Hull Girder Ultimate Strength Research Articles

Reliability assessment of ship hull girders considering pitting corrosion and crack

The current study aims to investigate the combined effect of cracking and pitting damage on the ultimate strength of ships. The well-known Smith’s approach is modified considering the random number and distribution of cracked-pitted plates in the ship cross-section. Using the Monte Carlo approach, the structural reliability index of the cracked-pitted ship is determined. A single-bottom oil tanker’s ultimate strength is computed, and it turns out that the reliability indices for various damage scenarios are nearly identical when the ship is at its early age. When the ship ages, its reliability index rises to its maximum if the damage is concentrated at the bottom under sagging conditions and at the sides and longitudinal bulkheads in hogging conditions. The reliability indices in the hogging conditions are often greater than those in the sagging conditions. Furthermore, it is determined that, while the ship is at its early age, the detrimental effect of pitting, cracking, or a combination of both on the reduction of the ship’s hull girder ultimate strength is equal. The lowest reliability index is seen in aged ships when cracking and pitting are combined, followed by cracking and pitting damage separately. It is shown that pitting corrosion has a lower reliability index than the general type of corrosion.

A Bayesian analysis for the quantification of strength model uncertainty factor of ship structures in ultimate limit state

The assessment of ship structural reliability involves the quantification of hull girder ultimate bending capacity. Traditionally, Smith’s method is employed for the probabilistic modeling of capacity. The modeling uncertainty associated with Smith’s method is considered by an independent multiplicative random variable Xr. As real-scale data from hull collapses are not available, the quantification of Xr is usually based on the combination of engineering judgment with more objective information, such as non-linear finite element analysis (NLFEA). In this paper, we propose a Bayesian analysis for the determination of Xr. Specifically, we use Bayesian statistical inference to estimate the parameters that characterize the probabilistic model of Xr based on expert judgment and a limited number of high-fidelity NLFEA data. We demonstrate the applicability of the method on container ships, for which two typical load scenarios are considered: (i) pure hogging moment and (ii) combined hogging moment with local bottom loads. For each load scenario, the corresponding Xr is determined. For cases where specific information from a target ship is available, a classical Bayesian updating scheme is proposed to adjust the distribution of Xr based on the individual ship’s structural characteristics. We present a numerical demonstration for the case of the MOL Comfort at the time of the accident. Finally, the impact of the proposed Xr on the failure probability estimate of a 4,400 TEU and a 9,400 TEU container ship is investigated. We show that using the proposed Xr the estimate of the uncertainty in Smith’s model prediction in pure hogging condition is considerably reduced. In addition, we demonstrate that the action of bottom local loads, which considerably decreases the hull girder ultimate strength and the reliability level of container ships in hogging, can be captured by the proposed Xr without any intervention in the conventional Smith method.

Hull Girder Ultimate Strength Analysis of 17500 LTDW Oil Tanker under the Combined Global and Local Load using Explicit Finite Element Analysis

This study investigates the hull girder’s ultimate strength of 17500 LTDW Oil Tanker. The explicit finite element analysis is carried out to estimate the hull girder longitudinal strength of the Oil Tanker. The numerical analysis starts with the longitudinal strength analyses that examine the ship’s structural response behavior due to sagging and hogging bending moment load. The structural strength analyses were conducted to determine the maximum structural response behavior for withstanding the operational load. Afterward, the hull girder’s ultimate strength is undertaken to reflect the progressive collapse behavior of the oil tanker structure under the combined global bending moment and local hydrostatic pressure load. The explicit finite element analysis is performed to estimate the ultimate strength behavior, considering the effect of the hydrostatic pressure load and the material nonlinearities. The typical 17500 LTDW oil tanker represents Indonesia’s common oil vessel that supports national fuel oil distribution. Furthermore, this study can recognize the oil tanker’s ultimate hull girder strength characteristics.

