UNIVERSITY OF TORONTO

Nikola Kosteski

A thesis submitted in confonnity with the requirement.

for the degree of Doctor of Philosophy,

Department of Civil Engineering,

in the University of Toronto

Q Copyright by Nikola Kosteski (200 1)

National Librafy Bibiioîhèque nationale du Canada

Acquisitions and Acquisitii et Bibliogaphic Services senrices bibliographiques 3 5 Wellington Street 395, ni6 WeUington Ottawa ON KlAON4 Ottawa ON K I A ON4 CaMda CaMda

The author has granted a non- L'auteur a accordé une licence non exclusive licence aiiowing the exclusive permettant à la National Lhrary of Canada to Bibliothèque nationale du Canada de reproduce, loan, distrr'bute or seil reprodinre, prêter, distriiuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de

reproduction sur papier ou sur format électronique.

The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.

Doctor of Philosophy (2001)

Nikola Kosteski

Depamnent of Civil Engineering,

in the University of Toronto

In recent years, the use of recmgular Hollow Structural Sections (HSS) as columns has becorne

increasingly popular. In many instances rectangular HSS column members are replacing custornary I-

section members due to their superior column performance. In turn. welded longitudinal branch plates

that have been a traditional and convenient method for the connection of brace members and other

aaachrnents to 1-section columns are now similarly used for rectangular HSS columns. The current

design method, consisting of welding a branch plate parallei to the axis of the column has not been

thoroughly investigated, especially for the effects of connection flexibility, of branch plate inclination

angle and of axial compression load in the column. This represents a known omission in cumnt HSS

column connection design knowledge and published design specifications.

Based on experimental testing of isolated connections, parametric non-linear Finite Element analysis

and analytical yield line analysis, the strength and ùehaviour of longitudinal branch plate-to-rectangular

HSS rnember connections have been deterrnined. On the basis of this, design criteria are herein

proposed. ïhese recommendations have also been reported in technical Iiterature and the

recommendations are being incorporated into design specifications and guides for HSS connections.

A conventional longitudinal branch plate-to-rectangular HSS member connection tends to cause

excessive distortion of the HSS connecting face. Such a connection therefore results in a low,

deformation limit state, design resistance. In an effort to reduce this inherent flexibiiity of longitudinal

branch plate connections, stiffening plates or structural tees can be welded to the HSS connecting face.

Also, a "through" branch plate connection that extends through both walls of the rectangular HSS

member can be used to increase the strength of a standard longitudinal branch plate connection. These

"alternative" connections represent the next generation in rectangular HSS connection design. Once

again. based on experimental testing of such connections, non-linear Finite Element analysis. and

analytical yield line analysis, the strength and behaviour of "alternative" branch plate-to-rectangular HSS

rnember connections have been determined and modelled, resulting in published recornmendations.

This thesis develops comprehensive, rational, limit States design procedures and equations that

encompass, and wherever possible consolidate the behaviour of, the multitude of branch plate-to-

rectangular HSS member connection types that will now be available to designers.

iii

First and foremost 1 would like to thank my supervisor, Professor J.A. Packer. In 1993 1 met hirn in

the Sandford Fleming laboratory during "U of T Day" to discuss an undergraduate thesis topic. The rest,

as they say, is history but 1 would like to personally thank him for everything that he has done for me

over the years.

1 would like to acknowledge the contributions of Christoph Horenbaum, an exchange student from

Univeristiit Karlsruhe (Germany) during 1996. Aiso, i would like to thank Robert Coultes for his

contributions during an undergraduate thesis in 1997. Finally, I would like to acknowledge the

contributions of Junjie Cao, a Postdoctoral Fellow with whom 1 had the privilege of working from 1996

to 1998.

My appreciation goes to the office staff, shop personnel, and technicians in the Depanment of Civil

Engineering for their expert and kind assistance. On a penonal note, l would like to especially thank

John Buzzeo and Alan McClenaghan for their Friendship throughout the years.

Financial support for this project was provided by the Steel Structures Education Foundation, the

Steel Tube Institute of North America, the Comité International pour le Développement et l'Étude de la

Construction Tubulaire (CDECT), and the Natural Sciences and Engineering Research Council of

Canada (NSERC).

Scholarship support was provided by an Industrial NSERC scholarship, an Ontaric Giaduate

Scholarship (OGS), a University of Toronto Open Fellowship, and a Canadian institute of Steel

Construction (CISC) Kellerman Fellowship. This support is greatly appreciated.

Finally 1 would like to thank my mother, father, and my older brother Tome for. quite sirnply,

everything.

AISTRACT ........................................................................................................................................... ii

ACKNOWLEDCEMENTS .................................................................................................................. iv

TABLE OF CONTENTS ........................................................................................................................ v

LIST OF TABLES ................................................................................................................................. x

LIST OF FIGURES ................................................................................................................................ xii

NOTATION ........................................................................................................................................... xvii

1 . INTRODUCTION AND LITERITURE REVIEW

1.1 Introduction ........................................................................................................................... 1-1

1.2 Analytical models .................................................................................................................. 1-6

1 2 . 1 Weld nid branch plate failure ..................................................................................... 1-6

.......................................... ! .2.2 General yielding of rhe reczangular HSS connecting face 1-8

1.2.3 General punching shear model ................................................................................... I . 15

......................................................*.... . 1 2.4 Combined/Iexural and punching shear model 1 16

...................................................................... 1 .2.5 Branch efîectir width failure criterion 1-18

......................................... 13 Notionai ultimate and serviceability deformation limit states 1-21

1.4 Summary of reiated experimeaîal and numerical studies .............................................. 1-23

........................... 1.4. I Transverse branch plate-to-rec~anguiar HSS member connections 1-13

.................................................. 1.4.2 Stiflened circular HSS-10-HSS member connections 1-25

............................................ 1.4.3 Stifened rectangufar HSS-ru-tiSS member connections 1-26

........................ 1.4.4 Shear loaded longitudinal branch plate-to-HSS column connections 1-18

..................... 1 .4.5 Tension loaded longitudinal branch plate-to-HSS column connecrions 1-33

2.1 Test spimens .................. .... ........................................................................................ 2-1

........................................................................................................... 2.1.1 Instrumentation 2-9

............................................................................................................. 2.1 -2 Test procedure 2-10

2.2 Test results ............................................................................................................................. 2-11

2 1 Variable branch plate-to-HSS member connection angles ......................................... 2-11

..................................... 2.2.2 Variable column preload for 45" and 90" connection angles 2-13

............................................................................................................... 2.2.3 Failure mode 2-17

2.2.4 Main HSS member connecring face deformation profile ............................................ 2-19

.................................................................................. 2.2.5 Branch plate stress distribution 2-22

3 . FEM ANALYSiS OF LONGITUDINAL BRANCH PLATE-TO-RECTANCULAR HSS MEMBER CONNECTIONS

3.1 FEM models .......................................................................................................................... 3-1

................................................................................................... . 3.1 - 1 Bomdary conditions 3 I

..................................................................................... 3.1.2 Mode1 geomerry and meshing 3-j

..................................................................................................... 3.1 3 ~Material properties 3-5

3.2 FEM results ........................................................................................................................... 3-6 .............................................................................................. 3.2.1 FEM model verification 3-6

3.2.2 Parametric modellingprogramme ............................................................................. 3-9

..................................................... 3.2.3 Determination of the critical loading combination 3-11

......................................... 3 .2.4 Parame tric modelling of the critical loading combination 3-15

3 . 7.5 Branch plate stress disnibution .................................................................................. 3-18

4 . EXPERIMENTAL STUDY OF ALTERNATIVE BRANCH PLATE-TO-RECT~GULAR HSS MEMBER CONNECTION TYPES

....................................................................................................................... 4.1 Test specimens 4-2

4.1.1 Test set-up ................................................................................................................ 4-5

4.2 Test results ............................................................................................................................. 4-5

............................................................................................ 4.2.1 Loaddeformatim curves 4-5

.................................................. 42.7 Goveming strength versus serviceabiii@ condition 4-7

..................... 4.3 Overall design of brancb plate-to-rectangular HSS member connections I I 1

....................................... 4.3.1 Single branch plate and rhrough branch plate connecrions 4-11

......................................................... 4.3.2 Sllrened longitudinal branch plate connenions -1- 12

.......................................................................... 4.3.3 Transverse branch plate connections 4-13

......................................................................................................... 4.3.4 Connecrion cosrs 4-14

................................................................................... 4.3.5 Practicai limits of appiicability 4-15

5 . FEM EVALUATION OF STIFFENED LONGITUDINAL BIUNCH PLATE-TO-RECTA~YGULAR HSS MEMBER CONNECTIONS

.......................................................................................................................... 5.1 FEM mdels 5-1

................................................................................................... 5.1 . 1 Boundav conditions 5-1

5.1.2 .b fodel geometry and meshing ..................................................................................... 5-5

..................................................................................................... j 1 3 Material properties 5-6

.............................................................................................. 5.1.4 FEM mode1 verijkation 5-8

j . 1.5 Paramefiic modelling programme .............................................................................. 5-11

5.2 Required stiffening plate thickn- ..................................................................................... 513

5.3 B r n d plate stress distribution ....... .......................................... ..................................... 5-18

5.4 Summary of Cbapter 5 ................................................................................................... 5-20

vii

6 . FEM ANALYSIS OF THROUGH BRANCEI PLATE CONNECTIONS

.......................................................................................................................... 6.1 FEM models 6-1

6.1.1 Boundary conditions ................................................................................................... 6-1

6.1.2 Mode! geomeny and meshing ..................................................................................... 6-3

..................................................................................................... 6.1.3 hfateriai properties 6-5

.............................................................................................. 6.1.4 FEM modei verifcation 6-6

.............................................................................. 6.1 -5 Parame fric modelling programme 6-8

................................................................................................................. 6.2 Analysis of results 6-11

7.1 Notional deformation limits ............................................................................................ 7-2

7.1.1 Development of the 3%bo utfimate deformation limit ................................................. 7-3

7.2 Existing methods for determining the yield load from loaddeformation curves .......... 7-6

7 3 Proposed FEM-based approach for deteminiog the yield load from ...................................................................................................... load-deformation curves 7-10

8 . CONCLU~IONS & RECOMMENDATIONS FOR FURTHER RESEARCH

...................................... 8.2 General design formula for EISS conwcting face plastifiçation 8-1

.............................................................................. 8.2.1 Influence of main member preioad 8-2

8.2.2 Serviceabilis, condition ............................................................................................... 8-3

8.3 Design considerations for sporific connection types ........................................................ 8 4

................................... 8.3.1 Single branch plate versus through branch plate connections 8-4

......................................................... 8.3.2 Stifened longitudinaZ branch p h e connections 8 4

........................................................................ 8.3.3 Transverse branch plate connections 8-5

8.4 Range of applicability ............................................ .......................................................... 8-6

8.5 Recornrnendations for further research ............................................................................ &7

... Vl l l

APPENDIX A: Material properties ................................................................................................... A-1 .................................................. APPENDIX B: Deformation profile and stress distribution plots 5 1

Table 2-1: Experimental test specimen details for longitudinal branch plate-to-rectangular HSS member connections ..................................................................................... 7-8

Table 2-2: Experimental test results for longitudinal branch plate-to-rectangular HSS rnember connections ......................................................................................... 1-1 6

Table 3-1: Experimental test and FEM modelled results for longitudinal branch plate connections ................................................................................................ 3-8

Table 3-2: FEM results for a longitudinal branch plate-to-rectangular HSS rnember connection subjected to four possible loading sense combinations ......................... 3- t O

Table 3-3: FEM results for longitudinal branch plate-to-rectangular HSS member connections subjected to the critical loading sense combination ................................................. 3- 16

Table 3-4: Required branch plate thickness to satisQ the calculated ........................................................................................... connection capacity (Pr) 3-1 9

Table 4-1 : Experimental test specimen details and results for alternative branch plate connections ...................................................................................................... 4 4

Table 4-2: CANICSA-S16.1-94 rectangular HSS classes .......................................................... 4-9

Table 4-3: Relative connection costs [adapted from Sherman (1996)] ..................................... 4-1 4

Table 5-1: Experimental test and FEM modelled results for stiffened longitudinal branch plate-to-rectangular HSS member connections .......................................... 5-2

Table 5-2: Parametric FEM modelling ma& for a stiffened branch plate-to-rectanguiar .......................................................................................... HSS member connection 5-1 2

Table 5-3: FEM and predicted results for stiffened branch plate-to-rectanguIar ......................................................................................... HSS member connections 5- 1 5

Table 6-1 : Experimental test and FEM modelled results for single branch plate and through branch plate connections ...................................................................... 6-7

Table 6-2: Parametric FEM modelling matrix for a single branch plate and a corresponding through branch plate connection ................................................. 6-9

.... Table 6-3: Parametric FEM modelling matrix for variable branch plate length connections 6-10

Table 6-4: FEM results for single branch plate and corresponding through branch ...................................................................................................... plate connections 6- t 3

Table 6-5: FEM results for variable branch plate length connections ....................................... 6-14

Table 7-1 : Parametric FEM modelling matrix for a generalised rectangular HSS ..................................................................................................... T-type connection 7- 1 1

Table 7-2: FEM results for the proposed rigid. perfectly-plastic yield load ............................................................................................... determination method 7- 1 7

Table A l : Measured material properties ............................................................................... A- l

Figure 1- 1 : Simplified lateral wind loading on a planar braced frame ........................................ Figure 1-2: Detail B from Figure 1-1 showing a typical longitudinal branch

plate-CO-HSS column connection ........................... ... ........................................... Figure 1-3: A diagonal circular HSS bracing member connected to a square

HSS column via a longitudinal branch plate ........................................................... Figure 1-4: Longitudinal branch plate-to-1-section member versus HSS rnember connections ..

Figure 1-5: Branch plate-to-rectangular HSS member connection types .................................... Figure 1-6: Punching shear in HSS wall adjacent to fillet weld ...............................................

Figure 1-8: Classical normal stress versus plastic moment capacity interaction mode1 ............. Figure 1-9: Stepped yield line method for the analysis of inclined yield Iines ...........................

Figure 1-1 0: General punching shear mode1 ................................................................................. Figure 1-1 1: Combined flexural and punching shear yield line model

fiom Davies and Packer (1982) ................................................................................ Figure 1-12: Analytical model failure envelope for a longitudinal and a transverse

branch plate-to-rectangular HSS member connection .............................................. Figure 1 . 13 : Variation of stress distribution in a transverse branch plate for full widtb

connections from Davies and Packer (1982) ............................................................ Figure 1-14: "Stress flow" for transverse branch plate-to-rectangular HSS member

connections from Wardenier (1982) ......................................................................... Figure I . 15: Typical loaddeformation behaviour for an HSS connection

............................................................................................. from Wardenier (1 982)

Figure 1-1 6: Transverse branch plate-to-rectangular HSS connections analysed by Lu and Wardenier (1995) .....................................................................................

Figure 1-17: Typical test specimens of Dawe and Guravich (1993) ............................................. Figure 1-18: Experimental test specimen and corresponding FEM model of a stiffened

circular HSS-to-HSS T-type comection from Fung et al . (1999) ...........................

Figure 1-19: Stiffened rectangular HSS-to-HSS T-type connections studied by Korol et al . (1982) ................................................................................................

Figure 1-20: Yield line patterns and corresponding solutions for stiffened rectangutar HSS-to-HSS T-type connections fiom Korol et al . (1982) .......................................

............. Figure 1-2 1 : Types of shear rab-to-HSS column connections tested by Sherman (1996)

Figure 1-22: Beam-to-HSS column connection test set-up by Sherman (1996) ........................... Figure 1-23: Possible failure modes for shear loaded longitudinal branch plate-to- HSS

colurnn connections h m Saidani and Nethercot (1994) .........................................

xii

Figure 1-24: Test set-up by Dawe and Mehandale (1995) ......................................................... 1-3 1

Figure 1-25: Yield line patterns of Dawe and Mehandale (1995) ................................................. 1-37

Figure 1-26: Specimen details and test apparatus of Jarrett and Malik (1993) ............................. 1-33

Figure 1-27: Deformation of HSS connecting face from Jarrett and Malik (1993) ...................... 1-34

Figure 1-28: Load-deformation response of branch plate-to-HSS column connections from Jarrett and Malik (1 993) ................................................................................ 1-35

Figure 1-29: Details of stiffened longitudinal branch plate-to-rectangular HSS column connections tested by Yeomans (200 1) .................................................................. : 1-36

Figure 1-30: Effect of stiffening plate thickness observed by Yeomans (2001) ........................... 1-37

Figure 2-1 : 90" longitudinal branch plate test specimens after testing ........................................ ............ Figure 2-2: 4S0 longitudinal branch plate test specirnens ailer testing ................... ...

Figure 2-3: 30'. 45'. 60'. and 90" longitudinal branch plate test specimens after testing ........... Figure 2-4: 90' longitudinal branch plate-to-rectangular HSS member connection

....................................................................................................... geomemc details

Figure 2-5: 90" Longitudinal branch plate-to-rectangular HSS mernber connection test set-up ..

Figure 2-6: 30'. 45". and 60" longitudinal branch plate-to-rectangular HSS member connection geometric details ....................................................................................

Figure 2-7: 45" longitudinal branch plate-to-rectangular HSS member connection test set-up ..

Figure 2-8: Standard arrangement of LVDTs and strain gauges ................................................. Figure 2-9: Standard LVDT set-up ..............................................................................................

Figure 2- 10: LVDT set-up for 30" test .......................................................................................... Figure 2-1 1: Load-deformation curves for various longitudinal branch plate-to-HSS

member connection angles ........................................................................................ Figure 2-12: Load-deformation curves for the 45' longitudinal branch plate-to-HSS

member connection angle test series ........................................................................ Figure 2-13: Load-deformation curves for the 90' longitudinal branch plate-to-HSS

member connection angle test series ........................................................................ Figure 2- 14: Typical tex-out cracking pattern for longitudinal branch

plate-to-rectangular HSS member connections ........................................................ Figure 2-1 5: Typical HSS connecting face deformation profile for 90' longitudinal

branch plate connections .......................................................................................... Figure 2-16: Typical HSS connecting face deformation profile for 45" longitudinal

branch plate connections .......................................................................................... Figure 2-17: Typical branch plate stress distribution for 90" connections .................................... Figure 2-1 8: Typical branch plate stress distribution for 45" connections .......................... .. ....

xiii

Figure 3-1: FEM modelling of longitudinal branch plate-to-rectangular HSS . rnember experimental test specimens .............................,....................................... 3-2

Figure 3-2: Parametric FEM modelling details for longitudinal branch plate-to-rectangular HSS member connections ....................... .. .......................... 3-4

Figure 3-3: Material stress-strain curves .............................................................................. 3-5

Figure 3-4: FEM and experimentat load-deformation curves Cor longitudinal branch plate connections ......................................................................................... 3-7

Figure 3-5: FEM venus experimental results for longitudinal branch plate connections ........... 3-7

Figure 3-6: Connection strength reduction factor, f(n), curves for column compression ........... 3-12

Figure 3-7: Connection strength reduction factor, f(n), curves for column tension .................... 3-13

Figure 3-8: P-A effect in branch plate-to-rectangular HSS rnember connections ....................... 3-13

Figure 3-9: Connection strength reduction factor. Rn). curves for the critical loading sense combination ................................................................................................. 3-17

Figure 3-10: Experimental and FEM branch plate stress distributions ......................................... 3-18

Figure 3-1 .! : FEM mode1 for a branch plate-to-HSS 89x89fl.53 connection .............................. 3-20

Figure 3-1 2: Branch plate stress distribution ................................................................................ 3-21

Figure 4-I: Longitudinal branch plate-to-rectangular HSS member connection face deformation .................................................................................... 4-1

Figure 4-2: Branch plate-to-rectangular HSS member connection types .................................... 4-2

Figure 4-3: Testing arrangements for alternative branch plate-ta-rectangular ......................................................................................... HSS member connections 4-3

Figure 4-4: Loaddeformation curves for alternative branch plate-to-rectangular ......................................................................................... HSS member connections 4-6

Figure 4-5: Governing strength versus serviceability limit States for experimental and FEM branch plate-to-rectangular HSS member connections ................................... 4-8 . . Figure 4-6: StiRening plate nomenclature ............................................................................... 3-12

Figure 4-7: PracticaI limits of applicability for branch plate-to-rectangular HSS member connections ................................................................................................. 4-16

Figure 5-1 : FEM modelliag details for stiffened branch plate-to-rectangular HSS mernber connections ................................................................................................. 5-3

Figure 5-2: Effect of mode1 boundary conditions on the FEM loaddefonnation behaviour of a stiffened branch plate-to-rectangular HSS member connection ........................ 5-4

..................................................................................... Figure 5-3: Material stress-strain curves 5-6

xiv

Figure 5-4: Effect of steel matenal type on the load-deforrnation behaviour of a FEM ............... modelled stiffened branch plate-to-rectangular HSS rnember connection 5-7

Figure 5-5: FEM and experimental load-defonnation curves for stiffened longitudinal branch plate-to-rectangular HSS member connections ............................................ 5-9

Figure 5-6: FEM versus experimental results for stiffened branch plate-to-rectangular HSS member connections ......................................................................................... 5-10

Figure 5-7: Loaddeformation curves and relative connection capacity curves showing the typical effect of stiffening plate thickness for a FEM modelled connection ............ 5-14

Figure 5-8: Required stiffening plate thickness to achieve a 95% relative connection capacity .................................................................................................. 5-17

Figure 5-9: FEM branch plate stress distribution for a main HSS 305~305~6.35 ......................................................................................................... Class 3 member 5-19

Figure 5-1 O: FEM branch plate stress distribution for a main HSS 127~127~6.35 Class l member ........................................................................................................ 5-20

Figure 6-1 : FEM modelling of single branch plate and through branch plate experimental test specimens ................................................................................... 6-7

Figure 6-2: Overall flexural action of the HSS test specimen ..................................................... 6-3

Figure 6-3: Parametric FEM modelling details for single branch plate and ............................................................................. through branch plate connections 6-4

Figure 6-4: Material stress-strain curves ................................................................................... 6-5

Figure 6-5: FEM and experirnental loaddeformation curves for single branch plate and through branch plate connections ..................................... .. .......... 6-6

Figure 6-6: Loaddeformation response for FEM modelled single branch plate and ..................................................... corresponding through branch plate connections 6-11

Figure 6-7: Loaddeformation response for FEM modelled variable branch plate length connections ............................................................................ 6-12

Figure 7-1: Typical welded HSS connections from Lu et al . (1994b) ........................................ 7-1

Figure 7-2: FEM loaddeformation curves for transverse branch plate-to-HSS column connections from Lu and Wardenier (1995) .......................................................... 7 4

Figure 7-3: Effect of a defonnation limit on observed parameter influences ............................................................................................. from Wardenier (2000) 7-5

Figure 7-4: Example of the classical bi-linear tangent yield load approximation method ...................................................................................... [Zhao and Hancock (1 99 1)] 7-6

Figure 7-5: Example of the classical bi-linear tangent yield load approximation method ................................................................................................ [Packer et al . (1 980)] 7-7

Figure 7-6: Definition of yield load by Kurobane et al . (1984) ....................... .. ................... 7-8

Figure 7-7: Definition of yield load by Kamba and Taclendo (1998) ......................................... 7-9

Figure 7-8: Rectangular HSS T-type connection ........................................................................ 7-10

Figure 7-9: Bi-linear tangent method for detennination of connection yield load ...................... 7-12

Figure 7-10: Log-Log plotting method for determination of connection yield load ..................... 7-13

Figure 7-1 1: Notional deformation limit rnethod for determination of connection yield load ..... 7-14

Figure 7-1 2: Proposed rigid. perfectly-plastic yield load determination method .......................... 7-15

Figure Al: Typical coupon taken h m rectangular HSS and steel plate stock .......................... A-l

Figure A2: Duplicate rectangular HSS coupon locations ........................................................... A-1

Figure A3: HSS 178~127~7.6 tensile coupon curves ............................................................ A-2

................................................................. Figure A4: HSS 178~127~4.8 tensile coupon curves A-2

Figure A5: 13.1 mm plate stock tensile coupon curves ............................................................. A-3

Figure A6: 9.4 mm plate stock tensile coupon curves ............................................................... A-3

Figure A7: 6.3 mm plate stock tensiIe coupon curves ................................................................ A 4

Figure B 1 : HSS connecting face deformation profile for specimen 90LPO ............................... ............................................... Figure B2: Branch plate stress distribution for specimen 9OLPO

Figure B3: HSS connecting face defonnation profile for specimen 90LP40 ............................. Figure B4: Branch plate stress distribution for specimen 90LP40 ............................................. Figure B5: HSS connecting face defoimation profile for specirnen 90LP60 .............................

