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

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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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