AALTO UNIVERSITY

School of Engineering

Department of Applied Mechanics

Oliver Parmasto

Mechanics of the passenger ship structure with non-longitudinal-load-carrying accommodation decks

Thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in

Technology

Espoo, 04.11.2012

Supervisor: Professor Jani Romanoff (Aalto University)

Instructors: D.Sc. (Tech.) Heikki Remes. (Aalto University)

D.Sc. Hendrik Naar, (Tallinn University of Technology)

Aalto University, P.O. BOX 11000, 00076 AALTOwww.aalto.fi

Abstract of master's thesis

ii

Author Oliver Parmasto Title of thesis Mechanics of the passenger ship structure with non-longitudinal-load-carrying accommodation decks Department Department of Applied Mechanics Professorship Naval Architecture Code of professorship Kul-24 Thesis supervisor Professor Jani Romanoff (Aalto University) Thesis instructors D.Sc. (Tech.) Heikki Remes (Aalto University) D.Sc. Hendrik Naar (Tallinn University of Technology) Date 04.11.2012 Number of pages 53+6 Language English

Abstract

The current thesis investigates a cruise ship structural concept which enables to use large

interchangeable modules for interior outfitting. The structure has non-longitudinal-load-

carrying accommodation decks and a narrow deckhouse. The hull-deckhouse interaction

and performance of the proposed structure under vertical bending is determined and

compared to a conventional cruise ship structure which has internal longitudinal bulkheads

for carrying the shear forces in the superstructure. The investigation is conducted by

implementing Finite Element Method.

The results indicate that the removal of the decks from the conventional cruise ship

structure does not change the nature of the hull-deckhouse interaction. The responses of the

compared structures were strongly affected by shear lag hull-deckhouse interaction induced

secondary effects. It is also shown that the proposed structure can achieve the same stiffness

under vertical bending as the conventional cruise ship structure while achieving smaller

weight and the height of the vertical centre of gravity of the steel structure.

The investigation assures that even at the early design phase, the Finite Element Method is

the only reliable way to evaluate the response of the modern cruise ship structures.

Keywords hull-superstructure interaction; hull-deckhouse interaction; passenger ship; cruise ship

Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi

Magistrtöö resümee

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Autor Oliver Parmasto Töö pealkiri Mechanics of the passenger ship structure with non-longitudinal-load-carrying accommodation decks Teaduskond Department of Applied Mechanics Professuur Naval Architecture Kood Kul-24 Järelevaataja Professor Jani Romanoff (Aalto University) Instruktorid D.Sc. (Tech.) Heikki Remes (Aalto University) D.Sc. Hendrik Naar (Tallinn University of Technology) Kuupäev 04.11.2012 Lehekülgede arv 53+6 Keel English

Käesolev magistritöö uurib kruiisilaeva struktuuri konseptsiooni, mis võimaldab kasutada

suuri vahetatavaid mooduleid pealeehituse sisustamiseks. Pakutud struktuuril puuduvad

pealisehituses pikisuunalisi jõude kandvad dekid ning küljeplaadistus. Antud töös uuritakse

laevakere ja pealisehituse koostoimet pakutud kruiisilaeva struktuuris ning võrreldakse seda

traditsionaalse kruiisilaevaga millel on pealisehituses sisemised pikisuunalised vaheseinad

vertikaalse põikjõu kandmiseks ja suured avavused küljeplaadistuses. Antud töös kasutatakse

võrreldavate struktuuride uurimiseks Lõplike Elementide Meetodit ning võrreldavaid

struktuure vaadeldakse vertikaalse paindemomendi mõju all.

Tulemused näitavad, et võrreldud struktuurides oli pealisehituse ja laevakere vaheline

koostoime sarnane. Samuti ilmnes et shear lag nähtus mõjutas tugevalt uuritud struktuuride

käitumist. Tulemused näitavad veel et pealisehituse ja laevakere vaheline koostoime

põhjustab tugevaid sekundaarseid nähtuseid.

Keywords laevakere ja pealisehituse koostoime, reisilaev

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Acknowledgements

The current thesis was written in the Marine Structures research group as a part of the Aalto University

Program Cruise and Ferry in the Department of Applied Mechanics of Aalto University School of

Engineering. The financial support from FIMECC Innovation and Networks – research project is

gratefully appreciated.

I would like to thank D.Sc. (Tec.) Heikki Remes and Professor Jani Romanoff for their comments and

patience. The value of their support in the thesis writing process is impossible to overestimate. I would

also express my gratitude towards the other co-workers in the research group for bringing laugh and

joy into the daily routine.

I would also like to thank all my friends in Finland and in Estonia and also my family and especially

Susanna for the moral support during the thesis writing process.

Espoo 2012

Oliver Parmasto

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Table of Contents

Abstract of the Master’s Thesis…………………………………………………………………………………ii Magistritöö resümee…………………………………………..…………………………………………………iii Acknowledgments ………………………………………………………………………………………………iv Table of Contents……………………………………………………………………………………………….. v 1. Introduction .................................................................................................................................... 1

1.1 Background .............................................................................................................................. 1 1.2 State of the art .......................................................................................................................... 2 1.3 Aim of the thesis ....................................................................................................................... 7

2. Methods ......................................................................................................................................... 9 2.1 Calculation methods ................................................................................................................. 9

2.1.1 Finite Element Method ......................................................................................................11 2.1.2 Finite Element Method in ship structural design.................................................................12 2.1.3 Finite Element model of the investigated structure ............................................................14

2.2 Post-processing.......................................................................................................................16 2.2.1 Displacements ..................................................................................................................16 2.2.2 Stresses ...........................................................................................................................18 2.2.3 Forces and moments ........................................................................................................19

2.3 Description of research procedure ...........................................................................................19 2.3.1 Comparison of the proposed structure and conventional cruise ship structure ...................19 2.3.2 Sensitivity analysis............................................................................................................21

3. Results ..........................................................................................................................................23 3.1 Comparison of responses of the traditional and the proposed structure ....................................23

3.1.1 Hull-deckhouse interaction ................................................................................................23 3.1.2 Stresses and stiffness .......................................................................................................27 3.1.2 Forces and moments ........................................................................................................29 3.1.3 Secondary effects .............................................................................................................32

3.2 Sensitivity analysis ..................................................................................................................38 3.2.1 Thin and thick deckhouse side on a thin boat deck ............................................................38 3.2.2 Thin and thick deckhouse side on a thick boat deck ..........................................................41

4. Discussion and Conclusions ..........................................................................................................45 References .......................................................................................................................................50 List of Appendices .............................................................................................................................53 Appendix 1. The main frame of the traditional cruise ship structure (traditional) Appendix 2. The main frame of the proposed cruise ship structure (m2cell) Appendix 3. The main frame of design m2cell_1 Appendix 4. The main frame of design m2cell_2 Appendix 5. The main frame of design m2cell_3 Appendix 6. The main frame of design m2cell_4

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1. Introduction

1.1 Background

The interior outfitting and the general arrangement of the passenger vessels cannot be changed in

reasonable time and cost because outfitting is integrated into the steel structure of the vessel. For

example, cabin areas are constructed of modules which are welded to the decks. The water, HVAC,

electricity and other systems have then to be connected and finally floors are constructed using

various types of screeds which are then covered by carpets or other materials. After the completion,

the cabin modules cannot be removed easily, making conversions and refitting of the cabin areas

labour intensive and time consuming endeavour. Conversion of public areas is even more challenging

since in addition to removing the old interior, outfitting is completely installed in situ using prefabricated

elements. As a result, the interior of a passenger ship is static and cannot be adapted effectively for

different needs of various markets. Moreover, the long operational life of a cruise ship means that

several re-fittings are needed for keeping the vessel competitive in the cruise market. Consequently, it

has become appealing to seek new methods for facilitating outfitting and converting the cruise ship's

interior.

A new concept called m2cell has been proposed for rapid outfitting and conversion of the passenger

ship’s superstructure (Kauppi, 2012). This new concept intends to exploit large interchangeable

modules, size of which extend throughout two decks and accommodate a number of cabins or public

spaces. An example of the m2cell module is given in Figure 1 together with the illustration of their

positioning in the ship structure.

Figure 1. A m2cell module (Ylirisku, 2012) and their positioning in the ship structure (Kauppi, 2012)

However, the proposed modular outfitting system poses a number of challenges on the structural

design of the vessel. Firstly, due to the size of the modules, decks need to be removed from the

superstructure at the location of the modules. Secondly, since the modules are designed to be

interchangeable within a small timeframe, superstructure side shell will be offset from the side of the

Steel structure

m2cell modules

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main hull to a location near to the centre line. The concept of this kind of structure is new to cruise ship

design and needs to be investigated.

1.2 State of the art

From the beginning of building steel ships, the behaviour of passenger vessels has changed due to

increased size and structural complexity of newer generations of vessels. The understandings of the

behaviour and design principles of large passenger ships have also changed over time. A brief insight

into selected concepts of passenger ship structures is given in Figure 2.

Figure 2. Illustration of typical cross sections in equal scale and shear force flow in passenger ships

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The location of lifeboats and larger openings are also shown with their influence on the shear flow. All

these factors are crucial in the cruise ship structures since they determine the structural behaviour of

the overall response of the hull girder (deOliveira, 1983).

The relative size of the deckhouse in older generations of passenger ships (i.e. RMS Titanic in Figure

2), was small and it was often not considered when evaluating the response of the hull girder. The

outer shell of the hull was continuous with small porthole openings. Thus, the global response of the

structure was considered to follow Euler-Bernoulli beam theory. However, as the relative size of the

deckhouse increased, evaluation of its contribution to the global strength became important.

Numerous experiments conducted on the passenger vessels at the end of 1940’s indicated that the

longitudinal strains do not generally follow linear distribution in the mid-ship section like it is assumed

for Euler-Bernoulli beam (Vasta, 1949). One of the first theories describing this phenomenon stated

that the non-linarites in the longitudinal strain distribution are caused by the distortion of the combined

cross section of the hull and deckhouse, making Navier’s hypothesis inapplicable (Crawford, 1950).

However, it was assumed that Navier’s hypothesis is valid for the hull and the deckhouse separately.

In essence, the deckhouse was observed as an elastically supported beam because the longitudinal

and vertical forces resisting the relative displacement of the deckhouse and the hull at their

connections (Bleich, 1952). As illustrated in Figure 3, the longitudinal shear force in connection of the

deckhouse side will cause a moment resisting the moment in the deckhouse, meaning that the

curvatures of the deckhouse and the hull tend to differ.

Figure 3. Forces at the connection of deckhouse side and the hull

Consequently, in hogging condition the deckhouse tends to deflect into the main hull at the mid-ship.

This phenomenon is resisted by vertical stiffness of the main deck as illustrated in Figure 4.

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Figure 4. Deformed shape of the combined hull and deckhouse

As the understanding of the hull-deckhouse interaction improved, elaborate theories implementing

theory of elasticity appeared (Caldwell, 1957). Eventually, it became clear that the deckhouse has an

important influence on the global response of the passenger vessel and its effect has to be considered

regardless of its relative size. Even if the deckhouse is small, and the contribution to the overall load

carrying capacity is minute, throughout understanding of the hull-deckhouse interaction must be

obtained to avoid local failures, especially at the openings and the deckhouse ends (deOliveria, 1983).

After the revolution in air transportation in 1960-s, the intercontinental travelling by large ocean liners

declined and the share of cruising industry started to increase. Consequently, the design of large

passenger ships also changed. A demand for large open spaces and larger cabins with the sea view

contributed to increasing of the size of passenger ships. Eventually, deckhouse was replaced by

superstructure, sides of which were not offset from the hull side shell (i.e. MS Fantasy in Figure 2). A

deckhouse differs from a superstructure by definition. According to classification societies, a

deckhouse is a decked structure above the strength deck with the side plating being inboard of the hull

shell plating more than 4% of the breadth (DNV, 2009). A superstructure however is a decked

structure on the freeboard deck, sides of which are not offset from the hull side shell more than 4% of

the breath of the vessel (DNV, 2009).

