Guidance Notes for the Classiﬁcation of Special Service Craft

Guidance Notesfor theClassification ofSpecial Service Craft

Calculation Procedures forComposite ConstructionJuly 2014

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Chapter ContentsGUIDANCE NOTES FOR THE CLASSIFICATION OF SPECIAL SERVICE CRAFT, July 2014

Procedures Manual

LLOYD’S REGISTER 1

CALCULATION PROCEDURES FOR COMPOSITE CONSTRUCTION

Introduction

Chapter 1 Design Procedures

2 Design of Single Skin Hull Laminates

3 Design of Sandwich Panel Laminates

4 Design of Stiffening Members

© Lloyd's Register Group Limited, 2014. All rights reserved.

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ContentsGUIDANCE NOTES FOR THE CLASSIFICATION OF SPECIAL SERVICE CRAFT, July 2014

Procedures Manual


INTRODUCTION

Application of procedures

Alternative procedures

Symbols and definitions

CHAPTER 1 DESIGN PROCEDURES

Section 1 General

2 Structural analysis

3 Fibre composites

4 Fibre reinforced composite construction

5 Direct calculations

CHAPTER 2 DESIGN OF SINGLE SKIN HULL LAMINATES

Section 1 Calculation procedure

2 Concluding remarks

CHAPTER 3 DESIGN OF SANDWICH PANEL LAMINATES


2 Deflection of sandwich panel

3 Bending moment applied

4 Stresses in facings

CHAPTER 4 DESIGN OF STIFFENING MEMBERS


2 Bending moment at fixed end of stiffener

3 Web thickness to meet shear requirement

4 Calculation of deflection

Section

Application of procedures

Alternative procedures

Symbols and definitions

■ Application of procedures

To clarify the procedures contained in the Rules andRegulations for the Classification of Special Service Craft(hereinafter referred to as the Rules for Special Service Craft)a series of typical calculation procedures are contained inthese ‘Guidance Notes’. The procedures describe the funda-mental principles contained in Part 8 of the Rules for SpecialService Craft and the associated computer software.

The procedures contained in these Guidance Notes are for:(a) Design of single skin hull laminates.(b) Design of sandwich panel laminates.(c) Design of typical stiffening members.

■ Alternative procedures

The procedures describe the Rule method of calculating thevarious stresses in laminates. Where alternative theoreticalmethods are to be adopted they are to be in addition to theRule calculation procedures and the designer is to submit fulldetails of their assumptions and calculation procedures suchthat the submitted calculations may be validated.

■ Symbols and definitions

All symbols and definitions are as indicated in Pt 8, Ch 3 ofthe Rules for Special Service Craft.

GUIDANCE NOTES FOR THE CLASSIFICATION OF SPECIAL SERVICE CRAFT, July 2014

Introduction


Section

1 General

2 Structural analysis

3 Fibre composites

4 Fibre reinforced composite construction

5 Direct calculations

■ Section 1General

1.1 This Section outlines the Rule approach to thedesign of structural members to be built in FRP and providesexample calculations.

1.2 The procedures contained in these Guidance Notesare for:(a) Design of single skin hull laminates.(b) Design of sandwich panel laminates.(c) Design of typical stiffening members.

■ Section 2Structural analysis

2.1 The Rules for Special Service Craft provide scant-ling requirements for a basic structural configuration for bothmono and multi-hull craft with multi-deck or single deck hullswhich include a double bottom, or a single bottom arrange-ment. The structural configuration may also include a singleor multiple arrangement of cargo hatch openings. The Rulesfor Special Service Craft provide for both longitudinal andtransverse framing systems. Alternative types of framingsystems will be specially considered on the basis of the Rulesfor Special Service Craft.

2.2 Every effort has been taken to make the Rules forSpecial Service Craft scantling formulae as transparent aspossible, and to achieve this objective the following approachhas been adopted:• lay down requirements,• specify modelling considerations,• indicate limit states, • state constraints in an explicit manner.

2.3 This approach will enable the designers andBuilders to decide for themselves the suitability of the Rulesfor Special Service Craft for their project. Further and perhapsmore importantly changes may be easily made to the require-ments based upon experience gained, discussions withinterested parties and as development progresses. This issimilar to the current Rule development process which iscontinually updating and ‘tailoring’ Rule requirements.

■ Section 3Fibre composites

3.1 Part 8 of the Rules for Special Service Crafts applyto craft constructed of fibre reinforced plastics using hand lay-up, mechanical deposition, contact moulding techniques orvacuum assisted techniques. Construction may be eithersingle-skin or sandwich construction, or a combination ofboth. Where moulding techniques and methods of construc-tion differing from those assumed to be used within the Rulesfor Special Service Craft are proposed, details are required tobe submitted for consideration.

3.2 For the purposes of the Rules for Special ServiceCraft a ‘plastic’ is regarded as an organic substance whichmay be thermosetting or thermoplastic and which, in itsfinished state, may contain reinforcements or additives. Thequantities of such additives are strictly limited by the Rules forSpecial Service Craft.

3.3 The resins used in production are to be of a typewhich have been approved by Lloyd’s Register (hereinafterreferred to as LR) for marine construction purposes. Samplesof the resin batches being used in the construction mayrequire to be taken for limited quality control examinations.

3.4 All fibre reinforcements are to be of a type approvedby LR. The other materials used in the construction of thecraft are also to be manufactured and tested in accordancewith the requirements of the Rules for the Manufacture,Testing and Certification of Materials (hereinafter referred toas the Rules for Materials), of the Rules for Special ServiceCraft, with particular reference to Chapter 14 for plasticsmaterials.

■ Section 4Fibre reinforced composite construction

4.1 The properties of composite sections and laminatesare to be determined from the results of test data. Themechanical properties to be used for scantling calculationpurposes are to be 90 per cent of the mean first ply/resincracking failure values determined from accepted mechanical tests. All test pieces are to be representative ofthe product to be manufactured. This is particularly importantsince the material of construction is ‘manufactured’ on site,at the same time as the product.

4.2 The mechanical properties of the materials are alsoto be estimated from the appropriate procedures and formu-lae contained within the Rules for Special Service Craft. Theacceptable design values for glass reinforced polyester resinlaminates are not to be greater than those contained with theRules for Special Service Craft unless agreed otherwise byLR. Additional information on the application of the variousformulae is given in these Guidance Notes.


Design Procedures Chapter 1Sections 1 to 4


4.3 The various formulae referred to above require thatsufficient input data be available which relates to each of theproposed materials. Where it is proposed to use design valuesgreater than the nominal value indicated in the Rules forSpecial Service Craft the designers and/or Builders shouldagree the values for use in the scantling analysis with LR atthe design stage and prior to the submission of plans anddata for appraisal.

