analysis of hull girder ultimate strength and residual...

Research ArticleAnalysis of Hull Girder Ultimate Strength and Residual StrengthBased on IACS CSR-H

Gui-jie Shi ,1 Da-wei Gao ,2 and Hong Zhou3

1State Key Laboratory of Ocean Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,China Strategy Institute ofOcean Engineering, School of Naval Architecture, Ocean& Civil Engineering, Shanghai JiaotongUniversity,Shanghai 200240, China2School of Mechanical Engineering, University of Shanghai for Science & Technology, Shanghai 200093, China3School of Ocean and Civil Engineering, Jiangsu University of Science and Technology, Jiangsu, Zhenjiang 212003, China

Correspondence should be addressed to Gui-jie Shi; [email protected]

Received 24 December 2018; Accepted 2 June 2019; Published 27 June 2019

Academic Editor: Surajit Kumar Paul

Copyright © 2019 Gui-jie Shi et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to express the safety level of hull structures, IACS Common Structure Rules of Bulk Carriers and Oil Tankers (CSR-H) makes new requirements of hull girder ultimate strength. Compared with original CSR (i.e., CSR-OT and CSR-BC), partialsafety factors of hull girder ultimate strength in CSR-H have been partly modified, and new requirements of residual strength havebeen added in the rules for hull safety after grounded/collided damage. This paper compares the rule requirements of ultimatestrength in CSR-H and CSR-OT/CSR-BC and explains the technical background of rule requirements. The hull girder ultimatestrength is mainly analyzed by SMITH method in rule requirements due to fast and stable calculation results. This paper also usesnonlinear finite element method (NFEM) to explain the critical influence factors for hull girder ultimate strength implied in therule requirements. Based on 5 typical Bulk Carriers and 4 typical Oil Tankers, the influence of hull girder ultimate strength andresidual strength in CSR-H has been evaluated for ship building industry. The actual ship evaluation results can be used to instructthe new CSR-H ship design.

1. Background

The CSR rules proposed by International Association ofClassification Societies (IACS) have brought about significantinfluence on the procedure of ship design and building ofBulk Carriers andOil Tankers. CSR rules are divided into twoparts, that is, Common Structure Rules of Double Hull OilTankers (abbreviation CSR-OT) [1] and Common StructureRules of Bulk Carriers (abbreviation CSR-BC) [2]. BecauseCSR-OT and CSR-BC are complex rule systems and theirdevelopment time is very short and urgent, some technicalpoints in these rules are subjected to disputation of shipindustry. Especially for the common part of CSR-OT andCSR-BC, the two rules have not always given the samerequirements. Although the ship industry has given someproposal of rules improvement and update, they would preferthat IACS can make harmonized rules for Bulk Carriers andOil Tankers.

In order to satisfy the industry expectations, IACSpromises to harmonize the differences between CSR-OT andCSR-BC and draft Common Structure Rules of Bulk Carriersand Oil Tankers (abbreviation CSR-H) [3] based on the sametechnical routes and methodologies. The safety level impliedin CSR-H will not be lower than original CSR-OT and CSR-BC. At the same time, International Maritime Organization(IMO) has proposed new regulations for Bulk Carriers andOil Tanker, i.e., Goal Based New Ship Construction Standard(GBS) [4, 5]. So CSR-H should satisfy the GBS functionrequirements.

After several years work of IACS society members, theCSR-H rules were approved by IACS council on 18th Decem-ber 2013. CSR-H will be applied on Bulk Carriers havinga length of 90 m or above and double hull Oil Tankershaving length L of 150 m or above, which is contracted forconstruction on or after 1st July 2015. IACS rules set forBulk Carriers and Oil Tankers, including CSR-H rules, URs

HindawiMathematical Problems in EngineeringVolume 2019, Article ID 2098492, 11 pageshttps://doi.org/10.1155/2019/2098492

https://orcid.org/0000-0002-7707-8821

https://orcid.org/0000-0001-6410-5619

https://creativecommons.org/licenses/by/4.0/

https://doi.org/10.1155/2019/2098492

2 Mathematical Problems in Engineering

(Unified Requirements), and Recommendations, cover allthe IMO GBS function requirements, such as human ele-ment considerations, structural redundancy, and structuralstrength.

Hull girder ultimate strength belongs to the 3rd functionrequirement of IMO GBS and residual strength is the 5thfunction requirement. The rule requirements of hull girderultimate strength are covered both in CSR-OT and CSR-BC,but there are large differences between these two rules. Theconcept of residual strength is only mentioned in principle,but the calculation methods and evaluation criteria are notrequired in CSR-OT and CSR-BC. In order to satisfy GBSrequirements, CSR-H should add the rule requirements ofresidual strength, which could assure the hull safety aftercollision or grounding damage in this rule.

ISSC summarized the recent research results about resid-ual strength of ship and offshore structures after collisionand grounding damage [6, 7]. Amante et al. [8] investigatedthe residual strength of a semisubmersible platform columndamaged by a supply vessel collision and estimated the safetymargin associated with the column structural capability afterthe collisions. Paik et al. [9] developed empirical formulas forresidual strength of double hull Oil Tankers of the form ofResidual Strength vs. Damage Index (R-D) diagrams. Kim etal. [10] used a similar approach to develop R-D diagrams andempirical relations for container ship designs with groundingdamage. Choung et al. [11] analyzed the effect of neutral axisrotation on hull girder ultimate strength.

