Stress concentration factors for tubular complex joints … · · 2017-07-15OTH 91 353 STRESS CONCENTRATION FACTORS FOR TUBULAR COMPLEX JOINTS Author Lloyd’s Register of Shipping

OTH 91 353

STRESS CONCENTRATIONFACTORS FOR TUBULAR

COMPLEX JOINTS

Author

Lloyd’s Register of Shipping71 Fenchurch StreetLondon EC3M 4BS

Health and Safety Executive - Offshore Technology Report

i

© Crown copyright 1992Applications for reproduction should be made to HMSO

First published 1992ISBN 0 11 886363 0

This report is published by the Health and Safety Executive aspart of a series of reports of work which has been supported byfunds formerly provided by the Department of Energy and latelyby the Executive. Neither the Executive, the Department nor thecontractors concerned assume any liability for the reports not dothey necessarily reflect the views or policy of the Executive orthe Department

Results, including detailed evaluation and, where relevant,recommendations stemming from their research projects arepublished in the OTH series of reports.

Background information and data arising from these researchprojects are published in the OTI series of reports.

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ii

CONTENTS

67APPENDIX A - Acrylic Modelling

66REFERENCES

59FIGURES

7TABLES

6CONCLUSIONS4.

333333445

PRESENTATION AND DISCUSSION OF RESULTS3.1 SCF comparison for single-plane joints

3.1.1 Task 6 KT joint3.1.2 Task 7 K joint

3.2 Determination of carry-over effects3.3 Observations on carry-over effects3.4 Calculation of SCFs for load combinations

3.4.1 Axial loading3.4.2 Out -of-plane bending

3.

2222

DETAILS OF INVESTIGATION2.1 Acrylic modelling

2.1.1 Strain gauge locations2.1.2 Extrapolation procedures

2.

1INTRODUCTION1.

PART 1 MULTI-PLANAR JOINTS

VSUMMARY

Page

iii

CONTENTS (cont)

40APPENDIX A - Veritec Joint Configuration

39REFERENCES

26FIGURES

8TABLES

7SUMMARY AND CONCLUSIONS5.

44444555566

DISCUSSION OF RESULTS4.1 Introduction4.2 Task 8

4.2.1 Single brace loaded cases4.2.2 Balanced axial loading4.2.3 Unbalanced axial loading4.2.4 Unbalanced OPB4.2.5 Balanced OPB4.2.6 Balanced IPB4.2.7 Unbalanced IPB

4.3 Veritec configuration (balanced axial loading)

4.

3PRESENTATION OF RESULTS3.

2222

TEST DETAILS2.1 Task 8A2.2 Task 8.B2.3 Veritec configuration

2.

1INTRODUCTION1.

PART 2 OVERLAPPED JOINTS

Page

iv

SUMMARY

The work covered in this report was carried out as part of the group sponsoredproject “Stress Concentration Factors for Tubular Complex Joints”. The primaryobjective of this project was to obtain improved methods of dealing with the fatigueaspects of complex joints and loadings. The main emphasis was on ring-stiffenedjoints, however, work was also performed on unstiffened multi-planar and overlappedjoints.

In fatigue analysis, single-plane SCF parametric equations are generally used formulti-planar joints and this required validation. In the multi-planar joint programme,covered in Part 1 of this report, 12 joint configurations were tested using acrylicmodelling. Carry-over effects for axial loading and out-of-plane bending weredetermined. Typical multi-planar overall joint loading patterns were investigated toidentify those patterns which give increased SCF levels when multi-planar effects areincluded.

For the most common fatigue loading cases, the results obtained indicated that theuse of the existing single-plane SCF equations for multi-planar joints was probablyjustifiable. However, some loading conditions produced very significant carry-overeffects which required further investigation. A follow-up study, commissioned by theUK Department of Energy entitled “Investigation of Stress Concentration Factors forMulti-planar Joints in Offshore Structures” has been completed. The studyinvestigated typical loading cases that occur in practice and lead to significantcarry-over effects. †

The overlapped joint programme, covered in Part 2 of this report, was essentially anSCF comparison study between measured and predicted values from existingparametric equations. The measured SCFs were obtained by Koninkliike/ShellExploratie en Produktie Laboratorium (KSEPL) and Wimpey using finite elementusing finite element analysis techniques and by Lloyd’s Register using acrylicmodelling. The eight joint configurations considered included the overlapped steelspecimen from the UKOSRP II project, however, the steel SCF results were notincluded due to confidentiality restrictions at the time the report was prepared. AnSCF comparison including the UKOSRP II results can be found in “A review ofstress concentration factors for tubular complex joints”, by Smedley P. and Fisher P.,Integrity of Offshore Structures - 4, Glasgow.

Additionally, an acrylic model was tested with the same configuration as anoverlapped steel joint tested by Veritec as part of another programme. An SCFcomparison was made for this joint, including the steel and also finite elementanalysis SCF results which were made available by Veritec.

From this programme of work, regarding measures SCFs, good agreement wasobtained for the different techniques considered. In the SCF comparison withparametric equations, for all modes of loading considered, the closest agreement wasobtained with the equations by Efthymiou/Durkin of KSEPL. The Veritecconfiguration results highlighted the differences that can be obtained in extrapolatedSCFs due to different strain gauge positions and extrapolation procedures.

† OTH 91 346 Investigation of Stress Concentration Factors for Multi-planarJoints in Offshore Structures (to be published).

v

PART 1

MULTI-PLANAR JOINTS

1. INTRODUCTION

It is common practice to predict SCFs in a particular plane of a multi-planarcomplex joint by including only the effects from loads applied to braces which lie inthat same plane. This report covers the Tasks 6.A and 6.B tests on multi-planar KTjoints and Task 7 6.A on multi-planar K joints, which were devised to check thevalidity of this method, by establishing the significance of carry-over effects on theSCFs from brace loads in other planes.

In the tests axial loads, out-of-plane (OPB) moments and in-plane (IPB) moments areapplied to each brace member of the joint in turn. IPB moments have small effectsand are not reported here. Superposition is used to calculate the distribution ofSCF’s for different patterns of axial loads and OPB moments applied to the joint. Byevaluating the superposition, both with and without inter-plane carry-over effects, theimportance of including such terms is established, together with the load patternscausing the greatest increase in SCF levels.

1

2. DETAILS OF INVESTIGATION

2.1 ACRYLIC MODELLING

The acrylic modelling, as detailed in Figures 1, 2 and 3, involves the testing of 12unstiffened joints. The tube wall thickness are changed between the four 6.A test (y= 12) and the corresponding 6.B tests (y = 24). The four 6.B tests on KT jointscorrespond to the four 7.A tests of K joints. The test model was built up from thebasic 6.A1, 6.B1 and 7.A1 single-plane geometries by the addition of extra bracesand strain gauges.

2.1.1 Strain gauge locations

Two hundred strains gauges were present on the final 6.A4, 6.B4 and 7.A4multi-planar joints. The position of these gauges relative to the chord-braceintersection line are as detailed in Appendix A1. Only the chord saddle gauges areused in this report and their locations are given on Figures 4 to 6 for the Task 6 KTjoints, and on Figures 7 to 9 for the Task 7 K joints.

2.1.2 Extrapolation procedures

The extrapolation methods available for determining SCFs are given inAppendix A2.

2

3. PRESENTATION AND DISCUSSION OF RESULTS

3.1 SCF COMPARISON FOR SINGLE-PLANE JOINTS

3.1.1 Task 6 KT joint

Table 1 shows the single-plane average measured SCFs for balanced axial load andunbalanced OPB compared with the predicted SCFs derived from the equations ofWordsworth(1), Efthymiou/Durkin(2) and Kuang et al(3). Only the main braces areloaded since not all of the equations are really applicable for KT joints or where theT brace is of different diameter from the main braces (ie joints are treated as widegap K joints). It can be seen from Table 1 that reasonable agreement is achieved,with predicted SCFs always higher than the measured values.

3.1.2 Task 7 K joint

Table 36 shows the single plane average measured SCFs for balanced axial load andunbalanced OPB compared with the predicted SCFs derived from the Wordsworth(1),Efthymiou/Durkin(2), and Kuang et al(3) equations. It can be seen that reasonableagreement is achieved from all equations. The predicted SCFs are larger than themeasured values in all cases, except for the Efthymiou equation under unbalancedOPB.

3.2 DETERMINATION OF CARRY-OVER EFFECTS

Test strain gauge results are recorded for single loads or moments applied to eachbrace in turn with the chord ends reacted. The chord saddle SCFs obtained fromthese results are processed to give the carry-over effects detailed in Tables 2 to 17 forKT joints, and in Tables 37 to 44 for K joints.

To enable the effects of load combinations to be obtained from superposition of thesingle load tests results, the SCFs have been based on extrapolation methods 3 and 4,involving the chord circumferential strains only.

The symmetry of the structure and the positions of the loads required that given setsof SCFs should have equal absolute value, with the sign dependent on the symmetryor anti-symmetry of the loads applied. For these sets of SCFs is a value has beenassigned based on the average of the group. The final set of SCFs is hence consistentwith symmetry requirements.

The SCF ratios given in Tables 2 and 17 and Tables 37 to 44, are obtained bydividing the actual SCFs by the maximum absolute SCF value occurring at the chordsaddle of the loaded brace. Each column of the table gives the carry-over effect tothe SCFs at the chord saddle positions of the unloaded braces. If required the actualrecorded test SCFs can be obtained by multiplying the values in each column by theappropriate term given at the bottom of the table.

