ISO 12215 Small craft - Hull construction and scantlings [7]

Citation preview

INTERNATIONAL STANDARD

ISO 12215-7 First edition 2020-11

Small craft — Hull construction and scantlings — Part 7: Determination of loads for multihulls and of their local scantlings using ISO 12215-5 Petits navires — Construction de la coque et échantillonnage — Partie 7: Détermination des charges des multicoques et de leur échantillonnage local en utilisant l'ISO 12215-5

Reference number ISO 12215-7:2020(E) © ISO 2020

ISO 12215-7:2020(E) 

COPYRIGHT PROTECTED DOCUMENT © ISO 2020 All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester. ISO copyright office CP 401 • Ch. de Blandonnet 8 CH-1214 Vernier, Geneva Phone: +41 22 749 01 11 Email: [email protected] Website: www.iso.org Published in Switzerland

ii



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Contents

Page

Foreword...........................................................................................................................................................................................................................................v Introduction................................................................................................................................................................................................................................. vi 1 Scope.................................................................................................................................................................................................................................. 1 2

3

Normative references....................................................................................................................................................................................... 1 Terms and definitions...................................................................................................................................................................................... 2

4 Symbols........................................................................................................................................................................................................................... 4 5

6

7

8 9

10 11 12

Application of this document................................................................................................................................................................... 6 5.1 Materials........................................................................................................................................................................................................ 6 5.2 Limitations................................................................................................................................................................................................... 6 5.3 Overall procedure for the application of this document...................................................................................... 7

Main dimensions, data and areas........................................................................................................................................................ 7 6.1 Dimensions and data.......................................................................................................................................................................... 7 6.1.1 General...................................................................................................................................................................................... 7 6.1.2 Bottom deadrise of the hulls βx and chine beam BCx of planing multihulls.................. 7 6.1.3 Wet deck bottom............................................................................................................................................................... 8 6.1.4 Crossbeams............................................................................................................................................................................ 8 6.2 Areas.............................................................................................................................................................................................................. 11 Dimensions and pressure for panels and stiffeners under local loads.....................................................14 7.1 General......................................................................................................................................................................................................... 14 7.2 Example of application on multihulls................................................................................................................................ 14 7.2.1 Sections.................................................................................................................................................................................. 14 7.2.2 Details on panel assessment and dimensions...................................................................................... 16 7.2.3 The constant averaged pressure method................................................................................................. 16 7.2.4 Other assessment and dimensioning methods.................................................................................... 17 7.2.5 Panels acting as "natural" stiffeners............................................................................................................. 17 7.3 Other topics on panel or stiffener dimensions.......................................................................................................... 17 Local pressure-adjusting factors.......................................................................................................................................................17

Local design pressures.................................................................................................................................................................................24 9.1 General......................................................................................................................................................................................................... 24 9.2 Limits of areas....................................................................................................................................................................................... 24 9.3 Tables defining the local design pressures for multihulls............................................................................... 24 9.4 Design pressure for trimaran floats PTRFx .................................................................................................................... 27 9.4.1 Pressure reduction factors.................................................................................................................................... 27 9.4.2 Pressure................................................................................................................................................................................. 27 9.5 Design pressure on watertight bulkheads and integral tanks..................................................................... 27 Further treatment of structural elements subject to local loads.....................................................................27 Assessment of multihulls rudders, appendages and their wells......................................................................28

Multihull global loads....................................................................................................................................................................................28 12.1 General......................................................................................................................................................................................................... 28 12.2 Typical structural arrangements........................................................................................................................................... 28 12.3 Global load assessment.................................................................................................................................................................. 30 12.3.1 General................................................................................................................................................................................... 30 12.3.2 The simplified method.............................................................................................................................................. 30 12.3.3 The enhanced method............................................................................................................................................... 31 12.4 Design stresses under global loads..................................................................................................................................... 32 12.5 Global load case GLC1: Diagonal load in quartering sea................................................................................... 32 12.6 Global load case GLC 2: Rig loads.......................................................................................................................................... 33 12.7 Combination of diagonal load GLC 1 and rig load GLC 2 for sailing multihulls............................. 33 12.8 Global load case GLC 3: Asymmetric broaching loads in sailing multihulls..................................... 33

© ISO 2020 – All rights reserved



iii

ISO 12215-7:2020(E)  12.9

13 14 15

Global load case GLC 4: Longitudinal broaching/pitchpoling...................................................................... 34 12.9.1 General................................................................................................................................................................................... 34 12.9.2 Full method of analysis of the buoyancy load when the craft pitchpoles..................... 35 12.10 Global load case GLC 5: Longitudinal force on one hull..................................................................................... 36 12.10.1 General................................................................................................................................................................................... 36 12.10.2 Longitudinal force......................................................................................................................................................... 36 12.11 Global load case GLC 6: Bending of crossbeams connecting hulls for motor catamarans... 37

Structural arrangement for supporting global loads...................................................................................................38 Multihulls used as commercial craft and workboats....................................................................................................38

Information to be included in the owner's manual........................................................................................................38 15.1 General......................................................................................................................................................................................................... 38 15.2 Respect of maximum loaded displacement.................................................................................................................. 38 15.3 Operational guidance...................................................................................................................................................................... 38 15.4 Information to take care of sandwich plating............................................................................................................ 38 15.5 Information required by Annex J of ISO 12215-5:2019 - for commercial craft and workboat.................................................................................................................................................................................................... 38

Annex A (informative) Application sheet of ISO 12215-7.............................................................................................................39 Annex B (informative) "Established practice" recommendations for global loads assessment using FEM methods and reporting..................................................................................................................41 Annex C (informative) "Established practice" details.......................................................................................................................43 Annex D (informative) Technical background and example of torsional moment analysis with differential deflection of crossbeams.............................................................................................................................51 Bibliography.............................................................................................................................................................................................................................. 58

iv



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www​.iso​.org/​directives). Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www​.iso​.org/​patents). Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO's adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www​.iso​.org/​ iso/​foreword​.html. This document was prepared by Technical Committee ISO/TC 188, Small craft. A list of all parts in the ISO 12215 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www​.iso​.org/​members​.html.

© ISO 2020 – All rights reserved



v

ISO 12215-7:2020(E) 

Introduction The reason underlying the preparation of this document is that standards and recommended practices for loads on the hull and the dimensioning of small craft differ considerably, thus limiting the general worldwide acceptability of boat scantlings. This document has been set towards the minimal requirements of the current practice.

The dimensioning according to this document is regarded as reflecting current practice, provided the craft is correctly handled in the sense of good seamanship and operated at a speed appropriate to the prevailing sea state in a safe and responsible manner, having due cognisance of the prevailing conditions.

Implementation of this document allows to achieve an overall structural strength that ensures the watertight and weathertight integrity of the craft. This document is intended to be a tool to determine the scantlings of a craft as per minimal requirements. It is not intended to be a structural design procedure.

The mechanical property data supplied as default values in this document make no explicit allowance for deterioration in service nor provide any guarantee that these values can be obtained for any particular craft. Like the other parts of ISO 12215, this document was developed to assess the structure of recreational craft up to 24 m LH, but it can also be used, where relevant, for non-recreational craft, workboats or yachts with an IMO load line length of up to 24 m, with the necessary critical mind.

vi



© ISO 2020 – All rights reserved

INTERNATIONAL STANDARD

ISO 12215-7:2020(E)

Small craft — Hull construction and scantlings — Part 7: Determination of loads for multihulls and of their local scantlings using ISO 12215-5 1 Scope This document defines the dimensions, local design pressures and global loads acting on multihull craft with a hull length (LH) or load line length of up to 24 m (see Note). It considers all parts of the craft that are assumed watertight or weathertight when assessing stability, freeboard and buoyancy in accordance with ISO 12217 (all parts). Scantlings corresponding to the local design pressures are then assessed using ISO 12215-5. NOTE The load line length is defined in the OMI "International Load Lines Convention 1966/2005", it can be smaller than LH for craft with overhangs. This length also sets up at 24 m the lower limit of several IMO conventions.

