project 5 - notes

Universiti Teknologi MalaysiaUniversiti Teknologi Malaysia

Faculty of Mechanical EngineeringDepartment of Marine Technology

STRUCTURAL DESIGNAND STRENGTH ASSESSMENT

Prepared By

HJ. YAHYA BIN [email protected]

Department of Marine TechnologyFaculty of Mechanical Engineering

Universiti Teknologi Malaysia81310, UTM SkudaiJohor Bahru, JOHOR

July 2005

Structural Design and Strength Assessment Note - 1/16

SHIP STRUCTURES DESIGN

Department of Marine Technology, FKM, UTM, 2005

3.0 Introduction

Structural design is an important design task andone of the most difficult parts in ship design thatoften required deep understanding and vastexperience. It requires good knowledge on shipstructures and often involves a lot and tediouscalculation, initial estimation (guestimate) with littleinformation, judgement and critical decision making.Whilst strength is the most important aspect instructural design which is not to be compromised atany time, it is also important to consider the weightand function of the ship so that the ship can beoperated in cost effective manner. Therefore it isessential that the designer have a good exposure andhad gone through structural design exercise beforeembarking on serious design project.

4.0 Aim of the Note

This note is written to facilitate the participants witha brief guideline on how ship structures should bedesigned based on the Lloyds Register Rules andRegulations. The details can be referred to the rulesand the participant will be given a copy of theselected part of the rule during the hands on project.

1.0 Structural Design Process

The ship structure is design upon completion of linesplan and general arrangement design as indicated inFigure 1. Structural design is also an essential part ofproduction process as it provides important data formaterial ordering and costing. In general practice, themidship scantling of the ship is to be designed firstand the rests / detailing of the structures will bederived from it. Midship scantling is also important todetermine the overall strength of the ship, whichneed to be known at the early of design stage. Thedesign process may differ from one rule to another,but generally it involves determination of ruledimensions, material selection, framing systems,determination of plating thickness and stiffener /frames sizes, midship scantling drawing and strengthassessment.

2.0 Midship Scantling CalculationProcedures Using Lloyds Rules

The ship structures can be designed with threedifferent approach; From first principles (rationaldesign), using rules and regulation / standards, ormixed of both above. Design from first principles istedious and involves a large amount of man- hours. It


often done for novel or military vessels. For Merchantships, the structural design is normally designedbased on rules and regulation developed byclassification societies. The conventional rules useformula that were based purely on empirical data ofprevious good designs and often are overly designed.The new approach, however, as in Lloyds Register,had incorporated first principles calculation in theformula especially in the strength assessment. Thiswill allow the designer to rationalize his/her design inorder to be more cost effective.

The midship scantling calculation procedures usingLloyds Register Rules is shown in Figure 2. Itbasically involves determination of rule dimensionsmeasured from lines plan drawing, selection ofmaterial properties, equipment number and designloading appropriate to the required location. Oncethese basic data have been determined (sameprocedure for all types of ships), the followingcalculation will be based on the specific type of shipbeing designed. As an example in Figure 2, thegeneral cargo is selected and the scantling designinvolves calculation of plating thickness for deck,shell envelope, scantling for deck and shell envelopestiffening members, bottom structures andbulkheads thickness and stiffeners sizes. Uponcompletion of midship scantling calculation, strength

assessment need to be carried out. In order to do thisaccurately, first the midship scantling need to bedrawn / sketched in scaled and all measurementmust be taken from this drawing. Then the overallsection modulus of the ship structures or hull girdercan be calculated using the standard procedures. TheHull bending strength and shear strength will bedetermined based on the hull girder section modulus.For local strength, the plate panel strengthassessment will be done using hull buckling strengthcriteria. The strength assessment procedure is shownin Figure 4.

Although the scantling formula used in Lloyds rulesmay differ form other rules, the basic concept andcalculation procedures in general, remain the same.Therefore it is expected that once the designer hasexperienced in one particular rule, he/she will beable to design in other rules without any difficulty.

5.0 Hands on Structural Design Project

The participants will be given a hands on structuraldesign task of a selected general cargo. The step bystep design procedure is given in Table 1. All thenecessary formula, calculation sheets, drawings anddiagrams will also be given during the hands onstructural design project.


SHIP STRUCTURES DESIGN


FIGURE 1: Structural Design Process

DESIGNREQUIREMENTS

MAINDIMENSIONS

HULL FORMDESIGN

HYDROSTATICSCALCULATION

GENERALARRANGEMENT

PRELIMINARYWEIGHT ESTIMATION

Preliminary Design

RULE DIMENSION

MATERIAL PROPERTIES

LOADING CALCULATION

PLATING THICKNESS

STIFENERS SCANTLING

SELECTION OF FRAMING SYSTEM

OTHER STRUCTURES SCANTLING

STRUCTURES SCANTLING LIST

MIDSHIP SCANTLINGDRAWING

STRENGTH ASSESSMENT

Strutural Design Process

NESTING

MATERIALTAKE OFF

SHELLEXPANSION

STRUCTURALDETAILING

MATERIALCOST

Production Design



FIGURE 2 : Midship Scantling Calculation Procedures – Lloyds Rules


RULE DIMENSIONS(Part 3, Chapter 1, Section 6.1- 6.8)

EQUIPMENT NUMBER(Part 3, Chapter 1, Section 7.1)

ALL SHIPS

MATERIAL PROPERTIES(Part 3, Chapter 2, Section 1.1- 2.1)

STRUCTURAL IDEALIZATION(Part 3, Chapter 3, Section 3.1- 3.3)

BULKHEAD REQUIREMENTS(Part 3, Chapter 3, Section 4.1- 4.4)

DESIGN LOADING(Part 3, Chapter 3, Section 5.1- 5.3)

GENERAL CARGO

SYMBOLS & DEFINITIONS(Part 4, Chapter 1, Section 1.5)

DECK PLATING(Part 4, Chapter 1, Section 4.2)

SHELL ENVELOPE PLATING(Part 4, Chapter 1, Section 5.1 – 5.4)

SHELL STIFFENING(Part 4, Chapter 1, Section 6.1 – 6.4)

DECK STIFFENING(Part 4, Chapter 1, Section 4.3 – 4.4)

BOTTOM STRUCTURES(Part 4, Chapter 1, Section 7.1 – 8.5)

BULKHEADS(Part 4, Chapter 1, Section 9.1 – 9.2)

STRENGTH

HULL BENDING STRENGTH(Part 3, Chapter 4, Section 5.1 –5.9

HULL SHEAR STRENGTH(Part 3, Chapter 4, Section 6.1 –6.7

HULL BUCKLING STRENGTH(Part 3, Chapter 4, Section 7.1 –7.5

MIDSHIPSCANTLING DRAWING

MIDSHIPSECTION MODULUS


STEP TASKS

1 Preparing Data and Drawings (Lines Plan, GA, Hydrostatics, Capacity Plan etc). A sketch (scaled)on Midship Frame Section is required based on Lines Plan and GA Drawing.