4.4 Strength calculations for all advanced fibrecomposites are to be based on the Rules values and theresults of testing of truly representative sections of theproposed design. The sections are to be manufactured undertypical production conditions using the same materials, fibrecontents, methods of lay-up and time delays. Mechanicaltesting is, in general, to be based upon the requirementsspecified in Chapter 14 of the Rules for Materials.

4.5 A through ply analysis is required to be conductedfor both plate and stiffener elements and the resultant stressescompared with the allowable stress limits for the particularelement. Example procedures are described in theseGuidance Notes.

■ Section 5Direct calculations

5.1 Direct calculations may be specifically required bythe Rules for Special Service Craft. They may be required forcraft having novel design features, or may be submitted insupport of alternative arrangements and scantlings. LR may,when requested, undertake calculations on behalf of design-ers or Builders and make recommendations with regard to thesuitability of any required model tests. Where model testing isundertaken to complement direct calculations details wouldnormally be required to be submitted indicating the scheduleof tests, details of test equipment, input data, analysis andcalibration procedures together with tabulated and plottedoutput.

5.2 All direct calculations are to be submitted for examination. Where calculation procedures other than thoseavailable within the Rules for Special Service Craft areemployed, supporting documentation is to be submitted forappraisal and this is to include details of the following:• calculation methods,• assumptions and references,• loading data,• structural modelling,• design criteria.

5.3 LR will consider the use of Builder’s and/ordesigner’s programs for direct calculations in the following cases:• where it can be established that the program has previ-

ously been satisfactorily used to perform a directcalculation similar to that now submitted,

• where sufficient information and evidence of satisfactory performance is submitted to substantiate thevalidity of the computation performed by the program.

5.4 Where items are of a novel or unconventionaldesign or manufacture, it is the responsibility of the Builderand/or designer to demonstrate their suitability and equiva-lence to the Rule requirements. Alternative arrangements,which are in accordance with the requirements of a NationalAuthority, may be accepted as equivalent to the requirementsof the Rules for Special Service Craft.

5.5 These Guidance Notes are published to enabledesigners/Builders to carry out the Rule calculations without using the Rules for Special Service Craft software.


Design Procedures Chapter 1Sections 4 & 5

LLOYD’S REGISTER2

Section

1 Calculation procedure

2 Concluding remarks

■ Section 1Calculation procedure

1.1 The stress in individual plies of a laminate is calculated in accordance with Pt 8, Ch 3,1.12 of the Rules forSpecial Service Craft, based on bending moment (see 1.9)and the laminate stiffness of a 1 cm wide elemental strip ofmaterial.

1.2 Considering the model shown in Figs. 2.1.1 and2.1.2 of a typical single skin hull laminate. Assume a pressureof 33 kN/m2 and that there is no significant panel curvature.

1.3 In this example the maximum bending moment isdetermined from Pt 8, Ch 3,1.9 of the Rules for SpecialService Craft and occurs under the web at the base of thestiffener. It should be noted that no reduction in the bendingmoment, Mb, due to aspect ratio effect is given since thepanel aspect ratio, i.e. panel length/panel breadth is greaterthan 2. See Pt 8, Ch 3,1.10.1 of the Rules for Special ServiceCraft.

γ = = = 0,3

k = = 0,79

Mb = x 10–5 Nm

= x 33 x 5002 x 10–5

= 5,43 Nm.

1.4 The laminate section modulus calculation is shownin Table 2.1.1 at the end of this Section. From Fig. 2.1.3 it willbe noted that there will be positions where tension andcompression considerations will apply. Such calculations areideally suited to computer based investigation.

1.5 In order to apply a more detailed investigation it isnecessary to establish the position of the neutral axis.However, in relatively balanced laminates this may beassumed to be at mid-depth. The procedure is simply to carryout the calculations assuming compressive properties on oneface and tensile properties on the other face. Subsequently,the properties should be reversed and the layer stress calcu-lations repeated. The calculated values should then becompared with the appropriate ultimate properties, i.e.,dependent upon whether tension or compression considera-tions apply.

1.6 In the example the moments were evaluated aboutthe base, which was taken to be the outer (wet) surface. Thestiffness, EI, per 1 cm width, about the neutral axis, is deter-mined using the parallel axis theorem:In general:

Ina = Ixx – Ay2

EIsect = Σ EIbase – (Σ Et) x 10 x y2

wherey = distance of neutral axis above the base (mm).

γ3 + 1γ + 1

bw

b150500

0,7912

k p b2

12


Design of Single Skin Hull Laminates Chapter 2Section 1


1 cm strip

2000 mm

b = 500 mm

Pressure = 33 kN/m2

4390/220

Fig. 2.1.1 Single skin example model

bw = 150 mm 4390/220a

Fig. 2.1.2 ‘Top-hat’ stiffener used in model

4390/219

C

T

T

C

C

T

C

T

T

C

Fig. 2.1.3Regions of tension (T) and compression (C)

in example model



LLOYD’S REGISTER2

Ply

No.

Des

crip

tion

Gc

Wei

ght

tLe

ver

@E

E.t

E.t.x

I @EI

@(g

/m2 )

(mm

)ba

se, x

(mm

)(N

/mm

2 )ba

seba

se

Dry

, see

Not

e1

CS

M0,

3360

01,

250

10,1

4972

0090

0091

341

1289

,292

8191

7

2C

SM

0,33

600

1,25

08,

899

7200

9000

8009

199

1,5

7139

017

3C

SM

0,33

600

1,25

07,

649

7200

9000

6884

173

3,0

5277

367

4C

SM

0,33

600

1,25

06,

399

7200

9000

5759

151

3,5

3696

967

5W

R0,

560

00,

734

5,40

714

000

1027

655

562

214,

930

0886

9

6C

SM

0,33

600

1,25

04,

415

6950

8688

3835

524

5,3

1704

699

7C

SM

0,33

600

1,25

03,

165

6950

8688

2749

612

6,8

8815

58

8W

R0,

560

00,

734

2,17

314

500

1064

323

127

35,0

5073

33

9C

SM

0,33

600

1,25

01,

181

6950

8688

1026

019

,113

2482

Wet

(see

Not

e)10

CS

M0,

286

225

0,55

60,

278

6290

3497

972

0,6

3604

TOTA

LS10

,774

8647

945

3637

3163

3812

NO

TE‘D

ry’ i

ndic

ates

the

inne

r su

rface

of t

he h

ull a

nd ‘w

et’ t

he o

utsi

de o

f the

she

ll la

min

ate.

Pos

ition

of n

eutr

al a

xis

abov

e ba

se=

=

5,

246

mm

Tens

ile m

odul

us o

f sec

tion

=

=

8027

N/m

m2

Stif

fnes

s EI

abou

t ne

utra

l axi

s =

7

83,8

N c

m4 /

mm

2 (b

ased

on

1 cm

wid

e st

rip)

8647

910

,774

4536

3786

479

Tab

le 2

.1.1

Tab

ulat

ion

of

sing

le s

kin

lam

inat

e ca

lcul

atio

ns

1.13 Consider the inner (dry) surface:The 600 g/m2 chopped strand mat reinforcements at theinner surface in compression:

σci = 693 x 10–6 x Ei yi= 693 x 10–6 x 7200 x (10,774–5,246)= 27,6 N/mm2

σult comp = 122 N/mm2 for CSM at Gc = 0,33

Stress fraction = 27,6/122 = 0,226Hence acceptable.

