Dia
do
ii) Bottom Circular Cone Angle
θc :
:
312 mm
=
30.0°
(Conical Hopper slope measured from Vertical, Deg (°))
Page 8 of 45
0.312 m
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Maximum Pressures :
Cylindrical Shell:
The maximum values of the horizontal pressures on the wall ( Ph ), the vertical pressure on the horizontal cross section of
the stored material ( Pv ) and the vertical load transferred to the wall per unit area due to friction ( Pw ) shall be calculated
as follows
Name of Pressure
During Filling
During Emptying
Maximum Pw
WR
WR
Maximum Ph
WR/μf
WR/μe
Maximum Pv
WR/μf λf
WR/μe λe
Where,
W=
=
Bulk density of the stored material
Kg/m3
530
A=
=
Horizontal cross sectional area of the stored material at depth Z.
m2
15.91
Z=
=
=
Depth below the levelled surface of the maximum possible fill in the bin
4.0
m
-Shell 1
12
m
-Shell 2
U=
=
=
Perimeter of the cross-section of the stored material at depth Z
14.14
m
-Shell 1
14.14
m
-Shell 2
R=
=
A/U
1.13
μf =
1.0
λf =
0.5
μe =
1.0
λe =
1.0
Name of Pressure
During Filling
During Emptying
Maximum Pw
598.9
598.9
Maximum Ph
598.9
598.9
Maximum Pv
1197.8
598.9
Bottom Cone:
Pv and Pw cannot be maximum at the same time. Hence for the design of hopper bottom, maximum Pv (during
filling) should be considered and this value will be the maximum Pv at the particular depth multiplied by area of
cross-section of bin. The maximum Pw (emptying) shall be calculated when the side walls are to be designed
at a particular depth as:
Pw = π DWR [ Z - Zoe (1 - e (-)Z/Zoe]
Z/Z0
=
(1 - e (-)Z/Zoe) =
0.5
0.393
(from Appendix-A)
Page 9 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Pw =
102786.3363
Pressures on Bin walls, pv and ph.
Vertical Pressure of Contents
pv
=
=
Horizontal Pressure on Silo Walls,
ph
=
ph
=
245.33 psf
1.71 psi
122.67 psf
0.86 psi
Page 10 of 45
8466.749281
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
WEIGHT CALCULATIONS
1)
Weight ,
W1
=
W + Wc
W
=
=
=
Total Weight of Silo Contents, lb or kg
143 T
143106 Kg
WC
=
Weight of Cone & Lining below Elevation under Consideration, lb or kg
W
Weight of Bottom Circular Cone (Circular Outlet)
d
=
Inside Diameter,
Bottom Circular Cone Smaller Dia
do
:
Bottom Circular Cone Incl. Angle
:
Height of Bottom Circular Cone
h1
:
Slant Height of Cone,
l
=
Thickness of Bottom Circular Cone,
tr
=
4500 mm
312 mm
30.0°
3900 mm
4503 mm
8 mm
= 4.50 m
= 0.31 m
(Conical Hopper slope measured from Vertical, Deg (°))
= 3.90 m
= 4.51 m
= 0.008 m
(Assumed)
1.5708 x l x (d + d0)
1.5708 x 4.51 x (4.5 + 0.312 )
34.09 m^2
Surface Area of Top Cone,
S
S
S
=
=
=
Weight of Bottom Circ. Cone plate,
Wc' =
Surface area x Thickness x Density of material
Wc' =
2140.9 Kg
Wc' =
Weight of Stiffeners
34.09 x 8 x 7.85
=
Weight of Bottom Circular Cone
750.0 Kg
Wc =
Wc =
Wc =
2140.852 + 750
2890.9 Kg
6373.3 lb
2) Weight of Contents in cylindrical portion of Silo,
W2
=
pi()*R^2*H*w
W2
H
w
=
=
=
Weight of Contents in cylindrical portion of Silo, lb or kg
Height of Cylinder, ft or m
Density of Contents, lb/ft3 or kg/m3
Where,
H
w
Substituting Values,
W2
W2
=
=
=
=
52.5 ft =
3
33.10 lb/ft
3.1416 x 7.3818^2 x 52.5 x33.1
297483.40 lb =
16.0 m
3
530 kg/m
134936.1 kg
3) Load caused by Vertical Pressure of Contents,
W3
=
pv * PI() * R^2
W3
pv
R
Substituting Values,
W3
W3
=
=
=
Load caused by Vertical Pressure of Contents, lb or kg
245.33 psf
2250.0 mm =
7.4 ft
=
=
245.33 x 3.1416 x 7.39^2
3901814186 lb =
1769831700.0 kg
4) Portion of Silo Contents carried by Silo Walls due to friction,
W4
=
W2-W3
W4
=
Portion of Silo Contents carried by Silo Walls due to friction, lb or kg
W4
=
297483.4 - ( 3901814185.5 )
W4
=
-3901516702.1 lb =
Page 11 of 45
-1769696764 kg
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
5) D.L. + L.L. of roof plus applied loads,
WR
=
D.L. + L.L. of roof plus applied loads, lb
WR
=
9668.7 lb lb =
4385.65 kg (Assuming Roof Thickness of 8.0mm)
Weight of Roof :
d
=
Inside Diameter,
4500 mm
= 4.50 m
Top Cone Nozzle ID,
d1 =
312 mm
= 0.31 m
Top Cone Slope Angle,
=
10.0°
h3 =
Height of Top Cone,
255 mm
= 0.26 m
Slant Height of Cone,
l
=
1475 mm
= 1.48 m
Thickness of Roof Plate,
tr
=
6 mm
= 0.01 m
(Assumed)
=
=
=
1.5708 x l x (d + d1)
1.5708 x 1.48 x (4.5 + 0.312 )
11.19 m^2
Surface Area of Top Cone,
S
S
S
Weight of Roof plate,
W R' =
Surface area x Thickness x Density of material
W R' =
527.0 Kg
W R' =
11.19 x 6 x 7.85
Other Structural Supports, Nozzles & additional Dead load on the Roof
=
3558.6 Kg
(Assumed)
Live Load on the Roof
LL =
300.0 Kg
(Assumed)
Total Weight of Roof with DL & LL,
WR =
527.049 + 3558.6 + 300
4385.6 Kg
9668.7 lb
WR =
WR =
6) Weight of Shell (Cylindrical portion only),
Inside Diameter,
d
=
Height of Cylindrical Shell-1,
Height of Cylindrical Shell-2,
Thickness of Shell-1 Plate,
Thickness of Shell-2 Plate,
Weight of Shell-1 plate,
h1
=
h2
=
ts1
=
ts2
=
W s' =
4000 mm
= 4.00 m
12000 mm
= 12.00 m
6 mm
= 0.006 m
(Assumed- Top Shell-1 Sections)
8 mm
= 0.008 m
(Assumed- Bott Shell-2 Sections)
p x Mean Diameter x Height x Thickness x Density of material
Weight of Shell-1 plate,
W s'1 =
2667.00 Kg
W s'1 =
W s'2 =
Weight of Shell-2 plate,
W s' =
Total Weight of Shell Plates,
Weight of Stiffeners, Anchor Rings &
additional weight on Shell
Weight of Shell, Stiffeners etc.,
=
Ws =
Ws =
Ws =
Ws =
7)
W5
W5
W5
=
=
=
=
4500 mm
= 4.50 m
3.1416 x 4.506 x 4 x 6 x 7.85
10672.74 Kg
13339.74 Kg
5255.6 Kg
Weight of Shell + Weight of Stiffeners & additional items
13339.74 + 5255.57
18595.3 Kg
40995.7 lb
W4+WR+Ws
-3901516702.1 + 9668.71 + 40995.68
-3901466037.7 lb
-1769372353 Kg
8) Total Weight of Silo & Contents,
WT
WT
WT
WT
=
=
=
=
=
Total Weight of Silo & Contents,
Empty Weight of Silo + Weight of Contents
16720+143000
=
159720.0 Kg
352182.6 lb
159720.0 Kg
Page 12 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
9) Weight , W6
W6
=
WT - WC - WC1
WC1
WC1
=
=
=
Weight of Contents in bottom, lb
11771.3 Kg
25955.7 lb
WT
=
352182.6 lb
Wc
=
6373.3 lb
W6
W6
=
=
=
=
WT - WC - WC1
352182.6 - 6373.25 - 25955.72
319853.6 lb
145058.3 Kg
Where,
W C1
W6
10) Weight of Silo below point of supports plus total weight of contents,
W7
=
Weight of Silo below point of supports plus total weight of contents, lb
Weight of Contents in Bottom Cone + Weight of Bottom Cone +Weight of Shell portion
=
below Support + Weight of Contents in Shell below point of Support
Weight of Contents in Bottom Cone
=
=
Weight of Bottom Cone
Wc" =
Wc" =
Volume of Bottom Cone x Density of Stored Material
11771.3 Kg
2890.85 Kg
6373.3 lb
Length of Shell Portion below Point of Support
9000.0 mm
=
Weight of Contents in Shell below point of Support
75863.75 Kg
=
W7
W7
W7
=
=
=
11771.3 + 2890.852 + 75863.75
90525.9 Kg
199575.6 lb
11) Summary of Silo Weights
Weight of Shell
Weight of Bottom Circular Cone
=
=
2667.0 Kg
2140.9 Kg
Weight of Top Cone
Weight of Structurals, Stiffeners etc
Weight of above Components
=
=
=
527.0 Kg
9864.2 Kg
15199.1 Kg
Add 10% Weight for other items
=
1520.0 Kg
Total Empty Weight of Silo
=
16720.0 Kg
Weight of Contents in Silo
Weight of Contents in Silo
=
=
143106.4 Kg
143000.0 Kg
Weight of Silo with Contents
=
159720 Kg
Page 13 of 45
= 143.1 T (Nominal Capacity as per Drg.)