2 Preparation of Calculation Sheets – see examples in Table 2(a) and 2 (b).

FOR ALL TYPES OF SHIPS

3Based on the GA and Lines Plan Drawing Determine the Rules Dimension, L, B, D, T, CB etc. Alsodetermine the weather /strength /freeboard deck as required by (Part 3, Chapter 1, Section 6.1-6.8). Also calculate the Equipment Number based on (Part 3, Chapter 1, Section 7.1).

4Select material to be used. For high Tensile steel or Aluminum, determine the Material PropertiesFactors as in (Part 3, Chapter 2, Section 1.1- 2.1). These factors will be used throughout thescantling calculation.

5If Bulkheads Number and Location need to be checked, used (Part 3, Chapter 3, Section 4.1-4.4) to determine the minimum number of bulkheads, position of collision bulkhead and aft end bkhdarrangement. Transverse bkhds location need to be adjusted to the nearest frame location.

6Loading Calculation – Based on (Part 3, Chapter 3, Section 5.1- 5.3), Determine the appropriatedesign Load, design head, stowage factors etc for decks, tanks and bkhds. The design load must becalculated based on the position (height) of the structures in consideration.

TABLE 1 : Structural Design Project – Hands On

Department. of Marine Technology, FKM, UTM, 2005


STEP TASKS

FOR GENERAL CARGO

7 Determining the Basic Data for calculation as required in (Part 4, Chapter 1, Section 1.5).

8Selection of Framing Systems (Longitudinal or Transverse) and Frame Spacing. Stiffeners,Longitudinals, Stringers, etc spacing need also to be selected. No specific formula is given, thus itshould be determined based on shipyard standard practices.

9 Calculation of Deck Plating Thickness based on (Part 4, Chapter 1, Section 4.2).

10 Calculation of Shell Envelope Plating Thickness (Keel, Bottom & Bilge, and Side Shell)as requiredby (Part 4, Chapter 1, Section 5.1 – 5.4).

11Calculation of Deck Stiffening Section Modulus for Deck Longitudinals, Beams, and Girdersbased on (Part 4, Chapter 1, Section 4.3 – 4.4). The scantling of deck stiffening members should bedetermined based on Structural Idealization as specified in (Part 3, Chapter 3, Section 3.1- 3.3).

12

Calculation of Shell Envelope Stiffening Section Modulus for Logituidinals or Transverse, andPrimary Structures based on (Part 4, Chapter 1, Section 6.1 – 6.4). The scantling of shell envelopestiffening members should also be determined based on Structural Idealization as specified in(Part 3, Chapter 3, Section 3.1- 3.3).

Structural Design Project – Hands On



STEP TASKS

13Calculation of Bottom (Single or Double Bottom) Structures Plating Thickness and Stiffeningmembers Section Modulus as required by (Part 4, Chapter 1, Section 7.1 – 8.5). The calculationincludes Girders, Floors, and Inner Bottom Plating and Longitudinals.

14 Calculation of Bulkheads Platting Thickness and Stiffeners Section Modulus for watertightdeep tank bulkheads and Shaft Tunnel based on (Part 4, Chapter 1, Section 9.1 – 9.2).

STRENGTH ASSESSEMNT

15Preparation of Scantling List, which should at least includes Name, numbers, sizes (thickness andstiffeners scantling). See example in Table 3. This list will be used for strength calculation andmaterials take off.

16Preparation of Midship Scantling Drawing / sketches based on lines plan, GA and scantling list.The scantling drawing should be drawn in scale. Clearly label the structures name and size. Seeexample Figure 3.

17Calculation of Moment of Inertia and Section Modulus of the Hull Girders. Hull girder shouldconsists of all continuous longitudinal structures as specified in (Part 3, Chapter 3, Section 3.4). UseCalculation Tables as shown in the example in Table 4 and the formula given Table 5 & 6.




18

Determine the Hull Bending Strength by Calculation of Design Vertical Wave BM, Design StillWater BM, Minimum section Modulus, Permissible Still Water BM, Permissible HullVertical Bending Stress, Factors of reduction, and Minimum Moment of Inertia as requiredby (Part 3, Chapter 4, Section 5.1 – 5.9). Strength is to be determine by comparing the requiredminimum or permissible to the actual or design value.

19

Determine the Hull Shear Strength by calculating Design Wave SF, Design Still Water SF,Design Shear Stress, Permissible Still Water SF, Permissible Shear Stress as required by(Part 3, Chapter 4, Section 6.1 – 6.7). Strength is to be determine by comparing the permissible tothe design value

20Determine the Hull Buckling Strength (Local Strength) by calculating or checking the ElasticCritical Buckling Stress, Design Stress and comparing with Scantling Criteria as given by(Part 3, Chapter 4, Section 7.1 – 7.5).

21

Based on the Strength Assessment, Modification of Structural Scantling may be required eitherto increase the strength (in case of inadequate strength) or reducing strength (in case of excessivestrength / overly design). The modification can be in the form of adding/removing structures,changing plating thickness or/and changing section modulus for stiffening members. It isrecommended that once modification has been carried out, the strength Assessment need to becarried out once again.