Based on the IACS CSR-OT requirement for hull girderultimate strength, Xu et al. [12] carried out reliability assess-ment of a tanker using the model correction factor method.It is shown that using semiempirical response models includ-ing the important mechanical features with respect to thebending capacity of hull girder, the reliability evaluation canbe performed with a limited number of nonlinear FEM (lessthan 10) promoting the application of advanced responseand reliability methods to complex structures. The nonlinearFEM results prove that CSR incremental-iterative methodcan provide conservative results of hull girder ultimatestrength.

Based on the IACS CSR-OT requirement for hull girderresidual strength, Hussein and Guedes Soares [13] carried outreliability and residual strength of double hull tankers. Dif-ferent damage scenarios at side and bottom were consideredwith different damage sizes to define a lower limit of strength,which might be accounted for during design. The residualstrength is calculated using incremental-iterative method.Reliability of the damaged ships is calculated considering theincrease in the still-water bending moment due to damageand the loss in ultimate strength.

Amlashi and Moan [14] carried out hogging ultimatestrength analysis of a bulk carrier hull girder under alter-nate hold loading condition. The significant double bottombending in empty holds in AHL due to combined globalhull girder bending moment and local loads is researched.The local loads on double bottom substantially reduce theultimate strength of the hull girder. The implication of usingdifferent design pressures based on CSR and DNV rules onthe hull girder strength is assessed.The FE results can be used

as a basis for establishing simplified methods applicable topractical design of ship hulls under combined loading.

Witkowska and Guedes Soares [15] also studied ultimatestrength of locally damaged panels. The damage is in theform of a local imperfection and represents a dent that couldbe caused by a fall or strike of an object. The influenceof several parameters has been studied to establish theirinteractionwith the presence of the local dent.The large panelis compared with smaller transverse model made of threeplates and with a single plate model in order to evaluate theeffects of adjacent plates and define the minimum size ofthe model necessary to obtain proper results. Saad-Eldeenet al. [16] studied ultimate compression strength of highdamaged plates resulting from dropping objects, groundingor collision.The effect of dent depth, dent shape, and dent sizeis studied. An expression to estimate the average reductionof ultimate strength of highly damaged steel plates, subjectedto compression loading as a function of the residual breadthratio, is also developed.

Alfred Mohammed et al. [17] carried out design safetymargin of hull girder ultimate strength under vertical bend-ing and torsion combined loads. The results show thatthe vertical bending moment capacity of the hull girder isreduced when torsion is incorporated. The design extremevalues of principal global wave-induced load componentsand their combinations in irregular seaways are predictedusing a cross-spectral method together with short-term andlong-term statistical formulations. Consequently, the marginof safety between the ultimate capacity and the maximumexpected moment is established. Shi and Wang [18] studiedthe similar model for hull girder ultimate strength undercombined loads of bending and torsion. The similar modelof actual ship was derived based on the thin-walled beamtheory. A mathematical model optimizing the similar modelwas set up to improve the design scantlings. The ultimatestrength consistency of the actual ship and similar model arevalidated by nonlinear FEM under the action of bending andtorsion, so the similar model can be used in experiment totest the actual ship ultimate strength.

In case of design rule, previously Pre-CSR & CSR designhave been compared by Paik et al. [19]. Recently,Wu et al. [20]have clearly reviewed previous design rule (CSR) and newrule (CSR-H) on effect of structural design and scantlings.The effects of corrosion suggested by Pre-CSR, CSR, andCSR-H on ultimate hull girder strength are also recentlyinvestigated by Kim et al. [21]. In addition, in the presentstudy CSR vs. CSR-H can also be covered for the comparisonpurpose.

In this paper, the rule requirements of ultimate strengthand residual strength in CSR-H are compared in detailwith CSR-OT and CSR-BC, and the technical backgroundsfor making the rule requirements are also explained. Thehull girder ultimate strength is mainly analyzed by SMITHmethod in rule requirements because of fast calculation andtime saving. This paper also uses nonlinear finite elementmethod to explain the critical influence factors for hullgirder ultimate strength implied in the rule requirements. Inaddition, 5 typical Bulk Carriers and 4 typical Oil Tankers aresampled for ship building industry and the influence of hull

Mathematical Problems in Engineering 3

girder ultimate strength and residual strength in CSR-H hasbeen evaluated for actual ships.

2. Rule Requirements Comparison betweenCSR-H and CSR

2.1. Hull Girder Ultimate Strength. CSR rules (includingboth CSR-OT and CSR-BC) introduce the design concept ofultimate state, local hull members are permitted to produceplastic buckling/yield deformation, and hull girder ultimatestrength should be evaluated under extreme wave condition.Before reaching the hull girder ultimate strength, the hullgirder bending moment including static water moment andwave moment may lead to nonlinear deformation in hullmembers; that is, the plating, stiffeners, and longitudinalgirders of deck or bottom in tension area may producelocal plastic deformation and compression area may produceplastic buckling deformation. Therefore, from the designpoint, plastic deformation and stress redistribution in struc-ture members are necessary to be evaluated for hull girderultimate strength. Reasonable structure scantlings and staticwater bendingmoment should be designed so as tomaximizethe utilization of hull girder ultimate strength.