= 143.0 T (Nom.Capacity based on Volume & % filling)
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
FORCE, STRESS, THICKNESS CALCULATIONS FOR CYLINDRICAL SHELL
(FOR SOLID MATERIAL)
a) Longitudinal Force on Shell due to Solid Material
T1
=
-W5/π*D - M48/πD
T1
D
M
=
=
=
Longitudinal Force, lb/ft or kg/m
Diameter of Silo, ft or m
Overturning Moment, ft-lb or kg-m
Where,
D
=
14.77 ft
M
M
=
=
Windload x Height of Support location
558827.1 ft-lb
W5
=
40995.7 lb
T1
=
=
=
- (40995.68/ 3.1416 x 14.77) - (48 x 558827.06/ 3.1416 x 14.77)
-578962.62 lb/ft
-861496.379 kg/m
=
4.50m
b) Circulferential Force on Shell due to Solid Material
T2
Where,
ph
R
T2
=
phR
=
=
=
=
=
=
122.67
7.382
psf
ft
122.67 x 7.3818
905.53 lb/ft
1347.34 kg/m
c) Maximum Allowable Compressive Stress (Boardman Formula)
Fa
=
20,000 psi maximum
d) Required Shell Thickness for Solid Material,
t
=
T/(12 * Fa)
Where,
T
T
T
=
=
=
Max(T1, T2)
Max(-578962.62 , 905.53)
905.53
lb/ft
Fa
=
20,000
Substituting Values,
t
=
=
=
psi maximum
T/(12 * Fa)
905.53 / (12 x 20000 )
0.00377 in
Hence Required Shell Thickness for Solid Material,
t
=
0.096 mm
Add Corrosion Allowance
CA =
0.00 mm
Minimum Required Thickness with C.A for Solid Material,
=
0.10 mm
Minimum Required Shell Thickness without C.A as per IS:9178 Part -II
=
6.0 mm
Page 14 of 45
(Refer Ring Support Ring Cals)
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Provided Shell Thickness for Solid Material,
t=
6.0 mm
t=
8.0 mm
> Calculated (Upper Shell-1 Portions of 4.0m Height)
> Calculated (Lower Shell-2 Portions of 12.0m Height)
Hence Safe
Page 15 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
FORCE, STRESS, THICKNESS CALCULATIONS FOR CYLINDRICAL BOTTOM CIRCULAR CONE
FOR SOLID MATERIAL
A) Cylindrical Bottom Cone Thickness for Solid Material
a) Vertical pressure of Contents in Bottom Cone
pv
=
w*H
H
=
=
=
=
=
Height of Cylinder Shell + Bottom Cone, ft or m
h + h1
16000 + 3900
19900 mm
65.29 ft
w
=
=
=
Density of Contents, lb/ft3 or kg/m3
kg/m3
530
lb/ft3
33.1
Therefore, pv
=
w*H
pv
pv
=
=
H
w
pv
=
33.09 x 65.29
2160.45 psf
15.01 psi
b) Pressure Normal to Surface of Cone due to Solid Material
pn
=
pv*Sin^2(α+θ)/Sin^3α(1+Sinθ/Sinα)^2
Where,
θ
θ
=
=
Angle of Repose of Contents, Degrees (°)
30.0°
α
=
60.0°
Cone Angle with Horizontal
pv
=
2160.45
psf
=
=
=
=
pv*Sin^2(α+θ)/Sin^3α(1+Sinθ/Sinα)^2
2160.45 x Sin^2 (60 + 30) / ( Sin^3( 60) x (1+Sin30 / Sin60)^2)
1336.9
psf
9.28
psi
Substituting Values,
pn
pn
pn
c) Weight for Bottom Circular Cone, W1
Where,
W1
=
W + Wc
WC
=
=
=
=
=
Weight of Cone & Lining below Elevation under Consideration, lb or kg
6373.3 lb
Total Weight of Silo Contents, lb or kg
143000 Kg
315315.0 lb
=
=
=
W + Wc
315315 + 6373.25
321688.3 lb
W
W
Substituting Values,
W1
W1
d) Longitudinal Force on Bottom Circular Cone due to Solid Material
T1
=
W1 / (2 p R Sinα)
Page 16 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Where,
W1
R
α
Substituting Values,
T1
T1
T1
=
=
=
321688.3 lb
7.38 ft
60.0°
=
=
=
=
W1 / (2 π R Sinα)
321688.25/(2 x 3.1415 x 7.3818 x Sin(60))
8008.95
lb/ft
11917.3176
kg/m
= 89 in
Cone Angle with Horizontal
e) Circumferential Force on Bottom Circular Cone due to Solid Material
T2
=
pn*R/Sinα
pn
R
α
=
=
=
1336.9
7.38 ft
60.0°
Substituting Values,
T2
T2
=
=
pn*R/Sinα
1336.9 x 7.3818 / Sin( 60 )
Where,
T2
T2
=
=
psf
Cone Angle with Horizontal
11395.43
16956.4
lb/ft
kg/m
f) Required Thickness of Bottom Circular Cone for Solid Material
t
=
(T1 or T2) / (12xSxE) +C.A
Where,
S
S
=
=
Maximum Allowable tension Stress for Cone Material
17068.02
psi
E
E
=
=
Joint Effeciency
0.7
C.A.
=
=
=
Corrosion Allowance
0.00 mm
0.00 in
=
=
=
(T1 or T2) / (12SE)
MAX (8008.95 or 11395.43) / ( 12 x 17068.02 x 0.7 )
0.08 in
C.A.
Substituting Values,
t
t
Hence Required Bottom Cone Thickness for Solid Material,
t
=
2.032 mm
Add Corrosion Allowance
CA =
0.00 mm
Minimum Required Thickness of Bottom Cone with C.A for Solid Material,
=
2.032 mm
Minimum Required Thickness of Bottom Cone without C.A as per IS:9178 Part -II
=
6.0 mm
Provided Thickness of Bottom Cone for Solid Material,
t=
8.0 mm
> Calculated
Hence Safe
Page 17 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
g) Calculating Required Bottom Cone Ring Compression for Solid Material
Q
=
T1*R*Cosα
Where,
Q
=
Total Circumferential Force
T1
=
=
Longitudinal Force
8008.95
lb/ft
R
=
7.38 ft
=
=
=
T1*R*Cosα
8008.95 x 7.3818 x Cos (60)
29560.2 lb
Substituting Values,
Q
Q
Page 18 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
CHECKING SILO SHELL, BOTTOM CONE & TOP CONE FOR SMALL INTERNAL PRESSURE
a)
Calculating Pressures acting on Silo
i) Pressure due to Gas Pressure during filling / emptying
P1
=
=
=
=
Pressure due to Gas Pressure during filling / emptying
(+/-) 1500mmWC
307.23
psf
2.14
psi
P3
=
Pressure due to Solid Material
P3
=
w*H*K*Cosf / 144
Where,
f
=
=
Angle of Filling, Angle of Surcharge, Friction Angle.
