• Vol 10, No 5 (2019)
  • Mechanical Engineering

Progressive Collapse Analysis of the Local Elements and Ultimate Strength of a Ro-Ro Ship

Muhammad Zubair Muis Alie, Samuel Izaak Latumahina

Corresponding email: zubair.m@eng.unhas.ac.id

Cite this article as:
Alie, M.Z.M., Latumahina, S.I., 2019. Progressive Collapse Analysis of the Local Elements and Ultimate Strength of a Ro-Ro Ship. International Journal of Technology. Volume 10(5), pp. 1065-1074
Muhammad Zubair Muis Alie Department of Ocean Engineering, Engineering Faculty, Hasanuddin University, Gowa 92171, Indonesia
Samuel Izaak Latumahina Department of Ocean Engineering, Engineering Faculty, Hasanuddin University, Gowa 92171, Indonesia
Email to Corresponding Author


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.

Cross section; Hull girder; Intact condition; Local elements; Ro-Ro ship; Ultimate strength


It is well known that ultimate strength is vital in ship design. This strength must be assessed to protect ships from damage. In this study, three types of strength will be assessed: longitudinal, transversal and local. Longitudinal strength is the most significant of these, and the parameter which is always assessed to establish the bending moment capacity of a ship against external loads when at sea.

Previous studies have discussed the ultimate strength of ship structures. Tekgoz et al. (2018) analyzed a container ship under asymmetrical bending conditions, taking into account the influence of structural damage, the associated neutral axis translation, and the rotation of the residual load carrying capacity. FE analysis and a formulation based on the Common Structural Rules (CSR) were employed. The ship was analyzed in intact and damaged conditions. An asymmetrically damaged ship under a sagging condition was investigated by Muis-Alie (2018). A plate and/or stiffened plate element in the so-called “critical element” specified location reached its ultimate strength, demonstrating that the hull girder had also attained ultimate strength. Nugroho et al. (2018) elaborated a conventional tee stiffener profile on the midship section of an oil tanker structure. Ultimate strength analysis was conducted using the finite element method for all the stiffeners with various geometrical dimensions, according to the International Association of Classification Societies.  Kim and Paik (2017) expanded a fully automated method to optimize design for the hull structural scantling of merchant cargo ships, with a plate-shell used for modeling. To minimize the structural weight and maximize structural safety, a technique for full optimization with multi-objectives was employed, based on the design constraint related to the ultimate limit states of the plate panels, support members and hull girders. The development procedure was implemented on a Very Large Crude Carrier (VLCC) hull structure, the procedure's capacity is shown by this test for requirement of common structural rules. An assessment of the ultimate strength of a Ro-Ro ship after damage was conducted by Muis Alie et al. (2017), with the calculation focused on the cross section. The side shell of the hull and bottom part were assumed to be damaged by simply removing those elements on the bottom part. The results of the analytical solution were compared for intact and damaged statuses under hogging and sagging conditions. Reliability analysis of an oil tanker in an intact condition was conducted by Campanile et al. (2017) to investigate the incidence of load combination methods on hull girder sagging/hogging time-variant failure probability. Using Monte Carlo simulation, the statistical properties of time-variant ultimate strength were determined up to a 25-year ship lifetime. To determine the bending capacity, a modified incremental-iterative method was used, taking into account the corrosion wastage of the structural members influencing hull girder strength, welding residual stresses, and material properties randomness. Gaspar et al. (2016) evaluated the influence of nonlinear vertical wave-induced bending moments on ship hull girder reliability. A chemical tanker, for which the nonlinearity of the vertical wave-induced bending moments was found to be significant, was used as a case study.  Muis Alie et al. (2016) used the finite element method to analyze the ultimate strength of asymmetrically damaged ships. The collision damage was simply created and removes the elements. A comparison between the FE analysis and analytical solution was made, including the collapse behavior of the ship’s hull. The ultimate strength of Floating Production Storage Offloading (FPSO) was calculated by Chen (2016) using reliability assessment methodology. Application of Smith’s method was made to calculate the hull girder ultimate strength of an FPSO. Ultimate strength analysis, including buckling and fatigue, was conducted by Muis Alie (2016) on a fixed jacket platform. The finite element method was employed to analyze the structure, and the symmetrical and asymmetrical shape was taken as the object of the analysis. Ultimate limit state-based ultimate longitudinal strength analysis was performed by Park et al. (2015) to identify the operability of aged non-ice class ships in the Arctic Ocean with consideration of aging. Hull girder ultimate strength was verified by Garbatov et al. (2015) based on the class society and the results obtained by experimental and dimensional theory. Kukkanen and Matusiak (2014) presented a nonlinear time domain calculation method, taking the model test of a roll-on/roll-off passenger ship with a flat bottom stern into account. Using the calculation method and model test results, the nonlinearities in ship motion and hull girder loads were investigated. Residual strength analysis of a ship with bottom damage was conducted by Muis Alie (2014) taking the full cross section into consideration and using the nonlinear finite element method. Improved assessment of ultimate bending capacity was proposed by Kitarovic and Zanic (2014) to enhance the ultimate limit state evaluation in the concept design of monotonous thin-walled structures, predominantly subjected to vertical bending loads during their exploration. The hull girder moment capacity of a Very Large Crude Carrier (VLCC), called energy concentration (EC), for which many benchmark studies have been conducted using the simple progressive collapse method (SPCM), was predicted by Tayyar et al. (2014). The structural strength of the MV Nakhodka was investigated by Yao et al. (1998); applying the NK Rule, longitudinal strength was examined and evaluated using a simplified method of progressive collapse analysis.

In this study, the local elements of the ship cross section and ultimate strength are analyzed, including their progressive collapse behavior. The example for the calculation is a Roll-on/Roll-off (Ro-Ro) ship and only one frame space is employed. An in-house program and finite element analysis are used to calculate the ultimate strength of the Ro-Ro ship. The applied moments are given on both sides of the cross section, together with the boundary conditions, which are assumed to be simply supported. Ultimate strength is analyzed by considering hogging and sagging under longitudinal bending only for an intact condition. For the simple calculation, other parameters such as welding residual stress, cracks, corrosion, and initial imperfections are not taken into account. The finite element method is also employed to investigate the collapse modes for local elements and the global ship structure.


Analysis of the local elements and the ultimate strength of the Ro-Ro ship, including their progressive collapse, has been made using Smith’s method implemented into an in-house program, and the results compared to the numerical solution for comparison purposes. The investigation of the local elements is considered for intact in hogging and sagging conditions. In summary, the conclusion is that the deformation of the local elements on the deck and bottom parts indicate that stress concentration appears in that region. The comparison of the moment-curvature relationship for the cross section of the Ro-Ro ship is identical to the numerical solution obtained by nonlinear finite element analysis. The deformation is not significant on the passenger or car decks, because a Ro-Ro ship has several decks on the cross section.


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