■ Section 2Concluding remarks

2.1 From the example, the highest stress factor occursin the outer 225 g/m2 chopped strand mat reinforcement (intension) but this is significantly lower than the limiting stressfraction required by the Rules. The bending moment at thecentre of the panel is smaller than that at the boundary andconsequently, the stress factor will be correspondinglyreduced. The design may be optimised by sequentially remov-ing plies, changing reinforcement weights and/or by providingreceiving strips under the base of the ‘top-hat’ stiffeners.

2.2 For the design of side shell laminates there are noshear and deflection criteria to be fulfilled. In this example asignificant reserve exists between the actual and the ultimate stresses.

2.3 It is of paramount importance that the straincompatibility of the component materials is carefully consid-ered.

2.4 Consider typical values of apparent strain, εa, at failure for the following materials in laminate form:

Tension Compression‘E’ glass 1,3% 1,05%Carbon fibre 0,9% 0,55%Aramid fibre 1,3% 0,60%

2.5 The actual strain permissible is controlled by thematerial with the lowest apparent strain. The level of straindepends upon whether the reinforcements are in tension orcompression and depends on their relative positions withinthe laminate. Consequently if, for example, a carbon fibre rein-forcement is used in the outer plies of laminate then the strainmust be constrained to a maximum of 0,33 x 0,9 per cent,i.e., 0,297 per cent. Therefore, the corresponding allowablestress in the other reinforcements must be related to the strainin the reinforcement relative to its position away from theneutral axis and that of the carbon fibre reinforcement, e.g.:

εlimitCSM =εallowable carbon x yCSM

ycarbon

1.7 A factor of 10 (width in mm) is introduced to correctthe value of area used in the parallel axis theorem, since a 1 cmwide strip of material is considered in the calculations.From the tabulation:

EIsect = 31633812 – (86479 x 10 x 5,2462)= 7837614 Nmm4/mm2

= 783,8 Ncm4/mm2.

1.8 From Pt 8, Ch 3,1.12 of the Rules for SpecialService Craft the individual layer stresses (tensile considera-tion) are determined from:

σti = x 10–1 N/mm2

1.9 More generally, the calculation of the stresses inindividual layers becomes:

σti = x Ei yi x 10–1 N/mm2

= 693 x 10–6 x Ei yi N/mm2

where

Ei = Eti or Eci for the ply relative to its position above orbelow the neutral axis

yi = distance from the neutral axis to the outer extrem-ity of an individual ply, i, in mm.

1.10 Consider the following typical arrangement and theassociated stresses for a single shell panel outside of theslamming zone:

Consider the outer (wet) surface:Consider the 225g/m2 chopped strand mat reinforcement intension:

σti = 693 x 10–6 x Ei yi= 693 x 10–6 x 6290 x 5,246= 22,9 N/mm2.

From Pt 8, Ch 3, Table 3.1.1 of the Rules for Special ServiceCraft.σult tension = 82,2 N/mm2 for CSM at Gc =0,286

Hence, stress fraction = 22,9/82,2 = 0,278.

1.11 From Table 7.3.1 in Pt 8, Ch 7 of the Rules forSpecial Service Craft, the limiting tensile stress fraction is 0,33for the side shell outside of the slamming zone. Hence, thecalculated stress fraction is lower than the limiting stressfactor and is therefore acceptable.

1.12 Similarly, consider the 600g/m2 woven roving rein-forcement in tension:

σti = 693 x 10–6 x Ei yi= 693 x 10–6 x 14500 x (5,246–0,556–1,25)= 34,6 N/mm2

σult tension = 190 N/mm2 for woven roving at Gc = 0,5

Stress fraction = 34,6/190 = 0,182Hence acceptable.

5,43783,8

Eti yi M

Σ (Ei Ii)


Design of Single Skin Hull Laminates Chapter 2Sections 1 & 2


2.6 Where aramid reinforcements are being used,special consideration must be given to the compressive prop-erties. For comparison purposes aramid reinforcements, at afibre content of 0,45 (by weight), typically have the followingproperties:

Tension CompressionUltimate strength (N/mm2) 300 100Elastic modulus (N/mm2) 21000 17000

2.7 The radical reduction in ultimate compressive strengthmay prove to be unacceptable on the inside at the panelboundaries or on the outside at the panel centre. Designswhich feature aramid fibres in the outer plies, in an attempt tomake use of the superior impact properties, must be checkedat the panel centre for compression in the individual layers.This also applies to hybrid reinforcements containing aramidfibres. These reinforcements have one off properties of higherthan one of the constituent fibres however, in service the indi-vidual allowable strains for each fibre reinforcement should notbe exceeded.



LLOYD’S REGISTER4

Section


2 Deflection of sandwich panel

3 Bending moment applied

4 Stresses in facings


1.1 Consider the model of a side shell sandwich panelhaving dimensions 700 mm x 2000 mm shown in Fig. 3.1.1.Assume a design pressure of 50 kN/m2 and a panel of negli-gible curvature.

1.2 The panel is to be designed in accordance with therequirements of Pt 8, Ch 3 of the Rules for Special ServiceCraft. Firstly it is necessary to estimate the core thicknessusing Pt 8, Ch 3,1.13.2 of the Rules for Special Service Craftassuming a nominal value of tensile modulus of 11000 N/mm2

for sandwich panel facings:

ts = φ ks b3

mm

= 0,144 x 700 x 3

= 16,7 mm

Hence, select 20 mm core as a typically available size.

5011000

pEtpS

4390/218

Pressure = 50 kN/m2

2000 mm

700 mm

Fig. 3.1.1 Sandwich panel laminate example model

1LLOYD’S REGISTER

Chapter 3Section 1

Design of Sandwich Panel LaminatesGUIDANCE NOTES FOR THE CLASSIFICATION OF SPECIAL SERVICE CRAFT, July 2014

1.3 From Pt 8, Ch 3,1.13.9 of the Rules for SpecialService Craft the maximum core shear at the mid-point alongthe edge of the sandwich panel is given by:

τc = x 10–3 N/mm2

= x 10–3

= 0,875 N/mm2

1.4 The panel aspect ratio correction factor is given inPt 8, Ch 3,1.13.9 of the Rules for Special Service Craft. AR = 2000/700 = 2,86, hence kS = 1.No correction factor applied since AR > 2.

1.5 To achieve an allowable shear stress fraction of0,30, see Pt 8, Ch 7,3.5 of the Rules for Special Service Craft,this design would require the selection of 200 kg/m3 foamcore. Clearly being unacceptable the conclusion is to adopta 50 mm thick core to reduce the core shear stress. Thestress varies inversely with core thickness:

τ50 = τ20 x = 0,35 N/mm2.

