i
THE STATIC STRENGTH OF UNIPLANAR AND
MULTIPLANAR TU
LAR T- AND X-JOINTS
:
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G.J. van de
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Deift University of Technology
Ship Hydromechanics Laboratory
Library
Mekeiweg 2, 2628 CD Deift
The Netherlands
STELLINGEN
behorende bij het proefschrift
The Static Strength of Uniplanar and Multiplanar Tubular T- and X-Joints
van
GJ. van der Vegte
Bij bet ontwikkelen van nieuwe, verbeterde ontwerpregels voor ruimtelijke verhindingen van buisprofielen dient een gethndeerde keuze gemaakt te worden nissen het geven van één (gecompliceerde) formule voor allerlei verhindingstypen of een veelvoud van eenvoudige formules die elk maar voor één verbindingstype
gelden.
De door de AP.!. aanbevolen can" lengte kan leiden tot onveilige verbindingen van ronde buisprofielen.
Sterkteformules dienen in principe gebaseerd te worden op analytische modellen en niet alleen op regressie modellen.
Het steeds gecompliceerder maken van de rekenregels in voorschriften, staat in contrast tot bet steeds lager wordende kostenaandeel van een staalconstructie in een
totale constructie.
Ret gebruik van zogenaamde 'default' waarden, die toegepast worden ter vergroting van de gebruikersvriendelijkheid in eindige elementen programma's, kan leiden tot onbetrouwbare resultaten ten gevolge van verborgen aannames.
Toepassing van computers heeft als gevaar dat deze niet langer als hulpmiddel worden beschouwd, maar dat bet gebruik ervan een dod op zich wordt.
Het oplossen van het file probleem door middel van heI aanleggen van extra wegen leidt tot hetzelfde resultaat als bet oplossen van ruimtegebrek op computers door middel van het aanbrengen van extra schijfruimte : binnen de kortste tijd staan beide weer vol.
Indien de bezuinigingsgolven die de universiteiten de laatste jaren treffen, qua aanta! en grootte vertaald zouden worden naar belastingsgolven op een constructie, dan zou deze reeds ten gevolge van 'low cycle fatigue" zijn bezweken.
Terwiji concurrentie nissen fabrikanten in de strijd orn kopers leidt tot een gewenste
dating van de prijzen van produkten,
leidt concurrentie nissen verschillende onderwijsinstellingen in de strijd orn leerlingen in veel gevallen tot een ongewenste dating van het onderwijsniveau.De bepaling tot bet opnemen van een curriculum vitae in een proefschrift, zoals
ornschreven in artikel 13.8 van het promotiereglement, druist in tegen de
bescherming van de privacy zoals weergegeven in de Wet Persoonsregistratie.
Het gebruik van de 0V. kaart
voor studenten resulteert in verminderde lichaamsbeweging van de bezitters. De hierdoor versiechterde lichamelijke conditie za! op lange termijn resulteren in verhoogde aanspraak op medische voorzieningen en za! de op korte termijn gerealiseerde bezuinigingen teniet doen.THE STATIC STRENGTH OF UNIPLAN4R AND
MULTIPLANAR TUBULAR T- AND X-JOINTS
THE STATIC STRENGTH OF UNIPLANAR AND
MULTIPLANAR TUBULAR T- AND X-JOINTS
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Deift,
op gezag van de Rector Magnificus Prof.ir. KF. Wakker, in het openbaar te verdedigen ten overstaan van een commissie,
door het College van Dekanen aangewezen, op maandag 30 januari 1995 te 10:30 uur
door
Gerhardus Jacob van der VEGTE
civiel ingenieur geboren te Genemuiden
Dit proefschrift is goedgekeurd door de promotor Prof. dr. ir. J. Wardenier
Samenstelling promotiecommissie
Prof. ir. J. de Back : Em. hgl. Faculteit der Civiele Techniek, Technische Universiteit Delft
Prof. Dr. -Ing. H.J. Blaß : Faculteit der Civiele Techniek,
Technische Universiteit Deift
Prof. ir. B. Boon : Faculteit Werktuigbouwkunde en Maritieme Techniek,
Technische Universiteit Deift
Prof. ir. M. van Holst : Faculteit Werktuigbouwkunde en Maritieme Techniek,
Technische Universiteit Delft
Prof. dr. RS. Puthli : Versuchsanstalt für Stahl, Holz und Steine, Universität Karlsruhe
Prof. ir. H.H. Snijder Faculteit Bouwkunde,
Technische Universiteit Emdhoven Prof. dr. ir. J. Wardenier : Faculteit der Civiele Techniek,
Technische Universiteit Deift
CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG Vegte, G.J. van der
The Static Strength of Uniplanar and Multiplanar Tubular T- and X-Joints / G.J. van der Vegte - Deift : Delft University Press. - Ill.
Thesis Delft University of Technology. - With ref. - With summary in Dutch. ISBN 90-407-1081-3
NUGI 841
Subject Headings Welded tubular joints, Static strength, Circular hollow sections
Experiments, Numerical simulations, Finite element analyses. Copyright © 1995 by G.J. van der Vegte
All rights reserved.
No part of this material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including
photocopying, recording or by any information storage and retrieval system, without permission from the publisher
Delft University Press, Stevinweg 1, 2628 CN DeIft, The Netherlands.
ACKNOWLEDGEMENTS
The research reported in this thesis has been carried out at the Faculty of Civil
Engineering of Deift University of Technology.Thanks are expressed to Prof.dr.ir. J. Wardenier, Prof.dr. R.S. Puthli and the members of commission CS-W9 (Tubular Structures) for their support throughout the research.
Furthermore, Mr. C.H.M. de Koning and Mr. H.L.N. Munter are
gratefullyacknowledged for their work regarding the experiments.
Thanks are also expressed to Van Leeuwen Buizen, Zwijndrecht, The Netherlands for the donation of the hollow sections.
Finally,
the financial support provided by the Delft University Funds is
highly appreciated.KEYWORDS
Static Strength, Uniplanar, Multiplanar, Welded Tubular Joints, Circular Hollow Sections, Cans, Numerical Modelling, Experiments, Analytical Models.