As the size of the passenger ships grew, the lifeboats could not be stored on top of the superstructure

since they cannot be positioned higher than 15 meters from the design water line (IMO, 1999). As a

response, a recess was created in the superstructure for accommodating the life boats and muster

stations (i.e. MS Aida in Figure 2). Simultaneously, relative size of the openings for windows and

balconies at the sides of the superstructure increased, reducing the shear stiffness of the side shell

and started to have significant influence on the hull-superstructure interaction (Jaeger and Woortman.,

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1961; Muckle, 1962). The response of the cruise ship structures elaborated since in addition of the

offsetting of the sides of the superstructure, the effect of large side openings also had to be

considered. Shear deformation in the superstructure sides relieves normal stresses in the decks and

also causes difference in curvature of deckhouse and the main hull (Fransman, 1988).

For maximizing the number of outside cabins, the deckhouses became higher and were not widened

above the boat deck (i.e. MS Grand Princess in Figure 2). However, the top of the deckhouse still had

to be wide to provide valuable space for the sun deck. The growing demand for balcony cabins also

meant that the side shell of the superstructure could not be implemented for carrying the global shear

loads. Thus, internal longitudinal bulkheads which are offset from the sides of the hull were added for

carrying shear forces (i.e. GTS Millennium in Figure 2). In some modern designs, the side shell of the

deckhouse is not participating in the shear flow of the vertical shear force (Kujala, 2003).

The cruise ship structures have also elaborated due to fierce competition for a share in the cruise

market. A recent trend in the cruise business is to provide unique holistic experience for the customer

(Ahola, 2010). This has contributed to the appearance of novel design concepts such as the

superstructure with an internal promenade (i.e. MS Voyager of the Seas in Figure 2). As a result, the

structure of modern cruise ship is complex, with elaborate distribution of normal strains in the decks

(Naar et al., 2004). The increased size of the superstructure also means that in modern designs, over

50% of the vertical bending moment is carried by the deckhouse. However, most of the shear force is

carried by hull side shell (Kujala, 2003).

In 2009, a revolutionary design of a passenger ship appeared where the superstructure has been split

into two, creating a wide promenade (Oasis of the Seas in Figure 2). The cabins with balconies are

located both at the sides of the vessel and the promenade. However, in order to provide a wide

promenade, the size of the vessel had to be increased considerably. Although the design has greatly

improved the cruising experience for the passengers, it also has some drawbacks. The size of the

vessel makes its cost very high. There is also a restriction on the number of destination, thus making

the cruising experience less unique. Consequently, ship owners have become interested in smaller

vessels exclusively with balcony cabins for passengers (Ahola, 2010). As a response, a new cruise

ship concept known as XpTray was proposed (Bergström, 2010). The main frame of this concept is

illustrated in Figure 5. The main dimensions of the XpTray vessel are comparable to Voyager class

and it has exclusively balcony cabins for the passengers. As a result, the XpTray vessel has a very

narrow deckhouse when compared with the conventional passenger ship structures.

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Figure 5. Cross section of XpTray structure

When comparing XpTray structural concept with the conventional designs presented in Figure 2, it can

be seen that the mechanism of transmitting the shear forces is similar to the conventional cruise ship

design where the internal longitudinal bulkheads carry the shear load inside the superstructure (GTS

Millennium). The similarity stems from the fact that the boat deck plays an important role in carrying

the shear forces to the deckhouse. In the case of the XpTray, the structure is somewhat simpler than

in conventional design. The wide accommodation decks have been removed from the superstructure

which created a narrow deckhouse. The life boat recess is also absent, meaning that only the boat

deck participates in the flow of shear force in the case of the XpTray structure. The knowledge about

the influence of these changes on the hull-deckhouse interaction and load carrying influence is limited;

however, Bergström (2010) conducted extensive sensitivity analysis on the XpTray structure on the

feasibility point of view. Bergström (2010) concluded that the large openings in the side shell of the

deckhouse relieved the normal stresses in the deckhouse decks. However, high shear stress levels

were present on the deckhouse sides, especially at the connection of the deckhouse side shell and

the boat deck which required the use of very thick steel plating.

In essence, the m2cell structural concept requires similar changes to the conventional cruise ship

structure as the XpTray structure; although large openings are not needed in the deckhouse side of

the m2cell structure. In addition, the m2cell structure will have a wide sundeck. Thus, the challenges

regarding high shear stresses at the deckhouse sides might be avoided. However, considering the

complexity of the hull-deckhouse interaction and the overall design procedure of the cruise ship

structure, throughout understanding of the load carrying mechanism of the proposed structure has to

be obtained prior to further development of m2cell structural concept. Understanding of the load

7

carrying mechanism of the cruise ship structure is especially important in the optimisation phase of the

structural design process where the response of the same structure can vary considerably among

different designs (Remes et al., 2011). Thus, the impact of removing the decks from the superstructure

of the cruise ship and creating a narrow deckhouse has to be studied.

1.3 Aim of the thesis

The current work addresses two main concerns related to the structure which could meet the

demands posed by the m2cell modular outfitting concept. Firstly, the positioning of the deckhouse

sides close to the centreline and removal of wide accommodation decks imply that the nature of the

hull-deckhouse interaction and the load carrying mechanism might deviate considerably when

compared with traditional cruise ship structures. Secondly, the changes made to the structure,

especially the removal of wide accommodation decks, might have devastating effect on the

performance of the structure. Namely, the decks are considered vital in carrying the global vertical

bending moment. Even if the structure could carry the global bending moment, the vertical stiffness of

the structure should also be examined since the cruise ships are sensitive to the vibration issues.

When considering the first issue focusing on the hull-deckhouse interaction and the load carrying

mechanism, the challenge is to compare the response of the proposed structure with a common cruise

ship structure. However, the hull-deckhouse interaction and load carrying mechanism of the modern

cruise ship structures has not been described profoundly in literature.. Previous works addressing the

hull-deckhouse interaction are mainly focused on presenting the results from experiments on older

generations of passenger ships and simplified models or introducing various calculation methods for

evaluating the response of the passenger ship structures (i.e. Vasta, 1949; Bleich, 1952; Mukle, 1962;

Pauling and Payer, 1968; Fransman, 1988). However, these works are not investigating modern

cruise ship designs. Thereby, a modern structural concept of a conventional cruise ship will also be

examined in the scope of this work in order to establish the moment of comparison. Naturally, the

traditional structure has to be selected to be as similar as possible to the proposed structure. When

examining the structural concepts presented in Figure 2, it appears that the structural concept where

the shear forces are carried by the internal longitudinal bulkheads (GTS Millennium) may be used for

the comparison with the proposed structure. This claim is explained with the help of Figure 6, where

the cross sections of the proposed and the conventional cruise ship structures are compared.

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Figure 6. The conventional and the proposed structure

When observing the conventional structure in Figure 6, it is seen that above the life boat recess, the

shear forces are carried by the longitudinal bulkheads which are positioned close to the centre line of

the vessel. This means that in the case of the conventional structure, decks participate in the flow of

shear forces like it is needed for the proposed structure. When the superstructure side at the lifeboat

recess is relocated under the longitudinal bulkhead and the accommodation decks removed at the

outer side of the longitudinal bulkheads, the proposed structure is obtained. The proposed structure

will be created with the same scantlings as the conventional structure. In this stage, the emphasis is

on investigating three aspects. Firstly, focus will be on examining the differences in the hull-deckhouse

interaction of the proposed and the traditional structures under vertical bending. Secondly, the impact

of the changes to the stress levels and stiffness of the proposed structure will be evaluated due their

practical importance. Finally, the differences in the load carrying mechanism of the compared

structures will be investigated. The first stage of the current investigation will provide detailed

description and comparison of the hull-deckhouse interaction for traditional and the proposed

structure. The findings of the first stage would also indicate in what extent the absence of wide

accommodation decks would compromise the performance of the proposed structure.

At the second stage, the sensitivity analysis is conducted on the proposed structure. The aim is to

deepen the knowledge about factors influencing the load carrying mechanism and hull-deckhouse

interaction of the proposed structure with the goal to enhance its performance. The second phase

should reveal whether the proposed structure could achieve the same vertical stiffness as the

traditional structure using reasonable measures.

The work is limited to the static analysis of the proposed and the traditional structure under vertical

bending moment. The current thesis will not focus on the structural behaviour under torsion and

horizontal bending nor does it address the issues related to the dynamic response. These tasks will be

left for the future work.

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2. Methods

The current chapter describes the methods used in the current thesis. In principle, the current chapter

can be divided into three parts. The first part describes the calculation methods and modelling

techniques used for evaluating the response of the investigated structures. The second part focuses

on the means to analyse the obtained results for describing the load carrying mechanism and hull-

deckhouse interaction of the investigated structures. The third part will describe the research

procedure which is followed for comparing the responses of the investigated structures and the

sensitivity analysis of the proposed structure.

2.1 Calculation methods

When investigating the hull girder bending, it is traditionally assumed that the behaviour of a ship

structure follows Euler-Bernoulli beam theory (Hughes et al., 2010). This means that a number of a

priori assumptions have been made on the deformation kinematics of the cross-section of a ship

structure:

1) the cross-section is rigid on its plane

2) the cross-section rotates around the neutral surface

3) the cross-section remains perpendicular to the neutral surface

These assumptions hold fairly well in long, slender and relatively continuous ship hull girders under

moderate transversal loading (deOliveira, 1983). In cases of the ship structures where shear induced

deflections become important; Timoshenko beam theory has been applied where the third assumption

of Euler-Bernoulli beam theory is dismissed. The previous two theories are often referred to as

classical beam theories (Carrera, 2011). However, it has been shown that the distortions occur in the

cross section of large passenger vessels, making classical beam theories inapplicable in these kinds

of vessels (Bleich, 1952). Thus, a number of methods have been proposed for investigating the

behaviour of passenger ships (deOliveira, 1983).

Earliest calculation methods for evaluating the response of the passenger ships were developed at the

time when computers were not effectively used in the ship design. Thus, the earliest methods were

based on the theory of strength of materials among which classical beam theories played a focal role.

One of the first methods which found wider implementation in the design process was provided by

Bleich (1952) and was based on the two beam approach described in the previous chapter

(deOliveira, 1983). A number of theories have appeared thereafter which fall into the same category

(i.e. Chapman, 1957; Muckle, 1962; Schade, 1966; Naar et al.2004).

There are also methods based on the theory of elasticity implementing plane stress theory (Caldwell,

1957). Caldwell’s theory has been enhanced by many authors to take into account the openings in the

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side of the deckhouse and geometrical discontinuities (i.e. Jaeger and Woortman, 1961). However,

implementing these methods in design office routine is demanding.

Currently, advances in the computing technology and software have facilitated the evaluation of the

structural response of passenger vessels. For example, Finite Element Method (FEM) is sufficiently

reliable for investigating the modern cruise ship structures (ISSC, 1997). However, the demands on

the functionality of the passenger ship structures have increased considerably during last decades.

Consequently, the structural design issues should already be addressed in the conceptual design

phase of the innovative cruise ships (Remes et al., 2009). However, in case of the ship structures,

implementing FEM in the iterative design process is time-consuming and thereby not suitable for the

use in the early design phase. Thus analytical and semi-analytical methods still play an important role

in the passenger ship design due to their speed and flexibility when compared with FEM. For example,

methods proposed by Caldwell (1957) and Jaeger and Woortman (1961) have been adapted for

implementation with a computer, thus making them useful at early design phases (Fransman, 1988). A

relatively simple, yet fairly useful approach was provided by Heder and Ulfvarson (1991) where 3D

FEM analysis of a passenger ship structure was reduced to 2D. The sides of the structure were

described with orthotropic plate elements which took into account the presence of openings whereas

the decks were represented with bar elements which was defined by taking into account the reduced

efficiency of the deck due to the shear lag.