Comparison between CSR-OT and CSR-BC shows thatthere are some differences in rule requirements of hull girderultimate strength. CSR Oil Tankers only permit the shipdesign of double side and double bottom, so these shipshave strong hogging bending capacity due to compressionstress acting on double bottom and relatively weak saggingbending capacity due to compression stress acting on singlelay of deck structures. In CSR-OT, only sagging ultimatestrength is required to be verified in seagoing condition, butno requirements about hogging ultimate strength or harborcondition. InCSR-BC, hogging and sagging ultimate strengthare both required to be verified in seagoing, harbor, andflooding conditions, and especially the flooding conditionis special important condition for bulk carrier safety con-sidering history marine casualties. The detail comparisonsbetween CSR-OT and CSR-BC rule requirements are listedin Table 1.

Evaluation criteria of hull girder ultimate strength areexpressed in partial safety factors, which have been calibratedby reliability analysis, to cover undetermined influence fac-tors. The evaluation criteria is shown as follows [3]:

𝛾𝑆𝑀𝑆𝑊+ 𝛾𝑊𝑀𝑊𝑉≤𝑀𝑈

𝛾𝑅

(1)

where

MSW denotes still-water bending moment;𝛾S denotes partial safety factor of still-water bendingmoment;MWV denotes wave bending moment;𝛾W denotes partial safety factor of wave bendingmoment;MU denotes hull girder ultimate strength;

𝛾R denotes partial safety factor of hull girder ultimatestrength.

ComparedwithCSR-OTandCSR-BC, the changes of rulerequirements of hull girder ultimate strength in CSR-H aremainly reflected as follows:

(1) The rule requirements of Oil Tankers have addedanalysis conditions.

(2) For the calculation of hull girder ultimate strength,one step method has been removed to prevent incon-sistent results from different methods.

(3) For partial safety factor of hull girder ultimatestrength, a new double bottom factor 𝛾DB has beenadded in the rule.

In CSR-H, partial safety factor of hull girder ultimatestrength 𝛾R=𝛾m⋅𝛾DB. 𝛾m covers the uncertainty of material,geometry, and strength and its value is taken as 1.1, whichis the same as the partial safety factor of hull girder ulti-mate strength in CSR-OT and CSR-BC. The double bottomfactor 𝛾DB covers the reduction influence of double bottomdeformation on hull girder ultimate strength. For emptycargo hold under alternative loading condition, there arebig differences between sea water pressure of ship outerbottom and cargo pressure of inner bottom, so the doublebottom may produce relatively larger deformation and thebottom plating in the center may be subjected to biaxialcompression stress including longitudinal and transversedirection. The bottom deformation and biaxial compressionstress would both reduce buckling strength of local panelin double bottom, which would further reduce hull girderultimate strength [22].

2.2. Hull Girder Residual Strength. Collision and groundingaccidents are the main reasons for ship hull damage, fracture,and sinking, which will simultaneously induce catastrophicconsequence, such as liquid cargo leakage, environmentpollution, and life casualties. In order to reduce the lossinduced by ship accidents, the collided/grounded ship shouldmaintain some residual strength to prevent the collapsefailure of whole hull girders and also the damaged ship cansustain the flooding water to provide enough time for savingpersonnel on board.

Residual strength is the 5th function requirement of IMOGBS. The concept of residual strength only is mentioned inprinciple in CSR-OT, which permits considering the post-buckling capacity and plastic yielding strength. However, thecalculation method and evaluation criteria are not given inCSR-OT and CSR-BC requirements. In order to satisfy GBSrequirements, CSR-H has added new requirements of resid-ual strength to prove hull safety after collision/grounding inrule aspect.

The first aspect for the evaluation criteria of residualstrength is the reasonable definition of collision/groundingdamage scope. Based on IMO statics of ship accidents[23], the probability distribution characteristic of colli-sion/grounding damage scope is determined, including colli-sion height in vertical direction, collision penetration depth,


Table 1: Rule comparison of hull girder ultimate strength.

CSR-OT CSR-BC CSR-HShip length 150m or above 150m or above 150m or above

Analysis conditions Seagoing Seagoing, harbor, floodingOil Tanker: seagoing, harborBulk Carrier: seagoing, harbor,

floodingScope Mid Cargo and engine area Cargo and engine areaHogging/sagging Sagging Hogging & sagging Hogging & sagging

Still water bending moment

Allowable still water bendingmoment;

Maximum sagging bendingmoment of still water.

Allowable still water bendingmoment

Allowable still water bending moment;Maximum sagging bending moment

of still water only for oil tanker.

Wave bending moment Same as UR S11

For seagoing, Same as UR S11;For flooding, reduction as 0.8

times;For harbor, reduction as 0.4

times.

For seagoing, Same as UR S11;For flooding, reduction as 0.8 times;For harbor, reduction as 0.4 times.

