Similar to Design of a 20,000 t double acting ice class general cargo ship of service speed 17.0 knots in open water and 5.0 knots in severe ice condition
IRJET- Design and Development of Hydraulic Tank through Structural and Fa...IRJET Journal
Similar to Design of a 20,000 t double acting ice class general cargo ship of service speed 17.0 knots in open water and 5.0 knots in severe ice condition (20)
Judging the Relevance and worth of ideas part 2.pptx
Design of a 20,000 t double acting ice class general cargo ship of service speed 17.0 knots in open water and 5.0 knots in severe ice condition
1. PROJECT REPORT
DESIGN OF A 20,000 t DOUBLE ACTING ICE CLASS GENERAL
CARGO SHIP OF SERVICE SPEED 17.0 KNOTS IN OPEN WATER
AND 5.0 KNOTS IN SEVERE ICE CONDITION
Project submitted in partial fulfillment
of the Requirements for the Award of
The Degree of
Bachelor of Science
in
Naval Architecture & Marine Engineering
DEPARTMENT OF NAVAL ARCHITECTURE AND
MARINE ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING &
TECHNOLOGY
APRIL 2017
2. Certified that this is the bonafide record of the projrct submitted in
partial fulfillment of the requirements for the award of the degree of
Bachelor of Science
in
Naval Architecture & Marine Engineeering
DEPARTMENT OF NAVAL ARCHITECTURE AND
MARINE ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING &
TECHNOLOGY
Project Submitted by Project Accepted by
Dr. Md. Shahjada Tarafder
Professor, Department of Naval
Architecture and Marine Engineering
(NAME)
BANGLADESH UNIVERSITY OF
ENGINEERING & TECHNOLOGY
Md . Ashifur Rahaman (1312029)
Md . Abdur Rahim(1312036)
Md . Maruf Billah (1312006)
3. AIM OF THE PROJECT
Aim of this project is to prepare a preliminary design of a Double Acting Ice
Class general cargo ship to meet the owner’s requirements given in the assignment sheet:
ASSIGNMENT SHEET
DEPARTMENT OF NAVAL ARCHITECTURE AND MARINE ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY
Ship Design Project work Assignment sheet
:
:
Ship Type
Deadweight
Service speed (open water)
Service speed (1.0 m thick Ice) :
Double Acting General Cargo Ship (Ice Class1AS)
20,000 t
17.0 Knots
5.0 Knots
Signature of Project guide
:
4. Contents
1 Introduction 1
2 Fixing of main dimensions 4
2.1 Owner’s Requirements 5
2.2 Basis Ship Data 6
2.3 Principal Particulars of New Ship 6
2.3.1 Preliminary Power Calculation 6
2.3.2 Dead Weight of New Ship 7
2.3.3 Draft Calculation 10
2.3.4 Breadth Calculation 10
2.3.5 Length Calculation 11
2.3.6 Depth Calculation 11
2.3.7 Summary of Principal particulars of New Ship 11
2.3.8 Free Board Calculation 12
2.3.9 Sheer Calculation 12
2.3.10 Minimum Bow Height 12
2.3.11 Wheel House Height 13
2.3.12 Length of Poop Deck 13
2.3.13 Dimension of Bulbusbow 14
2.3.14 Navigation in Ice 16
2.3.15 Length of Cargo Hold 16
2.4 Typical GA 18
3 Lines Plan & Offset Table 19
3.1 Profile 20
3.2 Half Breadth Plan 20
3.3 Body Plan 20
3.4 Offset Table 21
4 Hydrostatic Calculations 23
4.1 Hydrostatic Detailed Calculations 24
4.2 Hydrostatic Curves 32
i
5. 5 Scantling Calculations 33
5.1 Type of Framing System 34
5.1.1 Strength/Weather Deck Plating 35
5.1.2 Lower Deck Plating 36
5.1.3 Strength/Weather Deck Longitudinal 37
5.1.4 Cargo and Accommodation Deck Longitudinal 37
5.1.5 Strength/Weather Cargo and Accommodation Deck Bea 38
5.1.6 Bar and Plate Keels 41
5.1.7 Bottom Shell and Bilge Plating 42
5.1.8 Side Shell Plating 43
5.1.9 Shell Framing (Longitudinal) 44
5.1.10 Single Bottom Girders and Floors 47
5.1.11 Summary of Scantling 48
5.1.12 Equipment Number 49
5.2 Midship Section 52
5.3 Profile,Deck & Bottom constructions 53
5.4 Shell Expansion 54
6 Weight Calculation 56
6.1 Deadweight Calculation 59
6.2 Lightweight Calculation 59
6.2.1 Detail Steel Weight Calculation 59
6.2.2 Detail Outfit Calculation 60
6.2.3 Detail Machinery Weight Calculation 61
6.2.4 Total Light Weight 61
6.3 Summary 61
7 Capacity Calculation 62
7.1 Capacity Calculation 63
7.2 Summary 63
8 Stability Calculation 64
8.1 GZ Calculation 65
8.2 GZ Curves 78
9 Trim Calculation 80
10 Crane Selection 83
11 Resistance and Power Calculation 85
11.1 Total Resistance 87
11.2 Shaft Power 88
11.3 Break Horse Power 88
11.4 Summary of power calculation 88
ii
6. 12 Engine and Gear Box Selection 89
12.1 Engine Selection 90
12.2 Gear Box Selection 92
13 Engine Foundation 93
13.1 Floor Plate Thickness 94
13.2 Inner Bottom Plating 95
13.3 Longitudinal Girder Thickness 95
13.4 Foundation Bolt Diameter 95
13.5 Engine Seating 95
13.6 Web Frame 95
13.7 Summary of Scantling 96
14 Propeller Design 97
15 Rudder Calculation 103
15.1 Rudder Area 104
15.2 Rudder Force and Torque 106
15.3 Rudder Stock 108
15.4 Rudder Coupling 108
15.5 Rudder Frames 109
15.6 Rudder Plates and Web 110
15.7 Pintle 110
15.8 Bearing 111
15.9 Rudder Design 112
16 Shaft Arrangement Calculation 113
16.1 Calculation of Shaft Diameter 114
16.1.1 Theoretical Formula 114
16.1.2 Using Imperical Formula 115
16.2 Angle of Twist 116
16.3 Minimum Liner Thickness 116
16.4 Coupling 117
16.5 Shaft Bearing 117
16.6 Shaft Details 118
16.7 Shaft Arrangement drawing 119
17 Steering Arrangement 120
References 122
iii
7. 2
13
14
16
18
20
20
20
32
52
53
54
78
78
82
82
102
109
112
LIST OF ILLUSTRATIONS
Fig 1.1 Ship design spiral
Fig 2.1 Distance between Wheel house & top of stem Fig 2.2
Dimension for bulbusbow
Fig 2.3 Navigation in ice
Fig 2.4 Typical GA
Fig 3.1 Profile View
Fig 3.2 Hal Breath Plan
Fig 3.3 Body plan
Fig 4.1 Hydrostatic Curves
Fig 5.1 Midship Scantling
Fig 5.2 Longitudinal Scantling
Fig 5.3 Shell Expansion
Fig 8.1 GZ curve ( Full Load Condition)
Fig 8.2 GZ curve ( No Load Condition)
Fig 9.1 Draft vs TPC Curve
Fig 9.2 Draft vs MCTC curve
Fig 14.1 Propeller details
Fig 15.1 Rudder stock Connection
Fig 15.2 Rudder Arrangement
Fig 16.1 Propeller shaft Assembly
120
iv
10. The Design Spiral
The design spiral is one of the most important pieces of the technical know-how of a
Naval Architect and/or Ocean Engineer. So what exactly is the Design Spiral and why is
it so important for a typical ship designer in the marine industry or any personnel
concerned with the design development of a marine structure?
Fig1.1 :SHIP DESIGN SPIRAL
Designing a ship is perhaps the most rigorous of all engineering problems. It takes a lot
of technical expertise, often across many disciplines to design such structures.A ship
not only floats on the surface of the ocean but also makes its way around the world,
along different routes through rough weather - "in one piece". The SDesign Spiral is a
systematic approach to achieving near perfect designs for a given ship design problem.
A naval architect traces his way along the design spiral through the different stages of
design given below:
1.CONCEPT DESIGN
2.PRELIMINARY DESIGN
3.CONTRACT DESIGN
4.DETAILED DESIGN
As we move along the spiral into its core, we move from a zone of less information to
extremely specific instruction for the construction of ship or in other words- "Realization
of the design into a product". Given below are the definitions of each stage of design
spiral along with the typical effort/man days required for a large merchant ship.
Chapter 1
Introduction
Ship Design & Project
Page 2
11. Concept design :
This stage witnesses the translation of the mission requirements into naval architectural
and engineering characteristics. The fundamental elements of the ship such as length,
beam, depth, draft, fullness, power, or alternative sets of characteristics, all of which
meet the required speed, range,cargo cubic and dead weight are used to perform
feasibility studies.
Light-ship weight estimation is done.
Alternative designs are analyzed during this phase to determine the most economical
design solution.
Preliminary design :
This stage essentially improves and elaborates the major ship characteristics affecting
cost and performance. The factors such as length ,beam, horsepower deadweight,
would not be expected to change after the completion of this stage. It also provides
basis for the development of contract plans and specifications.
Contract design :
This stage describes more precisely features such as hull form based on a faired set of
lines, powering based on model testing, sea keeping and maneuvering characteristics,
the effect of number of propellers on hull form, structural details, use of different types of
steel, spacing and type of frames . Paramount, among the contract design features, is a
weight and center of gravity-estimate taking into account the location and weight of
each major item in the ship. The final general arrangement is also developed during this
stage. This fixes the overall volumes and areas of cargo, machinery, stores, fuel oil,
fresh water, living and utility spaces and their interrelationship,as well as their
relationship to other features such as cargo handling equipment, and machinery
components.
Check on Quality standards of hull and outfit and the anticipated performance for each
item of machinery and equipment is done. Also describe the tests and trials required.
Detailed design :
Comprises of detailed working plans .These plans are the installation and construction
instructions to the ship fitters, welders, outfitters, metal workers, machinery vendors,
pipe-fitters, etc. At this stage the interchange is from engineer to artisan, that is, the
engineer's product at this point is no longer to be interpreted, adjusted, or corrected by
any other engineer.