3.3 OBSERVATIONS ON CARRY-OVER EFFECTS

3

For the 8 KT joints tested, Tables 2 to 9 give the carry-over effects for axial load andTables 10 to 17 give the carry-over effects for OPB applied.

For the 4 K joints tested, Tables 37 to 40 give the carry-over effects for axial loadand Tables 41 to 44 give the carry-over effects for OPB applied.

The following general observations relate to the results given in these tables:

(i) The carry-over effects for axial load are more significantthan those for OPB.

(ii) The distribution of chord stresses, resulting from loadsapplied to braces in a given plane, is little affected by thepresence of the other bracing planes. The carry-over effectsfor the single-plane joints 6.A1, 6.B1 and 7.A1 given inTables 2, 3, 10, 11, 37 and 41 are little different from theresults for any of the single planes chosen from themulti-planar joints in the other tables. The carry-overeffects in the 90o and 180o planes of the two-plane joints6.A2, 6.B2, 7.A2, 6.A3, 6.B3 and 7.A3 are similar to theresults for these planes from the 3-plane joints 6.A4, 6.B4and 7.A4.

(iii) An indication of the effect of tube wall thickness oncarry-over effects is provided from the 6.A (y = 12) resultsand the 6.B (y = 24) results.

A comparison of the results in Table 8 with Table 9, andTable 16 with Table 17 shows that changes of the order of20-30% are present with the most significant changesapplying to carry-over effects in the plane of the loadedbrace. The carry-over effects both increase and decreasewith increasing wall thickness.

(iv) An indication of the effect of the addition central T-brace isprovided from the 6.B KT joint results and the 7.A K jointresults (y = 24).

A comparison of the results of Table 9 with Table 40, andTable 17 with Table 44 shows that the carry-over effectbetween the inclined braces is of the same order, except forthe plane containing the loaded brace. The decrease incarry-over noted for the KT joint is more likely to be due tothe increased separation between the inclined braces than tothe stiffening effect of the T brace.

3.4 CALCULATION OF SCFS FOR LOAD COMBINATIONS

The SCFs for load combinations are obtained by superposition of the results from thesingle load tests given in Tables 2 to 17 and Tables 37 to 44.

4

For the single-plane predicted SCFs only carry-over effects on unloaded bracemembers in the same plane as the loading are included. The multi-planar predictioninvolves the full set of carry-over effects listed in Tables 2 to 17 and Tables 37 to 44.

3.4.1 Axial loading

An examination of the signs of the carry-over effects in Tables 8 and 9 for joints6.A4 and 6.B4 and Table 40 for joint 7.A1, shows that the multi-planar terms willhave the greatest effect when all the braces in the 0o and 180o planes are either intension or compression whilst all those in the 90o plane are either in compression ortension respectively. The results for this case are given in Table 18 and Table 45showing that the multi-planar SCFs are two to three times those predicted by thesingle-plane calculation.

Tables 19, 20, 21 and Tables 46, 47 and 48 shows results for joints where a uniformtension was kept in the 0o and 180o planes whilst varying the form of loading in the90o plane. The SCFs from the multi-planar predictions are greater than thesingle-plane predictions except when the 90o plane is in tension.

Tables 22 to 24 and Tables 49 to 51 show results for joints which have tensionacross one diagonal and compression across the other diagonal of the 0o - 180o plane,with load varying in the 90o plane. The multi-planar and single-plane predictions arenot significantly different in overall magnitude but individual SCFs may beconsiderably affected, for example gauge e163 in Table 51.

For the 90o joints, 6.A2, 6.B2 and 7.A1, the multi-planar carry-over effects have themaximum effect when all braces in the 0o plane are either in tension or compressionwhilst all those in the 90o plane are either in compression or tension respectively.The results in Tables 25 and 52 for these cases show that the multi-planar effects are50-100% greater than the single-plane calculations.

Tables 26, 27, 53 and 54 gives the results for balanced axial loading in the twoplanes of the 90o joints. The multi-planar effects are not significant for this case. InTables 28 and 55 joints have tension in the braces of both planes and significantreductions in the SCFs are noted.

For the 180o joints, 6.A3, 6.B3 and 7.B3 the maximum effect of multi-planarcarry-over is when all brace members are either in tension or compression. Increasesin SCFs of up to 70% occur for the KT joint (Table 29). In Tables 30 and 56 resultsare given for tension in the diagonal members of the KT and K joint, respectively;here only 50% increases can be noted. Tables 31 and 57 show results for jointswhich have tension across one diagonal and compression in the other which leads tosmall decreases in SCF.

3.4.2 Out-of-plane bending

The carry-over effects for OPB are less significant than those for axial load (compareTables 8, 9 and 40 with 16, 17 and 44 for joints 6.A4, 6.B4 and 7.A4).

For the 0o and 180o planes the multi-planar effects will be most significant when allapplied moments have the same sign. The effect of the signs of moments in the 90o

plane is less obvious.

5

In Tables 32 and 58 results are given for the cases where positive moments wereapplied to the 0o and 180o planes, leaving the 90o plane unloaded. The multi-planarcarry-over effects cause an increase of approximately 15% in the SCFs.

Results in Tables 33 and 59 include the effects of positive moments in the 90o planewhilst in Tables 34, 35, 60 and 61 results are given for cases where moments ofdifferent signs were applied to the diagonals in the 0o and 180o planes. SCF changesare not significant for any of these cases.

The carry-over effects for the 6.A2, 6.B2, 7.A2, 6.A3, 6.B3 and 7.A3 tests aresimilar to those of the component planes in the 6.A4, 6.B4 and 7.A4 tests. As the6.A4, 6.B4 and 7.A4 tests show no significant effects for OPB, no further cases arepresented.

6

4. CONCLUSIONS

This has been a limited study to establish the possible importance of includinginter-plane carry-over effects when predicting the SCFs on complex multi-planarjoints. With respect to axial loading it has been shown that such effects can behighly significant for certain patterns of loading. However, it may be that theseparticular loading patterns do not have a major influence in fatigue analyses ofoffshore structures; this requires further investigation†. Carry-over effects werefound to be less important for OPB.

† This has since been undertaken in a separate study; see report OTH 91 346Investigation of Stress Concentration Factors for Multi-planar Joints inOffshore Structures.

7

TABLES

Comparison of single-plane and multi-planar SCF predictions forOPB load patterns (K joint)

58-61

Comparison of single-plane and multi-planar SCF predictions foraxial load patterns (K joint)

45-57

SCF carry-over ratios for OPB (K joint)41-44

SCF carry-over ratios for axial load (K joints)37-40

Comparison of single-plane chord saddle SCFs with K jointparametric equations

36

Comparison of single-plane and multi-planar SCF predictions foraxial load patterns (KT joint)

18-31

SCF carry-over ratios for OPB (KT joint)10-17

SCF carry-over ratios for axial load (KT joint)2-9

Comparison of single-plane chord saddle SCFs with KT jointparametric equations

1

8

Table 1 Comparison of single-plane chord saddle SCF's with parametric equations

-7.027.886.756.B1UnbalancedOPB

4.154.675.084.036.B1BalancedAxial

-3.593.613.226.A1UnbalancedOPB

2.623.303.242.266.A1Balancedaxial

KuangEfthymiouWordsworth

SCF from parametric equationsAveragemeasured

SCF

JointLoading

Note: Only braces a and c are loaded, hence parametric equations for K joint areused for comparison.

