SummaryThis paper discusses the influence of the rotation of the neutral axis on the residual hull girder strength of asymmetrically damaged ships under longitudinal bending. Progressive collapse analysis of the damaged cross section is performed applying the Smith's method for the biaxial bending problem. An explicit expression of the location of the neutral axis including its rotation is given as a function of biaxial curvatures. The procedures of the progressive collapse analysis of the cross section under biaxial bending are presented for several loading and constraining conditions. A series of progressive collapse analysis of bulk carriers and double-hull tankers having collision damages at the side structures is performed. The residual hull girder strength of damaged ships considering the rotation of the neutral axis is found to be reduced from that obtained by constraining the rotation. The reduction rate of the ultimate strength is investigated for different damage location and extent. For a sagging condition, simple formulae to estimate the residual strength and the reduction rate due to the rotation of the neutral axis are proposed using the elastic cross-sectional properties and critical member strength. The effectiveness of the formulae is examined through a comparison with the progressive collapse analysis. The proposed analysis method and formulae can be utilized for the rational assessment of the residual hull girder strength of damaged ships.
One of the most important criteria in ship design is strength. When a ship is under external loads such as waves, buoyancy or pressure, its internal reaction must resists those external loads. In this regard, external loads are retained by the hull girder, whose cross section is composed of plates and stiffeners, which have a significant influence on ultimate strength, especially in the longitudinal direction. Therefore, this strength must be assessed and evaluated for the ship structure and functional requirements. In this study, local elements of the ship cross section, such as plates and stiffeners, are analyzed, including their progressive collapse behavior. The example used for the calculation is a Roll-on/Roll-off (Ro-Ro) ship. The analysis is performed by assuming that the cross section remains plane and a one-frame space is considered. To calculate the ultimate strength of the Ro-Ro ship under hogging and sagging conditions, Smith's method is used and applied to an in-house program. The applied moment is given on the Multi Point Constraint (MPC) as the reference point of the neutral axis position. In this MPC position, a simple support is attached. The calculation of ultimate strength is made under hogging and sagging conditions, and the intact condition is focused on for the simple calculation. Welding residual stress, cracks, corrosion and initial deflection are not taken into account. Application of the FE method is also made to investigate the characteristics of the collapse mode for local elements and global structure, including ultimate strength.
The fixed jacket is still the most common offshore structure used for drilling and oil production. The structure consists of tubular members interconnected to form a three-dimensional space frame, which can be categorized into a column structure. The structure usually has four to eight legs that are battered to achieve stability against axial compressive loads and toppling due to wave loads. The configuration of a typical member on the jacket structure has significant influence on buckling and fatigue strength. Horizontal and diagonal braces play an important role in resisting the axial compression and wave load on the global structure. This paper discusses the effect of symmetrical and asymmetrical configuration shapes in buckling and fatigue strength analysis on two types of fixed jacket offshore platforms. The axial compressive and lateral (wave) loads were considered and applied to both structures. The material and dimensions of the two structures were assumed to be constant and homogenous. Crack extension and corrosion were not considered. To assess the buckling and fatigue strength of these structures, due to the symmetrical and asymmetrical configuration shape, the finite element method (FEM) was adopted. Buckling analysis was performed on these structures by taking two-dimensional planes into consideration to obtain the critical buckling load for the local plane; fatigue life analysis was then calculated to produce the fatigue life of those structures. The result obtained by FEM was compared with the analytical solution for the critical buckling load. The stress-strain curve was also applied to show the difference between symmetrical and asymmetrical shapes. For fatigue life analysis, the procedure of the response amplitude operator was applied.
The objective of the present study is to analyze the residual strength of asymmetrically damaged ship hull girder under longitudinal bending. Beam Finite Element Method is used for the assessment of the residual strength of two single hull bulk carriers (Ship B1 and Ship B4) and a three-cargo-hold model of a single-side Panamax Bulk Carrier in hogging and sagging conditions. The Smith's method is adopted and implemented into Beam Finite Element Method. An efficient solution procedure is applied; i.e. by assuming the cross section remains plane, the vertical bending moment is applied to the cross section and three-cargo-hold model. As a fundamental case, the damage is simply created by removing the elements from the cross section, neglecting any welding residual stress and initial imperfection. Also no crack extension is considered. The result obtained by Beam Finite Element Method so-called Beam-HULLST is compared to the progressive collapse analysis obtained by HULLST for the validation of the present work. Then, for the three-hold-model, the Beam-HULLST is used to investigate the effect of the rotation of the netral axis both intact and damage condition taking the one and five frame spaces into account. Abstrak Analisis Kekuatan Sisa Penumpu Lambung Kapal Asimetris Pasca Rusak dengan Metode Beam Finite Element. Tujuan dari studi ini adalah untuk menganalisis kekuatan sisa dari penumpu lambung kapal rusak tidak simetris dalam pengaruh lentur memanjang. Metode Beam Finite Element diadopsi untuk pengujian dari kekuatan sisa dari dua kapal bulk carrier (Ship B1 dan Ship B4) dan sebuah model tiga-ruang-muat dari kapal bulk carrier dengan tipe Panamax berlambung tunggal pada kondisi hogging dan sagging. Suatu prosedur penyelesaian yang efisien dengan kata lain lambung kapal diasumsikan tetap pada bidang, momen lentur vertikal bekerja pada penampang dan model tiga-ruang-muat. Untuk kasus kerusakan, bagian yang rusak dibuat sederhana dengan menghilangkan elemen-elemen dari penampang, tegangan sisa pengelasan, dan ketidaksempurnaan awal diabaikan. Tidak ada perpanjangan retak yang dipertimbangkan. Hasil yang diperoleh dengan menggunakan metode Beam Finite Element disebut Beam-HULLST dibandingkan dengan analisis progressive collapse yang diperoleh dengan menggunakan HULLST untuk validasi dari metode yang digunakan. Kemudian, pada model tiga-ruang-muat, digunakan Beam-HULLST untuk menginvestigasi pengaruh rotasi sumbu netral pada kondisi intact dan damage dengan mempertimbangkan satu dan lima jarak gading.
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