Ultimate strengthcalculation

One stepSMITH methodNonlinear FEM

SMITH method SMITH methodNonlinear FEM

Corrosion addition 0.5tc 0.5tc 0.5tc𝛾s 1.0 1.0 1.0𝛾w 1.2 1.2 1.2

𝛾R 1.1 1.1

𝛾R=𝛾m⋅𝛾DB𝛾m=1.1

For hogging,𝛾DB=1.25 for empty cargo hold of BC-A

bulk carrier;𝛾DB=1.1 for other cargo holds

For sagging,𝛾DB=1.0;

Table 2: Collision/grounding damage scope.

Collision Single side Double sideHeight 0.75D 0.60DDepth B/16 B/16Grounding Bulk carriers Oil TankersHeight Min(B/20 and 2m) Min(B/15 and 2m)Width 0.60B 0.60B

grounding width in transverse direction, and groundingpenetration height. Compared with local structures suchas plating, stiffener, and panel strength, ultimate strengthand residual strength of hull girder both belong to thewhole ship structures. From the view of consistent rulerequirements, the failure probability of residual strengthshould be equivalent to that of hull girder ultimate strength.Therefore, based on structure reliability analysis, the dam-age scope of collision/grounding and partial safety fac-tors in evaluation criteria are determined [24]. The dam-age scope of collision/grounding in CSR-H is listed inTable 2.

The evaluation criteria of residual strength are required asfollows:

𝛾𝑆𝐷𝑀𝑆+ 𝛾𝑊𝐷𝑀𝑊≤𝑀𝑈𝐷

𝐶𝑁𝐴

(2)

where𝛾SD denotes partial safety factor of still-water bending

moment after damage; 𝛾SD = 1.1, which covers the incrementof bending moment due to flooding.𝛾WD denotes partial safety factor of wave bending mo-

ment after damage; 𝛾WD = 0.67, which covers only one weekexposure period on the sea after ship damage.

MUD denotes residual ultimate strength after deductingthe damage structural members in collision/grounding acci-dent.

CNA denotes rotation coefficient of neutral axis afterdamage; CNA = 1.1 for collision and CNA = 1.0 for grounding.For collided ships, the structural members of one side indamage scopewould not contribute to the hull girder ultimatestrength, so the cross section of hull girder would not besymmetric and neutral axial of the cross section would rotatein some degree. However, the calculation method of ultimatestrength inCSR-Hhas not considering the influence of neural


Table 3: Boundary conditions used in NFEM.

Position Displacement constraint Rotation constraint𝛿X 𝛿Y 𝛿Z 𝜃X 𝜃Y 𝜃Z

Fore end plane Coupling Coupling Coupling - Coupling -Aft end plane Coupling Coupling Coupling - Coupling -Independent point A Fixed Fixed Fixed Fixed Fixed -Independent point B - Fixed Fixed - Fixed -Note: independent point A and point B are defined in FE model, of which position can be located at the intersection point of neutral axis in cross section.

axis rotation, so the evaluation criteria add the coefficient ofneural axis rotation.

3. Ultimate Strength Analysis of Hull Girder

3.1. Incremental-Iterative Method. The incremental-iterativemethods of CSR-OT and CSR-BC are harmonized intoCSR-H, including element type, meshing, load-displacementcurve of element, and calculation procedures, which arealmost consistent in these rules. Based on plane cross-section assumption, hull girder section is divided into aseries of stiffener element, plating element, and hard cornerelement, and several critical failure types are assumed foreach type element. The stiffener element under compressionmay produce beam-column buckling, torsion buckling, andweb buckling. The plating element under compression mayproduce plating buckling. Other types of element undercompression or tension will produce idealized elastic-plasticfailure. Based on the concept of effective attaching plating,average stress-strain curve of each failure type is provided inCSR-H.

The incremental-iterative method assumes that hullgirder failure occurs in adjacent strong frames. Only longi-tudinal stress is considered, biaxial stress and shear stressare neglected, and the effect of initial deflection is also notdirectly considered. At the rule level, all the influence factorsare covered in CSR partial safety factors. Relatively speaking,the incremental-iterative method has characters of simplecalculation procedure and stable calculation results.

3.2. Nonlinear Finite Element Method. For ultimate strengthcalculation method, CSR-H requires that nonlinear finiteelement method (abbreviation NFEM) can be used foran alternative method, but the evaluation criteria of hullgirder ultimate strength should be specially considered. Onlygeneral requirements about thismethod are listed in principlein CSR-H. Detailed implementation procedure is a gap andleft to classification societies, which implies that nonlinearfinite element method is relatively complex and cannot beeasily implemented by ship designers in present stage.

NFEM is a powerful tool to solve the problems ofcomplex engineering structures. Hull ultimate strength anal-ysis involves material nonlinearity and large deformationnonlinearity. NFEM can be used to accurately evaluate theeffects of various factors on ultimate strength, which aremainly including model longitudinal scope, element type,mesh size, material constitutive model, boundary condition,

Table 4: Amplitude of initial deformation.