Figure 86: Branch plate stress distribution for specimen 90LP60 ....................... .,. ............. Figure B7: HSS comecting face deformation profile for specimen 45LPO ............................... Figure B8: Branch plate stress distribution for specimen 45LPO .................................... .... ....... Figure 99: HSS connecting face deformation profile for specimen 45LP20 ..........................

............................................. Figure B 10: Branch plate stress distribution for specimen 45LP20

Figure B 1 1 : HSS connecting face deformation profile for specirnen 45LP40 ............................. ............................................. Figure B 12: Branch plate stress distribution for specimen 4SLP40

Figure B13: HSS comecting face deformation profile for specimen 30LPO ............................... ............................................... Figure B14: Branch plate stress distribution for specimen 30LPO

............................... Figure B 15: HSS connecting face defonnation profile for specimen 60LPO

.............................................. Figure B 16: Branch plate stress distribution for specimen 60LPO

xvi

muer case svmbols

C, = factored compressive resistance of a member or component

FO = applied main member normal stress due to axial load plus bending

F,,, = uniform shear stress of main rnember material [from Davies and Packer ( l982)]

Fu, F*, Fui = ultimate stress of material, uhimate stress of main member, ultimate stress of connecting branch member

= ultimate stress of base metal material

Fu(weld) = ultimate stress of weld material

F,, Fb0, FYI = yield stress of material, yield stress of main member, yield stress of connecting branch member

& = initial tangent stifiess of a loaddeformation curve [refer to Figure 7-71

12f = bending moment

No = toial axial Ioad (preload) applied to main HSS mernber

P, PL = branch plate load, component of branch plate load normal to HSS connecting face

Pr = factored branch member load

Pnextbtphe = branch plate load fora stiffened branch plate-to-rectangular HSS member connection

P , = goveming branch plate capacity given by the lesser of PL3%and 1 .5P,Io, [fiom Lu et al. (1 994b)]

P(n), P(n=O) = branch member load with a main member preload ratio (n), branch member load without a main member preload (n = 0)

PQ = connection strength predicted by punching shear [from Davies and Packer (1982)]

Pngid.plisac = proposed FEM-based rigid, perfectly-plastic yield load determination

P-ngd-pLuc = branch plate load benchmark for a "perfectly-rigid" stiffened branch plate-to- rectangular HSS member co~ec t ion [refer to Section 5.21

P*J% = connection load detennined by a 1%& serviceability deformation limit

P*, P e = shear component of branch plate load, tension component of branch plate load

Pu = ultimate (maximum sustained) connection load

PK3% = connecfion load detennined by a 3%bo ultimate deformation limit

P,, PM&,, = ultimate (or design) branch plate load using an effective width criterion [fiom Wardenier et al. (1981), and Davies and Packer (1982)l

Pr = connection çtrength predicted a plastifkation mechanism in the HSS conoecting face [using Equation (1-9)j

xvii

PYK = yield line solution for stiffened rectangular HSS connections from Korol et al. (1982) [refer to Figure 1-20]

P,(n), P)(n=O) = calculated connection yield load [using Equation (1-9)] with a main member preload ratio (n), calculated connection yield load [using Equation (1-9)] without a main membet preload (n = O)

PyQ = connection strength predicted by combined moment and punching shear [ h m Davies and Packer (I982)l

PWld = defined "yield load" determined h m a loaddeformation curve

T, = factored tensile resistance of a member or component

V, = factored shear resistance of a member or component

lorver case svmbols

a = weld size (throat size)

bo, Bo = outside width of main member, effective width (= bo - to)

I%ba = connecting face deformation of 1 % of the main HSS member width (serviceability deformation limit)

3%bo = connecting face deformation of 3% of tfie main HSS mernber width (ultimate deformation limit)

b1,6'1, 61' = outside width of connecting branch member, effective width (= b1 + 2w), unrestrained width (= bl - 2w - rb), transverse to the main HSS member âuis

bb = outside width of a rectangular HSS branch member [from Figure 1-20]

b, = effective width of a transverse branch plate [ h m Rolloos (1969), Wardenier et a1.(198 I ), and Davies and Packer (1982)l

bhwdih = flat width of rectangular HSS member face [refer to Figure 4-71

blowabound = approximate minimum practical connection width [refer to Figure 4-71

blt = outside width-to-wall thickness ratio for an HSS rnember cross-section

do, dl = outside diameter of main HSS member, outside diameter of connecting branch HSS member

eb, eV = eccentricity of co~ect ing branch plate with respect to main membet centre line. eccentricity of applied branch plate shear load (Ph) with respect to the stiffening plate connecting face [ h m Figure 1-29]

f(B) = function of p, as it relates to the effective width failure criterion from Wardenier et al. (1981) [refer to Figure 1-14]

fin) = function (or factor) to quanti@ the influence of an applied normal stress in the main HSS mernber on the strength of the connection [= P(n) / P(n=O)]

ho = outside depth of main HSS member

hl, N I = outside length of connecting member, effective outside length of connecting member (= hllsinû + 2w), parallel to the main HSS mernber axis

hb = outside length of a rectangular HSS branch rnember [from Figure 1-20]

P = I i i t of shear yielding in main member from Davies and Packer (1982) Figure [-1 I]

m , ~ = plastic moment capacity of the main HSS member watl, per unit length, without an applied normal stress (= ~ , , , r ~ 14)

m,q,, = plastic moment capacity of the main HSS member wall per unit length, with an applied normal stress to yield stress ratio (n = FdFJ0 )

n = main member "prestress" (or normal stress due to axial load plus bending) ratio (= FdF'o)

to,tl = wall thickness of main HSS rnember, wall thickness of connecting branch HSS rnember

t b = branch plate thickness

t, t ~ ~ , = stiffening plate thickness, minimum required stiffening plate thickness

w = weld size (leg length)

sc' = limit of shear yielding in main mernber from Davies and Packer (1982) [Figure 1-1 11

xi, xz = stress blockdimensions [refer to Figure 1-81

Greek svmbols

a = angle of inclination of a yield Iine [from Figures 1- 1 1 and 1-20]

p, P. = nominal width ratio (= bllbo), effective width ratio (= b'J&), unrestrained width ratio (= bl*/&)

PlhwYtdlh = flat width width ratio (= bn,&l bo) [refer to Figure 9-71

Plowabocmd = approximate minimum width ratio (= blauoboimd/ bO) [refer to Figure 4-71

A, Ai = connection deformation, normal component of connection deformation

Ay = connection deformation at the calculated yieId load [Pr using Equation (1-9)]

E, hg & = strain, engineering strain, true strain [refer to Equation (3- I)]

4, & = Limit States Design resistance factor, Limit States Design resistance factor for weld materia1

y' = nondimensional position of end of punching shear zone (= 2iW0) [from Davies and Packer (1982)l

2fi,2y'o = width-to-thickness ratio of main member (bdto), effective width-to-thickness ratio of main member (= b'dto),

2y'l = effective width-to-thickness ratio of stiffening plate (= b'tlt,,)

2 f ~ = stiffening plate thickness parameter ratio, (2fo)/( 2 f i )

q, q' = branch member length to main member width ratio (= hllbo),

effective branch member length to main member width ratio (= HllHo)

0 = angle of inclination with respect to main i-iSS member axis

o, O,, CI,, = stress, engineering stress, true stress [refer to Equations (3-1) and (3-2)]

a p ~ = stress in branch plate member

u = Poisson's ratio [taken to be 0.3 for structural steel]

ucronvms und terminoliwies

AiSC = Amencan hstitute of Steel Construction

ASCE = American Society of Civil Engineers

CiDECT = Comité International pour le Développement et l'Étude de la Construction TubuIaire

C[SC = Canadian lnstitute of Steel Construction

CSA = Canadian Standards Association

FEM = Finite Element Method

HSS = Hollow Structural Section

iiW = International institute of Weiding

KT- = co~ection involving three b m h members on the same side of a main member

LSD = Limit States Design

LVDT = Linear Variable Differential Transformer

NA = Neutra1 Axis

NSERC = Natural Sciences and Engineering Research Council of Canada

OGS = Ontario Graduate Scholarship

RHS = Rectangular Hollow Section

T- = connection involving one branch member and a main member at a 90'' angle

X- = connection involving two or more branch members on opposite sides of a main member, with the force being transferred through the main member

Y- = connection involving one branch mernber and a main member at a non-90" angle

1.1 Introduction

Hollow Structural Section (HSS) membets are becoming a popular alternative to steel open section

members, particularly due to their aesthetic appeal with exposed steelwork. This architectural trend has

been well documented by Eekhout (1996). in many instances, the superior compression resistance of

hollow section steel mernbers over steel open section members has resulted in Iighter and cheaper

compression members if HSS are used. This is even in spite of the higher cost of HSS per tonne relative

to open section members. Moreover, HSS compression members typically have a Iower surface area

(hence lower painting costs), incur lower transportation costs (due to their lighter weight) and are easier to

erect (due to their lighter weight) relative to open sections (Packer and Henderson 1997). Hence, project

cost savings are also driving the adoption of HSS for colurnns and in trusses (where approximately half

the members can be expected to be in compression).

One impediment to the more widespread utilisation of HSS' chat has been cited by industry in the

past, has been the insuffïciency of design guidance for connections to HSS members. AIthough a great

deal of synthesised connection design information has been published in the last 10 years, the design

guidance is not totally cornprehensive and some types of connections have been overlooked. An example

of the latter is the case of an axially-loaded plate welded longitudinally to the face of a HSS member. The

lack of design recommendations for this connection type (or inappropriate recommendations in some

cases, where advice had been extrapolated frorn HSS-CO-HSS connections) was noted in Europe by

CIDECT (Comité International pour le Développement et l'Étude de la Construction Tubulaire) in 1993

and also by industry in Canada, independently, soon after. As a result of the latter the Steel Structures

Education Foundation (a part of the Canadian institute of Steel Consûuction) issued a Request for

Proposals on the topic of, "Plate Connections to HSS Members ut Bruce Points" in I995. The seed

rnoney resulting from chat gant in 1995/1996 eventually resulted in this doctoral thesis. between 1996

and 200 1 .

Longitudinal plates, welded to HSS members and subject to an axial load, are common in low and

medium-rise steel braced hunes, such as illustrated in Figure 1-1, where the governing lateral load

condition is due to wind. With such connections the plate is typically shop-welded to the column and

then, for erection convenience, field-bolted to the connection material attached to the end of the brace

member. A typical comection arrangement is shown in Figure 1-2. Neighbouring steel elements, such as

the column base-plate in Figure 1-2 or the roof beam at Connection A in Fiyre 1-1, may sewe to stiRen

the longitudinal branch plate-to-HSS connection, but this depends on the detailing arrangement selected

by the engineerifabricator, and in many circumstances there may be no connection restraint f?om nearby

steel attachments. A photograph of a connection similar to that in Figure 1-2 is shown in Figure 1-3. In

the latter case the longitudinal branch plate is partially stiffened by also welding to the base-plate.

Welded longitudinal branch plate-to-HSS rnember connections also occur in HSS trusses, where a plate is

sometimes welded to a truss chord member to attach a "hanger load" to the truss. In this case the

likelihood of connection support fiom neighbouring steel attachrnents is remote. In this thesis the general

longitudinal branch plate-to-HSS member connection is studied assuming no support or influence from

neighbouring steel attachments. (It is worthwhile noting here that in a later part of this thesis, where

paramehic FE modelling of connections is undertaken, it is show that neighbouring steel attachrnents

need to be very close to the longitudinal branch plate to have any influence on the connection resistance:

i.e. within a distance of about the HSS rnernber width).

Figure 1-1: Simplikd lateral wind loading on a planar braced frame

Square HSS column

Cucular HSS bracing member welded to a Tee end connection which is subsequently bolted to a longitudinal plate on the colurnn

Figure 1-2: Detail B lrom Figure 1-1 showing a typical longitudinal branch plate-to-HSS column connection

Figure 1-3: A diagonal circuler HSS bracing member coonected to a square HSS column via a longitudinal branch plate

(Note Iihat in th& instance the plate is partially stiffened by ah0 weIding IO the base-plute)

The attachment of longitudinal branch plates dong the HSS member axis is a habit carried over from

sirnilar plate connections to 1-section (or wide flange) members. Indeed, in braced hmes, such plates are

ememely convenient for connecting one or more bracing members at any bracing mernber angle. A

slight variant is sometimes produced when the longitudinal branch plate is offset from the column cenue-

line so that the centre-line of the brace member cm coincide with that of the column. There is an

important difference, however, between the behaviour of the longitudinal branch plate-to-1-section

memkr connection and the counterpart connection to a HSS member. For the 1-section member the

branch plate is welded at (or very close to) the centre of the connecting flange. so the axial load from the

branch plate is transferred directly to the web of the member. Thus, the web acts like a stiffener for the

connecting flange. The situation is quite different for the case of the rectangular HSS rnember because

the axial load frorn the branch plate must be carried into the two remote webs of the HSS member, while

the connecting face of the HSS is subjected to considerable bending, This phenornenon is illustrated in

Figure 1-4.

(a) Branch phte to 1-section mernber

(b) Branch plate-to-reciangular HSS mernber

Figure 1-4: Longitudinal branch plate-to-1-section member versus FiSS member conneetions

As a result of this connection flexibility, the conventional longitudinal branch plate-to-rectangular

HSS member connection tends to result in excessive distortion or plastification of the HSS connecting

face. Such a connection hence has a low design resistance that is govemed by the formation of a yield

Iine mechanism. In limit States design terms, this design resistance should satisfy an ultimate deformation

lirnit and a serviceability deformation limit for the HSS connecting face. Despite having a relatively low

connection design resistance, the longitudinal branch plate connection may still suffice as a wind bracing

connection in some low-rise fiames with HSS columns, since the forces in the wind bracings will be low.

With this type of connection king very flexible, it is not suitable for stnictures for which the design is

governed by dynamic loads. Thus, the longitudinal branch plate connection is suitable for structures

under quasi-static loading (including wind), but not fatigue-loaded structures or seismic-loaded structures.

Where a branch plate-to-HSS member connection is still desired, but the design resistance of a

longitudinal branch plate is inadequate, an alternative stronger plate m g e m e n t must be sought. For

example, this would likely occur in a medium-rise braced frame where the bracing member force in the

bonom stories would be significant. In such situations alternative branch plate connections, which would

be expected to have higher connection resistances, are:

A through branch plate connection

A stiffened branch plate connection

A transverse branch plate connection

These connection types are illustrated in Figure 1-5.

(a) Longitudinal branch plate

(b) Through

branch plate

(CI Stiffened

branch plate

. . A.. [RI l

(4 Transverse branc h plate

Figure 1-5: Bnnch plate-to-rectangula HSS member connection types

1.2 Analytical models

1.2.1 Weld and brmrch plate failute

The three global failure modes for a welded branch plate connection are failure of the branch plate.

failure of the weld, and failure of the HSS connecting face. Relatively simple cnteria for the branch plate

thickness and the weld size can be applied to the design of these two components. Sherman (1996) has

presented simple design recommendations to directly relate the strength of the fillet welds and the branch

plate (shear tab) to the strength of the HSS connecting face. Shermads recommendations were based on

shear tabs but similar reasoning can be applied to longitudinal branch plates (shear cabs) Ioaded in tension

rather than shear. Figure 1-6 shows a schernatic representation of a welded longitudinal branch plate-to-

rectangular HSS rnember connection.

uniform punching local punching shear :

/ locai punching shear mpiures

Figure 1-6: Punching shear in HSS wall adjacent to fillet weld

If one uses the Limit States Design resistance expressions for fillet welds in the Canadian structural

steelwork specification (CANICSA-S16.1-94) then the weld resistance per unit length is given by the

Iower o t

Y, = 0.674, (weld leg, w)(unit length)F&,,, , for base metal failure, and

V, = 0.67$,(weld throat,a)(unit length)F&,

for the weld metal failure, neglecting any enhancement in fillet weld strength due to the direction of

loading (which is the practice of most connection detailers). 4, is specified (CANICSA-S 16.1-94) as 0.67.

Presuming that the ultimate strength of the weld metal is approximately the same as that of the base

metal, (which is m e since for 300W and 350W grade steels, F* md) = 450 MPa and the matching

electrode E480XX has Fdwcld) = 480 MPa), then failure tIirough the weld throat will be criticai [Equation

(1-2)] since the weld leg (size) = f i a . By only considering a unit length of the weld joint any non-

uniform stress distribution applies equally to the weld throat, weld base metal zone. to the longitudinal

branch plate, or the wall of the HSS.

The punching shear strength of the HSS connecting face can be expressed as:

wherein the same constant (0.67) is used as for weld failure to relate ultirnate shear strength to ultimate

tensile strength. If one also presumes that a resistance factor (4 = 0.75) can be used in Equation (1-3), (as

adopted by AISC for punching shear failure modes using the uhimate stress), then weld failure [Equation

(1-2)] would not be critical in design, over HSS wall punching shear, provided that:

weld throat size, a 2 - - [ ::;; l[:::,*,)to

For the sole Canadian HSS grade (350W) and matching weld rnetal, as described above,

weid throat size, a 2 1 .O5 r, ( 1 -5a)

weld leg size, w 2 1.48 to ( 1 -5b)

Weld sizing on this basis may frequentiy be excessively conservative, but Equation (1-5) also gives

an upper bound on the weld size. In general, it is preferable to proportion the welds on the basis of the

actual load applied to the connection, and at the same tirne empioy an effective length concept for the

weld (and branch plate), as discussed later in this thesis, to account for non-uniform loading on the weld

(and branch plate).

One can also treat the longitudinal branch plate in a similar rnanner as done above for the weld joint.

The limiting tensiIe or compressive resistance of the branch plate material can be expressed (per unit

iength) as:

where bl and FyI represent the thickness and yield strength of the longitudinal branch plate respectively.

Adopting a resistance factor (4) of 0.9 in Equation (1-6), yielding of the branch plate would not be critical

in design, over HSS wall punching shear, provided that:

where the number 2 on the right hand side of the equation acknowledges that punching shear must occur

on both sides of the longitudinal branch plate and ignores the small arnount of punching shear at the top

and bottom edges ofthe branch plate. Equatior, ii-ïa) can be simplified to:

thickness of Iongitudi~I branch plate, 6, 2 1.12 - t, (3 As with the weld, the branch plate is most likely going to be proportioned on the maximum load

applied to the branch plate, in which case one should also employ an effective length concept for the

branch plate, as discussed later in this thesis, to account for any non-uniforrn loading in the branch plate

(and hence weld).

The thickness of the HSS main member, to, is most likely going to be pre-determined prior to the

branch plate or weld size by the building structural engineer. The resistance of the HSS connecting face

is considered further in the next section.

1 2.2 General yielding of the rectanguiw HSS connecting face

The yield line rnethod of analysis has been used successfully for estimating the strength of different

HSS connections due to development of yield line mechanisms (or pladfication) of the connecting face

of the main member. Figure 1-7 shows a general case of a rectangular HSS co~ection. The yield

strength of a 90" connection without any applied normal stress present in the main HSS member was first

derived by Jubb and Redwood (1966) as:

A ment analysis by Cao et al. (1998a and 1998b) has accounted for non-90" connections as well as

the influence of an applied normal stress present in the main HSS mernber resulting in the following

formula:

applied stress (6 ) n =

yield stress (5,)

Hogging Saggtng Yield Lines Yieid Lines

Figure 1-7: Yield line pattern for an axially loaded rectangular HSS connection

in Equation (1-9) the wall thickness (to) and weld leg size (w) are taken into account, as proposed by

Davies and Packer (1982). The plastic hinges around the branch can be assumed to be around the edge of

the weld and those at the main member corners along the side wall centre lines. Hence the hl. bo and P in

Equation (1-8) were replaced by "effective values" hll, and B' where:

The plastification of the HSS connecting face is mainly caused by the nomai component of the

applied branch plate load for non-90" connections. The term Pr sin0 in Equation (1-9) represents the

normal component of the applied branch plate load. The term d s accomts for the reduction in

connection strength due to the influence of an applied normal stress in the connecting face of the main HSS

mernber where:

applied normal stress due to axial loading + bending F, n = -- - yield stress F y o

The influence of this applied normal stress in the connecting face of the HSS member on the overall

connection capacity (Pr) c m be described using a classical normal stress versus plastic moment capacicy

interaction model. Figure 1-8 shows the classical normal stress versus plastic moment capacity interaction

rnodel and how it applies to a particular yield line [identified as yield line O in Figure I-8(a)] as an

example. If no applied normal stress is present [i-e. Fo = O in Figure 1-8(b)] then the plastic moment

capacity of the HSS connecting face, per unit length of a yield line is given by the classical stress block

solution:

However, if an applied normal stress (Fo) is considered, then the plastic moment capacity of the HSS

connecting face, per unit length of a yield line that is oriented perpendicular to the applied normal stress can

be calculated using a classical stress block diagram as show in Figure 1-8(c). Figure 1-8 shows an exampie

case of the interaction between an applied compressive stress and a sagging yield line that is perpendicular

to the applied stress. The applied normal force, per unit length (= Foro), s h o w in Figure 1-8(b) is in

equilibriurn with the intemal normal force [= Ffl(xl -xz)] shown in Figure 1-8(c)ii thus:

(a) Example yield line pattern h m Figure 14

(b) Unit length of yield line

( i ) Axial sness + bending stress (ii) Axial mess component (üi) Bending sness component

(c) Stress block representation for yield line O

Figure 1-8: Classical normal stress venus plastic moment capacity interaction mode1

From the defined geomeby shown in Figure 1-8(c)i:

fO = XI f X2

Solving forxz from Equations (1-13) and (1-14):

Fo Restating Equation (1-15a) by substituting the term n = - defined previously in Equation (1-1 1): FY0

The plastic moment capacity, per unit length, of a yield Iine that is oriented perpendicular to the applied

normal stress is calculated using the classical stress block diagram shown in Figure 1 -8(c)iii as:

1 Substituting .Y: = -r0(1 - n ) from Equation (1-15b):

2

F rz Restating Equation (1-Nb) by substituting the term nr, ="dsfiued previously in Equation (1-12)

4

results in the classicd normal stress versus plastic moment capacity interaction equation:

Equation (1-16c) was derived using an example case of the interaction between an applied compressive

stress and a sagging yield line that is oriented perpendicular to the applied stress. However, Equation

(1-16c) holds crue for al1 of the combinations of a sagging or a hogging yield line oriented perpendicular to

an applied tensile or an applied compressive stress.