1.6 To achieve the required allowable shear stress fraction the foam core must have a core shear strength of0,35/0,30 = 1,17 N/mm2. This may be achieved using a 100 kg/m3 foam core using 90 per cent of the manufacturer’squoted value.

1.7 However, there are numerous solutions to achievean acceptable arrangement. The options include:(a) Repositioning the stiffeners to reduce panel sizes.(b) Inclusion of shear ties in accordance with Pt 8,

Ch 3,1.13.10 of the Rules for Special Service Craft.(c) Accept the higher density core solution.

1.8 From Pt 8, Ch 3,1.13.3 of the Rules for SpecialService Craft the skin thicknesses may be re-calculated allowing for the change in core thickness:

tS = φ2 x 10–3 mm

tinner = 0,446 x x x 10–3 = 0,28 mm

touter = 0,594 x x x 10–3 = 0,37 mm

Clearly, the increase in core thickness gives a substantialincrease in panel stiffness. Consequently the skin thicknessesdefault to the minimum requirement quoted in Pt 8, Ch 3,3.5.5of the Rules for Special Service Craft. The minimum side shellsandwich skin thicknesses are:

Outer 4 mmInner 3 mm.

5011000

7003

502

50

11000

7003

502

p b3

Etps tc2

2050

50 x 700 x 12 x 20

p b kS

2tc

2 LLOYD’S REGISTER

Chapter 3Section 1


1.9 The minimum skin thicknesses relate to anassumed fibre content, fc, of 0,5. Where the fibre content byweight is less than 0,5 the required minimum thickness are tobe determined from Pt 8, Ch 3,2.4.2 of the Rules for SpecialService Craft.

1.10 In order to comply with the Rules for SpecialService Craft, chopped strand mat reinforcements arerequired against the core. The initial proposal to meet therequirement, features such CSM reinforcements together witha CSM against the gel coat surface.

1.11 The proposed sandwich skin laminate schedule forthe outer skin is:

1 x 450 g/m2 CSM @ Gc = 0,286 = 1,112 mm3 x 600 g/m2 WR @ Gc = 0,5 = 2,202 mm1 x 300 g/m2 CSM @ Gc = 0,33 = 0,625 mmTotal outer skin thickness = 3,94 mmTotal reinforcement weight = 2550 g/m2

1.12 By transforming the relationship given in Pt 8, Ch 3,1.6.1 of the Rules for Special Service Craft the equiva-lent fibre content by weight, fc, is 0,42.The adjusted minimum skin thickness for the outer skin is:

touter = t0,5 (1,65 – 1,3fc)

= 4 x (1,65 – 1,3 x 0,42)

touter = 4,42 mm.

1.13 The proposed outer skin is deficient by 4,42 – 3,94= 0,48 mm. Hence one additional woven roving reinforcementmay be added to achieve the minimum requirement. Theactual thickness of outer skin is 4,67 mm.

1.14 The proposed sandwich skin laminate schedule forthe inner skin is:

1 x 300 g/m2 CSM @ Gc = 0,33 = 0,625 mm4 x 600 g/m2 WR @ Gc = 0,5 = 2,936 mmTotal inner skin thickness = 3,56 mmTotal reinforcement weight = 2700 g/m2

The equivalent overall fibre content of the inner skin is 0,473.The adjusted minimum skin thickness for the inner skin is:

tinner = t0,5 (1,65 – 1,3fc)

= 3 x (1,65 – 1,3 x 0,473)

tinner = 3,1 mm.

1.15 The proposed arrangement which meets both coreshear and minimum sandwich skin requirements is given inTable 3.1.1.

Tab

le 3

.1.1

Tab

ulat

ion

of

sand

wic

h p

anel

cal

cula

tio

ns

Ref

No.

Des

crip

tion

Gc

Wei

ght

tLe

ver

@E

E.t

E.t.x

I@

EI@

(g/m

2 )(m

m)

base

, x(m

m)

(N/m

m2 )

base

base

Inne

r sk

in1

WR

0,5

600

0,73

457

,87

1400

010

276

5946

4124

579

3441

0569

0

2W

R0,

560

00,

734

57,1

314

000

1027

658

7099

2395

933

5431

718

3W

R0,

560

00,

734

56,4

014

000

1027

657

9556

2334

832

6868

472

4W

R0,

560

00,

734

55,6

714

000

1027

657

2014

2274

431

8415

951

5C

SM

0,33

300

0,62

554

,99

7200

4500

2474

3518

896

1360

5469

9

Cor

e 6

100

kg/m

3–

–50

,000

29,6

783

,741

8512

4182

5444

1045

5671

28

7C

SM

0,33

300

0,62

54,

3669

5043

4418

941

119

8273

33

8W

R0,

560

00,

734

3,68

1450

010

643

3917

710

014

4687

9

9W

R0,

560

00,

734

2,95

1450

010

643

3136

564

9291

03

10W

R0,

560

00,

734

2,21

1450

010

643

2355

336

5260

05

Out

er s

kin

11W

R0,

560

00,

734

1,48

1450

010

643

1574

116

2375

88

12C

SM

0,28

645

01,

112

0,56

6290

6994

3889

528

830

TOTA

LS58

,23

1036

9928

3759

215

1043

9396

Inne

r sk

in in

com

pres

sion

/out

er s

kin

in t

ensi

on.

Pos

ition

of n

eutr

al a

xis

abov

e ba

se =

=

2

7,36

mm

Tens

ile m

odul

us o

f ela

stic

ity o

f sec

tion

=

=

=

1

2086

N/m

m2

Stif

fnes

s EI

abou

t ne

utra

l axi

s =

733

97 N

cm

4 /m

m2

per

1 cm

wid

e st

rip

2837

592

1036

99

1036

99 –

418

558

,234

– 5

099

514

8,23

4

3LLOYD’S REGISTER

Chapter 3Section 1


■ Section 2Deflection of sandwich panel

2.1 Consider the revised model shown in Fig. 3.2.1:Ems = 12086 N/mm2 from Table 3.1.1

b = breadth in direction of bending = 700 mmG = shear modulus for 100 kg/m3 core

= 36 N/mm2 being 90 per cent of themanufacturer’s quoted value

ts = mean skin thickness(3,56 + 4,67)/2 = 4,11 mm

(1 – vf2) = unity (approximately)

Calculation of deflection in accordance with Pt 8, Ch 3,1.13.15of the Rules for Special Service Craft

δ = + x 10–3 mm( )= + x( )

10–3 mm= 61,25 x (0,00822 + 0,0278)= 2,2 mm total deflection.

2.2 The total deflection comprises 23 per cent due tobending and 77 per cent due to shear.The deflection criterion is given in Table 7.2.1 in Pt 8, Ch 7 ofthe Rules for Special Service Craft.