CONTENTS
SUMMARYLIST OF SYMBOLS 2
INTRODUCTION 5
1.1 Structural applications of hollow sections 5
1.2 Current design of multiplanar joints 5
1.3 Joint classification 6
1.4 Aims of the present research 6
1.4.1 Survey of relevant literature 8
1.4.2 Experimental research 8
1.4.3 Numerical calibration 9
1.4.4 Numerical research on uniplanar joints 9
1.4.5 Numerical research on multiplanar joints 10
1.4.6 Simplification of the basic ultimate strength formulae and
evaluation to design rules 11
1.4.7 Conclusions and summary of the basic ultimate capacity equations 11
SUMMARY OF RELEVANT RESEARCH 12
2.1 Experimental research on multiplanar joints 12
2.2 Numerical research on multiplanar joints 15
2.3 Analytical research 17
2.4 Design codes and recommendations 19
2.4.1 General 19
2.4.2 A.W.S. 19
2.4.2.1 Description of the A.W.S. formulation 19
2.4.2.2 Comparison of experimental and numerical results with
the A.W.S. 21
2.4.3 Eurocode 3 22
2.4.3.1 Description of the Eurocode 3 formulation 22
2.4.3.2 Comparison of experimental results with Eurocode 3 22
EXPERIMENTS ON UNIPLANAR X- AND MULTIPLANAR
XX-JOINTS 23
3.1 Introduction 23
3.2 Research programme 23
3.3.1 Axially loaded X-joints 31
3.3.2 X-joints loaded by in-plane bending 31
3.3.3 X-joints loaded by out-of-plane bending 31
3.4 Test results 33
3.4.1 Axially loaded X-joints 33
3.4.2 X-joints loaded by in-plane bending 33
3.4.3 X-joints loaded by out-of-plane bending 33
3.5 Discussion of the test results 35
3.5.1 Joints with unloaded out-of-plane braces (XX2, XX6 and XX1O) 35
3.5.2 Joints with pre-compressed out-of-plane braces (XX3, XX7
and XXii) 35
3.5.3 Joints with pre-tensioned out-of-plane braces (XX4, XX8
and XX12) 36
3.6 Comparison with several design codes 37
3.6.1 Design codes and recommendations considered 37
3.6.2 Axially loaded joints 38
3.6.3 Joints loaded by in-plane bending 39
3.6.4 Joints loaded by out-of-plane bending 40
4. GENERAL ASPECTS REGARDING FINITE ELEMENT ANALYSES
ON TUBULAR JOINTS 41
4.1 Introduction 41
4.2 Finite element programs and hardware used 41
4.3 Main characteristics of the fe work with regard to tubular joints 42
4.3.1 Finite element meshes and boundary conditions 42
4.3.2 Finite element type 42
4.3.3 Loading of the joints 42
4.3.4 Modelling of the post-yield material property 43
4.3.5 Iteration procedure and convergence criteria 44
4.3.6 Numerical modelling of the weld geometry 45
4.4 Effects of the type of finite element 45
4.4.1 Available types of elements 45
4.4.2 Quantitative and qualitative comparison of different types
of elements 46
4.4.3 The effects of the finite element type on the strength of
tubular joints 49
4.4.4 Recommended finite element type 54
4.5 Effects of modelling of weld geometry 55
NUMERICAL SIMULATION OF THE EXPERIMENTS ON
UNIPLANAR X- AND MULTIPLANAR XX-JOINTS 60
5.1 Research programme and general fmite element aspects 60
5.2 Axially loaded X-joints Xl to XX4 60
5.3 X-joints loaded by in-plane bending X5 to XX8 64
5.4 X-joints loaded by out-of-plane bending X9 to XX12 68
5.5 Comparison between the experimental and numerical results 72
GENERAL ASPECTS WITH RESPECT TO THE
NUMERICAL PARAMETRIC STUDIES 73
6.1 Assumptions for the numerical models 73
6.1.1 The dimensions of the joints 73
6.1.2 Modelling of the welds 73
6.1.3 Yield strength and material post-yield properties 75
6.1.4 Load controlled analyses versus displacement controlled analyses 77
6.2 Deformation limits suggested by Yura 77
6.3 Program used for the regression analyses 78
UNIPLANAR X-JOINTS 79
7.1 Axially loaded uniplanar X-joints 79
7.1.1 Introduction 79
7.1.2 Research programme 79
7.1.3 Finite element analyses 82
7.1.4 Numerical results 82
7.1.5 Analytical approach for axially loaded uniplanar X-joints
ring model 85
7.1.6 Basic ultimate strength formula for axially loaded uniplanar
X-joints 87
7.2 Uniplanar X-joints loaded by in-plane bending 89
7.2.1 Introduction 89
7.2.2 Research programme 89
7.2.3 Finite element analyses 92
7.2.4 Numerical results 92
7.2.5 Basic ultimate strength formula for uniplanar X-joints loaded by
in-plane bending 96
7.3 Uniplanar X-joints loaded by out-of-plane bending 99
7.3.1 Introduction 99
7.3.2 Research programme 99
7.3.3 Finite element analyses 100
7.3.4 Numerical results 104
7.3.5 Analytical approach for uniplanar X-joints loaded by
7.3.6 Basic ultimate strength formula for uniplanar X-joints loaded
by out-of-plane bending 109
7.4 Axially loaded uniplanar X-joints with variable chord lengths 111
7.4.1 Introduction 111
7.4.2 Research programme 112
7.4.3 Finite element analyses 112
7.4.4 Numerical results 115
7.4.5 Basic ultimate strength formula for axially loaded uniplanar
X-joints with variable chord lengths 115
7.5 Axially loaded uniplanar X-joints with variable can lengths 118
7.5.1 Introduction 118
7.5.2 Research programme 118
7.5.3 Finite element analyses 120
7.5.4 Numerical results 121
7.5.5 Basic ultimate strength formula for axially loaded uniplanar
X-joints reinforced by a can 121
8. UNIPLANAR T-JOINTS 126
8.1 Axially loaded uniplanar T-joints 126
8.1.1 Introduction 126
8.1.2 FE analyses on axially loaded uniplanar T-joints excluding
the effects of chord bending 126
8.1.2.1 Research programme 126
8.1.2.2 Finite element analyses 128
8.1.2.3 Numerical results 131
8.1.2.4 Analytical approach for axially loaded uniplanar T-joints
ring model 131
8.1.2.5 Basic ultimate strength formula for axially loaded uniplanar
T-joints excluding the effects of overall chord bending 138
8.1.3 FE analyses on axially loaded uniplanar T-joints including
the effects of chord bending 139
8.1.3.1 Research programme 139
8.1.3.2 Finite element analyses 140
8.1.3.3 Numerical results 143
8.1.3.4 Analytical approach : failure due to a combination of
overall chord bending and shear 146
8.1.3.5 Interaction contour between local failure and failure due to
overall chord bending, based on the FE results 147
8.2 Uniplanar T-joints loaded by in-plane bending 149
8.2.1 Introduction 149
8.2.2 Research programme 149
8.3 Uniplanar T-joints loaded by out-of-plane bending 156
8.3.1 Introduction 156
8.3.2 Research programme 156
8.3.3 Finite element analyses 157
8.3.4 Numerical results 159
8.3.5 Analytical approach for uniplanar T-joints loaded by
out-of-plane bending : ring model 161
8.3.6 Basic ultimate strength formula for uniplanar T-joints loaded
by out-of-plane bending 164
9. MULTIPLANAR XX-JOINTS 167
9.1 Axially loaded multiplanar XX-joints 167
9.1.1 Introduction 167
9.1.2 Research programme 167
9.1.3 Finite element analyses 170
9.1.4 Numerical results 171
9.1.5 Analytical approach for axially loaded multiplanar XX-joints
ring model 177
9.1.5.1 Ring model approach for multiplanar XX-joints - mechanism I . 177
9.1.5.2 Ring model approach for multiplanar XX-joints - mechanism II 179
9.1.5.3 Ring model approach for multiplanar XX-joints - exact
yield contour 181
9.1.6 Basic ultimate strength formulae for axially loaded multiplanar
XX-joints 183
9.2 Multiplanar XX-joints loaded by in-plane bending on the in-plane braces
and axial forces on the out-of-plane braces 186
9.2.1 Introduction 186
9.2.2 Research programme 186
9.2.3 Finite element analyses 188
9.2.4 Numerical results 190
9.2.5 Basic ultimate strength formula for multiplanar XX-joints loaded
by in-plane bending on the in-plane braces and axial forces
on the out-of-plane braces 194
9.3 Multiplanar XX-joints loaded by in-plane bending on the in-plane and
out-of-plane braces 196
9.3.1 Introduction 196
9.3.2 Research programme 196
9.3.3 Finite element analyses 197
9.3.4 Numerical results 198
9.3.5 Basic ultimate strength formulae for multiplanar XX-joints
loaded by in-plane bending on the in-plane and
out-of-plane braces 202
9.4 Axially loaded multiplanar XX-joints with variable chord lengths 206
9.4.1 Introduction 206
9.4.3 Finite element analyses 208
9.4.4 Numerical results 208
9.4.5 Basic ultimate strength formula for axially loaded multiplanar
