Effect of Misalignment on the Stress Concetration of a Weld hopper knuckle connection

Lloyd’s Register Technical Association

Effect of misalignment on the stressEffect of misalignment on the stressconcentration of a welded hopperconcentration of a welded hopperknuckle connectionknuckle connection

ABCDABCD Paper No 3Session 2001-20022001-2002

________________________________________________________________________________________________________________Lloyd’s Register Technical Association: Paper No. 3, Session 2001-2002

The authors of this paper retain the right of subsequent publication, subject to the sanction of theCommittee of Lloyd’s Register of Shipping. Any opinions expressed and statements made in thispaper and in the subsequent discussions are those of the individuals and not those of Lloyd’s Registerof Shipping.

© Lloyd’s Register of Shipping 2002. All rights reserved. Except as permitted under currentlegislation no part of this work may be photocopied, stored in a retrieval system, published,performed in public, adapted, broadcast, transmitted, recorded or reproduced in any form or means,without the prior permission of the copyright owner.

Enquiries should be addressed to Lloyd’s Register of Shipping, 71 Fenchurch Street, London EC3M4BS, England.

Web site: www.lr.org

Secretary, Lloyd’s Register Technical AssociationNiels [email protected]

________________________________________________________________________________________________________________Lloyd’s Register Technical Association: Paper No.3, Session 2000 - 2001 1

Effect of misalignment on the stressconcentration of a welded hopper knuckleconnection

Synopsis

This paper provides a review of current shipbuilding practices on alignment and tolerances forangled joints. It shows that a clear and solid technical basis is required for assessing the alignmentprinciple and for setting appropriate tolerances.

A preliminary numerical study was carried out to identify the effect of misalignment on the stressconcentration of a welded hopper knuckle connection. Finite element analysis was performed for adouble hull VLCC. A three level top down procedure was used that utilises a global model of theship, a zoom model of the hopper and a local model of the welded connection. The characteristicloading mode is considered to be motion induced pressure acting inside the cargo tank. Acomparative analysis of the hopper knuckle connection welded with -5, 0, 5 and 10 mm offset fromthe median line was carried out under this loading. Applying a simplified assumption of planestress, two-dimensional finite element local models were used. The global and zoom models wereanalysed using the LR STRAND finite element package. The local models were analysed using thefinite element package Pro/MECHANICA.

It was found that a 5 mm offset of the girder outboard of the median line could theoreticallyreduce the stress concentration in the hopper knuckle weld toe.

Based on the analysis findings, recommendations have been put forward for obtaining theoptimum alignment and the allowable tolerance during construction.

Authors

H Polezhaeva , B.Eng., M.Sc., Ph.D.D Holmes, B.Eng.H Chung, B.Eng., M.Sc.


Table of Contents……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

1 Introduction 3…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… ……….

2 Current Practice 4……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

2.1 Median Line Alignment 4……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

2.2 Heel Line Alignment 5……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

2.3 Tolerances 5……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

3 Finite Element Study on Effect of Misalignment on the Stress Concentration of a Welded

Hopper Knuckle Connection 6……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

3.1 Analysis Scheme 6……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

3.2 Results 9……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

3.3 Discussion 10……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

4 Future Development 11

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

5 Conclusions 12……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

References 13……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

Authors’ Biographies 14……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

Appendix A – Validation of the Approach 15


1 IntroductionSince the dawn of 'mass produced' all-welded ship construction, heralded by the ‘Liberty’ ships builtin yards all around the United States, fatigue and fracture have been a major problem. Of the 2721liberty ships for which records exist, 310 suffered at least one instance of serious fracture [6]. In factsome of these vessels lasted only a matter of days before signs of poor workmanship and detaildesign became apparent.

Fortunately for today’s modern shipbuildingindustry, such instances of severe structural failureare rare. However, given the size of current vesselsand their cargoes, loss or even withdrawal fromservice caused by relatively minor fatigue crackingmay be considered by some to be no less severe ineconomic terms.