9

Table 2Task 6.A1 - SCF ratio at the chord saddle positions for axial load

2.894.922.89cba

Ratio multiplier to give actual SCFs

1.00.28.26104c1.00.28.26118c

.671.00.6782b

.671.00.6794b

.26.281.0034a

.26.281.0071a

cbaGaugeBrace

Loaded braceMeasuring position

Table 3Task 6.B1 - SCF ratio at the chord saddle positions for axial load

6.428.636.42cba


1.00.38.39104c1.00.38.39118c

.611.00.6182b

.611.00.6194b

.39.381.0034a

.39.381.0071a

cbaGaugeBrace


10


3.165.763.163.165.763.16fedcba


.95.26.27-.30-1.5-.28195f1.00.26.23-.65-.28-.35199f

.75.97.75-.43-.21-.43183e

.711.00.71-.47-.27-.47189e

.27.26.95-.28-.15-.30160d

.23.261.00-.35-.28-.65172d

-.65-.28-.351.00.26.23104c-.30-.15-.28.95.26.27118c

-.47-.27-.47.711.00.7182b-.43-.21-.43.75.97.7594b

-.35-.28-.65.23.261.0034a-.28-.15-.30.27.26.9571a

fedcbaGaugeBrace



6.479.676.476.479.676.47fedcba


1.00.37.41-.33-.19-.34195f1.00.34.36-.66-.32-.38199f

.661.00.66-.36-.18-.36183e

.56.82.56-.38-.19-.38189e

.41.371.00-.34-.19-.33160d

.36.341.00-.38-.32-.66172d

-.66-.32-.381.00.34.36104c-.33-.19-.341.00.37.41118c

-.38-.19-.38.56.82.5682b-.36-.18-.36.661.00.6694b

-.38-.32-.66.36.341.0034a-.34-.19-.33.41.371.0071a

fedcbaGaugeBrace


11


3.035.423.033.035.423.03fedcba


.98.26.27.40.19.33151f1.00.27.26.47.22.36155f

.701.00.70.29.15.29139e

.66.92.66.28.15.28145e

.27.26.98.33.19.40126d

.26.271.00.36.22.47133d

.47.22.361.00.27.26104c

.40.19.33.98.26.27118c

.28.15.28.66.92.6682b

.29.15.29.701.00.7094b

.36.22.47.26.271.0034a

.33.19.40.27.26.9871a

fedcbaGaugeBrace



6.619.226.616.619.226.61fedcba


.99.37.38.37.21.35151f1.00.37.39.36.21.34155f

.621.00.62.25.14.25139e

.55.89.55.21.12.21145e

.38.37.99.35.21.37126d

.39.371.00.34.21.36133d

.36.21.341.00.37.39104c

.37.21.35.99.37.38118c

.21.12.21.55.89.5582b

.25.14.25.621.00.6294b

.34.21.36.39.371.0034a

.35.21.37.38.37.9971a

fedcbaGaugeBrace


12


2.945.202.943.256.193.252.945.202.94ihgfedcba


.97.27.27-.26-.13-.24.44.21.36151i1.00.25.22-.59-.23-.31.40.20.33155i

.741.00.74-.37-.17-.37.32.17.32139h

.65.98.65-.39-.21-.39.26.15.26145h

.27.27.97-.24-.13-.26.36.21.44126g

.22.251.00-.31-.23-.59.33.20.40133g-.78-.35-.401.0024.25-.30-.16-.28195f-.300.16-.281.00.24.25-.78-.35-.40199f

-.56-.32-.56.731.00.73-.47-.23-.47183e-.47-.23-.47.731.00.73-.56-.32-.56189e

-.40-.35-.78.25.241.00-.28-.16-.30160d-.28-.16-.30.25.241.00-.40-.35-.78172d

.40.20.33-.58-.23-.311.00.25.22104c

.44.21.36-.26-.13-.24.97.27.27118c

.26.15.26-.39-.21-.39.65.98.6582b

.32.17.32-.37-.17-.37.741.00.7494b

.33.20.40-.31-.23-.59.22.251.0034a

.36.21.44-.24-.13-.26.27.27.9771a

ihgfedcbaGaugeBrace

Loaded braceMeasuringposition

13


6.348.966.346.538.736.536.348.986.34ihgfedcba


1.00.37.39-.30-.19-.31.39.22.37151i1.00.34.35-.60-.33-.35.32.17.28155i

.651.00.65-.34-.19-.34.27.15.27139h

.56.90.56-.37-.20-.37.21.11.21145h

.39.371.00-.31-.19-.30.37.22.39126g

.35.341.00-.35-.33-.60.28.17.32133g-.72-.35-.421.00.40.36-.30-.18-.33195f-.300.18-.331.00.40.36-.72-.35-.42199f

-.42-.21-.42.571.00.57-.32-.16-.32183e-.32-.16-.32.571.00.57-.42-.21-.42189e

-.42-.35-.72.36.401.00-.33-.18-.30160d-.33-.18-.30.36.401.00-.42-.35-.72172d

.32.17.28-.60-.33-.351.00.34.35104c

.39.22.37-.30-.19-.311.00.37.39118c

.21.11.21-.37-.20-.37.56.90.5682b

.27.15.27-.34-.19-.34.651.00.6594b

.28.17.32-.35-.33-.60.35.341.0034a

.37.22.39-.31-.19-.30.39.371.0071a

ihgfedcbaGaugeBrace


14

Table 10Task 6.A1 - SCF ratio at the chord saddle positions for O.P.B.

2.623.292.62cba


1.00.19.16104c-1.00-.19-.16118c

.261.00.2682b-.26-1.00-.2694b

.16.191.0034a-.16-.19-1.0071a

cbaGaugeBrace


Table 11Task 6.B1 - SCF ratio at the chord saddle positions for O.P.B.

5.026.325.02cba


1.00.24.24104c-1.00-.24-.24118c

.321.00.3282b-.32-1.00-.3294b

.24.241.0034a-.24-.24-1.0071a

cbaGaugeBrace


15


2.783.682.782.783.682.78fedcba


.97.17.16-.19-.08-.12195f-1.00-.17-.16-.10-.0.00.09199f

.281.00.28-.17-.07-.17183e-.28-.98-.28-.05-.05-.05189e

.16.17.97-.12-.08-.19160d-.16-.17-1.00.09-.0.00-.10172d

.100.00-.091.00.17.16104c

.19.08.12-.97-.17-.16118c

.05.05.05.28.98.2882b

.17.07.17-.28-1.00-.2894b

-.090.00.10.16.171.0034a.1208.19-.16-.17-.9771a

fedcbaGaugeBrace



5.206.705.205.206.705.20fedcba


.99.22.25-.19-.09-.16195f-1.00-.22-.23-.15-.02.10199f

.321.00.32-.17-.06-.17183e-.28-.87-.28-.08-.02-.08189e

.25.22.99-.16-.09-.19160d-.23-.22-1.00.10-.02-.15172d

.15.02-.101.00.22.23104c

.19.09.16-.99-.22-.25118c

.08.02.08.28.87.2882b

.17.06.17-.32-1.00-.3294b

-.10.02.15.23.221.0034a.16.09.19-.25-.22-.9971a

fedcbaGaugeBrace


16


2.743.552.742.743.552.74ihgcba


.97.18.17.07.03.09151i-1.00-.19-.17-.05-.03-.08155i

.261.00.26.03.02.04139h-.24-.89-.24-.03-.02-.03145h

.17.18.97.09.03.07126g-.17-.19-1.00-.08-.03-.05133g

.05.03.081.00.19.17104c-.07-.03-.09-.97-.18-.17118c

.03.02.03.24.89.2482b-.04-.02-.04-.26-1.00-.2694b

.08.03.05.17.191.0034a-.09-.03-.07-.17-.18-.9771a

ihgcbaGaugeBrace



5.226.585.225.226.585.22fedcba


.97.23.23.05.03.07151i-1.00-.24-.24-.06-.03-.09155i

.311.00.31.02.01.02139h-.28-.89-.28-.03-.01-.03145h

.23.23.97.07.03.05126g-.24-.24-1.00-.09-.03-.06133g

.06.03.091.00.24.24104c-.05-.03-.07-.97-.23-.23118c

.03.01.03.28.89.2882b-.02-.01-.02-.31-1.00-.3194b

.09.03.06.24.241.0034a-.07-.03-.05-.23-.23-.9771a

ihgcbaGaugeBrace


17


2.703.562.702.933.802.932.703.562.70ihgfedcba


1.00.17.16-.17-.08-.12.06.03.08151i-.99-.17-.15-.08-.010.7-.08-.04-.09155i

.281.00.28-.16-.07-.16.04.02.04139h-.25-.88-.25-.04-.05-.04-.04-.02-.04145h

.16.171.00-.12-.08-.17.08.03.06126g-.15-.17-.99.07-.01-.08-.09-.04-.08133g.100.00-.091.00.18.14-.22-.09-.14195f.22.09.14-1.00-.18-.14-.10-.0.00.09199f

.04.05.04.271.00.27-.19-.08-.19183e

.19.08.19-.27-1.00-.27-.04-.05-.04189e

-.090.00.10.14.181.00-.14-.09-.22160d.14.09-.14-.14-.18-1.00.09-.0.00-.10172d

.08.04.09.08.01-.07.99.17.15104c-.06-.03-.08.17.08.12-1.00-.17-.16118c

.04.02.04.04.05.04.25.88.2582b-.04-.02-.04.16.07.16-.28-1.00-.2894b

.09.04.08-.07.01.08.15.17.9934a-.08-.03-.06.12.08.17-.16-.17-1.0071a

ihgfedcbaGaugeBrace


18


5.286.53

5.285.566.165.565.566.535.28ihgfedcba


.98.23.24-.18-.10-.15.05.02.06151i-1.00-.23-.22-.15-.040.8-.09-.04-.11155i

-1.00.23.22-.15-.04-.08.02.02.02139h-.29-.89-.29-.08-.04-.08-.04-.03-.04145h

.24.23.98-.15-.10-.18.06.02.05126g

-.22-.23-1.00

.08-.04-.15-.11-.04-09133g.16.03-.091.00.25.22-.21-.10-.18195f.21.10.18-1.00-.25-.22-.16-.03.09199f