Hull girder ultimate strength of bulk carrier (HGUS-BC) evaluation: Structural performances subjected to true inclination conditions of stiffened panel members

To enhance the safety of ship structure design, this study evaluated time-dependent hull girder ultimate strength considering thick corrosion and the inclination conditions of stiffened panels. The hull girder ultimate strength was calculated using incremental–iterative methods based on IACS-CSR in a bulk carrier hull model. The corrosion effect was measured as the thickness reduction in structural members, and inclination conditions were considered such as non-uniform uniaxial thrust, which influences the yield strength of structural members. The corrosion effect was investigated from 5 to 20 years of service time, wherein the corrosion rate was obtained based on a reference and was then divided into standard and severe corrosion rate conditions. The effect of non-uniform uniaxial thrust was considered the yield stress reduction on all the stiffener elements in an inclined position. The safety level of the design within each timeframe of the measured corrosion effect was then considered based on the ultimate limit state. This study found that the corrosion rate greatly affects HGUS, with severe corrosion having a greater affect than standard corrosion. In 20 years of service time with uniform loads in hogging conditions, the highest HGUS reduction caused by standard corrosion is 5.87%, while severe corrosion causes a reduction of 24.48%. Moreover, non-uniform uniaxial thrust was found to have a negative effect on HGUS, lowering the HGUS value on benchmark hull models both in hogging and sagging conditions.

Reliability-based assessment of ship hull girder ultimate strength

Abstract A reliability-based approach is presented to investigate the effects of structural and load uncertainties on the reliability estimation of ship hull girders. Structural uncertainties included randomness in material properties, geometric properties, initial geometric imperfections, and corrosion behavior. Load uncertainties included statistical uncertainties, model uncertainties, environmental uncertainties, and uncertainties related to nonlinearity. The hull girder ultimate strength was calculated using Smith’s method, and the probabilistic density function was evaluated by employing Monte Carlo simulations. In the load estimation, the still water bending moment and wave-induced bending moment were calculated using a simplified formula of the International Association of Classification Societies-Common Structural Rules code and then modified with load parameters. The reliability index was estimated using a first-order reliability method considering the operating time, the duration of the ship in the alternate hold loading condition, and the severity of the corrosion rate. As a result, sagging conditions dominated the collapse mode. The reliability indexes were obtained for the observed cases, and the viability of the ship was assessed accordingly.

Application of Equivalent Single Layer Approach for Ultimate Strength Analyses of Ship Hull Girder

The objective of this paper is to present the application of equivalent single layer (ESL) approach for the ultimate strength assessment of ship hull girder in the context of numerical finite element (FE) simulations. In the ESL approach, the stiffened panel is replaced with a single plate, which has the equivalent stiffness of the original panel. Removal of tertiary stiffening elements from the numerical model facilitates time-savings in pre-processing and FE analysis stage. The applicability of ESL approach is demonstrated with two case studies, one compartment model and full-sized double hull tanker model in intact and damaged conditions. The damage extents are determined based on the international association of classification societies from common structural rules (IACS-CSR) for oil tanker. Ship hull girder is exposed to distributed pressure with the sinusoidal shape that bends the hull girder. This pressure load is applied separately to bottom and side structures to obtain the vertical and horizontal bending moments of the hull girder, respectively. Ultimate strength predictions obtained from ESL approach are compared to full three-dimensional finite element method (3D FEM) and IACS incremental-iterative method. The comparison between different methods is provided in terms of longitudinal bending moment and cross sectional stress distribution. Overall, ESL approach yields good agreement compared to the 3D FEM results in predicting the ultimate strength of ship hull girder while providing up to 3 times computational efficiency and ease of modeling.

Comparative investigation on ultimate strength of hull girder with laser-welded web-core sandwich deck

This paper numerically studies the ultimate strength characteristics of the hull girder with the upper deck made of the laser-welded web-core sandwich plates subjected to the vertical bending, the horizontal bending, the torsion and the combined loads among them. The hull girder with the upper sandwich deck is designed from the typical midship section of a light cargo ship as the prototype on the basis of equal cross-sectional area. Compared with the prototype hull girder, the advantages of the hull girder with the upper sandwich deck in the ultimate strength are fully demonstrated in this paper. The results show that by using the laser-welded web-core sandwich deck, the stiffness of the hull girder under sagging has been improved. The sagging ultimate strength of the hull girder can be increased by 15%, and the horizontal bending ultimate strength can be increased by 6.2%. The finite laser weld rotation stiffness has no significant effect on the ultimate strength of the hull girder with the upper sandwich deck. Based on the numerical results, the ultimate strength interaction relationships for the hull girders under the combined two or three moments are established with high accuracy.