XX-joints with variable chord lengths 213
9.5 Axially loaded multiplanar XX-joints with variable can lengths 217
9.5.1 Introduction 217
9.5.2 Research programme 217
9.5.3 Finite element analyses 218
9.5.4 Numerical results 218
9.5.5 Basic ultimate strength formula for axially loaded multiplanar
XX-joints reinforced by a can 224
10. MULTIPLANAR TX-JOINTS 229
10.1 Axially loaded multiplanar TX-joints 229
10.1.1 Introduction 229
10.1.2 FE analyses on multiplanar TX-joints excluding the effects
of overall chord bending 229
10.1.2.1 Research programme 229
10.1.2.2 Finite element analyses 233
10.1.2.3 Numerical results 234
10.1.2.4 The influence due to the tying of the out-of-plane brace 241
10.1.2.5 Analytical approach for axially loaded multiplanar TX-joints
ring model 243
10.1.2.6 Basic ultimate strength formulae for axially loaded multiplanar
TX-joints excluding the effects of overall chord bending 252
10.1.3 FE analyses on axially loaded multiplanar TX-joints including
the effects of chord bending 259
10.1.3.1 Research programme 259
10.1.3.2 Finite element analyses 260
10.1.3.3 Numerical results 262
10.1.3.4 The influence due to the tying of the out-of-plane brace 274
10.1.3.5 Analytical approach : failure due to a combination of overall
chord bending and shear 275
10.1.3.6 Interaction contour between local failure and failure due to
overall chord bending, based on the FE results 276
10.2 Multiplanar TX-joints loaded by in-plane bending on the in-plane brace
and axial forces on the out-of-plane braces 278
10.2.1 Introduction 278
10.2.2 Research programme 279
10.2.3 Finite element analyses 281
10.2.4 Numerical results 283
10.3 Multiplanar TX-joints loaded by in-plane bending on the in-plane and
out-of-plane braces 288
10.3.1 Introduction 288
10.3.2 Research programme 289
10.3.3 Finite element analyses 290
10.3.4 Numerical results 290
10.3.5 The influence due to fixed out-of-plane braces and tying 296
10.3.6 Basic ultimate strength formulae for multiplanar TX-joints
loaded by in-plane bending on the in-plane and
out-of-plane braces 297
11. AXIALLY LOADED MULTIPLANAR TT-JOINTS 303
11.1 Introduction 303
11.2 FE analyses on multiplanar TI-joints excluding the effects of chord
bending 304
11.2.1 Research programme 304
11.2.2 Finite element analyses 306
11.2.3 Numerical results 310
11.2.4 Analytical approach for axially loaded multiplanar TT-joints
ring model 311
11.2.4.1 Ring model approach for local failure of TTjoints
-I-joint mechanism 312
11.2.4.2 Ring model approach for local failure of TTjoints
-X-joint mechanism 315
11.2.4.3 Results of the ring model approach for TI-joints 317
11.2.5 Ultimate strength formulae for local failure of axially loaded
TI-joints 318
11.2.5.1 Ultimate strength formula for local failure of axially loaded
TT-joints - T-joint failure type 318
11.2.5.2 Ultimate strength formula for local failure of axially loaded
TT-joints - X-joint failure type 322
11.3 FE analyses on axially loaded multiplanar TT-joints including the effects
of chord bending 323
11.3.1 Research programme 323
11.3.2 Finite element analyses 324
11 .3.3 Numerical results 325
11.3.4 Comparison of the FE results with Paul's experimental results . 328
11.3.5 Analytical approach : chord failure due to a combination of
overall chord bending and shear 329
11.3.6 Interaction contour between local failure and failure due to
SIMPLIFICATION OF THE BASIC STRENGTH FORMULAE
AND EVALUATION TO DESIGN RULES 333
12.1 Simplification of the basic ultimate strength formulae 333
12.2 Evaluation to design rules 335
CONCLUSIONS AND RECOMMENDATIONS FOR
FURTHER RESEARCH 337
13.1 Experimental research 337
13.2 Numerical calibration 338
13.3 Numerical parametric studies 338
13.3.1 Uniplanar X-joints 339
13.3.2 Uniplanar T-joints 344
13.3.3 Multiplanar XX-joints 348
13.3.4 Multiplanar TX-joints 354
13.3.5 Multiplanar TT-joints 360
13.4 Proposals for further research 361
REFERENCES 363
14.1 Literature before 1982 363
14.2 Literature after 1982 364
14.3 Design codes and recommendations 375
14.4 References related to finite element analyses 376
SAMENVATTING 377
SUMMARY
Circular hollow sections are applied in a wide range of onshore and offshore structures. However, insufficient information is available for the design of multiplanar connections between circular hollow sections. Therefore, in this study, experimental and numerical research has been carried out in order to increase the insight in the static behaviour of
multiplanar joints and to provide a better basis for the design of uniplanar and
multip lanar joints.
In the experimental research programme, the influence of out-of-plane loading (i.e. axial force which varies from tension to compression) has been determined for different types of loading on the in-plane braces.
Based on numerical models, which have been calibrated against the experimental results, extensive numerical parametric studies have been carried out for different types of joints. The influences of the geometrical parameters a, f3 and 2-y and the load ratio between the
load on the out-of-plane brace and the in-plane brace, have been determined for various types of loading on the in-plane and out-of-plane brace.
In addition, analytical models have been developed which provide a theoretical basis for the strength of uniplanar and multiplanar connections for different failure mechanisms. Combining the numerical results with the analytically developed strength formulae has
led to ultimate strength formulae for uniplanar and multiplanar joints which may serve as a basis for future design recommendations.
LIST OF SYMBOLS
Io CROWN POINT SADDLE POINT to Jindices i : O : chord i : m-plane brace 2 : out-of-plane brace
a : constant used in the Ramberg-Osgood relationship
Be : effective chord length
CoV. : coefficient of variation
outer diameter of the chord
do,eq. : equivalent chord diameter (see chapter 11, figure 11.14)
d1 outer diameter of the brace
di,eq. equivalent brace diameter (see chapter 11, figure 11.10)
Ç, : yield stress
Ç,0 yield stress of the chord member
(measured) yield stress of the chord member in longitudinal direction
f0 : ultimate tensile stress
ultimate tensile stress of the chord member
U,0,L (measured) ultimate tensile stress of the chord member in longitudinal direction
g1 : in-plane (= longitudinal) gap between the braces
out-of-plane (= transverse) gap between the braces
1 : length of the chord
'CAN : can length
u : j = x, y or z : displacement in X, Y or Z-direction (used to describe boundary conditions)
t0 : wall thickness of the chord
t1 : wall thickness of the brace
FE : finite element
F : axial force on the in-plane brace (ring model approach)
F1 axial force on member i (i = 1... 2)
J L M M0chord end
Moiv
Mo M1,Yura, test M1 ,Yura,num Mjjpb MjUjpb Mjopb MlyOPb MjUOpb N N Qgi Qgt Q3 VP vP.s R Rz
a
a0 3 oi 27axial brace force based on chord failure due to bending and shear of the chord
ultimate axial force on member i (i = i . . .2)
ultimate axial force on member i (i = 1. . .2) excluding the influence of overall chord bending
ultimate strength of a uniplanar X-joint determined with Kurobane's strength formula, (negative forces refer to tension, positive forces to
compression)
load ratio between the load on the out-of-plane brace and the in-plane
brace
distance on the chord surface between the centerlines of the braces, according to A.W.S. (see chapter 2, figure 2.2)
full plastic moment capacity
compensating moment applied to each chord end
reduced plastic moment capacity of the chord due to the combination of bending moments and shear forces in the chord
bending moment in the chord as a result of ultimate axial brace force experimentally determined bending moment on the in-plane brace at Yura's deformation limit
numerically determined bending moment on the in-plane brace at Yura's deformation limit
in-plane bending moment on member i (i = i . . .2)
ultimate in-plane bending moment on member i
(i = i .