LLOYDS SCANTLING CALCULATION : LOADING

NO ITEM (unit) SYMBOL FORMULA INPUT CALCULATIONRESULT DESIGN REF

1 General Loading - - - - - Pt.3, Ch.3 - 5.2.1(Table 3.5.1)

2 Weather Deck (Standard Cargo)2(a) Frd. - 0.075L from FP

Design Load for Beam/Long(KN/m^2)

p 12.73

Design Load for Prime Structure(KN/m^2)

p 29.64 + 14.41E

E = (0.0914 + 0.003L)/(D-T)-0.15

Pt.3, Ch.3 - 5.2.1(Table 3.5.1)

but must 0.0 ≤ E ≤ 0.147

Equivalent Design Head -Beam/Long(m) h1 1.8

Equivalent Design Head - PrimeStructures(m) h1 4.2 + 2.04E Pt.3, Ch.3 - 5.2.1

(Table 3.5.1)

Standard Stowage (m^3/tonnes) C 1.39Permissible Cargo Loading(KN/m^2) 8.5

Equivalent Permissible Head (m) 1.2

TABLE 2(a) : Example of Scantling Calculation Sheet



LLOYDS SCANTLING CALCULATION : BKHD NUMBER AND COLLISION BKHD


1 No of Bulkheads See Table 3.4.1 Pt.3, Ch.3 - 4.1.1(Table 3.4.1)

2 : Ship Without Extending Part of Underwater Body more than LL (Other Than Passenger Ships)

2(a) Collsion Bulkhead Ship <= 200 mDistance From Fore End of LL(m)

Pt.3, Ch.3 - 4.2.1(Table 3.4.2)

Minimum 0.05LL LL from Pt.3,Ch.1 -6.1.8

Maximum 0.08LL

2(b) Collsion Bulkhead Ship > 200 mDistance From Fore End of LL(m)

Pt.3, Ch.3 - 4.2.1(Table 3.4.2)

Minimum 10

Maximum 0.08LLLL from Pt.3,Ch.1 -6.1.8

TABLE 2(b): Example of Scantling Calculation Sheet



Size ZSTRUCTUREDESCRIPTION Thickness (mm) Web (mm)

No.(m From Keel)

Bottom Plate 6 - 0Inner Bottom Plate 6 - 2.8Deck Plate 8 - 10Side Plating 7 - 6.15Centre Girder 7.5 1 1.4Side Girder 6 1 1.4Long BKHD 6 1 6.4bilge Plating 8 - 1.15Margin Plate 6 - 2.55Deck Longi L - 6x20x20 4 9.8Side Longi -1 T - 6x15x15 8.3Side Longi -2 T- 6x15x15 6.3Side Longi -3 T- 6x15x15

34.3

Inner Botton Longi Bulb - 5x20x10 5 2.5Bottom Longi Top Hat - 5x10x10 2 0Bilge Longi -1 I – 6x15x15 0.43Bilge Longi -2 I – 6x15x15

21.15

TABLE 3: Example of Scantling List



4 m

SIDE GIRDERt = 6 mm

BOTTOM LONGL

A = 12 cm2

BILGE LONGL

A = 10 cm2

BOTTOM PLATEt = 10 mm

BILGE PLATEt = 10 mm

INNER BOTTOM LONGL

A = 12 cm2

INNER BOTTOM PLATEt = 6 mm

BILGE PLATEt = 6 mm

SIDE PLATEt = 7 mm

LONG BKHD PLATEt = 6 mm

DECK PLATEt = 8 mm

SIDE LONGL

A = 12 cm2

CENTREGIRDERt = 6 mm

DECK LONGL

A = 12 cm2

8 m

1.5 m 1.75 m 1.5 m 1.5 m

1.5m

2.0m

2.0m

2.0m

2.3m

1 m 2.5 m 1.25 m 1.25 m

0.5 m1 m 1 m1 m2 m

2.8 m

2.5m

FIGURE 3: Example of Midship Scantling Drawing



L t Z A 1st Mmt 2nd Mmt Io Angle hNO STRUCTURE

DESCRIPTION (m) (mm) (m From Keel) (m.mm) (m2.mm) (m3.mm) (m3.mm)Type

(deg) (m)1 Bottom Plate 4 6 0 24 0 0 0 HP

2 Inner Bottom Plate 5.5 6 2.8 33 92.4 258.72 0 HP

3 Deck Plate 4 8 10 32 320 3200 0 HP

Side Plating 7.7 7 6.15 53.9 331.485 2038.63275 266.311 VP

4 Centre Girder 2.8 7.5 1.4 21 29.4 41.16 13.72 VP

5 Side Girder 2.8 6 1.4 16.8 23.52 32.928 10.976 VP

6 Long BKHD 7.2 6 6.4 43.2 276.48 1769.472 186.624 VP

7 bilge Plating 4.61 8 1.15 36.88 42.41 48.77 16.33 IP 30 1.15

8 Margin Plate 2.54 6 2.55 15.24 38.84 99.01 0.31 IP 11.3 0.25

9Deck Longi x 4(4x10/10) 9.8 4 39.20 384.16 0 Sec

10Side Longi -1(1x12/10) 8.3 1.2 9.96 82.67 0 Sec

11 Side Longi -2 6.3 1.2 7.56 47.63 0 Sec

12 Side Longi -3 4.3 1.2 5.16 22.19 0 Sec

13 Inner Botton Longi x 5 2.5 4 10.00 25.00 0 Sec

14 Bottom Longi x 2 0 2.4 0.00 0.00 0 Sec

15 Bilge Longi -1 0.43 1 0.43 0.18 0 Sec

16 Bilge Longi -2 1.15 1 1.15 1.32 0 Sec

292.02 1228.00 8051.85 494.28

∑∑ A ∑∑1st Mmt ∑∑2nd. Mmt ∑∑ Io

TABLE 4: Example of Section ModulusCalculation



Actual Section Modulus

FORMULA ITEM VALUE UNIT VALUE UNIT

(a) ∑∑ A Total Area = 292.02 m.mm

(b) ∑∑1st Mmt Total 1st. Moment = 1228.00 m2.mm

( c) (b)/(a) Dist of NA from Keel = 4.21 m

(d) ∑∑2nd. Mmt Total 2nd. Moment = 8051.85 m3.mm 80518.49 m2.cm2

(e) ∑∑ Io Total Io = 494.28 m3.mm 4942.78 m2.cm2

(f) (d) + (e) Total I about Keel = 85461.27 m2.cm2

(g) (f) – (a)*(c)2 Total I about NA = 80297.28 m2.cm2

(h) Measure Height of Deck = 10.00 m

(i) (h) – ( c) or (c )whichever greater

Max y (ydeck or Ykeel) = 5.79 or 4.21 5.79 m

(j) (g) / (i) Section Modulus (Half) = 13856.78 m2.cm2

(k) (j) x 2 Section Modulus (Full) = 27713.5562 m2.cm2

Required Section Modulus (Lloyds Rules)

