Shear Strength Assessment of Ship Hulls Alice Mathai, Alice T.V., Ancy Joseph

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1 Shear Strength Assessment of Ship Hulls Alice Mathai, Alice T.V., Ancy Joseph Abstract The primary aim of the study is to investigate the ultimate strength characteristics of ship hulls with large hatch opening subjected to vertical and horizontal, shearing forces. As part of this study, the finite element package ANSYS was used for the efficient analysis of the ultimate strength of ship hulls subjected to shear forces. Progressive collapse behavior of a typical container vessel under vertical shear force, and horizontal shear force was analyzed. For analysis full hull model between bulkheads was modeled. When vertical shear force is applied, failure is due to warping of side shells of the vessel and stressing of bilge and top side areas where as the failure by horizontal shear force is mainly due to the warping of bottom shells of the vessel and due to stressing of bilge area. Index Terms ontainer Ship Hull, Finite Element Analysis, Ultimate Shear Strength. I. INTRODUTION ontainer shipping has been not only the facilitator of phenomenal growth in world trade, but is now itself a key driver of growth based on its low cost, reliability, fast transit and ease of use. ontainer ships are open deck ships because of the fact that there are large hatch openings in the deck to permit the stowage of containers in the holds. The hatchways are enclosed by flush hatch covers and additional containers are stored on the open deck. The fact that a large portion of the deck is cut away, creates structural problems, and it is often necessary to use high strength steel to obtain the required structural strength. ontainer ships are much faster than normal cargo ships. They are ships of the linear type in that they work on fixed schedules and between fixed ports. Because of their high speeds and complicated arrangements they are of necessity very costly, but apparently large sums of money which have been spend on them are justified by the speed with which cargo can be dispatched [1]. Fig.1 shows general view of a container ship. It is a double bottom container ship. It is divided into different compartments by transverse bulkheads. Each compartment is called as hold. The arrangement of containers is as shown in the figure. It is a 4500 TEU (Twenty foot equivalent unit) capacity container ship. The primary requirement of the ship structure is that it should resist longitudinal bending, necessitates that a considerable amount of material should be distributed in the fore and aft direction. This longitudinal material is provided by the plating of decks, sides and bottom shell and tank top and any girders which extend over an appreciable portion of the length. Additional longitudinal strength is provided by longitudinal girders in the bottom of the ship. The centre girder is an important member in this respect. It is a continuous plate running all fore and aft and extending from the outer bottom to tank top. Side girders are also fitted, and they are usually intercostals, that is cut at each floor and welded to them. Longitudinal deck girders, even though in general not completely effective for the longitudinal hull girder strength, are also subject to high longitudinal stresses. Fig.1.Hatch overless ontainer Ship Advantages of the longitudinal system are that the longitudinal take part in the longitudinal strength of the ship. The bottom and side shell plating has to resist water pressure in addition to providing overall longitudinal strength of the structure. Thus local stresses can arise due to bending of the plating between frames or floors [2]. When considering the load features where the load is transmitted gradually and continuously from a local structural member to an adjacent bigger supporting member, the best way to categorize loads on the hull structure is as follows: Longitudinal strength loads Transverse strength loads Local strength loads II. HULL GIRDER UNDER SHEAR FORES All bulk carriers classed with IAS Member Societies are assigned permissible still water shear forces (SWSF). When a ship is floating in still water, the ship's lightweight (the weight of the ship's structure and its machinery) and deadweight (all other weights, such as the weight of the bunkers, ballast, provisions and cargo) are supported by the global buoyancy up thrust acting on the exterior of the hull. Along the ship's length there will be local differences in the vertical forces of buoyancy and the ship's weight. These unbalanced net vertical forces acting along the length of the ship will cause the hull girder to shear (fig.2). Fig.2. Shearing Action of the Hull Girder in Still Water At sea, the ship is subjected to cyclical shearing induced by continuously changing wave pressures acting on the hull. These cyclical shearing give rises to an additional component of dynamic, wave induced, shear force in the hull girder [3]. 161