Initial deformation Maximum allowablevalue( mm)

Whole deformation of stiffened panel l/1000Local deformation of plating s/200Lateral deformation of stiffener web l/1000Note: l denotes the length of stiffened plating between frames, and s denotesthe width of stiffened plating between stiffeners.

initial deformation, weld residual stress, lateral pressure, andplastic buckling [25].

Boundary conditions in NFEM in NFEM are given inTable 3.

3.3. Effect of Initial Deformation on Ultimate Strength. Basedon ISSC conclusion report [26], the initial deformation ofhull structures should generally consider the whole defor-mation of stiffened panel, plating local deformation, stiffenerlateral deformation, and so on. The mode and amplitude ofinitial deformation in hull structures should be accuratelysimulated, especially out-plane deformation due to weldingor fabrication, so the considered deformation can triggerthe most dangerous failure mode of hull girder collapse andthe minimum value of hull girder ultimate strength canbe obtained. The general initial deformations are shown inFigure 1, such as whole deformation of stiffened panel, localdeformation of plating, and lateral deformation of stiffenerweb.

The NFEM listed in previous paper [25], including ele-ment type, meshing density, model extent, and calculationmethod, is also used here to calculate the ultimate strength ofhull girder. Then the effect of initial deformation on ultimatestrength is analyzed. For actual ships, the initial deformationof structure members should be limited within the allowablevalue of industry standards, such as IACS Rec.47 [27]. In thispaper, the maximum allowable value of initial deformationsas listed in Table 4 is applied on finite element model, in orderto analyze their reduction effect on ultimate strength.

The ultimate strength results calculated by NFEM arelisted in Table 5. The reduction effect of initial deformationon hull girder ultimate strength is 1%∼8%. Compared withhogging ultimate strength, the initial deformation has biggerinfluence on reduction of sagging ultimate strength for BulkCarriers. For Oil Tankers, initial deformation has biggerreduction effect on hogging ultimate strength.


Table 5: Effect of initial deformation on hull girder ultimate strength.

Ship type Case Ultimate strength(kN⋅m) RatioWithout initial deformation With initial deformation With/Without

58kWBulk Carrier

Hogging 8.38E+06 7.98E+06 0.95Sagging -6.78E+06 -6.21E+06 0.92

115kWBulk Carrier


115kWOil Tanker


Z

X Y

(a) Whole deformation of stiffened panel

Z

X Y

(b) Local deformation of plating

Z

X Y

(c) Lateral deformation of stiffener web

Z

X Y

(d) Combination of aforementioned three deformations

Figure 1: Initial deformation.

3.4. Effect of Lateral Pressure on Ultimate Strength. In orderto analyze the effect of lateral pressure on ultimate strength,the lateral pressure of outer bottom and side shell underdifferent loading conditions should be considered. For emptycargo hold under alternative loading condition, there are bigdifferences between sea water pressure of ship outer bottomand cargo pressure of inner bottom, so the double bottommay produce relatively larger deformation. In NFEM, thelongitudinal extent of model should relatively increase, i.e.,extending to whole cargo hold between transverse bulkheads,in order to reduce the effect of boundary conditions ondouble bottom deformation.

All longitudinal continuous structure members andtransverse structure members between two adjacent bulk-heads are included in FEmodel. However, the two bulkheads,

upper stools and lower stools, are simulated by boundaryconditions to simplify the FEmodel.The initial deformationsmentioned in Section 3.3 are also included, which is conve-nient to convergence of nonlinear calculation. The FE modelis showed in Figure 2.

Based on CSR-H rules Pt1Ch4Sec8, the lateral pressureof outer bottom and side shell under full loading conditions,ballast conditions, and alternative loading conditions is sepa-rately applied in FE model (Figure 3) . According to loadingmanuals, a series of different draught is chosen based onthe principle of maximum lateral pressure on bottom panelsfor these three kinds of main load mode. For conventionview, dynamic pressure is equivalent to static pressure appliedsymmetrically on outer shell. The ultimate strength resultscalculated by NFEM are listed in Table 6. The results show


Table 6: Effect of lateral pressure on ultimate strength.

Ship type Loading condition under hogging Ultimate strength(kN⋅m) RatioWithout lateral pressure With lateral pressure With/Without

115kWBulk Carrier

Full 1.07E+07 9.18E+06 0.85Ballast 1.07E+07 9.66E+06 0.90

Alternative 1.07E+07 8.48E+06 0.79115kWOil Tanker

Full 1.04E+07 9.65E+06 0.93Ballast 1.04E+07 1.01E+07 0.97

(a) Bulk Carrier (b) Oil Tanker

Figure 2: FE model between adjacent bulkheads.

Z

TLC

Figure 3: Application of lateral pressure on outer bottom and sideshell.

that the reduction effect of lateral pressure under alternativeloading condition is about 21%, and the reduction effectunder other loading condition is 7%∼15%.

3.5. Effect of Neutral Axis Rotation on Residual Strength.For actual ships, cross section of hull girder is gener-ally symmetric, so the neutral axis of the cross sectionis parallel to horizontal plane. As the external bendingmoment increases, the hull girder will produce some bendingdeformation. Even when the longitudinal stress of bottomor deck structures enters into nonlinear stress stage, theposition of neutral axis will only move up or down. Butfor collision damage ships, the cross section will not keepsymmetric. Therefore, when the structural elements producenonlinear deformation under external bending moment, theposition of neutral axis will produce translation and rotationmovement.