SM required = 10422.272 m2.cm2 Calculated based on emphirical Formula

SF = SM actual / SM required = 2.66 Acceptable but overly designed

TABLE 5 : Example of Section Modulus Calculation



TYPE 1 : Vertical PlateData Required and Calculation Diagram

L = Length (m)t = Thickness (mm)Z = Distance of Centroid from keel (m)A = Area = L x t (m.mm)1st. Moment = A x Z (m2.mm)2nd. Moment = A x Z2 or 1st Moment x Z (m3.mm)Io = Inertia Moment = L3 x t (m3.mm)

TYPE 2 : Horizontal PlateData Required and Calculation Diagram

L = Length (m)t = Thickness (mm)Z = Distance of Centroid from keel (m)A = Area = L x t (m.mm)1st. Moment = A x Z (m2.mm)2nd. Moment = A x Z2 or 1st Moment x Z(m3.mm)Io = Inertia Moment = 0 (Negligible)

TYPE 3 : Inclined PlateData Required and Calculation Diagram

L = Length (m)t = Thickness (mm)h = Distance of Centroid to base = L/2 x Sin(θθ )Z = Distance of Centroid from keel (m)A = Area = L x t (m.mm)1st. Moment = A x Z (m2.mm)2nd. Moment = A x Z2 or 1st Moment x Z(m3.mm)Io = [A x (2xh)2 ] / 12 (m3.mm)

TYPE 4 : SectionsData Required and Calculation Diagram

A = Area (m.mm) = Area (cm2/100) = Area (mm2/1000)Z = Distance of Centroid from keel (m)1st. Moment = A x Z (m2.mm)2nd. Moment = A x Z2 or 1st Moment x Z(m3.mm)Io = 0 (Negligable)Sections can be grouped together provided theyhave the same centroid position (Z)

L

t

Z From Keel

L

t

Z From Keel

L

t

Z From Keel

hθθ

Z From Keel

TABLE 6: Formula for Midship Section Modulus



FIGURE 4: Strength Assessment Procedure

HULL BUCKLING STRENGTH

Scantling

MIDSHIP SCANTLINGDRAWING / SKETCHES

MIDSHIPSECTION MODULUS & INERTIA

DETERMINATION OFRULE DIMENSION

ASSUMING INITIAL DESIGNVALUES & FACTORS

CALCULATION OF PLATES ANDSTIFFENERS SCANTLING

Overall Strength

HULL BENDING STRENGTH

Calculation of;f) Design Wave Bending Momentg) Design Still Water Bending Momenth) Minimum Hull Section Modulusi) Permissible Still Water BMj) Permissible Vertical BMk) Local Scantling Reduction Factors

ComparisonBetween Design and

Permissible

CHANGING INITIAL DESIGNVALUES & FACTORS

NO

ComparisonBetween Design

and Criteria

Local Strength

Calculation of;a) Critical Buckling For Plateb) Critical Buckling For Longic) Design Stressd) Scantling Criteria

HULL SHEAR STRENGTH

Calculation of;a) Design Wave Shear Forceb) Design Still Water Shear

Forcec) Design Shear Stressd) Permissible Still Water SF

NO

STOP

YES

Department. of Marine Technology, FKM, UTM, 2005

YES

YES

Department of Marine Technology, FKM, UTM. 2005

STRUCTURAL SCANTLING CALCULATION SHEETS(Based on LLOYDS Rules and Regulation 1997)

Important Note

The calculation sheets used in this short course were designed for the purpose ofdemonstrating the calculation procedures and examples of selected structures andfor a specific type of ship. Under no circumstances do they represent the completecalculation process provided in the rules. All formula shown in the calculationsheets should be checked with the formula given in rules.

Calculation Sheet – Rule Dimensions - 1

STRUCTURAL DESIGN CALCULATION SHEET – RULE DIMENSIONS & EQUIPMENT NUMBER

NO ITEM (unit) SYMBOL FORMULA INPUTCALCULATION

RESULT DESIGN REF

1 Length (m) L Pt.3,Ch.1 - 6.1.1

2 Breadth (m) B Pt.3,Ch.1 - 6.1.3

3 Depth (m) D Pt.3,Ch.1 - 6.1.4

4 Draught (m) T Pt.3,Ch.1 - 6.1.5

5 Block Coef Cb Pt.3,Ch.1 - 6.1.6

6 Length Bet PP (m) Lpp Pt.3,Ch.1 - 6.1.7

7 Length Load Line (m) LL Pt.3,Ch.1 - 6.1.8

8 Block Coef at LL Cbl Pt.3,Ch.1 - 6.1.9

9 Equipment Number EqNEqN = Disp^2/3 +2BH+A/10

Displacement (Tonnes) Disp

Freeboard Height (m) H

Area in Profile View(m2) A

A = L x (H + Hss)Hss = Height ofSuperStrctures

Pt.3,Ch.1 - 7.1.1


Calculation Sheet – Material Properties - 1

STRUCTURAL DESIGN CALCULATION SHEET – MATERIAL PROPERTIES


RESULT DESIGN REF

A : For Steel (Mild and High Tensile Steel)

1 Material Types - - Pt.3,Ch.2 - 1.1

2High Tensile SteelFactor For Hull GirderSM

KL

3 Specific Min Yield Stress SigmaO

Pt.3,Ch.2 - 1.2.2(Table 2.1.1)

4High Tensile SteelFactor For LocalStrength

Kk = 235/SigmaOor = 0.66 whiheverhigher

Pt.3,Ch.2 - 1.2.3

B : Aluminum Alloy

1 Aluminum Alloy Types - -

2 Yield Stress (N/mm^2) SigmaAPt.3,Ch.2 - 1.3(Table 2.1.2)

3 Thickness Equi Factor TeF (ka)^0.5*c

ka = 245/sigmaA

Factor c = 0.95 or 1.0

4 SM equi Factor SMeF ka*c

Pt.3,Ch.2 - 1.3.2


Calculation Sheet – Loading - 1

STRUCTURAL DESIGN CALCULATION SHEET – LOADING


RESULT DESIGN REF

1 General LoadingPt.3, Ch.3 - 5.2.1(Table 3.5.1)

2 : Weather Deck (Standard Cargo)Aft of 0.12L from FP (KN/m^2)

Design Load for Beam/Long p 8.5+ 14.41E

Design Load for PrimeStructure p 8.5+ 14.41E

E = (0.0914 +0.003L)/(D-T)-0.15but must0.0 <= E <= 0.147

Pt.3, Ch.3 - 5.2.1(Table 3.5.1)L, D & T refer toPt.3,Ch.1 - 6.1.5

Equi Design Head -Beam/Long(m) h1 1.2 + 2.04E

Equi Design Head - PrimeStruct(m) h1 1.2 + 2.04E

Pt.3, Ch.3 - 5.2.1(Table 3.5.1)