The plastic moment capacity of a yield line that is located parallel to [e.g. yield line types 6> and @ in

Figure 1-8(a)] , or at an incline to [ e g yield line type 6 in Figure 1-8(a)], an applied normal stress must

also be considered. For a yield Iine located parailel to an applied nomal stress, Cao et al. (1998b) show that

the plastic moment capacity can be calculated using a Von Mises yield criterion or a Tresca yield criterion.

However. Cao et al. (1998b) note that in a real rectangular HSS connection, the main HSS connecting face

is connected to the attached branch member and extends to hvo side walls which provide restraint at the

round corners. This degree of constraint to the HSS connecting face is difficult to quantifi and the actual

plastic moment capacity of a yield line Iocated parallel to an applied normal stress in a real rectangular HSS

connection is uncertain. A simplifling assumption can be made that the plastic moment capacity of a yield

line located exactly parallel CO an app1ied normal stress is essentially uninfluenced by the presence of that

applied normal stress. This sirnplifiing assumption was used by Cao et al. (1998b). Researcherç such as

Mouty (1976), Davies et al. (1975) and Bakker (1990) have developed models for the plastic capacity of a

yield line located at an incline to an applied normal stress. In the lirnit where the inclined yield line becomes

parallel to the applied normal stress, the results of these models indicate that the plastic moment capacity of

a yield line located exactly parallel to an applied normal stress is uninfluenced by the presence of that

applied normal stress.

An inclined yield line can be analysed using a stepped yield Ihe equivalent. Wood (1961) proposed a

stepped yield line failure model for the analysis of reinforced concrete slabs with orthotropic reinforcement.

In this model the original inclined failure line is replaced by a stepped line, so the calculation of the yield

moment along the inclined line was replaced by the calculation of the orthogonal yield moments dong

stepwise increments, whose orientation was coincident with the orthotropic reinforcement. This approach

can be used for the analysis of inclined yield lines in rectangular HSS connections as shown in Figure 1-9.

The yield line pattern shown in Figure 1-9(a) can be analysed as an orthotropic problem. Refemng to

Figure 1-9(a), the plastic moment capacities of yield Line types O and 0, oriented perpendicular to the

applied normal stress (Fo), are given by Equation (1-I6c) which takes into account the influence of the

applied normal stress. The plastic moment capacities of yieid line types @ and @, oriented parallel to the

applied normal stress (Fo), are given by Equation (1-12) and are considered to be uninîluenced by the

presence of the applied normal stress. FinaIly, the plastic moment capacity of the inclined yield line type O,

oriented neither parallel to nor perpendiculat to the applied normal stress (Fo), is calculated using orthogonal

cornponents of the inclined yield line. These orthogonal components are oriented parallel to and

perpendicular to the applied normal stress (Fo) and are shown in Figure 1-9(b). The plastic moment

capacities of these orthogonal components are then calculated as shown in Figure 1-9(b). Using this

procedure for calculating the plastic moment capacities of yield line types O through (3, the overall yield

strength [Pr using Equation (1-9)] of the general rectangular HSS connection shown in Figure 1-7 was

derived.

(a) Yield line pattern fiom Figure 1-4

h', - applied stress (6) yield stress (F,,)

(b) Unit length of yield line O

Figure 1-9: Stepped yield line method for tbe analysis of uiclined yield lines

1 2.3 General punching sheur model

As shown in Figure 1-10, general punching shear c m occur in the HSS connecting face, around the

perimeter of the connecting branch member. Making allowance for the weld size in cornputing the

"footprint" of the branch member on the HSS connecting face, Davies and Packer (1982) give the gneral

punching shear strength as:

In applying the general punching shear criterion, it is assumed that the uniform punching shear strength of

the material is:

Figure 1-10: Ceneral puoching shear model

1.2.4 CombinedJmuraI and p c h i n g shem mode1

From Equation (1-9), it can be seen that the yield strength of a connection increases as P' hcreases.

When P' is close to unity the strength defined by Equation (1-9) tends rowards infinity. Actually, when P' is close to unity (the branch member width is nearly the same, or is the same, as the main mernber width),

a connection tends to fail in the main member side walls or the branch member itself. For a connection

with relatively hi& B' (but < 1 punching shear around the branch member may be critical. Davies

and Packer (1982) intrùduced a combined yield Iine pattern for transverse branch plate-to-rectangular

HSS rnember connections (where B' <I-tdb'o), as show in Figure 1-1 1. to include possibk shear

yielding. [n their analysis the wall thickness and weld size have been considered.

-

Sagging moment yield lines

--- Hogging moment

yield lines

X X X X X X

Shear yield Iines

Figure 1-11: Combined flexural and punching shear yield line madel from Davies and Packer (1982)

In the yield line rnodel shown in Figure 1-1 I punching shear failure occurs at the two ends of the

branch plate and the mechanism is defined by the angle a and the position of the end of the shear failure

zone, determined by either x' or P. Davies and Packer (1982) derived the solution in the form of a

relationship described by Equation (1-19)

where,

hence,

where m,o is the plastic moment capacity of the connecting face pet unit length:

For a given value of fl (hence fl?, bdto (hence b'dto) and hl/to (hence h'&), a 7' rnay be calculated from

Equation (1-19). Equation (1-19) can be solved iteratively or by a graphical technique (Davies and

Packer 1982). Next, the angle (a) and yield strength (PYQ) can be obtained from Equation (1-20) and

Equation ( 1-2 1).

The analytical envelope of predicted connection capacities is defined by the lower bound of the

general yielding model (Pr), the gened punching shear mode1 (PQ), and the cornbined tlexure and

punching shear model (PYQ). Figure 1-12 shows a connection capacity envelope for a typical longitudinal

and transverse branch plate-to-tectangular HSS member connection. From Figure 1-12, it can be seen chat

the strength of a branch plate-to-rectangular HSS member connection increases as f!' increases. When is

close to unity the strength defined by the general yieIding model of the HSS connecting face tends towards

infinity. Thus, for a connection witti relativeiy hi& P' values, but where the effective branch plate width (bFr)

is still less than the effective HSS width (&) minus the HSS wall thickness (p < 1 -tdb'o), punching shear

around the branch member may be critical as defined by the general punching shear model andor the

combined flexure and punchiig shear model. When P' is close to unity (the branch member width is nearly

the sarne or is the same, as the main member width), the branch member will bear directly on the rectangular

HSS side walls.

ïhe combined moment and punching shear model is too complicated for routine design. However, the

branch plate load capacity can also be reduced by a non-uniform stress distribution in the branch plate, which

is temeci a branch "effective width" failure critenon. ïhis branch effective width failure criterion will be

discussed in the next section.

1 HSSwidth.b,,=17(lnn HSS Wall Ih~ckncss. t,, = 4.8 mm HSS yield roength F , = 408 MPa 1 (a) Longitudinal bmch pLte(qt= 1.0)

I W Q m

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 OS 0 9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 06 O7 08 0 9 IO

Branch plaie width-IO-tectangdar HSS width ratio. Branch plat widih-to-rectangulnr HSS width niio. P'

Figure 1-12: Analytical model failure envelopc for a longitudinal and a transverse branch plate-t+reeîanguIar HSS mtrnber connection

1.2.5 Branch eflecfive width failure crirerion

For transverse branch plate connections, an empirical branch "effective width" failure criterion can be

used for design. The typical stress distribution in a transverse branch plate welded to a rectangular HSS

member is shown in Figure 1-13. The peak stresses will occur at the stiff points, which in the case of

rectangular HSS members will be at the corners of the outside webs. Where the materiai has suficient

plasticity the effective width (b,) of the branch plate can be expected to be larger at failure thm under

elastic behaviour as illustrateci in Figure 1-13.

(a) Elastic

Transverse

(b) Failure

branch plate , \

Figure 1-13: Variation ofstress distribution in a transvene branch plate for full width connections from Davies and Packer (1982)

, hl

L

When a full width branch plate is connected by welding to the relatively flexible wall of a rectangular

HSS rnember, a significant non-linear axial stress distribution occurs in the branch plate. This effect was

studied by Rolloos (1969) for full width (p = 1.0) branch plate to 1- and rectangular HSS rnembers,

particularly in order to establish the effective length of the connecting fillet welds.

2

7 .

L + P

The approach for expressing connection strength by means of an effective width of the branch plate is

based upon empirical research. Wardenier et al. (1981) developed a more general sohtion for the

effective width of the branch plate (b,) for l a s îhan full width connections (f3' I 1 .O) as:

13.5 F,o41 b. = f(P)[--i) f o r grade Fe 160 steel (5 = 21 5 MPa)

bolto F,,4

11.5 q o h b = - - b ] ..for grade ire il 10 steel (i, =III MPI)

bo lto Fyh

but 6,s b l , and b1 and hl are shown in Figure 1-13.

The term f(j3) is s h o w in Figure 1-14 but is conservatively taken to be equal to unity. Furthemore,

Wardenier et ai. (1981) note that a value of f(p) pater than unity for connections with low P ratios (as is

the trend shown in Figure 1-14) is not recommended because the initiation of cracks or the deformation of

such connections can become critical.

i bJr,= 13.5 0 = 20 x = 30 0 = 35

r punching shear

01 1 1 1 1 I 1 I I t I

O 0.2 0.4 0.6 0.8 1 .O

Branch plate width-to-HSS width ratio, j3

Figure 1-14 "Stress now" for transverse branch plate-to-rectangular HSS member connections h m Wardenier (1982)

The product of the effective branch plate width (b,), branch plate thickness (hl ) and branch plate yield

strength (F,,) gives the nominal strength of the co~ec t ion (P,). Thus, Equations (1-23a) and (1-23b)

become:

P, = 1 3 . 5 ~ ~ ~ , < ... for grade Fe 360 steel (F, = 235 MPa)

P, = 1 ISPF,~; ... forgrade Fe510steel(Fy =355 MPa)

In Canada, using 350W steel, Davies and Packer (1982) interplate the specified capacity of the

connection (P,) ta be:

As failure by the "effective width" mode can be quite sudden in some cases, Wardenier et al. (1981)

suggest a resistance factor of 4 = 0.8 to be applied to Equations (1-241) and (I-24b) [hence Equation (1-

25) also] to obtain a limit states design resistance.

13 Notional ultimate and seniceabiliîy deformation limit states

The concept of a limit on defonnation has been proposed numerous tirnes for structures and

cornponents that do not show a pronounced peak load. Figure 1-15 shows the general load-deformation

behaviour for an HSS connection. Especially for the case of a tension load, membrane action and strain

hardening lead to additionai load carrying capacity at large defonnations. For this reason a pronounced

yield load or even a peak load is oflen dificult to ascertain.

- Comection deformation, A

1: elastic limit 2: fint sign of crack

3 : load based on defomation limit

1: load based on rernaining defomation

5: ultimate load - Connection deformation, h

Figure 1-15: Typical Ioad-deformation behaviour for an HSS connection from Wardenier (1982)

ïhus, in conjunction with HSS connections which are known to be generally very flexible, ultimate

deformation limits, at which the connection is deemed to have failed, have been suggested by Mouty

(1976, 1977), Yura et al. (1980, 1981), Korol and Mima (1982) and Lu et al. (1994b). These various

deformation limits are described further in Section 7.1 of the thesis. In the case of Lu et al. (1994b), an

ultimate deformation for the HSS connecting face of 3% of a rectangular HSS member width (3%bo) or

3% of a circular HSS member diameter (3%do) was proposed. The ioad corresponding to this deformation

compared reasonably well with the connection peak load in many HSS connections which did e.uhibit a

pronounced peak load. Furthermore, for transverse branch plate-to-rectangular HSS member connections

the 3%bo deformation ievel was close to the points where the loaddeformation curves crossed each other,

for various HSS wall slendemess values. The suitabitity of this ultimate deformation limit for a variety of

rectangular HSS connections was investigated (Lu et al. I994b, Zhao 1996) and it was subsequently

adopted by the Intemational Institute of Welding (IIW) Subcommission XV-E.

For HSS connections a connecting face deformation of 1% of the main member width (l%bo) has

generally been used as a serviceability deformation limit, as given by IIW (1989). For this connecting

face deformation of \%&O, one cm obtain (from a Iaboratory experiment or a numerical analysis) a

corresponding load in a branch member (P,J~). Similarly, a branch member load can also be obtained for

the "ultimate" load level (P& corresponding to a connecting face deformation of 3%bo.

Based on a ratio of the factored load effect to the connection resistance of 1.5, Lu et al. (1994b)

suggest using the ratio PL3?.. i Ps.,X to decide whether the ultimate deformation limit state or the

serviceability deformation Iimit state governs:

> 1.5, seniceability (P.,,, ) govems. PS.,?6

PUJK - D

S 1.5, uItimate(Pwr,) govems.

Using this ratio of the factored load effect to the comection resistance of 1.5, the goveming limit state

Ioad of the connection (P,) is deemed to be the Iesser of the ultirnate deformation limit state load (PUJX)

and the serviceability deformation lirnit state Ioad rnultiplied by a factor of 1.5 (1 .~P . J~) .

The ratio of the factored load effect to the connection resistance of 1.5 is derived using Eurocode 3

(1992) provisions. According to the provisions of Eurocode 3 (1992), considering the combination of

different unfavourable action loads on structures, the minimum value of the "action load factor"

(equivalent to the overail effect of a Limit States design load factor, load combination factor, and

importance factor) should be taken as 1.35. Relating to the connection resistance, the material resistance

factor (equivalent to the inverse of a Limit Sates Design resistance factor, 4) for different faiIure modes

varies from 1.0 (4 = 1/1.0 = 1.0) to 1.25 (4 = 111 .X = 0.8) as suggested by Wardenier (1982). For

plastification, the Eurocode 3 (1992) material resistance factor is taken as 1. I (4 = 111.1 = 0.9 1). The

product of the Eurocode 3 (1992) action load factor of 1.35 and the material resistance factor of I . 1

represents this ratio of 1.5 suggested by Lu et al. (1994b).

1.4 Summary of related experimeotal and numerical studies

Extensive research has been carried out on welded HSS-to-HSS connections. Various independent

test programmes were conducted at a number of European, Japanese, Australian. and Canadian

universities under the direction of ClDECT (Comité [nternational pour le Développement et l'Étude de la

Construction Tubulaire). Wardenier (1982) compileci and synthesised a large body of this research work up

to 1982. However, relatively little research has ken done, until recently, into the behaviour of connections

between [-section beams and HSS columns.

1.4.1 Transverse &ranch plare-to-rectangular HSS member connections

Transverse branch plate-to-rectangular HSS member connections have been studied by RoIloos

(1969), Wardenier et al. (1981) and Davies and Packer (1982). This research led to the branch effective

width criterion discussed in Section 1.2.5.

To study the behaviour of semi-rigid connections between I-beams and HSS columns, hnher

research work has been carried out for connections beiween transverse branch plates and rectangular HSS

columns. Lu (1997), Lu and Wardenier (1995), and Lu et al. (1993) have analysed a large number of

connections between transverse branch plates and rectangular HSS columns using experiments and finite

element models. Numerical analyses were carried out on connections benveen branch plates and

rectangular HSS columns loaded with compression on the branch plates (see Figure 1-16). In this way, a

pair of branch plates would be used to represent the flanges of an I-section beam-to-rectangular HSS

coIumn connection.

(c) Typical fuiite elernent rnesh for

a rnultiplanar X-comection

Figure 1-16: Transverse branch plate-to-rectangular HSS connections analysed by Lu and Wardenier (1995)

Dawe and Guravich (1993) also tested 13 connections between transverse branch plates and

rectangular HSS columns but with stifFening plates welded on to the connecting face of the HSS member

(Figure 1-17), Dawe and Guravich (1993) present a series of ernpirica:ly based expressions to relate the

strength of the connections to the failure modes of punching shear and HSS sidewall bearing.

HSS 254~254x795

(a) Tension series

HSS 203x203~ r,

(b) Compression senes

Figure 1-17: Typieal test specimens olDawe and Curnvich (1993)

1.4.3 Stiffened circular HSS-ro-HSS member conneciions

Fung et al. (1999) studied the ultirnate capacity of stiffened circular HSS-to-HSS T-type connections.

A stiffening plate was welded to the connecting face of the main circular HSS member which in turn was

welded to the connecting circular HSS branch member. The connecting branch member was loaded in

axial compression. A single fidl scale experimental test was conducted and then modelled using FEM

analysis. Figure 1-18 shows the experimental and corresponding FEM model. Fung et al. (1999)

presented the initial findings but a more detaiIed paramecric study and the establishment of pararnetric

equations for the ultimate capacity of such stiffened circular HSS-to-HSS T-type connections is the topic

of their future research.

Branch end plate dt = 1683

Chord end plate \.I

---1----1_----------- - I 2 499 1 i

I I -

4 998

(a) Dimensions of specimen

(b) Finite Element mode1

Figure 1-18: ExperimentaI test specimen and corresponding E'EM model of a stiffened circular T-îype HSSto-EISS connection from Fung et al. (1999)

1.4.3 Si~yened rectanguIar HSS-to-HSS member connections

Korol et al. (1977, 1982) studied stiffened rectangular HSS-CO-HSS T-type connections as shown

below in Figure 1-19. A stiffening plate, welded to the connecting face of the main HSS member.

represents the least obtrusive and most economical method of reinforcing the otherwise flexible HSS

connecting face.

Figure 1-19: Stiffened rectangular HSS-to-HSS T-type connections studied by Korol et al. (1982)

Korol et al. (1982) developed a yield line analysis which described the strength of the stiffened T-type

connection and led to generalised stiffening plate parameters to develop the fu l l strength of the

connection. The analytical yield line models and corresponding solutions are shown in Figure 1-20. The

solutions are valid for the case of the connecting branch plate loaded by axial compression and are not

applicable for the case of the connecting branch plate loaded by axial tension.

Later in this thesis, an empirical formula is developed to determine the required plate thickness for

stiffened longitudinal branch plate-to-tectangular HSS connections to develop the full strength of the

connection. However, the stiffening plate thickness was chosen to behave effectively-rigid with respect

to the plastic collapse mechanism of the HSS connecting face. In this way, a plastitication mechanism in

the stiffening plate itself was precluded. This approach led Co an empirical formula describing the

required thickness of the stiffening plate to develop the full capacity of a stiffened longitudinal branch

plate-to-rectangular HSS connection. Also, this empirical formula is valid for both cases of axial tension

and axial compression ioaded branch plates.

MODE 1:

MQDE II:

MODE III;

MODE 1:

4i;[2b1,-26, +(bl - bb)]sin2 a + 4(t0 + t p Y [ 2 4 - (bi + bh)]sin'

(8,-b,)sinacosa (b', 4, )sin a cor a 1

MODE il:

4ti [2bf0-bb(l +sin2 a)-(hl - hb)cota] P =- ? {63!bb -k +(r, + t p ) f ] + (b', -b,)sin acosa

Figure 1-2O: Yield line patterns and corresponding solutions for stiffened rectangular HSS-to-HSS T-type connectiaaî from Korol et a t (1982)

1.4.4 Shem louded longitudinal branch plate-io-HSS column connections

The topic of HSS-to-HSS memkr connections is a railier mature field of research. Stiffened HSS-to-

HSS member connections have also k e n studied by various researchers, some of which were presented in

the previous section. Connections between 1-section beams and HSS columns are now attracting more

research attention. Connections between transverse branch plates and rectangular HSS members have been

studied as a means of modeiling flanges of an [-section beam-to-rectangular HSS column connection.

Also, stiffened transverse branch plate-to-rectangular HSS rnember connections have been studied.

Longitudinal branch plate-to-HSS member connections, on the oiher hand, have received far less

attention. Sherman (1996) performed a large number of tests for nine different types of simple shear

connections for wide flange beams c o ~ e c t e d to HSS columns as shown schematically in Figure 1-21. In

particula., the design criteria presented by Sherman (1996) pertained to jua the longitudinal branch plate

co~ec t ion Ioaded in shear. As describeci in Section t 2 .1 , those criteria for conservatively proponioning

the branch plate and weld cm be adapted to longitudinal branch plate-to-HSS connections loaded in both

shear and tension.

(a) Longinidinal branch pl*

(d) Single angle

(b) Through branch phte id Seal

(e) OoubIeanglt

(g) Shearcnd plate

Fi ire 131: Types of shear îab-to-HSS column connections tested by Sherman (1996)

Sherman (1996) a h studied the effect of HSS wall distortion on colurnn swength. In Section 1.2.2 an

analytical mode1 was presented that reduces the connection capacity of a branch plate connection due to the

presence of an applied normal stress in the HSS connecting face (which would result fiotn a column axial

Load for e m p l e ) . Sherman on the other hand, experirnentally studied the effect of local distortions of the

HSS column connecting face (due to the branch plate connection) on the overall strength of the HSS

column. The test set-up for Sherman's bearn-to-column connection tem is show below in Figure 1-27.

1 ' ( "transverse" sûain o~mration

HSS 8 x 3 x ll4" HSS8x3x3 /16" L U

Figure 1-22: Beam-t+HSS column connection test set-UQ by Sherman (1996)

In order io first determine the effect of connection types on local distortion of the HSS columns, Sherman

had strain gauges mounted at the centre of the HSS connecting face one inch below the connecting

element for each of his connection tests. The transverse strains measured forrned a bais for cornparison

amongst the different connection types. Connections such as longitudinal branch plates and single angles

that have Ioad transfer through a weId at the centre of the HSS connecting face had the highest transverse

smins. On the other hand, the through branch plate co~ec t ion which inherently reinforces the centre of

the HSS connecting face had negligible transverse strains. These two types of connections represented

the extrernes of inducing transverse strain into the HSS wail. In order to address the question of whether

local distortion of the HSS has a detrimental effect on the overall column capacity, a series of tests was

conducted by Sherrnan to compare the influence of longitudinal branch plate and through branch plate

connections. Three different HSS wall slenderness ratios were tested (b&= 16, 29, and 40). The tests

concluded that longitudinal branch plate connections used with HSS columns thai are not "thin-walted"

(bdto = 16 and 29) developed essentially the same strength as those in which the wall is reinforced with a

through branch plate. The AiSC (1993) criterion for "thin-walled" HSS members is:

- - r 36 (for E = 200 000 MPa and F,, = 350 MPa) r, 0.67 Io

With a thin-walled HSS (bdto = 40), the longitudinal branch plate resulted in a 22% reduction in overall

colurnn capacity cornpared with the through b m h plate. However, in general, many formulae and

design guidelines for HSS connections preclude "thin-walled" HSS members.