This document is applicable to multihulls built from the same materials as in ISO  12215-5, in intact condition, and of the two following types: — recreational craft, including recreational charter vessels; — commercial craft and workboats.

It is not applicable to multihull racing craft designed only for professional racing.

This document is applicable to the structures supporting windows, portlights, hatches, deadlights and doors. For the complete scantlings of the craft, this document is intended to be used in conjunction with ISO 12215-8 for rudders, ISO 12215-9 for appendages of sailing craft and ISO 12215-10 for rig loads and rig attachment in sailing craft. ISO 12215-6 can be used for additional details. Throughout this document, unless otherwise specified, dimensions are in (m), areas in (m2), masses in (kg), forces in (N), moments in (Nm), Pressures in (kN/m2) (1 kN/m2 = 1 kPa), stresses and elastic modulus in (N/mm2) (1 N/mm2 = 1 MPa).

2 Normative references

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 8666:2020, Small craft — Principal data

ISO 12215-5:2019, Small craft — Hull construction and scantlings — Part 5: Design pressures for monohulls, design stress, scantlings determination ISO 12215-8:2009, Small craft — Hull construction and scantlings — Part 8: Rudders

ISO 12215-9:2012, Small craft — Hull construction and scantlings — Part 9: Sailing craft appendages

ISO  12215-10:2020, Small craft — Hull construction and scantlings — Part 10: Rig loads and rig attachments in sailing craft © ISO 2020 – All rights reserved



1

ISO 12215-7:2020(E)  ISO  12217-1:2015, Small craft — Stability and buoyancy assessment and categorization — Part 1: Nonsailing boats of hull length greater than or equal to 6 m ISO 12217-2:2015, Small craft — Stability and buoyancy assessment and categorization — Part 2: Sailing boats of hull length greater than or equal to 6 m ISO 12217-3:2015, Small craft — Stability and buoyancy assessment and categorization — Part 3: Boats of hull length less than 6 m

3 Terms and definitions For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses: — ISO Online browsing platform: available at https://​w ww​.iso​.org/​obp

— IEC Electropedia: available at http://​w ww​.electropedia​.org/​

3.1 multihull craft with two or more hulls with a connecting wet deck (3.8)/crossbeams above the loaded waterline, as opposed to a tunnel boat or scow Note 1 to entry: See Clause 6 and Figure 2 for the main dimensions of a multihull.

3.2 design categories description of the sea and wind conditions for which a craft is assessed to be suitable Note 1 to entry: The design categories are defined in ISO 12217 (all parts).

Note 2 to entry: The definitions of the design categories are in line with the European Recreational Craft Directive 2013/53/EU.

[SOURCE: ISO 12215-5:2019, 3.1.]

3.3 loaded displacement mLDC mass of water displaced by the craft, including all appendages, when in fully loaded ready for use condition Note 1 to entry: The fully loaded ready for use condition is further defined in ISO 8666.

[SOURCE: ISO 12215-5:2019, 3.2.]

3.4 mass in minimum operating conditions mOC mass of the craft in minimum operating condition

Note 1 to entry: The minimum operating condition is further defined in ISO 8666.

3.5 sailing craft craft for which the primary means of propulsion is wind power Note 1 to entry: It is further defined in ISO 8666.

Note 2 to entry: In this document, non-sailing craft are considered as motor craft.

2



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  [SOURCE: ISO 12215-5:2019, 3.3.] 3.6 beam of hull BH beam across the outer hulls

Note 1 to entry: The measurement of the beam of hulls is specified in ISO 8666.

3.7 chine beam BC beam at chine of planing hulls

Note 1 to entry: It is further characterized in 6.1.2.

3.8 wet deck underside area of the structure connecting hulls with an area greater than 5 % LH BH

Note 1 to entry: Some multihulls (3.1) have no wet deck but just crossbeams. i.e. connecting beams.

3.9 craft speed V for motor craft, maximum speed in calm water and mLDC condition that is declared by the manufacturer, expressed in knots [SOURCE: ISO 12215-5:2019, 3.6.]

3.10 displacement craft motor craft whose speed is such that V < 5 LWL

[SOURCE: ISO 12215-5:2019, 3.7, modified - the definition is reworded.]

3.11 displacement mode mode of running of a motor craft in the sea such that its mass is mainly supported by buoyancy forces

Note 1 to entry: This is the case where the actual speed in a seaway in mLDC condition is such that its speed/ length ratio makes the craft behave as a displacement craft (3.10).

[SOURCE: ISO 12215-5:2019, 3.8, modified - in the definition, "craft" is replaced with "motor craft".] 3.12 planing craft motor craft whose speed is such that V ≥ 5 LWL

Note 1 to entry: This speed/length ratio limit has been arbitrarily set up in this document, but it can vary from one craft to another according to hull shape and other parameters.

[SOURCE: ISO 12215-5:2019, 3.9, modified - the definition is reworded.]

3.13 planing mode mode of running of a motor craft in the sea such that a significantly part of its mass is supported by forces coming from dynamic lift due to speed in the water Note 1 to entry: A planing craft (3.12) in calm water runs in planing mode, but it can be obliged to significantly reduce its speed when the sea gets worse, running in that case in displacement mode (3.11). © ISO 2020 – All rights reserved



3

ISO 12215-7:2020(E)  [SOURCE: ISO 12215-5:2019, 3.10, modified - the definition slightly reworded and "craft" replaced with "motor craft".]

3.14 non-walking area area of the craft comprising those areas defined in the owner's manual as being both outside of the working deck and where people are not liable to stand or walk in normal or emergency operation, and those of the working deck of a multihull (3.1) with an inclination of more than 25° against the horizontal in the longitudinal and transverse directions Note  1  to  entry:  All other areas of the working deck, cockpit bottom and superstructures are deemed to be walking areas.

4 Symbols

Unless specifically otherwise defined, the symbols shown in Table 1 are used in this document. The symbols are shown by group type and in alphabetical order. Unless otherwise specified, all dimensions, measured in mLDC condition, are according to ISO 12217. Table 1 — Symbols, dimensions, factors, parameters

Symbol

Unit

Reference/ Clause concerned

Designation/Meaning of symbol General dimensions and data

BBH

Beam between hulls as defined in Table 4

m

Beam between centres of buoyancy

m

Beam at the inside of wet deck/beam connection with hulls at section x

BC

m

BCP

m

BCB B WDx BH

Chine beam at 0,4 LWL from the origin used for kDYNM1 and P BMUP BASE

6.1.1, Fig 1 & Table 7

Beam between upper shrouds chainplates

Annex B

6.1, 12.5 & Fig 2

6.1.3 & Fig 2

Beam of hull according to 3.6

6.1 & Fig 2

m

Depth of hull at overhang root

Table 11, Fig 9

m

DWL

 

DROH

6.1, Fig 2 & Annex D

m

BnOHi LnOHi

m

Beam at overhang root, n = F(fwd) M(mid), A(Aft), and i = H(Hull), F(Float) Table 11, Fig 9 Length of overhang, n = F(fwd) M(mid), A(Aft), and i = H(Hull), F(Float) Design Waterline plan or section