δRULE < where = 7 mm

Hence the 2,2 mm total deflection is acceptable.

b100

b100

50 x 7002

8 x 50

7002

24 x 12086 x 4,11 x 50136

p b2

8tc

b2

24Ems ts tc

1G


Design of Sandwich Panel Laminates Chapter 3Section 2

LLOYD’S REGISTER4

4,67 mm

3,56 mm

50 mm

2000 mm700 mm

4390/217Pressure = 50 kN/m2

Fig. 3.2.1 Sandwich panel example model

■ Section 3Bending moment applied

3.1 The bending moment to be applied at 1 cm widthof the sandwich panel is given by Pt 8, Ch 3,1.9 of the Rulesfor Special Service Craft. In this example it is evident that themaximum bending moment and hence maximum stressoccurs under the base of the stiffener. Due to the high aspectratio no correction factor needs to be applied to modify theapplied bending moment.

γ = = = 0,2143

k = = 0,8316

Mb = x 10–5 Nm

= x 50 x 7002 x 10–5

= 17 Nm.

■ Section 4Stresses in facings

4.1 Consider the revised model, see Fig 3.4.2, with 50 mm thick and 100 kg/m3 density core having the proposedside shell sandwich skins which comply with the Rules forSpecial Service Craft minimum requirements. As indicated inFig. 3.4.1 there will be positions where tension and compres-sion considerations will apply. The relevant elastic modulus hasbeen applied to the element dependent upon its relative posi-tion in the sandwich. The proposed schedule together with thetabular calculations are given in Table 3.1.1. Such calculationsare ideally suited to computer based investigation.

4.2 The stiffness, EI, per 1 cm width is determined usingthe parallel axis theorem:In general,

Ina = Ixx – Ay2

EIsect = Σ EIbase – (Σ Et) x 10 x y2

wherey = distance of neutral axis above base (mm).

4.3 It should be noted that the factor 10 (width in mm) isintroduced to correct the value of area used in the parallel axistheorem, since a 1 cm wide strip of material is considered inthe calculations.

From the tabulated calculations the overall stiffness of thesection is calculated:EIsect = 1510439396 – (103699 x 10 x 27,362)

= 1510439396 – 776259189 Nmm4/mm2

= 734200000 Nmm4/mm2

= 73,4 x 103 Ncm4/mm2.

0,831612

k p b2

12

γ3 + 1γ + 1

bw

b150700

4.4 From Pt 8, Ch 3,1.13.7 of the Rules for SpecialService Craft the individual layer stresses are determinedfrom:

σti = x 10–1 N/mm2

The calculation of the tensile stress in the individual layersbecomes:

σti = x Eti yi x 10–1 N/mm2

σti = 23,2 x 10–6 x Ei yi N/mm2

whereEi = modulus of elasticity of layer (N/mm2)yi = distance of layer from the neutral axis (mm).

4.5 Consider the model as shown in Fig. 3.4.1.

4.5.1 Consider wet surface in tension at the panel boundary:(a) Consider the CSM reinforcement in the outer ply

(450 g/m2 and Gc = 0,286)σCSMult = 82,2 N/mm2

Et = 6290 N/mm2

yi = 27,36 mmσCSM = 23,2 x 10–6 Et yi N/mm2

= 23,2 x 10–6 x 6290 x 27,36 N/mm2

= 3,99 N/mm2

Stress factor = 3,99/82,2 = 0,05 < 0,33 hence accept.

17,073,4 x 103

Eti yi M

Σ (Ei Ii)


Design of Sandwich Panel Laminates Chapter 3Sections 3 & 4


T

T T

C CC

4390/214

2000 mm

700 mm


in example model

4.7 As indicated in Chapter 2, Sections 2.4 to 2.7 ofthese Guidance Notes for Single Skin Laminates, considera-tion must be given to the strain compatibility of thereinforcements incorporated in the sandwich skins.

(b) Consider the WR reinforcement in the in outer plies(600 g/m2 and Gc = 0,5)

σWRult = 190 N/mm2

Et = 14500 N/mm2

yi = 27,36 – 1,112 = 26,25 mmσWR = 23,2 x 10–6 Et yi N/mm2

= 23,2 x 10–6 x 14500 x 26,25 N/mm2

= 8,83 N/mm2

Stress factor = 8,83/190 = 0,046 < 0,33 hence accept.

4.5.2 Consider inner surface in compression at the panelboundary:(a) Consider top WR reinforcement in compression

(600 g/m2 and Gc = 0,5)

σWRult = 147 N/mm2

Ec = 14000 N/mm2

yi = 58,23 – 27,36 = 30,87 mmσWR = 23,2 x 10–6 Ec yi N/mm2

= 23,2 x 10–6 x 14000 x 30,87 N/mm2

= 10,03 N/mm2

Stress factor = 10,03/147 = 0,068 < 0,33 hence accept.(b) Consider CSM reinforcement in compression

(300 g/m2 and Gc = 0,33)

σCSMult = 122 N/mm2

Ec = 7200 N/mm2

yi = 30,87 – (4 x 0,734) = 27,93 mmσCSM = 23,2 x 10–6 Ec yi N/mm2

= 23,2 x 10–6 x 7200 x 27,93 N/mm2

= 4,67 N/mm2

Stress fraction = 4,67/122 = 0,038 < 0,33 hence accept.

4.6 Stress fractions in this example are considerablylower than those required by the Rules for Special ServiceCraft and it is evident that the design is controlled by and coreshear considerations and minimum skin thickness require-ments.

3,56 mm

4,67 mm

27,3

1 m

m22

,69

mm

27,3

6 m

m30

,87

mm

50 m

m

58,2

3 m

m

600 WR

300 CSM

300 CSM

450 CSM

600 WR

4390/216

Core 100 kg/m3

Inner skin

Outer skin

Fig. 3.4.2 Sandwich skin laminate details

6 LLOYD’S REGISTER

Chapter 3Section 4


Section


2 Bending moment at fixed end of stiffener

3 Web thickness to meet shear requirement

4 Calculation of deflection


1.1 Assume a design pressure of 70 kN/m2 applied toa fully fixed bottom longitudinal located outside of the slamming zone as shown in Fig. 4.1.1.

1.2 The bending moment is determined from Pt 8, Ch 3,1.14.1 of the Rules for Special Service Craft. For a fullyfixed stiffener the maximum bending moment coefficient fromTable 3.1.5(a) in Pt 8, Ch 3 of the Rules for Special ServiceCraft is 1/12.