Saidani and Nethercot (1994) presenfed a paper on the design of longitudinal branch plate-CO-HSS

colurnn connections. A full description of al1 possible faiIure modes was given and then associated with

corresponding design checks, mainly based on Eurocode 3 (1992). Figure 1-23 shows a ypical

longinidinal branch plate connection and the possible failure modes.

HSS alumn Iongitudiml (a) Circular HSS mlumn

bmch plate

bmm (b) Rectangular HSS c o l m

1 I I I I 1 I 1 I I I

t Tube Wall

failrire

- Wcld Branch plau Bolt Failure by shtar Block shear failurc failm. faiIure failure andlor h d i n g of the bem wveb

ofthe beam web

Figure 1-23: Possible failure modes for shear loaded longitudinal branch plate-to-HSS column connections from Saidani and Nethercot (1994)

Referring to Figure 1-23, failure modes @ through @ are common for longitudinal branch plate (shear

tab) connections to [-section as well as HSS columns. Thus, failure modes @ through @ can be

associated with corresponding design checks in various European or North Arnerican design codes.

Failure mode O was not associated with a curent design check by Saidani and Nethercot. However,

Sherman (1996) presentd a simple criterion to reiate the strength of the weld to the punching shear

capacity of the HSS connecting wall (refer back to Section 1.2.1). Failure mode O is unique to HSS

columns and was characten'sed by bending or a shear-type teanhg of the HSS connecting face wall.

Shearing of the HSS wall was related to a Eurocode 3 (1992) check corresponding to a uniform shearing

of the HSS wall on either side of the fin plate, adjacent to the welds. The issue of local outsf-plane shear

ruptures, caused by eccentricity of the applied shear load, as s h o w earlier in Figure 1-6, was not

addressed. Also, bending of the HSS wall, which waç grouped into failure mode was not related to a

published design guideline. Saidani and Nethercot (1994) note that codes of practice traditionally contain

considerable guidance on the design of structural mernbers, but contain cornparatively little information

on connection design.

The use of a tee snib to connect an I-section beam to an HSS column can be advantageously used

since the tee flange serves to reinforce the HSS wall whiIe the tee stem serves as a shear tab elernent.

Pioneering research on the use of a tee stub to connect I-section beams and HSS columns was carried out

by White and Fang (1966). While the tee flange served to reinforce the HSS wall, the tee flange was also

required to permit a reasonable amount of rotation by virtue of its own flange flexibility. Based on six

tests, the study recommended using the tee flange to span the flexible HSS wall while maintaining enough

flexibility in the tee flange itself to accommodate a beam end rotation.

More recently, Dawe and Mehandale (1995) have tested ten specimens consisting of wide flange

bearns shear connected by means of tee stubs to HSS colurnns as shown in Figure 1-24.

Loading Beam l

Adjustable SUPPO*

Test machine pIatten 1 Figure 1-24: Test set-up by Dawe and Mebandale (1995)

They observed and identified five possible failure modes:

1) Yielding of the tee stem

2) Shearing of tee stem

3) Bolt bearing failure of tee stem

4) Shear failure of bolts

5) Bending of HSS wall

All observed failure modes, except bending of the HSS wall, could be related to well known bearn-to-

column connection failure modes. Bending of the HSS wall was characterised by the formation of yield

lines leading to a plastification mechanism. Dawe and Mehandale (1995) used a yield line analysis to

model the HSS connecting face and the tee flange. The HSS wall was rnodelled as a simply supponed

plate, while the tee stub was modelled as another plate rigidly connected to the HSS wall at the welds.

Based on the observed results of their ten specimens, tension side and compression side parcial

mechanisrns as shown in Figure 155 were estabtished. Predicted capacities based on these failure

rnechanisms compared well with the test results.

Mode I Tension

Mode 3 Tension

Mode 1 Mode 2 Mode 3 Compression Compression Compression

Figure 1-25: Yieid line patterns olDawe and Mehandale (1995)

1.4.5 Tension loaded longimiinal branch p a r e - O colmn connections

Jarrett and Malik (1993) carried out a series of fifieen experirnental tests to determine the maximum

tying force and failure modes of longitudinal branch plate-to-HSS column connections. Jarrett and Malik

(1993) were investigating the ability of a longitudinal branch plate-to-HSS column "shear" connection to

resist an unusually high tying "tension" force to reduce the sensitivity of buildings to progressive collapse,

Thus, longitudinal branch plate connections between 1-beams and rectangular HSS columns were tested

with a tensile force applied to the bearn. Also, the maximum connection capacities and failure modes

were determined with an axial compressive load applied to the column. A column compressive load as

high as the squash load (fi = A&) of the column was applied in one test. However, the rernaining tests

were subjected to 67% of the squash load of the colurnn. Figure 1-26 shows the specimen details and test

apparatus.

(b) Typical T-connection

REACTiON FRAME

(a) Typical X-connection

Outline of test Siuidle box section with 2 ables thmugh

(c) Test apparatus for T-connection

Figure 1-26: Specimea details and test apparatus of Jarrett and Malik (1993)

The following failure modes were observed in the test series:

Fracture of the rectangular HSS around the weld penmeter

Bolt bearing and bolt tearout in the beam web

Bolt shear

Net-section fracture of the branch plate at the bolt row

Fracture of the branch plate starting at the weld cornbined with shear of one bolt [combination of failure mode 3) and failure mode 4)]

Plasrification of the HSS connecting face

Failure modes 2) through 5 ) can be applied to the connecting branch plate in isolation and are relatively

independent of longitudinal branch plate connections to 1-section or HSS colurnns. Failure modes 1) and

6) are only applicabie for branch plate connections to HSS columns. Failure mode 6) was analysed using

yield Line analysis from Kapp (1974). The axial load applied to the column was not included in the data

analyses or calcuiations. Jarren and Malik (1993) make a general note that for the colurnns loaded to 67%

of the squash load, the axial load in the colurnn started to drop off at between 80% and 100% of the

m~ximum applied branch plate tensile load. it should be noted that the maximum applied branch plate

tensile load was cornmensurate with extensive out-of-plane defonnation of the HSS connecting face

(between 30 mm and 80 mm). Figure 1-27 shows significant defonnation of the HSS connecting faces.

which is characteristic of longitudinal branch plate-to-HSS member connections.

Figure 1-27: Deformation of ASS connecting face from Jarrett and Malik (1993)

Figure 1-28 shows a loaddefonnation plot from Jarrett and Malik (1993). They define the strength of

the branch plate connection as the maximum branch plate load achieved in the test. However, as

evidenced by Figure 1-27, the maximum branch plate load is preceded by enorrnous defomations and

significant local tearing of the HSS connecting face, which also represent failure criteria of the

connection. Jarrett and Malik (1993) were investigating the ability of a structure to resist accidental

loading leading to progressive collapse, in which case the maximum connection load or ultimate reserve

strength of the connection may be an applicable limit state.

In any event, a 3%bo ultimate deformation limit has been superimposed onto Figure 1-28 to serve as a

general comparison between the design load IeveI of the connection (considering a notional deformation

limit state) and the remaining reserve strength or maximum load Ievel sustained by the connection. The

maximum branch plate load is on the order of three to five times the 3%bo ultimate deformation limit

design load level (PQso). Figure 1-28 was annotated to illustrate the deformation-critical nature of the

design strength of a longitudinal branch plate-to-HSS member connection as well as the abundant post-

yield reserve load c q i n g capacity of this type of connection.

A longitudinal branch plate-to-MSS column connection tends to result in excessive distortion or

plastification of the HSS connecting face. The design resistance of such connections is best described by

a notional ultimate deformation limit or a notional "yield" load levei, in which case the design resistance

is relatively low.

O 5 1 O 15 20 25 30 35 JO 45

Connection deformation, A (mm)

Figure 1-28: had-delormaiion response of bnnch phte-to-HSS column connections from Jarntt and Malik (1993)

Yeomans (2001) carried out a series of ten experimental tests on stiffened longitudinal branch pIate

connections between I-beams and rectangular HSS coiumns. Figure 1-29 shows the details of a typical

connection tested by Yeomans. Similar to the experimental tests conducted by Jarrett and Malik (1993).

the I-beam was subjected to a tensile load rather than a shear load. A branch plate connection benveen an

I-beam and an HSS column is usually intended to be a shear connection. However, Yeomans considered

that this type of connection can also be used in other applications where a bolted connection to a

rectangular HSS main member is required, such as wind or other types of bracing, in which the

connection is required to cany a tension load. Also, as noted by Jarrett and Malik (1993). the

specifications of many countries require a connection robustness, which means that as well as a vertical

shear load, shear-type connections rnust also be capable of carrying a notional horizontal load to prevent

collapse due to any accidental forces in this direction. Cornpared to an unstiffened longitudinal branch

plate connection, which is inherently very flexible, the tlange of the tee stub (stiffening plate) is intended

to stiffen and strengthen the otherwise flexible rectangular HSS connecting face. Figure 1-29 shows that

the plate is slightiy offset from the column centre line by a distance (eh) so that the centre line of the

connecting longitudinal branch plate can coincide with that of the column.

Figure 1-29: Deîails ofstiffened longitudinal bnncb plate-to-rectaogular HSS column mnncetions tested by Yeomans (2001)

The parameters in Yeoman's experiments included three different HSS wall thicknesses, three different

stiffening plate widths, and three different stiffening plate thicknesses. Figure 1-30 shows one of

Yeoman's loaddeformation plots illustrating the effect of changing the stiffening plate thickness (t,). The

three nominal stiffening plate thicknesses were 12 mm, 10 mm, and 8 mm. Yeomans adopted the l%bo

and 3%& notional deformation limits to define the strength of the connections. Yeomans generally States

a pronounced interaction effect between the stiffening plate-to-rectangular HSS width ratio (blfbo) and the

branch plate thickness-to-stiffening plate width (tdb,). This interaction is not rnodelled by Yeomans

(2001) but is noted as topical for subsequent research.

Stiffening plate width, b, = 120 mm Nominal HSS width, b,, = 150 mm Measured HSS wall thickness, r, = 6.13 mm

O 5 10 15 20 25

Connection defonnation, A (mm)

Figure 1-30: Effet of stiffening plate thickness obsewed by Yeomans (2001)

1.5 Thesis research

The following chapters present a comprehensive study of longitudinal branch plate, through branch

plate, stiffened branch plate and transverse branch plate-to-rectangular HSS member connections, which

are illustrated in Figure 1-5. The foregoing literature review has shown that the longitudinal branch plate

connection, under axial loading on the plate, has hitherto received almost no research attention and the

allied through branch plate connection has been totally neglected. On the other hand, the transverse

branch plate connection has been heavily researched and disparate studies have looked at types of

stiffened branch plate connections to HSS members. In this thesis a unified design approach is developed

for al1 these types of branch plate connections, under any combination of HSS or plate axial loadings. for

design "failure" modes governed by the flexure of the HSS connecting face, This synthesised and novel

approach to design of a group of HSS connections is the principal contribution of this thesis.

2. EXPE~UMENTAL STUDY OF LONGITUDINAL BRANCH PLATE-TO-RECTANCULAR HSS MEMBER CONNECTIONS

An experimental test programme was conducted to investigate two main influences on the strength of

a longitudinal branch plate-to-rectangular HSS membet connection. One major influence on the strength

of a branch plate connection is the presence of an axial load in the main rectangular HSS member

(column). Another major influence on the strength of a branch plate connection is the angle of inclination

of the branch plate force to the axis of the main HSS member (column). Tfie results of the experimental

investigation are then compared with proposed analytical models. Later in the thesis, the experimental

results represent a benchmark for an expanded FEM parametric analysis that serves to broaden the

experimental database.

2.1 Test specimens

A total of ten isolated longitudinal branch plate-to-rectangular HSS member connections were tested

in an X-type configuration. Nominal axial loads of 0% (no axial load), 20%, 40%, and 60% of the HSS

squash load were applied CO the main HSS member (column) for two groups of branch plate connection

angles. The first group of four test specimens had a branch plate-to-rectangular HSS member connection

angle of 90" and is shown in Figure 2- 1.

F i u n 2-1: 9û" longitudinal brancb plate t u t specimens aftcr tcsting

The second group of four test specimens had a branch plate-to-rectangular HSS rnember connection angle

of 45" and is shown in Figure 2-2. Thus, the influence of an axial load in the main HSS member (colurnn)

was investigated and bounded by two different branch plate-to-rectangular HSS member inclination

angles.

Figure 2-2: 45" longitudinal branch plate test specimens after testing

The third group of test specimens was used to simulate a cornplete range of branch plate-to-

rectangular HSS member connection angles and is shown in Figure 2-3. In addition to the 90" and 45"

connections tested without an axial load, a 30" and a 60" connection were tested without an axial load. In

this way, a full range of branch plate-to-rectangular HSS member connection angles was tested.

Figure 2-3: W, 49, W, and !W longitudinal branch phte test specimens afttr testiag

Figure 2-4 documents the geometric details for a typical 900 longitudinal branch plate-to-rectangular

HSS member connection. Similarly, Figure 2-5 shows a typical test set-up for a 90" longitudinal branch

plate-to-rectangular HSS member connection. The main (column) member is a KSS 178~127~7.6. A

13.1 mm thick plate was fillet welded to the top face of the column to simulate a longitudinal branch plate

attachment. The welding of the test specimens was done at the University of Toronto laboratories using

metal-cored wire and the MIG welding process. A 1,000 kN capacity MTS testing machine was used to

apply a tensile load directly to the branch plate. The branch plate was gripped in the upper head of the

MTS machine. A reaction load was provided via a much stiffer opposing 127x127~11 HSS branch

member that was fillet welded to the bottom face of the main HSS member (column) and gripped in the

fixed bonom head of the testing machine.

A manual hydraulic jack was used to apply a simulated compression load to the main HSS mernber

(column). The compression load was applied through a tensioned hi&-strength rod that was inserted

through the main HSS member. Analogous to a post-tensioning procedure, the manual jack was used to

tension the hi@-strength steel rod which in tum reacted against stiff (30mm thick) plates attached to

either end of the main HSS member. In this way, a simultaneous tensile branch plate load and a

compressive column load were applied to the test specimen.

Figure 2-6 documents the geometric details for the remaining 30°, 45", and 60" longitudinal branch

plate-to-rectangular HSS rnember connections. Figure 2-7 shows a typical test set-up for a 45'

longitudinal btanch plate-to-rectangular HSS rnember connection, which is similar for both the 42" and

60" connection tests. As the angle of inclination between the branch plate and rectangular HSS rnember

was varied in increments between 30° and 60°, the longitudinal fooiprint (or joint length) was held

constant at 178 mm. In order to allow rotation of the flexible branch plate-to-rectangular HSS member

connection (as would be the case to sorne extent in a real building), the bmch plate load was applied

through a pin-type connection.

Each test specimen "column" was fabricated h m the same length of rectangular HSS (178~127~7.6)

steel stock. Similarly, each of the various branch plates was fabricated h m the same sheet of steel plate

stock. In this way, the material properties between the test specirnens were held constant. The measured

dimensions of the rectangular HSS cross-section, the plate thickness and the size of the tillet welds

connecting the rectangular HSS columns and longitudinal branch plates are docurnented in Table 2-1. A

column preload of nil, 300 kN, 600 kN, and 900 kN was applied to the test specimens. A preload ratio (n)

was defined as the percentage of the squash load applied to the column (main rectangular HSS member).

The squash load was defined as the measured yield strength of the material (determined fiom tensile

coupon tests) times the measured cross-sectional area of the colunui rnember.

Figure 2-5: 90" longitudinal branch plate-brecîangular HSS member conncction test set-up

Figure 2-7: 4 5 longitudinal bnncb phte-to-rceianguhr HSS mcmber connection test set-up

Tensile tests have been carried out on duplicate coupons for the rectangular HSS (taken from the

flats) and branch plate materials. The HSS material conformed to CANICSA-G40.20/G40.2 1-98 Class H

Grade 350W. The average values of these material properties are documented in Table 2-1.

Comprehensive details of the measured mechanical and geometrical pmperties of the test specimen stock

material c m be found in Appendix A. Both the yield sûength (F,) and the static yield strength (F,t,u"c,)

are documented in Appendix A. The static yield strength (FH-,) is obtained by holding the

displacement at a strain equivalent to 0.002 and 0.005 of the coupon fixed to allow the static loads (and

thus corresponding static stresses) to be obtained at these two strain levels. Othenvise, the yield strength

(F,) obtained h m the continuous stress-strain curve is only a quasi-static yield stress. However,

experimental test specimens are usually tested at a quasi-static loading rate (as was the case for the test

specimen connections reported in this thesis), without the benefit of holding the displacement constant at

regular intervals throughout the loading curve. Thus for the analysis of experimental results, the quasi-

static yield strength (F,), as opposed to the static yield strength (FH-,J, was used to interpret the

corresponding quasi--tic load-deformation curves obtained from the experimental test specimen

connections.

Table 2-1: Experimental test specimcn details for longitudinal branch plate-to-rectangular HSS membcr connections

hl ,=h l l s inO+w[mm]l 197 1% -194 196 1 193 193 194 196 1 191 193 HSS main member propettics

F , , Wal il [mm') 4 242

Preload, N o [kEi] O 300 600 900 O 3Oû 600 900 O

Preload ratio, n = No/ F , J , 0.0% 17.9% 35.9% 53.8% 0.0% 17.9?? 35.9% 53.8% 0.0%

Al1 the tests were canied out using a 1000 kN capacity MTS Universal Testing Machine along with a

data acquisition system. The test specimens consist of a stub rectangular HSS main mernber with the

longitudinai branch plate connection welded to the mid-face of the HSS. A tensile load was applied

directly to the branch plate as it was gripped inside the upper head of the testing machine and the load was

measured by the MTS load cell. The test specimens were instrumented with Linear Variable Differential

Transfomers (LVDTs) to record the loaddeformation behaviour of the rectangular HSS member

connecting face. Also, five strain gauges were located across the width of the branch plate of each

specimen to measure the strain distribution across the plate. Figure 2-8 and Figure 2.9 show the standard

LVDT and strain gauge set-up for the 4S0, 60°, and 90" branch plate connection angles. The 30" branch

plate-to-rectangular HSS rnernber connection angle was particularly acute, and did not accommodate the

standard LVDT set-up, thus a moditied LVDT arrangement was used as shown in Figure 2-1 0.

Conneaion centre

note: 30" specimen LVDT arrangement modified because of very ûcute angle

LVDTs

Positions varied

I Strain gauges

6 45". 60". and 90"

Figure 2-8: Standard arrangement of LVDTs and straia gauges

Figure 23: Standard LVDT set-up Figure 2-10: LYDT set-op for 30" test

The branch plate tension load (P) was applied by the MTS testing machine under displacement

control until rupture. For the test specimens that included a simuiianeous compression load (fi) in the

main HSS (column) member, this compression load was applied using a hand purnp. Depending on the

test specimen, the desirecl column preload (either 300kN, 600 kN, or 900 kN) was monitored and held

constant throughout the test.

23 Test resalts

The applied branch plate load versus the connection deformation response is the principle rneans of

analysing and charactetising the behaviour of longitudinal branch plate-to-rectangular HSS member

connections. Multiple LVDTs were used to measure the defonnation profile of the HSS connecting face

as well as to provide redundant, verifiable experimental data.

The stress distribution within the branch plate must be also be analysed and characterised. One

standard approach for designing a transverse branch plate is to base it on an "effective width" criterion (as

discussed previously in Section 1.2.5) that accounts for the presence and severity of a non-unifonn stress

distribution within the branch plate. Strain gauges were thus placed along the length of the longitudinal

branch plate to measure any non-unifon sûess distribution.

Finally, the experimental results and observations serve to provide an overall qualitative insight into

the behaviour and the failure mode of the connection type.

2.2.1 Variable branch plate-IO-HSS member conneaion angles

The applied branch plate load (P) can be resolved into a normal component and a shear component.

The normal component of the branch plate load (PL) acts perpendicuiar to the plane of the rectangular

HSS connecting face and causes a significant outward (tension load) or inward (compression load)

deformation of the relatively flexible HSS connecting face. Altematively, the shear component of the

applied branch plate load, acting parallel to the plane of the HSS connecting face does not cause

appreciable deformation. Figure 2-1 1 shows the loaddeformation responses of the 30°, 4j0, 60°, and 90"

longitudinal branch plate-to-rectangular HSS member connection angles. Figure 2-1 1 shows the overall

load-deformation connection responses as well as the nonnalised load-deformation connection responses.

By ploîting the normal component of the applied bmnch plate load (PL= Psinû), it can be seen in

Figure 2-1 1 that the nomalised load-deformation responses of the 30°, 45O, 60°, and 90" branch plate-to-

rectangular HSS member connection angles are virtually identical. Hence, for flexible longitudinal branch

plate-to-rectangular HSS member connections, the experimental results confirm the principle that the

normal component of the applied branch plate load dictates the overall deformation response of the joint.

HSS 178~127~7.6 1

Branch la te angle 8 (Specirnen identification)

O 5 10 15 ?O 25 30

Connection deformation, A, (mm)

O 5 I O 15 20 25 30

Comection defocmation, A, (mm)

Figure 2-11: Loaddeformatioa curves for various longitudinal brnnch plate-to-HSS membcr connectioa angles

2.2.2 Variable column preload for 4.5" and !JO0 connection angles

Figure 2-12 shows the load-deformation responses of the 45" longitudinal branch plate-to-rectangular

WSS member connection angle series with a main member (column) preload of O%, 18%, 36%, and 54%

of the squash Ioad of the main member (column). Similady, Figure 2-13 shows the loaddeformation

responses of the 90' branch plate-to-rectangular HSS member connection angle series with a main

member (column) preload of O%, 18%, 36%, and 54% of the squash load of the main member (column).

The strength of these connections was determined fiom the loaddefonnation curves using the

serviceability defonnation limit and the ultimate deformation Iimit. The notional serviceability and

ultimate defonnation Iimit states were described in Section 1.3.

Table 2-2 lisrs the l%bo serviceability deformation limit (P,.l.lSi)r and the 3%bo ultimate defonnation

limit (Pk3%) load levels obtained fiom the experimental loaddefonnation curves (Figures 2-1 1 through

2-13). Table 2-2 also lis& the predicted yield strength [Pr using Equation (1-91 of each connection. The

calculable connection yield load (Pr) corresponds well (avg. PdPk3%= 0.86) with the notionat 3%bo

ultimate deformation limit load level (P,,J~. Also, the calculable connection yield load (Pr) corresponds

well (avg. PyIP,, = 0.96) with the governing deformation limit state load level (P,,). As desctibed in

Section 1.3, the governing deformation limit state load level (P,,) is deemed to be the lesser of the

ultimate defonnation limit state load level (Put%) and the serviceability deformation limit state load level

rnultiplied by a factor of 1.5 (1 .5Ps,145) as given by Lu et al. (1 994b).