Table 11, Fig 9

6.1.3, Figure 2

hSIDEx

m

LBB

m

Length between main beams centre of inertia

Annex B & C

m

Length of waterline

Fig 2

HSUPx LC i

m m

LH

m

mLDC

kg

LFLOAT LWL

mMO TC V

AD

4

m

m

kg

Height of mid panel of cockpit side or stiffener below overflow level Height of mid panel or stiffener above the lesser of ZSDTMx or ZSDAMx Length of crossbeam i

Length of hull

Length of a trimaran float

Mass of craft in fully loaded condition

Mass in minimum operating condition

m

Max canoe body draught (see Figure 2)

m2

Panel or stiffener supported area

Knots

Craft maximum speed in mLDC condition

Panels, stiffeners and local dimensions and data



Table 5 it. 10

Table 5 it. 10

Table 11, Fig 9

1

9.4 & Fig 9 3.3, 9

3.4, 11

Fig 2, 9.3

3.9, Table 5 it. 2 Table 5 it. 9

© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  Table 1 (continued) Symbol

Unit

b

mm

Small unsupported dimension of panel plating

mm

Stiffener length: long unsupported dimension of stiffener (frame/ stringer)

l s lu

Qx

mm mm  

Designation/Meaning of symbol

Large unsupported dimension of panel plating

Stiffener spacing (small unsupported dimension of stiffener) Point at section x where the pressure is assessed

Tx

m

Local canoe body draught at section x (see Figure 2)

ZTx

m

Height of local canoe body above DWL at section x (usually  4BnOH i

GLC 4a Longitudinal broaching

GLC 5b Longitudinal force

Hull/floats Wet deck if LnOHi > 4 DnOHi if LWD ≤ 0,4 LHb

Crossbeams Crossbeams Quartering sea to be Crossbeams hull/floats hull/floats checked in Design categoif ΣLc  ≤ 0,4LHb ries A and B sail and motor if LnOHi > 4 BnOH i if LnOHi > 4 DnOHi Crossbeams hull/ Crossbeams For sailing multihulls, Crossbeams floats hull/floats GLC1 and GLC2 combined if Lic ≤ 0,4 LHb if LnOHi > 4 BnOHi if LnOHi > 4 DnOHi according toc

GLC 6 Free standing

Usually only relevant for motor

LnOHi is the length of overhang or between supports with n  =  F(fwd), A(aft) and M(mid) and i  =  H(hull) of F(Float) BnOHi is the beam at overhang root or between supports with n  =  F(fwd), A(aft) and M(mid) and i  =  H(hull) of F(Float) DnOHi is the depth at overhang root or between supports with n = F(fwd), A(aft) and M(mid) and i = H(hull) or F(Float).

a

b c

d

LWD is the length of the wet deck and LCi he lengthwise dimension of crossbeam i.

Combine 0,5 GLC1 + GLC2 or GLC1 + 0,5 GLC2 whichever the greater. Only for sailing multihulls.

See Figures 9 to 14.

NOTE   The wish to simplify calculations and the limited bending moments due to small overhangs or distance between supports, and hulls/floats with large beam or depth are the basis for the exemption of checking.

12.3.3 The enhanced method

This method analyses as follows the craft through a modelisation of the loads exerted when moving in a seaway. a) Sailing multihulls:

1) When sailing upwind, the loads from the rig (given by ISO  12215-10 or equivalent) induce longitudinal and transverse forces and moments on the craft, which are balanced by forces and moments from the hulls and appendages. The resulting loads on the structure are similar to load cases GLC 2 to GLC 4 defined in 12.4 but adjusted so that the whole system is globally balanced (zero final forces and moments). 2) When sailing in waves or swell in a quartering sea, the loads of indent 1) shall be combined with GLC 1. 3) When sailing downwind, the loads of indent 1) shall be combined with GLC 5. NOTE

GLC 6 is usually not relevant, as less demanding than GLC 3 or GLC 4.

b) Motor multihulls:

All combinations of GLC 6 with GLC 1 and GLC 3 to GLC5 shall be assessed, or its worst combination.

c) Analysis method:

FEM analysis, using beam elements and/or full modelisation shall be applied. The stresses shall not be greater than the ones defined in Table 12.

The scale and method of meshing are quite sensible and need experience and specific expertise in the applied method compared to other methods.

© ISO 2020 – All rights reserved



31

ISO 12215-7:2020(E)  12.4 Design stresses under global loads The stresses (direct, shear, or buckling) deriving from single or combined global loads shall not be greater than the design stress for global loads defined in Table 12. When analysing stiffeners with an analytic method for global loads, such as crossbeams, beams (tubular or not), etc., there is no need to check deflection. Table 12 — Design stresses for global loads

Tensile/compressive design stress

Design shear stress

Design buckling stresses

σd

τd

σ db , τ db

Material FRP

Aluminium alloys Steel

N/mm2

N/mm2

0,5 σut and 0,5 σuca

Laminated wooden frames Solid stock wooden frames Plywood on edge frames

0,7 σyw 0,8 σy

0,5 τu

b

0,7 σywb 0,45 τu

c

0,45 σuf

0,4 τ buckling

0,45 σy

0,45 σufc 0,4 σuf

N/mm2

0,5 σ buckling

0,4 τu

c

0,45 τu

NOTE   These design stresses also apply for the attached plating of the stiffener, according to its material, determined according to ISO 12215-5:2019. is considered where stressed in compression (usually the stiffener top flange) and σt is considered where stressed in tension (usually the plating); both verifications need to be calculated. a   σ c

b   For welded stiffeners. If aluminium stiffeners are not welded, i.e. riveted, glued, etc. the non-welded properties

shall be used.

for laminated wooded stiffeners and σuf for solid stock shall be taken from Table E.1 of ISO 12215-5:2019: For plywood, σuf shall not be taken from Table E.2 but from Tables E.3 or E.6 of ISO 12215-5:2019. c   σ uf

NOTE    The design stresses are the same as in ISO 12215-5:2019 for stiffeners, and this relatively high value (or low safety factor) is connected to the use, where relevant, of kDYNM in load formulas.

12.5 Global load case GLC1: Diagonal load in quartering sea

The loads considered are those induced when a catamaran is supported by the two adjacent crests of a swell of wave one at the aft of the port hull, the other at the front of the starboard hull. Similar situation for a trimaran, replacing the port hull by the port float. The design torsional moment under quartering waves and parameters are defined in Table 13 and Figure 10. Table 13 — Global load GLC1 — Design torsional moment in quartering sea (see Figure 10)

Torsional moment MTD around transversal axis

Diagonal length for catamarans Diagonal length for trimarans

0,5 mLDC M TD = k DC ×

1 000

LDIAG =

L WL

× ( 9 , 81 × k DYNM ) × 0 , 076 LDIAG ( kNm ) where

= L WL ² + B CB ² ( m ) where α = Atan

B CB

(degree) L WL cosα Diagonal between the aft end of the port float and the fore end of the starboard float, not to be taken >1,4 LWL

NOTE 1   The factor 0,076 corresponds to a symmetrical triangular loading on a beam simply supported (q1L2/12) with a distance between supports of 046 LDIAG. The symmetrical triangular loading corresponds to a load greater in the middle (more accommodation) than at the ends. See Figure 10 b).

The formula for torsional moment is a proposed default value, but it may be replaced by any documented value, including a full calculation derived from the buoyancy calculated from the intersection of the hull with a sinusoidal swell, with the masses distributed according to a detailed bill of masses. 32



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

a) Diagonal length assessment

b) Support of the craft

Key 1 crest of swell or wave 2 through of swell or wave

Figure 10 — Sketches explaining how load case LC1 is defined

12.6 Global load case GLC 2: Rig loads The rig loads acting on the craft's structure shall be according to ISO  12215-10, meeting, where relevant, the heel and trim conditions defined therein. They shall be balanced with the other loads, such as buoyancy, hydrodynamic forces and moments and masses. The load increase due to dynamic effect shall be considered.