A similar approach to Bleich’s (1952) work was offered by Naar et al. (2004) where the cruise ship

structure was divided into a number of beams with vertical and horizontal coupling. This, Coupled

Beams method has been integrated into a powerful conceptual design platform which also

encompasses local response and strength models together with elaborate optimisation capability

(Remes et al. 2009).

There are also more robust approaches to optimizing the ship structures in the early design phase. In

case of the ship hull girder which follows fairly well beam theory, the optimization in the concept

design phase is usually carried out implementing 2D section models (Klanac and Jelovica, 2009; Rigo

2001). In these cases, a common approach is to minimize the weight and production costs. The

stiffness of the structure is then maximised by demanding a larger moment of inertia (Rigo, 2001). A

similar approach has been implemented also for the cruise ships (Andric & Zanic, 2010; Richir, 2010;

Caprace et al., 2010). The method comprises initial evaluation of the cruise ship structure with 3D

FEM for obtaining the normal strain distribution. Then the optimisation is conducted on the 2D section

assuming that the normal strains will be distributed similarly in the different designs. This approach

has been questioned by some authors (Remes et al., 2011).

However, in the current work, a novel cruise ship structure is investigated without the aim to reach the

best design solution. Thereby, FEM is suitable for the current work since FEA based methods are

currently considered as most reliable means for investigating the structural response of passenger

ships (ISSC, 1997).

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2.1.1 Finite Element Method The central idea of the Finite Element Methods (FEM) is to divide the continuum with infinite degrees

of freedom (DOF) into discrete sub-regions with a finite number of DOF (Zienkiewicz,1971). This kind

of idealisation means that various physical phenomena can be treated numerically inside the

continuum under investigation. Since a steel ship structure is under investigation in the current thesis,

it is appropriate to describe FEM for an elastic continuum with the displacement approach

(Zienkiewicz, 1971).

The elastic continuum of the structure can be divided into structural elements interconnected by a

finite number of points at which the resultant force from the actual stress on the element boundaries is

introduced (Turner et al. 1956). The displacements at the points of connection of the elements, also

known as nodal displacements, are the unknowns for which the system will be solved. A typical

element is defined by a finite number of nodes and its boundaries. Let there be an element with n

nodes occupying the volume . The displacements at any point inside the element can be defined by

displacement at nodes as functions

( , , )( , , )( , , )

= [ ]{ } = [ ( , , ), … , ( , , ) ] (2.1)

where [ ] is a shape function used for approximating the displacements inside the element from the

nodal displacements { } where

= , [1, ] (2.2)

When the displacements are known at any point inside the element, the strains can also be

determined for any point inside the element. These can always be presented in the following notation

(Zienkiewicz 1971)

{ } = [ ]{ } (2.3)

where { } is a strain vector and [ ] is known as deformation matrix. It should be noted that the shape

functions [ ] are already incorporated in the deformation matrix. Assuming elastic behaviour, the

relation between strains and stresses will be in linear form

{ } = [ ]{ } (2.4)

where [ ] is known as elasticity matrix and is determined by the physical properties of the material.

Knowing the stresses inside the material, the elemental nodal forces can be obtained which are

determined statically by boundary stresses as

{ } = [ ] [ ][ ] { } (2.5)

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where the integral is known as elemental stiffness matrix (Zienkiewicz 1971).

[ ] = [ ] [ ][ ] (2.6)

Knowing all the external forces at the nodes of the element, the displacements can be found by

demanding equilibrium of forces at the nodes

{ } = { } = [ ]{ } (2.7)

The displacements can also be found by using virtues of variation calculus and demanding that the

virtual work performed by external forces is equal to the one of internal forces. The other possibility

could be to minimize the potential energy of the whole system. However, these lead to solving the

same system of linear equations and are in principle different mathematical approaches for

interpreting the same physical phenomenon.

The principles implemented for a single element can be extended to the whole structure so that the

overall system of equations needed to be solved are in the same form as (2.7) (Zienkiewicz, 1971).

However, successful application FEM assumes the use of proper element types, meaning that the

stiffness matrix of the element needs to be defined correctly for describing the physical phenomenon.

Moreover, the degree of simplifications made for modelling the problem needs to be appropriate. All

this means that proven practices need to be followed when dividing the structure into elements and

choosing the types of elements used for modelling.

2.1.2 Finite Element Method in ship structural design The analysis of the ship structures is generally performed in two stages. The global response is

investigating by a coarse mesh model and then local response is evaluated by separating areas of

interest, re-meshing them with finer mesh and applying boundary conditions from the global analysis

(ISSC, 1997). Consequently, a vast number of FE models are used for evaluating the response of the

passenger ship structures. Since the current work is limited only to global analysis of the proposed

ship structure, the principles used for coarse mesh modelling is described in this paragraph.

The level of discretisation of the global ship model depends on the complexity and size of the model.

Ship structure is generally modelled by assembling structural elements such as stiffened panels and

stiffeners. A stiffened plate is composed of a plate and its stiffeners, considered as secondary

stiffeners. The web frames and girders are considered as primary stiffeners. The classification of

stiffeners is illustrated in Figure 7.

13

Figure 7. Classification of stiffeners (Amini, 2009)

The primary stiffeners are explicitly modelled due to their significant influence on the response of the

structure (Amini et al, 2009). The stiffened panels can be modelled with elements with equivalent

stiffness where the behaviour of the plate and secondary stiffeners has been homogenised into one

element (Hughes et al., 1983; Avi 2012). In global analysis, structural details such as window and door

openings with their stiffeners are also modelled using homogenised coarse mesh elements (Amini,

2009).

Another approach is to use a combination of beam and shell elements to represent the stiffened panel.

An example of this is lumping where the stiffness and mass properties of all the secondary stiffeners

on the panel are represented by beam elements located at the edge of the shell elements (Hughes,

1983). This method is also accepted by classification society when passenger ship structure is

investigated at the global level (DNV, 2007).

Naturally, if the size of the problem allows, the secondary stiffeners can be modelled explicitly. A

common practice for modelling the secondary stiffeners is the offset beam concept (Ehlers, 2011). As

illustrated in Figure 8, quadrangular shell elements are used for modelling the web and two node

beam elements are used for modelling the flange of the stiffener.

Figure 8. Discretisation of stiffeners with offset beam technique (Ehlers, 2011)

14

The minimum length of the beam element is the same as for the shell elements meaning that no

reduction of minimum element length is caused with the discretisation. In case of using the previously

described method, it must be kept in mind that the moment of inertia and the area of the combined

shell and beam elements has to be equal to the one of the modelled stiffener’s (Ehlers, 2011).

The curved surfaces of the hull structure are usually discretised with plate finite elements due to the

complications managing the shell elements (Amini, 2009). This means that approximation also

includes faceting of the surface which results in overestimation of the stiffness. However, this is a

common engineering practice and when the element size is appropriately selected; the error is not

significant (Sörensen, 1969). In case of passenger ships, classification societies demand the use of at

least two plate elements at the turn of the bilge. (DNV, 2007)

Generally, the boundary conditions are not used in global FE-models where the whole structure is

modelled. The model is loaded so that the system is in equilibrium and a small number of nodes are

fixed to avoid rigid body motions. The symmetry conditions with force boundary conditions are more

frequently used in local FE-models (DNV, 2007). The loads are generally defined as nodal forces or

distributed loads on the shell elements. The wave and still water bending moments and shear forces

are modelled by distributed loads on the outer side of the bottom plating (DNV, 2007).

The dynamic analysis differs considerably from the static analysis, mainly by definition of loads.

Usually different global FE-model is also required with more precise definition of mass distribution.

However, since the current thesis is limited only to static analysis of the structure, these techniques

are not described here.

2.1.3 Finite Element model of the investigated structure Since the aim is to investigate the load carrying mechanism of the structure, static analysis with a

global 3D FE-model is conducted. The model is simplified by excluding bow and aft of the ship

structure and having the cross-section with constant dimensions. The simplified structure cannot be

considered as a prismatic beam since transversal bulkheads and pillars also modelled. As there are a

number of models created, detailed topological description of specific models will be given later.

However, the main dimensions will remain the same for all the models.

The 3D FE-model was created using FEMAP 10.1.1 and processed using Abaqus/CAE 6.11-2. An

example of use of elements for modelling structural details is given in Figure 9 where the beam

elements are shown as red and S4 shell elements in grey colours.

15

Figure 9. Structural members and the use of elements

Quadrangular 4-noded and triangular 3-noded S4 shell elements were used for modelling plating. The

length of the elements was half of the frame spacing (1.365 m) and width was equal to stiffener

spacing (0.68 m in general) which is sufficient according to classification society guidelines when

observing the global response (DNV, 2007). The secondary stiffeners were modelled using offset

beam technique, where the web of the stiffener was modelled using 4-noded rectangular S4 shell

elements and the flange as 2-noded B31 beam element. It should be noted that the aspect ratio for the

web of the secondary stiffeners can be considered as poor (0.0176 – 0.0733), thus making them

prone to shear locking when exposed to in-plane bending. However, the structure is investigated in the

global scale and under vertical bending where the load is applied as a pressure only on the bottom

plating. Thus, the tertiary effects are not investigated and the structure is considered as beam

structure where the external vertical shear force is carried by resisting bending. Internal moment of the

structure is developed mainly by the decks which will undergo tension or compression, meaning that

the stiffener web will not be exposed to considerable in-plane bending. The web and the flange of

primary stiffeners were also modelled as 4-noded quadrangular S4 shell elements. However, unlike in

the case of secondary stiffeners, the aspect ratio of the web of the longitudinal girders is within the

reasonable limits staying just under 1/3. The pillars were modelled as 2-noded B31 beam elements.

Due to the symmetry about the centre line and mid-ship, only quarter of the ship was modelled using

appropriate boundary conditions. The bending moment and shear forces were modelled as

sinusoidally distributed pressure load on the wetted surface of the bottom plating so that the model is

in equilibrium. Since the material properties were considered linear, results can be scaled to

correspond to desired bending moment. The current thesis will be limited to investigating the structure

only in hogging condition.

16

2.2 Post-processing

One of the known disadvantages of numerical methods such as FEM is that they do not readily

provide usable design information. Thus, interpreting the results is an important part of FEA.

Information about the elemental stresses and nodal displacements is extracted from FEA results using

FEMAP 10.1.1. The use of this information for investing the structural behaviour of investigated

structures is described in the following paragraphs.

2.2.1 Displacements Shear deformation between the individual decks is one of the main peculiarities in the response of

large passenger vessels (i.e. Naar et al., 2004; ISSC, 1997). In essence, this phenomenon arises from

the warping of the cross section of the passenger ship structure which departs its behaviour from

classical beam theories (Bleich, 1952). Thus, vertical deflections of decks become a subject of interest

since they provide information about the deformation kinematics of the cross-section of the

investigated structure. As was described in the previous chapter, in hogging condition the deckhouse

tends to sink into the boat deck at the mid-ship and rise from the boat deck at the end. Consequently,

from the point of view of hull-deckhouse interaction, it is sufficient to present vertical deflections at the

connection of the deckhouse side and the boat deck and at the top of the deckhouse in the structural

co-ordinate system located at the bottom of the structure. The relevant locations are presented in

Figure 10.