HSS 178~127~7 .6

CoIumn oreIoad (Soecimen identification) - O % (45LPO) -- 18% (45LP20) - 36% (45LP40) -- 54% (45LP60)

O 5 10 15 20 25 30

C o ~ e c t i o n deformation, A, (mm)

O 1 2 3 4 5 6

Comection deformation, AL (mm)

Figure 2-12: Loaddeformation curvcs for the 45" longitudinal bnnch plate-to-HSS member conneetion angle test serics

Column preload (Specimen identitiution) - 0%(90LPO) -- 18% (90LP20) - 36% (90LPJO) -- 54% (9OLP60)

+ ............. ....................... .............-.....----.-.. d e

O 5 I O I5 20 25 30

Connecdon deformation, Al (mm)

+ HSS 178~127~7.6 +

0 1 2 3 4 5 6

Cornation deformûtion, A, (mm)

e

Figure 2-13: LUad-delonnation curves Tor the 90. longitudinal brancb plate-to-HSS membcr conneetion angle test series

-, .... ..............-. ".. ..-......... . -..-- ............................... e "-te

2-16

Table 2-2: Experimental test resulîs for longitudinal braach plate-to-rectangular HSS member connectioas

Saecimen Identification -r

Brinch alite arondes

1 calcuhted withour wing appliedpreload. n =O 1

L [mm7 Preload.N,[kNI

ztoad ratio. n = No/ F y d O

[Eq. 1-91 P v(n =O) [ w 166 165 163 1 6 4 1 228 228 230 233 1 1 8 6 324 Icatcutated wing applied preload, n 1

HSS connecting faet propertiu

I o [mm11 7.6

4242

[Eq. 1-91 166 164 156 149 1 2 2 8 225 220 211 [ 186 324

q n ) ( 1.00 0.99 0.96 0.90 11 .00 0.99 0.96 0.901 1.00 1.00 Test r u u k Scrvietibility and ultimite deformation limit sintes

PxlK[kNl1 120 108 107 101 150 155 146 167 137 230

O 0.0%

O 300 600 900 0.0% 17.9% 35.9% 53.8%

O 300 600 900 0.0% 17.9% 35.9% 53.8%

Far HSS Colwnns: Yicld strcngth (F,,) 394 MPa

I . ~ P , , ~ [ w J ~ P,,.>([kN]

P,[1<N]

180 162 161 152 225 233 -19 251 206 355 192 186 176 166 261 260 246 243 352 378

P, =minimum(l.5P,.,., P.>%) [hl 1 6 2 m 1 5 2 2 2 5 2 3 3 @ 2 4 3 a 3 J S 180 -

Cornparison of test predictions and test rau lb

PrlP,jK

p,.lP,

0.86 0.88 0.89 0.90 0.87 0.87 0.90 0.87 0.74 0.86

average = 0.86 std. deviation = 4.4Y0 COV = 5.1% 0.92 1.01 0.97 0.98 1,Ol 0.97 1.01 0.87 0.90 0.94

average = 0.96 std. deviation = 4.7% COV = 4.9%

2.2.3 Faiiwe mode

Figure 2-14 shows the cracking or tear-out pattern around the fillet weld joining the longitudinal

branch plate to the HSS connecting face for a typical 45", 60°, and 90" btanch plate connection angle.

Failure of the 4S0, 60°, and 90" longitudinal branch plate connection angles was characterised by a

punching shear-type crack, initiated at either end (typically at the toe and then the heel) of the connection.

and then progressing along the full length of the branch plate resulting in a tear-out separation between

the branch plate and the HSS connecting face.

Figures 2-1 1 through 2-13 showed the load venus deformation responses for the longitudinal branch

plate-CO-HSS member connection tests. The limit States design load of the connection (either a prescribed

yield load or a prescribed deformation limit load) tends to occur before the onset of cracking. However.

the onset of cracking does not result in a load drop, or even a loss of stifhess. Although a punching shear-

type of crack has been initiated (typically at either end of the branch plate) and advances along the width

of the branch plate in a ductile manner, membrane action begins to dominate and the connection

maintains additional load canying capacity at a relatively constant stiffness.

For design purposes, this additional load canying capacity attributed to membrane action provides a

significant reserve of strength and ductility in extraordinary loading situations. The 30" test specimen

represented a minimum practical branch plate angle and experienced a tensile failure of the branch plate

after the practical design load of the connection had been reached. This mode of failwe cm be averted by

using a thicker branch plate member, but the thickness of the branch plate members was a parameter that

was held constant for the experimental test programme.

Figure 2-14: Typiesl tear-out cfpcking pmttem for longitudinal brancb plrteto-rcctangiihr HSS member connections

2.2.4 Main HSS member connecting face dejormation profle

The deformation profile along the length of the main HSS connecting face was obtained fiom the

series of LVDTs shown in Figures 2-8 through 2-10. Figure 2-15 shows a typical deformation profile of

the main HSS c o ~ e c t i n g face for a 90" test specimen. The rernaining 90' test specimens e'rhibited a

sirnilar deformation profile and are documented in Appendix B. The deformation or bulging of the

flexible HSS connecting face is pronounced but localised to the immediate vicinity of the branch plate

connection region. Final failure of the 90" test specimens is characterised by a punching shear-type

crack, initiated at either end of the connection, and then progressing along the fidl length of the branch

plate, resulting in a tear-out separation ktween the b m c h plate and the HSS connecting face. This final

t e m u t separation is not perfectly syrnmetrical and results in a rigid-body rotation of the branch plate in

the final stages of loading. Figure 2-15 shows a clockwise rotation of the branch plate for specimen

90LP20 in the final stages of loading.

Figure 2-16 shows a typical deformation profile of the main HSS connecting face for a non-90" test

specimens. The rernaining 30°, 45", and 60' test specimens exhibit a similar defonnation profile and are

documented in Appendix B. The defonnation or bulging of the flexible HSS connecting face is

dominated by the component of the applied branch plate loading, acting normal to the plane of the HSS

connecting face. Final failure of the 30°, 45", and 60" test specimens was characterised by a punching

shear-type crack, initiated at the toe of the connection, and then progressing along the length of the branch

plate. resulting in a tear-out separation between the toe end of the branch plate and the HSS connecting

face.

3 5 Branch plate tensile load, P

Lefi side Centre of comection Right side

Position dong HSS comecting face centre line (mm)

Figure 2-15: Typical HSS eonncfthg face defornation profile for 90" longitudinal bnnch plate connrctioas

3%b, = 5.34 mm ---A--.

ultimate de formation limit state 4

a

30 - 1

Letl side Centre of comection Right side

Position along HSS comecting face centre line (mm)

Branch plate tensile load, P

- - -5

Figure 2-16: Typical ii!jS conarcting lace deformation profile for 45" longitudinal braach piate connections

Toe Heel

I l I 1 l 1 I 1 I l I I I l I I I

2.2.5 Branch plate Stress diwiburion

Five main gauges were place along the width of the branch plate as shown in Figures 2-17 and 2-18.

These strain gauge readings were used to determine the stress distribution along the branch pIate. The

stress distribution in the branch plate can be expected to be non-uniform and higher at the corners, or

branch plate ends, as is the general case with HSS member connections. Figure 2-17 shows this non-

uniform stress distribution in the c o ~ e c t i n g branch plate for a typical 90' connection (Spcimen 90LP20

as documented in Table 2-2). Referring to Table 2-2, test specimen 90LP20 has a calculated connection

yield load (PY) of 164 kN. Figure 2-17 shows that near the calculated connection yield load (P = 170 kN),

the maximum measured stress (calculated from the strain gauge reading) was approximately 140 MPa and

the minimum measured stress was approximately 40 MPa. At an applied branch plate load of 170 kN. the

calculated uniform tende stress in the branch plate [a = 170 kN + (13.1 mm thickness x 178 mm branch

plate width)l is 73 MPa. In this case, the maximum measured branch plate stress (140 MPa) is roughly

double the calculated uniform branch plate stress (73 MPa).

Figure 2-1 8 shows the non-unifon stress distribution in the connecting branch plate for a typical 4j0

connection (Specimen 45LP60 as documented in Table 2-2). Refemng to Table 2-2, test specimen

45LP6O bas a calculated connection yield load (Pu) of 21 1 kN. Figure 2-1 8 shows that near the calculated

connection yield load (P = 200 kN), the maximum measured stress (calculated from the strain gauge

reading) was approximately 200 MPa and the minimum measured stress was approximately 105 MPa. At

an applied bmnch plate load of 200 kN, the calculated uniform tensile stress in the branch plate [a = 200

kN + (1 3.1 mm thickness x sin4S0 x 178 mm branch plate width)] is 121 MPa. In this case, the mmimum

measured branch plate stress (200 MPa) is roughly 1.6 times the calculated uniform branch plate stress

(121 MPa).

However, in both cases, a more uniform stress redistribution would tend to occur as portions of the

branch plate approaches their yield strength. Appendix B documents the stress distribution in the branch

plate for the remaining test specimens. in order to realistically determine the severity of the non-uniform

stress distribution in the branch plate, a thinner branch plate thickness associated with the calculated yield

load of the connection must be analysed. A more comprehensive parametric analysis of the branch plate

stress distribution is presented in Chapter 3 of the thesis using FEM analysis.

Stress on branch plate surface (MPa) - - IJ 1.J O 8 8 V, O O E

- Initial punching sherir-typc crack originaied on / this side of the branch plcic

Slress on branch plntc surface (MPa)

Initial punching shrar-type crack originatrd on this side ("toe") of the branch plate

3. FEM ANALYSIS OF LONGITUDINAL BRANCH PLATE-TO-RECTANCULAR HSS MEMBER CONNECTIONS

A FEM numerical programme was undertaken to further study the strength of a branch plate

connection under the influence of an axial load in the main HSS member (column). The experirnental

test programme, presented in the previous chapter, consisted of a column axial compressive preload ratio

(n) of O%, 18%, 36%, and 54% of the HSS yield (squash) load. The experimental test specimens were

limited to a maximum preload ratio of 54% of the HSS squash load for the sake of safety since the axial

load was introduced into the main HSS member by means of a potentially dangerous post-tensioning type

process.

3.1 FEM models

The FEM numerical models were varied to coincide with, interpolate between. and extrapolate

beyond the experimental test programme. The numerical FEM models were verified using the

experimentally-obtained test data and then varied to expand the parametric database. Thus, supplernental

numerical test data for higher mial loads and a broader range of connections could be obtained.

Numerical modelling was done using the Finite Element package ANSYS 5.5 (Swanson Analysis Systems

Inc. 1998a).

3.1.1 Boundary conditions

The boundary conditions for the FEM pararnetric models matched those imposed by the experimentat

testing conditions. The experimental longitudinal branch plate connections were arranged in the testing

machine using a h e d branch "X" configuration. Both the experimental and matching FEM model

specimen are shown in Figure 3-1. The 90" experimental test specimens contain two planes of syrnmetry

and thus a 1/4 FEM model was used.

The experimental test specimens were tested with a main member (column) compressive load and a

branch plate tensile load. This ioad combination was intended to simulate the more likely situation of a

tensile bracing force k ing applied to a compression loaded column. The FEM parametric models, on the

oîher hand, were tested using both a main member tensile load as well as a compressive load. In

combination with the column load, both a branch plate tende load as weli as a compressive load were

modelled. A column tensile load can occur under the action of column uplift forces. Aiso, a branch plate

compressive load will occur for bracing members designed to resist both tension and compression. The

research programme was mainly geared toward a study of main HSS (column) members under the influence

of (bracing type) branch plate forces. However, the main HSS member need not be a column and a brace

member need not apply the applied branch plate load. For example, the main HSS member can be a truss

member and the applied branch plate load can be introduced through a hangar type connection.

TOTALS 1 .l3O elements 8.178 nodes

FEM Modelling of ExperimentaI Test Specimens Typicai Experimental Test Specimen (using acnial measured dimensions and material pmperties:

Figure 3-1: FEM modelling of longitudinal branch plate-to-rectangular HSS member experimenîal test specimens

3 .12 Mode1 geomehy and meshing

The experimental test specirnens used in the 90" test series were numerically modelled to substantiate

the overall FEM parametric model. The actual measured dimensions and material properties of the

experimental test specirnens were used in the FEM models. However, once the overall FEM models were

verified with the experimental test results, minor refinements were made to the overall FEM model to allow

its use in an expanded pararnetric nurnencal programme.

The fiee length of the rectangular HSS chord extending beyond the branch plate connection is an

important modelling dimension for the parametric FEM model. This distance must be made suficiently

long to negate any end-effects relative to the local deformation of the HSS connecting face. FEM analysis

showed that the free length of the chord must be greater than 1.25 times the HSS chord width (bo) to avoid

end-effects. As a precaution, a more conservative value of 1.75bo was used in the FEM parametric study. A

very conservative value of 2b0 was used in the experimental test series.

The branch plate length (h l ) is another consideration for the paramecric FEM model. The effective

branch plate length-to-HSS chord width ratio (q'= N i l b t ~ ) was taken to be 1 .O. This value represents a

typical proportion for branch plate-to-HSS member connections.

Assuming that the weld size is designed to match the shear strength of the connecting material, the weld

leg size (w) was taken to beho - The weld leg size (iv) of f i t , (or the throat size a = t0) is derived from

Equation (1-4) by sening the material resistance factors (4) rqual to unity.

Mesh convergence studies were carried out to determine a suitable level of discretization. The FEM

mapped mesh originates at the corner weld of the branch plate and gradually fans ouhvard using a series of

minimum element sue constraints and biasing panuneters within each portion of the model (Le. HSS top,

side, corner, fke chord length, etc.). nius, the semi-automated mapped meshing of each FEM model is

consistent but the meshes thernselves are dependent on the overall geometry of the connection. Twenty

noded solid elements (SOLiD95) were used for al1 components of the FEM models. Figure 3-2 shows the

details of the generalised paramefric FEM mode].

TOTALS 1,79 1 elernents

12,830 nodes

Mes h

- weld site, >v = 1.41ta

radius + la (= s> t I

Figure 3-2: Parametric FEM modelling details for longitudinal brancb plate-to-rectangular HSS member connections

3.1.3 Materio1 properties

A multi-linear mapping of the exact material properties (detemined by tensile coupon tests) was used

for the FEM models. The stress-strain responses for the HSS material and branch plate material are shown

in Figure 3-3. Insofar as FEM modelling was concerned, the exact material properties of the weId material

were unimportant and thus the weld material was taken to be the same as the attached branch plate material.

HSS 178 x 127 x 7.6 600 . , 1

500 j FM = 506 MPa

- Coupon 1 Coupon 2 4

1 0 FEM rnulti-linear

rnapping

13.1 mm THK. PLATE

300

100 - Coupon I Coupon 2

1 O0 0 FEkI rnulti-linear l 1 rnapping

t

0 6 . : 0 6 . 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.10 0.75

Strain. E Strain. E

Figure 3-3: Material stress-strain curves

The "engineering" stress-strain material c w e s are plotted in Figure 3-3 and in Appendix A. However,

for large deformation analyses, ANSYS release 5.5 (Swanson Analysis Systems Inc. I998b) documents a

recommended "true" stress-strain conversion of:

Using Equations (3-1 and 3-2), a muti-linear mapping of the "me" stress-strain material response was used

as material property input for the FEM models.

3.2 FEM results

3 2 . 1 FEM model verification

Figure 3-4 shows the loaddeformation curves for the 90" experimental test series and corresponding

FEM rnodels. The details of the experimental and corresponding FEM rnodeIs are contained in Table 3-1.

Both geometrical and material non-linearities were used in the solution of the FEM models. Thus, the FEM

rnodels accuratety captured the elastic-bending, plastic-yielding, and membrane-action behaviour of the

rectangular HSS connecting face. However, the FEM models did not include cracking behaviour. Local

punching shear type cracks do begin to form around the perirneter of the welds between the branch plate and

HSS rnember at pst-yield deformation levels for the experimental test specimens. Thus, the FEM load-

deformation response begins to deviate h m the experimental test specimen response at large deformations

in which cracking dominates over ductile membrane action in the pst-yield stages of Ioading.

However, such large deformations are not acceptable in real structures and connections are considered

to have failed when defonnations attain limiting values. Notional deformation limits (Lu et al. 199Jb. Zhao

1996) have been used to define the strength of such a connection: these are an ultimate deformation limit

(3% bo) and a serviceability deformation limit (1% bo). The FEM models are verified by the experimental

resulis within this deformation range. Figure 3-5 shows a direct cornparison of the FEM and experimental

test results contained in Table 3-1. The average ratio of the FEM load to the experimental load is 1 .O3 for

the serviceability condition with a standard deviation of 4.1%. This proves a good correlation between the

FEM and experimental test results in the serviceability condition deformation range. The average ratio of

the FEN load to the experimental load is 0.86 for the ultimate condition with a standard deviation of 3.0%.

ïhis correlation represents good precision (standard deviation = 3.0%) but a lesser accuracy (average =

0.86). However, an average FEM to experimental test result ratio of 0.86 represents an acceptable tolerance

especially since it errs on the conservative side.

Greater accuracy could have possibly been obtained by considering initial geometric imperfections of

the HSS member including, for example, overall out-of-straightness and convexity or concavity of the HSS

faces. A h , very complex FEM modelling including anisotropic andlor heterogeneous material properties,

residuai stresses, and strain hardening in the corners of the HSS member could possibly enhance the

accuracy of the FEM results. Such refmements are worth noting but represent a disparate second-order type

analysis that was beyond the scope of the paramefric FEM modelling programmes presented in this thesis.

- Experimental renilts

---. FEM renilts

Connection deformation, A (mm)

O 5 10

Connection deformation. A (mm)

Figure El: FEM and experimental load-defonnation cuwes for longitudinal branch plate connections

O 50 100 150 200 Expenmental Load (kN)

Figure 3-5: FEM venus experimental results for longitudinal branch plate connections

3.2.2 Pmametric modelling programme

The maximum compressive load tested in the experimental test series was 540'0 of the main HSS

member (column) squash load. The tirst FEM parametric numerical model was designed to augment the

results of the experimental test series by increasing the axial compressive load in the main HSS member

beyond 54%. A maximum compressive load of 80% was achieved in the FEM numerical models. A

95% compressive load FEM numerical series was attempted but the solutions did not converge.

The applied branch plate load was tested in both tension and compression in the FEM numerical

models for the sake of completeness. The physical experimental test specimens were tested with only a

branch plate tensile load but a branch plate compressive Ioad was not expected to produce a significant

difference. The FEM results, documented in Table 3-2, confirm that only a marginal difference exists

between ihe results for a branch plate loaded in tension versus compression at the calculated connection

yield load level (Pu) and within the ultimate deformation limit (3%b0) range.

Finally, a main HSS member (column) axial tension was also investigated in the FEM parametric

numerical models. By cornparison, the physical experimental test series contained only main HSS

member (column) compressive Ioads.

A standard CANICSA-G312.3-98 rectangular HSS 178x127x8.0 cross-section was used for the

physical experimental test series. As a realistic parameter database, standard CANICSA-G3 12.3-98

square HSS cross-sections were used in the FEM parametric numerical rnodeis. A square HSS

127~127~6.35 cross-section was used in the first pararnetric numerical model series Iisted in TabIe 3-2.

Table 3-2: FEM results for a longitudinal branch plate-to-rectangular HSS member connection subjected to four possible loading sense combinations

~ H S S Fixed end

Branch plate in COMPRESSION 1 Branch plate in TENSION

Notional Deformation Limit States Capacity

Notional Deformation I CalcuIarcd Limit Statcs Capacity - -

Swiccability Ultimate Yicld straigth P d condition condition condition FEM

P . f ( n ) P . , tTn) P r Rn) P r

. (W) (W tkM P".S% note [A] [Al iBl [Al

0% 82.2 1.00 1 114.8 IM)

Scrviccability condition

Pr . ,% fin)

(LN) note [A

79.3 1.00 78.9 0.99 78.1 0.98 75.7 0.95 72.2 0.91

Ultimarc 1 Ykld m n g h 1 Prcd. condition condition FEM

Average 1.09

Sld. Drvtaiion 29% COV 2.7% COV 3.0%

110.1 0.95 101.5 0.88 86.8 0.75

426 0.37

Average 0.87 Srd Deviation 13.5%

COV 15.6%

Average 1.02 Sid Dcviation 6.9%

COV 6.%

[A] strength reduction factor. Rn ) = P (n ) 1 P (n =O) [BI P r using Eq. (1-9) where: (Fyo=394 MPa, WOa , h'llb 'o=i, = 0754)

3 -2.3 Determination of the critical foading combination

A connection strength reduction factor, f(n), was used to quantifi the influence of an axial Ioad on

the strength of a branch plate-to-rectangular HSS member connection. The idealised theoretical yield

load of the connection [Pr using Equation (1-911, is not dependent on the sense of the applied loads. In

terms of the main HSS member axial load, either an axial compression or an axial tension would result in

an equivalent premature yielding of the branch plate-to-HSS member connection. Similarly, the strength

of the branch plate connection is independent of the branch being loaded in compression or tension. In

both instances, the assurned yield-Iina pattern that develops would be equivalent, with only the rotational

sense of each yield line (Le. hogging versus sagging) changing.

Figure 3-6 and Figure 3-7 show the connection strength reduction factor, Rn), for the four possible

loading combinations of the main HSS member axial load and applied branch plate load. Figure 3-6

shows that when the main HSS rnember is loaded in axial compression, the FEM results for the strength

reduction factor. f(n), follow the theoretical f(n) factor calculated using the calculated yield load of the

connection (Pu). The theoretical strength reduction factor. f(n), based on the calculated yield load (Pr) of

the connection is compared directly with the notional 3% ultimate deformation limit state (Pu.3ri) in Table

3-2. The calculated yield load of the connection (Pr) and corresponding strength reduction factor. Rn),

corresponds well with the notional 3% ultimate defonnation limit state. The FEM results listed in Table

3-2 show only a small difference between the branch plate loaded in tension or compression. Thus, for

the case of a main HSS member axial compression, the branch plate connection strength cm be

considered equivalent, whether loaded in tension or compression. In both instances, the calculated yieId

load (Pr) of the connection agrees adequately with a 3% ultimate deformation limit state.

Table 3-2 documents the average ratio of the predicted yield load (Pr) to the FEM determined 3%b0

ultimate deformation Iirnit state load (Pu>%) of 1 .O4 with a standard deviation of 3.1%, for the branch plate

loaded in tension. Similarly, the average ratio of the predicted yield load (Pr) to the FEM determined 3%bo

ultirnate deformation limit state load (PUJsc) is 1.09 with a standard deviation of 2.9% for the branch plaie

loaded in compression. This illustrates a good correlation between the predicted yield load (Pr) and the

FEM determined ultimate defonnation limit state load (Pd%).