..2)out-of-plane bending moment on member i (i = i . . .2)
out-of-plane bending moment on the in-plane brace which leads to failure in the ring model approach
ultimate out-of-plane bending moment on member i (i = i.. .2) constant used in the Ramberg-Osgood relationship
plastic yield capacity
in-plane gap modifier, proposed by Lalani and Bolt (1989) out-of-plane gap modifier, proposed by Lalani and Bolt (1989) geometric modifier according to A.W.S.
plastic shear yield capacity punching shear capacity regression constant j
correlation coefficient in regression analyses
decay function according to A.W.S. (see chapter 2, figure 2.2) chord length parameter 2.10/d0
ovalisation parameter according to A.W.S. diameter ratio d1/d0
relative vertical displacement of the crown point of member i (i
1..2)
true strain
0
: reference strain used in the Ramberg-Osgood relationshipu t true stress
u0 : reference stress used in the Ramberg-Osgood relationship
out-of-plane angle between the planes in which the braces are located
rotation of member i (i = 1. .2)
j
= x, y or z
rotation about the X, Y or Z-axis (used to describeboundary conditions)
angle which indicates the position of yield hinge j in the ring model approach
angle between the compression brace and the chord angle between the tension brace and the chord
1.
INTRODUCTION
1.1 STRUCTURAL APPLICATIONS OF HOLLOW SECTIONS
In nature, many applications of hollow sections as a structural element can be observed. Besides excellent properties with regard to resisting compression, tension, bending and torsion forces, hollow sections offer the possibility for architecturally attractive designs. In particular, circular hollow sections have proved to be suitable structural elements. Due to their shape, circular hollow sections have relatively low drag coefficients and are therefore the most favourite choice for elements subjected to wind and wave loading. In addition, the surface area of structures made of circular hollow sections, is much smaller than for comparable structures made of open structures. This, in combination with the smooth circular shape, requires lower costs for protection against corrosion and maintenance of circular members.
Therefore, circular hollow sections are applied in a wide range of onshore and offshore structures e.g. buildings, barriers, towers, bridges, offshore platforms etc.
Since all of these structures are three dimensional, it is obvious that in many cases multiplanar connectìons are present at the intersection of several circular members.
1.2 CURRENT DESIGN OF MULTIPLANAR JOINTS
During the last 30 years, extensive series of experiments have been carried out on tubular joints involving the static and fatigue strength of simple uniplanar joints. Most of the tests concern axially loaded joints. Only a few tests have been performed on joints loaded by bending. Regression analyses and other curve fitting methods have been used to establish design formulae for these simple uniplanar joints.
Until a few years ago, no experimental test results on multiplanar joints were available. Of the existing design codes, only A.W.S. Dl. 1-92 (1992) and Eurocode 3 (1992) take multiplanar effects into account for joints made of circular hollow sections. However, the A.W.S. code is only based on elastic considerations and not on experimental results. A detailed description of the A.W.S. recommendations is given by Marshall (1991). The design recommendations of Eurocode 3 for multiplanar joints are based on test results.
However, this code only considers a few types of multiplanar joints.
Most of the other design codes treat multiplanar joints as being uniplanar, thereby ignoring the interaction between the different planes. Depending on the geometry and the loading of the multiplanar joints, this may result in conservative or unsafe actual strengths. For multiplanar joints loaded by bending, no recommendations are given at
In summary, it can be stated that the basis for the design of multiplanar joints is still
insufficient.
1.3 JOINT CLASSIFICATION
The joint types which are discussed in this thesis, consist of uniplanar and multiplanar coimectjons between circular hollow section members, directly welded together without the use of gussets or stiffener plates. A uniplanar joint is a type of joint where the braces are located in the same plane along the chord axis, while for a multiplanar joint, the braces lie in different planes along the chord axis.
Several basic types of uniplanar and multiplanar joints, including their classification, are shown in table 1.1. Axial loads have been applied to the braces for illustration. The geometry of joints can be described by the geometrical dimensions d0, t0 etc. However, a more common way to describe the geometry of joints is by non-dimensional geometrical parameters. The most important non-dimensional geometrical parameters of joints made of circular hollow sections, are defined in figure 1. 1.
Figure 1.1 Dimensions and non-dimensional geometrical parameters of tubular joints.
1.4 AIMS OF THE PRESENT RESEARCH
As mentioned in section 1.2, the basis for the design of multiplanar is still insufficient.
Therefore, the present research is focused on the extension of experimental and
numerical data with regard to the static strength of uniplanar and multiplanar joints made of circular hollow sections.In the first place, experiments have been performed on uniplanar and multiplanar joints for different types of loading on the in-plane braces.
available experimental evidence (see table 6.1 for a summary of the joint types and types of loading considered in the numerical studies). In addition, for each joint type and type of loading, analytical models have been developed based on the plasticity theory (i.e. in line with Togo's ring model approach (Togo, 1967)). These analytically derived formulae provide a theoretical description of the joint strength and are used as a basis for the ultimate strength equations for each type of joint.
Table 1.1: Classification of tubular joints
Uniplanar joints Multiplanar joints
X-joints X F
O
T-joints TV
TT TX F1 K-jointsiiiitiii;;:.
K ¡FThe objective of the present research is to combine the results of the numerical analyses of uniplanar and multiplanar joints subjected to different types of loading with the analytically derived strength expressions in order to establish (basic) strength formulae which form the basis for future design recommendations. Simplifications of the basic ultimate strength equations to design rules in combination with the available experimental results, is not included in this Ph.D. project.
The strategy to comply with the aims of the present research can be summarized as
follows
- 1.4.1 Survey of relevant literature (chapters 2 and 14)
- 1.4.2 Experimental research (chapter 3)
- 1.4.3 Numerical calibration (chapters 4, 5 and 6)
- 1.4.4 Numerical research on uniplanar joints (chapters 7 and 8)
- 1.4.5 Numerical research on multiplanar joints (chapters 9, 10 and 11)
- 1.4.6 Simplification of the basic ultimate strength formulae and evaluation to design
rules (chapter 12)
- 1.4.7 Conclusions and summary of the basic ultimate capacity equations (chapter 13)
1.4.1 Survey of relevant literature
In chapter2,a description is given of relevant literature with respect to the static strength
of uniplanar and multiplanar connections between circular hollow sections. Both references related to experimental as well as numerical work are included.
A complete overview of literature which addresses the static strength of circular hollow section joints, is presented in the last chapter. This bibliography only includes references
after 1982, since an extensive summary of publications before this year can be found in
Hollow Section Joints by Wardenier (1982).
1.4.2 Experimental research
Since very few test results on multiplanar joints are available, an experimental research
programme has been set up. The study consisted of an experimental investigation of 3
uniplanar X- and 9 multiplanar XX-joints for one set of geometrical parameters. The
main reason to choose for joints is based on the fact that the load transfer through X-joints is relative simple and easier to understand than for other types of X-joints. In the
experimental research programme, the influence of various loading conditions on the out-of-plane braces (tension, zero-load, compression) has been investigated for different types
of loading on the in-plane braces. Uniplanar X-joints have also been tested
for1.4.3 Numerical calibration
The experimental results have been used for calibration of numerical models. General aspects with respect to finite element analyses are discussed in detail in chapter 4, followed by the description of the numerical simulations of the experiments in chapter 5.
Due to the good agreement between the experimental and numerical load-deformation curves for the axially loaded joints as well as for the joints loaded by in-plane bending, extensive numerical parametric studies have been set up for uniplanar T- and X-joints and multiplanar TT-, TX- and XX-joints under axial load and in-plane bending. The general features of these numerical studies are presented in chapter 6. Table 6.1 gives an overview of the joint types and types of loading considered in the various numerical
studies.
1.4.4 Numerical research on uniplanar joints
Before a good understanding of the static behaviour of multiplariar joints can be obtained, it is necessary to gain accurate insight into the behaviour of the relative simple uniplanar joints. Therefore, the following numerical parametric studies have been performed on uniplanar X- and T-joints.