Ship Design & Project
Page 3
13. 2.1 Owner’s Requirements
Ship type : General Cargo
Dead Weight : 20,000 tonnes
Route :
Distances :
Chittagong Port to Keppel Harbor Port, Singapore 1863 Nautical
miles Distance from Bangladesh to China 3231 Nautical miles
Distance from Bangladesh to Hong kong 3038 Nautical miles
Distance from Bangladesh to Japan 4284 Nautical miles
Distance from Bangladesh to Malaysia 2021 Nautical miles
Average distance : 3500 Nautical mile
Speed : 17 knots
Endurance : 10 days
There is some restriction to design our ship. Which are given below[1]:
1. The maximum length overall, including bulbous bow, for a commercial
vessel acceptable for regular transit is 289.6 meters.
2. The allowable height for any vessel transiting the Canal or entering the Port
of Balboa is 57.91 meters .
3. The maximum beam for a commercial vessel and the integrated tug-barge
combination acceptable for regular transit is 32.3 meters
Chapter 2
Fixing Of Main Dimension
World Wide
Ship Design & Project
Page 5
22. =
8135.7 �1 −
145.28
500
� 1.36
0.79 + 0.68
𝑚𝑚𝑚𝑚
= 5339.89 𝑚𝑚𝑚𝑚
2.3.11 Wheel House Height
[According to https: panama-canal-bridge-visibility-requirements]
AC = 2× 145.28 m = 290560 mm
Bow height h = 5339.89
2.3.12 Primary Length of Poop Deck[5]
Poop deck covers 15% of ships length & Pood Deck’s front should not
exceed 50% Of Length Amitship.
fig2.1:
Ship Design & Project
Page 13
[4]
For Our ship Poop deck Height =
36.25+2×145.28
2×145.28
× (5.3 + 12.79) m = 20 m
(maximum)
23. 2.3.13 Dimention for Bulbusbow
Length of Bulbusbow Will be calculated by subtracting at X distance forward per
pendicular .
𝑋𝑋 =
a
2
= 0.015L = 2.175 m
a = 4.35m (maximum)
Ship Design & Project
Page 14
Fig 2.2 : Dimension for bulbusbow
[5]
24. Length of collision bulkhead should not be more than 7% of L
So 0.07×145.28 m = 10.15 m
Hc = Height Of Hatchways = 600mm
Calculation of Determining the Distance of Cargo holds
from Collision Bulkhead:
For Position 1 : Hatchway height Hc = 600 mm
𝐿𝐿𝑓𝑓 = 5 × ( 𝐻𝐻𝐻𝐻 − 𝐻𝐻𝐻𝐻)0.5
𝑚𝑚 = 3.53 m
Hf = (Hc+0.5) mm = 600.5 mm
Ship Design & Project
Page 15
25. Angles Ranges ( °) For Our Ship
Α ( A1) 15 ˜ 55 45
ß (A2) 25 ˜ 90 48
2.3.14 Navigation In Ice
Awf = Area of waterplane in Bow
B/4 = Breadth /4 = 6.133 m
2.3.15 Primary Length Of Cargo Hold
Length remaining = L - (7% of L For Forcastle ) –( 15% of L/2 For
Poop deck) – Lf
Ship Design & Project
Page 16
Fig2.3 : Navigation in ice
26. = 145.28 – ( .07×145.28+.15×(145.28/2)+3.53) m
= 145.28 – 25.59 m
=120.68 m
So Length of Cargo hold = 120/5 = 24 m (minimum)
Ship Design & Project
Page 17
27. GALLEY
WARDROBE
WARDROBE
LCD TV
SAFE
SAFE
WARDROBE
SAFEWARDROBE
LCD TV
SAFE
SAFE
WARDROBE
WARDROBE
WARDROBE
WARDROBE
FRIDGE
LCD TV
WARDROBE
WARDROBE
WARDROBE
WARDROBE
WARDROBE
LCD TV
SAFE
SAFE
WARDROBE
SAFE
WARDROBE
SAFE
WARDROBE
SAFESAFE
LCDTV
First
Engr.
Asst.
Cook2Gps
Operator
TOILET
AND
BATH
UP
UP
DN
DN
TOILET
AND
BATH
ELECTRICIAN
TOILET
AND
BATH
TOILET
AND
BATH
UP
DN
FUNNEL
OWNER
DN
UP
DN
UP
DN
STORE
ROOM
E.L.H
Second
Engr
DECK
MAINTENANCE
BATHROOM
BATHROOM
Exra Cabin 2
CHIEF
MATE
2nd MATE
TOILET
DN
TOILET
AND
BATH
Sea Man
UP
Asst.
Cook1
TOILET
AND
BATH
E.L.H
Chief
Steward
TOILET
AND
BATH
BATHROOM
TOILET
CAPTAIN
BATHROOM
Electric
Storage
Cleaner
TOILET
TOILET
DN
WHEEL
HOUSE
DN
E.L.H
GANTRY CRANE
OPERATOR 1
Extra Cabin
DN
W. T.
DINING
ROOM
Chief
Cook
TOILET
AND
BATH
TOILET
AND
BATH
TOILET
AND
BATH
Radio
Operator
TOILET
AND
BATH
Deck
Maintenence
Steward 1
TOILET
AND
BATH
Extra Cabin 3
CREW
DINING
ROOM
DINING
ROOM
W W
24
WW
36
W
WATER BALLASTWATER BALLAST
W
48
WATER BALLAST
CHAIN LOCKER
HATCH COVER
W
Engine Room
UNDER DECK
HATCH COVER
BHD BHDW
60
BHDBHDW
BOW
THRUSTER
FORE PEAK
W W
BRIDGE DECK 2
FIRST AID
W
WATER BALLAST
WATER BALLASTWATER BALLAST
W
72
WATER BALLAST
WATER BALLAST
W
WATER BALLAST
WATER BALLAST
W
84
WATER BALLASTWATER BALLAST
W
CARGO HOLD 4CARGO HOLD 3CARGO HOLD 2
WW
96
WWW WWW
108
WWW W
PAINT
STORECO2
BOTTLE
ROOM
WW
120
W
DECK
MAINTEN-
ANCE
ROOM
SLOP
CHEST
STEWARDS
STORE &
PROVISSIONS
LAUNDRYENG. SHOP
& STORES
ELECTRIC
SHOP &
STORES
GARVAGE
STORE
EMERGENCY
GENERATOR
ROOM
AC&
REFRIGERATION
ROOM
PASSAGE
PASSAGE
LIFE
BOAT
LIFE
BOAT
CARGO HOLD 1
WW W
CARGO HOLD 5
W
WATER BALLAST
W
WATER BALLAST
132
WATER BALLAST
W
WATER BALLAST
W
WATER BALLAST
W
WATER BALLAST
WW W
HATCH COVER
143
NAVIGATION DECK
W
MAIN DECK
W
AFT PEAK
WBHD W
BHD W
BHD W
145
W
HATCH COVER
W
HATCH COVER
W
WATER BALLAST
W
WATER BALLAST
W WWW WW
ELEVATION
W
Frame spaceing = 1200 mm
W
W
RADAR
W W
12
Ship Design & Project
Page 18
33. The following formulas are used to perform hydrostatic calculation and to obtain hydrostatic
curves:
1. Calculation of Displacement
Half of water plane area = AWP = ∫ y dx
Using Simpsons first rule, AWP = 2∫ y dx =
1
3
× h ×∑ y × Simpson′
s multiplier
Displacement of the ship,
V = ∬ y dx dz =
1
3
× k × (
1
3
h ∑ y × Simpson′
s multiplier ) × Simpson’s multiplier
2. Vertical Centre of Buoyancy (VCB)
Total displacement of the ship
KB =
Moment of the volume about the keel
3. Longitudinal centre of buoyancy (LCB)
Total displacement of the ship
LCB =
Moment of the volume about amidship
4. Tons Per Centimetre Immersion (TPC)
TPC =
𝐴𝐴 𝑊𝑊𝑊𝑊
100
5. Transverse Metacentre
Transverse Metacentre, BMT =
𝐼𝐼
𝛻𝛻
=
1
3
∫ 𝑦𝑦3 𝑑𝑑𝑑𝑑
𝛻𝛻
=
1
3
× 1
3
×h × ∑ y3 ×Simpson′s multiplier
∇
6. Longitudinal metacentre
Longitudinal Metacentre BML =
ICF
∇
=
IM−Ah2
∇
=
1
3
∫ yx2dx− Ah2
∇
=3
1
×
1
3
×h × ∑ yx2 ×Simpson′smultiplier− Ah2
∇
7. Longitudinal centre of flotatation (LCF)
LCF =
Moment of the waterplane area about amidship
Waterplane area ∫ y dx
=
∫ yx dx
8. Moment to change trim 1 centimeter (MCTC)
MCTC =
∆ × GML
12 L 12 L
≈
∆ × BML
9. Form coefficients
∆
Block coefficient, 𝐶𝐶𝐵𝐵 =
𝐿𝐿 ×𝐵𝐵×𝐻𝐻
Prismatic coefficient, 𝐶𝐶𝑃𝑃 =
∆
𝐿𝐿 ×𝐵𝐵
𝐿𝐿 ×𝐴𝐴 𝑀𝑀
Midship area coefficient, 𝐶𝐶𝑚𝑚 =
𝐴𝐴 𝑀𝑀
𝐵𝐵 ×𝐻𝐻
Water plane area coefficient, 𝐶𝐶𝑤𝑤 =
𝐴𝐴 𝑊𝑊𝑊𝑊
34. SM
section SM y0 y x SM y1 y x SM y2 y x SM
0 0.5 0.0000 0 1836.6500 918.325 2119.4600 1059.73 6286.87 1902407 951203.43 ‐10 ‐9512034
0.5 2 967.2900 1934.58 2266.9200 4533.84 2512.3200 5024.64 10229.75 3095521 6191041.7 ‐9.5 ‐5.9E+07
1 1 1202.7900 1202.79 2445.1900 2445.19 2818.2400 2818.24 11378.62 3443169 3443168.9 ‐9 ‐3.1E+07
1.5 2 1275.4200 2550.84 2700.5000 5401 3293.6400 6587.28 12343.73 3735213 7470425.4 ‐8.5 ‐6.3E+07
2 1.5 1492.2100 2238.315 3077.9500 4616.925 3931.9000 5897.85 14076.38 4259511 6389266.6 ‐8 ‐5.1E+07
3 4 1886.1700 7544.68 4010.0300 16040.12 5366.8800 21467.52 18072.11 5468619 21874476 ‐7 ‐1.5E+08
4 2 2406.6800 4813.36 4994.9300 9989.86 7143.0000 14286 22424.92 6785781 13571562 ‐6 ‐8.1E+07
5 4 3733.8100 14935.24 6374.8900 25499.56 9296.5700 37186.28 30185.8 9134223 36536892 ‐5 ‐1.8E+08
6 2 6104.1800 12208.36 9214.0400 18428.08 10640.2200 21280.44 46796.5 14160621 28321242 ‐4 ‐1.1E+08
7 4 8445.9300 33783.72 10881.2100 43524.84 11603.1100 46412.44 58838.11 17804412 71217648 ‐3 ‐2.1E+08
8 2 9428.6300 18857.26 11478.7600 22957.52 12042.1900 24084.38 63465.52 19204666 38409333 ‐2 ‐7.7E+07
9 4 9427.5200 37710.08 11477.6600 45910.64 12041.0800 48164.32 63458.9 19202663 76810653 ‐1 ‐7.7E+07
10 2 9426.4200 18852.84 11476.5600 22953.12 12039.9800 24079.96 63452.3 19200666 38401332 0 0
11 4 9425.3200 37701.28 11475.4600 45901.84 12037.7800 48151.12 63446.25 19198835 76795341 1 76795341
12 2 9423.1200 18846.24 11474.3500 22948.7 12036.6800 24073.36 63436.86 19195994 38391988 2 76783975
13 4 9422.0200 37688.08 11473.2500 45893 12035.5800 48142.32 63430.26 19193997 76775987 3 2.3E+08
14 2 9420.9200 18841.84 11471.0500 22942.1 12034.4800 24068.96 63419.26 19190668 38381336 4 1.54E+08
15 4 9078.6800 36314.72 11285.0800 45140.32 11921.1400 47684.56 61876.45 18723814 74895255 5 3.74E+08
16 2 6083.2700 12166.54 9648.7100 19297.42 10821.7900 21643.58 48392.12 14643456 29286911 6 1.76E+08
17 4 3136.2700 12545.08 6031.5500 24126.2 9405.5200 37622.08 27264.12 8250121 33000485 7 2.31E+08
18 1.5 1941.1900 2911.785 3882.3800 5823.57 7350.9800 11026.47 16707.01 5055540 7583309.6 8 60666477
18.5 2 1572.5400 3145.08 3150.5800 6301.16 6071.1600 12142.32 13498.09 4084522 8169044.1 8.5 69436875