2 At any one time, the hull girder is subjected to a combination of still water and wave induced shear forces. The stresses in the hull section caused by these shearing forces are carried by continuous longitudinal structural members. These structural members are the strength deck, side shell and bottom shell plating and longitudinal, inner bottom plating and longitudinal, double bottom girders and topside and hopper tank sloping plating and longitudinal, which are generally defined as the hull girder. III. GENERATION OF VERTIAL AND HORIZONTAL SHEAR To produce vertical or horizontal sectional shear forces, a set of uniform nodal displacements are applied at all nodes of the unrestrained end section of the hull module in the hull depth or beam direction (fig.3&fig.4)[6]. Fig.5. Warping Stress for the Model Fig 3.Generation of Vertical Sectional Shear by Uniform Nodal Displacements Applied At All Nodal Points of the Unrestrained Hull End Section Fig.6. Warping Stress for Side Shell Fig.4. Generation Of Horizontal Sectional Shear By Uniform Nodal Displacements Which are Applied at All Nodal Points Of The Unrestrained Hull End Section. IV. ULTIMATE VERTIAL SHEAR ANALYSIS For the shear strength assessment non-linear analysis is carried out incorporating material and geometric nonlinearities [7]. It calculates the effect of incremental loading conditions on the structure [8]. It is used to determine displacements, stresses strains and forces in structures and components caused by the shearing loads. In the present case a multiple segment full hull model subjected to vertical shear is considered. The ultimate vertical shear strength for the model is obtained as kN.The value is found to be 3.3 times the design shear force. The figures below (fig 5 and fig.6) display the warping characteristics as well as shear characteristics for the hull model subjected to vertical shear force [9]. Fig.7. Shear Stress for the Model Fig.8. Effect of Shear Stress on Longitudinal Frames 162

3 Thus in summary, the failure of the structure when subjected to vertical shear force is mainly due to the warping of side shells of the vessel and due to stressing of bilge area i.e.; mainly due to the failure of vertical members and ultimate vertical shear strength based safety factor for the vessel, which is defined as the ratio of the ultimate vertical shear strength to the design vertical shear strength is 3.3, which is sufficient enough to withstand the applied extreme shear forces. Fig.9. Shear Stress on Outer Bottom Plate It is seen from Fig. 7 to 9 that the shear stresses are developed in the model. The effect of warping stresses is more pronounced at the end where the restraints are provided where as the shear stresses are higher near to the hard plate provided. It is seen that axial stress (warping stress) is maximum at the bilge and top side part of the outer side shell. For the outer side shell it is seen that at top side compressive stresses are developed and from middle to bottom tensile stresses are acting. From fig.7 and fig.8 it is seen that shear stress is higher on the longitudinal frames near to the end where the hard plate unit is attached and at the bilge area. omplimentary shear stress developed on the outer bottom shell plating of the model is shown in Fig 9.It is seen that the stresses are maximum at the corner where outer bottom shell and inner vertical shell meet. onsidering the hull cross-section displacement paths as defined in fig.3 the following details are obtained. Fig.10 shows the distribution of the three displacement components (i.e., ux, uy, uz nodal displacements in x, y, z directions respectively) at the hull corner along the vessel length at the ultimate limit state. It is seen from the figure that warping (axial) displacements occur symmetrically at the top and bottom corner paths of the hull cross sections. Also, it is seen that the distribution of transverse displacements uz along the vessel length is slightly non-linear but symmetrical. B V. ULTIMATE HORIZONTAL SHEAR ANALYSIS In the present case a multiple segment full hull model subjected to horizontal shear forces is considered.the ultimate Horizontal shear strength for the model is kn The value is 17 times the design horizontal shear force. The figures below (fig.11 and fig.12) display the warping characteristics as well as shear characteristics for the multiple segment full hull model subjected to horizontal shear force. Fig.11. Warping stresses for the model D A Fig.12. Warping Stresses on Bottom Inner Shell Fig.10. Distributions of Displacement in x, y and z directions for each path (Path Plot) Fig.13. Shear Stress on Outer Side Shell 163