Equal to θ for free filling or 0 if filled flush, Degree
60°
H
=
=
=
Height of Cylinder, ft or m
16.000m
52.50 ft
w
=
=
=
Density of Contents, lb/ft3 or kg/m3
kg/m3
530
lb/ft3
33
=
=
Rankines Factors, Ratio of Lateral to Vertical Pressure
1
=
=
=
=
w*H*K*Cosf / 144
33.09 x 52.5 x 1 x COS(60) / 144
6.04
psf
0.050
psi
P1
ii) Pressure due to Solid Material
f
w
K
Substituting Values,
P3
P3
P3
iii) Total Pressure due to Solid Material & Gas Pressure
P
=
Total Pressure
P
=
=
=
=
P1 + P3
307.23 + 6.04
313.27
2.175
P
b)
psf
psi
Calculating Forces acting on Shell (as per API-620)
i) Summation of all vertical downward forces
Summation of all vertical downward forces,
F
=
WT
Where,
WT
=
=
159720.0 Kg
WT
=
352182.6 lb
WT
Total Weight of Silo & Contents, lb
Page 19 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Substituting Values,
F
F
F
=
=
=
WT
352182.6 lb
159720.0 Kg
W6
=
WT - WC - WC1
WT
=
Total Weight of Silo & Contents, lb
WC
=
Weight of Cone below Elevation under Consideration, lb or kg
=
25955.7 lb
=
=
=
=
WT - WC - WC1
352182.6 - 6373.25 - 25955.72
319853.6 lb
145083.1 Kg
A
=
p * R2
R
=
7.38 ft
=
=
=
=
π * R2
3.1416 x 7.3818^2
ft2
171.19
m2
15.91
ii) Weight, W6
Where,
WT
Wc
W c1
W c1
Substituting Values,
W6
W6
W6
=
=
352182.6 lb
6373.3 lb
Weight of Contents in bottom, lb or kg
iii) Cross Sectional Area of Silo
Where,
Substituting Values,
A
A
A
iv) Longitudinal Force on Shell due to Internal Pressure
Where,
T1s
=
R/2*(P+(-W6+F)/A)
P
=
=
=
Internal Pressure, psi
307.23
psf
2.134
psi
W6
=
=
W T - W C - W C1
319853.6 lb
F
=
=
Summation of all vertical downward forces, lb or kg
352182.6 lb
A
=
=
Cross-Section area of Silo, ft2 or m2
ft2
171.19
R
=
7.38 ft
=
=
=
=
R/2*(P+(-W6+F)/A)
7.3818/2 x (307.23+ ( - 319853.63 + 352182.6) / 171.19)
1830.98
lb/ft
2724.50
kg/m
Substituting Values,
T1s
T1s
T1s
Page 20 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
iv) Circumferential Force on Shell due to Internal Pressure
T2s
=
P*R
Where,
R
=
7.38 ft
P
=
=
=
Total Pressure
307.23
2.134
psf
psi
=
=
=
=
P*R
307.23 x 7.3818
2267.92
3374.66
lb/ft
kg/m
Substituting Values,
T2s
T2s
T2s
c)
Calculating Shell Thickness for Internal Pressure (as per API-620)
i) Required Shell Thickness for Internal Pressure
t
=
Maximum(T1s or T2s)/(12* S*E)+C.A.
t
=
(T1s or T2s) / (12* SE) +C.A
Where,
T1s
=
Longitudinal Force on Bottom Cone
T2s
=
Circumferential Force on Bottom Cone
S
S
=
=
Maximum Allowable tension Stress for Cone Material
17068.02
psi
E
E
=
=
Joint Effeciency
0.7
C.A.
=
=
=
Corrosion Allowance
0.00 mm
0.00 in
=
=
=
(T1s or T2s) / (12 SE)
MAX (1830.98 or 2267.92) / ( 12 x 17068.02 x 0.7 )
0.02 in
T1s
T2s
C.A.
Substituting Values,
t
t
=
=
1830.98
lb/ft
2267.92
lb/ft
Hence Required Shell Thickness for Internal Pressure,
t
=
0.508 mm
Add Corrosion Allowance
CA =
0.00 mm
Minimum Required Shell Thickness with C.A for Internal Pressure,
=
0.5 mm
Minimum Required Shell Thickness without C.A as per IS:9178 Part -II
=
6.0 mm
Provided Shell Thickness for Internal Pressure,
t=
6.0 mm
t=
8.0 mm
> Calculated (Upper Shell-1 Portions of 4.0m Height)
> Calculated (Lower Shell-2 Portions of 12.0m Height)
Hence Safe
Page 21 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
d)
Calculating Forces acting on Bottom Cone (as per API-620)
i) Longitudinal Force on Bottom Cone due to Internal Pressure
T1s
=
R/2Cosα*(P+(-W6+F)/A)
P
=
=
=
Internal Pressure, psi
307.23
psf
2.134
psi
W6
=
=
W T - W C - W C1
319853.6 lb
F
=
=
Summation of all vertical downward forces, lb or kg
352182.6 lb
A
=
=
Cross-Section area of Silo, ft2 or m2
ft2
171.19
R
=
7.38 ft
α
=
60.0°
=
=
=
=
=
R/2Cosα*(P+(-W6+F)/A)
7.3818/ 2 x Cos60 x (307.23 + ( - 319853.63 + 352182.6) / 171.19)
3661.96
1830.98
lb/ft
2724.50
kg/m
Where,
Substituting Values,
T1s
T1s
T1s
Cone Angle with Horizontal
ii) Circumferential Force on Bottom Cone due to Internal Pressure
Where,
T2s
=
PR / SIN(a)
R
=
7.38 ft
P
=
=
=
=
Total Pressure
307.23
2.134
60.0°
=
=
=
=
PR / SIN(α)
307.23 x 7.3818/SIN(60)
2618.76
lb/ft
3896.71
kg/m
α
Substituting Values,
T2s
T2s
T2s
e)
psf
psi
Cone Angle with Horizontal
Calculating Bottom Circular Cone Thickness for Internal Pressure (as per API-620)
Required Bottom Circular Cone Thickness for Internal Pressure
t
=
Maximum(T1s or T2s)/(12 * S*E)+C.A.
t
=
(T1s or T2s) / (12 SE) +C.A
Where,
S
S
=
=
Maximum Allowable tension Stress for Cone Material
20000.00
psi
E
E
=
=
Joint Efficiency
0.7
Page 22 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
C.A.
C.A.
Substituting Values,
tc =
tc =
=
=
=
Corrosion Allowance
0.00 mm
0.00 in
=
=
=
(T1 or T2) / (12 SE)
MAX(1830.98 OR 2618.76) / ( 12 x 20000 x 0.7 ) )
0.02 in
Hence Required Bottom Cone Thickness for Internal Pressure,
t
=
0.508 mm
Add Corrosion Allowance
CA =
0.00 mm
Minimum Required Thckness with C.A for Internal Pressure,
=
0.5080 mm
Minimum Required Thickness without C.A as per IS:9178 Part -II
=
6.0 mm
Provided Bottom Cone Thickness for Internal Pressure,
tc =
8.0 mm
> Calculated
Hence Safe
f)
Calculating Bottom Circular Cone Compression for Internal Pressure (as per API-620)
i) Compression Area Length in Cone Part,
Wh
=
0.6*SQRT (R2*(tc - C.A.) )
Where,
R
=
7.38 ft
α
=
60.0°
R2
=
=
=
=
R / SIN(a)
7.3818 / SIN(60)
8.53 ft
102.360 in
tc
=
=
=
Cone Thickness
8.0 mm
0.315 in
CA
CA
=
=
0.00 mm
0.000 in
=
=
=
=
0.6*SQRT (R2*(tc - C.A.) )
0.6 x SQRT(102.36(x (0.31496 - 0 ) )
3.410 in
=
0.284 ft
86.6 mm
R2
tc
Substituting Values,
Wh
Wh
Wh
ii) Compression Area Length in Cone Part,
Wc
=
0.6*sqrt(R*(t - C.A.)