Assessment the influences of initial imperfections on the hull girder ultimate strength of ships

In the process of shipbuilding, many methods of processing, assembling, erection, and welding are applied to build the panels, blocks and ship hull. The above-mentioned factors cause the appearance of deformations and residual stresses on the hull structure with different levels and ranges. The assessment of the influence of these imperfections on the hull girder ultimate strength is a matter of great significance in order to assess the seaworthiness, thereby making recommendations to overcome and ensure the ship's safety and operation’s satisfaction. To determine the hull girder ultimate bending moment, an iterative method is used and improved to cover the deformation and residual stress parameters into the structural components. The double hull very large crude-oil tanker, 313,000 tons of deadweight, is used to calculate the value of the ultimate bending moment for two conditions of ship such as hogging and sagging. The results of the ultimate bending moment for the above two conditions under the influence of the imperfections are given and evaluated. Several conclusions have also been drawn in this paper.

Numerical and experimental analyses of ultimate longitudinal strength of a small-scale hull box girder

Hull girder ultimate strength is an essential parameter for the ship's structural design. Numerous research studies have been done about hull girder bending. However, few experimental tests have been carried out due to the fabrication cost, the difficulty of monitoring loads, and mapping surfaces of models on large- and medium-scale. This paper conducted a four-point bending test of a small-scale hull box girder. The dimensions of the box girder model are defined from geometric slenderness ratios representing a double bottom panel at the midship of a typical Suezmax tanker. Numerical finite element models are developed, where the friction coefficient between the model and its supports is determined based on experimental correlation. The numerical models with different initial imperfection distributions are considered to perform ultimate strength analyses. Initial imperfections implemented in the models are based on least-squares regression of the geometric imperfections measured from the experimental models. Strain gauges were installed at the upper panel and obtained measurements compared with local numerical strains. Both experimental and numerical models showed that the upper panel of the box girder presented initial structural failure in the plating between stiffeners, which evolved to the stiffeners, following the expected buckling sequence of a reinforced panel. IACS formulation and direct methods have been employed to evaluate the ultimate bending moment. A correlation between the theoretical and experimental results indicates that the IACS formulation better predicts the ultimate bending moment, with the additional advantage of estimating the curvature. This paper also provides methodology and parameters for future studies of the ultimate strength of ship panels with different slenderness ratios.

Scaling characteristics of the hull girder's ultimate strength subjected to the combined hogging moment and bottom lateral pressure: An empirically modified scaling criterion

The ultimate strength of the ship hull girder under combined loads is closer to the load-carrying capacity during the actual sailing for considering the negative effect of the secondary load in some cases. Scaled models are designed to represent the prototype in ultimate strength experiments. To study the effect of the bottom lateral pressure on the scaled hull girder under combined loads thoroughly, a series of hull girders of a 10,000TEU container ship under different scale combinations of geometric length and plate thickness are analyzed. The relevant changes in the characteristics of ultimate strength and collapse behaviors caused by bottom lateral pressure are investigated. Results show that the ultimate hogging moment predicted by the traditional or the empirical scaling law proposed in the reference is significantly different from that obtained by numerical analysis when the scale ratio of the plate thickness is much smaller than the geometric scale ratio for ignoring the significant effect of the bottom lateral pressure. Correspondingly, an empirical scaling criterion is proposed to improve the accuracy of the converting process of the ultimate strength between scaled models and the full-scale prototype. Finally, the applicability of the proposed scaling criterion is verified by numerical results of a series of simplified hull girder models.

Numerical investigation of the hull girder ultimate strength under realistic cyclic loading derived from long-term hydroelastic analysis

ABSTRACT Traditionally, the hull girder ultimate strength is determined by subjecting the structure to monotonic increasing loads. However, it is well-known that ships are continuously subjected to cyclic loads induced by waves. Therefore, some doubts are cast on the probability that alternating loads may reduce the hull girder ultimate strength. This research aims to analyze the influence of cyclic loads over the structural capacity by considering realistic loading scenarios resulting from a longterm hydroelastic analysis. The ultimate strength of a containership is analyzed numerically on a partial structural model using the nonlinear finite element approach. Different material properties are considered to investigate how the hardening and softening effects in steel affect the structural capacity. Finally, the ultimate strength determined under cyclic loading is compared to the standard ultimate strength determined under monotonic increasing loads. It is shown that for the considered containership, the cyclic loading has a negligible effect on the ultimate strength.

