Structural Redundancy Verification for Side Shell Frame of Single Side Skin Bulk Carriers

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(1.College of Civil Engineering and Architecture,Zhejiang University of Technology,Hangzhou 310014,China; 2.China Ship Scientific Research Center,Wuxi 214082,China;3.Shanghai Rules&Research Institute,CCS,Shanghai 200135,China)

Abstract:According to the IMO regulations and stiffened panel buckling failure criteria of IACS Har⁃monized Common Structural Rules (CSR), this paper put forward a new methodology for the verifica⁃tion on the IMO Goal Based Standard (GBS) compliance of structural redundancy requirements to the side shell frame of single side skin bulk carriers (SSS-BC). The concepts and definitions in this meth⁃odology,such as the structural redundancy acceptance criterion,damage assumption based on the real ship, load scenarios, non-linear finite element analysis (FEA) approach of the stiffened panels, etc.,were proposed,and the calculation verification on the real ship was also carried out.By the calculation results,it is demonstrated that the side shell structures of SSS-BC designed as per CSR rules can satis⁃fy the strength requirement that‘localized damage of any stiffening structural member will not lead to immediate consequential collapse of the complete stiffened panel’,and have the appropriate structural redundancy accordingly.

Key words:structural redundancy;single side skin bulk carrier;stiffened panel;nonlinear finite element analysis

0 Introductioin

The structural redundancy can be defined as a kind of capability of a structural system that can maintain to withstand the external loads after some members are damaged or fail. In recent years, from a series of damage accidents caused by the insufficient redundancy, it can be realized that some structural redundancy which is inherently in the requirements of the current rules may not ensure the structural safety after some members damage or fail. In last 90’s, it was found that some damage accidents occurred on side shell frame of SSS BC,where the single mechanical failure(likely due to cargo handling) of a side frame may lead to an overloading of its side frame neigh⁃bours and finally cause the collapse of the whole side frame structure, as shown in Fig.1. This phe⁃nomenon is called‘Domino effect’of the side frame. The statistics show that most bulk carriers with damage accidents have 15 years of age and above,and it seems that for early period, the major reason of the damage accidents is the underestimate of the hull structure damage or the sensitivity of the structure un⁃der special damage,sensitive degree of the structure un⁃der the special damage, which leads to the severe insuf⁃ficiency of hull residual capability. For this reason, in IMO MSC. 296(87) Resolution 7.3.1[1], it was pointed out that‘Does a ship designed to the rules have suffi⁃cient structural redundancy to survive localized damage to a stiffening member?’.

Fig.1 Collapse of side shell frame on real ship stiffened panel of SSS-BC

By now, some approaches for the structural redundancy criteria and their calculations have been proposed in the literatures.For example,the structural redundancy required by SOLAS Regu⁃lation XII/6.5.1 and 6.5.3[2]concerning the cargo hold range of bulk carriers has been verified by IACS using‘overload’approach.The concept of‘overload’approach is clear and understandable.However, the calculation model is rather too simple, and only one axial load action can be consid⁃ered. Decò et al[3]proposed another new kind of methodology to evaluate the redundancy of hull girder bending strength based on the probability assessment. In addition, Decò[4]also provided a comprehensive study report on the structural reliability and redundancy under all the working con⁃ditions with the corrosion effect, various sea conditions and ship speeds. Although this approach sounds good theoretically, it is really difficult in practice due to the data collection. Wu[5]detailed his concept of ship structural redundancy and explained the structural redundancy through his phi⁃losophy to perform‘one by one’step way to delete the yield strength of the longitudinal primary support member. Wu’s thought was just based on the yield strength failure but not on the typical panel buckling. Chen et al[6]investigated the failure progress of the side shell structures of the oil tanker to define its local structural redundancy.

In accordance with the IMO GBS structural redundancy requirements and based on the dam⁃age assumption referring to the real ship and CSR stiffened panel buckling failure criteria, this pa⁃per proposed a new methodology for the verification on the IMO GBS compliance of structural re⁃dundancy requirements to the side shell frame of SSS-BC. The proposed methodology contains the structural redundancy acceptance criterion,damage assumption based on the real ship,load scenar⁃ios,non-linear FE collapse analysis approach of the stiffened panels,and numerical test on the real ships as well.This study can provide some important technical background to support IACS project of the verification on IMO GBS compliance for CSR.