Where,
R
α
t
t
=
=
=
7.38 ft
88.582 in
60.0°
=
=
=
Shell Thickness
6.0 mm
0.240 in
Page 23 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
CA
CA
=
=
0.00 mm
0.000 in
=
=
=
=
0.6*SQRT (R*(t - C.A.) )
0.6 x SQRT(88.5816x (0.24 - 0 ) )
2.770 in
=
0.231 ft
70.4 mm
Substituting Values,
Wc
Wc
Wc
iii) Total Required Compression for Compression Ring for Internal Pressure
Q
=
T2*Wh+T2s*Wc-T1*R2*Cosa
Where,
T1
T2
T2s
Wh
Wc
R2
α
=
=
=
=
=
=
=
8008.95 lb/ft
11395.43 lb/ft
2618.76 lb/ft
0.2850 ft
0.2310 ft
7.38 ft
60.0°
=
=
=
T2*Wh+T2s*Wc-T1*R2*Cosa
11395.43 x 0.285 + 2618.76 x0.231 - 8008.95 x 7.3818 x COS(60 )
-25707.6 lb
Substituting Values,
Q
Q
Page 24 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
DESIGN OF TOP CURB ANGLE AND STIFFENERS
a)
Top Curb Angle Size Calculations:
( As Per API 650, Clause No : 5.9.6.1 )
D,
H2,
Z,
V,
Nominal Dia
Height of Silo Shell, incl. Any free board
Required Minimum Section Modulus, in cm^3
Design Wind Speed (as per wind cals.)
Reqd. Section Modulus of Top Curb Angle,
Selected Curb Angle
=
=
=
=
Z=
Z=
Z=
4.5 m
16.0 m
To Be Calculated
140.4 Km/ Hr
(D2 H2 /17 )* ( V /190) 2
((4.5^2 x 16 )/17) x (140.4 / 190 )
14.09 cm^3
=
ISA- 100 x 100 x 10 Thk
Section Modulus of Selected Curb Channel - 'Z' =
24.7 cm^3
Provided 'Z' (24.7 ) > Required 'Z' (14.09)
Hence selected Top Curb Angle ISA 100 x 100 x 10Thk is Safe.
b)
Stiffening Ring Calculations :
Maximum Height of Unstiffened Shell
(As per API 650, Clause no : 5.9.7.1)
H1,
t,
D,
V,
Max.Height of the Unstiffned Shell
=
As Ordered Thickness of Top Shell Course
Nominal Dia
Design Wind Speed
H1
Transposed Width of Shell Course
9.47 x t x
=
6.00 mm
=
4.50 m
=
140.4 Km/ Hr
= 9.47 x 6 x (SQRT ( (6/4.5)^3) ) x ( 190 /140.4 )^2
H1
=
160.21 m
( As per API 650, Clause no : 5.9.7.2 )
Wtr, Transposed Width of each Shell Course
W, Actual Width of each Shell Course
t uniform, As Ordered Thickness of Top Shell Course (thinnest)
=
W
( t uniform / t actual )^5
=
6.00 mm Incl. CA
t actual, As Ordered Thickness of Shell Course,for Which Transposed Width is being Calculated
Shell Course
(from bottom)
W,
mm
First
Second
Third
Fourth
Fifth
Sixth
Seventh
Eighth
2000
2000
2000
2000
2000
2000
2000
2000
Height of Transformed Shell
Height of Transformed Shell
t actual ,
(Incl C.A.) mm
8.0
8.0
8.0
8.0
8.0
8.0
6.0
6.0
Total ( Σ Wtr )
Wtr ,
mm
974.3
974.3
974.3
974.3
974.3
974.3
2000.0
2000.0
9845.7
= Sum of Transposed Widths of All Shell Courses
= 9846 mm = 9.8 m
Check for Requirement of Intermediate Wind Girders /Stiffeners
(As Per API 650 ,Clause No : 5.9.7.3)
( t / D)^3 x (190 / V)^2
9.8 m
Σ W tr
<
<
160.21 m
H1
Height of Transformed Shell < Max.Height of the Unstiffned Shell
Since Height of Transformed Shell is Less than Max. Unstiffened Height
Intermediate Wind Girder (Stiffener) is Not Required, but provided for safety
Provided 3-Nos Stiffeners of ISMC-150
Page 25 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Stiffening Ring Size Calculations:
( As Per API 650, Clause No : 5.9.6.1 )
D,
H2,
Z,
V,
Nominal Dia
Height of Silo Shell, incl. Any free board
Required Minimum Section Modulus, in cm^3
Design Wind Speed (as per wind cals.)
Reqd. Section Modulus of Stiffening Ring
=
=
=
=
Z=
Z=
Z=
Selected Stiffening Ring
=
4.5 m
16.0 m
To Be Calculated
140.4 Km/ Hr
(D2 H2 /17 )* ( V /190) 2
((4.5^2 x 16 )/17) x (140.4 / 190 )
14.09 cm^3
ISMC-150
Section Modulus of Selected Stiffening Ring Channel - 'Z' =
Provided 'Z' (103.9 ) > Required 'Z' (14.09)
Hence selected Stiffening Ring Size of ISMC-150 is Safe.
No. of Stiffening Rings Provided on Shell =
3 Nos
No. of Stiffening Rings on Bottom Cone =
2 Nos
Page 26 of 45
103.9 cm^3
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
TOP CONICAL ROOF PLATE DESIGN FOR INTERNAL PRESSURE & DEAD LOADS
ROOF PLATE DESIGN:
(As per API 620 ,Clause no:3.10.2.5,c)
ROOF TYPE :
STIFFENED
Slope of the Conical Roof Angle (Roof Angle)
=
10.0°
=
=
=
=
=
6 mm
mm =
tanθ x D/2
395.00
mm
Vertical ht /sin θ
2284.48
mm
0.236 in
=
0.00
0.000 in
As per API 650 ,Clause no:3.10.2.2
Proposed Thickness of Roof
The Vertical Height of Conical Roof (H Roof)
Slant Height of the Roof Cone
Nominal Thickness of Roof Plate Shall be Equal to Shell Thick (Excl. C.A.)
Corrosion Allowance
mm =
ROOF PLATE WEIGHT :
Weight, Including C.A
W =
4385.65 Kg =
For Nozzles, Pads, Handrails, Ladder, Supports Cleats Etc.,
F =
=
3858.6 Kg
8508.22 lb
9669 lb
(Assumed)
For Conical Roof :
R1 = Infinity
R2 = R3 / cos a
R3 =
a=
=
=
T1 =
2250.186 mm
512.71 in =
13022.76 mm
80.05
R2 = R3 / cos a
=
T1 =
88.59 in =
o
R3
2 cos a
P+
88.59
2 cos(80.05)
( 256.35 )
735.93
T2 = P R3
cos a
= 2.14 x 88.59
cos(80.05)
T2 =
1097.19
2.13 +
W+F
At
9668.54 + 8508.22
24656
x ( 2.87 )
lb/in
lb/in
t=
T1 + c
or
t = T2 + c
S tsE
S tsE
= 0.0616 in
or
= 0.0918 in
= 1.56 mm
or
= 2.33 mm
From the above calculations, the minimum required thickness of Roof is =
Add Corrosion Allowance, CA
= 0.00 mm
Minimum Reqd. Thickness of Top Roof Cone
= 2.34 mm
Minimum Required Thickness as per IS:9178
=
\ Provided Roof Cone thk = 6.00 mm
2.33
mm
6.0 mm , without corrosion allowance
>
2.34 mm
(Calculated with CA)
The Provided Roof Cone Thickness is more than minimum calculated thickness with CA. Hence Safe.