The position of neutral axis can be calculated by followingprocedures. As conservative assumption, the structuralmem-bers in damaged scope can be completely deducted from hullgirder and the cross section of damaged part is asymmetric.When the external bending moment is small and structuralmembers still remain in elastic stage, the neutral axis, i.e.,elastic neutral axis, can be calculated by the scantlings andgeometry coordinate of structural members. As the externalbending moment increases, some of structural membersenter into plastic or buckling stage, the stress distribution ofcross section will not be continuous, and the neutral axis,i.e., plastic neutral axis, will produce translation and rotation


Table 7: Effect of neutral axis rotation on residual strength of hull girder.

Ship type Case Residual strength(kNm) RatioWithout neutral axis rotation With neutral axis rotation With/Without

22.5 kWBulk Carrier


64kWBulk Carrier


Table 8: Actual ship assessment of bulk carrier ultimate strength.

Ship type Case Utilization factor of ultimate strength Utilization factor of residual strengthSeagoing Harbor Flooding Collision Grounding

BC1 Hogging 0.64 0.58 0.71 0.55 0.44Sagging 0.64 0.41 0.77 0.66 0.48





movement simultaneously. The position of neutral axis at thisstage can be determined by the following two conditions:

(1) The combined force in compressed region F1 andcombined force in tension region F

2have the same amplitude

but opposite direction.(2)The connection line of action point F

1and F2will keep

parallel to the action plane of external bending moment M ofhull girder.

The calculation results of hull girder residual strengthconsidering the effect of neutral axis rotation are listed inTable 7. The residual strength of hull girder will reduce4%∼9% after considering neutral axis rotation. So if theneutral axis rotation is neglected, the residual strength maybe overestimated, which is critical for the safety of damagedships.

4. Actual Ship Assessment of Hull GirderUltimate Strength

4.1. Target Ships. In order to analyze the influence of CSR-Hrules on ship industry, representative CSR Bulk Carriers andOil Tankers are chosen to carry out actual ship assessmentof hull girder ultimate strength and residual strength. Thesample ships generally include the following:

Bulk Carriers: Capesize, Panamax, and HandysizeOil Tankers: VLCC, Suezmax, Aframax, and Panamax

4.2. Actual Ship Assessment of Bulk Carriers. The actual shipsassessment results of bulk carrier hull girder ultimate strengthare listed in Table 7. The results show that most of CSRships can satisfy the rule requirements of hull girder ultimate

strength in CSR-H. Because of new partial safety factor ofdouble bottom 𝛾DB in CSR-H, the scantlings of structuralmembers of large Bulk Carriers may slightly increase.

The assessment results of hull girder ultimate strengthcan be expressed as utilization factor, which is equal tobending moment divided by ultimate strength, i.e., the leftpart divided by the right part in (1). The utilization factorof hull girder ultimate strength under flooding conditionsis relatively large, and the next one is seagoing condition.Because harbor condition only considers 0.4 times wave load,it is almost impossible to be critical load condition.

The utilization factors of ultimate strength in Table 8 arelisted as the increase of ship tonnage. The utilization factorgradually increases as the increase of ship tonnage, whichpredicts that the influence of ultimate strength rule require-ments on large bulk carrier safety will becomemore andmoreimportant. Failure mode of hull girder with collision damageafter collapse is showed in Figure 4.

The utilization factor of residual strength after collideddamage is 55%∼87%, and the utilization factor of residualstrength after grounding damage is 44%∼68%. So CSR BulkCarriers can satisfy the new addition of residual strengthrequirement in CSR-H.

4.3. Actual Ship Assessment of Oil Tankers. The actual shipsassessment results of oil tanker hull girder ultimate strengthare listed in Table 9 as the increase of ship tonnage.The resultsshow that most of CSR ships can satisfy the rule requirementsof hull girder ultimate strength in CSR-H. The utilizationfactor of hull girder ultimate strength under seagoing condi-tions is relatively large, and the next one is sagging conditionunder homogeneous loading. The utilization factor gradually


Table 9: Actual ship assessment of oil tanker ultimate strength.

Ship type Case Utilization factor of ultimate strength Utilization factor of residual strengthSeagoing Harbor Homogeneous loading Collision Grounding

OT1 Hogging 0.77 0.50 - 0.63 0.75Sagging 0.87 0.52 0.84 0.81 0.71




(Avg: 75%)Multiple section pointsS, Mises

+3.543e+02+3.248e+02+2.953e+02+2.658e+02+2.362e+02+2.067e+02+1.772e+02+1.477e+02+1.181e+02+8.862e+01+5.910e+01+2.957e+01+4.551e-02

Figure 4: Hogging failure mode of hull girder with damage.

increases as the increase of ship tonnage, which predicts thatthe influence of ultimate strength rule requirements on largeoil tanker safety will become more and more important.