19 1 1378.8600 1378.86 2808.3400 2808.34 5243.6300 5243.63 12058.7 3648961 3648961.1 9 32840650
19.5 2 0.0000 0 1519.7200 3039.44 3386.0700 6772.14 4385.845 1327157 2654313.4 9.5 25215977
20 0.5 0.0000 0 0.0000 0 0.0000 0 0 0 0 10 0
sum of the
area
products
of water
plane 0 338171.6
sum of the
area
products of
water plane
0.5 467441.1
sum of the
area
products of
water plane
1 544919.6 739171174
Summatio
n of
moments 3.95E+08
1.79E+12 LCB 3882.507
Summatio
n of
volume
products 1.18E+10 1.79E+12
Summatio
n of
moments 3.21E+09 492.3558
7264.25 1815.6
Table 1. Waterplane area, Displacement, LCB VCB calculation for WL‐0.5
Water planes 0 0.5 1
VOLUME
Volume
function levers
about
amidship
Different totals
Summation of
volume functions
2.5 4 ‐0.5 products
for
area
below
Waterplane area 1637708552 2263739389 2638954900
‐1319477450
SM 2.5 4 ‐0.5
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
VOLUME
levers 0 0.5 1
Volume products 4094271379 9054957556 ‐1319477450
Monent about the
keel 0 4527478778
Chapter 4
Hydrostatic Calculation
Ship Design & Project
Page 24
35. SM
section SM y0 y x SM y1 y x SM y2 y x SM
0 0.5 0.0000 0 1836.6500 918.325 2119.4600 1059.73 4733.03 5728860 2864430 ‐10 ‐2.9E+07
0.5 2 967.2900 1934.58 2266.9200 4533.84 2512.3200 5024.64 6273.645 7593620 15187240 ‐9.5 ‐1.4E+08
1 1 1202.7900 1202.79 2445.1900 2445.19 2818.2400 2818.24 6900.895 8352843 8352843 ‐9 ‐7.5E+07
1.5 2 1275.4200 2550.84 2700.5000 5401 3293.6400 6587.28 7685.53 9302566 18605131 ‐8.5 ‐1.6E+08
2 1.5 1492.2100 2238.315 3077.9500 4616.925 3931.9000 5897.85 8867.955 10733773 16100659 ‐8 ‐1.3E+08
3 4 1886.1700 7544.68 4010.0300 16040.12 5366.8800 21467.52 11646.59 14097026 56388106 ‐7 ‐3.9E+08
4 2 2406.6800 4813.36 4994.9300 9989.86 7143.0000 14286 14764.7 17871193 35742386 ‐6 ‐2.1E+08
5 4 3733.8100 14935.24 6374.8900 25499.56 9296.5700 37186.28 19264.97 23318320 93273279 ‐5 ‐4.7E+08
6 2 6104.1800 12208.36 9214.0400 18428.08 10640.2200 21280.44 26800.28 32439059 64878118 ‐4 ‐2.6E+08
7 4 8445.9300 33783.72 10881.2100 43524.84 11603.1100 46412.44 31786.94 38474912 1.54E+08 ‐3 ‐4.6E+08
8 2 9428.6300 18857.26 11478.7600 22957.52 12042.1900 24084.38 33692.93 40781922 81563845 ‐2 ‐1.6E+08
9 4 9427.5200 37710.08 11477.6600 45910.64 12041.0800 48164.32 33689.62 40777916 1.63E+08 ‐1 ‐1.6E+08
10 2 9426.4200 18852.84 11476.5600 22953.12 12039.9800 24079.96 33686.32 40773922 81547843 0 0
11 4 9425.3200 37701.28 11475.4600 45901.84 12037.7800 48151.12 33682.47 40769262 1.63E+08 1 1.63E+08
12 2 9423.1200 18846.24 11474.3500 22948.7 12036.6800 24073.36 33678.6 40764577 81529155 2 1.63E+08
13 4 9422.0200 37688.08 11473.2500 45893 12035.5800 48142.32 33675.3 40760583 1.63E+08 3 4.89E+08
14 2 9420.9200 18841.84 11471.0500 22942.1 12034.4800 24068.96 33669.8 40753926 81507852 4 3.26E+08
15 4 9078.6800 36314.72 11285.0800 45140.32 11921.1400 47684.56 33070.07 40028013 1.6E+08 5 8.01E+08
16 2 6083.2700 12166.54 9648.7100 19297.42 10821.7900 21643.58 27749.95 33588539 67177079 6 4.03E+08
17 4 3136.2700 12545.08 6031.5500 24126.2 9405.5200 37622.08 18334 22191468 88765870 7 6.21E+08
18 1.5 1941.1900 2911.785 3882.3800 5823.57 7350.9800 11026.47 12410.85 15022087 22533130 8 1.8E+08
18.5 2 1572.5400 3145.08 3150.5800 6301.16 6071.1600 12142.32 10123.01 12252891 24505783 8.5 2.08E+08
19 1 1378.8600 1378.86 2808.3400 2808.34 5243.6300 5243.63 8927.925 10806360 10806360 9 97257244
19.5 2 0.0000 0 1519.7200 3039.44 3386.0700 6772.14 4732.475 5728188 11456375 9.5 1.09E+08
20 0.5 0.0000 0 0.0000 0 0.0000 0 0 0 0 10 0
sum of the
area
products
of water
plane 0 338171.6
sum of the area
products of water
plane 0.5 467441.1
sum of the area
products of water
plane 1 544919.6 1.67E+09
Summatio
n of
moments 9.03E+08
4.03E+12 LCB 3936.838
Summatio
n of
volume
products 6.67E+09 4.03E+12
Summatio
n of
moments 3.58E+09 975.9786
7264.25 1815.6
Table 1. Waterplane area, Displacement, LCB VCB calculation for WL‐01
Water planes 0 0.5 1
VOLUME
Volume
function levers
about
amidship
Different totals
Summation of
volume functions
0.5 2 0.5 products
for
area
below
Waterplane Area 1637708552 2263739389 2638954900
1319477450
SM 0.5 2 0.5
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
VOLUME
levers 0 0.5 1
Volume products 818854275.8 4527478778 1319477450
Monent about the
keel 0 2263739389
Ship Design & Project
Page 25
36. SM
section SM y0 y x SM y1 y x SM y2 y x SM
0 0.5 0.0000 0 2119.4600 1059.73 1554.9300 777.465 10032.77 12143665 6071832 ‐10 ‐6.1E+07
0.5 2 967.2900 1934.58 2512.3200 5024.64 2134.8700 4269.74 13151.44 15918503 31837006 ‐9.5 ‐3E+08
1 1 1202.7900 1202.79 2818.2400 2818.24 2890.8700 2890.87 15366.62 18599757 18599757 ‐9 ‐1.7E+08
1.5 2 1275.4200 2550.84 3293.6400 6587.28 3805.3400 7610.68 18255.32 22096239 44192479 ‐8.5 ‐3.8E+08
2 1.5 1492.2100 2238.315 3931.9000 5897.85 4731.9200 7097.88 21951.73 26570374 39855561 ‐8 ‐3.2E+08
3 4 1886.1700 7544.68 5366.8800 21467.52 6692.9200 26771.68 30046.61 36368417 1.45E+08 ‐7 ‐1E+09
4 2 2406.6800 4813.36 7143.0000 14286 8767.2600 17534.52 39745.94 48108486 96216972 ‐6 ‐5.8E+08
5 4 3733.8100 14935.24 9296.5700 37186.28 10335.3900 41341.56 51255.48 62039633 2.48E+08 ‐5 ‐1.2E+09
6 2 6104.1800 12208.36 10640.2200 21280.44 11320.2900 22640.58 59985.35 72606268 1.45E+08 ‐4 ‐5.8E+08
7 4 8445.9300 33783.72 11603.1100 46412.44 12016.8800 48067.52 66875.25 80945803 3.24E+08 ‐3 ‐9.7E+08
8 2 9428.6300 18857.26 12042.1900 24084.38 12325.0000 24650 69922.39 84634061 1.69E+08 ‐2 ‐3.4E+08
9 4 9427.5200 37710.08 12041.0800 48164.32 12325.0000 49300 69916.84 84627343 3.39E+08 ‐1 ‐3.4E+08
10 2 9426.4200 18852.84 12039.9800 24079.96 12325.0000 24650 69911.34 84620686 1.69E+08 0 0
11 4 9425.3200 37701.28 12037.7800 48151.12 12325.0000 49300 69901.44 84608703 3.38E+08 1 3.38E+08
12 2 9423.1200 18846.24 12036.6800 24073.36 12325.0000 24650 69894.84 84600714 1.69E+08 2 3.38E+08
13 4 9422.0200 37688.08 12035.5800 48142.32 12325.0000 49300 69889.34 84594057 3.38E+08 3 1.02E+09
14 2 9420.9200 18841.84 12034.4800 24068.96 12325.0000 24650 69883.84 84587400 1.69E+08 4 6.77E+08
15 4 9078.6800 36314.72 11921.1400 47684.56 12301.8900 49207.56 69065.13 83596433 3.34E+08 5 1.67E+09
16 2 6083.2700 12166.54 10821.7900 21643.58 11633.9200 23267.84 61004.35 73839665 1.48E+08 6 8.86E+08
17 4 3136.2700 12545.08 9405.5200 37622.08 10799.7800 43199.12 51558.13 62405961 2.5E+08 7 1.75E+09
18 1.5 1941.1900 2911.785 7350.9800 11026.47 9764.2600 14646.39 41109.37 49758781 74638172 8 5.97E+08
18.5 2 1572.5400 3145.08 6071.1600 12142.32 9102.8900 18205.78 34960.07 42315669 84631337 8.5 7.19E+08
19 1 1378.8600 1378.86 5243.6300 5243.63 8358.9900 8358.99 30712.37 37174253 37174253 9 3.35E+08
19.5 2 0.0000 0 3386.0700 6772.14 6675.3100 13350.62 20219.59 24473792 48947583 9.5 4.65E+08
20 0.5 0.0000 0 0.0000 0 0.0000 0 0 0 0 10 0
sum of the area
products of
water plane 0 338171.6
sum of the area
products of
water plane 0.5 544919.6
sum of the area
products of water
plane 1 595738.8 3.77E+09
Summatio
n of
moments 2.5E+09
9.13E+12 LCB 4817.615
Summatio
n of
volume
products 1.51E+10 9.13E+12
Summatio
n of
moments 1.63E+10 1965.793
7264.25 1815.6
products
for
area
below
Volume
function levers
Waterplane area, Displacement, LCB VCB calculation for WL‐02
Water planes 0 1 2
5770127389
about
amidship
Different totals
Summation of
volume functions
SM 1 4 1 VOLUME
Water plane area 1637708552 2638954900 2885063694
1 4 1
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
VOLUME
levers 0 1 2
Volume products 1637708552 10555819599 2885063694
Monent about the
keel 0 10555819599
Ship Design & Project
Page 26
37. SM
section SM y y x SM y y x SM y y x SM y y x SM y y x SM
0.00000 0.50000 2119.46000 1059.73000 1554.93000 777.46500 3.30000 1.65000 1421.78000 710.89000 3017.42000 1508.71000 12879.08000 15588838.43200 7794419.21600 ‐10.00000 ‐77944192.16000
0.50000 2.00000 2512.32000 5024.64000 2134.87000 4269.74000 2462.80000 4925.60000 4084.86000 8169.72000 5325.06000 10650.12000 30884.60000 37382719.84000 74765439.68000 ‐9.50000 ‐710271676.96000
