Effect of profile element dimension to the ultimate hull girder strength

The hull girder plays an important role against those loads and to describe the structural behavior under longitudinal bending. The hull cross-sectional properties have a significant contribution to the ultimate strength investigation. Therefore, the influence of the element section properties to the ultimate hull girder strength must be evaluated. The objective of the present study is to calculate the ultimate hull girder strength considering the element section properties subjected to longitudinal bending. Two double-hull tankers are taken with the same dimension, but different from the element section properties characteristic such as number, dimension, and type of the stiffeners located on the bottom, shell and deck parts. The basic formula is adopted to calculate element section properties of the hull girder for double hull tanker. The double hull tanker is modeled as a cross-section having the stiffeners and attached plating. The stress due to the difference of the element section properties is less than allowable stress.


Introduction
The longitudinal strength is the most important aspect of ship design. To know the longitudinal strength of the ship, the calculation and evaluation must be conducted. These may be used as an analytical solution or numerical calculation. Classically, the longitudinal strength of the ship is analyzed by considering the beam theory approach. However, the other procedure may also be implemented as mentioned before.
The longitudinal strength analysis of ship has been done by many researchers particularly for tanker and bulk carrier. The residual strength of an Aframax-class double hull oil tanker damaged in the collision had been assessed by Parunov [1] by considering the influence of the rotation of the neutral axis. The influence of nonlinear finite element method models on the ultimate bending moment for hull girder was studied by Xu [2]. There was two analysis were performed, those were implicit static analysis and explicit dynamic analysis. A structural reliability analysis model based on a Bayesian belief network was proposed by Li and Tang [3] for the hull girder collapse risk after accidents. The Bayesian belief network was used to represent random states of variable risk events after accidents, as well as the dependencies between events, and the structural reliability analysis was used to evaluate the failure probability hull girder for each possible accident conditions. The incidence of collision damage models on an oil tanker and bulk carrier reliability was investigated by Campanile [4] considering the IACS deterministic model against GOLADS/IMO database statistics for collision events, substantiating the probabilistic model. Reliability of an oil tanker in intact condition was performed by Campanile [5] to investigate the incidence of load combination methods on hull girder  [6] considering the critical element under sagging condition. The residual hull girder strength in intact and damage condition under longitudinal bending moment using nonlinear finite element was conducted by Muis Alie [7], and damages were modeled simply by removing the element on the damaged part. The ultimate hull girder strength considering section modulus under longitudinal bending was analyzed by Muis Alie and Latumahina [8] and the cross-section of Ro-Ro ship was taken to be analyzed.
The comparative study of the element section properties to the hull girder ultimate strength on double hull tanker is studied. Two double-hull tankers are considered having same dimensions, but different characteristics for the element section properties such as number, dimension, and type of stiffeners located at the deck, inner and outer side shell and bottom part. The simplified calculation method is adopted to analyze the ultimate strength of double hull tanker. The influence of the characteristics is presented for number, dimension and type of the stiffeners to the ultimate hull girder strength.

Basic formula
The primary hull girder bending depends on the element composed of stiffened and unstiffened plates. The number, dimension, and type of the plate and stiffened plates give a contribution to the longitudinal strength. Therefore, these configurations should be analyzed for the design purpose. Figure 1 shows the cross-section of double hull tanker and figure 2 the typical type of stiffened plate with attached plating.      3  22 3  2  3   12  2  12  2  12  2 pp The where D represents as the ship's depth. The stress components on deck and bottom part can be obtained by using simple expression as follow, Where M is the moment on the deck or bottom part in hogging and sagging conditions. The bending moment may be used either for equation (7) or (8).

Ship properties
The ultimate hull girder strength analysis taking the influence of number, dimension, and type of the element section properties into consideration is conducted. Two double hull tanker is taken having the same particular dimension but different for dimension and type of the element section properties at the bottom, sides hell, and deck part of the cross-section. In the present study, the calculation of the element section properties is conducted for half part because the cross-section is symmetric. The difference is marked by the color lines at bottom, inner and outer side shell and deck part including the longitudinal bulkhead at the canter part of the cross-section. The half cross-section of double hull tanker for type-1 and type-2 are shown in figures 3 and 4.  It should be noted that the dimension of double hull tanker type-1 and type-2 is equal, including the material properties. Based on the calculation using the above formula, the still water, wave and total vertical bending moment under hogging and sagging conditions are summarized in table 1 as follow: The longitudinal bending moment obtained by the basic formula of double hull tanker for type-1 and type-2 is summarized in table 2 as follow

Conclusions
The longitudinal hull girder strength analysis of double hull tanker considering element section properties under hogging and sagging conditions have been performed based on the basic formula. Those results are compared to the formula described in classification rules. According to these results, the following conclusions may be taken as follow; the influence of the element section properties on the longitudinal hull girder strength is significant on the double hull tanker. The longitudinal bending moment and the allowable working stress occurs on the deck and bottom part under hogging and sagging conditions are smaller than a formula by the classification rules. It indicates that the longitudinal bending moment and working stress under the allowable requirement.