.07.03.07.281.00.28-.18-.06-.18183e

.18.06.18-.28-1.00-.28-.07-.03-.07189e

-.09.03.16.22.251.00-.18-.10-.21160d.18.10-.21-.22-.25-1.00.09-.03-.16172d

.09.04.11.15.04-.081.00.23.22104c-.05-.02-.06.18.10.15-98-.23-.24118c

.04.03.04.08.04.08.29.89.2982b-.02-.02-.02.17.07.17-.32-1.00-.3294b

.11.04.09-.08.04.15.22.231.0034a-.06-.02-.05.15.10.18-.24-.23-.9871a

ihgfedcbaGaugeBrace


19

Table 18SCF's at the chord saddle positions for axial loadings

Applied nominal brace loads

1.001.001.00-1.00-1.00-1.001.001.001.00

ihgfedcba

6.A4 Predicted chord saddle SCF's

10.9015.8110.90-13.34-19.81-13.3412.4615.0412.46Multi-planar

5.039.575.03-5.54-10.95-5.544.918.954.91Single plan

i151h139g126f195e183d160c104b82a34

12.4615.0412.46-13.34-19.81-13.3410.9015.8110.90Multi-planar

4.918.954.91-5.54-10.95-5.545.039.575.03Single plan

i155h145g133f199e189d172c118b94a71

Gauge positionsCalculationmethod

6.B4 Predicted chord saddle SCF's

24.5527.9924.55-28.94-28.29-28.1226.1225.4726.12Multi-planar

12.0717.1612.07-12.32-16.14-12.3211.6115.2111.61Single plan

i151h139g126f195e183d160c104b82a34

26.1225.4726.12-28.29-28.94-28.2924.5527.9924.55Multi-planar

11.6115.2111.61-12.32-16.14-12.3212.0717.1612.07Single plan

i155h145g133f199e189d172c118b94a71


20



1.001.001.000.000.000.001.001.001.00

ihgfedcba


8.4712.328.47-7.80-8.87-7.808.0811.248.08Multi-planar

5.039.575.030.000.000.004.918.954.91Single plan

i151h139g126f195e183d160c104b82a34

8.0811.248.08-7.80-8.87-7.808.4712.328.47Multi-planar

4.918.954.910.000.000.005.039.575.03Single plan

i155h145g133f199e189d172c118b94a71



18.8521.9418.85-15.97-12.80-15.9716.9618.8419.96Multi-planar

12.0717.1612.070.000.000.0011.6115.2111.61Single plan

i151h139g126f195e183d160c104b82a34

16.9618.8416.96-15.97-12.80-15.9718.8521.9418.85Multi-planar

11.6115.2111.610.000.000.0012.0717.1612.07Single plan

i155h145g133f199e189d172c118b94a71


21



1.001.001.00-1.000.001.001.001.001.00

ihgfedcba


8.5512.328.40-10.24-8.87-5.358.9911.247.16Multi-planar

5.039.575.03-2.450.002.454.918.954.91Single plan

i151h139g126f195e183d160c104b82a34

8.9911.247.1610.24-8.87-5.358.5512.328.40Multi-planar

4.918.954.91-2.450.002.455.039.575.03Single plan

i155h145g133f199e189d172c118b94a71



18.8221.9418.88-20.16-12.80-11.7818.6118.8415.31Multi-planar

12.0717.1612.07-4.190.004.1911.6115.2111.61Single plan

i151h139g126f195e183d160c104b82a34

18.6118.8415.31-20.16-12.80-11.7818.8221.9418.88Multi-planar

11.6115.2111.61-4.190.004.1912.0717.1612.07Single plan

i155h145g133f199e189d172c118b94a71


22


1.001.001.001.001.001.001.001.001.00

ihgfedcba


6.048.846.04-2.262.08-2.263.707.453.70Multi-planar

5.039.575.035.5410.955.544.918.954.91Single plan

i151h139g126f195e183d160c104b82a34

3.707.453.70-2.262.08-2.266.048.846.04Multi-planar

4.918.954.915.5410.955.545.039.575.03Single plan

i155h145g133f199e189d172c118b94a71



13.1515.8913.15-3.653.34-3.657.8012.227.80Multi-planar

12.0717.1612.0712.3216.1412.3211.6115.2111.61Single plan

i151h139g126f195e183d160c104b82a34

7.8012.227.80-3.653.34-3.6513.1515.8913.15Multi-planar

11.6115.2111.6112.3216.1412.3212.0717.1612.07Single plan

i155h145g133f199e189d172c118b94a71


23



1.000.00-1.000.000.000.00-1.000.001.00

ihgfedcba


1.810.00-1.81-1.070.001.07-2.080.002.08Multi-planar

2.060.00-2.060.000.000.00-2.300.002.30Single plan

i151h139g126f195e183d160c104b82a34

2.080.00-2.081.070.00-1.07-1.810.001.81Multi-planar

2.300.00-2.300.000.000.00-2.060.002.06Single plan

i155h145g133f199e189d172c118b94a71



3.730.00-3.73-2.040.002.04-3.930.003.93Multi-planar

3.880.00-3.880.000.000.00-4.140.004.14Single plan

i151h139g126f195e183d160c104b82a34

3.930.00-3.932.040.00-2.04-3.730.003.73Multi-planar

4.140.00-4.140.000.000.00-3.880.003.88Single plan

i155h145g133f199e189d172c118b94a71


24



1.000.00-1.00-1.000.001.00-1.000.001.00

ihgfedcba


1.880.00-1.81-3.520.003.521.170.001.17Multi-planar

2.060.00-2.06-2.450.002.45-2.300.002.30Single plan

i151h139g126f195e183d160c104b82a34

3.000.00-3.00-1.370.001.37-1.740.001.74Multi-planar

2.300.00-2.30-2.450.002.45-2.060.002.06Single plan

i155h145g133f199e189d172c118b94a71



3.700.00-3.70-6.230.006.23-2.280.002.28Multi-planar

3.880.00-3.88-4.190.004.19-4.140.004.14Single plan

i151h139g126f195e183d160c104b82a34

5.580.00-5.58-2.150.002.15-3.760.003.76Multi-planar

4.140.00-4.14-4.190.004.19-3.880.003.88Single plan

i155h145g133f199e189d172c118b94a71


25



1.000.00-1.001.001.001.00-1.000.001.00

ihgfedcba


-.623.49-4.244.4710.956.61-6.46-3.79-2.30Multi-planar

2.060.00-2.065.5410.955.54-2.300.002.30Single plan

i151h139g126f195e183d160c104b82a34

-2.303.79-6.466.6110.954.47-4.24-3.49-.62Multi-planar

2.300.00-2.305.5410.955.54-2.060.002.06Single plan

i155h145g133f199e189d172c118b94a71



-1.97-6.05-9.4310.2816.1414.3613.09-6.62-5.23Multi-planar

3.880.00-3.8812.3216.1412.32-4.140.004.14Single plan

i151h139g126f195e183d160c104b82a34

-5.23-6.62-13.0914.3616.1410.28-9.43-6.05-1.97Multi-planar

4.140.00-4.1412.3216.1412.32-3.880.003.88Single plan

i155h145g133f199e189d172c118b94a71


26



-1.00-1.00-1.001.001.001.00

fedcba

6.A2 Predicted chord saddle SCG's

-8.00-14.26-8.0010.1514.7610.15Multi-planar

-5.31-10.35-5.315.3710.275.37Single plan

f195e183d160c104b82a34

-10.15-14.76-10.158.0014.268.00Multi-planar

-5.37-10.27-5.375.3110.355.31Single plan

f199e189d172c118b94a71



-18.86-24.59-18.8621.8621.8921.86Multi-planar

-12.66-18.24-12.6612.0715.1412.07Single plan

f195e183d160c104b82a34

-21.86-21.89-21.8618.8624.5918.86Multi-planar

12.07-15.14-12.0712.6618.2412.66Single plan

f199e189d172c118b94a71


27



1.000.00-1.00-1.000.001.00

fedcba


2.200.00-2.20-3.400.003.40Multi-planar

2.140.00-2.14-2.430.002.43Single plan

f195e183d160c104b82a34

3.400.00-3.40-2.200.002.20Multi-planar

2.430.00-2.43-2.140.002.14Single plan

f199e189d172c118b94a71


3.790.00-3.79-5.920.005.92Multi-planar

3.830.00-3.83-4.120.004.12Single plan

f195e183d160c104b82a34

5.920.00-5.79-3.790.003.79Multi-planar

4.120.00-4.12-3.830.003.83Single plan

f199e189d172c118b94a71


28



-1.000.001.00-1.000.001.00

fedcba


-2.080.002.08-1.460.001.46Multi-planar

-2.140.002.14-2.430.002.43Single plan

f195e183d160c104b82a34

-1.460.001.46-2.080.002.08Multi-planar

-2.430.00-2.43-2.140.002.14Single plan

f199e189d172c118b94a71



-3.870.003.87-2.320.002.32Multi-planar

-3.830.003.83-4.120.004.12Single plan

f195e183d160c104b82a34

-2.320.002.32-3.870.003.87Multi-planar

-4.120.004.12-3.830.003.83Single plan

f199e189d172c118b94a71


29



1.001.001.001.001.001.00

ihgcba


8.4212.228.429.0011.569.00Multi-planar

5.189.665.185.279.005.27Single plan

i195h183g160c104b82a34

9.0011.569.008.4212.228.42Multi-planar

5.279.005.275.189.665.18Single plan

i199h189g172c118b94a71



19.1221.9719.1219.1619.3719.16Multi-planar

12.4317.4312.4312.6015.4912.60Single plan

i195h183f160c104b82a34

19.1619.3719.1619.1221.9719.12Multi-planar

12.6015.4912.6012.4317.4312.43Single plan

i199h189g172c118b94a71


30



1.000.001.001.000.001.00

ihgcba


5.976.005.976.355.736.35Multi-planar