1.00000 1.00000 2818.24000 2818.24000 2890.87000 2890.87000 4035.34000 4035.34000 5659.60000 5659.60000 6863.48000 6863.48000 42745.75000 51739455.80000 51739455.80000 ‐9.00000 ‐465655102.20000
1.50000 2.00000 3293.64000 6587.28000 3805.34000 7610.68000 5246.93000 10493.86000 6816.17000 13632.34000 8057.47000 16114.94000 52450.04500 63485534.46800 126971068.93600 ‐8.50000 ‐1079254085.95600
2.00000 1.50000 3931.90000 5897.85000 4731.92000 7097.88000 6218.62000 9327.93000 7725.13000 11587.69500 8987.35000 13481.02500 60645.59000 73405422.13600 110108133.20400 ‐8.00000 ‐880865065.63200
3.00000 4.00000 5366.88000 21467.52000 6692.92000 26771.68000 7939.72000 31758.88000 9195.33000 36781.32000 10252.86000 41011.44000 75013.04000 90795783.61600 363183134.46400 ‐7.00000 ‐2542281941.24800
4.00000 2.00000 7143.00000 14286.00000 8767.26000 17534.52000 9634.41000 19268.82000 10395.92000 20791.84000 11012.17000 22024.34000 88153.48500 106700978.24400 213401956.48800 ‐6.00000 ‐1280411738.92800
5.00000 4.00000 9296.57000 37186.28000 10335.39000 41341.56000 10825.09000 43300.36000 11211.35000 44845.40000 11544.78000 46179.12000 97946.88000 118554903.55200 474219614.20800 ‐5.00000 ‐2371098071.04000
6.00000 2.00000 10640.22000 21280.44000 11320.29000 22640.58000 11543.68000 23087.36000 11748.37000 23496.74000 11934.34000 23868.68000 104204.03000 126128557.91200 252257115.82400 ‐4.00000 ‐1009028463.29600
7.00000 4.00000 11603.11000 46412.44000 12016.88000 48067.52000 12065.29000 48261.16000 12134.62000 48538.48000 12191.85000 48767.40000 108663.58000 131526397.23200 526105588.92800 ‐3.00000 ‐1578316766.78400
8.00000 2.00000 12042.19000 24084.38000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 110783.59500 134092463.38800 268184926.77600 ‐2.00000 ‐536369853.55200
9.00000 4.00000 12041.08000 48164.32000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 110783.04000 134091791.61600 536367166.46400 ‐1.00000 ‐536367166.46400
10.00000 2.00000 12039.98000 24079.96000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 110782.49000 134091125.89600 268182251.79200 0.00000 0.00000
11.00000 4.00000 12037.78000 48151.12000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 110781.39000 134089794.45600 536359177.82400 1.00000 536359177.82400
12.00000 2.00000 12036.68000 24073.36000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 110780.84000 134089128.73600 268178257.47200 2.00000 536356514.94400
13.00000 4.00000 12035.58000 48142.32000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 12325.00000 49300.00000 110780.29000 134088463.01600 536353852.06400 3.00000 1609061556.19200
14.00000 2.00000 12034.48000 24068.96000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 12325.00000 24650.00000 110779.74000 134087797.29600 268175594.59200 4.00000 1072702378.36800
15.00000 4.00000 11921.14000 47684.56000 12301.89000 49207.56000 12273.28000 49093.12000 12298.59000 49194.36000 12314.00000 49256.00000 110482.63000 133728175.35200 534912701.40800 5.00000 2674563507.04000
16.00000 2.00000 10821.79000 21643.58000 11633.92000 23267.84000 11813.29000 23626.58000 11993.77000 23987.54000 12145.63000 24291.26000 106519.38000 128931057.55200 257862115.10400 6.00000 1547172690.62400
17.00000 4.00000 9405.52000 37622.08000 10799.78000 43199.12000 11253.17000 45012.68000 11611.91000 46447.64000 11916.73000 47666.92000 101546.44500 122911817.02800 491647268.11200 7.00000 3441530876.78400
18.00000 1.50000 7350.98000 11026.47000 9764.26000 14646.39000 10576.39000 15864.58500 11148.62000 16722.93000 11625.12000 17437.68000 95288.19500 115336831.22800 173005246.84200 8.00000 1384041974.73600
18.50000 2.00000 6071.16000 12142.32000 9102.89000 18205.78000 10124.11000 20248.22000 10810.79000 21621.58000 11367.61000 22735.22000 91038.29500 110192752.26800 220385504.53600 8.50000 1873276788.55600
19.00000 1.00000 5243.63000 5243.63000 8358.99000 8358.99000 9538.67000 9538.67000 10318.89000 10318.89000 10929.63000 10929.63000 85852.99000 103916459.09600 103916459.09600 9.00000 935248131.86400
19.50000 2.00000 3386.07000 6772.14000 6675.31000 13350.62000 8374.40000 16748.80000 9374.70000 18749.40000 10153.82000 20307.64000 75257.87500 91092131.90000 182184263.80000 9.50000 1730750506.10000
20.00000 0.50000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 6422.21000 3211.10500 8520.76000 4260.38000 34209.60000 41407299.84000 20703649.92000 10.00000 207036499.20000
sum of the
area products
of water plane
0 544919.62000
sum of the area
products of
water plane 0.5 595738.79500
sum of the area
products of
water plane 1 621093.61500
sum of the area
products of
water plane 2 650967.47000
sum of the area
products of
water plane 3 673853.98500 6866964362.55000
Summation
of moments 4480236478.01200
16627781956884.60000 LCB 4739.43887
Summation of
volume products 27474854522.28130 16627781956884.60000
Summation of
moments 42407146309.27540 2802.35933
7264.25000 1815.60000
Table 1. Waterplane area, Displacement, LCB VCB calculation for WL‐03
Water planes 0.00000 0.50000 1.00000 2.00000 3.00000
Sectional area below
waterline Volume function levers moments about amidship
Different totals Summation of volume functions
0.50000 2.00000 1.50000 4.00000 1.00000 Area products for
sectional area
SM 0.50000 2.00000 1.50000 4.00000 1.00000 VOLUME
Water plane area 2638954899.72333 2885063694.38583 3007852861.84250 3152526962.63167 3263362540.35750
VOLUME
levers 0.00000 0.50000 1.00000 2.00000 3.00000
Volume products 1319477449.86167 5770127388.77167 4511779292.76375 12610107850.52670 3263362540.35750
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
Monent about the keel 0.00000 2885063694.38583 4511779292.76375 25220215701.05330 9790087621.07250
Ship Design & Project
Page 27
38. SM
section SM y y x SM y y x SM y y x SM y y x SM y y x SM
0.0000 0.5000 0.0000 0.0000 2119.4600 1059.7300 1554.9300 777.4650 3.3000 1.6500 1421.7800 710.8900 13022.6800 15762651.8720 7881325.9360 ‐10.0000 ‐78813259.3600
0.5000 2.0000 967.2900 1934.5800 2512.3200 5024.6400 2134.8700 4269.7400 2462.8000 4925.6000 4084.8600 8169.7200 29222.3700 35370756.6480 70741513.2960 ‐9.5000 ‐672044376.3120
1.0000 1.0000 1202.7900 1202.7900 2818.2400 2818.2400 2890.8700 2890.8700 4035.3400 4035.3400 5659.6000 5659.6000 40058.4500 48486747.8800 48486747.8800 ‐9.0000 ‐436380730.9200
1.5000 2.0000 1275.4200 2550.8400 3293.6400 6587.2800 3805.3400 7610.6800 5246.9300 10493.8600 6816.1700 13632.3400 49864.5500 60356051.3200 120712102.6400 ‐8.5000 ‐1026052872.4400
2.0000 1.5000 1492.2100 2238.3150 3931.9000 5897.8500 4731.9200 7097.8800 6218.6200 9327.9300 7725.1300 11587.6950 59283.2600 71756457.9040 107634686.8560 ‐8.0000 ‐861077494.8480
3.0000 4.0000 1886.1700 7544.6800 5366.8800 21467.5200 6692.9200 26771.6800 7939.7200 31758.8800 9195.3300 36781.3200 77693.7400 94040502.8960 376162011.5840 ‐7.0000 ‐2633134081.0880
4.0000 2.0000 2406.6800 4813.3600 7143.0000 14286.0000 8767.2600 17534.5200 9634.4100 19268.8200 10395.9200 20791.8400 97446.7600 117949558.3040 235899116.6080 ‐6.0000 ‐1415394699.6480
5.0000 4.0000 3733.8100 14935.2400 9296.5700 37186.2800 10335.3900 41341.5600 10825.0900 43300.3600 11211.3500 44845.4000 116102.5800 140530562.8320 562122251.3280 ‐5.0000 ‐2810611256.6400
6.0000 2.0000 6104.1800 12208.3600 10640.2200 21280.4400 11320.2900 22640.5800 11543.6800 23087.3600 11748.3700 23496.7400 129228.7300 156418454.7920 312836909.5840 ‐4.0000 ‐1251347638.3360
7.0000 4.0000 8445.9300 33783.7200 11603.1100 46412.4400 12016.8800 48067.5200 12065.2900 48261.1600 12134.6200 48538.4800 139287.9100 168594086.2640 674376345.0560 ‐3.0000 ‐2023129035.1680
8.0000 2.0000 9428.6300 18857.2600 12042.1900 24084.3800 12325.0000 24650.0000 12325.0000 24650.0000 12325.0000 24650.0000 143872.3900 174143140.8560 348286281.7120 ‐2.0000 ‐696572563.4240
9.0000 4.0000 9427.5200 37710.0800 12041.0800 48164.3200 12325.0000 49300.0000 12325.0000 49300.0000 12325.0000 49300.0000 143866.8400 174136423.1360 696545692.5440 ‐1.0000 ‐696545692.5440
10.0000 2.0000 9426.4200 18852.8400 12039.9800 24079.9600 12325.0000 24650.0000 12325.0000 24650.0000 12325.0000 24650.0000 143861.3400 174129765.9360 348259531.8720 0.0000 0.0000