Established practice recommendations for global load assessment and reporting are given in informative Annex B.

12.7 Combination of diagonal load GLC 1 and rig load GLC 2 for sailing multihulls

Generally, the loads from rig can be considered as point loads (mast compression, shroud or mainsheet pull). When a load is not directly applied to a crossbeam, it can be decomposed into its fraction directly applied to the crossbeam plus a torsional moment.

When combining GLC 1 and GLC 2, one shall consider 0,5 GLC 1 + GLC 2 or GLC 1 + 0,5 GLC 2 whichever the greater.

12.8 Global load case GLC 3: Asymmetric broaching loads in sailing multihulls

Asymmetric broaching of a sailing catamaran occurs when it digs both front ends with horizontal transverse pressure corresponding to the lateral resistance of the hulls/float profile. For a trimaran, the force is applied on the leeward float and the hull, see Figure 11. The force is applied at mid-hull/ float depth.

It is considered that the front leeward part of hulls and floats are loaded as shown in Figure 11 and Table 14. The pressure is a linear pressure varying from zero at the foremost transversal bulkhead or crossbeam connecting the two hulls, to a maximum pressure at the stem. This force is therefore acting at 2/3 of the distance between fore bulkhead/crossbeam to stem.

© ISO 2020 – All rights reserved



33

ISO 12215-7:2020(E) 

a) Sailing catamaran

b) Sailing trimaran

Figure 11 — Asymmetric broaching loads (sailing multihulls only) Table 14 — Global load GLC 3 — Asymmetric broaching (see Figure 11) Definition Total resultant transverse force directed windward Resultant force on leeward hull/float fore overhang

Value F T1MAX (N)

a × F T1MAX at 0,67 LFOH (catamaran) or LFOHF (trimaran)

Resultant force on windward hull/float fore overhang (1−a) × FT1MAX at 0,67 LFOH (catamaran) or LFOHF (trimaran) Where

F T1MAX is the maximum value of the transverse forces (N) exerted by the sail plan in sail configuration 1 of ISO 12215-10, and; a = 0,67

a = 0,5

where there is no crossbeam between hulls or floats; and; where there is a crossbeam between hulls or floats.

Where there is no front crossbeam, the strength of the front of each hull or float shall be assessed as a cantilever longitudinal beam under the resultant force, Same assessment for catamarans with transverse front crossbeam, but for trimarans, a specific calculation considering the different stiffness/strength of hull and float is needed.

12.9 Global load case GLC 4: Longitudinal broaching/pitchpoling 12.9.1 General

A multihull, sail or motor, broaches when digging the stem of a hull/float into a wave which causes a deceleration force corresponding to the longitudinal loads defined below. The longitudinal dynamic energy is usually absorbed by a longitudinal righting moment called pitchpoling. The shear force and bending moment in the hull /floats and in the crossbeams resulting from the vertical buoyancy shall be checked, so that the resulting stresses are not greater than the design stresses defined in Table 12. To simplify, this checking need not be performed for hull/floats when LOHi ≤ 4 DOH, where, see Figure 12;

— LOHi is the relevant distance between supports or overhangs = LFOH, LAOH, LOFn, LFOH for hulls LFOF, LAOF, LFOF for floats, and 34



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  — DOH is the local depth at the root of the hull/float at overhang (point of max bending moment) either forward DFOH or aft DAOH. The loading may also be assessed by one of the methods given in 12.9.2.

12.9.2 Full method of analysis of the buoyancy load when the craft pitchpoles This method normally corresponds to the earlier occurrence of the following situations: — either bow down trim angle of 20°, or

— immersion of the deck at the stem (main hull for trimarans). Additionally, for sailing craft:

— the rig load and corresponding angle of heel/trim shall be according to ISO 12215-10;

— for more information, one may use the pitchpoling condition of ISO  12217-2:2015 but using the loaded displacement mLDC (ISO 12217 uses minimum operation condition mMO).

a) Buoyancy force FB and reactions of crossbeams where the deck at stem is immersed before 20°

b) General dimensions of hull or float and sketch of forces and reactions in crossbeams Figure 12 — Sketch of vertical forces and reactions on crossbeams when pitchpoling Figure 12 shows the front and aft forces FA1 and FA2 or the total buoyancy force FB and the values of LFOH, BFOH and DFOH or LAOH, BAOH and DAOH for respectively the front and aft overhangs, beam and depth as defined in Table 11 and shown in Figure 12 b). Annex D gives examples of the determination of FB and of the EI products of each crossbeam. © ISO 2020 – All rights reserved



35

ISO 12215-7:2020(E)  Where the enhanced method of 12.3.3 is used, the leeward hulls are asymmetrically loaded, as in GLC 3, and the leeward hull usually supports a higher loading than the windward one.

12.10 Global load case GLC 5: Longitudinal force on one hull 12.10.1 General

This load case considers the longitudinal force, defined in Table 15 and occurring either when hitting a floating object/whale or a steep wave. The resulting shear force and bending moment in the crossbeams or wet deck shall be checked, so that the resulting stresses are not greater than the design stresses defined in Table 12. To simplify, this checking need not be performed, as required in Table 11, where: — the length of the wet deck LWD >0,4LH for structural configuration a),

— the sum of the lengths of the crossbeams ΣLCi >0,4LH for structural configurations b) and c), — the length of the main crossbeam LCM > 0,4LH for structural configuration d). 12.10.2 Longitudinal force

Figure 13 shows the crossbeams and the beam between hulls BBHi for a multihull with 3 crossbeams, and Table 15 gives the longitudinal forces on hulls and crossbeams. Table 15 — Global load LC5 — Longitudinal force (see Figure 13) 1-Direct longitudinal force on hulls Longitudinal force on stem of catamaran hull F LC

F LC = min (2,5 mLDC; 2,5 mHULL) (kN)

Longitudinal force on stem of trimaran float F LT

F LT = min (5 mLDC; 5 mFLOAT ) (kN)

Where mHULL and mFLOAT are respectively the mass of one catamaran hull or one of the trimaran floats. NOTE 1   These forces respectively correspond to about 0,25 g and 0,5 g decelerations. 2-Resulting longitudinal force on crossbeams

 EI  B3  BHi

FLi = FL × 

Longitudinal force F Li acting on crossbeam i

  /  i

 EI   (N ) ,   BHi  i

∑  B 3

see Annex D, with F L = F LC or F LT where relevant

Longitudinal bending moment about a vertical axis at the MLi = F Li × BBi (Nm) connection of the crossbeam with the hull

 

NOTE 2   The EI value for each crossbeam is calculated about a vertical axis. (See Annexes C and D and ISO 12215-6).

36



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

a) Catamaran

b) Trimaran

Figure 13 — Longitudinal force on hull of catamaran or float of a trimaran

12.11 Global load case GLC 6: Bending of crossbeams connecting hulls for motor catamarans. Table 16 and Figure 14 give the shear force and bending moment on the crossbeams connecting hulls of motor catamarans. This bending moment may be shared by several crossbeams. This also applies where "classical" crossbeams are replaced by a continuous structure or a great number of small beams. For motor trimarans, unless using another specific documented method, the shear force, and corresponding bending moment, shall be taken as the one exerted by the float considered fully immersed. This case is similar to the one shown in Figure 12 but only when heeling. The resulting stresses shall not be greater than the design stresses defined in Table 12.