1.3 Hence, maximum bending moment, Ms, is givenby:

Ms = Nm

Ms = Nm

Ms = 2917 Nm

500 x l2 x 7012

s le2 p12

Assumed shell laminate:5 x 800/300 combination mats

Gc = 0,5 (WR in combination mat)tWR = 0,979 mm

Et = 14500 N/mm2

Gc = 0,33 (CSM in combination mat)tCSM = 0,625 mm

Et = 6950 N/mm2

1 x 450 CSM adjacent to gel coat Gc = 0,286

tCSM = 1,112 mmEt = 6290 N/mm2

Total thickness, tp = 9,132 mmThe effective width of attached plating 2b1 from Pt 8, Ch 3,1.7.1 of the Rules for Special Service Craft for single skinconstruction is:

b1 = 0,5bw + 10tap= 0,5 x 120 + 10 x 9,132= 151 mm

Hence, apply 302 mm attached plating.

Consider typical layup over ‘top hat’ stiffener:

450 g/m2 CSM @ Gc = 0,33 – first ply over former800 g/m2 WR @ Gc = 0,5800 g/m2 WR @ Gc = 0,5600 g/m2 UDT @ Gc = 0,54600 g/m2 UDT @ Gc = 0,54800 g/m2 WR @ Gc = 0,5800 g/m2 WR @ Gc = 0,5 – top ply

1.4 Consider the idealised section shown in Fig. 4.1.2.


Design of Stiffening Members Chapter 4Section 1


80 mm

70 mm

120 mm

s = 500 mm between centres of longitudinals

302 mm attached plating

9,132 mm

le = 1000 mm

4390 /222

Consider model bottom longitudinal

Fig. 4.1.1 ‘Top-hat’ stiffener example model

1.5 The stiffener bonding is to be in accordance with Pt 8, Ch 3,1.18.6 of the Rules for Special Service Craft and atypical arrangement is shown in Fig. 4.1.3. To simplify thecalculation of the stiffness of the overall section the taperedbonding is assumed to be an effective constant thickness.The effective thickness of the bonding is calculated as:

tbb =

tbb = = 3,15 mm

The boundary bonding may be approximated to a thickness of 3,15 mm over an (85 x 2) mm width to accountfor both flanges. The majority of the flange comprises ofwoven rovings and it may be assumed that the tensile modu-lus is 145000 N/mm2. The discrepancy is negligible since theelement is very close to the neutral axis.

268,2

85

(4,853 x 25) + (4 + 3 + 2 + 1) x 0,079 x 15

25 + (4 x 15)

The effective depth and width of the web used in the idealisedsection are:

dweb = 70 – effective thickness on bonding= 70 – 3,15= 66,85 mm

tweb = 2 x (0,937 + 4 x 0,979)= 2 x 4,853= 9,706 mm

Now the web consists of two types of reinforcements, namelyone ply of CSM and four plies of woven rovings. The majorityof the web will be in compression and the overall modulus ofelasticity may be calculated in accordance with Pt 8, Ch 3,1.13.5 of the Rules for Special Service Craft.

Eweb =

Eweb =

Eweb = 12687 N/mm2

The web may now be treated as a single laminate item havingan overall compressive modulus, given above.

1.6 The laminate section modulus calculation is shownin Table 4.1.1. The tabulation consists of each element havingthe compressive moduli in the section above the neutral axisand tensile moduli below. The actual breadth of each elementmust be entered to calculate the overall section properties.The tabulation corresponds to the idealised section in Fig. 4.1.2.

(0,937 x 7200) + (0,979 x 4 x 14000)

0,937 + (0,979 x 4)

Σ (Eci ti)

Σ ti



LLOYD’S REGISTER2

80 mm

3,15 mm 170 mm

302 mm

66,8

5 m

m

9,13

2 m

m

22,4

4 m

m

56,6

92 m

m

70 m

m

N AApprox.

boundary bonding

4390/215

6,173 mm

Fig. 4.1.2 Idealised section

4390/223

1 x 450 g/m2 CSM 4 x 800 g/m2 WR

25 mm 15 mm 15 mm 15 mm 15 mm

85 mm

4,853 mm3,916 mm

2,973 mm1,958 mm

0,979 mm

Fig. 4.1.3 Typical stiffener bonding arrangement




Ply

No.

Des

crip

tion

Gc

Wei

ght

tB

read

th,

Leve

r @

Et.b

E.t.b

E.t.b

.xI@

EI@

(g/m

2 )(m

m)

b(m

m)

base

, x(m

m)

(N/m

m2 )

base

base

Dry

, see

Not

e1

WR

0,

580

00,

979

8084

,816

1400

078

,32

1096

480

9299

8499

5634

14,4

7887

8018

05

2W

R0,

580

00,

979

8083

,837

1400

078

,32

1096

480

9192

5046

5504

83,0

7706

7616

55

3U

DT

0,54

600

0,66

080

83,0

1720

748

52,8

010

9549

490

9446

5936

3890

,175

4999

2490

4U

DT

0,54

600

0,66

080

82,3

5720

748

52,8

010

9549

490

2216

3235

8127

,274

3042

2738

5W

R0,

580

00,

979

8081

,538

1400

078

,32

1096

480

8940

4238

5207

06,1

7289

8856

32

6W

R0,

580

00,

979

8080

,559

1400

078

,32

1096

480

8833

0784

5082

77,4

7115

8830

45

7C

SM

0,33

450

0,93

780

79,6

0172

0074

,96

5397

1242

9613

4547

4970

,034

1978

4035

8W

eb0,

5–

66,8

59,

706

45,7

0712

687

648,

8582

3191

037

6255

932

1597

160,

720

2631

7737

2

9bo

ndin

g0,

5–

3,15

170

10,7

0714

500

535,

5077

6475

083

1371

7861

832,

489

6570

245

10W

R0,

580

00,

979

302

8,64

314

500

295,

6642

8704

137

0507

5222

107,

132

0553

529

11C

SM

0,33

300

0,62

530

27,

840

6950

188,

7513

1181

310

2852

6611

609,

380

6843

30

12W

R0,

580

00,

979

302

7,03

914

500

295,

6642

8704

130

1743

3814

670,

721

2724

485

13C

SM

0,33

300

0,62

530

26,

236

6950

188,

7513

1181

381

8111

973

47,4

5106

4249

14W

R0,

580

00,

979

302

5,43

514

500

295,

6642

8704

123

2979

2487

55,5

1269

5497

6

15C

SM

0,33

300

0,62

530

24,

632

6950

188,

7513

1181

360

7697

140

56,7

2819

4272

16W

R0,

580

00,

979

302

3,83

114

500

295,

6642

8704

116

4215

1143

61,7

6324

5002

17C

SM

0,33

300

0,62

530

23,

028

6950

188,

7513

1181

339

7282

417

37,3

1207

4400

18W

R0,

580

00,

979

302

2,22

714

500

295,

6642

8704

195

4509

714

89,3

2159

4564

19C

SM

0,33

300

0,62

530

21,

424

6950

188,

7513

1181

318

6867

738

9,2

2704

632

Wet

, see

Not

e20

CS

M0,

286

450

1,11

230

20,

556

6290

335,

8221

1233

311

7445

713

8,4

8706

64

TOTA

LS85

,305

4436

,05

5321

9882

1194

2282

4970

4809

4412

1

NO

TE

The

crow

n of

the

stif

fene

r is

con

side

red

to b

e in

com

pres

sion

in t

his

exam

ple.