1 Ultimate capacity calculation

In order to obtain the ultimate capacity of the stiffened panel under the intact and damaged condition respectively, the recognized non-linear software ABAQUS was adopted for the assess⁃ment.Calculation flow chart for the nonlinear finite element analysis is illustrated in Fig.2.

Fig.2 Calculation flow chart for nonlinear finite element analysis

1.1 Model extents and meshes

As shown in Fig.3, the side shell stiffened panel of SSS-BC is taken as the calculation model.Since the rigidity of the top tank and hopper tank is significantly harder than that of the side shell stiffened panel connected in between,the top tank and hopper tank can be set as the (fixed)bound⁃ary condition for the side shell stiffened panel model. In accordance with the provisions of NLFEA IACS, the model in width covers 5 transverse side frames arranged evenly. And the T-bar type which is often used for the ship structure is taken as the side frame in the model.The mesh density of the model can be set as:

(1) Side shell plating: six plate elements between the two adjacent side frames, with each ele⁃ment made close to square.

(2)Web plate of the side frame:at least three plate elements along the web depth,with each el⁃ement made close to square.

(3) Flange plate of the side frame: two plate elements for the flange plate on the T-bar cross section.

Fig.3 Calculation model of a side shell

1.2 Boundary conditions

The coordinate system of the model is shown in Fig.3, where B1, B2 (including brackets), B3 and B4 denote 4 sides of the side shell panel/grillage and C1,C2,C3 and C4 represent 4 panel cor⁃ners,respectively.The boundary conditions of this model are:B1 and B2 sides are connected to the web frame.B1 side should be fixed,but B2 side is free to the uniform translation inxdirection and with constrained rotations aboutyandzaxes. B3 and B4 sides are connected to the panel edge sides to keep the uniform translation inydirection. However, the translation is not allowed in the perpendicular direction to the panel. The corner point C1 is fully fixed in any translation and rota⁃tion,meanwhile other corner points can be allowed to rotate about y axis.

1.3 Assumption of localized damage

Based on the SOLAS Regulations[2]and relevant standards of the annual survey, two damage models are proposed in this paper. The first one is the weld crack about 300-500 mm at the lower bracket of the side frame (see Fig. 4). For simulating this case, some web elements at lower end bracket of the middle frame (the 3rd one) are deleted as shown in Fig.4. It should be pointed out that this damage is simulated for the‘desoldering’in this model, and there is no connection with the adjacent structures. As the buckling represents the overall structural behavior, it is not neces⁃sary to change the element mesh size in the localized damaged model. The second one is to intro⁃duce the global permanent deformation with the maximum value of 6l/1000, wherelis the span of the side frame,as shown in Fig.5.

Fig.4 Weld crack at lower end bracket of the frame

Fig.5 Model with large deformation permanent

1.4 Simulation of initial geometry imperfection

The total initial geometry imperfection combines with the local and global deformations. The local initial imperfection can be obtained by calculating the first eigenvalue, and the global initial imperfection can be assumed by a half sine wave pattern.The tripping/transverse titling of the stiff⁃ener will be represented by the double trigonometric function. The maximum imperfection value is determined by the statistics on the real ships.

1.5 Material properties

A bi-linear material model including the strain hardening effect was applied in the analysis,i.e. the modulus of elasticityE=206 000 N/mm2and strain hardening parameterET=1000 N/mm2in the elastic and inelastic range respectively.

1.6 Applied loads

There are various kinds of loads acting on the side shell grillage structure in the ship service.Three external load types including the axial compressive force along the frame,transverse compres⁃sive force, axial compressive force + transverse compressive force + lateral pressure (axial, trans⁃verse,combined force for short)are taken into account,as shown in Fig.6.In addition,in order to in⁃vestigate the effects of all kinds of loads,some uniaxial load actions have been also considered.

Fig.6 Applied loads

2 Structural redundancy criteria of side shell structures

2.1 Criterion 1

For the plate and stiffener of the stiffened panel, the structural buckling criterion in CSR[7]is shown as

whereηis defined as the buckling utilization factor corresponding to the actual applied design load.For combined load cases, the buckling utilization factorηcan be defined as the ratio between ap⁃plied working stress and structural buckling capacity andηalldenotes the allowable buckling utiliza⁃tion factor.