3.764.243.763.824.013.82Single plan

i195h183g160c104b82a34

6.355.736.355.976.005.97Multi-planar

3.824.013.823.764.243.76Single plan

i199h189g172c118b94a71



13.7711.5013.7713.8210.0913.82Multi-planar

9.028.219.029.187.299.18Single plan

i195h183g160c104b82a34

13.8210.0913.8213.7711.5013.77Multi-planar

9.187.299.189.028.219.02Single plan

i199h189g172c118b94a71


31



1.000.00-1.00-1.000.001.00

ihgcba


1.920.00-1.92-1.900.001.90Multi-planar

2.160.00-2.16-2.240.002.24Single plan

i195h183g160c104b82a34

1.900.00-1.90-1.920.001.92Multi-planar

2.240.00-2.24-2.160.002.16Single plan

i199h189g172c118b94a71



3.940.00-3.94-3.950.003.95Multi-planar

4.050.00-4.05-4.050.004.05Single plan

i195h183g160c104b82a34

3.950.00-3.95-3.940.003.94Multi-planar

4.050.00-4.05-4.050.004.05Single plan

i199h189g172c118b94a71


32

Table 32SCF's at the chord saddle positions for O.P.B. loading

Applied nominal brace moments

1.001.001.000.000.000.001.001.001.00

ihgfedcba


4.225.344.22-1.24-.90-1.244.274.784.27Multi-planar

3.765.053.760.000.000.003.674.473.67Single plan

i151h139g126f195e183d160c104b82a34

-4.27-4.78-4.271.24.901.24-4.22-5.34-4.22Multi-planar

-3.67-4.47-3.670.000.000.00-3.76-5.05-3.76Single plan

i155h145g133f199e189d172c118b94a71



8.6310.218.63-2.15-1.36-2.159.279.479.27Multi-planar

7.929.867.920.000.000.007.958.877.95Single plan

i151h139g126f195e183d160c104b82a34

-9.27-9.47-9.272.151.362.15-8.63-10.21-8.63Multi-planar

-7.95-8.87-7.950.000.000.00-7.92-9.86-7.92Single plan

i155h145g133f199e189d172c118b94a71


33

Table 33SCF's at the chord saddle positions for O.P.B. loadings


1.001.001.001.001.001.001.001.001.00

ihgfedcba


3.084.123.082.804.482.804.345.184.34Multi-planar

3.765.053.764.035.374.033.674.473.67Single plan

i151h139g126f195e183d160c104b82a34

-4.34-5.18-4.34-2.80-4.48-2.80-3.08-4.12-3.08Multi-planar

-3.67-4.47-3.67-4.03-5.37-4.03-3.76-5.05-3.76Single plan

i155h145g133f199e189d172c118b94a71



6.187.896.186.167.876.169.8810.569.88Multi-planar

7.929.867.928.329.238.327.958.877.95Single plan

i151h139g126f195e183d160c104b82a34

-9.88-10.56-9.88-6.16-7.87-6.16-6.18-7.89-6.18Multi-planar

-7.95-8.87-7.95-8.32-9.23-8.32-7.92-9.86-7.92Single plan

i155h145g133f199e189d172c118b94a71


34



1.000.00-1.000.000.000.00-1.000.001.00

ihgfedcba


2.310.00-2.31.750.00-.75-2.280.002.28Multi-planar

2.250.00-2.250.000.000.00-2.270.002.27Single plan

i151h139g126f195e183d160c104b82a34

-2.280.002.28.750.00-.752.310.00-2.31Multi-planar

-2.270.002.270.000.000.002.250.00-2.25Single plan

i155h145g133f199e189d172c118b94a71



3.950.00-3.951.510.00-1.51-4.200.004.20Multi-planar

3.910.00-3.910.000.000.00-4.100.004.10Single plan

i151h139g126f195e183d160c104b82a34

-4.200.004.201.510.00-1.513.950.00-3.95Multi-planar

-4.100.004.100.000.000.003.910.00-3.91Single plan

i155h145g133f199e189d172c118b94a71


35



1.000.00-1.001.001.001.00-1.000.001.00

ihgfedcba


1.17-1.22-3.454.785.373.29-2.20.412.35Multi-planar

2.250.00-2.254.035.374.03-2.270.002.27Single plan

i151h139g126f195e183d160c104b82a34

-2.35-.412.20-3.29-5.37-4.783.451.22-1.17Multi-planar

-2.270.002.27-4.03-5.37-4.032.250.00-2.25Single plan

i155h145g133f199e189d172c118b94a71



1.51-2.32-6.409.839.236.80-3.591.094.81Multi-planar

3.910.00-3.918.329.238.32-4.100.004.10Single plan

i151h139g126f195e183d160c104b82a34

-4.81-1.093.59-6.80-9.23-9.836.402.32-1.51Multi-planar

-4.100.004.10-8.32-9.23-8.323.910.00-3.91Single plan

i155h145g133f199e189d172c118b94a71


36

Table 36Comparison of sinlge-plane chord saddle SCF's with parametric equations

-7.748.737.97.A1UnbalancedOPB

3.653.993.693.037.A1Balancedaxial

KuangEfthymiouWordsworth

SCF from parametric equationsAveragemeasuredSCF

JointLoading

37

Table 37Task 7.A1 - SCF ratio at the chord saddle positions

for axial load

6.896.89ba


1.00.56117b1.00.56133b

.561.004a

.561.0076a

baGaugeBrace


Table 38Task 7.A2 - SCF at the chord saddle positions

for axial load

6.756.756.756.75dcba


1.00.56-.32-.35204d.90.47-.60-.48201d

.561.00-.35-.32198c

.47.90-.48-.60192c

-.60-.48.90.47117b-.32-.351.00.56133b

-.48-.60.47.904a-.35-.32.561.0076a

dcbaGaugeBrace


38

Table 39Task 7.A3 - SCF ratio at the chord saddle positions

for axial load

7.007.007.007.00feba


1.00.54-.37-.37176d.92.51-.34-.35186d

.541.00-.37-.37139c

.51.92-.35-.34163c

-.34-.35.92.51117b-.37-.371.00.54133b

-.35-.34.51.924a-.37-.37.541.0076a

febaGaugeBrace



6.796.796.096.096.796.79fedcba


1.00.55-.34-.37.38.38176f.87.46-.64-.52.30.30186f

.551.00-.37-.34.38.38139e

.46.87-.52-.64.30.30163e

-.62-.491.00.53-.27-.29204d-.27-.291.00.53-.62-.49201d

-.49-.62.531.00-.29-.27198c-.29-.27.531.00-.49-.62192c

.30.30-.64-.52.87.46117b

.38.38-.34-.371.00.55133b

.30.30-.52-.64.46.874a

.38.38-.37-.34.551.0076a

fedcbaGaugeBrace


39

Table 41Task 7.A1 - SCF ration at the chord saddle positions for O.P.B.

5.695.69ba


1.00.39117b-1.00-.39133b

.391.004a-.39-1.0076a

baGaugeBrace



5.615.615.615.61dcba


1.00.40-.19-.21204d-.95-.36-.11.01201d

.401.00-.21-.19198c-.36-.95.01-.11192c

.11-.01.95.36117b

.19.21-1.00-.40133b

-.01.11.36.954a.21.19-.40-1.0076a

dcbaGaugeBrace


40


5.745.745.745.74feba


1.00.40.06.06176f-.97-.38-.06-.07186f

.401.00.06.06139e-.38-.97-.07-.06163e

.06.07.97.38117b-.06-.06-1.00-.40133b

.07.06.38.974a-.06-.06-.40-1.0076a

febaGaugeBrace



5.635.635.345.345.635.63fedcba


1.00.40-.22-.23.06.06176f-.96-.37-.13-.01-.09-1.0186f

.401.00-.23-.22.06-.06139e-.37-.96-.01-.13-.10-.09163e.12-0.001.00.39-.20-.21204d.20.21-1.00-.39-.120.00201d

-0.00.12.391.00-.21-.20198c.21.20-.39-1.000.00-.12192c

.09.10.13.01.96.37117b-.06-.06.22.23-1.00-.40133b

.10.09.01.13.37.964a-.06-.06.23.22-.40-1.0076a

fedcbaGaugeBrace


41



1.001.00-1.00-1.001.001.00

fedcba


19.9519.95-20.62-20.6220.1220.12Multi-planar10.4910.49-9.32-9.328.988.98Single planef176e139d204c198b117a4

20.1220.12-20.62-20.9519.9519.95Multi-planar8.988.98-9.32-9.3210.4910.49Single plane

f186e163d201c192b133a76


42



1.001.000.000.001.001.00

fedcba


15.6615.66-11.30-11.3013.0813.08Multi-planar10.4910.490.000.008.988.98Single planef176e139d204c198b117a4

13.0813.08-11.30-11.3015.6615.66Multi-planar8.988.980.000.0010.4910.49Single plane

f186e163d201c192b133a76


43



1.001.00-1.001.001.001.00

fedcba


15.4815.83-14.16-8.4413.7712.38Multi-planar10.4910.49-2.862.868.988.98Single planef176e139d204c198b117a4

13.7712.38-14.16-8.4415.4815.83Multi-planar8.988.98-2.862.8610.4910.49Single plane

f186e163d201c192b133a76


44



1.001.001.001.001.001.00

fedcba



6.036.03-1.98-1.9811.3711.37Multi-planar8.988.989.329.3210.4910.49Single plane

f186e163d201c192b133a76


45



1.00-1.000.000.00-1.001.00

fedcba


3.06-3.06-.97.97-2.752.75Multi-planar3.09-3.090.000.00-2.802.80Single planef176e139d204c198b117a4

2.75-2.75.97-.97-3.063.06Multi-planar2.80-2.800.000.00-3.093.09Single plane

f186e163d201c192b133a76


46



1.00-1.00-1.001.00-1.001.00

fedcba


2.89-2.89-3.833.83-2.062.06Multi-planar3.09-3.09-2.862.86-2.802.80Single planef176e139d204c198b117a4