Figure 10. Locations in cross-section where deflections are investigated for the traditional and the proposed structrue

17

Location A refers to the centreline at the bottom of the vessel where the origin of the co-ordinate

system is located. In case of the proposed structure, point B coincides to the side of the superstructure

at the boat deck. In the traditional structure the location of point B is not changed because of the

presence of the longitudinal bulkhead on the upper decks which rests on the pillar line extending

throughout the hull. Location C is at the centre line on top of the whole structure.

In order to avoid confusion in terminology, displacements are also used for comparing the stiffnesses

of the investigated structures. By definition, stiffness is a ratio of the measures of load and

deformation. Thus, when defining the structural stiffness, unambiguous determination of loading and

measured deformations is required (Baumgart, 2000). In the current case, a potential source of

confusion lays in the fact that ship hull girders are traditionally considered as beams following classical

beam theories. For example, in case of Euler-Bernoulli beam theory, bending stiffness or flexural

rigidity k is defined as

= (2.8)

where Young’s modulus of the material, is second moment of area about principal y-axis, is

the applied bending moment about the y-axis and is the curvature of the beam (Timoshenko, 1948).

However, due to warping of the cross section of the passenger ship hull girders, relation (2.8) may not

be applicable. Nevertheless, relation (2.8) uniquely defines the measures of the load and the

deformation for evaluating bending stiffness of Euler-Bernoulli beam. It also indicates that when the

loading is kept constant and applied in exactly the same manner, the stiffness depends only on the

curvature. According to Euler-Bernoulli beam theory, the curvature is related to the vertical deflections

as

(2.9)

where w is deflection in z-direction and x is longitudinal co-ordinate of the beam. Thus, when the goal

is not to evaluate the exact value of bending stiffness of the investigated structure but to compare the

bending stiffness of different structures under identical external loading, vertical deflections can be

compared instead. Due to symmetry of the ship structure, the total vertical deflection will be defined in

the current work as shown in Figure 11. The total vertical displacement is measured at the location A

given in Figure 10.

18

Figure 11. Definition of the total vertical displacement

2.2.2 Stresses As was described in paragraph 2.1, one of the main paradigms of ship structural design is to consider

ship structures as beams in the global scale. At the beginning of the design of steel ships, the

behaviour of the ship structures has also been considered to follow the classical beam theories.

Consequently, it has always been common practice to use the terminology and methods from the

classical beam theories to describe the global response of the ship structures. Thus, the distribution

on normal strains in decks over the height of the ship structure has been one of the main methods of

describing the response of the ship structures under longitudinal bending. Even when the

inapplicability of classical beam theories on passenger ship structures was shown, attempts were

made to implement the classical theories in a certain manner to obtain enhanced normal strain

distribution over the height of the ship girder (i.e. Bleich, 1952). Moreover, after the implementation of

methods based on the theory of elasticity it became clear that the normal strain distribution cannot be

assumed uniform over the width of the decks of the passenger vessel (deOliveira, 1983). Thereby,

when observing normal strain distribution at a fixed longitudinal co-ordinate of the passenger ship

structure, the distribution of normal strains in decks does not only vary across the height but also

across the width of the structure. Thereby, since the FEM is used in the current global analysis,

average normal strain of all strains of all the plate elements across the width of individual decks will be

used in investigating the normal strain distribution. However, since the material is defined as steel with

the same Young’s modulus for the whole structure, the average normal stress distributions are

compared instead of average strains because it will also provide information about the usability of

selected plate thicknesses. This kind of approach has also been used before when studying hull-

deckhouse interaction with FEM (Paulling and Payer, 1968).

It should also be noted that the S4 shell element used for modelling the plating is three dimensional.

The output of normal stresses is presented at the plate top and plate bottom in FEMAP 10.1.1.

However, the current study is investigating the global behaviour of the structure. This means that the

membrane stresses are to be investigated. Thus, the average of plate top and bottom normal stresses

are used for calculating average normal stress in decks. Another approach would be to use membrane

forces for the plates which FEMAP 10.1.1 together with the plate thickness for obtaining the

Deformed state

Initial state

19

membrane stresses. However, the later approach is more labour intensive when compared with the

first option. The shear stresses are also investigated in critical locations in longitudinal bulkheads and

side shell of the hull.

2.2.3 Forces and moments Knowing the normal stresses in the deck elements, the membrane forces can be calculated. This is

used for obtaining the deck force distribution. The deck forces are used together with membrane force

of other longitudinal shell elements and axial forces from beam elements used in stiffener

discretisation for calculating the moment carried by the hull and superstructure.

When it comes to the separating the moments carried by the hull and superstructure, the moments are

traditionally calculated about the neutral axis which is the location of zero normal stresses which

develop in the vertical bending in longitudinal structural members of the ship girder (i.e. Remes et al.,

2011). In beams behaving according to classical beam theories, the neutral axis has a clear physical

meaning. A neutral axis is a line that forms when cross-section of the beam intersects the neutral

surface of the beam where the fibres do not undergo normal strain (Timoshenko, 1948). Thereby,

neutral axis denotes a part of the cross-section which is not longitudinally strained. However, as it was

previously discussed, uniform normal strain distribution cannot be assumed across the width of the

decks of the passenger vessels. Thus, the location of zero average normal stresses in decks could be

appropriate for define the location of the neutral axis. However, if the thickness of the deck plating is

not constant in breadth direction, the average normal stresses are not suitable for the definition neutral

axis. For this reason, in the current work, the neutral axis will be defined as a location of zero deck

force. The location of this neutral axis will be obtained in the local co-ordinate system, origin of which

lays in point A presented in Figure 10 by linear interpolation of the vertical co-ordinates of the decks

where membrane force changes signs.

The shear load carrying mechanism will be investigated by comparing shear flow in side shell of the

hull and longitudinal bulkheads. The reason lays in the fact that presenting elemental shear forces

does not give a good overview of the load carrying mechanism since the size of the elements varies

and thus, the forces carried by individual elements also vary considerably.

2.3 Description of research procedure

In this paragraph, the research procedure will be described. The investigation is divided into two

stages. Firstly, the responses of the proposed and the traditional structures are compared. Then the

sensitivity analysis will be performed on the proposed structure to enhance the understanding of the

load carrying mechanism and the performance of the proposed structure.

2.3.1 Comparison of the proposed structure and conventional cruise ship structure When compared with the traditional cruise ship structure, there are two distinctive requirements posed

on the structure which would enable to benefit from the m2cell modular outfitting concept. Firstly, the

accommodation decks have to be removed where to modules are to be positioned. Secondly, for

20

enabling rapid changing of modules, there should not be side plating for the superstructure. The

influence of these changes on hull-deckhouse interaction, stress levels, stiffness and load-carrying

mechanism has to be studied. For these purposes, two FE-models are created: one for representing

the conventional cruise ship structure and other for representing the proposed structure. The main

frame drawings of the traditional and proposed structure are given in Appendix 1 and 2 respectively.

The model of the traditional structure is shown in Figure 12.

Figure 12. Global FEA model of the traditional cruise ship structure

As can be seen from, transversal bulkheads in the main hull representing the watertight bulkheads

and the main fire zone bulkheads extending through the height of the entire structure are also

modelled. A closer look is also given to the side shell of the superstructure. The conventional structure

represents a modern design where the side shell of the structure does not participate in shear flow

and the shear forces are carried by the internal longitudinal bulkhead. A section of the model of the

proposed structure is illustrated in Figure 13.

21

Figure 13. Global FEA model of the proposed cruise ship structure

The proposed model was created based on the simplified structural model of the conventional cruise

ship. The side of the superstructure at the life boat recess has been moved closer to the centre line

and is located under the longitudinal bulkhead at y=4000. The decks and pillar lines were then

removed at the area where the outfitting modules are supposed to be positioned. The transversal

bulkheads have been kept at their original positions. However, the main fire bulkheads have been

widened to extend throughout the whole width of the hull.

2.3.2 Sensitivity analysis “Sensitivity analysis is an exploration of results from mathematical models to evaluate how they

depend on the values chosen for the parameters” (Rardin, 1998). Sensitivity analysis is usually

applied at the optimisation of structures for determining the influence of the design parameters on the

direction and rate of change of the performance function (Choi, 2005). For example, in the context of

ship structures, the performance can be measured by stiffness and weight whereas plate thicknesses

or stiffener spacing can be considered as design parameters. The aim of the sensitivity analysis in the

current context is to deepen the knowledge about the load carrying mechanism of the proposed

structure with the goal to enhance its performance. Thus, the sensitivity analysis will be conducted in a

simple form by changing important parameters which are selected based on the theories describing

hull-superstructure interaction and exploring and comparing the behaviour of the different designs.

The focus is on investigating the influence of changing the thickness of the plating at the boat deck

and at the side of the deckhouse on the performance and load carrying mechanism of the proposed

22

structure. Thinner plates on the main deck will reduce the amount of shear forces transmitted to the

side of the superstructure relieving the normal stresses in decks (Chapman,1951). The reduction of

thickness of the side plating of the deckhouse will have similar effect (Caldwell, 1957). However, these

alterations will also decrease the stiffness of the whole structure (deOliveira, 1983). On the other

hand, by increasing the plate thicknesses in these critical areas, the stiffness of the structure would

improve; however, normal stresses on the top of the deckhouse should increase. Nevertheless, these

parameters might hold the key to improve the performance of the proposed structure.

23

3. Results

This chapter is divided into two parts. Firstly, the comparison of responses of the proposed and the

traditional passenger ship structures is presented. This part will encompass detailed explanation of the

hull-deckhouse interaction and its influence on the load carrying mechanism of the structure.

Secondly, the results of the sensitivity analysis of the proposed structure are shown. All the results

have been scaled to correspond to the rule bending moment for the current vessel size.

3.1 Comparison of responses of the traditional and the proposed structure

In this paragraph, the responses of the traditional and the proposed structure are compared. Firstly,

the observed peculiarities in the hull-deckhouse interaction in the both structures will be presented

which due to their complicated nature have to be explained. Secondly, the stress levels and stiffness

of the investigated structures in order to determine in what extent the changes made to the traditional

structure would affect the performance of the proposed structure. The load carrying mechanism will be

explained by investigating force and moment distributions. Finally, the secondary effects are described

due to their strong influence on the primary scale.

3.1.1 Hull-deckhouse interaction In order to explain the differences in the response of the compared structures, observed peculiarities

in hull-deckhouse interaction have to be presented and explained. For achieving this, a closer look has

to be taken to the normal stress distribution in the individual decks and longitudinal bulkheads. The

normal stress distribution in decks and longitudinal bulkheads at mid-ship is illustrated for the

proposed and the traditional structures in Figure 14.

Figure 14 Normal stress distribution obtained with FEM in decks and longitudinal bulkheads at the mid-ship in proposed (on the left) and traditional (on the left) structures

139 MPa

123 MPa

75 MPa

-16 MPa

115 MPa

102 MPa

68 MPa 21 MPa

39 MPa

26 MPa

106 MPa 103 MPa

24

The normal stress distribution in individual longitudinal bulkheads can be considered more or less

linear. However, the normal stress distribution across the width of the decks is not uniform. This

phenomenon is also known as shear lag (Skaloud et al., 1991). At the connection of the

superstructure side and the deck, normal strains must be equal. The shear flow develops between the

superstructure side and deck plating which will cause shear deformation of the deck plating.

Consequently, the longitudinal displacements will lag behind those nearer to the superstructure side

leading to a non-uniform distribution of normal strains across the width of deck plating. Naturally, the

effects of shear lag become more pronounced when the offset distance of the deckhouse side from

the side of the hull increases

The non-uniformity of normal stress distribution is most visible on the boat deck of the proposed

structure. The normal stresses at the side of the boat deck plating are positive, whereas near the

centreline where the side of the superstructure is located, the normal stresses are negative. This

phenomenon can be explained with the help of a simple example showing the role of shear forces in

beam bending (Timoshenko, 1948). Let us consider two identical beams with solid cross-section

stacked on top of each other so that there is no friction between them and are both given the same

curvature as shown in Figure 15. It is also assumed that the responses of the beams follow Euler-

Bernoulli beam theory.