4

Branch plate loaded in TENSION : Branch plate loaded in COMPRESSION

O 10 20 30 40 50 60 70 80 90 100 ' O I O 20 30 40 50 60 70 80 90 100

CoIurnn preload ratio, n (%) Column preload ratio. n (O/O)

Figure 3-6: Connection strength reduction factor, f(n), curves for column compression

1*1 1.1 - _ - (P..,,) serviceability lirnit = 1-04 c - $ 0.9- -

'3

0.8 - c

0.8 - 0 ! .= 0.7 - O 3 (Pu,,) uitimate limit

0.6 - Li

' 0.6 - 5 0.5 - 0.5 - E

0.4 - 0.4 -

Critical load combinarion

Brnnch plate loaded in TENSION Branch plate loaded in COMPRESSION

I I I I I 1 I I i

n C 2 0.3 - .- d

3 2 0.2 - r 3 0.1-

0.0

Column preload ratio, n (%)

I I I I I I I I ,

1.1 i j 1.04 7

0.9-

! 0.8 - 0.7 - 0.6 - 0.5 - - theoretical Rn) 0.4-

4 Column preload ratio, n (%) 4 P T & ~ L - % Z - W - 7:----7-

0 3 - 7

; 0.2 - 1 0.1 -

0.0

7

0.3 - 3 3 0.2 - 1

0.1 - 0 . 0 -

Figure 3-7: Coanection strength reduction factor, Rn), curves for column tension

-o- (P,.,,) serviceability limit -O- (Pu& ultimate limit

I I i I 1 1 t I I

O 10 20 30 40 50 60 70 80 90 100 O I O 20 30 40 50 60 70 80 90 IO0

Figure 3-7 shows that when the main HSS mernber is loaded in axial tension, the FEM results for the

strength reduction factor, f(n), deviate fiom the theoretical f(n) factor based on the calculated yield load

of the connection (PY). For small to modetate levels of main HSS member tension (-10% to 50%), a

modest increase in the connection strength was achieved; Table 3-2 lists some connection strength

"reduction" factors actually greater than unity, albeit only slightly greater than unity (-1.01 to 1.03). At

higher levels of main member axial tension (beyond -50%) the strength reduction factor, f[n), faIls below

unity but not to the sarne degree as was the case for axial compression. This deviation can be attributed

to a beam-column type behaviour and the associated P-A effect. The resistance of branch plate-to-HSS

member connections is based on the load level achieved at prescribed notional deformation limits. Thus,

an increase or decrease in the HSS connection face deformation will result in a corresponding increase or

decrease in the prescribed resistance of the connection. Figure 3-8 shows a schematic representation of

the P d effect in a branch plate-to-rectangular HSS member connection. The P-A effect will increase the

rectangular HSS connection face deformation under the action of axial compression. Alternatively, the

P-Aeffect will tend to straighten the rectangular HSS connection face and decrease the overall

connection face deformation under the action of axial tension.

Figure 3-8: P-A e f k t In branch platc-to-rectangutar HSS member connections

Figure 3-7 illustrates the co~ec t ion strength reduction factor, Rn), under the influence of a main

member HSS axial tension. Whilst the main HSS member is under the influence of axial tension, the

applied branch plate load can either be in tension or compression. If the applied branch plate Load is in

tension, Figure 3-7 and Table 3-2 show that the strength reduction factor, f(n), does not fall below unity

until a rather substantial main member axial tension of -80% is applied. Furthemore, even at a very hi&

main member a-ial tension of 95%, the strength reduction factor still maintains a value close to unity of

0.87. For the case of the branch plate Loaded in tension, a recommended strength reduction factor of unity

(Le. no reduction in connection strength) is certainly justified for a main member axial tension up to

-80% of the squash load. In the less likely event that the main member axial tension exceeds 80% of the

squash load, Figure 3-7 shows that even at a main member axial tension as high as 90% of the squash

load, the strength reduction factor is still maintained near unity at a value of -0.94. For this load

combination, a constant strength reduction factor of unity can be reasonably proposed.

However, Figure 3-7 shows that the criticai load combination occurs when the branch plate is loaded

in compression. In this case the strength reduction factor falls to 0.89 for a main member axial tension of

80% of the squash load, and sharply plummets to 0.64 for a main member axial tension of 95% of the

squash load. In this case, a constant strenpth reduction factor of unity is less reasonable. Instead, the

theoretical connection strength reduction factor, Rn), calculated using the calculated yield Ioad of the

connection (Pr), should be considered. This theoretical connection strength reduction factor, f(n), would

be conservative for the case of a main member axial tension, but not overly conservative. In fact, of the

four possible load combinations s h o w in Figures 3-6 and 3-7, only the one load combination of a main

member axial tension and an applied branch plate tension would be considered overly conservative if

described by the theoretical connection strength reduction factor f(n). Thus, considering the uncertainty

of the exact loading combination and perhaps a Load reversal that would occur in the field, it wouid be

prudent to propose the overafl use of the theoretical connection sîrength reduction factor f(n) rhat is

implicitly contained in Equation (1-9).

3.2.4 Parametric modelling of the criticcd load combination

Figures 3-6 and 3-7 show the critical load combination for the main HSS member (column) under the

influence of axial tension or compression. Between the two loading conditions, the overall critical load

combination is shown in Figure 3-6 as a combination of an axial compression and an applied branch plate

tension. This load combination represents the greatest reduction in both the serviceability (P,,lw) and the

ultirnate (PUJsi) connection resistances, Having determined the critical loading condition, the n e a stap in

rhe FEM parametric rnodeiling programme was to apply this critical load combination to a series of

different HSS member cross-sections.

CANKSA-G3 12.3-98 square HSS sizes were used, for a realistic parameter database. A standard

dimensionless parameter used to describe rectangular HSS cross-sections is the width-to-thickness ratio

of the connecting face (2y0 = bdto). This width-to-thickness ratio (2yo) was varied by modelling various

CANKSA-G3 12.3-98 square HSS sizes with a common wall thickness of 6.35 mm. Five different square

HSS sizes were used in the FEM analyses as listed in Table 3-3. The five square HSS sizes correspond

to a width-to-thickness ratio ranging between a minimum value of 20 and a maximum value of 40.

Figure 3-9 shows a plot of the FEM strength reduction factor data contained in Table 3-3. The

theoretical connection strength reduction factor, f(n), is a good predictor for the FEM results. Howvever.

the ANSYS-derived FEM results are lacking for the combination of increasingly flexible HSS connection

faces (i.e. high 270 = bdto ratios) and higher axial loads. For this combination, the ANSYS solutions

would not converge. From Table 3-3, it can be seen that a complete set of ANSYS-derived FEM results

is available for a maximum connection face flexibility of 2y0 = bdto= 24. In a similar FEM study (Cao et

al. 1998a) using the FEM package ABAQUS (1996), the theoretical connection strength reduction factor

f(n) was verified for a maximum connection face flexibility of 2yo = bdto = 38 and a ma..imum main

member (column) compression preload ratio of 75%.

Table 3-3: FEM results for tongitudinal brancb platr-to-recbngular HSS member connections subjected to the critical loading sense combiaation

I B m h p h in TENSION

Sid ONiation 5 J?c COV 28% l

!r. = 1271635 - loi0 Sib Deviaion 3. tyi

1' - a.254 COV 3.0%

Noits: [A] P r u i n g Eq. (1-9) wherc: (F,,,=394 M P q &=XIo. h',lb',=i)

[BI strcngih ducrion C;ictor, Rn ) = P (n ) l P ( n 4 )

- 4 - Nt

r L -

t

t - t - C

.--....---.- &

U H S S Fixed end

' g 3 u 9 k ;*: E - 2 - C Q u

HSS ISÏrlS2r6.35 A w q c 1.09

ha= lsuSJS=U.9 Std. Dmmjon 3.2% 3--0210 cov 2.9%

au. NI op 108.8 m i.10 = Z 20% 95.4 O.% 107.5 0.99 1.13 i c g , 40% 90.6 0.91 102.9 0.95 I.t5

1.13 1.17

HSS 1781 l78x635 Avcngc 1.13 Zy*' 1mas = Zao SlbDcutrPjon ISY

p'a0.178 COV 12%

IO56 Igo iO2.2 0.97 97.6 0.92 90.4 O 86 Z 8 0.69

0%

20% 40% 60%

BD?h

95% 100%

111.8

110.4 0.99

105.8 0.95

97.5 0.87

63.2 0.74

616 0.56 40.7 0.36

1.06

1.08 1.08 1.08 1.14

1.1 Branch plate loaded in TENSION

theoretical f(n) curves for

O 10 20 30 40 50 60 70 80 90 100

Column compression preload ratio, n (%)

Figure 3-9: Connection strength reduction factor, f(n), curves for the critical loading sense combination

3.2.5 Branch plute sh-ess distribution

Figure 3-10 shows the branch plate stress distribution from an experimental test specimen and the

corresponding FEM model, at various load levels. The experimental test results, as determined by strain

gauge measurements, are subject to certain experimental errors including fabrication and testing

alignment tolerances. However, the FEM results are verified by the experimental test specimen branch

plate stresses (as detennined by strain gauge measurements) as show in Figure 3-10.

(a) Expcrimental test spccimen 90LPZO (b) FEM results

I Tension load (kN) (

1 50 I

l 1 (calcdaied nnnectioi yield load. Pd l7O ;

Lefi end Plate centre Right end

Position dong branch plate width (mm)

Figure 3-10: Experimental and FEM branch plate stress distributions

A longitudinal branch plate-to-recîangular HSS member co~ect ions is inherently flexible and thus

results in relatively low connection resistances. The FEM parametric study presented earlier in this

chapter was used to examine the strength reduction factor, Rn), as a hnction of the avial load present in

the main rectangular HSS mernber (colurnn). The branch plàte thickness used for the parametric FEM

study was chosen to be equal to twice the thickness of the connecting HSS member wall thickness to

keep the proportions of the connection teasonabte. However, if the thickness of the branch plate was

chosen to produce a tesistance equal to the calculated connection capacity (Pr), unreasonably thin branch

plates would be the result. Assuming a unifom stress distribution in the branch plate. Table 3-4 shows

what the required thickness of the branch plate would have been.

As shown in Table 3-4, longitudinal branch plate-to-rectangular HSS member connections wiil

typically result in relatively fow connection capacities (Pr) and correspondingly thin required branch

plate thicknesses. An extremely "çtocky" HSS memkr is required to achieve a considerably higher

connection capacity ( P r ) . Figure 3-1 1 shows such a stocky longitudinal branch plate-to-rectangular HSS

member connection.

Table 3-4: Required braach plate thickness to satisfy the calculated connection capacity (PY)

HSS 127~127~6.35 HSS 153152x6 35 HSS 178x178~6 35 HSS 2 0 3 ~ 2 0 3 x 6 35 HSS 3 4 ~ 2 5 4 x 6 35

HSS wdth b. 1 t ? 7 m 178 mm 203 mm 3 4 m 1

[A] P r using Eq. (1-9) wtme: (F,,=394 MPa, W. h',fb',=l)

HSS 89 x 89 r 9.53

effective HSS width. 6,' = 89 mm - 9.53 mm = 79.5 mm

effective bmch plate length h,' = 79.5 mm [using q' = h,'lb,,' = 1.0 proportion1

actual branch plate Iength, hl= h,' Zw = 67.5 mm [weld s i x lv = 6 mm]

calculatcd connection yield load, P, = 264 kN [using Eq. (1-9) where: F, = 394 MPa]

calculated branch plate thicknas, b,= P,i(F,, x h,) = 9.0 [where: F,, = 435 MPa/

Figure 3-1 1: FEM mode1 for a branch plate-to-HSS 89~89~9 .53 connection

tn this case, a very small width-to-thickness ratio of the HSS connection face (HSS 89 x 89x 9.53)

resulted in a higher calculated connection capacity of Pr = 264 W. This higher connection capacity

resulted in an increased required branch plate thickness of 9.0 mm as compared with the 1.0 mm to 2.6

mm thickness range listed in Table 3-4. However, even 9.0 mm is rather thin. A minimum 3/8" (9.5 mm)

or 1/2" (12.7 mm) plate would likely be used by a fabricator. In any event, the severity of the non-

uniform stress distribution was determined by the FEM model shown in Figure 3-1 1. in this case, the

branch plate thickness was determined based on the calculated connection capacity ( P r ) and an assumed

uniform stress distribution in the branch plate. The actual stress distribution in the branch plate, however,

is not uniform and is shown in Figure 3-12. Although the stress in the branch plate is much higher

toward the ends of the branch plate in the initial stages of Ioading, the ratio of the average (Le. uniform)

to the maximum branch plate stress is very close to unity (= 0.95) when the branch plate first begins to

yield. Thus, the effect of the non-uniform stress distribution in unstiffened longitudinal branch plate-to-

rectangular HSS rnember connections is of negligible consequence.

HSS 89 x 89 x 9.53 2y0 = 9.3 pt = 0.26

-40 -30 -20 -10 O IO 20 30 40

Position along plate width (mm)

1.2

1.1 -

Figure 3-12: Branch plate stress distribution

w VI

0.8 - 2 .d VI

0 0.7 - P) .-

P=ZW kN (4.95 Pr)

m P= 0.86 P,

F 2 0.4 E! - P= 0.5 Py

0.3 - " O -

0.2 - - 0.1 -

Branch plate load (P) = 0.25 Connection yield Load ( P r )

0.0 l ~ ~ ~ ~ l ~ l i ~ l ~ ~ ~ ~ l ~ ~ ~ r ~ ~ ~ ~ ~ ~ ~ ~ ~ l ~ l r c ~ ~ ~ ~ ~ ~

4. EXPERLMENTAL STUDY OF ALTERNATIVE BRANCH PLATE-TO-RECTANGULAR HSS MEMBER C O N N E ~ O N TYPES

A conventional longitudinal branch plate-to-rectangular HSS member connection exhibits excessive

distortion or plastifkation of the HSS connecting face under an applied branch plate load (P) as

illustrated in Figure 4-1. In an effort to reduce the inherent flexibility of longitudinal branch plate

connections, stiffening plates or stnictural tees are sometimes welded to the HSS connecting face [Figure

4-2(c)]. Also, a through branch plate connection can be used to increase the strength of a standard

longitudinal branch plate connection [Figure 4-2(b)]. Another method of reducing the out-of-plane

deformation of the HSS connecting face involves welding the connecting branch plate transverse to the

HSS member axis [Figure 4-2(d)]. The results of an experimental study of through plate, transverse

plate, and stiffened longitudinal branch plate-to-rectangular HSS member connections are presented in

this chapter. The strength and stiffness of these "alternativev plate connections are compared with the

traditional longitudinal plate connections. A consolidated design approach for the various plate-to-

rectangular HSS member connections is henceforth presented.

Figure 4-1: Longitudinal branch plate-to-rcetangular HSS member conneetion face ddormation

(a) Longitudinal (b) nmugh (c) Stiffened branch plate branch plate branch plate

(d) Transverse branch plate

Figure 4-2: Braach plate-to-rectangular HSS member connection types

4.1 Test specimens

Twelve connection specirnens, in a 90" "T" or "X" configuration have been tested in the laboratory.

The "T" and " X configurations are show in Figure 4-3. The test specimens consisted of IongitudinaI

branch plate, through branch plate, stiffened longitudinal branch plate, and transverse branch plate

connections. The details of each test specimen are listed in Table 4-1. Al1 piates were fillet welded to the

connecting surfaces amund their entire perimeter.

Each test specimen "column" was fabricated fiom the same length of HSS ( 1 78x 127~4.8) steel stock.

Similady, each of the various branch piates was fabricated h m the same sheet of steel plate stock. in this

way, the material properties between the test specimens were held constant. The measured dimensions of

the HSS cross section, plate thickness and the size of the fiilet weids comecthg the HSS columns and

branch plates are aiso documented in Table 4-1. Tensile tests have been carried out on duplicate coupons for

the rectangular HSS (taken h m the "flats") and branch plate materiais. The rectangular HSS materiai

conformed to CANICSA-G40.201G40.21-98 Class H Grade 350W. The average values of these material

properties are documented in Table 4-1 and fwther details can be found in Appendix A.

Tvoe 1: Fixed Chord T-Connections

Figure 4-3: Testing arrangements for alternative branch piate-to-rectangular HSS member connections

Table 4-1: Experimental detaib for alternative branch plate-to-rectaagular HSS member connections

(a) Single [ (b) Through 1 (c) StiKcaed Phtc (d) Transverse

90LP 90~~2190RP 9 0 4 8 0 4 ~ ~ 804-2 804-3 BO8LP B08-2 808-3 BO4TP BO8TP

"unrestnincd" plate widh, b 18=b l ' ~ b ' 2 ~ [mm] 43.1 43.3 44.1 112.9 1 13.3 115.3 (rcfer IO Figure 4-6) p9=b ,Y be0 0.249 0.250 0.255 0.653 0.655 0.666 (Eq. 4-10) minimum required hickncss, t , 2 [mm] 5.1 5.1 5.2 1 17.0 17.1 17.7

mcasured stiffening plak hickncss, t P [mm] 13.1 9.4 6.3 13.1 9.4 6.3 I

minimum requid hicloies satisfied J J J -L @tao thia

mm. load. P m [kN]1(>388) (B326) (M30) (>446) (>472) (>320) (23 12) 570 363 328 136 188

Zalculated h u g h plate capacity = 2 x qua1 s i m l (b',, hll) single plate calculated capacity

I

Measutrd HSS dimensions: 1% l2ïx4.8 1

~ J ) Longitudinal (b) Through (c) Stiffencd Plaie Platc Platc

For Branch and Stiflenrng Plaies: (d) Transvcrsc

h1-i t n Y O o d 1 s 1 21 3 P a O 1 G a 200

For HSS Colwnns:

Yield sucngih (F,,) 408 MPa

4.1.1 Test ser-up

All the tests were carried out using a 1000 kN capacity MTS Universal Testing Machine in the nvo

testing arrangements shown in Figure 4-3. The test specimens consist of a stub rectangular HSS main

member with the simulated branch plate connection welded to the mid-face of the HSS. A tende load was

applied directly to the branch plate as it was gripped inside the upper head of the testing machine. The test

spcimens were instnrmented with Linear Variable Differential Transfomers (LVDTs) to record the load-

deformation behaviour of the connection. Also, five m i n gauges were spaced across the width of the

branch plate of each specimen to sample the distribution of longinidinai min across the plate.

4.2 Test results

Since the limit state of a specimen is usually governed by excessive deformation of the HSS connecting

face, the load-deformation behaviour of the connection is the most important data obtained from the tests.

Figure 4-3 shows significant deformation of the HSS comecting face during testing. For connections in real

structures, such large deformations are not acceptable and connections are deemed to have reached their

limit state when deformations attain limiting values. Figure 4 4 shows the load-deformation curves for the

test specimens.

Table 4-1 lis& the l%bo serviceability deformation limit (P,,%), and the 3%bo ultimate deformation

limit (P,,J%) load levels obtained h m the experimental loaddeformation curves (Figure 4-4). Table 4-1

also lists the predicted yield saength [Pr using Equation (1-9)] of each connection. The predicted yield

strength (Pr) corresponds well (avg. P a 3 % = 0.92) with the notional 3%bo ultirnate deformation limit

load level. Thus, the calculable co~ection yield strengih (Pr) can be used in lieu of the 3%60

ultimate defonnation iimit (P i s34 load level.

(a) Longitudinal Plate (b) 'lhrough plate

Connection deformarian. A (mm)

(d) Stifined plate

O 10 20 30 40 50 Conncction defomatioh A (mm)

Figure 4-4: bad-defonnation curves for alternative brancb plate-to-rectangular HSS member conneetions

4.2.3 Governing strength versils senticeabiliry condition

Based on a ratio of factored to unfactored loads of 1.5, Lu et al. (1994b) suggest using the ratio Pa,?, t

to decide whether the ultirnate deformation limit state or the serviceability deformation limit state

govems:

> 1.5, serviceability(P,,,) govems. Ps.1~. - < 1.5, ultimate(P,,, ) governs. Pd%

Zhao (1996) proposed that the goveming deformation lirnit states expressed in Equations (4- 1 and 4 2 )

can be predicted by the following geornetric properties of the connection:

bo p < 0.6 and - > 15, serviceability (Px.,,) govems. [ O

bo p r 0.6 or - 5 15, ultirnate (PUJ,) limit govems. (0

Figure 4-5 is a cornprehensive plot of experimental and FEM test specimen results showing the

goveming strength or serviceability limit state. The FEM results for stiffened plate connections are

presented in their entirety in Chapter 5 of the thesis. In Figure 4-5 the calculable connection yield strength

(Pr) is used to replace the notional 3%bo ultimate deformation limit (P&J%) load level. The actuai goveming

limit states of branch plate to HSS connections can then be cornpared with the recornmended lirnit state

partitions set forth by Lu et al. (1994b) and Zhao (1996).

The ratio of factored to unfactored loads of 1.5 (Lu et al. 1994b) was plotted as a horizontal reference

fine using the (yield load Iserviceabiiity load) axis in Figure 4-5. The region above this reference line

represents a governing serviceability condition (Px,,%). Likewise, the region below this line represents a

governing strength condition (Pu).

The goveming strength or serviceability condition depends on the connection parameters /3 (or /3')

and 2yo(= b&). In general, at hi& B (or p) values the connection can be expected to be stiff and the

serviceability limit will not be expected to govern. Conversely, at high bdto values, the HSS chord face is

very flexible and the serviceabiiity limit will tend to govern. A range of conditions between these two

extrema must now be categorised in a rational fashion.

FEM RESULTS EXPERIMENTAL RESULTS

Loneitudinal & (Cao et al. 1998a) 4 b, lt0=23 .4 +J- b, /t0=15.6

Stiffened & (results contained in Chapter 5 )

-a- bolto=118.0 -Q- bo lt0=40.0 - b, lt0=32.0 -g- bo lt0=28.0 -t b, lto=20.O + b,lto=16.1 + bo Iro= 14.0 + b, II,= 12.0

Stiffened b, lt0=37. i

Transverse Plate + b, lro=3 7.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(Branch plate width) 1 (HSS connecting face width), P'

Figure 4-5: Coverning strength versus sewiceabüity Limit state for experimental and FEM branch plate-tcwectangulnr HSS mcmber connections

Figure 4-5 shows that for B' 1 0.6 the strength limit governs. The P' 1 0.6 governing limit state

generally agrees with that proposed by Zhao (1996) in Equation (4-4) but the bdto 2 15 limit proposed by

Zhao (1996) is too conservative. An alternative method of categorising the b d ; ~ limit would be to base it

on the "class of section". For example, the Canadian CANKSA-S16.1-94 limits for Class 1, 2, and 3

rectangular HSS cross-sections are listed in Table 4-2.

Table 4-2: CANICSA-516.1-91 rectangular HSS classes

1 note: using b,w,,fi=bo-4to and FY=35O MPa I

When the strength limit sbte govems, the connection capacity (Pr) cm be calculated using Equation

(1-9). However, if the serviceability limit state governs, the connection yield Load (Pr) must be reduced

to obtain the connection serviceability load Pr,l.. can now be related to Pu by using the

recommended Class 1, Class 2, and Class 3 design lines show in Figure 4-5. Recognise that the

serviceability load limit (P ,p , ) govems the deformation of the connection and not the strength (safety).