- In chapter 7, the results are presented of non-linear finite element analyses carried out
on uniplanar X-joints. Although many test results exist for axially loaded uniplanar joints, numerical simulations have been made for 16 axially loaded uniplanar X-joints in order to exclude the effects due to loading conditions, which often vary for
different series of experiments. The results can be found in section 7.1.
For X-joints loaded by bending, the number of experiments is less than for axially loaded joints. To obtain a better insight in the geometrical variables that control the strength of uniplanar X-joints under in-plane and out-of-plane bending, numerical parametric studies have been carried out. The results are described in sections 7.2 and 7.3 for X-joints under in-plane bending and out-of-plane bending respectively. In the past, many questions arose regarding the influence of the chord and can length on joint strength. Both the A.W.S. (1992) and the A.P.I. (1991) give (different) recommendations for the can length. In order to investigate the influence of the chord and can length on the static strength of uniplanar X-joints, non-linear finite element analyses have been performed. The results of the chord and can length analyses of axially loaded uniplanar X-joints are presented in sections 7.4 and 7.5 respectively. - For axially loaded uniplanar T-joints, the load transfer through the joint is more
complicated than for uniplanar X-joints. Failure of uniplanar T-joints is caused by a
order to separate these two influences, finite element analyses have been performed on uniplanar T-joints. Each joint has been analyzed numerically two times : once with and once without the influence of overall chord bending. The results of these analyses on axially loaded uniplanar T-joints are presented in section 8.1.
In line with the parametric studies on X-joints loaded by bending, numerical analyses have been made for uniplanar T-joints loaded by in-plane bending and out-of-plane bending (sections 8.2 and 8.3 respectively).
1.4.5 Numerical research on multiplanar joints
- Extensive numerical parametric studies have been performed on multiplanar XX-joints
(section 9.1), where axial loading has been applied to the in-plane braces. The load applied to the out-of-plane braces varied from tension to compression. In these analyses, the geometrical parameters a, i3 and 2-y as well as the ratio between the in-plane to out-of-in-plane loading have been varied over a wide range.
Since no experimental results are available for multiplanar joints loaded by in-plane bending apart from the three cases described in chapter 3 of the present research work, numerical parametric studies have been set up for multiplariar XX-joints in which the in-plane braces are loaded by in-plane bending. The loading conditions on the out-of-plane braces have been varied between axial forces (tension, zero-load or compression) and in-plane bending. The results of these analyses are presented in sections 9.2 and 9.3.
Finally, in sections 9.4 and 9.5, the influences of the chord and can length on the strength of axially loaded multiplanar XX-joints have been determined for various load
ratios.
- The numerical research programme which has been carried out for multiplanar
TX-joints, is similar to that for multiplanar XX-joints. However, due to the fact that the geometry of multiplanar TX-joints is less symmetrical than for multiplanar XX-joints, some additional analyses have been performed.
Furthermore, some of the axially loaded multiplanar TX-joints have been analyzed two times, once including and once excluding the overall chord bending effects (a effects), in agreement with the analyses of the axially loaded uniplanar T-joints. An extensive description of these studies can be found in section 10.1.
Since no experimental results are available for multiplanar TX-joints loaded by plane bending, numerical parametric studies have been set up. In these studies, the in-plane brace has been loaded by in-in-plane bending. The out-of-in-plane braces have been subjected to either axial forces (tension, zero-load or compression) or in-plane bending. The results of these analyses are presented in sections 10.2 and 10.3.
- Paul (1991) described the experiments on 12 multiplanar TI-joints. For only one a
and one 2y value, 12 static tests have been carried out for a wide range of , g/d0
and values. In Paul's study, however, no attempts were made to separate the overall
chord bending influence from the local strength. In the present study, described in chapter 11, numerical simulations have been made of multiplanar IT-joints with the same non-dimensional geometrical parameters as considered in Paul's experiments. Finally, the numerically determined strength values of TI-joints have been related to the strengths of uniplanar I- and X-joints.
1.4.6
Siinplifïcation of the basic ultimate strength formulae and evaluation to
design rules
The basic ultimate strength formulae which have been established in chapters 7 to 11 may be too complex to be used for design purposes. Therefore, simplifications of the formulae may be required. Although simplification of the ultimate strength equations is not included in this Ph.D. thesis, some general remarks have been made in chapter 12. Furthermore, the evaluation of the ultimate strength formulae to design rules is also briefly discussed in chapter 12.
1.4.7 Conclusions and summary of the basic ultimate capacity equations
As mentioned earlier, the objective of the present research is to establish basic ultimate strength equations for uniplanar and multiplanar joints under different types of loading, based on the results of the FE analyses in combination with analytically derived strength formulae. The basic ultimate strength formulae are summarized in chapter 13, thus enabling a good mutual comparison.
Chapter 13 is concluded by proposals for further research into the Static behaviour of uniplanar and multiplanar tubular joints.
2.
SUMMARY OF RELEVANT RESEARCH
In the last three decades, extensive series of experiments have been carried out on uniplanar K-, T- and X-joints, especially with axial loading. The number of experiments on joints loaded by in-plane or out-of-plane bending is much smaller. The tests until 1982 have well been documented by Wardenier (1982).
Since 1982, only a limited number of experiments on circular hollow section joints have been carried Out. Since the present study is concentrated on multiplanar joints, only experimental and numerical studies in this field have been summarized in this section. An extensive list of references with regard to the static strength of tubular joints have been recorded in chapter 14.
2.1 EXPERIMENTAL RESEARCH ON MULTIPLANAR JOINTS
The first experiments on multiplanar joints have been carried out by Akiyama (1974). Four double KK-joints with an angle of 1800 between the two uniplanar planes have been tested under axial brace loading. However, the direction of the applied brace forces was opposite between the uniplanar K-planes which means that equilibrium was maintained by the axial brace forces without axial forces at the chord ends (= anti-symmetrical
loading).
Two specimens failed prematurely, the two other specimens failed by plastification of the chord wall at the intersections with the compression braces.
Makino (1984) presented the results of 19 tests of axially loaded multiplanar KK-joints with an angle of 60° between the uniplanar planes. The diameter ratio ß as well as the in-plane angle between the compression brace and the chord and the in-plane angle between the tension brace and the chord have been varied, thus resulting in different combinations of the in-plane (= longitudinal) and out-of-plane (= transverse) gaps between the braces.
All joints
failed by plastification of the chord wall at the intersection with the
compression braces in combination with crack initiation at the weld toes of the tension braces (either at the chord surface or in the tension braces), followed by gross separation of the tension braces.Makino observed that the static behaviour of the multiplanar KK-joints was similar to that for uniplanar K-joints, except for larger g/d0 ratios where a remarkable local deflection of the chord wall between the two compression braces occurred. Therefore, Makino established two strength equations for multiplanar KK-joints, both related to the strength formula of axially loaded uniplanar K-joints by correction functions depending on the out-of-plane gap ratio gId0. One formula considered the actual joint parameters, the second equation was related to the strength of uniplanar K-joint with an equivalent
formulae were based on regression analyses of the 19 available test results.
The experimental research on multiplanar joints has been continued by Scola (1990). Scola performed 8 tests on axially loaded multiplanar TT-joints with an angle which varied from 60 to 1200 between the two uniplanar planes.
In addition, 5 tests on uniplanar T-joints have been carried out for comparison. All joints failed by chord plastification of the chord wall. Scola observed three failure modes, dependent on the size of the out-of-plane gap gt For the joints with a small transverse gap ratio gId0, the braces acted as one member without local deflections in the gap area between the braces. For the joints with a larger out-of-plane gap, local deformations were observed between the braces forming a fold in radial direction. One joint showed a non-symmetrical failure type, where one brace was indented in the direction of the applied load while the other brace displaced in the opposite direction.