Figure 15. Two beams without shear force at the interface.

The bottom fibres of both beams in the current configurations are compressed, whereas top fibres are

stretched. Now, let us consider a beam that is composed by the two beams described in the previous

example by introducing shear force in their interface and is given the same curvature. The normal

stress distribution of the combined beams is given in Figure 16.

25

Figure 16. Two beams with shear force at the interface.

The fibres at the bottom of the lower beam are still compressed and fibres on top of the upper beam

are stretched. The top fibres of the lower beam and the bottom fibres of the upper beam will have the

same length as they would have in non-deformed state. The reasons is that there cannot be any

sliding due to shear force acting at the connection of these two beams, meaning that the normal forces

acting in the top fibres of the lower beam and bottom fibres of the upper beam will cancel each other.

In essence, shear force makes these two beams act as one with a new neutral axis at the connection

of the beams. As a result, the two beams acting as one will be stiffer than the system of two beams

which are not forced to act together by the shear forces since the internal moment inside the

combined beam is greater.

The previous example can be adapted to the proposed structure in the hogging condition. At first, let

there be no horizontal forces between the main deck and the superstructure side but only the vertical

forces which will make the superstructure follow the curvature of the main deck. Consequently, the

lower side of the superstructure side will be compressed and the main deck of the hull will be under

tension. However, when introducing shear forces between the deckhouse side and the boat deck, it

must be considered that the nature of the shear coupling will be far more complicated than in case of

two identical beams with solid cross-section and of the same width. In the previous example, the

assumption of validity of Euler-Bernoulli beam theory means that the normal and shear stress

distribution is uniform over the width of the beams. As was shown before, this is not the case in the

decks of the investigated structures due to shear lag. Thereby, in case of the proposed structure it

becomes possible that the deck is under compression near the side of the superstructure and under

tension near the side of the hull.

When studying the normal stress distributions in the decks under the longitudinal bulkheads in the

traditional structure, it appears that the normal stresses are reduced in the same manner. However,

the distribution of normal stresses is more complicated than in case of the traditional structure due to

fact that there are two longitudinal bulkheads located at different decks with different offset distances

from the lower side shells.

26

Another peculiarity is that the deckhouse tends to sink into the boat deck at the mid ship and vice

versa at the end of the compared structures as illustrated in Figure 17 and Figure 18 for the traditional

and the proposed structure respectively.

Figure 17. Vertical deflection of decks in traditional structure

Figure 18. Vertical deflection of decks in the proposed structure

In the traditional and the proposed structure, the superstructure sinks into the boat deck about 4 and 5

mm respectively. At the ends, the superstructure rises from the boat deck about 9 and 6 mm in the

proposed and traditional structures respectively. This means that the shear force develops in the

connection of longitudinal bulkheads and the decks in both structures and develops moment in the

-175

-125

-75

-25

25

75

125

0 20000 40000 60000 80000 100000 120000 140000

Vert

ical

def

lect

ion,

mm

x co-ordinate, mmA (at the bottom) B (at the boat deck) C (at the sun deck)

-185

-135

-85

-35

15

65

115

0 20000 40000 60000 80000 100000 120000 140000

Vert

ical

def

lect

ion,

mm

x co-ordinate, mmA (at the bottom) B (at the boat deck) C (at the sun deck)

27

0

5000

10000

15000

20000

25000

30000

35000

40000

-200 -100 0 100 200

z co-

ordi

nate

, mm

Normal stress, MPa

m2cell traditionalA

0

5000

10000

15000

20000

25000

30000

35000

40000

-80 -30 20 70

z co-

ordi

nate

, mm

Normal stress, MPa

traditional m2cellB

TRADITIONAL

M2CELL

superstructure which opposes the external moment. Since the boat deck allows certain amount of

vertical deflection, the deckhouses takes slightly smaller curvature than the main hull. Thus, the

phenomena related to the hull-deckhouse interaction of the compared structures are similar.

3.1.2 Stresses and stiffness At first, the influence of the changes made to the traditional structure on the stress levels is presented.

The comparison of average normal stress distribution in the decks is given for the mid-ship and x=L/4

in Figure 19.

At the mid-ship, the change in average stresses at mid-ship is most significant at the top of the

structure, where it has increased 21% and in the bottom, the stress has reduced about 19%. In the

proposed structure, previously described reduction of normal stresses in the boat deck and at the

lowest deck of the deckhouse is clearly visible. In the traditional structure, the reduction of normal

stress is more pronounced at the location where the upper longitudinal bulkhead is situated, whereas

at the boat deck, the reduction is almost unnoticeable. The influence of the changes made to the

proposed structure on the shape of the average normal stress distribution is less significant at x=L/4,

where it is almost linear for both structures. However, the average normal stress has considerably

increased on top of the proposed structure.

The comparison of shear stresses at x=L/4 in the sides of the hull and the superstructure of traditional

and the proposed structure are given in Figure 20.

Figure 19. Comparison of average normal stresses at A) x=L/2 and B) x=L/4

TRADITIONAL

M2CELL

28

Figure 20. Comparison of shear stresses at x=L/4

The removal of decks in the proposed structure has also increased the maximum shear stresses in the

deck house side by about 25%. In the proposed structure, the offsetting of the side of the deckhouse

has reduced shear stresses in the side of deckhouse near the boat deck at z=21300. At the same

time, the shear stresses have reduced in the hull side close to the boat deck. This means that due to

shear lag, the transitions of shear forces from the side shell of the hull to the deckhouse side has

reduced. The sudden increase of shear stresses at z=29000 in both structures is due to use different

plate thicknesses used for the deckhouse side and the longitudinal bulkheads in the proposed and

traditional structures respectively (see main frame drawings in Appendices 1 and 2). In case of the

traditional structure, where the offset distance of the deckhouse side is considerably smaller, the

reduction of shear stresses is not as pronounce above the boat deck as in case of the proposed

structure. The participation of decks in the shear flow in the traditional structure can also be seen as

they reduce the shear stresses in longitudinal bulkheads.

The impact of removing the decks from the deckhouse on the stiffness of the structure is given in

Table 1 together with the mass of the unit length of the longitudinal members of the steel structure and

the location of the vertical centre of gravity relative to the bottom plating.

Table 1. Comparison of vertical deflections and cross-sectional properties

model Total deflection, mm VCOG, m mass, t/m m2cell 310 (+11.8%) 16.3 (-12.2 %) 48.3 (-14.7 %) traditional 277 18.5 56.6

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

30 50 70 90 110

z co-

ordi

nate

, mm

Shear stress, MPatraditional m2cell

TRADITIONAL

M2CELL

29

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

-30.00 -15.00 0.00 15.00 30.00

z co-

ordi

nate

, mm

Deck forces, MNm2cell traditional

A

M2CELL

TRADITIONAL

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

-15 -10 -5 0 5 10 15

z co-

ordi

nate

, mm

Deck forces, MNm2cell traditional

B

M2CELL

TRADITIONAL

The total deflection of the proposed structure is 11.8% larger than in case of traditional structure.

However, in case of the proposed structure, the mass and the height of VCOG are smaller by 14.7%

and 12.1% respectively.

3.1.2 Forces and moments In order to understand the differences in the load carrying mechanism, the force and moment

distributions are compared. The comparison of deck force distributions at x=L/2 and x=L/4 is given in

Figure 21.

As could have been expected, the narrow decks near the centre line of the proposed structure carry

considerably less normal force when compared to the wide decks in the traditional structure.

Consequently, the upper decks carry more normal force in the proposed structure.

In order to obtain a better understanding of the differences of the shear load carrying mechanism of

the investigated structures, shear flow in the sides of the hull and deckhouses are given for both

structures at x=L/4 in Figure 22.

Figure 21. Comparison of deck forces at A) x=L/2 and B) x=L/4

30

It can be seen that the removal of decks and offsetting the superstructure side has reduced the

contribution of the hull side for carrying the shear load. The importance of the side of the deckhouse

has however increased. As in the case of the shear stresses, the participation of decks in the shear

flow is also visible. In case of the traditional structure, the similar reductions of shear flow due to shear

lag appear in the upper longitudinal bulkhead as at the deckhouse side in the proposed structure.

For obtaining the bending moment distributions, the location of neutral axis which was defined in

paragraph 3.1.4, was found and is presented as a function of the longitudinal co-ordinate system for

both structures in Figure 23. The location of neutral axes varies along the length of the both structures,

being located under the boat deck near the mid-ship and rising when moving towards the end. In case

of the proposed structure, the maximum height of the neutral axis is above the boat deck. However, in

case of the traditional structure, the neutral axis rises to the deck where the upper longitudinal

bulkhead is located. In both structures, the maximum height of the neutral axis is located above the

deck where the deckhouse side or the longitudinal bulkhead is closer to the centre line. This means

that the location of the neutral axis is determined by the hull-deckhouse interaction since the

deckhouse side tends to reduce normal strains in the boat deck, thus increasing the height of the

neutral axis. When comparing the cross-section of the traditional and the proposed structure and the

location of the neutral axes, it appears that the reasons for the increased height of the neutral axes are

the same.

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

0.25 0.75 1.25

z co-

ordi

nate

, mm

Shear flow MN/mm2cell traditional

TRADITIONAL

M2CELL

Figure 22. Comparison of shear flow at x=L/4

31

Figure 23. Comparison of the height of neutral axis along the length with the vertical shear force distribution

Only difference is that the longitudinal bulkhead which is closer to the centre line is higher than in the

proposed structure. It should also be noted that due to complicated normal force distribution at the

ends where several locations of zero deck forces were observed, the neutral axis locations was not

calculated. It should also be noted that there is a large oscillation in the height of the neutral axis,

especially towards the ends. For explaining the change of the neutral axes heights and the oscillation

of neutral axis position, the look has to be taken into the longitudinal distribution of normal force in the

decks. This will be conducted in the next paragraph.

The bending moment variation along the length of the structures is given in Figure 24 along with the

contribution of hulls of the proposed and traditional structures.

05000

10000150002000025000300003500040000

0 20000 40000 60000 80000 100000 120000

z co-

ordi

nate

, mm

x co-ordinate, mm

m2cell traditional

traditional m2cell

web-frame fire bulkhead

watertight bulkhead

Q(x)

x

32

Figure 24. Bending moment variation along the ship length with the vertical shear force distribution

As can be seen, when the neutral axis is defined as the location of zero deck forces, the

superstructure where the decks have been removed would carry more bending moment at the mid

ship than in the case of the traditional structure. Similarly to the location of neutral axis, the ratios of

bending moment carried by the hull oscillate when moving closer to the end and are not calculate

where the neutral axes were not calculated. It should also be noted that the moment inside the

elements was not considered when calculating the total moment of the structure. However, when

calculating the total moment carried by the whole structure, the same value is obtained as the applied

moment on the structure. This means that the magnitude of the moments inside the individual

elements is trivial in the global scale or the moments cancel each other out when considering the hull

and superstructure together.

3.1.3 Secondary effects As was shown in the previous paragraph, the location of neutral axes and the ratios of the moment

carried by the hull and superstructure oscillated strongly when moving away from the mid-ship. These

are caused by strong secondary effects which will be described in this paragraph.

Since the location of neutral axis was determined as the location of zero deck force, the comparison of

deck forces is needed for determining the relevant factors influencing the location of the neutral axes

and the moment distributions. At first, the normal forces in the deckhouse decks of the proposed

structure are compared in Figure 25.