Therefore, the recommended serviceability load design lines shown in Figure 4-5 are ploaed through the

existing data without any undue consewatism. The relationship between the connection yield load (PY)

and the connection serviceability load (P,J%) for Class 1,2, and 3 HSS memkrs takes the form:

Now, both the yield load [Pu calculated using Equation (1-9)] and the serviceability load [P,.]?, using

Equation (4-9, (4-6), or (4-7)] of a branch plate-to-rectangular HSS member connection can be

calculated. The goveming strength or serviceability limit condition is determined using Limit States

Design (LSD) principtes. The calculated yield load of the connection (Pr) is compared with the total

applied factored load (Pf). The calculated serviceability load of the connection (P,,Is ) is compared with

the total specified unfactored load (P). Thus, the governing strength or serviceability condition is no

longer based on a recommended ratio of 1.5 for the factored to the unfactored load level. [nstead, the

strength or serviceability governing condition is determined using the actual factored and unfactored

loads.

ï h e ratio of Py to Pf detemines the extent to which the yield Ioad condition has been met:

PY Yield load ratio = - (4-8) Pf

The ratio of PT,,% to P determines the extcnt to which the serviceability load condition has been met:

p3.1~. Serviceability Joad ratio = - P

The lower of the two load ratios determines whether the yield condition or serviceability condition

governs. For design purposes, both ratios must be 2 1.0 to satisfy both the serviceability load and yieId

load conditions (limit states). The "design loop" would consist of initiaily designing the connection for

the strength condition (Pu) and then checking to see if the serviceability condition (Pr,lY.) is met, as is

customary with a Limit States Design (LSD) procedure.

4 3 Overall Design of branch plateto-rectanguiar HSS member connections

The design and fabrication of connections for HSS members has often been perceived as complicated

and expensive. Rational design methods are needed to encompass and, wherever possible, to consolidate

the multitude of connections available to the designer. The yield line method presented in Equation (1-8)

has already been incorporated in the design fomulae (IIW 1989; Packer and Henderson 1992, 1997) for T-

connections between rectangular HSS members and connections between rectangular HSS members and

plates. Equation (1-9) supersedes Equation (1-8) by accounting for the influence of a normal stress that

may be present in the chord member. The results of the experimental program, and the supplemental FEM

pararneûic studies presented throughout the thesis, indicate that the "alternativew longitudinal through plate,

stiffened longitudinal plate, and transverse plate-to-rectangular HSS member connections can be grouped

under the generai case of a rectangular HSS T-connection and designed as such for a plastification-type

failure of the HSS connecting face.

4.3.1 Single branch plate and through branch plate connec fions

The calculated yieId Ioad [Pu using Equation (1-9)J of a general rectangular HSS T-connection is based

on an idealised yield the pattern forming around the footprint of the connecting branch plate causing

plastification of the connecting HSS chord face. This represents a simplified but effective isolation and

approximation of the actual plastification mechanism. Within these limits of idealisation, a through branch

plate connection cm be expected to have approximately double the strength of a single branch plate

connection by causing plastification of two HSS chord faces rather than one. Experirnental results confirm

that a through branch plate connection can be reasonably approximated as having double the strength of a

correspondhg single branch plate connection for design purposes (Refer to Table 4-1 where the average

ratio for P , , J ~ and fr3% is 1.9). A supplemental FEM parametric study of through branch plate connections,

presented in Chapter 6 of the thesis, further substantiates this conclusion. On a general note, longitudinal

branch piate and through branch plate connections are characterised by low P ratios (s 0.1 to 0.25)

resulting in a relatively low connection yield Ioad (Pr).

4.3.2 Stiffened longitudinal branch plate connections

A stiffened branch plate connection can ultimately achieve a much higher design resistance

equivalent to the enlarged "footprint" of the stiffening plate as opposed to the modest footprint of the

branch plate itself. In order to achieve this load, the stiffening plate must be "effectively-rigid" with

respect to the HSS connecting face such that a plastification mechanism does not occur in the stiffening

plate itself.

Equation (4-10) is an empirical formula, developed using FEM-generated numerical data. This FEM

study and resulting equation is presented in its entirety in the next chapter of the thesis. Equation (4- 10) is a

k t - f i t exponential curve used to determine the minimum required effectively-rigid stiffening plate

thickness t ~ ~ , to satisfy both the (Pr) strength condition and the (P,J%) sewiceabiiity condition. The ratio

of the stiffening plate thickness rH-, to the HSS connecting face wall thickness ( to) is a function of (pl), the

"unrestrained" stiffening plate width (bla) to the HSS width ratio (as illustrated in Figure 4-6). The

"unrestrained" stiffening plate width (6,') was defined as the stiffening plate width (b l ) minus the branch

plate width (g) and both branch plate welds (214.

Based on this minimum required "effectively-rigid" stiffener plate thickness using Equation (4-

IO), the predicted connection yield load [Pr using Equation (1-9)J was deemed invalid for some of the

experimental stiffened longitudinal connections in Table 4-1 (where they are show crossed out and

labelled "too thin"). For these connections with a stiffening plate deemed as too thin, a plastification

mechanism would tend to develop in the stiffening plate itself.

(4- IO)

6,

Figure 4 4 Stiffeoiog plate oomeoclature

Provided that the stiffening plate remains "effectively-rigid", tests B04LP, B04-2 and BO44 (refer to

Table 4-1) confirm that the yield load of the connection (Pr) calculated using Equation (1-9) is a

conservative predictor of the ultimate deformation limit state load level (Puri%)

The stiffened longitudinal plate connections are used to increase the P' ratio up until P' = 0.8. From

Equation (1-9) it can be seen that the strength of the connection increases as B' increases. For P' > 0.8 the

strength of the connection increases rapidly and a prohibitively thick and impractical stiffening plate

would be required. Hence, in the upper range of fY > 0.8, a transverse branch plate connection is

recommended.

Also, as P (or fY) approaches unity the strength of the HSS connecting face tends towards infinity and

punching shear around the branch, or local failure of the rectangular HSS side walls, becomes the critical

failure mode for p 1 0.85 (Packer and Henderson 1997) and these failure modes can be checked using

current holtow section design manuals and specifîcations.

4.3 -3 Tramerse branch plate connecrions

A transverse branch plate-to-rectangular HSS member connection is significantly stiffer (due CO a higher

p ratio) and hence has a higher design resistance than a longitudinally-oriented branch plate. However. aside

fiom the behaviour of the HSS connecting face, the design strength of transverse plate connections may

also be governed by an "effective width" criterion applied to the branch plate, which accommodates the

highiy non-uniform stress distribution in the plate (de Koning and Wardenier 1985). This effective width

criterion was reviewed in Section 1.2.5.

The two transverse plate connections tested in this study inciuded a moderate P = 0.4 (p = 0.52) and

a relatively high P = 0.8 (p = 0.91) ratio. In both cases, the notional ultimate load Ievel (PUJu,)

corresponded well with the calculable yield load (Pr) [PflUSY = 0.92 and 0.891.

4.3.4 Connecrion costs

A rational and efficient design of HSS connections mua be coupled with econornical fabrication. A

study of the relative costs of shear connections to HSS members was presented by Shenna. (1996) and the

applicable results are Iisted in Table 4-3.

Table 4-3: Relative connection costs [adapted lrom Sherman (1996)l

Shear connection

type

Single angle, L-shaped welds

- - - . - - - - -

Shear tab

Vertical welds - - - -

Through plate

Equivalent branch plate Relative conneetion type cost

Longitudinal plate, 1 .O5

Transverse plate - - - - -- - - -- - - -

Stiffened 1 1.50 - -

longitudinal plate

The simple "shear tab" is one of the most economical connection types. A shear tab is oriented

parallel to the axis of a column in order to frame directly into the web of a connecting beam. However,

when a simple shear tab is used as a branch plate for an HSS member, the tab (or plate) may be oriented

either longitudinally or transversely. A single longitudinal plate can accommodate multiple connecting

branches (e.g. a K- or KT-type connection) framing into a single node of an HSS member. However,

three separate transverse plates would be required to connect each branch of a KT-type connection. Thus,

a single longitudinally-oriented branch plate is to be preferred for multiple branches in one plane h i n g

into a single node of an HSS member. A transverse branch plate-to-HSS mernber connection is

significantly stiffer and hence has a much higher design resistance than a longitudinally-oriented branch

plate but is more suitable for a single branch framing into an HSS member.

A stiffened longitudinal plate is often necessary to increase the design capacity of a longitudinally-

oriented branch plate. A through plate connection will also result in a higher design capacity but is

considerably more expensive than a stiffened branch plate. Also, a through plate connection is limited to

"doubling" the strength of the co~ect ion. increasing the effective width of a longitudinal branch plate

by using a stiffening plate is a far more effective method of increasing, doubling, or more than doubling

the design resistance of the connection.

Design equations for HSS connections are ofien governed by limits of applicability related CO the two

dimensioniess parameters 2y0(= b&) and P(= bllbo). Yield line mechanism-based forrnulae are usually

valid fiom low to moderately high B ratios. Different modes of failure such as punching shear or local

failure of the HSS side walls tend to govern at higher P ratios approaching unity. Likewise the goveming

strength or serviceability limit state condition is aiso generally related Co the dimensionless parameters

270 and P.

Practical limits of applicability also arise from a fabrication standpoint. In general, it is preferred to

connect to the "flat width" (bu dth) of a rectangular HSS member. Welding in the corner region of a

rectangular HSS member is more difficult than welding along a preferred flat surface and therefore

introduces additional fabrication costs. Also, the corners of a cold-formed rectangular HSS member

represent regions of Iower ductility. Notwithstanding an increased cost of fabrication. welding in rhis

region of lower ductility may undennine the integrity of the welded joint and may lead to premature

weldlbase metal fractures. Figure 4-7 shows the approximate practical lirnits of applicability for branch

plate-to-rectangular HSS member connections.

The geornetric limits of applicabiiity for branch plate-to-rectangular HSS member connections were

derived by approxirnating the upper bound (Plhtwidih) and lower bound (PI,, branch ptate width-to-

rectangular HSS width ratios. Figure 4-7 shows that the upper bound branch plate width-to-rectangular

HSS width ratio (Pu widih) is Iimited to the "flat width" (bm vndai) of the rectangular HSS member

connecting face. The Iower bound branch plate width-to-rectangular HSS width ratio (Pl, bnmd) \vas

derived to characterise the fact that the practicai effective minimum width of the connecting branch plate

(6,- baünd) is not zero. AS stated in Section 3.2.5 of the thesis, the minimum width (thickness) of a

Iongitudinal branch plate is likely to be set by the fabricator as 3/8" (9.5 mm) or 112" (12.7 mm).

However, as a proportion of the HSS wall thickness, the approxirnate width (thickness) of the connecting

branch plate is on the order of the HSS wall thickness. Also, the effective width of the connecting

branch plate includes the width (leg six, w) of the connecting welds. As a proportion of the HSS wall

thiçknerr (ro), the appmximate weld leg ske (w) is on the a d e r of f i t o . Based m these approximate

upper bound (Ba, wmb) and lower bound (Pl, bad) branch plate width-to-rectangular HSS width ratios,

Figure 4-7 is intended to illustrate the general geornetric limits of applicability for branch plate-to-

rectangular HSS member connections.

(a) Longitudinal (b) Through (c) Stiffened (d) Transverse plate plate plate plare

L " " ' " " " ' ' " ' ' l '

(a) [mg plate (c) stiffcned plate 0.8 1 (b) lhmugh pl- (d) iransvmc plate

c n

Cbord Face Yiclding P'< 0.85

Sranch width-to-HSS width ratio, P (or p)

Figure 4-7: Praetical limits of appiicabüiîy for branch plate-to-rectaagular FISS membcr connections

Refening to Figure 4-7, longitudinal and through plate connections are characterised by low P' ratios

(= 0.1 to 0.25). Next, stiffened plate connections may be used to increase the B' ratio up until fY=0.8.

From Equation (1-9) it can be seen that the strength of the connection increases as B' increases. For P' >

0.8 the strength of the connection increases rapidly and a prohibitively thick and impractical stiffening

plate would be required. Hence, in the upper range of P'> 0.8, a transverse branch plate connection is

recommended. Also, as B' approaches unity the strength of the rectangular HSS connecting face tends

towards infinity and punching shear around the branch, or local failure of the HSS side wall becomes the

critical failure mode for p 2 0.85 [Packer and Henderson (1997)].

Figure 4-7 also shows the goveming strength or serviceability regions for a comrnon ratio of a

factored to unfactored load level of 1.5 as an example. Otherwise, the strength or serviceability

governing condition is calculated using the actual ratio of the factored to unfactored load level and is

explicitly determined using a Limit States Design (LSD) procedure outlined in Section 1.2.2. Hoivever,

using a factored to unfactored load level of 1.5 for example, Figure 4-7 shows the regions in which the

strength condition or the serviceability condition would govem. Referring back to Figure 4-5, Class I

HSS members (bo Iro 5 2 6 as defined in TabIe 4-2) lie entirely within the region where the strength

condition (Pr) governs. Likewise, Figure 4-7 shows that Class 1 HSS members lie within the shaded

region of the graph where the strength condition (Pi.) governs. For Class 2 HSS members (bo /to s 32 as

defined in Table 4-2), Figure 4-5 shows that the strength condition govems for B' > 0.4. Likewise, Figure

4-7 shows that Class 2 HSS members lie within the shaded region of the graph where the strength

condition (Pr) governs for p' > 0.4. For Class 3 HSS members ( b ~ /!O 5 40 as defined in Table 4-2), Figure

4-5 shows that the strength condition governs for p' > 0.6. Likewise, Figure 4-7 shows that Class 3 HSS

members lie within the shaded region of the graph where the strength condition (Pr) governs for p' > 0.6.

Figure 4-7 is intended to illustrate the general practical geometric range of applicability for branch

plate-to-rectangular HSS member connections as well as the region where the strength condition (Pr) or

serviceability condition is expected to govem. Figure 4-7 is based on approxirnate practical

minimum and maximum branch plate-tw-ectangular HSS width ratios. These ratios define the soîalled

Ph w& and PI,, bund cuves s h o w in Figure 4-7. Although these ratios are approximate, they are

intended to illustrate an overall trend in the practical geometric range of applicability for bmch plate-to-

rectangular HSS member connections. Also, the shaded region of the @ph in Figure 4-7 representing a

governing strength condition (Pr ) is based on an example factored to unfactored load ratio of 1.5. This

region will become larger as the factored to unfactored Ioad ratio increases above 1 S. Alternatively, this

region will become smaller as the factored to unfactored load ratio decreases below 1 -5. Figure 4-5 more

clearly shows the overall effect of the factored load ("Yield load") to unfactored load ("Serviceability

load") ratio on the governing strength or sewiceability condition of Class 1, 2, and 3 HSS members.

Figure 4-5 shows an example factored load ("Yield load") to unfactored load ("Serviceability load") ratio

of 1.5 (shown as a horizontal line) to illustrate the governing strength or sewiceability condition. The

goveming strength condition (Pr) lies below the horizontal line and the goveming sewiceabiiity

condition (P,,,%) lies above it. However, this horizontal line cm be shifted upwards or downwards to

graphically represent the actual factored load ("Yield load") to unfactored load ("Serviceability load")

ratio (which is not necessarily equal to exactly 1.5) and corresponding strength or serviceability

governing condition.

5. FEM EVALUATION OF STIFFENED LONGITUDINAL BRANCH PLATE-TO-RECTANGUM HSS MEMBER CONNECTIONS

The results of a numerical study, using the Finite Element Method, with the aim of determining the

minimum required "effectively-rigid" stiffening plate thickness, are presented in this chapter. An

empirical formula is developed to produce the bounding stiffening plate thickness to satisQ both a

serviceability condition and an ultimate limit state condition.

5.1 F'EM models

Six stiffened longitudinal branch plate specimens, in a 90" "T" or "X" configuration have been tested in

a laboratory experimental programme. The measured dimensions of the test specimens are reproduced in

Table 5-1, Complete details regarding the experimental testing programme were presented in Chapter 4 of

the thesis. The FEM numerical models presented in this chapter were varied to coincide with, interpolate

between, and extrapolate beyond the expenmental test programme. Numerical rnodelling was done using

the Finite Element package ANSYS 5.5 (Swanson Analysis Systems inc. 1998a).

5.1 .1 Boundary conditions

The six experimental niffened branch plate connections were arrangeri in the testing machine using

either a fixed branch "X" configuration or a fked chord "T" configuration (FEM verification models show

in Figure 5- 1).

bsofar as experimental testing was concerned, the use of an "X" arrangement or "T" arrangement was a

matter of testing convenience and practicaiity. Furthemore, the difference between the "TM-type and "X"-

type testing arrangement was surmised to be negligible. One advantage of the flexibility and relative

economy of FEM analysis compared to physical experimental testing is the luxury to scrutinise these so-

called negligible effects.

Table 5-1: Experimental test and FEM modelled resulîs for stiffened longitudinal branch plate-to-rectangular HSS member connections

Fixed Chord "TI T Fived Branch "X" X X 1 X X

Measured HSS dimensions: l78x 127~4.8

t

Test FEM

FEMlTest

Pa3?,@cNl Pk1v.FN] F E M e s t

127% 106% 112% 120% 102% 100% 115 I l 6 110 286 190 140

116 105 100 270 175 136

101% 91% 91% 94% 92% 90%

weld size, w = min. (1 or t,)

1

l !

1

l I !

I !

1

I

Fixed B m c h ' Symrnetrical Boundary conditions 1 "Y- Type "Y- Type

1 I Pararnetric FEM Model FEM Modelling of Experimental Test Specimens / (usine acmal measured dimmrions and marerial ~ra~enier l -

Figure S I : FEM modelling details for stiffened branch plate-to-rectangular HSS member connections

The experimental test and corresponding FEM model specimen identified as "B04LPn (see Table 5-1)

was actually tested in a f~ed-chord "TW-type arrangement and the FEM verification model simulated those

boundary conditions. However, FEM analysis was also used to mode1 the experimental test specimen

"BO4LP" in a f i ed branch "Y-type testing arrangement. Figure 5-2 shows that the fixed branch "X"-type

testing arrangement boundary conditions resulted in a more flexible or lower strength connection. It is then

prudent to use the more conservative case of an "X"-type boundary condition in a parametric FEM study.

Pursuant to this choice of boundary condition, a fùrther refuiement to the fixed branch "X-type boundary

condition was made. Figure 5-1 shows an HSS member as a fmed branch to equilibrate the applied branch

plate load. The relative geometryfstifiess of the HSS fvred branch to the main HSS chord member is

another seemingly negligiile effect.

The only consistent methoci of modelling the opposing fmed branch in relation CO the branch plate

comection itself is to make both branches equivalent (as stiffened plates). This results in a self-

equilibrating 1/8 model "Y-type connection (show in Figure 5-1). Also, Figure 5-2 shows that the self-

equilibrating symmeîrical "Xn-type baundary condition is even slightly more conservative than the fixed

branch "XW-type boundttry condition.

In reality, the boundary conditions of a branch plate-terectangular HSS member connection c m

resemble anything behveen the two extremes of a 'T'-type or "X-type connection. i-iowever, it is both

conservative and consistent to use the 118 symmetncal "X"-type mode1 for the FEM paramehic study. The

118 mode1 is selfiequilibrating with symmetrical boundary conditions applied to al1 three Cartesian planes (x

=O,y=O,andr=O).

O 5 1 O 15 20 25 30 Connedon deformation, h (mm)

Figure 5-2: Elfcct of model boundary conditions on the FEM load-deformation bebaviour of a stiKened braaeh phte-to-rectangrrlar EB!3 member connection

5.1.2 Model geometry and meshing

The free length of the HSS member extending beyond the branch plate connection is an important

modelling dimension for the parametsic FEM model. This distance must be made suficiently long to negate

any end-effects relative to the local deformation of the HSS co~ecting face. FEM analysis showed that the

fke length of the chord mut be pa te r than 1 .25 times the HSS member width (bo) to avoid end-effects. As

a precaution, a more consewative value of 1 Sb0 was used in the FEM parametric nudy. By cornparison, the

experimental fixed branch, X-type specimens had a relatively long fiee chord length of four times the HSS

chord width (bo).

The branch plate length (hl) is another consideration for the parametric FEM model. The branch plate

length-to-HSS chord width ratio (q=hlJbo) was taken to be 1 .O. This value represents a typical proportion

for branch plate-to-rectangular HSS member connections.

Assuming that the weld size is designed to match the shear strength of the connecting material, the weld

leg size (w), for the stiffening plate-to-HSS weld, was taken ta befit,. Alternatively. the weld leg size was

bounded by the thickness of the stiffening plate for thin aiffening plates,

Mesh convergence studies were carried out to determine a suitable level of discretisatioo. The FEM

mapped mesh originates at the corner weld of the stiffening plate and gradually fans outward using a series

of minimum element size constraints and biasing parameters within each portion of the model (Le. HSS top,

side, corner, fke chord length, etc.). Thus, the semi-automated mapped meshing of each FEM model is

consistent but the meshes themselves are dependent on the overall geometry of the connection.

Twenty noded solid elements (SOLiD95) were used for al1 components of the FEM rnodels. For the

parameîric FEM model, a contact element was placed between the stiffening plate and the HSS chord face

to ensure that the hvo components did not emneously pass through one another since a wide range of

connection parameters were to be considered. However, it was found that the contact eIement was only

engaged under very high plastic defonnations (well beyond the I%bo and 3%bo deformation range). Even

then, the contact element only registered a minimal force. The difference in Ioad benveen sample models

analysed with and without contact elements was on the order of 2%. Thus, contact elernents were not

included in subsequent parametric FEM analyses.

5.1.3 Material properties

A multi-linear mapping of the exact material properties (determined by tensile coupon tests) was used

for the FEMExperimental verification modeb. However, for the FEM parametric analysis, a generic

(CANICSA-G40.20-98) 350W structural steel was chosen. The material for the branch plate-to-r~ctangular

HSS member connections, including the weld, was taken to be 350W structural steel with a yield stress F, =

350 MPa, an ultimate stress Fu = 450 MPa, Young's modulus E = 200 GPa, and Poisson's ratio u = 0.3.

Figure 5-3 shows the Spical stress-strain reçponse of grade 350W steel in a hot-rolled and cold-formed

state. in the absence of a clearly defined yield plateau for cold-formed steel, the 0.2% offset method is used

to confirm the specified yield strength of 350 MPa.

,, 1 F, = 350 MPa @ 0.2% offset

- hot-rolled - cold-formed -- elastic-perfectly plastic

0.00 0.05 0.10 0.15 0.20

Engineering main, E,,

Figure 5-3: Material stress-strain curves

in a real connection, the stiffening plate and branch plate materials are likely to be hot-roiled and the

HSS material is more likely to be cold-fomed. Since the yield strength of the material is an important

variable in analytical fomulae for HSS connections, a hot-rolled structural steel material was chosen since

it contains a more clearly defmed yield plateau strength. Conversely, the 0.2% offset effective yield strength

value associated with cold-formed steel creates ambiguity as to the m e yield strength of the material.