It is notable that the underlying principles uponwhich structural components are aligned, namelythe median line and the heel line method, havebeen unchanged for many years. Investigationsindicate that whilst the subject of alignment incruciform joints is an established field of study,

alignment and fatigue in angled cruciform joints has been largely ignored. One could argue that areason for the lack of study into angled cruciform joints is one of cost. Full scale and/or model testsare expensive. Standard yard procedures for improving fatigue life such as weld toe re-melting,peening, grinding etc. are considerably cheaper and provide a workable alternative. Much of theresearch work in the subject of welded connections has been done by institutions such as theInternational Institute of Welding (IIW) and The Welding Institute (TWI), and as such is presented ingeneralised form. Many of the issues pertaining to the ‘angled’ cruciform joint are specific to marinestructures and hence are often regarded as being outside the scope of research of such institutions.

Increasingly advancedanalytical tools provide for aproportionately higher levelof structural optimisation,which is good for both thebuilder and the owner/operator. The builder gainsfrom the marketability of ahighly efficient structure andthe owner benefits due to theincreased cargocapacity/steel weight ratio.However, the inherentdifficulty of predicting loadsand motions with anyprecision will inevitably leadto fatigue failures which maynot become evident for sometime but may be significantin number or severitybecause of the more highlystressed nature of optimisedstructures.

Welded connection oflower hopper knuckle

Fig.1. Welded connection between the hopper tank slopingplating and the inner bottom plating for double hull tankers


Reference line

t2

t3

t1

a

t3

t1

t2

a

θ

Fig.2. Median line alignment for straight and angled cruciform joints.

The welded connection between the hopper tank sloping plating and the inner bottom plating fordouble hull tankers and FPSO’s ( see Fig.1) has been recognised as a critical region for fatigueconsiderations due to very high local stress concentration. The maintenance of the integrity of thiswelded connection through the operational lifetime of a double hull tanker or FPSO is vitallyimportant, because a breach of the cargo containment barrier has serious economic andenvironmental consequences. It is also known that the welded knuckle connection is prone toadditional stress concentrations, due to difficulties in achieving accurate alignment duringconstruction.

The paper provides a review of current shipbuilding practices on alignment and tolerances for angledjoints, gives results of a preliminary numerical study on the effect of misalignment on the stressconcentration of a welded hopper knuckle connection and describes a future experimental andnumerical research programme aimed at defining the optimum alignment and the allowable tolerancefor angled joints during construction.

2 Current Practice

2.1 Median Line Alignment

The alignment is performed based on the median lines of the two abutting members, the allowabletolerance being based on the thickness of the thinnest of the abutting members.However, many of the welded connections within the structure of a ship are often of the angledcruciform type (Fig. 2) where one of the abutting members is set at an angle (θ) to the table member.This type of joint would typically be found at the upper and lower hopper knuckle, topside tanks andtransverse bulkhead stools.

It is clear that for the conventional cruciform arrangement true alignment is achieved when themedian lines intersect.


For the angled joint, the position is a little less clear. Geometric alignment may be achieved throughthe intersection of the median lines, with the build tolerance 'a' being measured as the distancebetween the intersections of the two abutting members. However, the ‘geometric alignment’ may notfully reflect the 'stress path' through the joint. The alignment is dependent on the thickness of thetable member (t3) and the inclined member (t2) i.e. doubling the thickness of either 't2' or ‘t3’ wouldresult in the heel of the plate moving to accommodate the increased scantling in order to maintain thealignment. Hence, the 'stress path' may in actuality be different for the same alignment.

2.2 Heel Line Alignment

This approach is based on the aligning the heel of one abutting member with an extrapolated linefrom the corresponding edge of the second abutting member (Fig. 3). The tolerance is measured as thedistance between the heel and the datum line.