-0.2

0

0.2

0.4

0.6

0.8

1

0 20000 40000 60000 80000 100000 120000

M to

tal/M

appl

ied.

max

x co-ordinate, mm

Mtotal Mhull (m2cell) Mhull (traditional)

x

web-framefire bulkhead

watertight bulkhead

Q(x) L/4

33

Figure 25. Deck force in the deckhouse decks of the proposed structure

The red lines in Figure 25 represent transversal fire bulkheads which extend throughout the height of

the whole structure. The grey lines represent the location of web-frames. As can be seen from Figure

25, the oscillation of neutral axis position is not caused by the deck force distribution in the deckhouse.

There is a minute oscillation of deck forces in decks 12 and 13 where side openings and also pillars

create the local stress concentrations which are visible in the overall force distribution. However, the

oscillation is so small that it cannot cause the change in neutral axis location in the magnitude visible

in Figure 23. The normal forces in the deckhouse decks of the traditional structure are compared in

Figure 26.

Figure 26. Deck force in the deckhouse decks of the traditional structure

As can be seen, the total membrane forces carried by the decks oscillate strongly in the deckhouse of

the traditional structure. The difference between the deckhouses of the proposed and traditional

structures is the absence of pillars in the proposed structure. Thereby, the pillars are the main source

-1

4

9

14

19

0 20000 40000 60000 80000 100000 120000

Deck

forc

e, M

N

x co-ordinate, mmD7 D8 D9 D10 D11 D12 D13 sundeck

web-framefire bulkhead

sundeck

D13D12D11D10D9D8D7

boat deck

-2

02

46

810

12

1416

18

0 20000 40000 60000 80000 100000 120000

Deck

forc

e, M

N

x co-ordinate, mmD7 D8 D9 D10 D11 D12 D13 sundeck

web-framefire bulkhead sundeck

D13

D11D10D9D8

D12

D7boat deck

34

of the strong secondary effects encountered in the primary response level. The source of these effects

lays in the peculiarities of the hull-deckhouse interaction. However, due to similarity of the hull-

deckhouse interaction of the compared structures, the source of the secondary effects will be

explained by investigating the deck forces in the proposed structure due to its simplicity when

compared to the traditional structure. The longitudinal distribution of normal forces in the hull,

excluding the double bottom, is given in Figure 27.

Figure 27 Deck forces force in the hull of the proposed structure with the vertical shear force distribution

As can be seen, the oscillation of normal force carried by the presented decks is strong. Thereby, in

case of the proposed structure, the oscillation of the location of neutral axis is directly related to the

presence of pillars in the hull. The other peculiarity is the upper decks of the hull (D4, D5 and the boat

deck) which were under tensions also become under compression when moving towards the end of

the structure. For opening up the physical causes of these behaviours, closer look has to be taken at

the deformation and the normal stress distribution of the boat deck in Figure 28.

-7

-5

-3

-1

1

3

5

7

0 20000 40000 60000 80000 100000 120000

Deck

forc

e, M

N

x co-ordinate, mm

D1 D2 D3 D4 D5 boat deck

web-frame

watertight bulkhead

boat deck

D5

fire bulkhead

D4D3D2D1

xL/4

Q(x)

35

Figure 28. Deformed main deck of the proposed structure with normal stress distribution

As can be seen from, the boat deck is completely under compression at the very end of the structure.

The reason is that there cannot exist any force which would resist the tendency of the lower part of the

deckhouse side to contract. At the mid-ship, the boat deck is under tension near the side shell of the

hull and under compression near the side of the deckhouse. However, as can be seen at section A in

Figure 28 the boat deck is under tension under the deckhouse and compressed when moving away

from the centre line. The reason lays in the fact that pillars have been used under the boat decks

which allow certain amount of shear deformation between decks without considerably influencing the

membrane forces. As can be seen in Figure 29, when comparing the locations of the web frames

under the boat deck in the initial and the deformed states, their longitudinal displacement is

cumulative, meaning that the shear deformation between the decks increases in the hull when moving

towards the end of the structure.

Figure 29. Deformed and initial state of the boat deck

77.7 MPA

-22.1 MPA

0

deckhouse side

centreline

mid

-shi

p A

A

initial state

deformed state

36

It should also be noted that the shear deformation between the decks is smaller near the sides of the

hull and larger when moving towards the centre-line. Consequently, as illustrated in Figure 30, the

pillars under the boat deck will start to restrict the shear deformation between the decks, causing

tension shown in the boat deck at section A in Figure 28.

Figure 30. Shear deformation between the decks in the hull

Tension visible at section A in Figure 28 is only present in the boat deck because the presence of the

deckhouse side which will deform the deck plating towards the mid-ship. Due to the absence of this

influence in lower decks, these decks will be compressed across the whole width. In addition, as

illustrated in Figure 31 the pillars will also be bent at the connections with decks. This is the reason of

the strong oscillation of the deck forces which are connected by pillars and thus, also the reason

behind the strong oscillation of the position of the defined neutral axis

Figure 31. Bending of the pillars

A-A

A

A

pillars

123 MPa

0

-80.7 MPa

Deckhouse side

Longitudinal girder Pillar

37

The deck cannot balance the bending moment of the pillars by itself, due to its small thickness. Thus,

longitudinal girders and the side of the deckhouse at the connection of the boat deck will carry the

moment. The mechanism of balancing the moment exposed by the pillars is illustrated in Figure 32

Figure 32. Local effects due to bending of pillars

The flange and web of the girder and the side of the deckhouse together with the deck plating carries

the moment. As a consequence, the membrane force in the deck will be reduced on the mid-ship side

of the pillar and vice versa on the other side. The mechanism is the same in case there is no

longitudinal bulkhead above the longitudinal girder.

The distribution of normal forces is also given for the double bottom in Figure 33

Figure 33. Deck forces in the double bottom of the proposed structure

-30

-25

-20

-15

-10

-5

0

5

0 20000 40000 60000 80000 100000 120000

Deck

forc

e, M

N

x co-ordinate, mmbottom tanktop average

web-frame

watertight bulkhead tanktop

web-frame

fire bulkhead

watertight bulkhead

bottom

38

As can be seen, there are strong secondary effects in the double bottom at the location of transversal

bulkheads. However, the oscillation of the normal forces carried in the bottom and tank top are in the

opposite phase. Thus, these forces will not cause the magnitude of oscillation in the location of neutral

axis seen in Figure 23. It can also be seen that at the end of the structure, the bottom becomes under

tension and tank top under compression at the end of the structure. The location where the transition

occurs is where second neutral axis is formed. The reason for the strong secondary effect in the

double bottom is caused by the complicated loading due to the hull deckhouse interaction. As was

shown in the previous paragraph in Figure 18 the end of the deckhouse will rise from the boat deck

and will sink into it at the mid-ship. This means that the vertical shear forces are applied to the main

hull and carried mainly by the transversal bulkheads to the double bottom as illustrated in Figure 34.

Figure 34. Loading of the double bottom

3.2 Sensitivity analysis

The results of the sensitivity analysis are presented in the current paragraph. A number of designs will

be investigated with different combinations of plate thicknesses used in the boat deck and the side of

the deckhouse. The aim is to investigate the influence of the varied parameters on the load carrying

mechanism of the proposed structure with the goal to enhance its performance

3.2.1 Thin and thick deckhouse side on a thin boat deck In the current comparison, boat deck thickness is kept the same as in the initial mode. The boat deck

thickness is small near the side wall of the super structure (5mm+HP 100x6), thus load carrying

capacity of the boat deck has been reduced considerably. The comparison of behaviour in hogging

condition is given for three models:

1) m2cell_initial – this is the initial model compared to a model of traditional structure in the

previous paragraph, main frame drawing given in Appendix 2

2) m2cell_1 –thin plating (5 mm) in deckhouse side, main frame drawing given in Appendix 3

3) m2cell_2 – thick plating (13 mm) in deckhouse side, main frame drawing given in Appendix 4

39

0

4 000

8 000

12 000

16 000

20 000

24 000

28 000

32 000

36 000

40 000

44 000

-30.00 -15.00 0.00 15.00 30.00

z co-

ordi

nate

, mm

Deck forces, MNm2cellm2cell_1m2cell_2

A

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

-15 -10 -5 0 5 10 15

z co-

ordi

nate

, mm

Deck forces, MNm2cellm2cell_1m2cell_2

B

The cross-sectional drawings of all the models are given in Appendix 1. The comparison of deck force

distribution is given in Figure 35.

As can be seen, the effect on the deck forces at the top of the superstructure is marginal. However,

the influence is noticeable at the bottom plating and most significant near the boat deck. In case of the

thicker plating in the longitudinal bulkhead, the force carried in the boat deck has decreased

considerably. Since the boat deck is relatively thin when compared to the thickness of the longitudinal

bulkhead, the extent of shear deformation and thus reduction of normal forces is larger when

compared to other designs. The deck distribution of deck forces have also changed in the bottom and

tank top. The comparison of shear flow and stresses is given in Figure 36.

Figure 35. Distribution of deck forces at A) x=L/2 and B) x=L/4

40

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

0.5 0.7 0.9 1.1

z co-

ordi

nate

, mm

Shear flow, MN/m

m2cell m2cell_1 m2cell_2

B

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

35 55 75 95 115

z co-

ordi

nate

, mm

Shear stress, MPa

m2cell m2cell_1 m2cell_2A

-10

-8

-6

-4

-2

0Boat deck Sun deck

Vert

ical

def

lect

ion,

mm

m2cell_1

m2cell_2

m2cell

A 0

2

4

6

8

10

12

Boat deck Sun deck

Vert

ical

def

lect

ion,

mm

m2cell_1

m2cell_2

m2cell

B

As could have been expected, the thicker longitudinal bulkhead carries more shear force than the

thinner one. As a result, the shear force carried by the side of the hull has been reduced in case of the

Thick deckhouse side and vice versa in case of the thinner deckhouse side. The comparison of

vertical deflections of decks in ship co-ordinate system is given in Figure 37.

It can be seen that the deckhouse sinks slightly deeper into the hull in case of the thick bulkhead. On

the other hand, the end of thick bulkhead raises considerably less from the main deck than the thinner

one. Thus, the difference in curvature of superstructure and the main hull is smaller in case of the

Figure 36. Comparison of A) the shear stresses and B) the shear flow

Figure 37. Relative deflection of the decks in A) x=L/2 and B) x=L

41

thicker bulkhead. The difference in curvature is caused by the moment produced by shear force at the

connection of deckhouse side and the main deck. However, the magnitude of the shear forces

depends on the main deck ability carry shear forces. In the current models, the deck thickness was

constant and only the deckhouse side thickness was varied. This means that the shear force causing

the difference of the curvature is the same for the compared models. However, the deckhouse side

with smaller plate thickness will deflect more when compared to the one with thicker plate thickness

when the moment caused by the moment is the same. The reasons is that the thin deckhouse side will

also deform more than the thicker one. Due to this, the thinner deckhouse side sinks less into the main

deck. This statement is also supported by larger vertical deflection of the sun deck in case of thin

deckhouse side.

The total deflections and mass of the unit length of the longitudinal members and the height of the

VCOG is given in Table 2 for the compared designs.

Table 2. Comparison of the total deflections, mass and height of VCOG

Although, the decks have been removed from the investigated structures, the total vertical deflections

in case of the thick longitudinal bulkhead the deflections are even comparable to the traditional

structure. The masses and the height of VCOG have decreased however.