Standard Stowage(m^3/tonnes) C 1.39

Permissible Cargo Loading(KN/m^2)

8.5

2(c)

Equivalent Permissible Head(m) 1.2




RESULT DESIGN REF

4 : Cargo Deck

Standard Cargo LoadPt.3, Ch.3 - 5.2.1(Table 3.5.1)

Design Load for All Structures(KN/m^2) p

7.07HtdHtd (m) = CargoHead in Twee Deck

Pt.3, Ch.3 - 5.2.1(Figure 3.5.1)

Equi Design Head (m) - AllStructures h1 Htd

Standard Stowage (m^3/tonnes) C 1.39Permissible Cargo Loading(KN/m^2) 7.07Htd

4(a)

Equivalent Permissible Head (m) Htd

Mach Space, W/Syop and StoresPt.3, Ch.3 - 5.2.1(Table 3.5.1)

Design Load for All Structures(KN/m^2)

p 18.37

Equi Design Head (m) - AllStructures h1 2.6

4(c)

Standard Stowage (m^3/tonnes) C 1.39

Ship StoresPt.3, Ch.3 - 5.2.1(Table 3.5.1)

Design Load for All Structures(KN/m^2) p 14.14

Equi Design Head (m) - AllStructures h1 2

4(d)





RESULT DESIGN REF

5: Accommodation Deck

Accommodation DeckPt.3, Ch.3 - 5.2.1(Table 3.5.1)

Design Load for All Structures(KN/m^2) p 8.5

Equi Design Head (m) - AllStructures

h1h3 or 1.2 which ever

greaterPt.3, Ch.3 - 5.2.1(Figure 3.5.1)

5(a)


6 : Superstructure DeckPt.3, Ch.3 - 5.2.1(Table 3.5.1)

6(a)For F'castle deck Frd of 0.12 Lfrom FP See Weather Deck (2)

6(b) Equi Design Head (m) - S/s Deck h1 h3Pt.3, Ch.3 - 5.2.1(Figure 3.5.1)

6( c)Equi Design Head (m) - 1st TierBeams & Longl h1

0.9 (+ 0.24E ifexposed)

6(d)Equi Design Head (m) - 2nd TierBeams & Longl h1


6(d)Equi Design Head (m) - 3rd TierBeams & Longl h1





RESULTDESIGN REF

8 : Inner BottomPt.3, Ch.3 - 5.2.1(Table 3.5.1)

Ship Without Heavy Cargo Notation

Design Loading (KN/m^2) - Plate& Stiffeners p

Equi Design Head (m) - - Plate &Stiffeners

h1


Permissible Cargo Loading(KN/m^2) 9.82T

T refer toPt.3,Ch.1 - 6.1.5

8(a)

Equivalent Permissible Head (m) 1.39T

Watertight Bulkhead

Design Loading (KN/m^2) - Plate& Stiffeners p 10.07h4

Pt.3, Ch.3 - 5.2.1(Figure 3.5.2)

Equi Design Head (m) - - Plate &Stiffeners

h1h4 = Appropriate

Design Head

8(c)



Calculation Sheet – Bkhd No & Collision Bkhd - 1

STRUCTURAL DESIGN CALCULATION SHEET – BKHD NO & POSITION OF COLLISON BKHD

NO ITEM (unit) SYMBOL FORMULA INPUT CALCULATIONRESULT

DESIGN REF

1 No of Bulkheads See Table 3.4.1Pt.3, Ch.3 - 4.1.1(Table 3.4.1)

2 : Ship Without Extending Part of Underwater Body more than LL (Other Than Passenger Ship)

2(a) Collision Bulkhead Ship <= 200 m

Distance From Fore Endof LL (m)

Pt.3, Ch.3 - 4.2.1(Table 3.4.2)

Minimum 0.05LL

Maximum 0.08LL

LL from Pt.3,Ch.1 -6.1.8

2(b) Collision Bulkhead Ship > 200 m

Distance From Fore Endof LL (m)

Pt.3, Ch.3 - 4.2.1(Table 3.4.2)

Minimum 10

Maximum 0.08LL

LL from Pt.3,Ch.1 -6.1.8


Calculation Sheet – Deck Plating - 1

STRUCTURAL DESIGN CALCULATION SHEET – DECK PLATING

ITEM (unit) SYMBOL FORMULA INPUT CALCULATIONRESULT

DESIGN REF

1 : Basic Input Data

1Higher Tensile StrengthFactor - For Hull Girder kL

Higher Tensile StrengthFactor - For LocalStrength

k

Pt.3,Ch.2 - 1.2.2(Table 2.1.1)

Spacing for SecondaryStiffeners (mm)

s

Spacing for PrimaryMembers (m) S

Wave Head (m) CW 7.71x10^-2 x Lx e^(-0.0044L)

Relative Density Rho not to lee than 1.025

Pt.4, Ch.1 - 1.5


Calculation Sheet – Deck Plating - 2


DESIGN REF

2 : Strength / Weather Deck Plating (Longitudinal Framing)

2(a) Outside Line of Opening

Thickness (mm) tt = 0.001 x s1 x(0.059L1+7) xSQRT(FD/KL) OR

Pt.4, Ch.1 - 4.2.1(Table 1.4.1)

t = 0.00083 x s1 xsqrt(LK)+2.5Which ever GreaterFD = Scant ReductionFactor Pt.3, Ch.4 - 5.7.2

s1 = s but bot to lessthan 470+L/0.6 or700 whichever LowerL1 = L but<=190

2(b) Inside Line of Opening

Thickness (mm) tt = 0.00083 x s1 xsqrt(LK)+2.5

But not less than 6.5s1 = s but bot to lessthan

470+L/0.6 or

700 whichever Lower

Pt.4, Ch.1 - 4.2.1(Table 1.4.1)


Calculation Sheet – Shell Plating - 1

STRUCTURAL DESIGN CALCULATION SHEET – SHELL ENVELOPE PLATING


DESIGN REF

1 : Basic Input Data and Preliminary Calculation

Basic Input Data

Higher Tensile StrengthFactor - For Hull Girder

kLPt.3,Ch.2 - 1.2.2(Table 2.1.1)


k

Spacing for SecondaryStiffeners (mm) s Pt.4, Ch.1 - 1.5

Spacing for PrimaryMembers (m) S

Wave Head CW7.71x10^-2xLxe^(-0.0044L)