Table 16 — Global load LC6 — Design bending moment and shear force for motor catamarans 0,5 M B = k DC ×

Total design Bending moment MB on crossbeam(s)

mLDC 1 000

0,5 F = 0 , 25 × k DC ×

Total design shear force F on crossbeam(s)

0,5 × 9 , 81 × k DYNM ×

mLDC 1 000

B CB 8

( kNm )

× 9 , 81 × k DYNM ( kN )

Figure 14 — Bending moments and shear forces in GLC 6

© ISO 2020 – All rights reserved



37

ISO 12215-7:2020(E) 

13 Structural arrangement for supporting global loads The structural arrangement shall be able to support and/or transmit local and global loads, without exceeding the design or buckling direct or shear stress defined in Table 12. Annexes  C and D give respectively examples of "established practice" or technical background calculation. Annex  B gives "Established practice" recommendations for global loads assessment and reporting.

14 Multihulls used as commercial craft and workboats

For multihulls used as commercial craft and workboats, Annex J of ISO 12215-5:2019 shall be applied in conjunction with this document.

15 Information to be included in the owner's manual 15.1 General

The information specified in 15.2 and, where relevant, in 15.3 to 15.5 shall be included in the owner's manual.

15.2 Respect of maximum loaded displacement

The owner’s manual shall include the following warning.

“CAUTION — The value of the maximum loaded displacement mLDC for multihulls has a greater direct influence on the loads than it has for monohulls. Exceeding its design value can cause significant load increase, for example a lower wet deck clearance inducing much higher pressures. Overloading shall therefore be avoided.”

15.3 Operational guidance

The owner’s manual shall include the following warning.

“The owner is advised that he/she is responsible for ensuring that the normal mode of operation is maintained. This means that the speed of the craft needs to be matched to the prevailing sea state, and that the craft is used ‘with good seamanship behaviour.’ ”

15.4 Information to take care of sandwich plating

Where sandwich outer skin is thinner or with lower fibre mass than the "good practice" values of Annex I of ISO 12215-5:2019, include the following information in the owner's manual, or any equivalent or more detailed information:

"CAUTION — The outer skin of your craft is strong enough to resist the design pressure but can suffer from local damage from hitting hard/sharp objects. If the outer skin is damaged, it shall be repaired immediately.”

15.5 Information required by Annex J of ISO 12215-5:2019 - for commercial craft and workboat Where relevant, include the information required by J.3 of ISO 12215-5:2019.

38



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Annex A (informative)

Application sheet of ISO 12215-7 Tick valid cell or give value Catamaran   Trimaran   Other, specify   Sail   Motor, displacement   Motor, planing   Steel   Aluminium   Wood   FRP   Symbol Unit Value LH m   LWL m   BH m   BC m   mLDC kg   V knots   TC m   β0,4 degree   Description kDC Tick cell A 1,00   B 0,80   C 0,60   D 0,40   Description   Tick cell Recreational/Charter  Use   Annex J Workboat light duty   of ISO Workboat heavy duty   12215-5 Use Annex  L of ISO 12215-5:2019

Type of multihull

Description

Type of multihull

Type of propulsion functioning mode

Building material Craft main data (Table 1) Length of hull Length waterline in maximum loaded condition Beam of hull Chine beam at x/LWL = 0,4 Loaded displacement Maximum speed in mLDC condition (motor craft) Maximum draught of canoe body Deadrise at 0,4 LWL (planing craft only) Design category (Table 5):

Type of usage Clause 14 and Annex J of ISO 12215-5;2019, where relevant Analysis method of local loads

© ISO 2020 – All rights reserved



39

ISO 12215-7:2020(E)  Analysis of global loads enter Yes or No Is the structural arrangement “Typical” according to Figure 9? enter Yes or No If the result is “No” the enhanced global load analysis needs to be performed and results produced If the result is “Yes” the simplified global load analysis needs to be performed but the simplified method may be used, and results produced, if this is the case click the simplified global load analysis performed Structural GLC GLC GLC GLC GLC GLC GLC arrangement (Fig 9) 1 2 1 and 2 3 4 5 6 a               b and c               d              

40



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Annex B (informative)

"Established practice" recommendations for global loads assessment using FEM methods and reporting

B.1 Examples of "Established practices" Examples of established practice in global loads assessment include:

— for sailing multihulls, balancing the rig/buoyancy loads and masses; — the simplified method for global load, GLC 4 (see 12.9);

B.2 Guidelines for reporting the structural analysis with FEM method Any structural analysis report, whatever the numerical calculation method is used, submitted, where relevant, to notify body or approbation office, should include the following information: Model description

— Reference units (of length, force, pressure, etc.) and geometric origin of the model — Reference of plans (CAD, 2D drawing…) used, including dates and versions — Numerical software used, including versions and dates — Modelling assumptions — Element types — Mesh size

— Any deviation in geometry and arrangement of structure compared with plans — Plot of complete model in 3D view

— Plot to demonstrate correct structural modelling — Plot to demonstrate assigned properties

— Bill of material properties used in the model Load and boundary conditions

— Details of boundary conditions

— Details of all load combination with calculated hull girder shear force, bending moment and torsional moment distributions — Plot of applied loads in 3D view — Sum of total load applied Design criterion

— Summary of allowable deflexion © ISO 2020 – All rights reserved



41

ISO 12215-7:2020(E)  — Summary of allowable stresses

— Details of selected composite failure criteria For each load case result:

— Details of reaction at boundary conditions

— Plots and results to demonstrate correct behaviour of structural model under the applied load combination — Summary and plots of global displacements

— Summary and plots of stresses to demonstrate that allowable stress are not exceeded anywhere in the structure — Contour plots for:

— Composite failure criteria

— Ply stresses, when relevant

Analysis used

— Linear or non-linear static analysis — Buckling analysis

— Other, if required: modal analysis, fatigue, etc.

42



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Annex C (informative)

"Established practice" details

C.1 Details for the connection of crossbeams with the hulls The connection between the crossbeams and the hulls transmits loads by shear flow (see the arrows in the drawings). This is mainly the case where the plating has an angle  3bewd.

44



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  The assessment is made for each bulkhead/crossbeam, checking that the direct (tensile, compressive) or shear stresses are below the design stresses of Table 12 for global loads, i.e.:

— direct compressive/tensile stresses in top and bottom flanges (analysed either with or without attached plating); — shear stresses in webs analysed according to Table C.1 and shear buckling stresses analysed in C.3.4 and Table C.2;

— increased direct and shear stresses from secondary bending moments from eventual cut-outs in the webs of crossbeams analysed according to Table C.3; — loads, and reactions defined in this Annex are correctly introduced by shear in the web;

— there is no abrupt discontinuity in the flanges and webs to avoid stress raisers, including the detailed recommendations of ISO 12215-6.

C.3.2 Method of analysis

The crossbeams are considered as I-beams, with the following simplifications: For a "high" I-shaped crossbeam, the following assumptions are usually made: a) the shear force is only resisted by the web;

b) the bending moment is only resisted by the upper and lower flanges, with eventual use of attached plating. More sophisticated analysis methods can be applied provided that they use sound engineering.

C.3.3 Dimensions, sections, neutral axis

Where the deck is added at the end of the construction, the link between the bulkhead and the web may be not fully efficient, and some designers do not consider the deck as an attached plating (see Figure C.2). A conservative calculation therefore only considers the flange/reinforcement connected to the web and neglecting the attached plating effect of the deck (at top) and, where relevant, wet deck (at bottom). The total section, position of yG (neutral axis), second moment I, and section modulus are calculated, to verify that the tensile or compression design stress, whichever is the lesser, is not exceeded. Clause H.4 of ISO 12215-5:2019, explaining stiffener calculation, may be used, especially if different materials are used in the beam. Table C.1 gives, in contrast, an example of calculation for an I-shaped beam where deck and wet deck are part of the upper and lower attached plating.