3.2.2 Thin and thick deckhouse side on a thick boat deck In the current comparison, boat deck thickness is increased to be uniform over the whole width

(13mm+HP 140x8). The comparison of behaviour of three models is given:

1) m2cell_initial – this is the initial model compared to a model of traditional structure in the first

paragraph, main frame drawing given in Appendix 2

2) m2cell_3 – this model has a superstructure wall made of relatively thin material (5mm), main

frame drawing given in Appendix 5

3) m2cell_4 – this model has a superstructure wall made of relatively thick material (13 mm),

main frame drawing given in Appendix 6

Design max vertical deflection, mm VCOG, m mass, t/m

m2cell_1 321 (+15.9 %) 16.1 (-12.9 %) 46.4 (-18.0 %)

m2cell_2 289 (+4.30 %) 16.7 (-9.40 %) 48.4 (-14.5 %) m2cell 310 (+11.8 %) 16.2 (-12.2 %) 48.3 (-14.7 %) traditional 277 18.5 56.6

42

0.00

4000.00

8000.00

12000.00

16000.00

20000.00

24000.00

28000.00

32000.00

36000.00

40000.00

44000.00

-30.00 -15.00 0.00 15.00 30.00

z co-

ordi

nate

, mm

Deck forces, MN

m2cellm2cell_3m2cell_4

A

0

4000

8000

12000

16000

20000

24000

28000

32000

36000

40000

44000

-15 -5 5 15

z co-

ordi

nate

, mm

Deck forces, MNm2cell

m2cell_3

m2cell_4

B

The comparison of deck force distribution is given in Figure 38.

As in the previous comparison, the change in the deck forces in the top deck is marginal. However,

changes of deck forces in the bottom and near the boat deck are more noticeable. The change in deck

forces can be explained using the analogy from the previous paragraph. The thicker longitudinal

bulkhead will reduce the stresses in the middle of the boat deck, thus reducing the whole force carried

by the deck. As in the previous cases, the alterations have also changed the deck force distribution in

the lower part of the hull. The comparison of shear stresses and flow is given in Figure 39.

Figure 38. Comparison of deck forces in A) x=L/2 and B) x=L/4

43

0

5000

10000

15000

20000

25000

30000

35000

40000

0.45 0.95

z co-

ordi

nate

, mm

Shear flow, MN/m

m2cell m2cell_3 m2cell_4A

0

5000

10000

15000

20000

25000

30000

35000

40000

45 95z c

o-or

dina

te, m

m

Shear stress, MPa

m2cell m2cell_3 m2cell_4B

-9-8

-7-6-5-4

-3-2-1

0Boat deck Sun deck

Vert

uica

l def

lect

ions

, mm

m2cell_3m2cell_4m2cell

A 0

2

4

6

8

10

12

Boat deck Sun deck

Vert

ical

def

lect

ion,

mm

m2cell_3m2cell_4m2cell

B

When comparing the results with the previous shear stress distribution, it reveals that the thicker boat

deck will increase the shear stresses at the connection of the deckhouse side. This is expected since

the thicker boat deck plating is able to carry more loads with smaller deformation. The comparison of

vertical deflections of decks in ship co-ordinate system is given in Figure 40.

Figure 39. Comparison of A) shear stresses and B) shear flow

Figure 40. Relative deflection of the decks in A) x=L/2 and B) x=L

44

Thick and thin deckhouse sides behave in the similar way on the thick boat deck as on the thin boat

deck. The relative deflections are smaller in case of thicker bulkhead which follows the logic of the

comparison presented in the previous paragraph. However, the deflections are slightly larger when

compared to the deflections on the thinner boat deck. This can be explained by the fact that the shear

force at the connection of the boat deck is larger and thus, larger moment develops in the side of the

deckhouse wall.

The total deflections and mass of the unit length of the longitudinal members and the height of the

VCOG is given in Table 3 for the compared designs.

Table 3. . Comparison of total deflections, mass and height of VCOG

As was found in the previous paragraph, the hull girder stiffness is higher in case of thicker deckhouse

side. As can be seen, when compared with the traditional structure, the vertical stiffness has increased

5.2% in the design where thicker plating was used in both the side of the deckhouse and the boat

deck. However, the overall weight is reduced 10.8 % and the height of VCOG 8.2 % when compared

to the proposed structure

model max deflection, mm VCOG, m mass, t/m m2cell_3 296 (+6.70 %) 16.3 (-11.5 %) 48.5 (-14.3 %)

m2cell_4 263 (-5.20%) 17.0 (-8.20 %) 50.5 (-10.8 %) m2cell 310 (+11.8 %) 16.2 (-12.2 %) 48.3 (-14.7 %) traditional 277 18.5 56.6

45

4. Discussion and Conclusions

The aim of the current thesis was to investigate the impact of the structural changes required for a

conventional cruise ship structure in order to satisfy the needs posed by the m2cell modular outfitting

concept. A conventional cruise ship structure with internal longitudinal bulkheads for carrying shear

forces was selected for the basis for creating the proposed structure. The differences in hull-

deckhouse interaction, load carrying mechanism and the performance between the proposed and the

traditional structures were examined. An attempt was also made to profit the knowledge about the

load carrying mechanism of the proposed structure to enhance its performance to a level comparable

to the traditional structure.

The results indicate that the nature of the hull-deckhouse interaction in the selected traditional cruise

ship structure and the proposed structure does not differ. Moreover, the mechanics of the hull-

deckhouse interaction follows the explanations given by various authors describing the phenomenon

(i.e. Bleich, 1952; Schade 1966). However, in the light of the current work, it would be appropriate to

take a closer look at the previous theories and methods used for evaluating the response of the

vessels where hull-superstructure or hull-deckhouse interaction must be considered from the

perspective of the modern cruise ship design.

For facilitating the discussion, the use of terms superstructure and deckhouse is loosen. In essence,

distinguishing deckhouses from superstructures is important since in case of deckhouses, the shear

lag effect at the boat deck is an important factor. However, if the superstructure is defined as general

decked structure on the boat deck and the relevant shear effects are classified, the loosening of this

term is justified. In essence, the shear effects can be generalized as the anomalies in the context of

classical beam theory which reveal as a warping of the cross-section of the whole hull girder. The

results indicate that the response of the investigated structures are defined by the shear coupling of

the hull and superstructure and the shear effects in the decks and longitudinal bulkheads or side shells

of the whole structure. Thus, the theories are also distinguished by the locations where they take into

account the shear effects since in the earliest works; the focus was on describing the shear effects at

the connection of the main deck and the superstructure only. In addition, three criteria are used in the

evaluation of the previously presented methods and theories which are important in the context of

modern cruise ship design. First of them is the applicability to multi-deck structures. This is important

in the modern cruise ship design and was not considered in the early works since the passenger ships

at the era had primitive deckhouses. The second criterion is the ability to grasp 3D-effects of the

structural behaviour. This is important since the behaviour of modern cruise ship structures cannot be

described by investigating 2D sections of the structure (Remes et al., 2011). The third criterion is the

suitability of the method for the early design process of the modern cruise ship structure.

46

A comparison of selected methods and theories based on the described phenomena is given in Table

4.

Table 4. Comparison of methods and theories

App

roac

h

Theory or method

Shear effects at the connection of the hull and

superstructure

Shear effects (in hull or

superstructure) Usable in multi-deck

super-structures

3D effects

Usable at early

design phase of modern

passenger vessels

shea

r lag

in t

he

mai

n de

ck

vert

ical

stiff

ness

of

mai

n de

ck shear effects

in the superstructure

side or longitudinal bulkheads

deck

s

supe

rstr

uctu

re si

de

or lo

ngitu

dina

l bu

lkhe

ad

Bea

m th

eory

Crawford, 1950

NO YES NO NO NO NO NO NO

Bleich, 1952

NO YES NO NO NO NO NO NO

Muckle, 1962

NO YES YES YES YES YES NO NO

Chapman, 1957

NO YES NO NO NO NO NO NO

Schade, 1966

YES YES NO YES NO NO NO NO

Naar et al., 2004

NO YES YES NO YES YES YES YES

Pla

ne s

tress

Caldwell, 1957

NO YES YES YES YES NO NO NO

Jaeger & Woortman,

1961 NO YES YES YES YES NO NO NO

Oth

er

Heder & Ulfvarson,

1991 NO NO NO YES YES YES NO YES

Fransman, 1988

NO YES YES YES YES YES NO YES

FEM YES YES YES YES YES YES YES NO

47

When examining the comparison of methods in Table 4, it can clearly be seen that the older methods

cannot be applied for investigating the modern cruise ship structure. However, the shortcomings of the

older methods are due to the peculiarities of the investigated structures rather than the researchers’

ability to grasp the physical phenomenon itself. At the era of presenting the older theories (i.e. Bleich,

1952; Cladwell, 1957 etc.) the passenger ship structures were considerably simpler when compared to

the modern cruise ship structures. Thus, a number of simplifications were allowed. The more recent

works can be implemented in some of the modern design. For example, the method offered by

Fransman (1988) proved to be a fairly good tool for evaluating the response of the large passenger

ship at the early design phase. However, Fransman’s (1988) work was an enhanced method proposed

by Caldwell (1957) and thereby it does not take into account shear lag at the boat deck where the

superstructure is located. Heder and Ulfvarson (1991) provided a method for evaluating the response

of the passenger ships which have large opening at the deckhouse side. However, their method

cannot describe the interaction between the hull and superstructure when the sides of the

superstructure are offset from the side shell of the hull. So far, the most versatile method for analysing

the large passenger ship structures has been provided by Naar et al. (2004). However, the method

cannot take into account the shear lag in the decks. One of the main assumptions made by Naar et al.

(2004) is that the decks of the large passenger ships can be considered as thin walled beams. In case

of the currently presented structures, this assumption is invalid for some decks. However, it seems

that the method can be modified to take into account the shear effects in the decks and could provide

a formidable tool for evaluating the response of a modern cruise ship structures at the early design

phase. The advances in the computing hardware and the development of equivalent shell elements

(i.e. Avi, 2012) suggest that the use of FEM might also become feasible at the early design phase of

modern passenger ships.

When it comes to comparing the responses of the investigated structures to the responses of the ship

structures which have been presented in the literature, it becomes apparent that there are very few

similarities. The reason is that the majority of the works dealing with the hull-deckhouse interaction

deal with the older generations of passenger ship (i.e. Vasta, 1949; Bleich, 1952) structures or the

presented structures are not comparable (i.e. Muckle, 1962; Fransman, 1988; Naar et al., 2004) to the

ones investigated in the current work. However, the structure investigated by Remes et al. (2011) was

comparable to the traditional structure presented in the current work. Remes et al. (2011) reported

similar effects in the response of the investigated structure as was encountered in the current thesis.

The height of the neutral axis also increased when moving toward the end of the structure and

secondary effects described in the current work were also encountered. However, Remes et al. (2011)

did not discuss the physical reasons behind those effects.