11.0000 4.0000 9425.3200 37701.2800 12037.7800 48151.1200 12325.0000 49300.0000 12325.0000 49300.0000 12325.0000 49300.0000 143851.4400 174117782.9760 696471131.9040 1.0000 696471131.9040
12.0000 2.0000 9423.1200 18846.2400 12036.6800 24073.3600 12325.0000 24650.0000 12325.0000 24650.0000 12325.0000 24650.0000 143844.8400 174109794.3360 348219588.6720 2.0000 696439177.3440
13.0000 4.0000 9422.0200 37688.0800 12035.5800 48142.3200 12325.0000 49300.0000 12325.0000 49300.0000 12325.0000 49300.0000 143839.3400 174103137.1360 696412548.5440 3.0000 2089237645.6320
14.0000 2.0000 9420.9200 18841.8400 12034.4800 24068.9600 12325.0000 24650.0000 12325.0000 24650.0000 12325.0000 24650.0000 143833.8400 174096479.9360 348192959.8720 4.0000 1392771839.4880
15.0000 4.0000 9078.6800 36314.7200 11921.1400 47684.5600 12301.8900 49207.5600 12273.2800 49093.1200 12298.5900 49194.3600 142758.7300 172795166.7920 691180667.1680 5.0000 3455903335.8400
16.0000 2.0000 6083.2700 12166.5400 10821.7900 21643.5800 11633.9200 23267.8400 11813.2900 23626.5800 11993.7700 23987.5400 131885.2000 159633846.0800 319267692.1600 6.0000 1915606152.9600
17.0000 4.0000 3136.2700 12545.0800 9405.5200 37622.0800 10799.7800 43199.1200 11253.1700 45012.6800 11611.9100 46447.6400 118982.5000 144016418.0000 576065672.0000 7.0000 4032459704.0000
18.0000 1.5000 1941.1900 2911.7850 7350.9800 11026.4700 9764.2600 14646.3900 10576.3900 15864.5850 11148.6200 16722.9300 104327.8100 126278381.2240 189417571.8360 8.0000 1515340574.6880
18.5000 2.0000 1572.5400 3145.0800 6071.1600 12142.3200 9102.8900 18205.7800 10124.1100 20248.2200 10810.7900 21621.5800 95370.1900 115436077.9760 230872155.9520 8.5000 1962413325.5920
19.0000 1.0000 1378.8600 1378.8600 5243.6300 5243.6300 8358.9900 8358.9900 9538.6700 9538.6700 10318.8900 10318.8900 87544.9300 105964383.2720 105964383.2720 9.0000 953679449.4480
19.5000 2.0000 0.0000 0.0000 3386.0700 6772.1400 6675.3100 13350.6200 8374.4000 16748.8000 9374.7000 18749.4000 69767.2000 84446218.8800 168892437.7600 9.5000 1604478158.7200
20.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 6422.2100 3211.1050 6422.2100 7773442.9840 3886721.4920 10.0000 38867214.9200
sum of the
area
products of
water plane
0 338171.5700
sum of the
area
products of
water plane
0.5 544919.6200
sum of the
area
products of
water plane
1 595738.7950
sum of the
area
products of
water plane
2 621093.6150
sum of the
area
products of
water plane
3 650967.4700 8284788047.5280
Summatio
n of
moments 5752564009.8080
20060923858085.1000 LCB 5043.9508
Summation of
volume
products 33147593949.2483 20060923858085.1000
Summation of
moments 70800416569.0733 3877.9658
7264.2500 1815.6000
Table 5. Waterplane area, Displacement, LCB VCB calculation for WL‐04
Water planes 0.0000 1.0000 2.0000 3.0000 4.0000
Sectional area
below waterline Volume function levers
moments about
amidship
Different totals Summation of volume functions
1.0000 4.0000 2.0000 4.0000 1.0000 Area products
for sectional
SM 1.0000 4.0000 2.0000 4.0000 1.0000 VOLUME
Water plane area 1637708551.5817 2638954899.7233 2885063694.3858 3007852861.8425 3152526962.6317
VOLUME
levers 0.0000 1.0000 2.0000 3.0000 4.0000
Volume products 1637708551.5817 10555819598.8933 5770127388.7717 12031411447.3700 3152526962.6317
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
Monent about the
keel 0.0000 10555819598.8933 11540254777.5433 36094234342.1100 12610107850.5267
Ship Design & Project
Page 28
39. SM
section SM y y x SM y y x SM y y x SM y y x SM y y x SM y y x SM y y x SM
0.000 0.500 0.000 0.000 1836.650 918.325 2119.460 1059.730 1554.930 777.465 3.300 1.650 1421.780 710.890 3017.420 1508.710 21783.350 26366566.840 13183283.420 ‐10.000 ‐131832834.200
0.500 2.000 967.290 1934.580 2266.920 4533.840 2512.320 5024.640 2134.870 4269.740 2462.800 4925.600 4084.860 8169.720 5325.060 10650.120 43915.545 53155375.668 106310751.336 ‐9.500 ‐1009952137.692
1.000 1.000 1202.790 1202.790 2445.190 2445.190 2818.240 2818.240 2890.870 2890.870 4035.340 4035.340 5659.600 5659.600 6863.480 6863.480 58855.175 71238303.820 71238303.820 ‐9.000 ‐641144734.380
1.500 2.000 1275.420 2550.840 2700.500 5401.000 3293.640 6587.280 3805.340 7610.680 5246.930 10493.860 6816.170 13632.340 8057.470 16114.940 72016.540 87168820.016 174337640.032 ‐8.500 ‐1481869940.272
2.000 1.500 1492.210 2238.315 3077.950 4616.925 3931.900 5897.850 4731.920 7097.880 6218.620 9327.930 7725.130 11587.695 8987.350 13481.025 84052.645 101737321.508 152605982.262 ‐8.000 ‐1220847858.096
3.000 4.000 1886.170 7544.680 4010.030 16040.120 5366.880 21467.520 6692.920 26771.680 7939.720 31758.880 9195.330 36781.320 10252.860 41011.440 106698.765 129148185.156 516592740.624 ‐7.000 ‐3616149184.368
4.000 2.000 2406.680 4813.360 4994.930 9989.860 7143.000 14286.000 8767.260 17534.520 9634.410 19268.820 10395.920 20791.840 11012.170 22024.340 128841.410 155949642.664 311899285.328 ‐6.000 ‐1871395711.968
5.000 4.000 3733.810 14935.240 6374.890 25499.560 9296.570 37186.280 10335.390 41341.560 10825.090 43300.360 11211.350 44845.400 11544.780 46179.120 147943.460 179070763.984 716283055.936 ‐5.000 ‐3581415279.680
6.000 2.000 6104.180 12208.360 9214.040 18428.080 10640.220 21280.440 11320.290 22640.580 11543.680 23087.360 11748.370 23496.740 11934.340 23868.680 164736.840 199397471.136 398794942.272 ‐4.000 ‐1595179769.088
7.000 4.000 8445.930 33783.720 10881.210 43524.840 11603.110 46412.440 12016.880 48067.520 12065.290 48261.160 12134.620 48538.480 12191.850 48767.400 176318.480 213415888.192 853663552.768 ‐3.000 ‐2560990658.304
8.000 2.000 9428.630 18857.260 11478.760 22957.520 12042.190 24084.380 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 181310.120 219457769.248 438915538.496 ‐2.000 ‐877831076.992
9.000 4.000 9427.520 37710.080 11477.660 45910.640 12041.080 48164.320 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 181305.700 219452419.280 877809677.120 ‐1.000 ‐877809677.120
10.000 2.000 9426.420 18852.840 11476.560 22953.120 12039.980 24079.960 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 181301.300 219447093.520 438894187.040 0.000 0.000
11.000 4.000 9425.320 37701.280 11475.460 45901.840 12037.780 48151.120 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 181295.250 219439770.600 877759082.400 1.000 877759082.400
12.000 2.000 9423.120 18846.240 11474.350 22948.700 12036.680 24073.360 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 181290.280 219433754.912 438867509.824 2.000 877735019.648
13.000 4.000 9422.020 37688.080 11473.250 45893.000 12035.580 48142.320 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 181285.880 219428429.152 877713716.608 3.000 2633141149.824
14.000 2.000 9420.920 18841.840 11471.050 22942.100 12034.480 24068.960 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 181279.280 219420440.512 438840881.024 4.000 1755363524.096
15.000 4.000 9078.680 36314.720 11285.080 45140.320 11921.140 47684.560 12301.890 49207.560 12273.280 49093.120 12298.590 49194.360 12314.000 49256.000 180253.690 218179066.376 872716265.504 5.000 4363581327.520
16.000 2.000 6083.270 12166.540 9648.710 19297.420 10821.790 21643.580 11633.920 23267.840 11813.290 23626.580 11993.770 23987.540 12145.630 24291.260 168854.710 204381740.984 408763481.968 6.000 2452580891.808
17.000 4.000 3136.270 12545.080 6031.550 24126.200 9405.520 37622.080 10799.780 43199.120 11253.170 45012.680 11611.910 46447.640 11916.730 47666.920 151809.345 183750031.188 735000124.752 7.000 5145000873.264
18.000 1.500 1941.190 2911.785 3882.380 5823.570 7350.980 11026.470 9764.260 14646.390 10576.390 15864.585 11148.620 16722.930 11625.120 17437.680 136191.245 164845882.948 247268824.422 8.000 1978150595.376
18.500 2.000 1572.540 3145.080 3150.580 6301.160 6071.160 12142.320 9102.890 18205.780 10124.110 20248.220 10810.790 21621.580 11367.610 22735.220 127464.720 154283297.088 308566594.176 8.500 2622816050.496
19.000 1.000 1378.860 1378.860 2808.340 2808.340 5243.630 5243.630 8358.990 8358.990 9538.670 9538.670 10318.890 10318.890 10929.630 10929.630 118890.045 143904510.468 143904510.468 9.000 1295140594.212