‘Dry

’ ind

icat

es t

he fa

ce o

f the

stif

fene

r w

ithin

the

hul

l and

‘wet

’ the

out

side

of t

he s

hell

lam

inat

e, s

eeFi

g. 4

.1.4

.

Pos

ition

of n

eutr

al a

xis

abov

e ba

se=

=

22,

44 m

m a

bove

bas

eTe

nsile

mod

ulus

of e

last

icity

of s

ectio

n =

=

119

97 N

/mm

2

Stif

fnes

s EI

of s

ectio

n ab

out

NA

= 4

3683

04 N

cm

4 /m

m2

1194

2282

4953

2198

8253

2198

8244

36,0

5

Tab

le 4

.1.1

Init

ial t

abul

atio

n o

f ‘t

op

-hat

’ sti

ffen

er c

alcu

lati

ons

1.7 The tabulation considers the entire section andcalculates all moments about the base, which is taken to bethe outer (wet) surface. The stiffness, EI, of the entire section,about the neutral axis, is determined using the parallel axistheorem:In general,

Ina = Ixx – Ay2

EIsect = Σ EIbase – (Σ Etb) x y2

where

y = distance of neutral axis above the base (mm)

From the tabulation:

EIsect = 70480944121 – 53219882 x (22,44)2

= 4368304336 Nmm4/mm2

EIsect = 4,368 x 106 Ncm4/mm2

From Pt 8, Ch 3,1.15 of the Rules for Special Service Craft theindividual layer stresses are determined from:

σti = x 10–1 N/mm2

The calculation of the stresses in individual layers becomes:


σti = 66,8 x 10–6 x Ei yi N/mm2

where

Ei = modulus of elasticity of layer (N/mm2)yi = distance of layer from the neutral axis (mm)

The ‘top-hat’ stiffener is subjected to a load model shown inFig. 4.1.4. The diagram indicates the areas of tension andcompression that exist on either side of the stiffener.

29174,368 x 106

Eti yi M

Σ (Ei Ii)

■ Section 2Bending moment at fixed end ofstiffener

2.1 The generalised stress equation is:

σi = 66,8 x 10–6 x Ei yi N/mm2

The ultimate material properties may be found from Tables3.1.1 and 3.1.2 in Pt 8, Ch 3 of the Rules for Special ServiceCraft and the limiting stress fractions from Table 7.3.1 in Pt 8, Ch 3 of the Rules for Special Service Craft.

2.1.1 Consider the crown of the stiffener:(a) Consider the WR (Gc = 0,5) in compression:

Ec = 14000 N/mm2

yi = 85,305 – 22,44= 62,865 mm

σWR comp = 66,8 x 10–6 x 14000 x 62,865= 58,8 N/mm2

σWR ucs = 147 N/mm2

Stress fraction = 58,8/147 = 0,40 hence reject.

(b) Consider the UDT (Gc = 0,54) in compression:

Ec = 20748 N/mm2

yi = 85,305 – 22,44 – (2 x 0,979)= 60,907 mm

σUDT comp = 66,8 x 10–6 x 20748 x 60,907= 84,4 N/mm2

σUDT ucs = 279 N/mm2

Stress fraction = 84,4/279 = 0,303 hence acceptable.

(c) Consider the CSM (Gc = 0,33) over the stiffener former incompression:

Ec = 7200 N/mm2

yi = (85,305 – 22,44) – (4 x 0,979) – (2 x 0,66) = 57,629 mm

σCSM comp = 66,8 x 10–6 x 7200 x 57,629 = 27,7 N/mm2

σCSM ucs = 122 N/mm2


2.1.2 Consider the loaded face of the shell:(a) Consider the wet surface CSM (Gc = 0,286) in tension:

Et = 6290 N/mm2

yi = 22,44 mmσCSM tension = 66,8 x 10–6 x 6290 x 22,44

= 9,4 N/mm2

σCSM uts = 91 N/mm2

Stress fraction = 9,4/91 = 0,10 hence acceptable.Due to such a low stress fraction the adjacent CSM (Gc = 0,33) will also be acceptable.

(b) Consider the WR (Gc = 0,5) in tension:

Et = 14500 N/mm2

yi = 22,44 – 1,112 – 0,625= 20,703 mm

σWR tension = 66,8 x 10–6 x 14500 x 20,703= 20,05 N/mm2

σWR uts = 190 N/mm2



Design of Stiffening Members Chapter 4Sections 1 & 2

LLOYD’S REGISTER4

T

T T

C CC

4390/221

Ms Ms

crown

plate


in example model

2.8 The radical reduction in ultimate compressivestrength may prove to be unsuitable in the crown of the stiffener at the end or in the panel at mid span. Designs whichfeature aramid fibres in the outer plies of the panel, in anattempt to make use of the superior impact properties, mustbe checked at mid span for compression in the individuallayers. This also applies to hybrid reinforcements containingaramid fibres. These reinforcements have one off propertiesof higher than one of the constituent fibres however, in servicethe individual allowable strains for each fibre reinforcementshould not be exceeded.

2.9 In accordance with Pt 8,Ch 3,1.5.1 of the Rules forSpecial Service Craft, it is of paramount importance that thestrain compatibility of the component materials is carefullyconsidered.

2.10 Consider typical values of apparent strain, εa, at failure for the following materials in laminate form:

Tension Compression‘E’ glass 1,3% 1,05%Carbon fibre 0,9% 0,55%Aramid fibre 1,3% 0,60%

2.11 The actual strain permissible is controlled by thematerial with the lowest apparent strain. The level of straindepends upon whether the reinforcements are in tension orcompression and depends on their relative positions withinthe laminate. Consequently if, for example, a carbon fibre rein-forcement is used in the crown of the stiffener then thecompression strain must be constrained to a maximum of0,33 x 0,55 per cent, i.e., 0,297 per cent. Therefore, thecorresponding allowable stress in the other reinforcementsmust be related to the strain in the reinforcement relative toits position away from the neutral axis and that of the carbonfibre reinforcement, e.g.:

εlimitWR =

2.12 Other materials incoporated into stiffeningmembers requiring strain compability consideration areplywoods, timbers, etc., which have very differing strains atfailure dependent upon the direction of the grain.

εallowable carbon x yWR

ycarbon

2.2 However, the conclusion is that the compressivestress fraction in the WR in the crown of the stiffener is unacceptable. A number of options exist, which include:(a) The use of higher strength materials such as carbon fibre

or aramid reinforcements.(b) Add UDT reinforcements in the crown of the stiffener.(c) Laminate local collars at the end of the stiffeners to

increase the section stiffness. This is usually labour inten-sive and not weight efficient.