This method, unlike the median line principle, is independent of plate thickness – increasing thethickness of table member, has no effect on the geometric alignment of the abutting plates. Thismethod provides for a quick and easily verifiable alignment method that is used as a standard in theshipbuilding industry.

For highly stressed cruciform joints, the heel line method outlined above is clearly less than ideal,particularly if the abutting members are of significantly different thickness in which case localbending may occur. However, for joints subject to ‘moderate’ stress levels, the heel line method isoften considered to be adequate when applied with a suitable tolerance.

2.3 Tolerances

The tolerance 'a' specified by the shipyard has a huge bearing on the fatigue resistance of a weldedjoint and is often the subject of much debate. The shipyards, whilst being fully aware of the need for

Reference line

t2

t3

t1

a

t3

t1

t2

aθ

Fig.3. Heel line alignment for straight and angled cruciform joints.


tighter tolerances at specific locations are under severe pressure to reduce costs and construction timeand hence tend to resist any attempt to tighten build tolerances. In practice, it is easy to specify atolerance of +/-4mm on paper, in reality the shipyard may assemble units up to 500t. When aligning aunit possibly weighing several hundred tonnes a 4mm alignment tolerance is not very much whenone considers the fact that the reference line itself may be 1mm wide leaving only 3mm of cleartolerance.

For critical joints, it is usual practice for the tolerance to be 1/3 of the thickness of the thinnestmember, independent of alignment method. This is where the problems start.

Shipyards traditionally favour the heel or moulded line method, whilst many classification societies(and IACS) recommend the use of a median line approach for critical locations. It is not an uncommonsituation where a difference of opinion arises between the classification society and the shipyard withregard to the alignment principle used.

In such cases it is possible for the associatedoffset to be mutually incompatible; that is tosay that a maximum heel line offset of t1/3(equal to the maximum allowable constructiontolerance) measured on the heel line may notsatisfy the t1/3 criteria measured at themedian lines. Figure 4 illustrates an angledcruciform joint with the plates aligned to themaximum allowable heel line tolerance. In thiscase, the median line offset is outsidepermissible construction parameters andhence would have to be retrospectivelyadjusted if median line alignment is to bemaintained.

In such circumstances a clear and solidtechnical basis is required for assessing thealignment principle required and settingappropriate tolerances. Whilst shipbuilding isnot a ‘watchmakers art’, selectiveenhancement of the construction standardsemployed can only serve to raise the generalquality of the fleet whilst specificallyimproving the fatigue resistance ofstructurally critical joints.

33 Finite element study on the effect ofmisalignment on the stress concentration of awelded hopper knuckle connection

Analysis scheme

A numerical study on the effect of misalignment on the stress concentration of a welded hopperknuckle was carried out under the Joint Industrial Project on Fatigue and Fracture Capacity of FPSO[1,4,5], where LR was a participant.

1823

5

15

11.7

Fig.4. Angled cruciform joint with 5mm offsetfrom the heel line (equal to maximumconstruction tolerance)


Analysis was performed for a 290,000 Dwt double hull VLCC. The key dimensions of the ship arepresented in Table 1.

The parameter considered for this study is theoffset from the median line (misalignment) ofthe hopper sloping plate and the longitudinalgirder (Fig.5). A positive misalignment refersto offsetting the longitudinal girder outboard.A negative misalignment refers to offsettingthe longitudinal girder inboard.Three levels of finite element analysis havebeen performed as shown in Table 2.

A top down procedure is used to transfer the boundary conditions from the global to the zoom modeland from the zoom model to the local model. Deflections and rotations are prescribed from the higherlevel model to the boundaries of the lower level model. Multi-point constraints are used to maintaincompatibility when going from a coarser mesh to a finer mesh. Any concurrently acting pressureloads are also applied to the lower level models.

The global finite element model is shown in Fig. 6 and the zoom finite element model is shown in Fig.7.