19.500 2.000 0.000 0.000 1519.720 3039.440 3386.070 6772.140 6675.310 13350.620 8374.400 16748.800 9374.700 18749.400 10153.820 20307.640 99221.205 120097346.532 240194693.064 9.500 2281849584.108
20.000 0.500 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6422.210 3211.105 8520.760 4260.380 34209.600 41407299.840 20703649.920 10.000 207036499.200
sum of the
area
products
of water
plane 0 338171.570
sum of the
area
products
of water
plane 0.5 467441.110
sum of the
area
products
of water
plane 1 544919.620
sum of the
area
products
of water
plane 2 595738.795
sum of the
area
products
of water
plane 3 621093.615
sum of the
area
products
of water
plane 4 650967.470
sum of the
area
products
of water
plane 5 673853.985 10680828274.584
Summation of
moments 7023736329.792
25862735597882.300 LCB 4776.987
Summation
of volume
products 42734196295.245 25862735597882.300
Summation
of moments 114107042568.499 4847.938
7264.250 1815.600
Displacement= 25862.7356
Cb = 0.795511716
Table 6. Waterplane area, Displacement, LCB VCB calculation for WL‐05
Water planes 0.000 0.500 1.000 2.000 3.000 4.000 5.000
moments about
amidship
0.500 2.000 1.500 4.000 2.000 4.000 1.000 Area
products
Sectional area
below waterline Volume function levers
Different totals Summation of volume functions
Water plane area 1637708551.582 2263739388.878 2638954899.723 2885063694.386 3007852861.843 3152526962.632 3263362540.358
SM 0.500 2.000 1.500 4.000 2.000 4.000 1.000 VOLUME
12610107850.527 3263362540.358 VOLUME
levers 0.000 0.500 1.000 2.000 3.000 4.000
Volume products 818854275.791 4527478777.757 3958432349.585 11540254777.543 6015705723.685
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
5.000
Monent about the
keel 0.000 2263739388.878 3958432349.585 23080509555.087 18047117171.055 50440431402.107 16316812701.788
Ship Design & Project
Page 29
40. SM
section SM y y x SM y y x SM y y x SM y y x SM y y x SM y y x SM y y x SM
0.000 0.500 4439.200 2219.600 1836.650 918.325 2119.460 1059.730 1554.930 777.465 3.300 1.650 1421.780 710.890 3017.420 1508.710 24002.950 29053170.680 14526585.340 ‐10.000 ‐145265853.400
0.500 2.000 6437.610 12875.220 2266.920 4533.840 2512.320 5024.640 2134.870 4269.740 2462.800 4925.600 4084.860 8169.720 5325.060 10650.120 46650.705 56466013.332 112932026.664 ‐9.500 ‐1072854253.308
1.000 1.000 7884.700 7884.700 2445.190 2445.190 2818.240 2818.240 2890.870 2890.870 4035.340 4035.340 5659.600 5659.600 6863.480 6863.480 62196.130 75282195.752 75282195.752 ‐9.000 ‐677539761.768
1.500 2.000 9017.060 18034.120 2700.500 5401.000 3293.640 6587.280 3805.340 7610.680 5246.930 10493.860 6816.170 13632.340 8057.470 16114.940 75887.360 91854060.544 183708121.088 ‐8.500 ‐1561519029.248
2.000 1.500 9873.210 14809.815 3077.950 4616.925 3931.900 5897.850 4731.920 7097.880 6218.620 9327.930 7725.130 11587.695 8987.350 13481.025 88243.145 106809502.708 160214254.062 ‐8.000 ‐1281714032.496
3.000 4.000 10930.730 43722.920 4010.030 16040.120 5366.880 21467.520 6692.920 26771.680 7939.720 31758.880 9195.330 36781.320 10252.860 41011.440 111221.045 134621952.868 538487811.472 ‐7.000 ‐3769414680.304
4.000 2.000 11474.350 22948.700 4994.930 9989.860 7143.000 14286.000 8767.260 17534.520 9634.410 19268.820 10395.920 20791.840 11012.170 22024.340 133375.245 161437396.548 322874793.096 ‐6.000 ‐1937248758.576
5.000 4.000 11854.010 47416.040 6374.890 25499.560 9296.570 37186.280 10335.390 41341.560 10825.090 43300.360 11211.350 44845.400 11544.780 46179.120 152003.560 183985109.024 735940436.096 ‐5.000 ‐3679702180.480
6.000 2.000 12113.710 24227.420 9214.040 18428.080 10640.220 21280.440 11320.290 22640.580 11543.680 23087.360 11748.370 23496.740 11934.340 23868.680 167741.605 203034438.692 406068877.384 ‐4.000 ‐1624275509.536
7.000 4.000 12249.070 48996.280 10881.210 43524.840 11603.110 46412.440 12016.880 48067.520 12065.290 48261.160 12134.620 48538.480 12191.850 48767.400 178220.050 215717548.520 862870194.080 ‐3.000 ‐2588610582.240
8.000 2.000 12325.000 24650.000 11478.760 22957.520 12042.190 24084.380 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 182758.305 221210652.372 442421304.744 ‐2.000 ‐884842609.488
9.000 4.000 12325.000 49300.000 11477.660 45910.640 12041.080 48164.320 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 182754.440 221205974.176 884823896.704 ‐1.000 ‐884823896.704
10.000 2.000 12325.000 24650.000 11476.560 22953.120 12039.980 24079.960 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 182750.590 221201314.136 442402628.272 0.000 0.000
11.000 4.000 12325.000 49300.000 11475.460 45901.840 12037.780 48151.120 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 182745.090 221194656.936 884778627.744 1.000 884778627.744
12.000 2.000 12325.000 24650.000 11474.350 22948.700 12036.680 24073.360 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 182741.220 221189972.688 442379945.376 2.000 884759890.752
13.000 4.000 12325.000 49300.000 11473.250 45893.000 12035.580 48142.320 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 12325.000 49300.000 182737.370 221185312.648 884741250.592 3.000 2654223751.776
14.000 2.000 12325.000 24650.000 11471.050 22942.100 12034.480 24068.960 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 12325.000 24650.000 182731.320 221177989.728 442355979.456 4.000 1769423917.824
15.000 4.000 12318.400 49273.600 11285.080 45140.320 11921.140 47684.560 12301.890 49207.560 12273.280 49093.120 12298.590 49194.360 12314.000 49256.000 181873.550 220139744.920 880558979.680 5.000 4402794898.400
16.000 2.000 12254.570 24509.140 9648.710 19297.420 10821.790 21643.580 11633.920 23267.840 11813.290 23626.580 11993.770 23987.540 12145.630 24291.260 171940.360 208116611.744 416233223.488 6.000 2497399340.928
17.000 4.000 12139.020 48556.080 6031.550 24126.200 9405.520 37622.080 10799.780 43199.120 11253.170 45012.680 11611.910 46447.640 11916.730 47666.920 156310.720 189198495.488 756793981.952 7.000 5297557873.664
18.000 1.500 11964.050 17946.075 3882.380 5823.570 7350.980 11026.470 9764.260 14646.390 10576.390 15864.585 11148.620 16722.930 11625.120 17437.680 141202.675 170911717.820 256367576.730 8.000 2050940613.840
18.500 2.000 11753.870 23507.740 3150.580 6301.160 6071.160 12142.320 9102.890 18205.780 10124.110 20248.220 10810.790 21621.580 11367.610 22735.220 132555.385 160445038.004 320890076.008 8.500 2727565646.068
19.000 1.000 11336.800 11336.800 2808.340 2808.340 5243.630 5243.630 8358.990 8358.990 9538.670 9538.670 10318.890 10318.890 10929.630 10929.630 123869.015 149931055.756 149931055.756 9.000 1349379501.804
19.500 2.000 10652.320 21304.640 1519.720 3039.440 3386.070 6772.140 6675.310 13350.620 8374.400 16748.800 9374.700 18749.400 10153.820 20307.640 104547.365 126544130.596 253088261.192 9.500 2404338481.324
20.000 0.500 9517.760 4758.880 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6422.210 3211.105 8520.760 4260.380 38968.480 47167448.192 23583724.096 10.000 235837240.960
sum of the
area
products
of water
plane 0 690827.770
sum of the
area
products
of water
plane 0.5 467441.110
sum of the
area
products
of water
plane 1 544919.620
sum of the
area
products
of water
plane 2 595738.795
sum of the
area
products
of water
plane 3 621093.615
sum of the
area
products
of water
plane 4 650967.470
sum of the
area
products
of water
plane 5 673853.985 10894255806.824
Summation of
moments 7051188637.536
26379532581573.700 LCB 4701.707
Summation
of volume
products 43588123895.528 26379532581573.700
Summation
of
moments 114107042568.499 4752.963
7264.250 1815.600
VCB
Distance between two consecutive sections Distance between two consecutive waterlines
5.000
Monent about the
keel 0.000 2263739388.878 3958432349.585 23080509555.087 18047117171.055 50440431402.107 16316812701.788
VOLUME
levers 0.000 0.500 1.000 2.000 3.000 4.000
Volume products 1672781876.074 4527478777.757 3958432349.585 11540254777.543 6015705723.685
2.000 4.000 1.000 VOLUME
12610107850.527 3263362540.358
SM 0.500 2.000 1.500 4.000
Different totals Summation of volume functions
