Geniş ambar ağzı açıklıklı konteyner gemilerindeki çarpılmanın incelenmesi
Investigation of warping of large container ships
Yazar: TUĞÇE EROL
Danışman: YRD. DOÇ. DR. ERTEKİN BAYRAKTARKATAL
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Deniz Bilimleri = Marine Science ; Denizcilik = Marine ; Gemi Mühendisliği = Marine Engineering
Dizin: Burulma momenti = Torsional moment ; Direkt kesme = Direct shear ; Eylemsizlik momenti = Inertia moment ; Eğilme momenti = Bending moment

Özet:
Dünya ekonomisindeki hacim artışı sebebiyle, deniz taşımacılığında hedeflenenleri karşılamak amaçlı, deniz ticaretinin en önemli ayağı olan konteyner gemilerinin boyutları büyümüş ve kapasiteleri artırılmıştır. Daha fazla konteyner taşıyabilmek için gemiler, daha geniş ambar açıklıkları ile inşa edilir duruma gelmiştir. Geniş ambar açıklıklı gemilerde meydana gelen yapısal problemleri çözmek amaçlı birçok çalışma yapılmıştır. Geminin seyri esnasında maruz kaldığı burulma yüklemesi bu problemlerin başında gelir.
Sunulan bu çalışmada geniş ambar açıklıklı konteyner gemilerinde burulma yüklemesinden meydana gelen çarpılma gerilmelerinin incelenmesi amaçlanmıştır. Geniş ambar açıklıkları gemide süreksizlik noktası yarattığından burulma rijitliğini azaltıcı rol üstlenir. İnce cidarlı yapılar olan konteyner gemilerinde ise burulma rijitliği konusu oldukça önemli olup, son yıllarda yapılan çalışmalarda başat bir rol üstlenmiştir.
İlk bölümde konteyner gemileri hakkında genel bilgi verilmiştir. Bunu takip eden ikinci bölümde yapısal problemleri beraberinde getiren geniş ambar açıklıklarına değinilmiştir. Bu süreksizlik yapısının dizayn aşamasında nasıl dikkate alınması gerektiği belirtilmiştir.
Üçüncü bölümde burulma konusu anlatılmıştır. Açık güverteli gemilerde burulmanın önemine değinilmiştir. Takip eden bölümlerde ise gemi kiriş kabulü ile burulma momentinin nasıl hesaplanacağı anlatılmış olup, bu hesabı gemi kirişinin burulmaya olan tepkisinin analizi izlemiştir. Bu bölümde son olarak gemi gövdesinin burulma momenti karşısında uğradığı deformasyonlara yer verilmiştir.
Bölüm dörtte, burulma kaynaklı çarpılma konusu öncelikle teorik olarak ele alınmıştır. İlk olarak, konteyner gemilerinin güverte yapısında meydana gelen deformasyon ve gerilmeler incelenmiştir. Daha sonra çarpılma temel olarak iki kesit grubunda anlatılmıştır. Açık ve kapalı kesitlerde çarpılmanın nasıl oluşacağı, serbest ve kısıtlanmış çarpılma denklemlerine yer verilmiştir. Takip eden bölümlerde ise çoklu ve karışık kesitlere değinilmiştir.
Beşinci bölümde teorik olarak bu çalışmada sunulan ifadeler, örnek bir konteyner gemisi kesiti üzerinden çözülmüştür. Konteyner gemi kesiti öncelikle çift yalnızca çift dip olarak ele alınmıştır. Kesitin özellikleri ve müteakiben çarpılma fonksiyonları hesaplanmıştır. İkinci kesitte ise birinci kesitin ara güverteli haline yer verilmiştir. Aynı şekilde ikinci kesit için de çarpılma katsayısı belirlenmiştir. Üçüncü ve son kesitte ise, ana ve ara güvertesi olan bir yapı göz önüne alınmıştır. Çapılma katsayısının hesabının ardından; güvertelerin kesitin rijitliğini artırdığı gözlemlenmiştir.
Sonuç bölümünde ise kesitlerin çarpılma katsayıları karşılaştırılmıştır. Gemi kesitinin kapalı kesite yaklaştıkça, çarpılma rijitliğinin arttığı ve buna bağlı olarak da çarpılma katsayının azaldığı görülmüştür.

Abstract:
Due to the fact that the world has a growing economy, the maritime transportation tools have begun to be developed in order to meet the intended purposes. The main instrument of maritime transport is container ship. To be able to carry more and more container, the ships are built with large deck openings. In the early 1900s, the container ship capacity was about 5000 TEU whereas in today's time the capacity is scaled up to 20000 TEU. The container ships of large deck openings have structural problems. Many researches have been done to sort out the structural problems. Almost every classification society do many research and statistics in order to lighten the design issues in a structural manner. If one have a look at the main structural problem, it is seen that the torsional loading that the ship is exposed to during seaway is the leading issue.