In Chapter XII of IMO SOLAS[8], the structural redundancy requirements of bulk carriers are clearly stated, i.e.‘the structure of cargo areas shall be such that single failure of one stiffening structural member will not lead to immediate consequential failure of other structural items poten⁃tially leading to the collapse of the entire stiffened panels’.Based on the study of‘IACS Joint Bulk⁃er Project–Technical Backgrounds’of‘Structural redundancy requirements of SOLAS regulation XII/6.5.1 and 6.5.3 in CSR for Bulk Carriers’and document of IACS SC209, IACS CSR-BC CH6,Sec.3 and IACS CSR Pt1,CH8,Sec.5,it is also clearly indicated that,for all‘facing cargo structur⁃al members’in cargo holds of bulk carriers, including hatchway coamings, transverse bulkheads,panel plates of the top-side tankers and bilge hopper tankers facing the cargo hold, inner bottom,side shell of single-side skin construction or longitudinal bulkhead of double-side skin construc⁃tion,the safety factor should be magnified to 15%,which is taken as 1.15.

Therefore,for the SSS-BC side shell frame that meets the structural redundancy requirements,the following criterion should be satisfied:

whereηDis the utilization factor of damaged stiffened panel,σDis the working stress of localized damaged stiffened panel,UDis the ultimate capacity of stiffened panel with localized damage.

whereγdenotes the index of the structural redundancy.

In comparison with Eq.(2), the advantage of the new expression Eq.(5) lies in that Eq.(5) links the relationship between four parameters of working stress, ultimate capacity of damage and intact stiffened panels, and also relates to the working stress level (i.e. corresponding to the safety margin of intact stiffened panels)byηI.

2.2 Criterion 2

It can be seen from an amount of calculation on real ships that the localized damage on one stiffening member hardly changes the global stress distribution of the entire panel. Based on this conclusion and the definition of the working stress of localized damaged stiffened panel,σDcould be expressed asσD≈σID(6)whereσIDdenotes the global stress distribution of the intact stiffened panel under the damaged con⁃dition.

Then,according to the corresponding definition,the utilization factors can be derived as

Criterion 2 emphasizes the difference betweenUDandUIin terms of the ultimate strength of the stiffened panel. It also ignores the global stress change of the cargo hold caused by the damage of one stiffening member.Compared with Criterion 1,this criterion does not contain the stress item,so that any stress combination need not be considered in the calculation fortunately.And the stiffen⁃er buckling is taken into account reasonably.

3 Verification on real ships

Based on the methodology described above, a structural redundancy assessment process is de⁃signed, and the verification has been performed on many actual CSR ships. In addition, non-linear FE analyses have been carried out to capture the ultimate capacity of the stiffened panel,i.e.firstly,take the stress value from the coarse mesh model results;secondly,get the stress ratio(e.g.y/x)(see in details in Section 4.4),and then increase the applied loads acting on the non-linear panel model in accordance with the stress ratio till the panel collapses; and finally, obtain the ultimate capacity of the stiffened panel both for intact and damaged model accordingly.

3.1 Working procedure for structural redundancy evaluation

The working procedure for structural redundancy evaluation on the side shell structure is shown in Fig.7.

Fig.7 Working procedure for structural redundancy evaluation on side shell structure

3.2 Load combination

In the IMO relevant structural redundancy documentation (IMO SLS.14/Circ.250[1]),it explicit⁃ly states that‘a single localized damage, which is of a size that is likely to be detected, should not lead to complete collapse of the stiffened panel under a load equal to the maximum allowable de⁃sign still water load plus 80% of the maximum lifetime dynamic load.’. In this paper, the applied load combinations are as follows:

(1)Damaged load combination:100%Static loads+80%Dynamic loads;(2)Intact load combination:100%Static loads+100%Dynamic loads.

where the extreme loads in the intact condition correspond to a probability level of 10-8.

Furthermore, the loading sequence of the combined operating conditions is described in Sec⁃tion 3.4 below.

3.3 Stress calculation

In order to seek the tendency of the working stress ratio between the damage and intact condi⁃tions, i.e.σD/σI, the statistics and analyses have been carried out to investigate the working stress from an amount of stiffened panels of actual bulk carriers and oil tankers under two conditions by cargo hold FE analysis. The cargo hold FE analysis is in line with the requirements of CSR, Pt1,Ch7,and the working stress is based on the coarse mesh cargo hold model[7].