Scantling ReductionFactor above Neutral Axis

FD Pt.3, Ch.4 - 5.7.2

1(a)

Scantling ReductionFactor below Neutral Axis FB


Calculation Sheet – Shell Plating - 2


DESIGN REF

f1f1 =1/(1+(s/1000S)^2)

hT2 hT2 = (T+0.5CW)

But hT2 <= 1.2T

s1s1 = s but not lessthan

470+L/0.6 or

700mm Whicheverless

L1 L1 = L but <= 190

RB Bilge Radius (mm)

Pt.4, Ch.1 - 5.3.1(Table 1.5.2)

hT1 hT1 = (T+CW)

But hT1 <= 3.6T

1(b) Preliminary Calculation

FMFM the greater betFD and FB

Pt.4, Ch.1 - 5.4.1(Table 1.5.3)

Calculation Sheet – Deck Stiffening - 1

STRUCTURAL DESIGN CALCULATION SHEET – DECK STIFFENING


RESULT DESIGN REF

Basic Input DataMaterial Factor - For HullGirder kL

Material Factor - ForLocal Strength

k

Pt.3,Ch.2 - 1.2.2(Table 2.1.1)

Spacing for SecondaryStiffeners (mm) s

1

Relative Density(Tonnes/m^3) Rho not to lee than 1.025

Pt.4, Ch.1 - 1.5

2 : Strength / Weather Deck LongitudinalsOutside Line of Opening

Section Modulus (cm^3) ZZ=0.043xsxkxhT1xle^2xF1

Pt.4, Ch.1 - 4.3.1(Table 1.4.3)

hT1 = L1/56 fo B-60ShiphT1 = L1/70 for B Shipor 1.2 whicever greaterL1 = L but <= 190le = span length >= 1.5 Pt.3, Ch.3 - 3F1 = 0.25C1C1 = 60/(225-165FD)

2(a)

FD = Scant ReductionFactor Pt.3, Ch.4 - 5.7.2


Calculation Sheet – Deck Stiffening - 2


RESULT DESIGN REF

4 : Deck Beams for Strength/weather, Cargo and Accomodation DeckStrength / Weather Decks

Section Modulus (cm^3) ZZ =(K1K2TD+K3B1sh1le^2)k/10^4 or

Pt.4, Ch.1 - 4.3.5(Table 1.4.5)

Z = 2K3B1skh1le^2/10^4K1 = Factor based onDeck No1 Deck = 202 Decks = 13.33 Decks = 10.54 decks or more = 9.3K2 = Factor based onLocationBridge & Poop = 133Elsewhere = 530K3 = Factor based onBeamAdjacent to Ship Side =3.6Elsewhere = 3.3B1 = B but <= 21.5

h1 = Weather HeadPt.3, Ch.3 - 5.2.1(Figure 3.5.2)

4(a)

le = span length >= 1.8 Pt.3, Ch.3 - 3


Calculation Sheet - Stiffener Section Modulus - 1


FACEPLATE

WEB PLATE

BASE (ATTACHED) PLATE

bf

tf

twdw

tp

b

SECTION IDEALIZATION FOR CALCULATION OF SECTION MODULUS

Calculation Sheet - Stiffener Section Modulus - 2

STRUCTURAL DESIGN CALCULATION SHEET – LONG/FRAME/STIFFENER SECTION MODULUS


RESULT DESIGN REF

1 Face Plate Area (cm^2) a bf*tf/100

bf (mm) = Flange Width

tf (mm) = Flange Thickness

2 Web Depth (mm) dw

3 Web Thickness (mm) tw

See Figure Above

4 Base Plate Area (cm^2) A 10*f*b*tpPt.3, Ch.3- 3.2.7

f = 0.3*(l/b)^(2/3) But <= 1.0Pt.3, Ch.3- 3.2.1 (Table3.3.1)

l (m) = (Dist of Primarysupport) Pt.3, Ch.3 - 3.2.1

b (m) = (Stiff Spacing)Pt.3, Ch.3- 3.2.1 (Fig3.3.2)

(l/b) = Ratio

tp (mm) = Base PlateThickness

Pt.3, Ch.3 - 3.2.1

5Section Modulus BuiltSection (cm^3) Z

a*dw/10 + tw*dw^2/6000 +(1+(200*(A-a)) /(200*A+tw*dw))

Pt.3, Ch.3 - 3.2.6

6Moment of Inertia aboutBase With AttachedPlating (cm^4)

Ia[bf*tf*(tf/2+dw+tp)^2 +(tw*dw^3)/12 + tw*dw*(dw/2+tp)^2] /10^4

Required in Pt.3,Ch.4 - 7.3 (Table3.3.1)


Calculation Sheet – Hull Girder Section Modulus - 1

STRUCTURAL DESIGN CALCULATION SHEET – HULL GIRDER SECTION MODULUS

L t Z A 1st Mmt 2nd Mmt Io Angle hNO STRUCTURE

DESCRIPTION (m) (mm) (m From Keel) (m.mm) (m2.mm) (m3.mm) (m3.mm)Type

(deg) (m)

∑∑ A ∑∑1st Mmt ∑∑2nd. Mmt ∑∑ Io


Calculation Sheet – Hull Girder Section Modulus - 2

Actual/Design Section Modulus

FORMULA ITEM VALUE UNIT VALUE UNIT

(a) ∑∑ A Total Area = m.mm

(b) ∑∑1st Mmt Total 1st. Moment = m2.mm

( c) (b)/(a) Dist of NA from Keel = m

(d) ∑∑2nd. Mmt Total 2nd. Moment = m3.mm m2.cm2

(e) ∑∑Io Total Io = m3.mm m2.cm2

(f) (d) + (e) Total I about Keel = m3.mm

(g) (f) – (a)*(c)2 Total I about NA = m3.mm

(h) Measure Height of Deck = m

(i) (h) – ( c) or (c )whichever greater

Max y (ydeck or Ykeel) = or m

(j) (g) / (i) Section Modulus (Half) = m2.mm

(k) (j) x 2 Section Modulus (Full) = m2.mm

Required Section Modulus (Lloyds Rules)