In this study, it is aimed to investigate the warping stresses induced by the torsional loading of the container ships with large deck openings. Larger and larger deck openings are being design in recent days in order to overcome the increasing demand for much more container transport. However, the large openings bring about lowering the torsional rigidity because large openings create discontinuity point. The cargo area, the area between engine room and cargo area or cross deck beams can be defined as discontinuities in ship hull. Besides the effect of the discontinuities, there are structural problems that comes from being designed as thin walled. To be able to lighten the container ships, they are designed as thin walled structures. That's why the torsional rigidity is quite important. In recent years, studies on warping have conducted a dominant role. 
In the first section, general information is given about container ships. The progress in the container carrying capacity and the development of larger container ships are the major topic in the beginning part.
In the following second section, large deck openings that bring about many problems are examined. What is more, some pictures of ship's deformations through the waves are given in order to emphasize the significance of the structural problems. Especially the discontinuity points are the main difficulty in design process.
In the third section, it is given wide coverage to torsion.  In this part, first of all, the development of the recent torsion theory is shared. Many physicists and structural researchers try to lighten the torsion base. For example, A. Michell and L. Prandtl searched flexural-torsional buckling whereas S. P. Timoshenko preferred to write a paper on the effects of warping torsion in I beams. In early 1900s, Vlasov presented the theory of general bending and twisting of thin walled beams. The importance of torsion for the ships with large deck openings is mentioned in third subdivision. In the next sections, the ship is assumed as a beam and the proper ways to calculate the torsional moment are analyzed. Lastly in this section, the several deformations under torsional moment are explained.
In the fourth section, warping induced by torsion is dealt with primarily in theoretic view. At first, the deformations and stresses on deck structure are examined. Many sketches are given to make the deformations and ship sections more clear. It is mentioned that all the ships are exposed to torsional loading during the sail. Although the structural torsional rigidity of the ship is adequate enough, this torsional loading is the major concern for the designer of the ship. The dynamic movement of the ship contributes to stress of the hatch opening edges. During the ships sail among oblique waves, the vertical bending moments are decreased whereas the bending moments in the horizontal direction and the torsional moments are increased. The model test shows the rolling's big effect on torsional moment.
Furthermore, there becomes a static loading to the ship's hull in some cases. One the most import case is the loading/unloading of the cargo in improper way. The sequence of the cargo handling and loading has a significant effect on still water torsional loading. One of the sketches shows the torsional moment distribution along the ship. One can understand that the most critical are is the cargo area of the ship.
Additionally, as the container ships are considered and designed as thin walled structures, the basics of the thin walled theory is given in order to make the ship's structural behavior more clear.
In the fourth section, warping is mentioned in two main groups. The open and closed cross section warping is explained in detail. After all, multiple cell and mixed sections are included.
In the fifth section, the sample sections of a containership are given to be able to understand the theory given in the previous sections more perceptible. The very first section contains only double bottom. It does not have any main deck or a second deck. The half section is being considered. The coordinate system is placed in the keel and mid plane as the ship is symmetrical. The centroid is calculated and placed in the beginning. The next step is the defining the nodes sectors and branches. The ship is sectioned to be able to make the calculations easy to follow. When the nodes are numbers, the geometrical properties are tabulated. In this part, one shall give attention to the coordinates in order to prevent a future mistake. After calculating the centroid, the moment of inertia of every section is being calculated. All in all, the ship's section's moment of inertia is figured out.
By using the geometrical properties of the nodes and sections, the sectoral properties are calculated. The start point is arbitrary and depends on the user's preference. After defining the arbitrary point, the tangent to this point is given. The perpendicular distance from the arbitrary point k to the unit arc is described as ρ. The second sectoral area is found by using this value. While defining the arbitrary point key, one shall kindly note that this point can be chosen as the centroid or the shear center. 
Afterwards, the angle between the user coordinate system and the principal coordinate system is used to determine the moment of inertia of the sections according to principal system. Both rotation and transition are taken into account while the transforming process of the coordinate system. All the nodes' coordinates are transformed into principal axis. 
In order to determine the warping constant, the shear flow properties can be adopted to the calculation. The assumption of the shear flow direction is again arbitrary; however it shall be consistent in its own right.
The following step is to undergo the data of the sections properties. By using those values the warping moment of inertia is found. After all, the integrations are done in order to figure out the warping constant.
In the last section, the statements which are presented theoretically are solve under consideration of an example containership cross section. Firstly the container ship is considered as open deck; only double bottom structure is taken into account. Then a containership section with a mid-plane deck is being considered, the calculation for warping constant is made in order to see the effect of the mid plane. After all, the container ship section is turned into closed section by adding the deck structure. In this study, it is shown that, the warping constant is decreased significantly when the ship section resembles much more a closed section than an open section. The warping constant value of the first section which has only double bottom, no mid plane deck or deck has decreased in the percentage of 20. When comparing to the reduction ratio in the warping function of the third section which is most resembling structure to the closed section to the second section with mid-plane is 24%. In overall result, if the first section (which can be described as open section) is compared to the third section (which is almost closed section), 39% of reduction rate is figured out. Consequently, the more the section resembles closed section, the lower the warping function is which means the closed section warps in a difficult manner.