4 From these figures it is seen that the stresses are maximum at the region where inner horizontal and vertical shells meet and also at the bilge area. Warping stresses are maximum near to the region where restrains are provided. It is clear from the figures that shear stress is uniformly distributed over the entire area with maximum shear stress at the area near to the vessels central line. onsidering the hull cross-section displacement paths as defined in Fig.4 the following details are obtained. Fig. 14 shows the distribution of the three displacement components (i.e., ux, uy, uz nodal displacements in x, y, z directions respectively) at the hull corner along the vessel length at the ultimate limit state. It is seen from the figure that only a small warping (axial) displacements occur at the top corner paths of the hull cross sections. Also, it is seen that the distribution of transverse displacement uy is symmetrical at all corner paths and uz is symmetrical on adjacent corner paths along the vessel length. B the ship hull occurs due to the collapse of vertical members. The Ultimate vertical shear strength based safety factor for the vessel, which is defined as the ratio of the ultimate vertical shear strength to the design vertical shear strength is 3.3, which is sufficient enough to withstand the applied extreme shear forces. The failure of the vessel when subjected to horizontal shear force is mainly due to the warping of bottom shells of the vessel and due to stressing of bilge area i.e. the vessel collapses due to the collapse of horizontal members. Ultimate horizontal shear strength based safety factor for the vessel, which is defined as the ratio of the ultimate horizontal shear strength to the design horizontal shear strength is 17 which is sufficient enough to withstand the applied extreme shear forces. AKNOWLEDGMENT Dr. Alice Mathai thanks Mrs. Nilofer, M Tech student, MAE for her support and assistance in the preparation of this paper. A Fig.14. Distributions of Displacement in X, Y and Z Directions for Each Path (Path Plot) Thus in summary,the failure of the structure when subjected to horizontal shear force is mainly due to the warping of bottom shells of the vessel and due to stressing of bilge area ie mainly due to the failure of horizontal members and ultimate horizontal shear strength based safety factor for the vessel, which is defined as the ratio of the ultimate horizontal shear strength to the design horizontal shear strength is 17 which is sufficient enough to withstand the applied extreme shear forces. From the above studies it is seen that the ultimate horizontal shear strength based safety factor for the vessel is 17 which is a higher value, so effect of horizontal shear strength on the ship hull is insignificant and may be neglected for further studies. VI.ONLUSION Using the ANSYS software, the progressive collapse behavior of a typical container vessel under vertical shear force and horizontal shear force was analyzed When vertical shear force is applied and when the ship hull would reach the ultimate strength, warping of side shells of the vessel and stressing of bilge and top side areas occurs. Thus failure of REFERENES [1] Tuper E., Introduction to Naval Architecture, third edition, Butterworth- Heinemann, June 27, [2] Benford.H, Naval Architecture for Non-Naval Architects, Society of Naval Architects and Marine Engineering, [3] IAS, Guide lines for Surveys, Assessment and repair of hull structures, container ships, First edition, [4] Jensen, J.J, Load and Global Response of Ships, Oxford: Elsevier, [5] William Muckle, Strength of ship structures, Edward Arnold Publishers Ltd, [6] Ostapenko, A., Vaucher, A. Ultimate strength of ship hull girders under moment, shear and torque, [7] Paik, J.K, Thayambilli, A.K, Pedersan, P.T., 1999.Ultimate strength of ship hull under torsion, Ocean Engineering 28, [8] Felippa..A, Lecture Notes in Non-linear Finite Element Methods, May 1999 University of olorado, Boulder, ANSYS manual [9] Bathe K.J., Finite Element Procedures, Prentice Hull, Englewood liffs, [10] Jensen, J.J. Load and Global Response of Ships, Oxford: Elsevier, [11] JBP, IAS ommon Structural Rules for Bulk arriers, AUTHOR S PROFILE Dr. Alice Mathai working as associate professor in ivil Engineering Department, MAE, graduated from GET, alicut University, has Master s degree in structural Engineering from ollege of Engineering Trivandrum and PhD from Department of Ship Technology, USAT. Her field of interest is Finite Element method and published 12 papers in this field. Prof. Alice T.V working as professor in ivil Engineering Department, MAE, graduated from MAE, M.G. University, has Master s degree in structural Engineering from NIT alicut. Her field of interest is Structural Dynamics and published 3 papers in this field. 164

5 working as professor in ivil Engineering Prof. Ancy Joseph Department, MAE, graduated from MAE, M.G. University, has Master s degree in structural Engineering. Anna University. Her field of interest is Structural Design. 165

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