2.3 Logically, for this example, the easiest solution is toadd UDT reinforcements in the crown of the stiffener. Twoadditional UDT reinforcements have been included in therevised arrangement. The effect on the section stiffness of therevised schedule is shown in Table 4.2.1.

2.4 Recalculation of stress in the WR reinforcement inthe stiffener crown using the revised section stiffness of5200996 Ncm/mm2:


σti = 56,09 x 10–6 x Ei yi N/mm2

Consider the WR (Gc = 0,5) in the crown of the stiffener incompression:

Ec = 14000 N/mm2

yi = 86,625 – 24,926= 61,7 mm

σWR comp = 56,09 x 10–6 x 14000 x 61,7= 48,4 N/mm2

σWR ucs = 147 N/mm2


2.5 Re-consider the outermost UDT (Gc = 0,54) incompression:

Ec = 20748 N/mm2

yi = 86,625 – 24,926 – 0,979= 60,720 mm

σUDT comp = 56,07 x 10–6 x 20748 x 60,720= 70,66 N/mm2

σUDT ucs = 279 N/mm2


2.6 The example demonstrates that the additional twoUDT’s in the crown increases the section stiffness by 19 percent and is accompanied by a movement in the neutral axisfrom 22,44 – 24,926 mm above the base. The stress fractionin the woven roving in the crown is reduced from 0,4 to 0,329and meets the Rule requirement of 0,33.Considerable care must be exercised when additional material radically affects the position of the neutral axis. Forthis reason the stress in the outermost UDT’s has also beenre-calculated and found to be satisfactory.

2.7 Where aramid reinforcements are being used thenspecial consideration must be given to the compressive prop-erties. For comparison purposes aramid reinforcements, at afibre content of 0,45, typically have the following properties:

Tension CompressionUltimate strength (N/mm2) 300 100Elastic modulus (N/mm2) 21000 17000

29175200996






LLOYD’S REGISTER6

Ply

No.

Des

crip

tion

Gc

Wei

ght

tB

read

th,

Leve

r @

Et.b

E.t.b

E.t.b

.xI

@EI

@(g

/m2 )

(mm

)b

(mm

)ba

se, x

(mm

)(N

/mm

2 )ba

seba

se

Dry

, see

Not

e1

WR

0,

580

00,

979

8086

,136

1400

078

,32

1096

480

9444

5853

5810

87,7

8135

2283

50

2U

DT

0,54

600

0,66

080

85,3

1620

748

52,8

010

9549

493

4632

0038

4323

,679

7394

6157

3W

R0,

560

00,

979

8084

,497

1400

078

,32

1096

480

9264

8722

5591

84,3

7828

5803

41

4U

DT

0,54

600

0,66

080

83,6

7720

748

52,8

010

9549

491

6676

8536

9699

,176

7051

6637

5U

DT

0,54

600

0,66

080

83,0

1720

748

52,8

010

9549

490

9446

5936

3890

,175

4999

2490

6W

R0,

580

00,

979

8082

,198

1400

078

,32

1096

480

9012

7915

5291

69,8

7408

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NO

TE:

‘Dry

’ ind

icat

es t

he fa

ce o

f the

stif

fene

r w

ithin

the

hul

l and

‘wet

’ the

out

side

of t

he s

hell

lam

inat

e, s

eeFi

g. 4

.1.4

. Con

side

r th

e cr

own

of t

he s

tiffe

ner

in c

ompr

essi

on.

Pos

ition

of n

eutr

al a

xis

abov

e ba

se=

=

24,

926

mm

abo

ve b

ase

Tens

ile m

odul

us o

f ela

stic

ity o

f sec

tion

=

=

122

01 N

/mm

2

Stif

fnes

s EI

of s

ectio

n ab

out

NA

= 5

2009

96 N

cm

4 /m

m2

Tab

le 4

.2.1

Rev

ised

tab

ulat

ion

of

‘to

p-h

at’ s

tiff

ener

cal

cula

tio

ns in

clud

ing

ad

dit

iona

l uni

-dir

ecti

ona

l rei

nfo

rcem

ents

1381

1813

5255

4108

7155

4108

7145

41,6

5

■ Section 4Calculation of deflection

4.1 The deflection is calculated from Pt 8, Ch 3,1.14.5of the Rules for Special Service Craft. From the tabulation theoverall section stiffness is (EI)s = 5200996 Ncm4/mm2

δs = x 105 mm

δs = x 105 mm

δs = 1,93 mm.

4.2 The limiting span/deflection ratio is given in Table7.2.1 in Pt 8, Ch 7 of the Rules for Special Service Craft andtypically for a bottom longitudinal (not in the slamming zone)the ratio required is 150.Span/deflection ratio = length/mid-point deflection

= 1000/1,7= 588 hence acceptable.

φS p s l4

(EI)s

1

348

70 x 500 x 14

5200996

■ Section 3Web thickness to meet shearrequirement

3.1 Ultimate shear stress from Table 3.1.2 in Pt 8, Ch 3of the Rules for Special Service Craft. From the web thickness(4,853 mm) given in 1.5 and the web laminate schedule givenin Fig. 4.1.3 (i.e. total weight of 3650 g/m2) the effective glasscontent may be calculated, by transforming the relationshipgiven in Pt 8, Ch 4,1.6.1 of the Rules for Special Service Craft.The effective glass content of the web is therefore 0,47.

τS = 80 Gc + 38 = 76 N/mm2

From Pt 8, Ch 7, Table 7.3.1 of the Rules for Special ServiceCraft. Limiting shear stress fraction = 0,33Limiting shear stress = 0,33 x 76 = 25,08 N/mm2.

3.2 The shear stress requirement is given in Pt 8, Ch 3,1.14.3 of the Rules for Special Service Craft. By settingthe shear stress to the limiting shear stress the equation maybe rearranged:

tw = FS/(2 x dw x τS) mm

The actual shear load is given in Pt 8, Ch 3,1.14.2 of the Rulesfor Special Service Craft.

Fs = φS p s le N

The shear stress coefficient is obtained from Table 3.1.5 in Pt 8, Ch 3 of the Rules for Special Service Craft.

Fs = 0,5 x 70 x 500 x 1 = 17500 N

Consequently, the minimum web thickness to meet the Rulerequirement is:

tw = 17500/(2 x 70 x 25,08) = 4,98 mm

The actual web thickness is 4,853 mm. The deficiency is only0,127 mm and is considered acceptable.

3.3 Finally, check the minimum Rule requirement forweb thickness. From Pt 8, Ch 3,1.16.2 of the Rules for SpecialService Craft.

tw =

For a web depth of 70 mm and fibre content of 0,47 the minimum web thickness is 2,33 mm. Hence the minimumrequirement is fulfilled.

0,025dw + 1,1

1,3fw + 0,61


Design of Stiffening Members Chapter 4Sections 3 & 4


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Documents

Guidance Notes for the Classiﬁcation of Special Service Craft