Scola related the ultimate load of all multiplanar TT-joints to the ultimate loads of the corresponding uniplanar T-joints by a correction function depending on g/d0. This correction function showed much similarities with the relationship found by Makino (1984) for axially loaded multiplanar KK-joints.
Mouty and Rondal (1990) tested 96 axially loaded multiplanar KK-joints. The angle between the two uniplanar planes has been taken as 60° or 90°. Of the 96 joints only 34 joints had normal profile cuttings.
The test set-up used for the KK-joints differed considerably from usual test set-ups for axially loaded KK-joints. The most common test set-up used for this type of joints has pins at the ends of the chord and the braces. The loads are applied to the tension braces and are reacted at the two other braces and at the chord end. Mouty and Rondal, however, fixed the brace ends against displacement and rotation while the chord ends were free. The loads have been applied at one of the free chord ends. However, this way of load introduction leads to additional bending moments. This might explain why the
results deviate considerably (i.e.
are lower) from the
results reported by otherinvestigators (Makino,
1984 and Paul,
1992). Therefore, these test results areinternationally in discussion (Kurobane, 1993, Rondal, 1993, Wilmshurst, 1993c). Tests on multiplanar TT-joints have also been performed by Paul (1991), who considered 12 axially loaded multiplanar TT-joints with different values of ¡3 and the out-of-plane angle between the two uniplanar planes (60° - 120°). Paul observed similar failure modes as found by Scola (1990). For small g/d0 ratios (< 0.20), the braces of the TT-joint acted as one member (by Paul indicated as failure type 1). For g/d0 ratios larger than 0.20, significant local deflections occurred in the gap area, forming a fold in radial direction (failure type 2). For one joint, the failure type was not symmetric and the deformation occurred only at one brace.
Based on regression analyses of these experimental results in combination with the results of Scola (1990), Paul (1992) established a strength equation for each of the two failure modes 1 and 2. Both strength equations were related to Kurobane 's strength formula for
axially loaded uniplanar T-joints. The strength equation of the multiplanar TT-joints with failure type 1, considers an equivalent brace diameter.
Subsequently, Paul (1992) continued with experimental tests on 18 axially loaded multiplanar KK-joints with an angle of 600 and 90° between the uniplanar planes. All joints failed by plastification of the chord wall at the compression braces. For the joints with small longitudinal gaps, this chord plastification was accompanied by cracks at the weld toes in the chord wall or by cracks in the welds on the tension braces. Three failure modes can be distinguished. For the KK-joints with small out-of-plane gaps, the compression braces acted as one member with negligible deformations of the chord wall between the compression braces (failure type 1). For larger out-of-plane gaps, significant deformations of the chord wall between the braces were observed (failure type 2). For the KK-joints with small in-plane gaps and large out-of-plane gaps, local deformation occurred at only one of the two compression braces (failure type 3).
In line with the multiplanar TT-joints, Paul proposed a strength equation for each of the two most occurring failure types, based on regression analyses of his test results combined with the results obtained from Makino (1984). Both strength formulae have been related to the strength formula of axially loaded uniplanar KK-joints, whereas for the joints with failure type 1 an equivalent brace diameter is used to determine the strength. For the joints which failed according to failure type 3, no strength formula has been established.
As part of an investigation into the static behaviour of diaphragm stiffened multiplanar KK-j oints, Makino (1993) reported the results of two symmetrically and one non-symmetrically loaded unstiffened multiplanar KK-joints under axial brace loading. For all joints, the out-of-plane angle between the uniplanar planes was 60°.
The failure mode of the two symmetrically loaded KK-joints was chord plastification of the chord wall at the compression braces. Due to the small transverse gaps, the braces acted as one member in agreement with failure type 1. For the non-symmetrically loaded KK joint,
local chord wall deformations were observed in the area between the
compression braces, accompanied by cracks at the weld toes in the tension braces (i.e. not at the chord surface).Makino (1994a) reported the results of nine tests on multiplanar KK-joints under anti-symmetrical axial brace loads. The out-of-plane angle between the uniplanar planes was taken as 60 and 90°. One joint with small values of the g1/t0 and g/d0 ratios, failed prematurely and was excluded from further analyses for the chord plastification failure mode. All other joints failed by chord plastification of the chord wall between the compression braces forming a wrinide running diagonally between the compression braces. The chord plastification was accompanied by the development of cracks at the weld toes of the tension braces (either at the chord surface or in the tension braces). The location of the cracks appeared to be dependent on the size of the out-of-plane gap ratio
of the tension braces in the transverse gaps between the tension braces, while for larger gId0 ratios, cracks occurred at the weld toes of the tension braces in the longitudinal gaps between the braces. For the KK-joints with small longitudinal gap ratios g1/t0, failure was caused by cracks at the weld toes in the tension braces (i.e. not at the chord
surface).
Since the failure pattern of the non-symmetrically loaded multiplanar KK-joints showed much resemblance with the failure pattern of axially loaded uniplanar K-joints, Makino related the strength of the multiplanar KK-joints to the strength formula for axially loaded uniplanar K-joints. Due to the limited number of tests, Makino did not provide a strength equation for the KK-joints considered.
Makino (1994b) performed two additional tests on symmetrically loaded multiplanar KK-joints to investigate the influence of 2y on the strength of the KK-joints. One joint had an out-of-plane angle of 600 between the uniplanar planes, the other one an angle of 90°. The failure mode of both KK-joints appeared to be plastification of the chord wall. The joint with the small out-of-plane gap showed a failure mode in line with type i as described by Paul (1992). The failure type of the other joint was in agreement with
failure type 2.
After comparing the ultimate loads of both KK-joints with the prediction formulae of Paul (1994), it appeared that Paul's strength equation agreed well for both joints considered with 2y = 27.4. Therefore, Makino recommended to extend the validity range of 2y of Paul's equation down to 27.
2.2 NUMERICAL RESEARCH ON MULTIPLANAR JOINTS
Paul (1989) extended the numerical work on uniplanar joints initiated by van der Valk (1988), to numerical research on axially loaded uniplanar and multiplanar XX-joints. The numerical analyses have been performed using the general purpose FE package MARC. Paul considered two ¡3 values (0.4 and 0.6) for one 2-y value (40.0). For both joints, several load ratios between the load on the out-of-plane braces and the load on the in-plane braces, varying from -1.0 to 1.0, have been analyzed. The corresponding uniplanar X-joints have been analyzed as well. Eight noded thin shell elements were used to model the joints. The geometry of the welds has not been included in the numerical modelling. For both joints, the presence of the unloaded out-of-plane braces resulted in an increase in strength compared to the strength of the corresponding uniplanar joints (stiffening effect). For the joints where the out-of-plane load was of the same magnitude as the in-plane load but opposite from sign, the joint strength was less than the strength of the uniplanar joint. In case the in-plane and out-of-plane brace loads acted in the same sense, a considerable increase in strength has been observed (multiplanar load interaction effects). Both the stiffening and the multiplanar load interaction effects appeared to be most pronounced for the joints with ¡3 = 0.60. However, no test evidence was available for verification.
Therefore, in 1990 a Joint Industry Project has been set up, considering experimental and numerical research on nine multiplanar XX-joints and three uniplanar X-joints. The results of these experiments and numerical analyses are described in detail in chapters 3, 4 and 5 of the present work. Based on the numerical models which have been calibrated against the experimental evidence, extensive numerical parameter studies have been carried Out for various types of joints under different types of loading, using the FE package MARC.
Ward (1992) published the results of numerical analyses on a nine brace multiplanar joint of an existing North Sea jacket structure in order to determine the effects due to the presence of unloaded out-of-plane braces and to determine the effects as a result of loads on the out-of-plane braces.
The numerical analyses have been performed using the FE program ABAQUS. The joints have been modelled with eight noded thin shell elements.