Length between perpendiculars, m 320.0Breadth, mld., m 58.0Depth to upper deck, mld., m 31.0Frame spacing, m 4.97Double bottom depth, m 3.0Double side width, m 3.48

Table 1.Key dimensions of double hullVLCC.

FE ModelLevel

ModelExtent Model Type

1 Global 1/2+1+1/2tanks

Coarse mesh, shellh-elements.

Misalignment is notmodelled

2 Zoom Hopperregion

txt mesh, shell h-elements.

Misalignment is notmodelled

3 Local Knuckle2D p-elements.Misalignment is

modelled

Table 2. Levels of finite element analysis

Inner bottomplate

Misalignment

Hopper sloping plate

Girder

−ve+ve

Reference(median) line

t2

t3

t1

Fig. 5. Welded hopper knuckle showingnegative misalignment.


The local shell models have been created with the finite element package Pro/MECHANICA[3].Pro/MECHANICA offers certain advantages over conventional finite element packages in having theability to automatically converge without costly re-meshing. This is achieved with p-type elements,which are able to adjust the order of the shape functions

The p-method represents thedisplacements within each elementusing high-order polynomials asopposed to the linear and sometimesquadratic or cubic functions used inconventional finite elements. A singlegeometric element can, therefore,represent a more complex state ofdeformation than a single,conventional h-finite element. Wherethe h-type elements are used, re-meshing is required to achieveconvergence. Where the p-typeelements are used, the order of theshape functions is automaticallyadjusted to achieve convergence. Thisfeature is particularly efficient inobtaining the stress at the criticallocation. Stress at the critical locationobtained using Pro/MECHANICA isthe notch stress. A local finite element2-D model is shown in Fig. 8.

Fig. 6. Global finite element model

Fig.7. Zoom finite element model


Fatigue damage at the hopper knuckle connection is predominantly caused by the deflection of thetransverse structure. This deflection is induced by hydrodynamic pressure and cargo inertia. Cargoinertia has been selected to illustrate the effect of misalignment.

3.2 Results

A comparative analysis of the hopper knuckle welded connection was carried out with -5, 0, 5 and 10mm offset from the median line (misalignment). Using a simplified assumption of plane stress (referto Appendix A), two-dimensional finite element models have been used. The results of the study arepresented as normalised stress at the critical location versus normalised misalignment (Fig.9).

The misalignment is normalised with respect to the thickness of the longitudinal girder t1 .

As seen from Fig.9, the stress at the critical location of the hopper knuckle could be reduced by 5% ifan offset of +t1/3 is used. This means that an offset of +t1/3 , where t1 is the longitudinal girderthickness, can have a beneficial effect on fatigue strength.

critical location

t1

t3

t2

t1

t3

t2

15 mm

19.5 mm

20 mm

+ve

Fig. 8. Local 2-D finite element model showing positive misalignment and criticallocation.


3.3 Discussion

According to the current IACS (International Association of Classification Societies) document“Shipbuilding and Repair Quality Standard”[2], the recommendation for the cruciform joint in way ofthe hopper knuckle connection is given in Fig.10.

Strength and higher tensile steel

31ta ≤ measured on the median lineθ

a

a1

t1

Other

21

1

ta ≤ measured on the heel line

Fig.10. IACS recommendation for hopper knuckle median line alignment and constructiontolerances (excerpted from [2])

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Normalised misalignment

No

rmal

ised

str

ess

Fig. 9. Normalised stress at the critical location versus normalised misalignment.


For the sample VLCC design, maximum allowable tolerance ‘a= ±t1/3’ translates to ±5mm for a girderthickness of 15mm. As can be seen from Fig.9, the stress concentration factor (SCF) is equal to 1.1 fora –t1 /3 misalignment and 0.95 for a +t1 /3 misalignment if median line approach is used.Application of the same IACS recommended maximum tolerance to a hopper knuckle joint alignedaccording to the optimum (+t1 /3 offset from the median line) would give SCF’s of 1.0 and 0.99 atoffsets of 0 and +2t1 /3 respectively. Applying a very crude reckoning that fatigue life follows aninverse cubic relationship with fatigue stress according to the classic Palmgren-Miner formulae, a 10%increase of stress can be estimated to lead to a 25% decrease in fatigue life. Conversely, reducing thestress by 5% will improve fatigue life by 16%.