Progressive collapse analysis of a bulk carrier hull girder under longitudinal vertical bending moment considering cracking damage

Existence of crack causes reduction of the load carrying capacity of ship hull structural elements and eventually reduces the hull girder strength. Previous numerical and semi-analytical studies by the same authors revealed that in addition to the value of ultimate strength, the deflection shape and plastic collapse mechanism of ship hull structural elements will change due to existence of cracking damage. In this paper results from previous studies are used to investigate the way cracks affect ultimate longitudinal strength of ship hull girder. Progressive collapse analysis of an ISSC2000 bulk carrier is carried out to estimate its ultimate strength considering existence of cracking damages at different locations of the hull girder; namely bottom, double bottom, side and deck structures. For this reason, HULLST software which is based on Smith's method was modified to be able to model specific cracks anywhere in the ship hull girder. Results show that the way cracking damage effects the ultimate strength of the ship depends highly on the ship's collapse modes in hogging and sagging conditions as well as behavior of the ship structural elements.

Incidence of Pitting Corrosion Wastage on the Hull Girder Ultimate Strength

The paper focuses on the assessment of the hull girder ultimate strength, combined with random pitting corrosion wastage, by the incremental-iterative method. After a brief review about the state of art, the local ultimate strength of pitted platings under uniaxial compression is preliminarily outlined and subsequently a closed-form design formula is endorsed in the Rule incremental-iterative method, to account for pitting corrosion wastage in the hull girder ultimate strength check. The ISSC bulk carrier is assumed as reference ship in a benchmark study, devoted to test the effectiveness of the incremental-iterative method, by a comparative analysis with a set of FE simulations, performed by Ansys Mechanical APDL. Four reference cases, with different locations of pitting corrosion wastage, are investigated focusing on nine combinations of pitting and corrosion intensity degrees. Finally, a comparative analysis between the hull girder ultimate strength, combined with pitting corrosion wastage, and the relevant values, complying with the Rule net scantling approach, is performed. Based on current results, the modified incremental-iterative method allows efficiently assessing the hull girder ultimate strength, combined with pitting corrosion wastage, so revealing useful both in the design process of new vessels and in the structural health monitoring of aged ships.

A probabilistic approach to assess the computational uncertainty of ultimate strength of hull girders

The simplified progressive collapse method is codified in the IACS Common Structural Rules (CSR) to calculate the ultimate strength of ship hull girders in longitudinal bending. Several benchmark studies have demonstrated the uncertainty of this method, which is primarily attributed to the variation in the load-shortening curve (LSC) of local structural components adopted by different participants. Quantifying this computational uncertainty will allow the model error factor applied for the ultimate strength of hull girder in a reliability-based ship structural design to be determined. A probabilistic approach is proposed in this paper to evaluate the prediction uncertainty of ultimate strength of the hull girder caused by the critical characteristics within the LSCs. The probability distributions of critical load-shortening characteristics of stiffened panels are developed based on a dataset generated by empirical formulae and the nonlinear finite element method. An adaptable LSC formulation, with the ability to cater for specific response features of local components, is utilised in conjunction with the Monte-Carlo simulation procedure and the simplified progressive collapse method to calculate the ultimate strength of a hull girder at each sampling. The proposed method is applied to four merchant ships and four naval vessels. The computational uncertainties of the ultimate strength of the case study vessels are discussed in association with their mean values and standard deviations. The study shows that the ultimate strength of ship hull girders is subjected to different uncertainties in sagging and hogging. Whist the strength of merchant ships are primarily governed by the ultimate compressive strength of critical stiffened panels, the strength of naval vessels are also sensitive to the post-collapse response of critical members.

Study of hull girder ultimate strength at elevated temperatures

ABSTRACT Fire poses a significant threat in the shipping industry not only for humans (passenger, seafarers) but also for the ship structure. It is of great concern how elevated temperatures from a fire can influence the bending moment capacity of a hull girder due to the degradation of steel’s mechanical properties. The aim of the paper is to evaluate the ultimate bending moment capacity of a chemical oil/product carrier at ambient and elevated temperature conditions. The study defines the parameters and modelling that need to be considered in the finite element analysis (FEA) and proposes a modified incremental–iterative procedure for the bending moment capacity calculation at elevated temperatures. Smith Method was extended in order to incorporate neutral axis rotation and steel’s mechanical properties at elevated temperatures. The proposed modified Smith Method’s results present good agreement with the equivalent FEA results. It is concluded that with the proposed modified Smith Method, it is possible to determine the loading that can be carried by a hull girder with a specified temperature profile. The study also determines an analysis technique for the stiffened panel ultimate strength analysis at elevated temperatures.