A simple, axially loaded uniplanar Y-joint was considered as the basic model and was used for reference. First, eight unloaded braces were introduced to the uniplanar Y-joint, to determine the influence of stiffening on the strength of the joint. Subsequently, all out-of-plane braces were proportionally loaded up to joint failure, to obtain the multiplanar load interaction effects. From the numerical analyses, considerable stiffening and load interaction effects became clear.
Wilmshurst (1993a) presented his
findings of 30 FE analyses on axially loaded
multiplanar KK-joints. The numerical study, using the FE program ABAQUS (1989), can be divided in the following sub-studiesdifferent mesh lay-outs and densities, using four noded shell elements, were examined to calibrate the numerical models against the results of four tests on axially loaded multiplanar KK-joints, carried Out by Makino (1984). Furthermore, two methods to model the geometry of the welds were investigated. The weld profile was modelled by solid elements and by shell elements. For the shell element models, various sizes of the weld profile were analyzed. From the numerical analyses, it appeared that the largest mesh density (i.e. with the largest number of elements) and the weld profile being modelled by shell elements, provided predictions of the ultimate loads which were in good agreement with the experimentally determined values.
- the boundary conditions and loading mode were varied for one of the multiplanar
KK-joint configurations. The aim was to establish uniform boundary conditions in future studies, both for axially loaded multiplanar KK-joints as well as for KK-joints loaded by bending. Based on the numerical results, it was recommended to apply loads to the end of the compression braces and to restrain the chord by pins at one end and by pin-rollers at the other end.
the influence of the chord length on the strength of multiplanar KK-joints was investigated. Over a large range of , the strength of the KK-joints varied only a few
- a series of analyses were performed to obtain insight in the effects of the f/f ratio as well as the shape of the stress-strain curve on the static strength. For the KK-joint considered, both the influence of the fIf ratio and the shape of the strain hardening curve had considerable influence on the strength of the joints.
Finally, numerical research on multiplanar TX-joints has been carried out by Davies (1994). Axially loaded multiplanar TX-joints have been investigated for two fi values (0.25 and 0.60) and one 2-y value (23.6). Various load ratios between the load on the out-of-plane and in-plane braces have been considered. The corresponding uniplanar joints have been analyzed as well. Furthermore, the restraints applied to the out-of-plane braces were varied. For one set of analyses, the out-of-plane brace tips were completely released while for the other set of analyses, the out-of-plane braces were restrained and kept parallel to their original direction during loading.
The numerical analyses have been performed using the FE program ABAQUS. The joints were modelled with eight noded thick shell elements.
Based on the numerical results, it was recommended that modelling of the weld geometry should be included in the numerical models to obtain realistic simulations of the joint behaviour.
The influence of unloaded out-of-plane braces on the strength appeared to be negligible for the joints with fi = 0.25. The strength of the TX-joints with unloaded out-of-plane braces and fi = 0.60 increased 12 %, compared to the strength of the corresponding umplanar T-joints. Furthermore, for all TX-joints where the loads on the in-plane and out-of-plane braces were opposite, a decrease in strength was observed, both for the joints with free and restrained out-of-plane braces. For the joints where the in-plane and out-of-plane braces were loaded in the same sense, a small increase in strength was observed compared to the strength of the corresponding uniplanar T-joints, in contradiction with similar analyses on multiplanar XX-joints. For large load ratios (i.e. large compression loads on the out-of-plane braces combined with smaller loads on the in-plane brace), the strength of the TX-joints strongly depended on the conditions applied to the out-of-plane brace tips.
2.3 ANALYTICAL RESEARCH
Due to the complexity of the load transfer in circular hollow section joints, only limited investigations are available for analytical models. The first simplified analytical models, based on the plasticity theory, have been developed by Togo (1967). In this approach, a three dimensional joint configuration has been simplified to a two dimensional model with the shape of a ring, representing the chord. Brace forces are approximated by line loads which act over a certain length. After assumptions with respect to the locations of possible yield hinges, formulae can be derived describing the (analytical) yield strength of the ring (= chord) due to a combination of applied line loads (= brace forces). Extensive applications of this ring model approach can be found in chapters 7 to 11 of
the present work.
Marshall and Toprac (1974) used the punching shear criterion. The punching shear approach assumes that local stresses at a potential failure surface through the chord wall limit the strength of a joint i.e. the acting punching shear stresses on the failure surface through the chord wall may not exceed the allowable punching shear stresses (see figure 2.1). The allowable punching shear stresses depend not only on the strength of the chord but also on the geometry of the connection. The punching shear criterion has become the basis for the A.P.I. design recommendations.
Acting punching shear stress
f
I
Figure 2.1 : Punching shear stress.
Makino (1989) tried to predict the strength of axially loaded uniplanar X-joints using the yield line model. Based on the deformation pattern often observed at tests on uniplanar X-joints, Makino assumed a collapse mechanism of the chord surface with the shape of
an ellipsoid. Triangular plane elements were proposed to simplify the description of the deformation of the chord wall. Some uncertainties about the dimensions of the yield pattern (i.e. for membrane force) were solved by trial and error. Furthermore, derivation of the yield strength could only be performed using numerical methods. Although the strengths derived from the yield line theory did not exactly describe the actual ultimate strengths of uniplanar X-joints, the yield line method provided good qualitative predictions of the strengths.
In principle, Togo's ring model approach and the punching shear criterion are the basic
[tO
/No
L_
' t2.4 DESIGN CODES AND RECOMMENDATIONS
2.4.1 General
About 15 years ago, the design recommendations for uniplanar joints of circular hollow sections differed considerably between various countries. Through the work of 1.1. W. -Subcomm. XV-E, considerable consensus has been obtained about the recommended design formulae. The first I.I.W. design recommendations were published in 1981, the updated version in 1989. These updated design recommendations have been adopted for Eurocode 3 (1992) and thus for the European countries, whereas they are also used in Scandinavian countries and Canada.
The Japanese design recommendations for tubular connections (A.I.J.) are similar to the formulae which have been used as a basis for the I.I.W. recommendations.
The recommendations used in the U.S.A., given by the A.P.I. RP2A (1991) and A.W.S. D1.l-92 (1992), differ considerably from those of the I.I.W., which is mainly due to the different models on which the codes are based (punching shear criterion versus ring model approach) (Kurobane, 1994).
For multiplanar joints, only A.W.S. and Eurocode 3 give recommendations which incorporate multiplanar effects. Both codes are discussed in the following sections.
2.4.2 A.W.S.
2.4.2.1 Description of the A.W.S. formulation
The A.W.S. recommendations are based on a lower bound interpretation of test data. Although the allowable capacity formulae are provided in a punching shear format, the A.W.S. formulation can easily be rewritten in the following form (without the safety factor of 1.8) FU1OverbOU -
6r3(-_
+ 0.18) O.7(a0-1)f0.t
-
aU with (2.1) Qß = 1.0for 13O.60
0.3 =(1-O.833)
for
> 0.60Multiplanar effects are incorporated by a chord ovalisation parameter a0, which includes the contribution of each individual brace to the strength of the multiplanar joint (see
figure 2.2). The formulation of the c parameter has been based on elastic considerations and has not been calibrated against experiments, due to the limited number of available test results on multiplanar joints at that time.
Reference brace for which a0 applies
F
Figure 2.2 : The definition of c according to the A.W.S. design recommendations.
For arbitrary (non-overlapping) joint configurations and (axial) brace loads, the chord ovalisation parameter a0 is calculated according to equation 2.2 (see figure 2.2 for the definitions of the angles and dimensions). No recommendations are given for multiplanar joints with braces loaded by in-plane or out-of-plane bending.
z
FsinOcos2exp(-____)
= 1.0 +0.7 allbraces
i.o
(F sin O)reference brace
The ovalisation parameter a has to be determined for all braces of the joint for which the capacity has to be checked, each time taking a different brace as reference brace. In the summation, the cosine term accounts for the position of the braces around the chord circumference, while the exponential decay term describes the decreasing influence of a brace if the distance L to the reference brace increases. From the definition of a, it follows that the presence of unloaded braces does not influence the joint strength, which is not correct.