© ISO 2020 – All rights reserved



45

ISO 12215-7:2020(E) 

Key 1 top reinforcement flange

Figure C.2 — Sketch of a bulkhead without considering the deck as an attached plating

46



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  Table C.1 — Shear forces in a structural bulkhead — Simplified beam analysis  

The shear force and bending moment are derived from the load case The top and bottom flanges are constituted by: — the deck attached plating

— extra top flange width btf, section btf × ttf

— extra bottom flange, width bbf, section bbf × t bf — the bottom/wet deck attached plating.

The width of top and bottom shell section is the attached plating as defined in ISO 12215-5:2019. All dimensions in mm and sections in mm2.

Annex H of ISO 12215-5:2019 dealing with stiffeners is used. ISO 12215-6 can be used for explanations.

Key 2

deck reinforcement for mast compression

3

4 identical UD GRP angles L × H

4

stiffener to introduce the mat compression

τ=

F

HW ×t W where F

Hw tw

q=

τcr

10

−3

HW

10 −3 to be ≤ τd and 0,40 τcrt defined below, kN,

mm, mm,

τd

F

Shear stress in the web

shear force from load case;

height of the web, measured between the CG of flanges; web thickness (sum of 2 skins tw/2);

N/mm2

design shear stress of the web defined in Table 13;

N/mm

shear flow, therefore τ =

N/mm2

critical shear buckling stress for defined in Table C.2; q

tW

(N/mm2).

NOTE   The example shown applies to one of the possible FRP arrangements.

C.3.4 Shear buckling analysis

C.3.4.1 Single skin shear buckling Large panels subject to shear tend to buckle and make wrinkles at 45° (Wagner field). This buckling may not be catastrophic in single skin construction and has been used for metal construction in aircraft industry, as it allows a lighter structure. In that case, the edges of the panel are overstressed and need a specific analysis. Where the dimension of the panels of the web are reduced by the use of vertical stiffeners, these stiffeners are loaded by the shear flow in the web and need a specific analysis, out of © ISO 2020 – All rights reserved



47

ISO 12215-7:2020(E)  the scope of this document. Examples can easily be found in aircraft design literature on spar beams, see e.g. References [2] and [3]. C.3.4.2 Sandwich shear buckling

In FRP, single skin and sandwich construction, shear buckling shell generally be avoided, unless a specific documented analysis based on practical experience is performed. Table 12 recommends a shear stress ≤40 % of the critical shear buckling stress. Table C.2 gives a method to define the value of the critical shear buckling stress in a single skin or sandwich panel. Table C.2 — Critical shear buckling stress in single skin and sandwich 1-Critical shear buckling stress for a single skin panel b  τ cr =  5 + 6  × E t l 

t × s  b 

  

2 (N/mm2)

2-Critical shear buckling stress for a symmetrical sandwich panel

(

Et × t s + t c τ = 2 , 98 × k SB × cr b2

b 5, 3 + 4 ×   l

k SB =

 E t   t s ×tc × 2  GC   b

1 + 5, 4 × 

where

)2

(N/mm2), with

2

2   b   4 , 3 3 × + ×      l   

shear stress factor,

Et

N/mm2

tensile modulus of the skins or the laminate;

tc

mm

thickness of the core;

Gc ts b l

N/mm2 mm mm mm

shear modulus of the core; thickness of the skins;

small dimension of the panel; large dimension of the panel.

C.3.5 Compression buckling and skins stability Where a sandwich bulkhead located below a deck is supporting a compression: — The deck core shall be able to locally support/transmit this compression.

— The bulkhead sandwich shall be able to support/transmit this load without surpassing the design (direct, shear or buckling) stress. It may need to be stabilized by a stiffener as shown in the Figure in Table C.1. This may lead in some cases to complex compression/shear stability calculation, bibliographic references in this document and in ISO 12215-5 can be helpful.

C.3.6 Eventual cut-out in the web C.3.6.1 Shear stress

F ×Q , where F is the I ×t shear force, and Q and I are respectively the first and second moments. In beams with thin webs, the In a thin web made of a homogeneous material, the shear stress is the ratio τ =

48



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

shear is nearly constant in the web and the concept of shear flow q is often used, where q = τ × t = For I-beams with thin webs, q = τ × t ≈ close to the actual height of the web.

F ×Q I

F , where H is the distance between the CG of flanges and very H

The example given in C.3.6.2 deals with a passage/opening cut in a web inside the hulls as shown in Figure C.3. The web usually needs to be reinforced at the edges of the opening, as q2 > q1 , see double hatched areas in Figure C.3 a), so that τ2 ≤ τd.

Where H1 ≠ H2, the shear forces are distributed on the top and bottom webs, according to the second moment of the top and bottom I-beams defined below, and create a secondary bending moment at the angles. C.3.6.2 Secondary bending moment This secondary bending moment M 1 =

q×a×b 4

(N.mm) can be very high, as explained in the last cell of

Table C.3 and it is often needed to round/fair the angles to limit this moment, which may then be approximated lowered to M2=α M1where α may be about 0,7. The same formula could be used to calculate the secondary bending moments at the bottom of the opening.

To resist this bending moment without exceeding the bending stress, the section often needs, in addition to rounding/fairing, to be made as an I-beam, adding a reinforcing flange around the opening (the lower flange being the deck, wet deck or hull plating). CAUTION — The stresses in the top or bottom of an I-beam (deck, or bottom of hull) add to the existing bending stress.

The section of maximal bending moment is along the distance H1 in Figure C.3. It is along this direction that the section modulus or the resisting bending moment are assessed against MBS1 or MBS2. Where necessary, the attached plating of the deck wet deck or hulls are used to calculate the section.

Other reinforcement methods may be used, e.g. continuous framing along the edges, etc. see References [2] and [3]. Table C.3 — Shear force and bending moment in a framed cut-out in a shear web Location

Shear flow/ bending moment

Before cutting out

Initial shear flow

After cutting out

Shear flow in remaining top and bottom webs where H1=H2

Formulas q1 = 10 −3

F a + 2H 1

q 2 = 10 −3

τ2 =

F 2H 1

q2

( N / mm )

( N / mm )

N / mm 2

tW shear stress to be ≤ τd and τcr

NOTE The formulas in the bottom of the last column of this Table give the maximal bending moment aligned with the diagonal of the cut-out, it is valid with pure shear stress and frames with constant stiffness, see References [2] and [3].

© ISO 2020 – All rights reserved



49

ISO 12215-7:2020(E)  Table C.3 (continued) Location

Shear flow/ bending moment

Cut-out dimensions

Bi-symmetrical statically undetermined system

Formulas For a shear flow q2 (N/mm²/mm), dim in mm, the shear forces in top and bottom of web are: q ×b q ×a F2 = ± 2 (N) F1 = ± 2 2 2 The bending moments at angle.is q ×a×b M1 = 2 (N.mm) 4

 

NOTE The formulas in the bottom of the last column of this Table give the maximal bending moment aligned with the diagonal of the cut-out, it is valid with pure shear stress and frames with constant stiffness, see References [2] and [3].

a) Cutting in a bulkhead

b) Secondary bending moments

Figure C.3 — Openings in a bulkhead and secondary bending moments due to shear

50



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

Annex D (informative)

Technical background and example of torsional moment analysis with differential deflection of crossbeams

D.1 General The structure of a multihull in the sea can be analysed as a rectangular frame with perpendicular loads. Usually the main beams are built-in into the hulls. This is a statically indeterminate structure for which the strain energy method is one of the methods to resolve this indetermination. Computational methods, such as multi frame, grid analysis or FEM, can be used, but this is often out of reach of small craft designers, builders and certification bodies, and simplified methods are sought. This Annex presents simplified methods of analysis.

