Model experiment of large superstructures’ influence on hull girder ultimate strength for cruise ships

Highlights

• A collapse experiment of steel model with superstructures was carried out simulate the failure procedure of cruise ship.

• The NFEA was validated by the experiment and applied to study the variation of superstructure effectiveness.

• The increment-iterative method was revised to consider the superstructure effectiveness for cruise ship.

• A new formula was proposed to predict the ultimate strength under combined load conditions with large superstructures.

Abstract

Cruise ships have large and long superstructures, which are almost extending the whole ship length with discontinuous characteristics, such as side shell recess and many window openings. The superstructure effectiveness on hull girder longitudinal strength is a complicated but unavoidable issue in ship design stage. This paper has carried out a collapse experiment of steel model with superstructures, which is designed based on one actual cruise ship. Critical factors including initial imperfections and welding residual stress used in nonlinear FE analysis have been validated by the experiment results. Then, the superstructure effectiveness is analyzed to revise the increment-iterative to be applicable for ultimate strength evaluation for cruise ships. At last the combination action of bending moment and shear force is studied, and a new combination formula is proposed. The conclusions in this paper will be useful for ship design, rules amendment and safety assessment for cruise ships.

Introduction

Compared with common ships with one deck, cruise ships have special structural configurations with large superstructures almost extending the whole ship length and ship width, which will bring in new design problems. The superstructures are the most important part for the attraction of passengers. In order to satisfy the travel and relaxation need at the sea, more cabins with balconies, atriums through several decks, theatres and dining halls with wide space in the superstructures. The sides are penetrated by many window openings, door openings, balconies opening and longitudinal bulkhead recess for lifeboat arrangement, which will reduce the shear stiffness within the plane.

Based on loading manuals of cruise ships, the still water bending moment is in hogging conditions for most cases due to a low deadweight requirement or a uniform loading at each deck with a low block ship coefficient (Bajic, 2015). The hogging condition under still water and wave moment will be the critical design case. This paper will deal with the issues of hogging condition in following analysis.

From the view of load carrying capacity, the bending moment can be carried by both the main hull and the superstructures. The hull girder can be seemed as a beam with various cross section characteristics for real combinations of open and closed cross section (Zanic and Prebeg, 2005). The longitudinal stress of superstructures is lower than that of expected from classic beam theory (Biot et al., 2006). The interaction between main hull and superstructure becomes complicated, the superstructures can not bend as fully consistent with main hull, and therefore the superstructures’ effectiveness on longitudinal strength is reduced (Fricke and Gerlach, 2015). The superstructures will bear a larger part of longitudinal loads after the optimal design with a lower neutral axis toward outer bottom (Romanoff et al., 2013).

The influence of superstructures on longitudinal strength should consider several main parameters, including side shell openings, side recess distribution, longitudinal bulkhead, and transverse supporting structures. The whole ship 3D FE analysis is considered sufficient for the complicated global response (ISSC, 1997), including superstructures' effectiveness, shear lag in superstructure's decks, and shear force transfer between hull and superstructures. The longitudinal strength of cruise ship with multi-layer superstructure decks was analyzed by a whole-ship FEM to study the interaction between main hull and superstructures (Zanic et al., 2009).

From elastic state to limit state, the effect of superstructure on hull girder strength may be changed as the variation of the force transfer path due to local buckling and local yielding failure. The ultimate strength of hull girder may be overestimated when no considering the change of the superstructure effectiveness (Shi and Gao, 2018). The superstructure influence on hull girder ultimate strength can also be analyzed by the model experiment method. There are model experiment reports about stiffened panels, box girders and scaled single-deck ships (Shi and Wang, 2012a). However, the collapse experiment with superstructures has no report now.

For commons ships with a single deck, the hull girder ultimate strength can be analyzed by the incremental-iterative method initially proposed by Smith (1977).The cross section is assumed to bend under an assumption of rigid boundary conditions and the neutral axis position of the cross section is the main parameter as a function of the curvature. However, this method has not considered the shear lag effect due to longitudinal bulkheads and side shells (Parmasto, 2012), and the superstructure effectiveness to the contribution of main hull strength.

For actual ships, the vertical bending moments and the vertical shear forces exist at the same time along ship length. The ratio of the bending moment and the shear force varies for the different loading conditions. Although the position at the maximum bending moment usually has the shear force close to zero (Yao et al., 2004), there are some cross sections with large bending moment and large shear force, such as the position within 1/4–1/2 ship length. The combination of shear force and bending moment will change the progressive failure mode and ultimate strength (Naar, 2006).

The effect of the vertical shear force on the bending ultimate strength should consider two factors:(1) the combination of shear stress and axial compression stress on structural members (Kitarović et al., 2010); (2) the increase of longitudinal stress due to shear induced warping deformation at the cross section (Žanić and Kitarović, 2015). For the double-side arrangement, such as Oil Tankers, the vertical shear forces have a little influence on the bending ultimate strength because the side shell has sufficient strength to withstand the shear deformation (Alfred Mohammed et al., 2016). But the single-side structures in cruise ships are more prone to shear loads. And also the side shell openings and recess in cruise ships will reduce shear stiffness to have significant effect on the hull-superstructure interaction (Parmasto, 2012).

This paper tries to solve the problems about the superstructures on hull girder ultimate strength for cruise ships, including the superstructure effectiveness, the applicability of increment-iterative method on ultimate strength evaluation for cruise ships, and the combined action of bending moment and shear force. Firstly, a collapse experiment of steel model with superstructures under hogging conditions is provided, and nonlinear FE analysis method is validated by the experiment results. Then, superstructure effectiveness is analyzed in detail, and the increment-iterative method is revised. At last the combination action of bending moment and shear force on hull girder ultimate strength is studied.