Water plane area 3345563752.148 2263739388.878 2638954899.723 2885063694.386 3007852861.843 3152526962.632 3263362540.358
moments about
amidship
0.500 2.000 1.500 4.000 2.000 4.000 1.000 Area
products for
Sectional area
below waterline Volume function levers
Table 6. Waterplane area, Displacement, LCB VCB calculation for WL‐06
Water planes 0.000 0.500 1.000 2.000 3.000 4.000 5.000
Ship Design & Project
Page 30
45. 5.1.1 Strength/weather Deck Plating
The greater of the following:
(1) t = 0,00083s1 (Lk)0.5
+ 2,5= 0.00083 ×700(132×0.78)0.5
+2.5=8.25
(2) t = 0,00083s1 (Lk)0.5
+ 2,5=0.00083 ×700(132×0.75)0.5
+2.5=8.25
(3) t = taken as (1)
Table 5.2 Strength/weather Deck Plating
Ship Design & Project
Page 35
LLOYD’S REGISTER
Location
Minimum thickness, in mm, see also 4.2.1
Longitudinal framing Transverse framing
(1) Outside line of openings
(see Notes 1 and 2)
The greater of the following:
(a) t = 0,001s1 (0,059L1 + 7)
FD
kL
(b) t = 0,00083s1 Lk + 2,5
Lk + 2,5t = 0,00083s1
but not less than 6,5
t = 0,004sf
ρkh4 + 3,5
1,025
or as (1) or (2), whichever is the greater,
but not less than 7,5 mm where L ≥ 90 m, or
6,5 mm where L < 90 m
t = 0,00083s1 Lk + 1,5
but not less than 6,5
The greater of the following:
(a) t = 0,001s1 f1 (0,083L1 + 10)
FD
kL
(b) t = 0,001s1 Lk + 2,5
(2) Inside line of openings (see Note 2)
(3) In way of the crown of a tank
Symbols
f = 1,1 –
L, kL, k, ρ, s, S as defined in 1.5.1
s
but not to be taken greater than 1,0
2500S
f1 =
1
1 +( s
)2
1000S
h4 = tank head, in metres, as defined in Pt 3, Ch 3,5
s1 = s but is not to be taken less than the smaller of
470 +
L
mm or 700 mm
0,6
FD = as defined in Pt 3, Ch 4,5.7
L1 = L but need not be taken greater than 190 m
46. 5.1.2 Lower Deck Plating
(1) T1= 0.012s1√𝑘𝑘
(2) T2= 0.01s1√𝑘𝑘
= 0.012×700×√0.78=7.5 mm =6.2 mm
(3) t = 0,004sf √(
þkh4
1.025 1.025
) + 3.5 = 0.004×700√
1.025×0.22×22.3 + 3.5 = 15.6
(4) t = 0,004sf √(
pkh4
1.025
) + 2.5 = 14.6
(5)
t= √ 1.8𝑘𝑘 =(66.3/(1.8×0.78))0.5
= 6.87
Table 5.3 Lower Deck Plating
Ship Design & Project
Page 36
t = 0,004sf
ρkh4
+ K11,025
but not less than 7,5 where L ≥ 90 m, or
6,5 where L < 90 m
t = 0,01s1 k
but not less than 6,5
Minimum thickness, in mm
In way of deck openings, t = 1,1
1,8k
Minimum breadth, b = 760 mm
Second deck
t = 0,012s1 k
but not less than 6,5
Clear of deck openings, t =
t = 0,01s1 k
but not less than 6,5
Third or platform decks
LocationSymbols
(1) Outside line of openings
(2) Inside line of openings
(3) In way of the crown or bottom
of a tank
(4) Plating forming the upper flange
of underdeck girders
s, S, k, ρ as defined in 1.5.1
b = breadth of increased plating, in mm
f = 1,1 –
s
but not to be taken
2500S
greater than 1,0
h4 = tank head, in metres, as defined in
Pt 3, Ch 3,5
s1 = s but is not to be taken less than
the smaller of 470 +
L
mm
0,6
or 700 mm
Af = girder face area, in cm2
K1= 2,5 mm at bottom of tank
= 3,5 mm at crown of tank
NOTE
Where a deck loading exceeds 43,2 kN/m2 (4,4 tonne-f/m2), the thickness of plating will be specially considered.
Af
1,8k
Af
47. 5.1.3 Strength/Weather Deck Longitudinals
Z = 0. 043skhT1le2F1= 0.043 × 700 × 0.78 × 1.88 × 0.148 × (3.35)2
C1=
60
225−165×0.67
= 73.31 cm3
5.1.4 Cargo and Accommodation Deck Longitudinals
Z = sk(5.9L1+25h2le
2
)×10-4
= 700× 0.78 (5.9×132 + 25×1.39(3.75)2
)×10-4
= 64.33
Table 5.4: Strength/Weather Deck Longitudinals
Table 5.5: Cargo and Accommodation Deck Longitudinals
Page 37
Symbols Location
Inertia,
in cm4Modulus, in cm3
L, s, kL, k, ρ as defined in 1.5.1
b =1,4 for rolled or built
sections
= 1,6 for flat bars
c1 =
dw = depth of longitudinal, in mm
F1 = 0,25c1
h1 = weather head, in metres, as
defined in Pt 3, Ch 3,5
h4 = tank head, in metres, as
defined in Pt 3, Ch 3,5
le = as defined in 1.5.1, but not
to be taken less than 1,5 m
FD = as defined in Pt 3, Ch 4,5.7
hT1 = for Type ‘B–60’ ships
or 1,20 m= the greater of
70
for Type ‘B’ ships
L1 = L but need not be taken
greater than 190 m
L2 = L but need not be taken
greater than 215 m
L1
L1
56
60
225 – 165 FD
(1) In way of dry cargo spaces,
see Note 1
(a) Outside line of openings
(b) Inside line of openings
(2) In way of the crown or bottom
of a tank
(3) In way of superstructure To be specially considered
Z = 0,043 s k hT1 le
2 F1
Z = s k (400h1 + 0,005 (le L2)2) x 10–4
Z =
or as (1)(a) or (1)(b) above,
whichever is the greater
0,0113 ρ sk h4 le
2
b
––
––
––
NOTES
1. Where weather decks are intended to carry deck cargo and the load is in excess of 8,5 kN/m2
(0,865 tonne-f/m2), the scantlings of longitudinals may be required to be increased to comply
with the requirements for location (1) Table 1.4.4 using the equivalent design head, for specified
cargo loading, for weather decks given in Table 3.5.1 in Pt 3, Ch 3.
2. The buckling requirements of Pt 3, Ch 4,7 are to be complied with. The ratio of the web depth dw
to web thickness t is to comply with the following requirements:
(a)
≤ 60 kL
(b)
≤ 18 kL when continuous at bulkheads
≤ 15 kL when non-continuous at bulkheads
3. The web depth of longitudinals, dw is to be not less than 60 mm.
dw
t
Flat bars:
dw
t
Built up profiles and rolled angles:
dw
t
I = le Z
2,3
k
Symbols Location
Inertia,
in cm4Modulus, in cm3
L, s, k, ρ as defined in 1.5.1
dw = web depth of longitudinal,
in mm, see Note 2
h2 = cargo head, in metres, as
defined in Pt 3, Ch 3,5
h3 = accommodation head, in
metres, as defined in Pt 3,
Ch 3,5
h4 = tank head, in metres, as
defined in Pt 3, Ch 3,5
le = as defined in 1.5.1, but not
to be taken less than 1,5 m
L1 = L but need not be taken
greater than 190 m
γ = 1,4 for rolled or built
sections
= 1,6 for flat bars
(1) Cargo decks
(a) L ≥ 90 m
(b) L < 90 m
(2) Accommodation decks
(a) L ≥ 90 m
(b) L < 90 m
(3) In way of the crown or bottom of
a tank
As in (1) or (2) as applicable, or
Z =
0,0113ρ s k h4 le
2
γ
whichever is the greater
Z = sk (5,9L1 + 25h2 le
2) x 10–4
Z = 0,005s k h2 le
2
Z = sk (5,1L1 + 25h3 le
2) x 10–4
Z = 0,00425s k h3 le
2
See Note 1
––
––
––
––
I =
2,3
leZ
k
NOTES
1. The section modulus of accommodation deck longitudinals
need not be taken greater than the value required by location
(1)(a), in Table 1.4.3.
2. The web depth of longitudinals, dw, to be not less than 60 mm.
48. Z = sk(5.1L1+25h3le
2
)×10-4
=700× 0.78 (5.1×132 + 25×1.39(3.75)2
)×10-4
=51.56
5.1.5 Strength/Weather,Cargo and Accommodation Deck Beam
Ship Design & Project
Page 38
Z = (k1k2TD+K3B1sh1le
2
)k × 10-4
=(20×133×8.25×11.3+3.6×22.3×1.8×(3.75)2
)×0.78×10-4
=19.5 cm3
Z =
(400k1TD+38.8h2le
2
)k × 10-4
= (400×20×8.25×11.3+38.3×1.8×(3.75)2
)×0.78×10-4
=58.24 cm3
Table 5.6: Strength/Weather,Cargo and Accommodation Deck Beam
Symbols Location
Inertia,
in cm4Modulus, in cm3
B, D, T, s, k, ρ as defined in 1.5.1
dw = depth of beam, in mm
h1 = weather deck head
h2 = cargo head
h3 = accommodation head
h4 = tank head
le as defined in 1.5.1, but to be taken as
not less than 1,83 m
B1 = B, but need not be taken greater
than 21,5 m
K1 = a factor dependent on the number
of decks (including poop and bridge
superstructures) at the position of
the beam under consideration:
1 deck 20,0 3 decks 10,5
2 decks 13,3 4 or more 9,3
K2 = a factor dependent on the location
133
of the beam:
at short bridge and poops
elsewhere 530
K3 = a factor dependent on the location
of the beam:
span adjacent to the ship side 3,6
elsewhere 3,3
γ = 1,4 for rolled or built sections
= 1,6 for flat bars
(1) Strength/weather
decks
(2) Cargo decks
(3) Accommodation
decks
(4) In way of the crown
or bottom of a tank
As (1), (2) or (3) as applicable, or
Z =
0,0113ρ s k h4 le
2
γ
whichever is the greater
The lesser of the following:
(a) Z = (K1 K2 T D + K3 B1 s h1 le
2) k x 10–4
(b) Z = 2K3 B1 s k h1 le
2 x 10–4
Z = (400K1 T D + 38,8s h2 le
2) k x 10–4
Z = (530K1 T D + 38,8s h3 le
2) k x 10–4
––
––
––
I =
2,3
leZ
k
NOTES
1. Where weather decks are intended to carry deck cargo and the load is in excess of
8,5 kN/m2 (0,865 tonne-f/m2), the scantlings of beams may be required to be increased
to comply with the requirements for location (2) using the equivalent design head, for
specified cargo loading, for weather decks given in Table 3.5.1 in Pt 3, Ch 3.