Page 27 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Design of 150 T PP Granules Storage Silo Body Flange
Design Int Pressure,Pi (Kg / cm2)
0.153
Design Ext Pressure,Pe(Kg / cm2)
0.153
Design Temperature (oC)
65
Flange material
SA 240 Gr. 304
Bolting Material
SA 193 Gr. B8
Neck I/D (mm)
Neck Thickness (mm)
Bolt Size
No. of Bolts
Corrosion Allowance (mm)
Gasket Material
Gasket Width (N)
Gasket thickenss (T)
Tongue width (w)
Gasket Mean Diameter (N)
4680 O/D
4600 P.C.D.
4680 Gasket O/D
4519 Flange I/D
Design Conditions
Design temp,Sfb
Amb temp, Sfa
Allowable Stresses
Flange
Bolting
Design temp,Sb
1249.42 kg / cm²
1292.45 kg / cm²
1406.14 kg / cm²
1321.77 kg / cm²
Amb temp, Sa
DESIGN INPUT DATA
Flange O/D (A)
4680
Flange I/D (B)
4519
Flange B.C.D. (C)
4600
Gasket O/D
4680
Gasket I/D
4519
Flange thickness provided
40
GASKET AND FACING DETAILS
Facing
Non-Asbestos (3 Thk)
Factor m
80.5
mm
Seating Stress (y)
3
mm
Basic Gasket Width (bo)
0
mm
Eff. Gasket Width (b)
4600
mm
4500
8
M36
88
0
80.5 x 3
4519 Gasket I/D
40
4500 Neck I/D
8 thk
Load
HD = πB2P/4
HG = Wm1 - H
HT = ( H - HD)
24539.52 Kg
1413.78 Kg
882.07 Kg
HD = πB2Pe/4
H = πG2Pe/4
HT = ( H - HD)
24539.52 Kg
25421.58 Kg
882.07 Kg
HG = W
559146.85 Kg
t = √(MoY)
(SfbB)
Operating Internal pressure
30.83 mm
THK OK
38 Ø Holes
88 Nos.
mm
mm
mm
mm
mm
mm
go (mm)
h (mm)
g1 (mm)
8
8
16
1b
2
1600
psi
40.25
mm
15.99
mm
SHAPE CONSTANTS
k = A/B
1.04
Y
54.84
BOLT SPACING
84.14 mm
Min. Bolt spacing (Bsmin)
164.22 mm
Act. Bolt spacing (Bsact)
168 mm
Max. Bolt spacing (Bsmax)
FLANGE DESIGN BOLT LOAD
H = G2πP/4
25421.58 Kg
HP=2bπGmP
1413.78 Kg
Operating Conditions
Wm1 = H + HP
26835.36 Kg
Am1=Wm1/Sb
21.48 cm²
Gasket Seating Conditions
Wm2=πGby
259865.47 Kg
Am2=Wm2/Sa
196.6 cm²
W=(Am+Ab)/2
559146.85 Kg
Actual
Reqd. bolt area Am
196.6 cm²
Act bolt area Ab
649.45 cm²
MOMENT CALCULATIONS
Lever Arm
Operating Internal pressure
hd = (C-B) / 2
4.05 cm
hg = (C-G) / 2
0.03 cm
ht = (hd+hg) / 2
2.04 cm
Operating External pressure
hd = (C-B) / 2
4.05 cm
hg = (C-G) / 2
0.03 cm
ht = (hd+hg) / 2
2.04 cm
Gasket Seating
hg = (C-G) / 2
0.03 cm
FLANGE THICKNESS INCLUDING CA
Operating External Pressure
t = √(MoeY)
30.73 mm
(SfbB)
Moments
MD = HD x hd
MG = HG x hg
MT = HT x ht
MO
99385.04 Kg cm
35.34 Kg cm
1797.21 Kg cm
#REF!
Moe = HD x (hd - hg) + HT x (ht - hg)
100546.71 Kg cm
Moe =
M'O
13978.67 Kg cm
Gasket Seating
t = √(M'oY)
10.98 mm
(SfaB)
THK. OK
THK OK
STRESSES INDUCED
Operating Internal pressure
Operating External Pressure
Gasket Seating
ST = YMO
ST = YMOe
ST = YM'O
767.71 kg / cm²
762.62 kg / cm²
106.02 kg / cm²
t² B
t² B
t² B
STRESS OK
STRESS OK
STRESS OK
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
DESIGN OF RING SUPPORT
( As per Pressure Vessels Hand Book By: Eugene F. Megesy)
Typ. Section with Notations
1)
2)
Base Data
Material of Construction
No. of supports
Base plate OD
Base plate thickness
Compression plate OD
Compression plate thk
Allowable stress
Support Member Flange Size
Bearing Area
Distance between Silo OD & BCD
Bolt Data
Material of Construction
No. of bolt / lug
Bolt diameter
PCD
Dia. of bolt hole
Allow. tensile stress
(From ASME Sec-II, Part-D, at Design Temp)
3)
Gusset Data
Thickness
Gusset height
Gusset angle
Gusset depth at top
Gusset depth at bottom
No. of gussets
Dist. between gussets
Slant Height of the Gussets
Factor
:
IS-2062-A Plate
N
OD
tb'
tc
Sb
a'
A
a
:
=
=
=
=
=
=
=
=
=
8.0 Nos.
5036.0 mm
50.0 mm
4936.0 mm
50.0 mm
12.0 Kg/mm^2
140.0 mm
62160.0 mm^2
142.0 mm
SA 307 Gr. B or IS:1367 Cl 4.6 / 4.0
Nb
=
2.0 Nos.
db
=
30.0 mm
D
=
4796.0 mm
=
33.0 mm
Fs
=
17.58Kg/mm^2
tg
h
θ
Lc
Lb
n
b
h'
Lb/b
Page 29 of 45
=
=
=
=
=
=
=
=
=
25.0 mm
600.0 mm
87.61
175.0 mm
200.0 mm
16
300.0 mm
600.53 mm
0.667
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
4)
5)
6)
Shell Data
Material of Construction
Outside diameter of Shell
Outside diameter of Shell
Thickness (corroded)
:
SA-240 Gr.304
OD
OD
ts
Load and Moment
Max. overturning moment
M
Empty weight of vessel
Operating weight of vessel
We
Wo
=
=
=
4516.0 mm
4500.0 mm
8.0 mm
=
=
=
=
77261.64 Kg-m
77261640.0 Kg-mm
16720.00 Kg
159720.00 Kg
Design of Anchor Bolts
a) Total uplift force on bolts :
Where,
Substituting the Values,
T
=
4 x M - We
DxN N
M
M
=
=
Max. overturning moment
77261640 Kg-mm
We
We
=
=
Empty weight of vessel
16720.00 Kg
D
D
=
=
Pitch Circle Diameter of Bolts
4796.0 mm
N
N
=
=
No. of supports
8.0 Nos.
T
=
=
=
4 x M - We
DxN N
(4 x 77261640 / 4796 x 8) - (16720 / 8)
5964.80 Kg
Am
=
T/Fs
T
T
=
=
Total uplift force on bolts
5964.80 Kg
Fs
Fs
=
Allow. tensile stress
17.577Kg/mm^2
Am
Am
Am
=
=
=
T/Fs
5964.8 / 17.577
339.4 mm^2
Ab
=
Ar x Nb
db
db
=
=
Bolt diameter
30.0 mm
Ar
Ar
=
=
Root area of bolt
615.7536
T
T
b) Required Area of Bolts :
Where,
Substituting the Values,
c) Available Area of Bolts :
Where,
Page 30 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Substituting the Values,
Nb
Nb
=
=
No. of bolt / lug
2 Nos.
Ab
Ab
Ab
=
=
=
Ar x Nb
(π / 4 ) x ( 30 - 2 ) ^2 x 2
1231.5 mm^2
Since, Ab > Am, No. of Bolts Provided are Sufficient.
7)
Base Plate And Gusset Design
a) Reaction force at each support :