3.45-3.45-1.891.89-3.243.24Multi-planar2.80-2.80-2.862.86-3.093.09Single plane

f186e163d201c192b133a76


47



1.00-1.001.001.00-1.001.00

fedcba


-1.23-7.368.3510.28-9.80-4.29Multi-planar3.09-3.099.329.32-2.802.80Single planef176e139d204c198b117a4

-4.29-9.8010.288.35-7.36-1.23Multi-planar2.80-2.809.329.32-3.093.09Single plane

f186e163d201c192b133a76


48

Table 52SCF's at the chord saddle positions for

axial loadings


-1.00-1.001.001.00

dcba


-15.10-15.1016.5616.56Multi-planar-10.54-10.549.309.30Single planed204c198b117a4

-16.56-16.5615.1015.10Multi-planar-9.30-9.3010.5410.54Single plane

d201c192b133a76


49


axial loadings


1.00-1.00-1.001.00

dcba


2.77-2.77-3.723.72Multi-planar2.97-2.97-2.892.89Single planed204c198b117a4

3.72-3.72-2.772.77Multi-planar2.89-2.89-2.972.97Single plane

d201c192b133a76


50


axial loadings


-1.001.00-1.001.00

dcba


-3.173.17-2.062.06Multi-planar-2.972.97-2.892.89Single planed204c198b117a4

-2.062.06-3.173.17Multi-planar-2.892.89-2.972.97Single plane

d201c192b133a76


51


axial loadings


1.001.001.001.00

dcba


5.995.992.042.04Multi-planar10.5410.549.309.30Single planed204c198b117a4

2.042.045.995.99Multi-planar9.309.3010.5410.54Single plane

d201c192b133a76


52


axial loadings


1.001.001.001.00

feba


15.9415.9414.8714.87Multi-planar10.7710.7710.0310.03Single planed204c198b117a4

14.8714.8715.9415.94Multi-planar10.0310.0310.7710.77Single plane

f01e92b133a76


53


axial loadings


1.00-1.00-1.001.00

feba


3.19-3.19-2.912.91Multi-planar3.22-3.22-2.892.89Single planed204c198b117a4

2.91-2.91-3.193.19Multi-planar2.89-2.89-3.223.22Single plane

f201e192b133a76


54



1.001.000.000.001.001.00

fedcba



-8.52-8.521.691.69-8.54-8.54Multi-planar-7.47-7.470.000.00-7.85-7.85Single plane

f186e163d201c192b133a76


55



1.001.001.001.001.001.00

fedcba


6.166.165.715.719.229.22Multi-planar7.857.857.407.407.477.47Single planef176e139d204c198b117a4

-9.22-9.22-5.71-5.71-6.16-6.16Multi-planar-7.47-7.47-7.40-7.40-7.85-7.85Single plane

f186e163d201c192b133a76


56



1.00-1.001.001.00-1.001.00

fedcba


1.04-5.808.006.79-2.684.09Multi-planar3.40-3.407.407.40-3.363.36Single planef176e139d204c198b117a4

-4.092.68-6.79-8.005.80-1.04Multi-planar-3.363.36-7.40-7.403.40-3.40Single plane

f186e163d201c192b133a76


57

Table 61SCF's at the chord saddle positions for O.P.B loadings


1.00-1.000.000.00-1.001.00

fedcba


3.42-3.42.61-.61-3.383.38Multi-planar3.40-3.400.000.00-3.363.36Single planef176e139d204c198b117a4

-3.383.38.61-.613.42-3.42Multi-planar-3.363.360.000.003.40-3.40Single plane

f186e163d201c192b133a76


58

FIGURES

Location of chord saddle strain gauges on K joint7-9

Location of chord saddle strain gauges on KT joint4-6

Geometric details of Task 7 K joints3

Geometric details of Task 6 KT joints1-2

59

Loading condition: axial load and out-of-plane bending applied to each main brace in turn

Figure 1Task 6.A

60


Figure 2Task 6.B

61


Figure 3Task 7.A

62

63

64

65

REFERENCES

KUANG J.G. POTVIN A.B., LEICK R.D. and KAHLICH J.L. Stressconcentration in tubular joints. Society of Petroleum Engineers Journal,August 1977.

3

EFTHYMIOU M and DURKIN S. Stress concentrations in T/Y andgap/overlap K-joints. BOSS conference, Delft, 1985

2

WORDSWORTH A.C Stress concentration factors at K and KT tubularjoints. Fatigue in offshore structural steel, ICE, London, 1981.

1

66

APPENDIX A - ACRYLIC MODELLING

CONTENTS

69EXTRAPOLATION PROCEDURESA2.

68STRAIN GAUGE POSITIONINGA1.

Page

67

A1. STRAIN GAUGE POSITIONING

The strains gauge locations for all joints in this programme of work were essentiallysimilar. Sets of three strain gauge rosettes were fitted at five separate locationsaround one quadrant of the brace to chord intersection whilst at the two opposingcrown and saddle positions four single element gauges were fitted, three of them on asingle axis aligned normal to the tube junction. At each location the gauge nearest tothe junction was positioned approximately 0.2 (rt) from the junction to avoid the„local notch effect. At the saddle position the second gauge was placed atapproximately 5o of the chord arc from the junction on the chord side and 0.65 (rt)„on the brace side. At the crown position the second gauge was placed atapproximately 0.4 (rtRT) from the junction on the chord side and 0.65 (rt) on the„ „brace side. The third gauge was spaced back from the second a distance equal to theseparation of the first two gauges.

68

A2. EXTRAPOLATION PROCEDURES

The extrapolation methods used to determine the brace to chord intersection SCFs atvarious positions are described below:-

METHOD 1

A linear extrapolation of the SCFs corresponding to the principal stresses at the tworosettes nearest the junction. At the rosette nearest the intersection the largest of thenumerical principal stress SCFs is used and at the second rosette the SCF which isalgebraically nearest to it. Thus, with SCFs of -3 and 1 at the nearest rosette and -1and 2 at the other one, the extrapolation would be carried out through -3 and -1.

METHOD 2

As for Method 1 except that a non-linear extrapolation is used on a quadratic curvethrough the three measuring points.

METHOD 3

A linear extrapolation is carried out of the SNCFs based on the strains normal to theintersection at the two points nearest to the intersection. This is then converted to anSCF using SNCF90 (ie the SNCF corresponding to the strain parallel to theintersection at the measuring point nearest to the intersection).

SNCF + ( X SNCF90)m SCF =

1 - 2m

where = Poisson's Ratiom

METHOD 4

As for Method 3 but using a non-linear extrapolation on a quadratic curve throughthe three measuring points.

METHOD 5

Data given in this method is either the SNCF at an isolated single element gauge orthe SCF corresponding to the greatest principal stress at an isolated rosette.

69

The method of extrapolation which can be employed at the various gaugeconfigurations at each position around the junction are therefore as follows:-

1, 2, 3 & 4Three 45o rosettes, each with one element aligned normal tothe intersection

(e)

1 & 3Two 45o rosettes, each with one element aligned normal tothe intersection

(d)

3 & 4Three single element gauges aligned normal to theintersection with one orthogonal gauge

(c)

3Two single element gauges aligned normal to the intersectionwith one orthogonal gauge

(b)

5Single isolated rosette or single element gauge(a)

70

PART 2OVERLAPPED JOINTS

71

72

1. INTRODUCTION

Work on overlapped joints is this project has been rather limited since it was knownat the beginning that other work was already planned. Some such work has now beencompleted (ie the Efthymiou and Durkin paper presented at the 1985 BOSSConference).

The main work in this project (ie Tasks 8.A and 8.B) consisted of eight overlappedjoints which were investigated using mainly finite element (FE) techniques with someback-up acrylic modelling. One specimen was similar to the steel overlapped K jointtested in the UKOSRP II programme.

Towards the end of the project Veritec kindly made available the results of two steeloverlapped joint tests including also associated FE results. An acrylic model test ofone of these configurations has also been completed and the details of this and theVeritec joint are reported here in Appendix A.

It was never intended to produce SCF equations for overlapped joints in this project,the work essentially being an SCF comparison study. For completeness all specimengeometric details are included in this report together with SCF comparisons ofmeasured and predicted values from various sources.

73

2. TEST DETAILS

The overlapped joint tests carried out in this project were as follows:

2.1 TASK 8.A

Four N joint with brace angles of 90o and 45o, see Figure 1. All four specimenswere analysed by KSEPL (the Hague) using the PMB Shell FE program and byWimpey using the PAFEC FE system employing semi-loof elements. Specimens8.A1 and 8.A2 were also tested using acrylic modelling as back-up to the FE results.

2.2 TASK 8.B

Four K joints with both brace angles 60o, see Figure 2. These four specimens wereonly analysed by KSEPL.

2.3 VERITEC CONFIGURATION

One K joint with both brace angels 60o, see Figure 3. This joint configuration wastested using an acrylic model at a scale approximately 1/3.45 of the steel joint.

74

3. PRESENTATION OF RESULTS

SCFs have been measured for different loading conditions; Figures 4 and 5 show theloading cases considered by KSEPL for Tasks 8.A and 8.B respectively. Only themore common loading cases were considered by Wimpey and in the acrylic modeltests. The comparison of measured and predicted SCFs for Task 8 are given inTables 1 to 16. The SCF comparison for the Veritec configuration is given in Table17; here only the balanced axial loading case was considered.