2. The web depth of beams, dw, is to be not less than 60 mm.
in metres,
see Pt 3,
Ch 3,5}
49. Ship Design & Project
Page 39
Table 5.1.6 Deck girders, transverses and hatch beams
Location and arrangements Modulus, in cm3 Inertia, in cm4
(1) Girders and transverses in way of dry cargo spaces and
clear of hatch openings:
(a) supporting up to three point loads
(b) supporting four or more point loads or a uniformly
distributed load
(2) Hatch side girders in way of dry cargo spaces at
weather decks (with deep coamings):
(a) supporting up to three point loads
(b) supporting four or more point loads or a uniformly
distributed load
(3) Hatch side girders in way of dry cargo spaces at lower
decks (without deep coamings):
(a) supporting up to three point loads
(b) supporting four or more point loads or a uniformly
distributed load
(4) Hatch end beams in way of dry cargo spaces and
supported at centreline, see Fig. 1.4.1:
(a)
(b)
(c)
(d)
In association with longitudinal framing when there
is no transverse between the hatch end beam and
adjacent transverse bulkhead or equivalent
supporting structure
In association with longitudinal framing where there
is one or more transverse between the hatch end
beam and adjacent transverse bulkhead or equiva-
lent supporting structure
In association with transverse framing when the
hatch end beam supports the hatch side girder and
in line girder only
In association with transverse framing when the
hatch end beam supports the hatch side girder, an
in line girder and an additional girder between the
hatch side and the centreline
(5) Girders and transverses in way of the crown or bottom
of a tank
See also Note
Z to be determined from calculations using Note
and stress
123,5
N/mm2
(12,6
kgf/mm2
)and
kk
assuming fixed ends
Z = 4,75k S Hg le
2
Z to be determined from calculations using Note
and stress
100,4
N/mm2
(10,25
kgf/mm2
)and
kk
assuming fixed ends
Z = 5,85k S1 Hg le
2
Z to be determined from calculations using stress
112,5
N/mm2
(11,5
kgf/mm2
)kk
Z = 5,20k S1 Hg le
2
Z = 19k K1 Hg le S1 l1 + 2,37k SeHg le
2
Z = 19k K1 Hg le (S1 l1 + S2 l2)
Z = 19k K1 Hg le (S1 l1 + S3 l3)
Z = 19k Hg le (K1 (S1 l1 + S4 l4) + K2 S5 l5)
Z = 11,7ρ k h4 S le
2
Symbols
S, le, k, ρ as defined in 1.5.1
h4 = tank head, in metres, as defined in Pt 3, Ch 3,5
l1, l2, l3, l4, l5, in metres, as indicated in Fig. 1.4.1
Bh = breadth of hatchway, in metres, as used to determine K1
Hg = weather head h1, or cargo head h2, or accommodation
head h3, in metres, as defined in Pt 3, Ch 3,5,
whichever is applicable
K1, K2 = factors, dependent on the girder arrangements, as
follows:
Bh
or
X
K1 or K22le le
0,2 0,143
0,3 0,177
0,4 0,191
0,5 0,187
0,6 0,179
0,7 0,169
0,8 0,141
0,9 0,085
1,0 0,000
Se,S1,S2,S3,S4,S5, in metres as indicated in Fig. 1.4.1
X = distance, in metres, from centreline of ship to an
additional girder, if fitted, as shown in Fig. 1.4.1, as used
to determine K2
I =
1,85
leZ
k
I =
1,85
leZ
k
I =
2,8
leZ
k
I =
2,8
leZ
k
I =
2,3
leZ
k
51. 5.1.6 Bar and Plate Keels
A = 1.8 L -16 cm2
= (1.8× 132 -16) cm2
= 221.6 cm2
T = 0.6L + 8 mm= 87 mm
B = 70B = 70 × 22.3 mm = 1561 mm
T = t1 +2 = 87+ 2 =89 mm
Table 5.7: Bar and Plate Keels
Ship Design & Project
Page 41
Item and parameter Requirement
(1) Bar keels:
Cross-sectional
area
Thickness
(2) Plate keels:
Breadth
Thickness
A = (1,8L – 16) cm2
t = (0,6L + 8) mm
b = 70B mm
but need not exceed 1800 mm
and is not to be less than
750 mm
t = (t1 + 2) mm
where t1 is as in location (1) in
Table 1.5.2, using the spacing
in way of the keel plate t is to
be taken not less than the
adjacent bottom shell
thickness
Symbols
L, B as defined in 1.5.1
b = breadth of keel, in mm
t = thickness of keel, in mm
A = cross-sectional area, in cm2
52. 5.1.7 Bottom Shell and Bilge Plating
= 9.51
HT2 = 1.2T =9.9 Fb = 0.67
Table 5.8 Bottom Shell and Bilge Plating
Ship Design & Project
Page 42
The greater of the following:
(a) t = 0,001s1f1 (0,056L1 + 16,7)
(see Note 4)
(b) t = 0,0063s1
hT2k
1,8 – FB
t as for (1)
FB
kL
Provided that transverses or adequate bilge brackets are spaced not more than
8t2 t
x 106 mm apart
DRB
t =
RBFB
RB
but is to be not less than the adjacent bottom plating
165kL
Minimum thickness, in mm, see also 5.3.1
Longitudinal framing Transverse framing
The greater of the following:
(a) t = 0,001s1 (0,043L1 + 10) (see Note 4)
(b) t = 0,0052s1
hT2k
1,8 – FB
t as for (1)
FB
kL
Location
Symbols
L, D, T, s, S, kL, k as defined in 1.5.1
Cw is as defined in 1.5.1. Where L > 227 m, Cw is not to be
taken less than 6,446 m
f1 =
hT2 = (T + 0,5 Cw), in metres but need not be taken greater
than 1,2T m
s1 = s, but is not to be taken less than the smaller of
+
0,6
470470 +
FB = as defined in Pt 3, Ch 4,5.7
L1 = L but need not be taken greater than 190 m
RB = bilge radius, in mm, see Note 3
L
1
1 +
s 2
(1000S)
NOTES
1. The thickness derived in accordance with (1) is also to satisfy the buckling requirements of Pt 3, Ch 4,7.
2. The thickness of bottom shell or bilge plating is to be not less than the basic shell end thickness for taper as given in Pt 3, Ch 5,3 and
Ch 6,3.
3. Where longitudinally framed and the lowest side longitudinal lies a distance a mm above the uppermost turn of bilge and/or the outer-
most bottom longitudinal lies a distance b inboard of the lower turn of bilge, the bilge radius is to be taken as RB + mm.
In no case is a or b to be greater than s.
4. Where separate maximum sagging and hogging still water bending moments are assigned, FB may be based on the hogging moment.
(a + b)
2
(1) Bottom plating,
see Notes 1 and 2
(3) Bilge plating – where
unframed, see Note 3
(2) Bilge plating – where
framed, see Notes 1 and 2
(b) t = 0,0052s1
hT2k
1,8 – FB
53. 5.1.8 Side shell Plating
Table 5.9: Side shell Plating
Ship Design & Project
Page 43
Thickness, in mm, see also 5.4.1
Transverse framingLongitudinal framing
Location
The greater of the following:
(i) t = 0,001s1 (0,059L1 + 7)
(ii) t = 0,00083s1 Lk + 2,5
but t is to be not less than the thickness of the
adjacent side plating
FD
kL
The greater of the following:
(i) t = 0,001s1 f1 (0,083L1 + 10)
(ii) t = 0,001s1 Lk + 2,5
but t is to be not less than the thickness of the
adjacent side plating
FD
kL
(c) Within from base (excluding bilge plating),
see Note 3:
The greater of the following:
(i) t = 0,00085s1 f1 (0,083L1 + 10)
(ii) t = 0,0056s1
hT2 k
1,8 – FB
FB
kL
D
4
from base:(c) Between upper turn of bilge and
The greater of the following:
(i) t from (b)(i)
(ii) t from interpolation between (a)(ii) and
(b)(ii)
D
2
(1) Side shell clear of sheerstrake,
see Notes 1, 2, 4 and 5
(2) Sheerstrake,
see Notes 1, 2 and 5
Symbols
L, D, T, S, s, kL, k, as defined in 1.5.1
Cw is as defined in 1.5.1. Where L > 227 m, Cw is not to be taken
less than 6,446 m
f1 =
hT1 = T + Cw m but need not be taken greater than 1,36T
hT2 = T + 0,5Cw m but need not be taken greater than 1,2T
s1 = s, but is not to be taken less than the smaller of
470 +470 + mm or 7
FD, FB = as defined in Pt 3, Ch 4,5.7
FM = the greater of FD or FB
L1 = L, but need not be taken greater than 190 m
L
0,6
1
1 +
s 2
(1000S)
NOTES
1. The thickness is also to satisfy the buckling requirements of Pt 3,
Ch 4,5.6.
2. The thickness of side shell or sheerstrake is to be not less than
the basic shell end thickness for taper, as given in Pt 3, Ch 5,3
and Ch 6,3. The width of the sheerstrake (where of different
thickness from the side shell) is to be not less than that required
by Table 2.2.1 in Pt 3, Ch 2.
3.
4.
The thickness of side shell need not exceed that determined from
Table 1.5.2 for bottom shell, but using the spacing of side frames
or longitudinals.
Outside the Rule minimum region of higher tensile steel as
defined in Pt 3, Ch 3,2.6.1 the value of kL may be taken as 1,0.
5. For the expressions contained in (i), where separate maximum
sagging and hogging still water bending moments are assigned,
FD may be based on the sagging moment and FB on the hogging
moment.
(a) Above
2
from base:
The greater of the following:
(i) t = 0,001s1 (0,059L1 + 7)
(ii) t = 0,0042s1 hT1 k
D
FD
kL
(a) Within from the gunwale:
The greater of the following:
(i) t = 0,00085s1 f1 (0,083L1 + 10)
(ii) t = 0,0042s1 hT1 k
D
4
FD
kL
(b) At upper turn of bilge, see Note 3:
The greater of the following:
(i) t = 0,001s1 (0,059L1 + 7)
(ii) t = 0,0054s1
hT2 k
2 – FB
FB
kL
(b) Withinhi om mid-depth:
The greater of the following:
(i) t = 0,001s1 (0,059L1 + 7)
(ii) t = 0,0051s1 hT1 k
D
t
4
FM
kL