Where,
Substituting the Values,
Q
=
4 x M + Wo
DxN- N
M
M
=
=
Max. overturning moment
77261640 Kg-mm
Wo
Wo
=
=
Operating weight of vessel
159720.00 Kg
D
D
=
=
Pitch Circle Diameter of Bolts
4796.0 mm
N
N
=
=
No. of supports
8.0 Nos.
Q
=
=
=
4 x M + Wo
DxN- N
(4 x 77261640 / 4796 x 8) + (159720 / 8)
28019.80 Kg
bp
=
Q/A
Q
Q
=
=
Reaction force at each support
28019.80 Kg
A
A
=
=
Bearing Area
62160.0 mm^2
bp
bp
bp
=
=
=
Q/A
28019.8 / 62160
0.46Kg/mm^2
PI
=
bp x Lb x b
bp
bp
=
=
Bearing Pressure
0.46Kg/mm^2
Lb
Lb
=
=
Gusset depth at bottom
200.0 mm
b
b
=
=
Dist. between gussets
300.0 mm
Q
Q
b) Bearing Pressure :
Where,
Substituting the Values,
c) Maximum axial force in gusset :
Where,
Page 31 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Substituting the Values,
PI
PI
PI
=
=
=
bp x Lb x b
0.46 x 200 x 300
27600.00 Kg
Sg
=
18000
1 + 12/18000 (h'/tg)2
h
h
=
=
Gusset height
600.0 mm
θ
θ
=
=
Gusset angle
87.61 °
h'
h'
=
=
Slant Height of the Gussets
600.53 mm
tg
tg
=
=
Thickness
25.0 mm
Sg
=
d) Allowable comp. stress in gusset:
Where,
Substituting the Values,
18000
1 + 12/18000 (h'/tg)2
1800 / 1 + (12 / 18000) x (600.53 / 25)^2
18000.38 Psi
12.66Kg/mm^2
Sg
Sg
Sg
=
=
=
tg'
=
PI
Sg x Lb
PI
PI
=
=
Maximum axial force in gusset
27600.00 Kg
Sg
Sg
=
=
Allowable comp. stress in gusset
12.66 Kg/mm^2
Lb
Lb
=
=
Gusset depth at bottom
200.0 mm
tg'
=
tg'
=
=
27600 ( 12.66 x 200)
10.90 mm
Mx
My
Mo
=
=
=
0.06 x bp x b^2
-0.23 x bp x Lb^2
Max (Mx,My)
Lb/b
=
0.6667
Mx
=
0.06 x bp x b^2
bp
bp
=
=
Bearing Pressure
0.46 Kg/mm^2
e) Required thickness of gusset
Where,
Substituting the Values,
tg'
PI
Sg x Lb
f) Calculating Moments Mx, My & Mo:
Moment,
Moment,
Max. Moment,
Factor,
Calculating Moment Mx:
Where,
Page 32 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
b
b
=
=
Dist. between gussets
300.0 mm
Mx
Mx
Moment of Force at X-axis, Mx
=
=
=
0.06 x bp x b^2
0.06 x 0.46 x 300^2
2484.00 Kg-mm
My
=
-0.23 x bp x Lb^2
bp
bp
=
=
Bearing Pressure
0.46 Kg/mm^2
Lb
Lb
=
=
Gusset depth at bottom
200.0 mm
My
My
Moment of Force at Y-axis, My
=
=
=
-0.23 x bp x Lb^2
-0.23 x 0.46 x 200^2
-4232.00 Kg-mm
Maximum Moment,
=
=
Max (Mx,My)
4232.00 Kg-mm
tb'
=
√(6 x Mo)/Sb
Sb
Sb
=
=
Allowable stress
12.0 Kg/mm^2
Mo
Mo
=
=
Maximum Moment
4232.00 Kg-mm
tb'
=
√(6 x Mo)/Sb
tb'
=
=
=
f
=
PI x a / h
PI
PI
=
=
Maximum axial force in gusset
27600.00 Kg
OD
OD
=
=
Outside diameter of Shell
4516.0 mm
a
a
=
Distance between Silo OD & BCD
142.0 mm
h
h
=
=
Gusset height
600.0 mm
Substituting the Values,
Calculating Moment My:
Where,
Substituting the Values,
Mo
Mo
g) Required thickness of base plate :
Where,
Substituting the Values,
tb'
Hence Provide Base Plate Thk
8)
√(6 x 4232) / 12
46.0 mm
50.0 mm (Nom)
Design of Compression Plate
a) Equivalent radial load :
Where,
Page 33 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Substituting the Values,
f
f
f
=
=
=
PI x a / h
27600 x 142 / 600
6532.00 Kg
β
=
π/N
N
N
=
=
No. of supports
8.0 Nos.
β
β
β
=
=
=
π/N
3.1415 / 8
0.400 Radians
Kr
=
0.5 x [ 1/β - cot (β)]
β
β
=
=
Angle between supports
0.400 Radians
Kr
Kr
Kr
=
=
=
0.5 x [ 1/β - cot (β)]
0.5 x (1 / 0.4 - Cot(0.4))
0.0700
Mc
=
0.5 x Kr x f x OD
f
f
=
=
Equivalent radial load
6532.00 Kg
OD
OD
=
=
Base plate
5036.0 mm
Mc
Mc
Mc
=
=
=
0.5 x Kr x f x OD
0.5 x 0.07 x 6532 x 5036
1151330.3 Kg-mm
Z
=
Lc2 x tc
6
Lc
Lc
=
=
Gusset depth at top
175.0 mm
tc
tc
=
=
Compression plate thk
50.0 mm
Z
=
b) Angle Between Supports :
Where,
Substituting the Values,
c) Internal Bending Moment :
Where,
Substituting the Values,
Where,
Substituting the Values,
d) Section Modulus :
Where,
Substituting the Values,
Z
Z
=
=
Page 34 of 45
Lc2 x tc
6
175^2 x 50 / 6
255208.33 mm^3
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
e) Bending stress induced in Compression Plate
Where,
Substituting the Values,
fb
=
Mc
Z
Z
Z
=
=
Section modulous
255208.34 mm^3
Mc
Mc
=
=
Internal bending moment
1151330.32 Kg-mm
fb
=
fb
fb
Induced Bending Stress in Compression Plate,
=
=
Mc
Z
1151330.32 / 255208.34
4.51 Kg/mm^2
4.51 < 12 Kg/mm2 (Allowable)
Hence Selected Compression plate Thickness is Safe in Bending.
Page 35 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
WIND LOAD CALCULATION
Basic Wind Velocity
Design Report
Height of the Tank
Dia of the Tank
Height of the Roof
(OPERATING CONDITTION)
=
140 KMPH =
Vb
H,
D,
h,
=
=
=
39 M/S
20.295 M
4.500 M
0.395 M
AS PER API 650,CLAUSE NO: 3.11.2
For Unanchored Tank
M < 2/3 ( WD / 2 )
Where,
M,
Overturning Moment For Wind Pressure,
N-M
W,
Shell Weight Available To Resist Uplift, In Corroded Condition + Dead Weight Supported by the Shell - Simultaneaous Uplift From Operating
Conditions Such as Internal Pressure on Roof
OVERTURNING MOMENT,M:
CALCULATIONS FOR DESIGN WIND SPEDD AS PER IS:875
Location of Silo
Basic Wind Speed
Design Wind Speed,
Risk Coefficient,
Terrain Category,
Topography Factor,
Vb
Vz
K1
K2
K3
=
=
=
=
=
=
Igatpuri Nashik, Maharashtra
38.9
Vb x K1 x K2 x K3
1.07
1.05
1
Vz
Vz
Vz
=
=
=
Vb x K1 x K2 x K3
38.89 x 1.07 x 1.05 x 1
43.7
m/sec
Design Wind Speed,
Vz
=
43.7
m/sec
Wind Pressure,
Pz
=
=
0.6 x Vz2
1145.8
N/M2
Therefore, Design Wind Speed,
Coeff. Of Tank, For Circular in Plan,
Overturning Moment
At Base
=
=
X
M
116.8
0.7
KG/M2
M
=
=
=
=
=
Shell Moment + Moment on the Roof
Weight ,W
=
Shell Weight (Excl. C.A.) + Roof Weight (Excl. C.A ) + Internals Supports Structure +
Hand Railing, Ladders Weight.
Shell Weight (Excl. C.A.)
Roof Weight (Excl. C.A )
Internals Supports Structure + Hand Railing, Ladders Weight
=
=
=
18,595.31
4,385.65
500.00
2/3(WD/2)
7,57,936.69
SINCE, M
=
=
=
>
>
18595.31 + 4385.649 + 500
230348.2Kg N
345522Kg
N-M
345522Kg
N-M
2/3(WD/2)
(Pz x D x H x X )H/2 + ( D x h / 2 ) x Pz x X ( H + h / 3 )
(116.81 x 4.5 x 20.295 x 0.7) x 20.295/2 + (4.5 x 0.395/2) x 116.81 x 0.7 x ( 20.295 + 0.395/3)
77261.64
7,57,936.7
Kg-m
N-M
Assumed
Hence, Anchors are Required For Wind Pressure
Uplift Due to Moment
Where,
M
M
=
4 M /Do
=
=
Overtuning Moment at base
77,261.64
Kg-m
Do
Do
=
=
Outside Diameter of Silo
4.52
m
=
=
4 x 77261.64 / 4.516
68433.7Kg
Page 36 of 45
KG.