The utilization factor of residual strength after collideddamage is 63%∼84%, and the utilization factor of residualstrength after grounding damage is 59%∼77%. So CSR Oil

Tankers can satisfy the new addition of residual strengthrequirement in CSR-H. The new requirement of residualstrength will not be a critical design case for enhancing scant-lings of hull girder members. However, the damage scope isassumed in the rule requirement, but not based on actual shipdamage condition. Residual strength assessment in design


stage should conserve enough safety preserve for collisionand grounding damage. Residual strength assessment forship after actual accident should be analyzed case by case,especially considering various damage conditions.

5. Conclusions

The rule requirements of hull girder ultimate strength andresidual strength in CSR-H and CSR-OT & CSR-BC arecompared in detail, and also the technical grounds of rulerequirements are explained. The nonlinear finite elementmethod is used in this paper to analyze the effect of criticalfactors, including initial deformation and lateral pressure, onhull girder ultimate strength. Finally, the influence of rulerequirements of hull girder ultimate strength and residualstrength is evaluated on general Bulk Carriers and OilTankers in ship industry. Based on the aforementionedresearch, the following conclusions can be obtained:

(1) The reduction effect of initial deformation assumedin this paper on hull girder ultimate strength is 1%∼8%. ForBulk Carriers, the initial deformation has bigger influenceon reduction of sagging ultimate strength than hoggingcondition. For Oil Tankers, initial deformation has biggerreduction effect on hogging ultimate strength than saggingcondition. Different type of initial deformation will changethe ultimate failure mode and even change the ultimatestrength. So initial deformation effect on bending, shear, andtorsion of hull girder is worth of analyzing in the future.

(2) For alternative loading condition, the reduction effectof lateral pressure on hull girder ultimate strength underhogging is about 21%. For other loading conditions, thereduction effect of lateral pressure on hogging ultimatestrength is 7%∼15%. This paper only considered the lateralpressure acting on outer bottom and side shell under waterline. For lateral pressure acting on other parts of ship body, itis also needed to be analyzed specially for large or ultra largeships.

(3) The reduction effect of neutral axis rotation onresidual strength after collision damage is about 5%. Theneutral axis rotation after damagewill have some influence onultimate capacity calculation by SMITHmethod.The residualstrength assessment in CSR-H rules is always assumed theship floating in vertical position. However, due to flooding ofsome cabin after damage, the ship may present some heelingrotation.

(4) Owing to the new addition of partial safety factor 𝛾DBabout double bottom effect in CSR-H, structural scantlingsof hull girder members of large Bulk Carriers may slightlyincrease. In this view, the CSR-Hwill enhance the safety mar-gin of large Bulk Carriers. In order to satisfy the requirementsof hull girder ultimate strength in CSR-H, the scantlings ofdouble bottom structures will be more conservative thanCSR-BC rules.

(5) CSR Bulk Carriers andOil Tankers can satisfy the newaddition of residual strength requirements in CSR-H. Thebiggest utilization factor of residual strength for these shipscalculated in this paper is 0.84, which means that the CSR-Hships have enough residual strength after assumed damage

to withstand the still-water and wave loads. Therefore, thenew requirement of residual strength in CSR-H will notincrease scantlings of hull girder members. However, residualstrength assessment for ship after actual accident should beanalyzed case by case, especially considering various damageconditions and loading conditions.

Data Availability

The data (such as FE model file and marine structuredrawings) used to support the findings of this study have notbeenmade available because the data belongs to ship designeror operator. In this manuscript, the data is analyzed to findthe general conclusions, which will be useful for future shipdesign and rule requirement making.

Disclosure

However, the views expressed in this paper are those of theauthors and do not necessarily reflect the official views ofaffiliations.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This project is supported by National Natural Science Foun-dation of China (Grant no. 51809168) and Startup Fund forYoungman Research at SJTU (17X100040060).

References

[1] IACS, “Common Structural Rules for Double Hull Oil Tankers(CSR-OT),” London, UK, 2012.

[2] IACS, “Common Structural Rules for Bulk Carriers (CSR-BC),”London, UK, 2012.

[3] IACS, “Common Structural Rules for Bulk Carriers and OilTankers (CSR-H),” London, UK, 2014.

[4] IMO, “Adoption of the international goal-based ship construc-tion standards for bulk carriers and oil tankers,” MSC.287(87),London, UK, 2010.

[5] IMO, “Adoption of the guidelines for verification of conformitywith goal-based ship construction standards for bulk carriersand oil tankers” (Arabic), MSC.296(87), London, UK, 2010.

[6] ISSC, “Committee III.1 ultimate strength,” in Proceedings ofthe 19th International Ship and Offshore Structures Congress,Cascais, Portugal, 2015.

[7] ISSC, “Committee III.1 Ultimate Strength,” in Proceedings ofthe 18th International Ship And Offshore Structures Congress,Rostock, Germany, 2012.

[8] D. D. A. Amante, R. M. Rossetto, and S. F. Estefen, “Strengthloss of SS platform column due to ship collision,” in Proceedingsof the ASME 2010 International Conference on Ocean, Offshoreand Arctic Engineering, 2010.