Table 3 compares the change in the number of cycles to failure or fatigue life N∆ and stress range ∆σdue to several offset scenarios.

It can be inferred from Table 3 that byfollowing the current proposal of optimumoffset of +t1 /3 from the median line and anallowable construction tolerance of ± t1 /3 , notonly is there a direct improvement in fatiguelife but the associated range of uncertainty isalso significantly reduced.

4 Future Development

To validate the results of the preliminary finite element study, Lloyds Register has initiated a researchprogramme including full-scale fatigue tests of a typical hopper knuckle connection. The model of thehopper knuckle connection to be investigated and the experimental set-up are shown in Fig. 11.

Four offset scenarios will be investigated, namely• perfect alignment of median lines• offset of –5 mm• offset of 5 mm• offset of 10 mm from the median line.

Full penetration welds will be provided between the sloping plating and the inner bottom plating andbetween the inner bottom plating and the longitudinal girder. The structural models will befabricated from grade A normal strength steel with a minimum yield stress of 235 MPa.

The S-N curves will be obtained for structural details with varying offset and the stress concentrationfactor due to the offset will be derived. The stress concentration factor plotted against normalisedoffset will allow comparison between the calculated and experimental data.

Median linealignment

Optimumalignment

Offset σ∆ ,%

N∆ ,%

σ∆ ,%

N∆ ,%

-t1/3 +10 –25 0 0

0 0 0 –5 16

t1/3 –5 16 -1 3

Range ofuncertainty – 41% – 16%

Table 3. Effect of offset on critical stress andfatigue life


Once the results of finite element study are validated by fatigue tests, a parametric numerical studywill be carried out to estimate effect of misalignment on stress concentration at the weld toe of thehopper knuckle joint with various thickness ratios and sloping plate angles. As a result of the study,the formulation for stress concentration factor, optimum alignment and construction tolerance will bederived as a function of thickness ratios and sloping plate angle.

5 Conclusions

Based on the review of current shipbuilding practices on alignment and tolerances for angled jointsthe conclusion was made that a clear and solid technical basis is required for assessing the alignmentprinciple and setting appropriate tolerances.

B

A

A

450

20

20

A-A

Detail B

Fig. 11. Full scale specimen for hopper knuckle connection


A preliminary numerical study has been carried out to identify the effect of misalignment on thestress concentration of a welded hopper knuckle connection.

It was found that for the given dimensions, a positive misalignment of 1/3 of the longitudinal girderthickness would reduce the stress concentration in the hopper knuckle weld toe. Full scale fatiguetests have been initiated to validate the results of finite element study.

A parametric numerical study will be carried out to estimate the effect of misalignment on stressconcentration at the weld toe of the hopper knuckle joint with various thickness ratios and slopingplate angles. As a result of the study, the formulation for stress concentration factor, optimumalignment and construction tolerance will be derived as a function of thickness ratios and slopingplate angles.

Based on the analysis findings, recommendations will be put forward for obtaining the optimumalignment and the allowable tolerance during construction.

It has been shown in this paper that through the application of an optimised alignment standard to anangled cruciform joint, it is possible to realise a potential improvement in fatigue life. However,without the application of suitable monitoring procedures during construction any positive effectsmay be negated. Construction quality has a significant bearing on the fatigue resistance of a structure.

A method such as LR’s ‘ShipRight Construction Monitoring’ procedure should be applied to makesure that the structure is built and inspected to an elevated standard to ensure the predicted fatiguelife is achieved. As stated previously, fatigue is a cumulative damage process and must not beignored once the vessel enters service. To this end, the ShipRight Construction Monitoring procedureraises awareness of the critical locations so that they may be targeted during any subsequentinspections.