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
Uplift Due to Internal Pressure
=
(TT/4)x Do^2 x P
Do
Do
=
=
Outside Diameter of Silo
4.52
P
P
=
=
Design Pressure
0.05
=
=
=
(TT/4)x Do^2 x P
TT / 4 x 4.516^2 x 0.05
Total Uplift
Total Uplift
=
=
=
=
Uplift Due to Moment + Uplift Due to Internal Pressure
68433.7 + 0.81
68433.7 + 0.81
68435Kg
Total Equipment Operating Weight
Total Uplift
68434.51 Kg
=
<
<
159720Kg
Total Equipment Operating Weight (Maximum)
159720Kg
0.810 Kg
Since Total Uplift is Less Than Equipment Operating Weight, Anchors are not Required.
Conclusion:
Hence Anchors are not Required for Wind Pressure in Operating Condition, but are provided for Stability.
Stress at Silo Base Due to Wind Load :
Where,
Substituting the Values,
S
=
M / TTx R2 x t
M
M
M
=
=
=
Moment at Base, Due to Seismic Load
77261.640
Kg-m
77261640.0 Kg-mm
t
=
=
Minimum Required Thickness as per IS:9178
6.0
mm
D
R
=
=
4500.000
2250
S
S
S
=
=
=
M / TTx R2 x t
0.80965
Kg/mm2
0.80965
<
mm
mm
Hence Equipment Selected Shell Thickness is Safe for Wind Load in Operating Condition.
Page 37 of 45
12.00 Kg/mm2
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
WIND LOAD CALCULATION
(EMPTY CONDITION)
Basic Wind Velocity
Design Report
Height of the Tank
Dia of the Tank
Height of the Roof
Vb
=
H,
D,
h,
=
=
=
140 KMPH =
38.9 M/S
20.295 m
4.500 m
0.395 m
AS PER API 650,CLAUSE NO: 3.11.2
For Unanchored Tank
M < 2/3 ( WD / 2 )
Where,
M,
Overturning Moment For Wind Pressure,
N-m
W,
Shell Weight Available To Resist Uplift, In Corroded Condition + Dead Weight Supported by the Shell - Simultaneaous Uplift
From Operating Conditions Such as Internal Pressure on Roof
OVERTURNING MOMENT, M:
CALCULATIONS FOR DESIGN WIND SPEDD AS PER IS:875
Location of Silo
Basic Wind Speed
Design Wind Speed,
Risk Coefficient,
Terrain Category,
Topography Factor,
Vb
Vz
K1
K2
K3
=
=
=
=
=
=
Igatpuri Nashik, Maharashtra
38.9
Vb x K1 x K2 x K3
1.07
1.05
1
Vz
Vz
Vz
=
=
=
Vb x K1 x K2 x K3
38.89 x 1.07 x 1.05 x 1
43.7
m/sec
Design Wind Speed,
Vz
=
43.7
Wind Pressure,
Pz
=
=
0.6 x Vz2
Therefore, Design Wind Speed,
Coeff. Of Tank, For Circular in Plan,
=
=
X
Overturning Moment
At Base
M
=
=
1145.8
116.8
0.7
m/sec
N/m2
Kg/m2
Shell Moment + Moment on the Roof
(Pz x D x H x X ) H/2 + ( D x h / 2 ) x Pz x X ( H + h / 3 )
(116.81 x 4.5 x 20.295 x 0.7) x 20.295/2 + (4.5 x 0.395/2) x 116.81 x 0.7 x ( 20.295 +
0.395/3)
M
=
=
77261.64
7,57,936.7
Kg-m
N-m
Weight ,W
=
Shell Weight (Excl. C.A.) + Roof Weight (Excl. C.A ) + Internals Supports
Structure + Hand Railing, Ladders Weight.
Shell Weight (Excl. C.A.)
Roof Weight (Excl. C.A )
Internals Supports Structure + Hand Railing, Ladders Weight
=
=
=
18,595.31
4,385.65
500.00
2/3(WD/2)
7,57,936.69
SINCE, M
=
=
=
>
>
18595.31 + 4385.649 + 500
230348.2
N
345522
N-m
345522
N-m
2/3(WD/2)
Assumed
Anchors are not Required for Wind Pressure
Uplift Due to Moment
Where,
M
M
=
4 M /Do
=
=
Overtuning Moment at base
77,261.64
Kg-m
Do
Do
=
=
Outside Diameter of Silo
4.52
m
Page 38 of 45
Kg
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
=
=
=
4 M /Do
4 x 77261.64 / 4.516
68433.7 Kg
Uplift Due to Internal Pressure
=
(TT/4)x Do^2 x P
Do
Do
=
=
Outside Diameter of Silo
4.52
P
P
=
=
Design Pressure
0.05
=
=
=
(TT/4)x Do^2 x P
TT / 4 x 4.516^2 x 0.05
Total Uplift
Total Uplift
=
=
=
Uplift Due to Moment + Uplift Due to Internal Pressure
68433.7 + 0.81
68435Kg
Equipment Empty Weight
=
16720.00 Kg
Total Uplift
68434.51 Kg
>
>
Total Equipment Weight (Maximum)
16720.00 Kg
0.810 Kg
Since Total Uplift is Less Than Equipment Empty Weight, Anchors are not Required.
Conclusion:
Hence Anchors are not Required for Wind Pressure in Empty Condition
Stress at Silo Base Due to Wind Load :
Where,
Substituting the Values,
S
=
M / TTx R2 x t
M
M
M
=
=
=
Moment at Base, Due to Seismic Load
77261.640
Kg-m
77261640.00
Kg-mm
t
=
=
Minimum Required Thickness as per IS:9178
6.0
mm
D
R
=
=
4500.000
2250
mm
mm
S
S
S
=
=
=
M / TTx R2 x t
0.80965
0.80965
Kg/mm2
<
Hence Equipment Selected Shell Thickness is Safe for Wind Load in Empty Condition.
Page 39 of 45
12.00 Kg/mm2
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SEISMIC DESIGN
( ERECTION CONDITION)
Design Report
D,
Nominal Diameter
H,
Height of the Equipment from the Support
W,
Empty Weight of the Equipment
Refer IS 1893-2002, 3.4.2.1
Location of the Equipment
Seismic Zone Number
Z,
Seismic Zone Factor
Soil Type
R,
Response Reduction Factor Table-7,Sr.No-iii (a)
I
Importance Factor
Sa/g,
Average Response Acceleration Coeff.
Ta,
Fundamental Natural Period
( For Steel Frame Building)
=
=
=
4.500 m
2.638 m
16720.00 Kg
=
=
=
=
=
Igatpuri Nashik, Maharashtra
III
0.16
Type-III, Soft Soil
4.00
=
=
1.00
To be Calculated From Fig.-2, & Clause-6.4.5
=
=
0.085 x (H)^0.75
0.18
Sec.
2.50 ,
FOR 0.1 < = T < = 0.67
Calculation of Sa/g Value :
For Soft Soil Sites,
Sa/g =
2.5
Design Horizontal Seismic Coefficient :
Design Horizontal Seismic Coefficient,
Ah =
Z
2
Ah =
Ah =
(0.16/ 2 ) (1/4) ( 2.5)
0.05
I
R
Sa
g
Ah Shall not be less Than Z/2, For T<=0.1 Sec, For any of the (I/R) Value.
Here, T
Value of ( Z / 2) =
>
0.10 Sec.
0.08
0.05
<
0.08
Ah
<
Z/2
Therefore New Value of Ah Will Be =
Ah =
0.05
Page 40 of 45
0.050
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SEISMIC DESIGN
( ERECTION CONDITION)
Total Shear at Base Due to Seismic Load :
V =
Where,
Ah * W
V = Total Base Shear Due to Seismic Load
Ah = Desgn Horizontal Seismic Coefficient, Based on Seimic Zone & As Calculated
Ah =
0.050
W = Empty Weight of the Equipment
=
16720.00 Kg.
Base Shear,
V = 0.05 x 16720 Kg
V=
836.00 Kg
Bending Moment at Base Due to Seismic Load :
M = 2 *Ah * W * H / 3
Where,
M = Moment at Base, Due to Seismic Load
Ah = Desgn Horizontal Seismic Coefficient, Based on Seimic Zone & As Calculated
= 0.050
W = Empty Weight of the Equipment
= 16720.0
Kg
H = Height of the Equipment from the Support
= 2.6380
M
Total Moment at Base,
M = 2 x 0.05 x 16720 x 2.638/3
M = 1470.250
Kg-m
Stress at Silo Base Due to Seismic Load :
S = M / TTx R^2 x t
Where,
M = Moment at Base, Due to Seismic Load
= 1470.250
Kg-m
= 1470250.00
Kg-mm
Sress,
t = Minimum Required Thickness as per IS:9178
6.00
MM
S = M / TTx R^2 x t
S = 0.01541
= 0.01541
Kg/mm2
<
12.00 Kg/mm2
Hence Equipment Selected Shell Thickness is Safe for Seismic Load in Empty Condition.