[9] J. K. Paik, D. K. Kim, D. H. Park, H. B. Kim, and M. S. Kim,“A new method for assessing the safety of ships damaged by


grounding,” International Journal of Maritime Engineering, vol.154, pp. 1–20, 2012.

[10] D. K. Kim, P. T. Pedersen, J. K. Paik, H. B. Kim, X. Zhang, andM. S. Kim, “Safety guidelines of ultimate hull girder strengthfor grounded container ships,” Safety Science, vol. 59, pp. 46–54,2013.

[11] J. Choung, J. Nam, and T. Ha, “Assessment of residual ultimatestrength of an asymmetrically damaged tanker consideringrotational and translational shifts of neutral axis plane,”MarineStructures, vol. 25, no. 1, pp. 71–84, 2012.

[12] M. C. Xu, A. Teixeira, and C. Guedes Soares, “Reliabilityassessment of a tanker using the model correction factormethod based on the IACS-CSR requirement for hull girderultimate strength,” Probabilistic Engineering Mechanics, vol. 42,pp. 42–53, 2015.

[13] A. W. Hussein and C. G. Soares, “Reliability and residualstrength of double hull tankers designed according to the newIACS common structural rules,” Ocean Engineering, vol. 36, no.17-18, pp. 1446–1459, 2009.

[14] H. K. Amlashi and T. Moan, “Ultimate strength analysis of abulk carrier hull girder under alternate hold loading condition– A case study,” Marine Structures, vol. 21, no. 4, pp. 327–352,2008.

[15] M. Witkowska and C. G. Soares, “Ultimate strength of locallydamaged panels,” �in-Walled Structures, vol. 97, pp. 225–240,2015.

[16] S. Saad-Eldeen, Y. Garbatov, and C. G. Soares, “Ultimatestrength analysis of highly damaged plates,”Marine Structures,vol. 45, pp. 63–85, 2016.

[17] E. A. Mohammed, S. Benson, S. Hirdaris, and R. S. Dow,“Design safety margin of a 10,000 TEU container ship throughultimate hull girder load combination analysis,” Marine Struc-tures, vol. 46, pp. 78–101, 2016.

[18] G. J. Shi and D. Y. Wang, “Analysis of the similar model forultimate strength subjected to combined action of bendingand torsion of a container ship,” Journal of Shanghai JiaotongUniversity, vol. 44, no. 6, pp. 782–786, 2010.

[19] J. K. Paik, D. K. Kim, and M. S. Kim, “Ultimate strengthperformance of suezmax tanker structures: Pre-CSR versusCSRdesigns,” International Journal of Maritime Engineering, vol. 151,no. 2, pp. 39–58, 2009.

[20] J. M. Wu, G. Wang, and S. J. Cai, “Ramification study on IACSHCSR: impact on structural design and scantlings,” in SNAMEMaritime Convention, Houston, TX, USA, 2014.

[21] D. K. Kim, S. J. Kim, and H. B. Kim, “Ultimate strengthperformance of bulk carriers with various corrosion additions,”Ships and Offshore Structures, vol. 10, no. 1, pp. 59–78, 2015.

[22] Final Report of Committee on Large Container Ship Safety,Committe on Large Container Ship Safety, Japan, 2015.

[23] D. S. Aldwinckle and J. E. Lock, StatisticAl Analysis of Classifi-cation Records for Oil Tanker Collision and Groundings, BritishMaritime Technology, 1992.

[24] IACS, “TB hull girder residual strength,” London, UK, 2014.[25] D. W. Gao, G. J. Shi, and D. Y. Wang, “Residual ultimate

strength of hull structures with crack and corrosion damage,”Engineering Failure Analysis, vol. 25, pp. 316–328, 2012.

[26] ISSC, “Committee III.1 ultimate strength,” in Proceedings of 17thinternational ship and offshore structures congress, Seoul, Korea,2009.

[27] IACS, “Rec.47 shipbuilding and repair quality standard,” Lon-don, UK, 2012.

Hindawiwww.hindawi.com Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwww.hindawi.com Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwww.hindawi.com Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation http://www.hindawi.com Volume 2013Hindawiwww.hindawi.com

The Scientific World Journal

Volume 2018

Hindawiwww.hindawi.com Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com

Di�erential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwww.hindawi.com

https://www.hindawi.com/journals/jmath/

https://www.hindawi.com/journals/mpe/

https://www.hindawi.com/journals/jam/

https://www.hindawi.com/journals/jps/

https://www.hindawi.com/journals/amp/

https://www.hindawi.com/journals/jca/

https://www.hindawi.com/journals/jopti/

https://www.hindawi.com/journals/ijem/

https://www.hindawi.com/journals/aor/

https://www.hindawi.com/journals/jfs/

https://www.hindawi.com/journals/aaa/

https://www.hindawi.com/journals/ijmms/

https://www.hindawi.com/journals/tswj/

https://www.hindawi.com/journals/ana/

https://www.hindawi.com/journals/ddns/

https://www.hindawi.com/journals/ijde/

https://www.hindawi.com/journals/ads/

https://www.hindawi.com/journals/ijanal/

https://www.hindawi.com/journals/ijsa/

https://www.hindawi.com/

https://www.hindawi.com/

analysis of hull girder ultimate strength and residual...

Documents