References

1. FPSO-Fatigue Capacity. Summary Report. Report No.2000-3264. Det Norske Veritas, August2000.

2. Shipbuilding and Repair Quality Standard for New Constructions. Part A. IACS, 19963. Pro/MECHANICA User’s Guide Release 18.0, Parametric Technology Corporation 1997.4. Lotsberg I.: Background and Scope of Work for the FPSO – Fatigue Capacity JIP. OMAE 2001.5. Polezhaeva H. and Chung H.: Effect of Misalignment on the Stress Concentration of a Welded

Hopper Knuckle for a Typical FPSO. OMAE 2001.6. Thompson P.: How Much Did the Liberty Shipbuilders Learn? New Evidence for an Old Case

Study. Journal of Political Economy, February, 2001.


Authors’ Biographies

Dr Helena Polezhaeva is a Naval Architect in the Research andDevelopment Department of Lloyd's Register of Shipping. She is aspecialist in finite element stress analysis and fatigue assessment of shipstructural details. Her previous experience includes research on thecyclic behaviour of aluminium-magnesium alloys and structural steels.

Mr Daniel Holmes is a Naval Architect in the Research and DevelopmentDepartment of Lloyds Register of Shipping.He has recently been working on the LR's ShipRight ConstructionMonitoring Procedure and is currently involved in updating the FatigueDesign Assessment procedures and rule development work for containerships.

Mr Henry Chung holds the position of Senior Naval Architect in theResearch and Development Department of Lloyd's Register of Shipping.His current duties include providing general support and advice onfatigue matters and continuing development of the ShipRight Fatigue.Design Assessment procedures. His expertise includes analyses of shipstructures using computational methods.


Appendix A -Validation of the Approach

The objective of this exercise is to investigate the validity of using a combination of a 3-D shell modeland a 2-D plane stress model to estimate the effect of misalignment for a welded hopper knuckle. Thesketch of the hopper knuckle detail under investigation is shown in Fig. 12.

The finite element analysis of a hopper corner structural detail was performed using 4-noded shellelements. A top-down procedure was then used to transfer the boundary conditions from this modelto the local 2-D plane stress model. Deflections and rotations were prescribed from the higher levelmodel to the boundaries of the lower level model.

LR STRAND (Lloyd’s Register in-house finite element package equivalent to NASTRAN) andPro/MECHANICA packages were used to perform finite element analysis for the 3-D shell and 2-Dlocal models respectively. Finite element models of the structural detail with loads and boundaryconditions are shown in Fig. 13.

The contour plot of X-direction stresses for the 2-D model is presented in Fig. 14. As seen from thefigure, the maximum X-direction stress at the critical location is 3.43 MPa.

A solid element model of the hopper corner detail has also been created using the Pro/MECHANICApackage. This model is shown in Fig. 15. The contour plot of X-direction stresses for the solid model ispresented in Fig. 16. The maximum X-direction stress is 3.55 MPa, which is only 3.5% greater than the


stress obtained using the top-down approach.

F=220.0 N

10 60(10)

(10)

(10)

(10)

445

450

450

Web leg length: 5 mm

Side view 2

Plan view

150

9560520

250 13

0(10) (10)

Fig. 12. Structural detail under consideration

X Y

Z

2

5050

40

planeconstrained

Fig.13. 3-D shell and local 2-D models of hopper corner detail.


Based on these findings, it is considered that analysis using a combination of a 3-D shell model and a2-D plane stress element model is sufficiently accurate to capture the changes in stress due tomisalignment. This method offers a practical alternative approach to an analysis using solid elements.

Fig. 14. X-direction stress for 2-D model.

Fig. 15. Solid model of hopper corner detail.


Fig. 16. X-direction stress for solid model.

Documents

Effect of Misalignment on the Stress Concetration of a Weld hopper knuckle connection