SM required = m2.mm

SF = SM actual / SM required =


Calculation Sheet – Hull Bending Strength - 1

STRUCTURAL DESIGN CALCULATION SHEET – HULL BENDING STRENGTH


1 Basic Input Data Pt.3,Ch.4 - 5.1.1Higher Tensile Strength Factor -For Hull Girder kL

Pt.3,Ch.2 - 1.2.2(Table 2.1.1)

Higher Tensile Strength Factor -For Local Strength k

Ship Service Factor f1 f1 >= 0.5

f1 =1.0 forUnrestricted Sea-going

Wave Bending Moment Factor f2f2 = -1.1 for saging (-ve) Moment

f2 = 1.9Cb/(Cb+0.7)for Hogging

Pt.3,Ch.4 - 5.1.1

2 : Design Value

2(a) Design of Vertical Wave BM

Mw for restricted (KN-m)Mw(sagging)

Mw = f1f2Mwo Pt.3,Ch.4 - 5.2.1

Mw(Hogging)

Mw = f1f2Mwo

Mwo (Kn-m)

Mwo =0.1C1C2L^2B(Cb+0.7)

Yahya Samian, Dept. of Marine Technology, FKM, UTM. 2005


C1 for L <90 C1 = 0.0412L +4

C1 for L90-300

C1 = 10.75-((300-L)/100)^1.5

C1 for300<L<=350

C1 = 10.75

C1 for350<L<=500

C1 = 10.75-((L-350)/150)^1.5

Pt.3,Ch.4 - 5.2.1(Table 4.5.1)

C2 forMidship C2 = 1.0 Pt.3,Ch.4 - 5.2.2

Mw for Sheltered Water (KN-m)Mw(sagging) Mw = 0.5f2Mwo

Mw(hogging) Mw = 0.5f2Mwo

Mw for short Voyage (KN-m)Mw(sagging)

Mw = 0.8f2Mwo

Mw(hogging) Mw = 0.8f2Mwo

Pt.3,Ch.4 - 5.2.2 -5.2.4




2(b) Design Still Water BM

Accurate (KN-m) MsCalculate Directly fromLoading

Still Water BMCalculation

Approximate (KN-m) MsMs = Cs L^2.5B(Cb +0.5)*9.81

Ship Design Book- Tanker

Cs =[0.618+(110 –L)/462]/100

for 61 <= L <=110 m

2( c) Design Section Modulus

SM at Deck (m^3) ZDDirectly CalculatedFrom Midship

SM at Base (m^3) ZBDirectly CalculatedFrom Midship

For Definition ofLong ContinuousSee Pt.3,Ch.3 -3.4




3 : Minimum or Permissible Value

3(a) Min Hull Section Modulus

Min Hull SM (m^3) ZminZmin =f1kLC1L^2B(Cb+0.7)/10^6

3(b) Permissible Still Water Bending Moment

Still Water BM (KN-m)Ms Bar(Sagging)

Ms Bar =FDxSigmaxZDx10^3 - MwMs Bar =FBxSigmaxZBx10^3 - MwWhicever Less

Ms Bar(Hogging)

Ms Bar =FDxSigmaxZDx10^3 - MwMs Bar =FBxSigmaxZBx10^3 – MwWhicever Less

FD (Start)

FB (Start)

Sigma(N/mm^2) Sigma = 175/kL

Pt.3,Ch.4 - 5.5 -5.6




Local Scantling ReductionVertical Bending Stress atDeck SigmaD

SigmaD =(Msbar +Mw)/ZD x 10^-3 Pt.3,Ch.4 - 5.7

Vertical Bending Stress atBase SigmaB

SigmaB =(Msbar +Mw)/ZB x 10^-4

Reduction Factor at Deck FD FD = SigmaD/sigma

3( c)

Reduction Factor at Base FB FB = SigmaB/sigma4 : Strength Assessment

Section Modulus Criteria COMPLIANCESection Modulud SafetyFactor

SF1 SF1 = ZD/Zmin or Acceptable4(a)

SF1 = ZB/Zmin whichever Less

Still Water BM criteria

Still Water BM Safety Factor SF2SF2 = Msbar/Ms(hogging) OR Acceptable

4(b)SF2 = Msbar/Ms(Sagging) ORWhichever Less

Reduction Factor CriteriaReduction Factor SF3 for plating SF3 = FD/0.67 or Aceptable

SF3 = FB/0.67whichever Less

SF3 forLongitudinals SF3 = FD/0.75 or Not Acceptable

4( c)

SF3 = FB/0.75Whichever Less

Use FB = 0.75 forLongitudinals


Calculation Sheet – Hull Buckling Strength - 1

STRUCTURAL DESIGN CALCULATION SHEET – HULL BUCKLING STRENGTH


RESULT DESIGN REF

Basic Input Data

Spacing for SecondaryStiffeners (mm) s

Spacing for PrimaryMembers (m)

SPt.4, Ch.1 - 1.5

Modulud of Elasticity(N/mm^2) E E = 206000 For Steel

Specified Min Yield Stress(N/mm^2) SigmaO SigmaO = 235

Specific Sheer Stress lamOlamO =sigmaO/sqrt(3)

Pt.3,Ch.4 - 7.2.1

Higher Tensile StrengthFactor - For Hull Girder kL

Pt.3,Ch.2 - 1.2.2(Table 2.1.1)

1


k




RESULT DESIGN REF

2 : Elastic Critical Buckling Stress For PlatingPlating With Longitudinal StiffenersOriginal Plate thickness(mm) t

Selected Plating /Stiffeners Pt.3,Ch.4 - 7.2.1

Standard Deduction forCorrosion (mm) dt

One side exposed -Vertical Plate (mm)

dt = 0.05t (Range 0.5 -1 mm)

One Side Exposed -Horizontal Plate (mm)

dt = 0.1t (Range 2 -3mm)

Two side exposed -Vertical Plate (mm)

dt = 0.1t (Range 2 -3mm)

Two Side Exposed -Horizontal Plate (mm)

dt = 0.15t (Range 2 - 4mm)

Pt.3,Ch.4 - 7.2.1(Table 4.7.1)

2(a)

Plate Thickness afterDeduction tp t - dt Pt.3,Ch.4 - 7.2.1

(i) Critical Buckling Stress(N/mm^2)

SigmaE SigmaE = 3.6E(tp/s)^2

(ii) Critical Shear Stress(N/mm^2) LamE

LamE = 3.6[1.335+(s/1000S)^2] x E(tp/s)^2

Pt.3,Ch.4 - 7.3.1(Table 4.7.2)