In these simplified methods, the hulls are assumed to be much stiffer than the beams, which is acceptable as the hull depth is >10 times the beam depth. In that case the hulls are considered "rigid" and the strain energy (bending and torsional) only affects the beams, with no twist of the hulls.

D.2 Theory

Figure D.1 — Multihull (with 3 crossbeams) The total strain energy developed by the torsional design moment under global sea load MT defined in Table 13 is resisted by torsional energy and bending energy in the beams.

© ISO 2020 – All rights reserved



51

ISO 12215-7:2020(E)  Table D.1 — Analysis formulas 1-Preliminary calculations Torsional design moment from Table 13

0,5

M TD = k DC ×

Total strain energy equals that from MTD

UB =

UT =

Strain energy in bending

∑

∑

θ=

∑ x i*

* x CT

Ei .Ii

Gi .Ji BBH

xi =

θ

x i*

−

* x CT

1 000

× ( 9 , 81 × k DYNM ) × 0 , 076 LDIAG

UB + UB = 0,5 MTD × θ 6E i I i × z² B Bi

1

where

mLDC

2

3

=

Gi J i ×θ ² B Bi M TD

12 E i I i × x 2 B Bi 3

+

∑

6E i I i × x ²×θ ² B Bi 3

where

strain energy in torsion (twisting) and Gi J i

∑B

Bi

angle of twist of the hulls

m

longitudinal distance, from an arbitrary datum, to CG of a crossbeam or centre of twist

m

longitudinal distance, between the datum and the centre of twist

x*

CT

∑

=

12 E i I i x i *

∑

B Bi 3 12 E i I i B Bi 3

kNm2

bending rigidity of each cross beam;

m

longitudinal distance, between each crossbeam centroid and the centre of twist

kNm2 m

radian

torsional rigidity of each cross beam;

average of the transverse distances between hulls, see 6.1 the angle of twist of the hulls

NOTE   The formula for twist angle could be corrected to include the torsional stiffness of the cross beams (i.e. ∑GJ/L) but this normally only affects the twist by a few per cent and the complication is not justified. However, for continuous ‘double-bottom’ style wet decks composed of wet deck and deck to constitute a ‘closed-cell’ the torsional stiffness may be more important than the bending stiffness 2-Final calculations

Once θ, is determined, the bending moment and shear force for each cross-beam at a distance x can be determined as follows. Bending moment in the cross beam i

Shear force in the crossbeam i

M Bi =

FBi = MB =

6 E i I i ×θ × x i B BHi 2

2 M BHi B BHi

=

( kNm )

12 E i I i × θ × x i B BHi 3

( kN ) or

FB × B BH 2

Bending moment at ends of BBH with F B = F B1 = F B2 where BBH is the average value of BBHi

The cross beams can then be analysed per Annex C.

CAUTION — The above method is only applicable to closed sections, i.e. with no significant opening in the hulls, as shown in Figures D.1 and D.2. As most of the cruising multihulls have large opening in the hulls, though covered by a large coachroof, this simplified method is questionable for this type of craft.

52



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  Table D.1 (continued) REMARKS: The ‘GJ’ term may be neglected for ‘open’ section or if a conservative solution is required. The shear strain energy is negligible for a catamaran with just two or three beams, but for a ‘double bottom’ style wet deck + deck + girders extending over 50 % of the LWL this might not be the case. So, providing the full formula might be helpful for craft, which are close to the limit in meeting the requirements. If the ‘GJ’ term is neglected, one can see that the torsional moment of the hulls due to quartering sea global load is resisted by the bending moments in the beams which are loaded by differential deflection: the beams are considered fully fixed at their connection with the hulls and one end is lifted relatively to the other.

D.3 Worked example D.3.1 General

The following worked example shows an application of the theory explained in Table D.1 It uses only two beams for simplicity, but it is a first step towards the analysis of more beams as given in D.3.4. This method also considers the torsional strain energy, which the simplified 2-beams method of Table D.1 does not.

D.3.2 Full method

Figure D.2 — Worked example — Sports catamaran The craft is a sports catamaran (see Figure D.2) with the following data and calculation of MTD taken from Table 13 and given in Table D.2.

© ISO 2020 – All rights reserved



53

ISO 12215-7:2020(E)  Table D.2 — Worked example calculation 1-Preliminary calculation - excerpt of a Table according to Annex H of ISO 12215 with kBB = 1GRP Infused N°

Ply

 

 

UD

Total

 

3

dry vol type mass frac

type

1 2

Fibre

 

G,C

1,60

G

1,60

BD

2,00

DB

ϕ

ti

E

Ei× ti

ψ

kg/

 

 

 

30 401

47 501

m frac

m2

0,40

0,59

0,98

1,56

 

0,40

0,59

0,98

5,08

0,40 0,40

0,59 0,59

0,98 0,98

N/mm2

mm

G G

5,20

t/w

1,95

18 750

1,56

8 460

19 169

 

36 622

G

Gi×ti

N/mm2

 

 

 

2 649

4 139

2 649

13 219

97 341

2-Preliminary calculation - following

5 174

8 476

13 244

4 442

22 558

σut  

σuc  

σuf

N/mm2

 

578 426 614

291 263 345 90

86

110

203 196 249

Forward Beam   Round tube aluminium alloy 6061 T6 non-welded σuw = 240 N/mm2 σd = 168 N/mm2 D

mm 150 H

mm 100

 

t walls

   

mm

B  

180

Detail of calculation:

5,0

E1

G1

I1

E1I1

N/mm2

N/mm2

mm4

MNm2

E2

G2

I2

E2I2

70 000

26 923 5,99E+06

J1

G1J1

mm 5,0

N/mm2 19 169

N/mm2 4 440

mm4

σd1

MNm2

cm3

N/mm2

J2

G2J2

SM2

σd2

0,420

1,20E+07

MNm2

mm4

0,323

Aft Beam      Rectangular GRP tube (see data in item 1)

t walls

SM1

mm4

MNm2

4,67E+06 0,089 5 1,02E+07 0,045 5

Forward beam (1) = 150 mm outside diameter, 5 mm wall thickness

80

cm3 93

168

N/mm2 100

Aluminium alloy 6061 T6 welded tube E1 = 70 000 N/mm2, G1 = E1/2,6 = 26 923 N/mm2. σd1 = 81 N/mm2 E1I1 = E1 × π/64 (Do4 − Di4) = 70 000 × π /64 (0,154 – 0,144) = 0,42 MN.m2.

G1J1 = G1 × π /32 (Do4 − Di4)= 26 538 × π /32 (0,154 – 0,144) = 0,318 1 MN.m2.

Aft beam (2) = 100 mm deep × 180 mm wide≈ 5 mm wall thickness rectangular tube GRP s in Item 1 E2 = 16 196 N/mm2, G2 = 4 442 N/mm2)

E2I2 = E2 × (Bo3Ho3 − Bi3H13)/12 = 16 169 × (0,18 × 0,103 – 0,17 × 0,093)/12 = 0,089 6 MN.m2. G2J2 = 4 G2 A2t/p

A = area enclosed by mid-wall thickness line = 0,175 × 0,095 = 0,016 6 m2. p = perimeter of this line = 2 × (0,175 + 0,095) = 0,54 m t = wall thickness = 0,005 m

G2J2 = 4 × 4 4 440 × 0,016 62 × 0,005/0,54 = 0,045 4 MN.m2.