Figures 6 to 12 show typical SCF distribution plots for the more important loadingcases.

75

4. DISCUSSION OF RESULTS

4.1 INTRODUCTION

In the Task 8 SCF comparisons, Tables 1 to 16, for the single loaded brace cases themeasured SCFs have been compared with predicted values from theWordsworth/Smedley(1), Efthymiou/Durkin(2) and Kuang et al(3) T/Y simple jointparametric equations.

For the more usual cases where both braces are loaded the only SCF parametricequations that specifically include overlapped joints are those presented byEfthymiou and Durkin at the 1985 BOSS Conference(2). In the past the offshoreindustry has used the simple non-overlapped K joint equations substituting for theg/D (brace gap to chord diameter) parameter a value of 0.01. In the SCFcomparisons, with both braces loaded, the Efthymiou equations have been consideredtogether with those of Wordsworth(4) and Kuang et al(3) with g/D = 0.01.

4.2 TASK 8

4.2.1 Single brace loaded cases

From the SCF comparisons, Tables 1 to 16, it can be seen that generally there isreasonable agreement for all measured and predicted SCFs.

4.2.2 Balanced axial loading

Balanced axial loading is a common loading case for K joints. The effect of the highdegree of overlap, in the joints considered, is that a large proportion of the load istransferred through the common weld between the braces. This tends to produce themaximum brace stresses in the common weld by virtue of the through brace acting asa chord to the overlapping brace.

From the SCF comparison, Tables 1 to 16, it can be seen that generally SCFs areconsiderably reduced compared with the single brace loaded cases. With respect tomeasured and predicted SCFs for balanced axial loading, all equations considered aregenerally conservative. The closet agreement is obtained using the Efthymiouequations which is not surprising since these formulae were specifically developed foroverlapped joints. In addition, most of the measures SCFs in Task 8 were obtainedby KSEPL using the same FE technique as used to develop the equations.

Typical plots of the chord and brace measured SCF distribution are shown in Figures6 and 7. It can be seen that reasonable agreement is obtained for the different SCFmeasurement methods considered.

4.2.3 Unbalanced axial loading

Here, unbalanced axial loading from Task 8.B is considered. Although high SCFsare produced in this case, see Tables 5 to 8 and 13 to 16, two braces loaded axially inthe same sense is not a common case. In the SCF comparisons the closest agreement

76

is obtained using the Efthymiou equations. The equations used to obtain the KuangSCFs were developed for balanced axial loading and, as can be seen, give a highunderprediction when used for the unbalanced axial loading case.

4.2.4 Unbalanced out-of-plane bending

This is considered to be an important case for K and N type joints, as this geometryis often subjected to out-of-plane bending (OPB) due to vertical wave loading inconductor guide frame areas. When both braces are loaded in the same sense acarry-over effect is produced from one brace to the other which increases the chordand brace saddle SCFs well above the single brace loaded cases, see Tables 1 to 16.This is the opposite effect to that for balanced axial loading, as discussed inSection 4.2.2.

With respect to SCF comparison, Table 1 to 16, using the Wordsworth and Kuangequations could lead to high underprediction. As for the balanced axial loading casethe Efthymiou equations give the closet agreement with measured SCFs, themaximum underprediction being 13% (specimen 8.B3 for both chord and bracesides).

Typical plots of the chord and brace measured SCF distribution are shown in Figures8 to 10; good agreement is obtained for the different SCF measurement methodsconsidered.

4.2.5 Balanced out-of-plane bending

The reverse effect to the unbalanced OPB case discussed in Section 4.2.4 occurs,with the SCFs being relatively low, see Tables 1 to 16. In this case all equations givehighly conservative SCFs including those of Efthymiou. Although the Efthymiouequations give the closet agreement there is a maximum overprediction approaching400% (specimen 8.B4 chord side).

For a typical SCF distribution plot see Figure 11.

4.2.6 Balanced in-plane bending

For chord SCFs the parametric equations tend to overpredict and in general theEfthymiou equation gives the closest agreement, see Tables 1 to 8. For the brace,Task 8.A specimens - Tables 9 to 12, all equations tend to underpredict themaximum SCF that occurs in the common weld. For the Task 8.B specimens,Tables 13 to 16, the Efthymiou equation gives close agreement. Using the Efthymiouequation the maximum underprediction is 32% for specimens 8.A1 and 8.A2.

For a typical SCF distribution plot see Figure 12.

4.2.7 Unbalanced in-plane bending

From Tables 1 to 8 it can be seen that for the chord, reasonable agreement isobtained between measured and predicted SCFs with in general the Efthymiouequation giving the closest agreement. As for balanced IPB there is some

77

underprediction of brace SCFs, Tables 9 to 16, with the Efthymiou equation givingthe closest agreement.

78

4.3 VERITEC CONFIGURATION (BALANCED AXIAL LOADING)

The details of the Veritec steel, FE and LRS acrylic model tests are given inAppendix A. An SCF comparison of measured and predicted values from parametricequations is given in Table 17. The equations have been applied in the same way asoutlined in Section 4.1 for Task 8 with both braces loaded.

When comparing the measured SCFs it can be seen that very good agreement hasbeen obtained by Veritec for the steel and FE results. It should be noted that Veritechave used the same PMB Shell FE program as used by KSEPL in Task 8 and byEfthymiou in developing the published equations(2). The measured SCFs from theacrylic model test tend to be lower than the Veritec results. With respect to the steeljoint, this is partially due to the different strain gauge positions and extrapolationprocedures adopted, see Appendix A, Section A4.

Regarding predicted SCFs from parametric equations, these are all conservative, theclosest agreement being with the Efthymiou equations, as also found in Task 8.

79

5. SUMMARY AND CONCLUSIONS

Stress concentration factors for a limited number of overlapped N and K joints havebeen determined using a number of different techniques, namely FE analysis, acrylicand steel modelling. These measured SCFs have been compared with existingparametric equations including those published by Efthymiou/Durkin.

For the common balanced axial loading case, from previous work, overlapping tendsto produce lower SCFs than for the non-overlapped case. From the work carried outin Task 8, SCFs were much lower than for the single brace loaded cases. In the SCFcomparisons with parametric equations the predicted SCFs were generallyconservative, with the closest agreement being obtained using the Efthymiouequations. This was the case for both Task 8 and the Veritec joint configuration.For unbalanced axial loading, which is not a common loading case, relatively highSCFs were produced, see section 4.2.3.

For the major OPB case (ie unbalanced with both braces loaded in the same sense),again from previous work, SCFs tend to be higher than for the non-overlapped case.From the work carried out in Task 8, for unbalanced OPB the SCFs were muchhigher than for the single brace loaded cases. In the SCF comparisons, using theWordsworth and Kuang equations, substituting 0.01 for the g/D term, could leave tohigh underprediction. As for the balanced axial loading case the Efthymiouequations gave the closest agreement with measured SCFs, maximumunderprediction being 13%.

For the IPB cases the parametric equations can underpredict the maximum braceSCF in the common weld between the braces. Generally, the Efthymiou equationsgave the closest agreement with a maximum underprediction of 32%.

The main conclusion from the overlapped joint work carried out in this project is thatconsidering all modes of loading the Efthymiou equations give the closest agreementto measured SCFs. However, some caution should be exercised with respect to braceSCFs where there is significant IPB.

The Veritec configuration investigation highlighted the differences in strain gaugepositions and extrapolation procedures between the DEn recommendations and thoseused elsewhere (ie by Veritec). This non-standardisation can lead to differences inextrapolated SCFs and requires further investigation.

80

TABLES

Comparison of maximum measured SCFs and parametric equations forVeritec configuration