(iii) 50 % of SigmaO 1/2sigmaO (ii) exceed (iii)Correction Required(ia) Critical Buckling Stress SigmaCR sigmaCR = SigmaO x

(1 - sigmaO/4sigmaE)

(iia) Critical Shear Stress LamCRLamCR = LamO x(1 -LamO/4LamE)

Pt.3,Ch.4 - 7.3.1(Table 4.7.2)




RESULT DESIGN REF

3 : Elastic Critical Buckling Stress For Longitudinals

3(a) Section / Longitudinal Properties

Face Plate Area (cm^2) a a = bf*tf/100 See Figure Above Flange Width (mm) bfFlange Thickness afterDeduction (mm)

tf

Web Depth (mm) dwWeb Thickness (mm) twBase Plate Area (cm^2) A 10*f*b*tp Pt.3, Ch.3 - 3.2.7

FactorD ff = 0.3*(l/b)^(2/3) But<= 1.0

Pt.3, Ch.3 -3.2.1(Table 3.3.1)

Distance of PrimarySupport (m) l Pt.3, Ch.3 - 3.2.1

Stiffener Spacing (m) bPt.3, Ch.3 - 3.2.1(Fig 3.3.2)

Ratio (I/b) (l/b)Base Plate Thickness AfterDeduction (mm) tp Pt.3, Ch.3 - 3.2.1

Total Area (cm^2) At A + a + (tw*dw)/100

Section Modulus BuiltSection (cm^3)

Z

a*dw/10 +tw*dw^2/6000 +(1+(200*(A-a)) /(200*A+tw*dw))

Pt.3, Ch.3 - 3.2.6



Inertia Mmt includingBace Plate (cm^4) Ia

bftf(dw+tp)^2 +twdw^3/12 + twdw(dw/2 + tp) +b/4x(tp)^3

St Venant's Inertia Mmtfor Flat Bars (cm^4) It It = dwtw^3/3 x 10^-3

St Venant's Inertia Mmtfor Section (cm^4)

It = 1/3[dwtw^3+bftf^3 x (1 - 0.63tf /bf)] /10^4

Polar Inertia Mmt for FlatBar (cm^4) Ip Ip = dw^3tw/3 x 10^-4

Polar Inertia Mmt forSection (cm^4)

Ip =( dw^3tw/3 +dw^2bftf) /10^4

Sectorial Inertia Mmt FlatBar (cm^4) Iw

Iw = dw^3tw^3 /(36x10^6)

Sectorial Inertia Mmt TeeSection (cm^4)

Iw = tfbf^3dw^2 /(12x10^6)

Sectorial Inertia Mmt forOther (cm^4)

Iw = p x (q+r)/10^6

p = bf^3dw^2 /(12x(bf+dw)^2)q = tf (bf^2 +2bfdw+4dw^2)

r = 3twbfdw

Pt.3, Ch.4 - 7.3(Table 4.7.3)




RESULT DESIGN REF

3(b) Elastic Critical Buckling Stress

(i)Column Buckling Stress(N/mm^2) SigmaE

SigmaE = 0.001ExIa /(AtxS^2)

(ii)Torsional Buckling Stress(N/mm^2)

SigmaEsigmaE =0.001EIw(m^2+k/m^2)/(ipS^2) + 0.385EIt/Ip

(iii)Web Buckling Stress(N/mm^2)

SigmaESigmaE = 3.8E(tw/dw)^2

kk = 1.03CS^4 x 10^4 /EIw

Spring Stiffeness CC = kpEtp^3 / [3s(1+1.33kpdwtp^3)/ stw^3]

kp kp = 1-ypyp yp = sigmaA / SigmaEP

SigmaEPas critical buckling stressof plate

Pt.3, Ch.4 - 7.3(Table 4.7.3)

mto be selected fromTable 4.7.3

(iv) 50 % of SigmaO 1/2sigmaO(i), (ii) and (iii)exceeds (iv)



Correction Required

(ia)Critical Column BucklingStress (N/mm^2) SigmaCR

sigmaCR = SigmaO x(1 - sigmaO/4sigmaE)

(iia)CriticalTorsional BucklingStress (N/mm^2)

SigmaCRsigmaCR = SigmaO x(1 - sigmaO/4sigmaE)

(iiia)Critical Web BucklingStress (N/mm^2) SigmaCR

sigmaCR = SigmaO x(1 - sigmaO/4sigmaE)


RESULT DESIGN REF

4 : Design Stress

Longitudial CompressiveStress (N/mm^2)Minimum CompressiveStress

SigmaA SigmaA = 30/kL

Minimum CompressiveStress above NA SigmaA sigmaA = sigmaDxZ/ZD

Minimum CompressiveStress Below NA SigmaA sigmaA = sigmaBxZ/ZB

4(a)

Vertical Distance from NAto structure Z Measure from dwg

Shear StressInitial estimation DesignShear Stress LamA LamA = 110/kL

4(b)Accurate Design ShearStress LamA Based on Part 3, Ch 4, 6

Pt.3, Ch.4 - 7.4




RESULT DESIGN REF

5 : Strength Assessment

5(a) Scantling criteria for platePlate Buckling Factor Beta Beta = 1 Pt.3, Ch.4 - 7.5Design Buckling Stress SigmaR Beta x sigmaA COMPLIANCECritical Buckling Stress SigmaCR as in 2(a) - (ia)Safety Factor SF SigmaCR/sigmaRDesign Shear Stress LamA as in 4(b)Critical Buckling ShearStress LamCR as in 2(a) - (iia)

Safety Factor SF SF = LamCR/LamA

5(b)Scantling criteria forLongitudinal Pt.3, Ch.4 - 7.5

Longitudinal BucklingFactor Beta Beta = 1.1

Design Buckling Stress SigmaR Beta x sigmaACritical Column BucklingStress SigmaCR as in 3(b) - (ia)

Safety Factor SF SigmaCR/sigmaRCriticalTorsional BucklingStress SigmaCR as in 3(b) - (iia)

Safety Factor SF SigmaCR/sigmaRCritical Web BucklingStress

SigmaCR as in 3(b) - (iiia)

Safety Factor SF SigmaCR/sigmaR


NO ITEM (unit) SYMBOL FORMULA INPUT CALCULATION DESIGN REF


SHEET NO : OF :CALCULATED BY : DATE :

project 5 - notes

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