54



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E)  Table D.2 (continued) 3-Calculation of the Torsional moment according to GLC1 LH

LWL

BBH

BCB

LBB

12,00

9,00

7,00

8,00

8,00

 

 

 

 

 

m

m

 

m

Num x

Denom x

xCT

m

m

m

 

 

m

m

mLDC

kDYNM

0,80

2 250

1,24

41,63

 

 

 

 

 

1

Denom Denom 1 of θ 2 of θ  

kDC

Cat B

kg

θ

 

0,117

0,02

6,59

0,165

0,05

0,103

m

N

Nm

N/mm2

σd/σi

m

Forward beam

x1

F1

1,408

2 127

∑

12 E i I i x *

M1

7 445

σ1

93,2

CF1

1,80

 

x2

deg

 

 

 

 

Aft beam

N

Nm

 

 

F2

6,592

 

1

 

rad

α

 

M2

2 127

7 445

3.1 Using the full method

 

σ2

Ldiag

MTD

SF U

12,04

0,022 4

2,0

0,045

 

 

 

 

 

m  

LC1

MNm

   

CF2

N/mm2 σd/σi 79,7

1,26

           

 

1            

Mtu  

MNm            

With LBB = 8 m, the applied torque = 22,4 kN.m (i.e. 0,022 4 MN.m). The span of each beam is BBB = 7 m. Taking the aft beam axis at the datum (so only the forward beam has a non-zero x*): x=

B BHi 3

12 E i I i

∑B

3 BHi

(

)

= 12 × 0 , 42 × 10 / 7 3 / 12 × 0 , 089 5 / 7 3 + 12 × 0 , 42 / 7 3 = 6 , 59 m .

i.e. the axis of twist is closer to the stiffer forward beam. The angle of twist is now found from θ =

∑

12 E i I i x 2 B Bi

3

M TD

∑

12 E i I i × x 2 B Bi

3

+

Gi J i

∑B

Bi

= 12 × 0 , 089 5 × 6 , 59 2 / 7 3 + 12 × 0 , 42 × ( 8 − 6 , 59 ) / 7 3 = 0 , 170 6 + 0 , 027 = 0 , 165 MN.m 2

G J

∑ BiBii =0 , 323 / 7 + 0 , 0455 / 7 = 0 , 05 MN.m

Hence θ = 0,022 5/(0,165 + 0,05) = 0,103 radians

REMARK: The twist angle is only an interim figure as part of a strength analysis of the cross beams and is not suitable for any stiffness analysis. The force can now be calculated for each beam: F =

2 M BA BB

=

12 E I × θ × x BB3

For the forward beam: x1 = 8-6,59 = 1,408 m

F1 = 12 × 0,42 × 0,103 × 1,408/73 = 2,127 × 10−3 MN = 2 127 N

M1 = F1 × BB /2 = 2,127 × 10−3 x 7/2 = 7,445 × 10−3 MN.m = 7 445 Nm For the aft beam: x2 = −6,592 m

F2 = 12 × 0,065 42 × 0,896 × 6,592/73 = 2,127 × 10−3 MN

M2 = F2 × BB /2 = 2,127 × 10−3 × 7/2 = 7,455 × 10−3 MN.m.m Maximum bending stress:

Forward beam σ1 = 7 455 /80 = 93,2 MPa compliance factor = 168/93,2 = 1,8 Aft beam σ2 = 7 455 /93 = 79,70 MPa compliance factor = 100/78,7 = 1,2

CAUTION — If the aluminum tube is welded σd would be 81 instead of 168 and the compliance factor would be 0,87 and a bigger aft beam would be needed. © ISO 2020 – All rights reserved



55

ISO 12215-7:2020(E)  Table D.2 (continued) NOTE   Ignoring the shear stiffness would increase θ to 0,02/0,197 6 = 0,101 2 radians. The force from 1,593 × 10−3 MN to 2,0 × 10−3 MN, a 25 % increase.

Therefore, for the torsional moment only, one can see that, with two beams, by matter of symmetry, the forces at the end of each beam are identical, and so are the bending moments. This would not be the case with 3 cross beams. CAUTION — For sailing craft, the loads from the rig would need to be added as required by Table 11 with a completely different effect.

D.3.3 Special case of two cross-beams only (suitable for small sports sailing catamarans) When there are only two beams, one normally located near the forward end and one nearer the aft end, and the torsional stiffness is small enough to be neglected, there is no need to carry out the full calculations since F1 = F2 = MT/LBB. EXAMPLE

F1 =F2 = MT/LBB = 0,022/8 = 0,002 127 MN = 2 127 N as in the example in Table D.2.

The bending moment in the beams is (see D.3.2) MB = F × BB/2.

Hence, the full method is only required when there are more than two cross-beams.

D.3.4 General case of more than 2 cross-beams

When there are more than 2 cross-beams, D.3.3 does not apply. The full method shall be used. A tabular method is recommended.

Alternatively, a finite element model may be used. As the aim is only to assess the strength of the crossbeams, beam-elements may be used with the hull modelled as ‘near-rigid’ elements. The cross-beams are assumed to be built-in at the intersection of the cross-beam with the demi-hull on one side. The other demi-hull, being nearly rigid, may be loaded by a couple composed of two equal and opposite vertical forces. In applying the method, a number of simplifications may be used, see Figure D.3: — The determination of the effective span is uncertain in some cases.

— The geometry is greatly simplified as demi-hull centroids and cross-beam end nodes are displaced in reality.

While it is possible to accommodate some of these issues by more sophisticated modelling such as node offsetting, the following approach is recommended: — analyse the highly idealised model as a ‘screening tool’ to detect whether cross-beam strength is an issue; — if so, create shell and beam FEA model and investigate further.

For catamarans with deep cross-beams, the global strength may not govern scantlings. Before proceeding to a more sophisticated analysis it might be worth conducting sensitivity studies with increasingly worse-case assumptions on beam span.

56



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

a) Real model

b) Simplified models with 3 rectangular beams Figure D.3 — Simplified model

D.3.5 Special case of a continuous cross-structure as found in some motor catamarans The method is less suitable where the cross-structure is continuous fore and aft over a significant length of the craft. Such bridging structures often consist of a ‘dry-deck’ and ‘wet-deck’ connected by plate floors and girders similar to a traditional ship double bottom. The bridging structure is essentially a grillage or grid.

D.3.6 Recommended application of this annex

This method is intended to indicate whether stress levels under global ‘pitching torque’ are significant. It is probably most applicable for:

— Screening checks on cruising sailing/motor catamarans where the cross structure consists of 3 or 4 beams (forward carrying the fore stay in the case of a sailing craft), central accommodation/ wheelhouse zone, aft beam);

— Racing catamarans consisting of two or three isolated cross beams where the simple space frame model/method is more realistic. — The method is not suitable for investigating trimaran cross-beams.

© ISO 2020 – All rights reserved



57

ISO 12215-7:2020(E) 

Bibliography [1]

ISO  12215-6,Small craft — Hull construction and scantlings — Part 6: Structural arrangements and details

[3]

Repair of double bullet S.H Myhre and J. Myhre AIAA

[2] [4]

[5]

58

Rules for the Classification and the Certification of Yacht. Bureau Veritas. NR 500-2012

Cours de résistance des matériaux à appliquée à l'Aviation (in French only)– Paul Vallat- 1945 Airframe stress analysis and sizing - Michael Chung-Yung Niu – Hong Kong Conmilit press



© ISO 2020 – All rights reserved

ISO 12215-7:2020(E) 

ICS 47.080 Price based on 58 pages

© ISO 2020 – All rights reserved