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

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.

Post-ultimate strength behaviour and collapse severity of ship hull girder under extreme wave load by an analytical method

ABSTRACT When the external load exceeds the ultimate strength of hull girder, the load-carrying capacity is not completely lost due to the supporting and constraint between structure members. It is also determined by the post-ultimate strength behaviour, and the collapse severity needs to be studied to evaluate the consequence of collapse. An analytic approach is presented in this paper to analyse the factors influencing the collapse severity of hull girder under extreme wave load. The equations of motion of hull girder are derived for an external moment unloading in different ranges of the generalised moment-curvature relationship so as to predict the corresponding final severity of collapse. The severity is also analysed from the energy point of view to investigate the influence of the capacity drop on the severity. The complete post-ultimate strength behaviour of hull girder revealed in this study provides a reference for structure safety design of ship hull girders.

Ultimate strength of ship hull girder with grounding damage

ABSTRACT The paper presents a method for the assessment of residual strength of a ship hull damaged in a grounding accident. The strength assessment is based on a coupled beam (CB) method that allows time-efficient analysis. As a case study the method is applied to a double hull tanker. Three grounding damages are defined based on IACS guidelines and with a dedicated grounding assessment tool. The CB method is based on an assumption that global bending response of a ship can be estimated with the help of beams coupled to each other by distributed springs. To include the damage opening in the residual strength assessment, the structural elements in the damaged region are excluded by reducing their elastic modulus. For the validation of the CB method, the residual strength is also evaluated with non-linear finite element method. Good correlation between the methods is reported.

Progressive Collapse Analysis of an FPSO Vessel Hull Girder Under Vertical Bending Considering Different Corrosion Models

Nowadays, with the increasing operational life of ships, the aging effects on their structural behavior need to be investigated precisely. With the corrosive marine environment taken into consideration, one of the important effects of aging that must be studied is thickness degradation. In this paper, with the use of previously proposed equivalent thickness formulations for corroded plates, the progressive collapse analysis software HULLST is enhanced, and then, the effects of different corrosion models of uniform, random, pitting, and tanker pattern types on the ultimate and residual strengths of a floating production, storage, and offloading vessel hull girder are evaluated for the ages of 0 to 25 years. Results reveal that the uniform corrosion and random corrosion models have close outcomes. The value of relative reduction in the ultimate strength of ship hull girder (compared with the intact condition) ranges roughly from 6% for the age of 5 years to 17% for the age of 25 years in the hogging mode. The relative reduction in the ultimate strength ranges from 4% to 16% in the sagging mode. Pitting corrosion and tanker pattern (random) corrosion models lead to higher relative reductions in ultimate strength. The pitting corrosion model leads to a 16%–32% relative reduction in the ultimate strength for the ages of 5–25 years of the ship in either hogging or sagging. The tanker pattern (random) corrosion model leads to a 6%–37% relative reduction in the ultimate strength in the hogging mode and 3%–31% in the sagging mode at ship ages of 5 to 25 years.

Hull Girder Ultimate Strength Assessment Considering Local Corrosion

The residual strength capacity of ship hull with full corrosion appearance in every structural member has been considered in a large number of research works; however, the influence of local corrosion on the ultimate strength and cross-section properties has not been taken into account and analyzed. Hence, this study aims to assess the effect of corrosion appearance in the flange section and web section on the ultimate vertical bending moment and several cross-section properties of a bulk carrier. To perform this task, a probabilistic corrosion rate estimation model and the common structural rule model are introduced and employed. The incremental-iterative method given by the International Association of Classification Societies-Common Structural Rules (IACS-CSR) is applied to determine the ultimate vertical bending moment, neutral axis position at the limit state, and other properties of the cross-section. The calculation results and discussions relative to the effect of corrosion on ship hull are presented.