3.4 Selection of load cases

The working stress to be selected for this study is based on the corresponding load case and combinations. The stress components are interactive on the buckling capacity curve, i.e. different ratio ofσy/σxcorresponds to different buckling capacity (see Fig.8). So not only should the selected working stress be based on the most severest/governing load case/condition, but also the panel capacity should correspond to the ratio ofσy/σxunder the most severe load condition. In order to deter⁃mine the governing load cases, the stress inxandydirec⁃tions,combined stress andηhave been taken out for mak⁃ing comparison as per the following process:

(1) For all the seagoing conditions, the load combina⁃tion of‘100%Static loads+80%Dynamic loads’is applied to conduct the cargo hold FE analysis.From all stiffened panels in each areas, the governing load condition is found out, which corre⁃sponds to maximumσDx,σDy,ηD, and also the relevant stresses(σDx,σDy,τD)ηD_MAX.σDcan be calcu⁃lated by the formula:

Fig.8 Relationship between biaxial stress and its ultimate capacity[7]

3.5 Stress filtering

Since there are large amounts of working stress data from the FE analyses, some filtering should be conducted to select the representative data to be used for structural redundancy assess⁃ment.The principles of the stress filtering are:

(1) Filter out the stress data ofηI＞1.It should be noted that some scantlings of CSR ships may not satisfy CSR rules, i.e. some of buckling utilization factors are greater than 1.0 under the CSR load combinations because the new version of CSR[7]is a little bit conservative than the old versions of CSR[9-10].Since it is meaningless to evaluate the redundancy for those not satisfying the rules,the stiffened panels with utilization factors greater than 1.0 should be filtered out firstly.

(2) Set the tensile stress equal to zero forσxandσy, because the tensile stress has less influ⁃ence on the stiffened panel buckling.

(3)Filter outσxorσywith values lower than 10 MPa since they are insignificant.

3.6 Calculation results

The calculation results of structural redundancy assessments of only a 180k SSS-BC ship are shown below due to the space limit of the paper. Tab.1 shows the intact and damaged ultimate ca⁃pacities of the side shell panel subjected to the uniaxial stress while Tab.2 shows the intact and damaged ultimate capacities of the side shell panel subjected to the combined stress. The calculat⁃ed collapse illustration in Fig.9 can reflect the actual damage shown in Fig.1.

Tab.1 Intact and damaged ultimate capacities of side shell panel subjected to the uniaxial stress

Tab.2 Intact and damaged ultimate capacities of side shell panel subjected to the combined stress*

Fig.9 Collapse illustration of damaged model I(deformation amplified 10 times)

According to the proposed structural redundancy criteria and in consideration of the influence of localized damage(as described in Section 2.3),the structural redundancies of the side shell panel plating and side frame of 180k SSS-BC ship are listed in Tab.3 and Tab.4,while Fig.10 and Fig.11 show the side shell panel structural redundancy of 180k SSS-BC ship according to Criterion 2. In general, the structural redundancy corresponding to the maximum combined stress is the lowest one.Besides,it should be noted that the panel number shown in Fig.10 and Fig.11 may be different due to the fact that the stresses have been filtered,as shown in Section 3.5 in detail.

Tab.3 Structural redundancy of the side shell panel plating*

Tab.4 Structural redundancy of the side frame*

Fig.10 Structural redundancy of the side shell plating

Fig.11 Structural redundancy of the side frame

It can be seen that the structural redundancies of all the considered structural members are greater than 1.15, which demonstrates that all the considered structural members have the‘inher⁃ent’structural redundancy. That is to say, the side shell panel structure designed to CSR rules has a sufficient structural redundancy.It also demonstrates that the structural redundancy requirements have been covered in the strength requirements of CSR rules.

4 Concluding remarks

On the basis of the guidance on the IMO GBS structural redundancy compliance verification requirements, this paper proposed a new methodology for the verification on the IMO GBS compli⁃ance of structural redundancy requirements to the side shell frame of SSS-BC. The proposed meth⁃odology set up 2 damage assumptions and damaged load combinations,and contained the structural redundancy criteria and non-linear FE collapse analysis approach as well. Numerical test on some real CSR ships were performed. It can be seen that all the calculation results have satisfied the structural requirements.Therefore,it is demonstrated that the side shell panel structure designed to CSR rules has a sufficient structural redundancy, and can also satisfy the structural redundancy re⁃quirement of‘that localized damage of any stiffening structural member will not lead to immediate consequential collapse of the complete stiffened panel’. The methodology and structural redundan⁃cy criteria proposed in this paper are suitable for other ship types.