17

Comparison of maximum measured brace SCFs and parametricequations for Task 8.B

13-16

Comparison of maximum measured brace SCFs and parametricequations for Task 8.A

9-12

Comparison of maximum measured chord SCFs and parametricequations for Task 8.B

5-8

Comparison of maximum measured chord SCFs and parametricequations for Task 8.A

1-4

81

Table 1Comparison of maximum chord SCF's and values obtained from parametric

equationsSpecimen 8.A1 ( = 14.3, = 0.5)c i

2.5*2.52.82.22.8UnbalancedIPB

2.5*2.52.51.51.31.5BalancedIPB

2.52.52.31.72.0IPBvertical brace

5.1*6.97.97.78.67.8UnbalancedOPB

5.1*4.03.71.12.01.9BalancedOPB

3.03.42.93.13.1OPBinclined brace

5.16.04.94.44.8OPBvertical brace

3.14.12.71.51.82.1Balancedaxial load

3.64.34.34.24.84.5Axial load inclined brace

6.58.07.45.67.27.0Axial load vertical brace

KuangWordsworthEfthymiouAcrylicWimpeyKSEPL

Parametric SCF'sMeasured SCF's

Max SCF's chord sideLoading

* T/Y equations used

82


equationsSpecimen 8.A2 ( = 14.3, = 0.86)c i

4.2*3.84.53.24.0UnbalancedIPB

4.2*3.83.41.31.41.8BalancedIPB

4.23.83.72.22.8IPBvertical brace

8.2*11.913.511.712.912.5UnbalancedOPB

8.2*6.96.42.72.8BalancedOPB

4.85.85.04.64.8OPBinclined brace

8.210.38.47.17.7OPBvertical brace

5.77.04.32.22.74.0Balancedaxial load

7.47.37.76.57.37.1Axial load inclined brace

13.413.713.59.411.212.8Axial load vertical brace

KuangWordsworthEfthymiouAcrylicWimpeyKSEPL




83


equationsSpecimen 8.A3 ( = 24, = 0.5)c i

3.1*3.43.93.9UnbalancedIPB

3.1*3.43.51.61.8BalancedIPB

3.13.43.32.8IPBvertical brace

8.6*12.212.313.613.0UnbalancedOPB

8.6*6.05.82.92.8BalancedOPB

5.05.74.65.2OPBinclined brace

8.610.07.67.9OPBvertical brace

4.45.33.42.52.8Balancedaxial load

5.57.27.17.27.5Axial load inclined brace

9.913.412.410.711.2Axial load vertical brace

KuangWordsworthEfthymiouWimpeyKSEPL




84


equationsSpecimen 8.A4 ( = 24, = 0.86)c i


5.1*5.24.72.22.1BalancedIPB

5.15.25.24.0IPBvertical brace

13.9*21.121.324.021.5UnbalancedOPB

13.9*10.410.04.74.1BalancedOPB

8.19.87.98.7OPBinclined brace

13.917.313.212.8OPBvertical brace

8.19.25.65.14.7Balancedaxial load

11.312.313.013.212.8Axial load inclined brace

20.423.122.620.420.0Axial load vertical brace

KuangWordsworthEfthymiouWimpeyKSEPL




85

Table 5Comparison of maximum chord SCF's and values obtained

from parametric equationsSpecimen 8.B1 ( = 12, = 0.5)c i


2.1*2.02.01.7BalancedIPB

2.12.01.91.8IPBoverlapping brace

2.12.01.91.7IPBthrough brace

3.4*4.96.56.2UnbalancedOPB

3.4*2.32.11.1BalancedOPB

3.44.03.43.4OPB onoverlapping brace

3.44.03.43.4OPB onthrough brace

2.27.58.08.6Unbalancedaxial load

2.22.81.91.7Balancedaxial load

4.45.24.94.9Axial load overlapping brace

4.45.24.94.3Axial load through brace

KuangWordsworthEfthymiouKSEPL

Parametric SCF'sMeasuredSCF's



86


from parametric equationsSpecimen 8.B2 ( = 12, = 0.86)c i

















87

Table 7Comparison of maximum chord SCF's and values obtained from

parametric equationsSpecimen 8.B3 ( = 24, = 0.5)c i

















88


from parametric equationsSpecimen 8.B4

89

90

91

92

93

94

95

96

97

98

FIGURES

Measured SCF distribution plot for balanced IPB12

Measured SCF distribution plot for balanced OPB11

Measured SCF distribution plots for unbalanced OPB8-10

Measured SCF distribution plots for balanced axial loading6-7

Loading conditions for Task 8.B5

Loading conditions for Task 8.A4

Geometric details of Veritec configuration3

Geometric details of Task 8.B specimens2

Geometric details of Task 8.A specimens1

99

100

101

102

103

104

105

106

107

108

109

110

111

REFERENCES

WORDSWORTH, A.C. Stress concentration factors at K and KTtubular joints. Fatigue in offshore structural steel, ICE, London, 1981.

4

KUANG J.G., POTVIN A.B., LEICK R.D. and KAHLICH J.L. Stressconcentration in tubular joints. Society of Petroleum Engineers Journal,August, 1977.

3

EFTHYMIOU M. and DURKIN. Stress concentrations in T/Y andgap/overlap K-joints. BOSS conference, Delft, 1985.

2

WORDSWORTH A.C and SMEDLEY G.P. Stress concentrations atunstiffened tubular joints. European offshore steels research seminar,Cambridge, 1978.

1

112

APPENDIX A - VERITEC JOINT CONFIGURATION

CONTENTS

48FIGURES

45TABLES

44DISCUSSION OF RESULTSA4.

43PRESENTATION OF RESULTSA3.

42A2.3 ACRYLIC MODEL

42A2.2 FINITE ELEMENT ANALYSIS

42A2.1 STEEL JOINT

42VERITEC JOINT CONFIGURATION INVESTIGATIONDETAILS

A2.

41INTRODUCTIONA1.

Page

113

A1. INTRODUCTION

Results from two steel overlapped joint tests and associated FE work have been madeavailable by Veritec. The detailed investigation of one of these joint configurations ispresented in this appendix.

Measured SCFs from the steel joint tests and from FE analysis using the PMB Shellprogram, supplied by Veritec, are compared with those obtained by LRS from anacrylic scale model of the joint. In addition, the measured SCFs are compared withthose predicted by the parametric equations as described in Section 4.1 of the mainreport.

114

A2. VERITEC JOINT CONFIGURATION INVESTIGATIONDETAILS

The joint parametric configuration and loading condition is given in Figure A1.Three SCF measurement techniques were considered as follows:

A2.1 STEEL JOINT

The main strain gauge locations are shown in Figure A2. The strain gaugesconsisted of strips containing five cross gauges 2mm apart and fitted normal top theweld toe with the nearest gauge a distance of 2mm from the toe. In addition to thesestrain gauges shown, single gauge rosettes were placed close to the weld toe to enablethe direction of the principal stresses to be found.

A2.2 FINITE ELEMENT ANALYSIS

In addition to the steel joint strain gauge measurements, Veritec also analysed thejoint configuration using the PMB Shell FE program. It should be noted that this isthe same FE package as used by KSEPL for the Task 8 work and by Efthymiou indeveloping his published equations.

A2.3 ACRYLIC MODEL

A scale model of the steel joint of approximately 1/3.45 was tested. Strain gaugeswere placed at locations around the chord/brace intersection periphery identical tothose on the steel joint as shown in Figure A3. The strain gauges consisting of threesingle rosettes were placed at the same positions, normal to the intersection, aspreviously used in acrylic model tests (ie DEn recommendations 0.2 rt etc). TheªSCF extrapolation procedures were again as used in previous acrylic model tests. Itshould be noted that the acrylic model did not include a weld fillet.

115

A3. PRESENTATION OF RESULTS

Stress concentration factors are presented for the balanced axial loading condition.Figures A4 to A7 show the average SNCF distributions obtained normal to the weldtoe/intersection for the steel and acrylic joints. Table A1 gives the extrapolatedSNCFs and SCFs obtained from the steel and acrylic joints at the four differentlocations. Table A2 shows the chord and brace SCFs for all three measuringtechniques. The maximum SCFs are compared with predicted values fromparametric equations in Table A3.

116

A4. DISCUSSION OF RESULTS

For the K joint configuration investigated, results have been obtained using threedifferent techniques (ie strain gauged steel joint, strain gauged acrylic model and FEanalysis). The measured results obtained from the steel and acrylic joints arediscussed first, as both of these techniques obtained SCFs by extrapolating straingauge measurements. The SCFs obtained from the steel and acrylic joints are thencompared with SCFs determined from FE analysis and those predicted usingparametric equations.

Figures A4 to A7 show the average SNCF distributions normal to the weldtoe/intersection at the four locations around the joint periphery. The difference instress sampling points (ie strain gauge locations) between the steel and acrylicspecimens can be clearly seen, also that SNCFs from the steel joint are generallyhigher than from the acrylic model.

Table A1 shows the extrapolated SNCFs and SCFs at the weld toe and brace/chordintersection for the steel and acrylic specimens respectively. For the steel joint,Veritec have extrapolated from the gauge 4 mm from the weld toe whereas LRS, forthe acrylic model, have used the maximum of linear and non-linear extrapolationfrom the DEn recommended nearest gauge distance 0.2 rt. Hence there are threeªreasons for differences in extrapolated SNCFs between the steel joint and acrylicmodel (ie strain gauge positions, measured strains and extrapolation procedure).

The steel joint chord and brace SCFs shown in Table A1 were obtained by using theSNCFs, normal and parallel to the weld toe, from the cross gauges and the principalstress direction from the rosette gauge. The equivalent SCFs for the acrylic modelwere determined using the procedure as used in previous acrylic model tests.

Table A2 shows a comparison of these SCFs and those obtained from the FEanalysis. It can be seen that good agreement has been achieved by Veritec for thesteel joint and SCFs derived from the FE analysis. The SCFs from the acrylic modeltend to be lower, particularly on the brace sides of the joint. With respect to the steeljoint this difference is partially due to reasons already discussed (ie gauge positions,extrapolation method etc).

Table A3 shows an SCF comparison of maximum measured values and thosepredicted from parametric equations. In all cases the equations are conservative withthe closest agreement being obtained using the Efthymiou equations, particularly withthe FE results. This is not surprising since the Efthymiou equations applyspecifically for overlapped joints and were developed using the same PMB Shell FEpackage as used by Veritec.

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TABLES

Comparison of maximum measured SCFs and parametric equationsA3

Chord and brace measured SCF comparisonA2

Extrapolated SNCFs and SCFs for steel and acrylic jointsA1

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FIGURES

Average SNCF distributions normal to the weld toe/intersectionA4-A7

Acrylic specimen strain gauge locationsA3

Steel joint main strain gauge locationsA2

Parametric configuration and loading conditionA1

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Stress concentration factors for tubular complex joints … · · 2017-07-15OTH 91 353 STRESS CONCENTRATION FACTORS FOR TUBULAR COMPLEX JOINTS Author Lloyd’s Register of Shipping