The load carrying mechanism of the investigated structures had surprisingly small differences. In both

structures, superstructures carried more bending moment than the main hull when the reference point

is selected at the location of zero deck forces. This follows well the description given for the modern

cruise ship structures (Kujala, 2003). However, it was noticed that the deckhouse of the proposed

48

structure contributed slightly more to the bending moment carrying capacity of the whole hull girder. In

a sense, this result is intriguing since the wide accommodation decks are not present in the proposed

structure. However, a critical mind has to be reserved when interpreting this result. The moment was

calculated about the location of zero deck forces. It was shown that the neutral axis changes position

over the length of the investigated structures due to the hull-superstructure interaction induced

secondary effects. Nevertheless, the neutral axis is often used for calculating the moment carried by

the passenger ship structure (i.e. Remes et al., 2011). However, the term neutral axis itself originates

from the classical beam theories. In the current and previous works investigating passenger ship

structures, it was clearly shown that the basic assumptions made in the classical beam theories are

violated. The loose treatment of the terms originating from the classical beam theories can lead to

invalid understandings and calculation methods when considering cruise ship structures. For example,

in the current work it was shown that the response of the proposed structure was strongly affected by

the shear stiffness of the boat deck. The shear stiffness has two components in the current approach:

the vertical and horizontal shear stiffness. It was shown that reduced horizontal shear stiffness

increased the effect of shear lag which decreased the overall vertical stiffness of the structure. In the

classical beam theories, the vertical stiffness is described by flexural stiffness which depends on the

Young’s modulus and the second moment of the cross-sectional area of the beam (Timoshenko,

1949). Maximising the second moment of the cross-section of the cruise ship structure has been

offered as one objective in the optimisation process (i.e. Caprace et al., 2010). This however does not

lead to optimal structural design solution since the maximisation of the second moment of the area in

cruise ship structure leads to increasing the amount of material in the top and the bottom plating and

reducing the amount of material used at the middle. This leads to a rapid decrease of the vertical

stiffness of the structure which is highly unwanted in case of the cruise ship structures. In essence,

using the terms such as flexural rigidity and neutral axis in the context of the compared cruise ship

structure is a paradox since the hull-deckhouse interaction at the boat deck needs to be described

with the theory of elasticity, rather than the terms which are based on the classical beam theories from

the strength of materials. However, the results indicated that the deckhouse and the hull separately

behave more or less according to the classical beam theories as have been suggested by early works

describing the hull-deckhouse interaction (i.e. Bleich, 1952).

When it comes to the impact of removing the decks and creating a narrow deckhouse on the

performance of the cruise ship structure, it was noted that the increase of the normal and shear

stresses was noticeable in the proposed structure. The vertical stiffness also suffered considerably.

However, the increase of stresses occurred at the locations where relatively thin plates were used.

Thus, it seems that the acceptable stress levels might be achieved with reasonable measures.

Moreover, the sensitivity analysis suggested that the vertical stiffness of the structure could increase

considerably when using thicker plating for the boat deck and the deckhouse side. In case of a one

design, even greater vertical stiffness was achieved than in case of the traditional structure. However,

the savings in the structural weight and the height of the VCOG was considerable when compared to

the traditional structure. Naturally, the vertical stiffness of the traditional structure can be increased in

49

the same manner as in the case of the proposed structure by using thicker plates at the longitudinal

bulkheads and the decks participating in the shear flow. On the other hand, these measures would

have negative impact on the height of the VCOG and the weight of the whole structure. However, it is

too early to make any conclusions one the weight savings of the whole cruise ship structure. The

m2cell modular outfitting system has not been developed yet and the weight of the modules and their

installation system is unknown. Thereby the gains in the weight and the location of VCOG of the whole

structure are hypothetical at the moment. Thus, further studies are needed for making any statements

about the feasibility of the m2cell modular outfitting system. Nevertheless, the necessity of using

accommodation decks for carrying the vertical bending moment can be questioned when considering

the investigated structures. In essence, the effectiveness of the deckhouse decks has been

investigated before (i.e. Caldwell, 1957; Muckle, 1966). It has been shown that the effect of shear lag

strongly affects the load carrying capacity of the decks (Muckle, 1966).

When considering further investigation of the m2cell structure, it must be considered that a number of

simplifications have been made in the current work when studying the proposed structure. However, it

seems that the influence of the simplification is not the main concern at this stage. Due to the removal

of the accommodation decks and absence of the side shell, torsional stiffness has been reduced

dramatically. The same applies to the horizontal stiffness. The dynamic response will have to be

investigated, since low eigen frequencies of the structure will have a devastating effect on the comfort

level. For this reason, the issues related to the torsional and horizontal stiffness and dynamic

response of the proposed structure should be addressed.

50

References

Ahola, M. 2010. Living in a Motion. Master’s thesis. Aalto University School of Art and Design.

Department of Design. Helsinki.88 p.

Andric, J. & Zanic, V. 2010. The Global Structural Response Model for Multi-Deck Ships in Concept

Design Stage. Ocean Engineering, Vol. 37, pp.688-704.

Avi, E. 2012. Equivalent shell element for ship structural design. Master’s thesis. Aalto University

School of Engineering, Department of mechanical Engineering, Ship Laboratory. Espoo. 62 p.

Baumgart, F. 2000. Stiffness – an unknown world of mechanical science. Injury, Int. J. Care Injured.

vol 31 pp. 14-23.

Bergström, M. 2010. Longitudinal Strength Analysis of a Cruise Ship with a Narrow Superstructure.

Master’s thesis. Aalto University School of Engineering, Department of mechanical Engineering, Ship

Laboratory. Espoo. 102 p.

Bleich, H.H. 1952. Nonlinear Distribution of Bending Stresses due to Distortion of the Cross Section.

J. Applied Mechanics. vol. 29. p. 95-104

Caldwell, J. B. 1957. The effect of superstructures on the longitudinal strength of ships. The Institution

of Naval Architects. Vol. 99, p. 664.

Caprace, J.D. et al. 2010. Multi-criteria Scantling Optimisation of Cruise Ships. Ship Technology

Research, Schifftechnik, Vol. 57, No. 3, pp. 210-220.

Carrera, E. et al. 2011.Beam Structures. Classical and Advanced Theories. UK: John Wiley & Sons,

Ltd. ISBN 9780470972007.

Chapman, J.C. 1957. The Interaction Between a Ship’s Hull and a Long Superstructure. Trans. INA. p.

618.

Choi, K. K. 2005. Structural sensitivity analysis and optimization. Germany: Springer Science+

Business Media. ISBN: 0387273069.

Crawford, L. 1950. Theory of Long Ship’s Superstructures. Trans. SNAME. Vol 58, p. 693-732.

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second cycle. USA: Cornell Maritime Press; p. 160–278.

Kujala, P. 2003. Development of Innovative Structural Concepts for advanced Passenger Vessels.

Det Norske Veritas (DNV), 2009. Rules for Classification of Ships

51

Det Norske Veritas (DNV), 2007. Direct Strength Analysis of Hull Structures in Passenger Ships.

Ehlers, S. 2011. Large Complex Structures. Lecture Notes (2nd version). Aalto University School of

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Fransman, J. 1988. The Influence of Passenger Ship Superstructures on the Response of the Hull

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Heder, M. & Ulfvarson, A. 1991. Hull Beam Behaviour of Passenger Ships. Marine Structures vol 4,

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Hughes, O.F. 1983. Ship Structural Design: A Rationally-Based, Computer-Aided Optimization

Approach. John Wiley &Sonds inc. ISBN 0471032417.

International Maritime Organisation, IMO. 1999. SOLAS, International Convention for the Safety of Life

at Sea. IMO Publishing. ISBN 9280161016.

ISSC, 1997. Proceedings of the 13th International Ship and Offshore Structures Congress. Trondheim

Jaeger, H.E. and Woortman J.J. 1961. Some New Factors in the Calculation of the Interaction

between a Ship’s Hull and a Long Deckhouse. Trans. RINA.

Kauppi, A. 2012. M2cell Concept – an interchangeable module system for cruise ship hotel spaces.

Master’s thesis. Aalto University School of Arts, Design and Architecture, Department of Architecture.

Helsinki. 40p.

Klanac, A. and Jelovica, J. 2009.Vectorization and constraint grouping to enhance optimization of

marine structures. Marine Structures 22(2). pp. 225-245.

Muckle, W. 1962. The Influence of Large Side Openings on the Efficiency of Superstructure. Trans.

RINA, p. 177-178.

Muckle, W. 1966. Superstructures with Large Side Openings: a Comparison between Theory and

Experiment. Trans. RINA.

Naar H. et al. 2004. A Theory of Coupled Beams for Strength Assessment of Passenger Ships. Marine

Structures 12. vol 17(8). pp. 590-611.

Paulling, J.R. and Payer, H.G. 1968. Hull-Deckhouse Interaction by Finite-Element Calculations.

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Rardin, R.L. 1998. Optimization in operations research. Prentice Hall. 919 p. ISBN 0023984155

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Remes, H. et al. 2009. ConStruct – Platform for Conceptual Structural Design. IMPROVE-

Conference, Dubrovnik, Croatia.

Remes, H. et al. 2011. Hull/Superstructure-interaction in optimized passenger ships. Advances in

Marine Structures. p. 625-632.

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International Conference on Advancements in Marine Structures, Glasgow, pp.483-488.

Schade, H.A. 1966. Two-Beam Deckhouse Theory with Shear Effects, Schiff und Hafen. Heft 5, p.

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Skaloud, M. & Kristek, V. 1991. Advanced Analysis and Design of Plated Structures. Elsevier Science

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23.

Vasta, J. 1949. Structural Tests on the Passenger Ship S.S. President Wilson – Interaction between

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Ylirisku, V. 2012. Building Blocks on the Sea – simulating the realisation of the M2Cell system in

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Zienkiewicz, O.C. 1971. The Finite Element in Engineering Science. USA: McGraw Hill.

53

List of Appendices

Appendix 1. The main frame of the traditional cruise ship structure (traditional)

Appendix 2. The main frame of the proposed cruise ship structure (m2cell)

Appendix 3. The main frame of the design m2cell_1

Appendix 4. The main frame of the design m2cell_2

Appendix 5. The main frame of the design m2cell_3

Appendix 6. The main frame of the design m2cell_4

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

T 440 x 8 + 200 x 10

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 65

HP 100 x 67

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7 13.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

203 x 12.5

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

Appendix 1. The main frame of the traditional

cruise ship structure (traditional)

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

T 440 x 8 + 200 x 10

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 65

HP 100 x 66

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7 13.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

HP 100 x 6 7.0

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 7 13.0T 440 x 8 + 200 x 10

Appendix 2. The main frame of the proposed

cruise ship structure (m2cell)

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

T 440 x 8 + 200 x 10

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 65

HP 100 x 66

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7

HP 100 x 6 5

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 7 T 440 x 8 + 200 x 10

5

5

5

5

5

5

Appendix 3. The main frame of thedesign m2cell_1

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

T 440 x 8 + 200 x 10

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 65

HP 100 x 66

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7 13.0

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 7 13.0T 440 x 8 + 200 x 10

13.0

13.0

13.0

13.0

13.0

Appendix 4. The main frame of thedesign m2cell_2

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

T 440 x 8 + 200 x 10

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 66

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7

HP 100 x 6 5

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 7 T 440 x 8 + 200 x 10

5

5

5

5

5

5

Appendix 5. The main frame of thedesign m2cell_3

Title:

Based on:

Part of:

Replaces:

Designer:

Date:

Checked by.:

Date:Approved by:

Date:Program:

Mass:A4

Paper size(210x297)

Scale: 1:300

Drawing number: Rev. Page

1(pages)

(1)

Oliver Parmasto

03.06.2012

AutoCAD 2010

FRAME SPACING (GENERALLY)WEB FRAME SPACING (GENERALLY)PILLAR SPACING (GENERALLY)

680 mm2730 mm2730 mm

2000

4100

2800

2800

3000

2800

3800

4100

3300

2750

2750

2750

2800

2800

1200

2000

6100

8900

11700

14700

17500

21300

25400

28700

31450

34200

36950

39750

42550

43750

D.1

D.2

D.3

D.4

D.5

D.6

D.7

D.8

D.9

D.10

D.11

D.12

D.13

D.15D.14

HP 240 x 1213.0

HP 280 x 1116.0

HP 240 x 1211.5

T 440 x 8 + 200 x 10

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 67.5

HP 100 x 65

HP 100 x 66

HP 100 x 67

14.0HP 180 x 11

15.0HP 180 x 11

16.0HP 180 x 11

HP 140 x 813.0

HP 100 x 7 13.0

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

HP 100 x 6

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

203 x 12.5

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 66.0

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

T 330 x 7 + 200 x 10

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 65

HP 100 x 7 13.0T 440 x 8 + 200 x 10

13.0

13.0

13.0

13.0

13.0

Appendix 6. The main frame of thedesign m2cell_4