In general, it can be stated that the chord ovalizing parameter accounts for the magnitude and direction of the brace loads in combination with the relative positions of the
F
CHORD
L (dO.tO
pronounced ovalisation of the chord cross section, thus resulting in a more severe reduction of the joint strength.
Although the formulation of the chord ovalisation parameter has been developed on a mathematical basis without any calibration against experiments on multiplanar joints, the A.W.S. formulation represents a major advance in tubular joint design since the same formulae can be used for different types of joints i.e. joint classification is not required. 2.4.2.2 Comparison of experimental and numerical results with the A.W.S. Based on comparisons of the experimental data on multiplanar KK-joints (Makino, 1984) and multiplanar TT-joints (Mitri, 1987) with the A.W.S. formulation, Lalani and Bolt (1989) concluded that A.W.S. tended to underpredict the strength of the joints with small in-plane gaps and small out-of-plane gaps. As a result, the following in-plane gap and out-of-plane gap modifiers have been proposed to enhance the reliability of the A.W.S. formulation
Based on the experimental results of multiplanar TT-joints (Scola, 1990, Paul, 1991) and multiplanar KK-joints (Makino, 1984, Paul, 1992), Paul also indicated that the A.W.S. formulae did not capture the multiplanar effects adequately. Comparing the test results of KK-joints with small in-plane gaps, and the A.W.S. predictions showed similar trends as observed by Lalani and Bolt (1989). However, for multiplanar KK-joints with small out-of-plane gaps, Paul disagreed with the trends found by Lalani and Bolt (equation 2.4).
Wilmshurst (1993b) indicated that, until then, most of the experimental research on
multiplanar joints was focused on joints with high 2-y ratios (2-y > 34.0). Therefore,
numerical research was carried out on multiplanar KK-joints with 2y values down to 18.0. Comparing these numerical results with the A.W.S. predictions, Wilmshurst found
that A.W.S. overpredicted the strength of the joints with 2-y < 24.0, while for larger
2'y values, the A.W.S. underpredicted the ultimate loads
(=
conservative). Forincreasing 2-y values, the A.W.S. predictions became more conservative. Application of
the small gap modifiers proposed by Lalani and Bolt decreased the amount of
overprediction for the joints with small gaps and large 2-y values, but now overpredictedthe strength of some joints with 2-y = 24.0 by 20 %.
Qgi =
1.4-2f
i.o
(2.3)2.4.3 Eurocode 3
2.4.3.1 Description of the Eurocode 3 formulation
The design rules recommended by Eurocode 3 for the design of multiplanar joints are
based on experiments. However, they are only valid for a small number of joint
geometries. Multiplanar effects are accounted for by (lower bound) correction factors which should be applied to the uniplanar strength formulae (see figure 2.3).Figure 2.3 Correction factors for multiplanar joints according to Eurocode 3.
2.4.3.2 Comparison of experimental results with Eurocode 3
Paul (1992) compared the ultimate loads resulting from tests on multiplanar TT-joints
(Paul, 1992, Scola, 1990) and KK-joints (Makino, 1984, Paul, 1992) with the characteristic strength predictions obtained from Eurocode 3. Although the definition of the characteristic strength is not identical to the definition of lower bound values, as used by A.W.S., the results are comparable to a certain extent.
Based on comparisons of the test results on multiplanar TT-joints with the Eurocode 3 formulae, Paul found that the actual strengths of the TT-joints varied between 1.13 and 2.04 times the characteristic strengths values of Eurocode 3. For the available test results of multiplanar KK-joints, these ratios varied from 1.40 to 2.14, thus implying that
Type of joint joints (60°Correction factor to uniplanar90°)
TT 1.0 t t XX
-N2 ¿Ni N.. 1 + 0.33Note : take account of the sign
of N1 and N2 (N1 N2) I t M N2 tNi KK
t,
r
0.93.
EXPERIMENTS ON UNIPLANAR X- AND
MULTI-PLANAR XX-JOINTS
3.1 INTRODUCTION
As mentioned in the introduction, current design codes, used to predict the ultimate static load capacity of uniplanar X- and rnultiplanar XX-joints in circular hollow sections, are mainly based on extensive tests on simple uniplanar joints. Very few test results on multiplanar joints are available for verification. In order to obtain more insight into the multiplanar effects, an experimental research programme regarding multiplanar XX-joints has been set up, since the influence of the multiplanar loading on strength and stiffness is expected to be most severe for X-joints. Furthermore, for this type of joint, the load transfer is more straightforward and the behaviour easier to understand than for other types of joints.
In this study, the influence of loaded and unloaded out-of-plane braces on the static strength, stiffness and the deformation capacity of XX-joints in circular hollow sections has been determined experimentally for different types of loading on the in-plane braces. The present study consists of an experimental investigation on
- the influence of the unloaded out-of-plane braces on the strength of the joint for different types of loading on the in-plane braces (the stiffening effect).
- the influence of compression or tension loading of the out-of-plane braces on the strength of the joint, for different types of loading on the in-plane braces (the load-interaction effect)
3.2 RESEARCH PROGRAMME
The research programme is summarized in table 3.1. The test series consists of three sets of four specimens. Each set consists of three multiplanar XX-joints and one uniplanar X-joint for reference. Only one set of geometrical parameters is used for the joints. The nominal dimensions and joint parameters of the specimens are given in table 3.2 and figure 3.1. The actual chord dimensions are presented in table 3.3 for the axially loaded joints, in table 3.4 for the joints loaded by in-plane bending and in table 3.5 for the joints loaded by out-of-plane bending.
The geometry is limited to joints with a diameter ratio ¡3 = 0.6 and a chord radius to thickness ratio 2y = 40.0. To prevent (in-plane bending) failure of the brace before joint failure, the wall thickness ratio r is taken as 1.0. The geometric chord length parameter
Table 3.1 : Research programme of uniplanar X- and multiplanar XX-joints.
Joint
Loading conditions
Axial
inBendingplaneout of plane
BendingUniplanar
Ø4
F FXI
Mipb Mjpb u iX5
j-'i
MQpb Mopb. iX9
Multiplanar
-
-«L
-XX2
ti!
XX6
ï XX1OMultiplanar
+ F2 +II
XX3
k-J IXX7
IXxii
Multiplanar
- F2 - F2 =-o 4- .. gXX4
gXX8
XX12
Table 3.2 : Nominal dimensions, material properties and joint parameters. SIZES IN MM. d1 hord: 04064x10 1220 2440 1220
NOTE NO NORIZONTAL BRACES FOR SPECIMENS Xl, X5 ANO X9
I
I
1225 braces: 2445X10IVA
iiYiiiiiï
Figure 3.1 : Configuration and dimensions of the specimens.
The in-plane braces have been loaded in incremental steps to joint failure (deformation controlled). The following loading conditions were applied to the in-plane braces
- compression forces for Xl, XX2, XX3 and XX4
- in-plane bending moments for X5, XX6, XX7 and XX8 (as a result of in-plane forces
perpendicular to the brace axis)
- plane bending moments for X9, XX1O, XXi i and XX12 (as a result of
out-of-plane forces perpendicular to the brace axis)
The following loading conditions were applied to the out-of-plane braces
- unloaded (XX2, XX6, XX1O)
- compressive forces equal to 60% of the calculated ultimate strength of a uniplanar
joint under compression load, using the mean strength formula of Kurobane (1980) for axially compression loaded uniplanar X-joints
Uniplanar X- and multiplanar XX-joints
dimensions cs ¡3 2y -r Steel grade EN 10210-1 f (N/mm2) chord braces 406.4 x 10.0 244.5 x 10.0 12. 0.6 40. 1.0 Fe 360 (S235) 235