Page 41 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SEISMIC DESIGN
( OPERATING CONDITION)
Design Report
D,
Nominal Diameter
H,
Height of the Equipment from the Support
W,
Operating Weight of the Equipment
=
=
=
Refer IS 1893-2002, 3.4.2.1
Location of the Equipment
Seismic Zone Number
Z,
Seismic Zone Factor
Soil Type
R,
Response Reduction Factor Table-7,Sr.No-iii (a)
I
Importance Factor
Sa/g,
Average Response Acceleration Coeff.
Ta,
Fundamental Natural Period
( For Steel Frame Building)
4.500 M
2.638 M
159720.00 Kg
=
=
=
=
=
Igatpuri Nashik, Maharashtra
III
0.16
Type-III, Soft Soil
4.00
=
=
1.00
To be Calculated From Fig.-2, & Clause-6.4.5
=
=
0.085 x (H)^0.75
0.18 Sec.
2.50 ,
FOR 0.1 < = T < = 0.67
Calculation of Sa/g Value :
For Soft Soil Sites,
Sa/g =
2.5000
Design Horizontal Seismic Coefficient :
Design Horizontal Seismic Coefficient,
Ah =
Z
2
Ah =
Ah =
(0.16/ 2 ) (1/4) ( 2.5)
0.05
I
R
Sa
g
Ah Shall not be less Than Z/2, For T<=0.1 Sec, For any of the (I/R) Value.
Here, T
>
0.10 SEC.
Value of ( Z / 2) =
0.05 <
Ah <
Therefore New Value of Ah Will Be =
Ah =
0.08
0.08
Z/2
0.05
Page 42 of 45
0.050
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SEISMIC DESIGN
( OPERATING CONDITION)
Total Shear at Base Due to Seismic Load :
V =
Where,
Ah * W
V = Total Base Shear Due to Seismic Load
Ah = Desgn Horizontal Seismic Coefficient, Based on Seimic Zone & As Calculated
Ah = 0.050
W = Empty Weight of the Equipment
= 159720.00
KG
Base Shear,
V = 0.05 x 159720 Kg
V = 7986.00
KG
Bending Moment at Base Due to Seismic Load :
M = 2 *Ah * W * H / 3
Where,
M = Moment at Base, Due to Seismic Load
Ah = Desgn Horizontal Seismic Coefficient, Based on Seimic Zone & As Calculated
= 0.050
W = Empty Weight of the Equipment
= 159720.0
Kg
H = Height of the Equipment from the Support
= 2.6380
M
Total Moment at Base,
M = 2 x 0.05 x 159720 x 2.638/3
M=
14044.720 Kg-m
Stress at Silo Base Due to Seismic Load :
S = M / TTx R^2 x t
Where,
M = Moment at Base, Due to Seismic Load
= 14044.720
Kg-m
= 14044720.00
Kg-mm
STRESS,
t = Minimum Required Thickness as per IS:9178
6.00
MM
S = M / TTx R^2 x t
S = 0.14718
= 0.14718
Kg/mm2
<
12.00 Kg/mm2
Hence Equipment Selected Shell Thickness is Safe for Seismic Load in Operating Condition.
Page 43 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SUMMARY OF LOAD DATA
150MT PP Granules Storage Silos
Sr.
No.
Description
Silo Weight
1 Empty Condition
16720.00 Kg
2 Operating Condition 159720.00 Kg
Notes :
a) Considerations :
Wind Design :
b)
Seismic Design :
Wind Design
Wind Load
2430.14 Kg
2430.14 Kg
Seismic Design
Moment
Base Shear
Moment
(at Silo Base Plate) (at base plate) (at Silo Base Plate)
8748.51 Kg-m
8748.51 Kg-m
836.00 Kg
7986.00 Kg
1470.25 Kg-m
14044.72 Kg-m
Base Plate
Dimensions
Anchor Bolt Details
No. of
Anchor
Points
Total No.
of Bolts
No. of Bolts
per Anchor
Point
Anchor
Bolt
Size
8 Nos.
16 Nos.
2 Nos.
M30
8 Nos.
16 Nos.
2 Nos.
M30
Bolt
Hole
Size
33mm
33mm
BCD
OD
4796mm
5036mm
4796mm
5036mm
IS:875, Basic Wind Speed = 39m/s, K1 =1.0, K2=1.07,K3=1.0, Design Wind Speed =43.7m/s, Wind pressure - 116.8Kg/m2, Silo Height from Anchor Baseplate to Top =6m
(assumed), Class-A, Cat-2, 50Yrs,
IS:1893, Seismic Zone =III, Zone factor = 0.16, Soil Type: Type-III, Soft Soil,R = 4, I =1.0
Refer Design Summary for Anchor Ring dimensional details.
Page 44 of 45
Mechanical Design Calculations for 150MT PP Storage Silo
Rev. No. : 01
SILO DESIGN SUMMARY
Sr.
No.
Item Description
Calculated
Thickness
(Without CA)
Solid
Int.
Material Pressure
1
Main Shell-1 (4000 HT- Top)
0.096 mm
0.5 mm
3
Bottom Circular Cone-(3900 HT)
2.032 mm
0.5 mm
2
4
5
6
7
8
9
Main Shell-2 (12000 HT-Lower)
Top Roof Cone -100
0.096 mm
-
0.5 mm
2.3 mm
Calculated Thickness
(With CA)
Min. Reqd. Thk.
As per IS:9178
(without CA)
Provided
Nominal
Thickness
0.5 mm
6.0 mm
6.0 mm
0.5 mm
6.0 mm
8.0 mm
Solid
Material
Int.
Pressure
0.1 mm
0.5 mm
0.1 mm
2.0 mm
-
2.3 mm
Stiffening Rings -Shell
3 Nos x ISMC-150, M.S. on SS.304 R.F. Pad
Stiffening Rings -Bottom Cone
2 Nos x ISMC-150, M.S. on SS.304 R.F. Pad
RF Pad for shell Stiffenning Ring
RF Pad for shell Stiffenning Ring
Radial Stiffenners -Roof
10 Curb Angle-Top of Shell
11 Silo Anchor Ring Support:
8 Nos x ISMC 75 (SS 304)
ISA 100 x 100 x 10 mm Thk (SS 304)
c Gussets
25 mm Thk x 600 HT (M.S.) (24 Nos)
e Anchor Bolt Size
f RF Pad Ring for Anchor
12 Body Flange
4936 OD x 200 W x 50 mm Thk (M.S.)
16 Nos ( 2 Nos per anchor bolt location)
M30
750 W x 12 mm Thk (SS 304 )
a OD
4680 mm
c BCD
4600 mm
e No. of Bolts & Bolts Size
M36 x 88 Nos
b ID
d Thk
f Gussets for Body Flg
13 Body Flange Gasket
a OD
b ID
c Thk
d MOC
6.0 mm
200Wx 6Thk
5036 OD x 250 W x 50 mm Thk (M.S.)
d No. of Anchor Bolts
6.0 mm
8.0 mm
200Wx 6Thk
a Base Ring
b Compression Ring
6.0 mm
4519 mm
40 mm
44 Nos x 6Thk - At alternate bolt hole location
Full face Gasket
4680 mm
4519 mm
3.0 mm
Compressed Non Asbestos Fiber- PTFE Enveloped
CONCLUSION:
1
2
3
4
The Provided Nominal Thicknesses for Shell, Bottom Cone, Roof Cone are more than minimum required thicknesses as
per calculations.
The Provided Nominal Thicknesses for anchor ring base plates and anchor ring compression plates are more than
minimum required thicknesses as per wind & seismic load calculations.
The Provided Anchor Bolt Sizes & Qty.are more than minimum required as per wind load & overturning moment
calculations.
The Shell, Cone Thicknesses are Safe for Overturning Moments due to Wind.
Page 45 of 45