Finally, as an academic exercise, an elastic-perfectly plastic material curve was examined (see Figure 5-3).

A 118 model of the experimental test specimen "B04LP" jrefer to T'able 5-1) was analysed using the

material properties of 35OW steel in a hot-rolled, cotd-formed, and elastic-perfectly plastic state. Figure 5 4

shows the connection load-deformation response of specimen "1304LP1' using the three different 350W steel

material curves (fiom Figure 5-3). Within the practical defonnation range of l%bo and 3%bo, the results are

virtually identical. However, in order to realistically capture a strain-hardening response (if required) and

maintain a clearly defined yield strength, the material curve associated with a grade 35OW hot-rolled

structural steel was chosen for the FEM pararnetric study.

Based on mecimen "BWLP" (refer to Table 5-1)

O 5 10 15 20 25 30

Connecrion defonnation, A (mm)

Figure 5-4: Effect of steel material type on the loaddeformation behaviour of a FEM modelled stiffeneà brancb plate-Co-rectangular HSS member connection

The "engineering" stress-drain material curves were plotted in Figure 5-3. However, for large

deformation analyses, ANSYS release 5.5 (Swanson Analysis Systems hc. 1998b) documents a

recommended "me" stress-.main conversion of:

Using Equations (5-1) and (5-2) a muti-linear mapping of the "true" stress-strain material response was used

as material property input for the FEM modeb.

5. 1.4 FEM modei verificaf ion

Figure 5-5 shows the loaddeformation c w e s for the experimentai test specimens and corresponding

FEM models (details in Table 5-1). Both geomeüical and material non-linearities were used in the solution

of the FEM models. Thus, the FEM models accornrnodated the elastic-bending, plastic-yielding, and

membrane-action behaviour of the HSS connecting face. However, the FEM models did not include

cracking behaviour. Local punching shear-type cracks do begin to form around the peimeter of the welds

between the stiffening plate and rectangdar HSS member at post-yield deformation levels for the

experimenral test specimens. Thus, the FEM loaddeformation response begins to deviate from the

experimental test specimen response at large deformations (especialiy for the wider Q = 0.8 specimens in

which cracking dominates over ductile membrane action in the pst-yield stages of loading).

O 5 I O 15 20 25 30 Comection deformation, h (mm)

O 5 10 15 20 25 30

Comection deformation, A (mm)

Figure 5-5: FEM and experimental load-deformation curves for stiffened longitudinal branch plate-10-recbngular HSS membcr connt!ctions

However, such large displacements are not acceptable in real structures and connections are considered to

have reached their factored resistance when dispIacernents attain limiting values. Two deformation limits

(Lu et. al. 1994, Zhao 1996) have been u d to define the strength of such a connection: these are an

ultimate deformation limit (3% bo) and a serviceability deformation lirnit (1% bo). The FEM models are

verified by the experirnental results within this deformation range. Figure 5-6 shows a direct cornparison of

the FEM and experirnental test results contained in Table 5-1. The average ratio of the FEM load to the

experirnental load is 1.1 1 for the serviceabiliiy condition and 0.93 for the ultirnate condition, with a standard

deviation of 10% and 4% respectively. This proves a good correlation between the experirnental and FEM

test results.

Avp. Std. Dev.

O Ultirnate 300 A

V a

200 1 - P>

I t 3 rso

CL s U C e Ioil j n

% 50 1 i O 50 100 150 200 250 300

Experimental bmch plate load, P OcN)

Figure 5-6: FEM versus experimental results for stifiened branch plate-to-rectangular HSS member connections

5.1.5 Parumerric modelling programme

A comprehensive numerical study using a matrix of three main parameters totalling 3 5 1 specimens is

shown in Table 5-2. Table 5-2 also illustrates some sample FEM connections from the parametric study

marrix. CANICSA-G3 12.3-98 square HSS members were used, for the parameter darabase. Two standard

parameters used were the width-to-thickness ratio of the HSS member (2y'o), and the branch plate-to-HSS

member width ratio (p), The width-to-thickness ratio of the main HSS member (Pto) was varied in

increments between a maximum value of 48.0 and a minimum value of 1 1 .O (the HSS wall thickness was

held constant at 6.35mm). The stiffening plate-to-HSS member width ratio (p) was varied in increments

between a minimum value of 0.2 and a maximum value of 0.8. The maximum value of P' was Iimited by

the flat width of the rectangular HSS connecting face. From a fabrication standpoint, a practical

(economic) upper limit for g' is limited by the flat width df the rectangular HSS connecting face. Thus,

as can be seen in Table 5-2, the upper limit of P' is geomemcally bound by the HSS flat width (especially

for low values of 2yto). fY 5 0.8 is the range of validity for this study.

The third and final parameter relates to the thickness of the stiffening plate. This non-dimensional

parameter (2fOli) was defrned as the ratio between the HSS connecting face slenderness ratio (2-110 = b)dto)

and the stiffening plate slenderness ratio (2y',= b'&). Equation (5-3) shows how this newlydefined non-

dimensional parameter ( î f o I l ) relates to the relative thickness of the stiffening plate ({,) with respect to

the thickness of the HSS connecting face (fo):

The stiffening plate thickness parameter ratio (2y'o/,) was varied in increments between a value of 1 .O and

5.0. A very large 2Vo,[ = 10.0 value was used as an upper Iimit representing a "rigid" stiffening plate.

Table 5-2: Parametric FEM modelling matrix for a stiffened branch plate-to-rectaagular HSS member coanection

e 1.6

1.7

1.8 - ).2

1.3

1.4

1.5

1.6

1.7

1.8 - 3 .: o.: 0.i

o.: O.(

O.'

0.1 - o.: 0 .: O -1

o..

I O.

0. - O.

0.

o. O. - o. o. o. o. - 0.

O.

O. - o.

Chord slendemess/Stiffener slendemess. (Zy',)

5.2 Required stiffening plate tbickness

Figure 5-7(a) shows the loaddeformation response for a branch plate connection with varying

stiffening plate thickness. For a particular set of independent parameters [2y'o = 27.0 and P' = 0.6 in

Figure 5-7(a) for example], the stiffening plate thickness was varied using the non-dimensional thickness

ratio (2ylon). As can be seen in Figure 5-7(a), the branch plate connection stifiess increases with an

increasing stiffening plate thickness until an upper bound plate thickness is reached. Beyond this

thickness, the stiffening plate is essentially "rigid". A very large stiffening plate thickness (2y'0,~ = 10.0)

was used as an absolute upper limit representing a "perfectly-rigid" stiffening plate. This upper Iimit was

used as a benchmark ro define the relative connection capacity of the thinner stiffening plates.

Figure 5-7(b) shows this relative connection capacity as a fùnction of the stiffening plate thickness

ratio, 2y'o,l. In order to achieve a high relative connection capacity, the stiffening plate musc act

"effectively-rigid" with respect to the HSS connecting face such chat a plastification mechanism does not

occur in the stiffening plate itself. The overall relative connection capacity [shown in Figure 5-7(b)] is

essentially a bilinear curve with a cusp point transition region. The curve asymptotically approaches a

"perfectiy-rigid" connection (Le. 100% relative connection capacity). This represents the typical relative

connection capacity behaviour for ail of the FEM connections analysed. For design purposes, a more

practical "effectively-rigid" stiffener plate thickness was chosen to be the 95% relative connection

capacity threshold shown in Figure 5-7(b). This 95% eficiency threshold lies within the transition region

of the bilinear curve intersection for al1 of the FEM connections analysed,

The required relative stiff'ening plate thickness parameter necessary to meet a 95% relative

connection capacity depends on whether the capacity of the connection is governed by strength or

serviceability. For rectangular HSS connections a connecting face deflection of 1% of the main member

width (I%bo) has generally k e n used as a serviceability deformation limit, as given by IIW (1989). For this

comecting face deformation of I%bo, one can obtain a corresponding load in a branch plate member (Px.I%).

Similarly, a branch plate load can also be obtained for the "ultimate" load Ievel (pK,%) corresponding to a

comecting face deformation of 3%bo. Table 5-3 lis& the l%bo serviceability deformation limit (P,.I%), and

the 3%bo ultimate defomtion limit (P,3%) load levels obtained fiom the FEM loaddeformation results.

Table 5-3 also lists the predicted yield strength [Py using Equation (1-9)] for each co~ection. The

predicted yield strength (Pr) corresponds well (avg. P,4P,3K= 0.91) with the notional 3%bo ultimate

deformation limit (Pr3%) load level. Thus, the calculable connection yield strength (Pr) can be used in lieu

of the 3%bo ultimate defomtion b i t (P43%) load level.

HSS 178~178~6.35 2y1,=27.0 B'4.6

250 (a) Load-defomtion curves

Connection deformation, A (mm)

b) Relative connection capacity

lative connection capaciiy

HSS comection face sfendemesslStiffening plate slendemess, 2f,,

Figure 5-7: Load-deformation curvcf and relative connection capacity curves showing the typical elteet of stiffening plate tbiciiness for a FEM modelled connection

Table 5-3: FEM and predicted results for stillened branch plate-to-rectangular HSS member connections

!yo b o h l b; P' b'l w h', b l * 8. P , . ~ ~ P ~ - P r P r rp,,,rp, Z Y W i [ p t a i a : i p t m , ~ WWI [ rcmi ,~~ro i i , x (mm)(mm~(-) ~ ~ ~ I ( I T I I I I ) ( ~ I I mm) ( k ~ ( ~ r ~ ) ( k ~ ~ . f i (mm 10 (mm) FEM [ O (mm, FEM

:fer ta Figure 5- 1 hr FEL

0.4 19.0 127 127 121 0.5

0.6 0.7 0.4

15.1 102 102 % o.: 0.t 0.7

0.4 13.0 89 89 83 0.:

O.( 0.4

11.0 76 76 70 O.! 0.t

1 Average 0.91 1 1 Avnagc 1.03 1 Avcragc O.%

HSS d l thickncss, r, = 6.35 mm Sid Deuiauon O. 13 Std. Devialion 0.17 Std. Devinrion 0.18

Branch plate thicknm, lb =6.35 mm COV 0.17 COV O 18 i

[A] Pr using Eq. (1-9) whac: (F,,,=350 MPa, û=W , n=0)

p] using Eq. (54) whcm r , = 6.35 mm

[Cl using Eq. (5-3) r,,,, 1 tO=(2y'wiXB') whcrr t a = 6-35 mm [Dl Prcdictcd 1 ,,,, using Eq. (El) I FEM i, ,,,

From Figure 5-7(b), the required stiffening plate thickness ratio (2y0,l) to satisfy a 95% relative

connection capacity is numerically interpolated to be 2.3 I for the yield (strength) condition and 2.67 for

the serviceability condition. Remember that this pair of results (shown highlighted in Table 5-3) is only

valid for a particular set of independent parameters (in this case 2y'o -27.0 and fP0.6, as plotted in

Figure 5-7). Accordingly, a pair of results for the remaining set of independent parameters was

determined and is documented in Table 5-3.

Figure 5-8 presents the complete FEM results for the minimum required stiffening plate thickness to

achieve a 95% relative connection capacity threshold. The required stiffening plate thickness has a

p a t e r dependence on the parameter P' (defined in Figure 5-8) than it has on 2 ~ ' ~ . The serviceability

condition thickness requirement is slightly higher than the strength condition thickness but these can be

reasonably grouped together for design simplicity.

The best-fit exponential curve in Figure 5-8 is an empirical equation used to determine the minimum

required effectively-rigid stiffening plate thickness (rH&,) to satisQ both the (PY) strength condition and the

(PR,%) serviceability condition. ïhe ratio of the stiffening plate thickness tflml to the HSS connecting face

wall thickness (IO) is a function of (P.), the "unresûained" stiffening plate width (bl*) to the HSS width (b',-,)

ratio, Illustrated in Figure 5-8, the "unresûained" stiffening plate width (61') was defined as the stifiening

plate width (b l ) minus the branch plate width (ta) and both branch plate welds (2w). Equation (5-4)

represents the best-fit exponential curve show in Figure 5-8.

Table 5-3 shows that Equation (5-4) is a g d predictor for the minimum required effectively-rigid

stiffening plate thickness for both the strength and sewiceabiiity limit state conditions (predictedlactual

=1.03 for the strength condition and 0.96 for the serviceability condition, with a coefficient of variation

of 17% and 18% respectively). This coefficient of variation is acceptable in order to accommodate a

single consolidated design equation that satisfies both the strength and serviceability Iimit state

conditions. Furthermore, a resistance factor (4) of 1.0 can be applied to Equation (5-4) for design

because the connection is deflection critical and the calculated connection yield load (Pr) is well below

the connection Fracture load.

" unrestrained" width

b; =b, -2w-r , .

2y', range of validity = 1 1 .O to 47.0

0.0 0 2 0.4 0.6 0.8

Unrestrained stiffening plate-to-HSS width ratio (P*)

Figure 5-8: Required stiffening plate thickaess to achieve a 95% relative connection capacity

5.3 Branch plate stress distribution

For ~s t i f fened longitudinal branch plate-to-rectangular HSS connections, it was shown in Chapter 3

that the ratio of the average (Le. uniform) to the maximum branch plate stress is very close to unis when

the branch plate first begins to yield, for the limiting case of connections in which the branch plate is

Iikely to be loaded to its yield level. Thus, the effect of the non-unifom stress distribution in unstiffened

longitudinal branch plate-to-rectangular HSS member connections was deemed to be of negligible

consequence. In situations where there is a higher non-uniformity in the branch plate stress at the

connection yield load (Pr) , the branch plate is likely to be loaded well below its facrored resistance. In

general, an unstiffened longitudinal plate connection is characterised by a low P ratio (= 0.1 to 0.25) and

is henceforth very flexible, resulting in a relatively low connection yield load (Py ) .

In the case of a stiffened branch plate-to-rectanguiar HSS member connection, the P ratio is

increased by the addition of the stiffening plate resulting in a higher connection yield load (Pr) . An FEM

study was undenaken for stiffened branch plate-to-rectangular HSS connections to determine the severity

of the non-uniform stress distribution in the branch plate. For the FEM study, an "effectively-rigid"

stiffening plate thickness was used. Defined eariier in the chapter, an effectively rigid stiffening plate

was dehned as one that results in a nearly full capacity, 95% relative connection capacity threshold. The

thickness of the branch plate (rb) was back-calculated to match the calculated yield strength ( P Y ) of the

connection. The branch plate thickness (tb) was detennined based on the calculated connection capacity

(Py ) and an assumed uniform stress distribution in the branch plate. Using the parametric FEM smdy

matrix s h o w in Table 5-2, the FEM analyses showed that the most severe non-uniform stress

distribution in the connecting branch plate occurred for the Class 3 HSS 305~305~6.35 main HSS

member. The HSS 305~305~6.35 cross-section represents the most flexible connection face in the text

matrix with a width-to-thickness ratio (2f0) of 47. Also, the worst case scenario for stiffened branch

plate connections occurs for higher j3 ratios, which inherently result in higher connection capacities.

Figure 5-9 shows the non-uniform stress distribution in the connecting branch plate for the HSS

305~305~6.35 main member with a stiffening plate-to-HSS width ratio (P') of 0.7. The calculated yield

load of the connection [Pr using Equation (1-911 was calculated to be 205 W. Thus, the branch plate

thickness (tb) was proportioned to yield at 205 kN, assuming a uniform stress distribution in the branch

plate. Instead, Figure 5-9 shows that due to the non-unifonn stress distribution in the connecting branch

plate, the ends of the branch plate first reach yield at a load of between 160 kN and 170 kN, or between

78% and 83% of the calculated connection capacity (Pr = 205 kN). Thus, a generalised 20% reduction

factor in the branch plate mngth is recommended to account for a worst case scenario, non-uniform

stress distribution in the branch plate for stiffened branch plate-to-rectangular HSS connections, with the

"effectively-rigid" stiffening plate proportioned on the buis of achieving a 95% relative connection

capacity.

.. -

HSS 305 x 305 x 6.35 2y', = 47 = 0.7 -

uniform yield stress reference line

. .A

- P = 200 kN =0.98Py

1.1 - - m- -

h

2- 0.9 - 5 6- ;O 0.8 - VI

e - "

0.7 -

-150 -100 -50 O 50 1 O0 150

Position dong plate width (mm)

= ei - .- È,

0.6 - .- 8

0.5 - 1 - L 0.4 - VI U

5 0.3 - &

0.2 - - 0.1 -

- 0.0

Figure 5-9: FEM branch plate stress distribution for a main HSS 305~305~6.35 Class 3 member

P = 170W=0.83 P, P= 160 kN = 0.78 P,

:: P = 100 kN = 0.49 P,

. . .... . . .... ..... , . . . . . . ............ . . ,

. . . . . . . . .

Branch plate load (P ) = 50 kN = 0.24 Comection yield load (P,)

, " ' ~ l " " l " ~ ' 1 ' " ' 1 " ~ ' , " " 1

Figure 5-10 shows the non-uniform stress distribution in the connecting branch plate for a relatively

stocky Class l HSS 127~127~6.35 main member with a stiffening plate-to-HSS width ratio (P3 of 0.7.

Figure 5-10 shows that due to the non-uniform stress distribution in the connecting branch plate, the ends

of the branch plate first reach yield at a load of between 180 kN and 190 kN, or between 83% and 88% of

the calculated connection capacity (Py = 216 kN). Thus, the recomrnended generalised 20% reduction

factor in the b m c h plate strength is not overly conservative in this case to account for the non-uniform

stress distribution in the branch plate.

1 HSS 1 2 7 ~ 1 2 7 ~ 6 . 3 5 2-y'"= 19 p=0.7 1

uniform yield stress reference line

Figure 5-10: FEM branch plate stress distribution Tor a main HSS 127x127~635 Class 1 member

Y n 0.8 - VI r " 0.7 - 0 LI .- A - 0.6 - d .- E 3 0.5 - 2 2 0.4 - - .n a 3 0.3 - C

0.2 -

0.1 -

5.4 Summary of Chapter 5

/ P= 190 kN (0.88 P,) P = 18o I ~ N (0.85 P,)

P=110kN=O.51 Pr

. . . . . . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . . . .

Branch plaie load (P) = 50 kN = 0.23 Conncction yield load (P,)

o . o , . m l ~ L ~ ~ l r r . . l l . ~ , l , , t T , , ~

.4 traditional yield line formula can be useâ to determine the yield load (Pr) of stiffened longitudinai

branch plate-to-rectangular HSS member comections, based on a flexural mechanism in the HSS

connecting face, provided that the stiffening plate on the HSS connecting face remains "effectively-rigid".

This calculable comection yield load (Pr) has been shown to correspond well with the notional 3%b0

ultimate deformation limit load level (Pd%) for the connection.

-50 -25 O 25 50

Pasition along plate width (mm)

An empirical formula has been developed using FEM results to provide the minimum required

"effectively-rigid stiffening plate hickness. The ratio of the stiffening plate thickness to the HSS

comecting face wall thickness is given by Equation (54). This minhum stiffening plate thickness will

a i s @ both a strength and a serviceability limit state for the stiffened longitudinal branch plate co~ection.

Finally, a generalised 20% reduction factor applied to the branch plate strength is proposed to

account for a non-uniform stress distribution in the bmch plate for stiffened branch plate-to-rectangular

HSS member connections.

6. F'EM ANALYSIS OF TRROUGH BRANCA PLATE CONNECTIONS

A through plate comection can be expected to have approximately two times the strength of a single

plate connection by causing plastification of two rectangular HSS chord faces rather than one. Experimental

results confirm that a through plate connection can ûe reasonabiy approximated as having double the

strength of a corresponding singie plate comection for design purposes (Refer to Table 4-1 where the

average ratio for and is 1-9).

An FEM numerical modeiling programme was undertaken to further study the strength of single plate

versus through plate-to-rectangular HSS member connections. The FEM numerical mode15 were varied

to coincide with, interpolate between, and extrapolate beyond the experimental parameters. The

numerical FEM models were verified using the experimentally obtained test data and then varied to

expand the parametric database. Thus, supplemental numericai test data for a broader range of

connections could k obtained. Numerical modelling was done using the Finite Eiement package ANSYS

5.5 (Swanson Analysis Systems Inc. 1998a).

6.1 FEM models

The boundary conditions for the FEM parameiric models matched those imposed by the experimental

testing conditions, The experimental connections were arranged in the testing machine using a Gxed chord

T-stub configuration. Botfi the experirnentat and rnalching FEM mode1 specimen are show in Figure 6-1.

The 90' experimentai test specimens contain two planes of symmetq and thus 114 FEM madels were used.

. -.. (a) Single plate . .;::;':-.

. . . . ..* ,,-',.

* , . . .,' ,,,'',,.

, . . _ < ' _ ' . ' . , .

Figure 6-1: FEM modelling of single brancb plate and tbrough branch plate experimeotal test specimens

Typical Experimental Test Specimen FEM Modelling of Experimental Test Specimens

(using actual measured dimensions and material properties)

6.1 2 Mode1 geomefry and neshing

The actual measured dimensions and material properties of the experîmental test specimens were used

in the FEM verification mdels. However, once the overall FEM models were veniïed with the

experirnental test results, minor refuiements were made to the overall FEM model to allow its use in an

expanded parameîric numerical modelling programme.

The free length of the HSS chord extending beyond the branch plate connection is an important

modelling dimension for the parametnc FEM model. This distance m u t be made sufficiently long to negate

any end-effects relative to the local deformation of the HSS connecting face. However, in the case of the

fixai chord T-stub configuration, the length of the chord m u t be kept to a minimum to minimise the

globally imposed beam bending moments (shown schematically in Figure 6-2) applied to the HSS member.

Figure 6-2: Ovcrall flexurd action rit the HSS test speeimen

FEM analysis showed that the fiee length of the chord rnust be greater than 1.25 times the HSS chord width

(bo) to avoid end-effects. As a precaution, a more conservative value of 1.5bo was used in the FEM

parametric snidy (refer to Figure 6-3). Also, FEM analysis confumed diat the globaily-applied bending

moments shown in Figure 6-2 are negligible relative to the loaddeformation behaviow of the HSS

connecting face.

The branch plate length (hl) is another consideration for the parametric FEM model. The branch plate

length-to-HSS chord width ratio (11 = hIfbo) was taken to be 1.0 for the experimental test specimens because

it represents a typicai proportion for branch plate-to-HSS member connections. For the FEM paramemc

rnodels, an effective branch plate length-to-HSS chord width ratio (q' = NJb'o) of 1.0 was used.

Furthemore, a FEM parametric study using an effective branch plate length-to-HSS chord width ratio (tl' =

Hl/b'o) of0.5, I .O, 1.5, and 2.0 was done.

Assuming that the weld size is designed to match the shear süength ofthe connecting material, the weld

Ieg size (w) was taken to be f i r, .

Mesh convergence studies were carried out to determine a suitable level of discretisation. Twenty noded

solid elernents (SOLiD95) were used for al1 components of the FEM rnodels, inchding aII welds. Figure 6-3

shows the details of the generalised parametric FEM model.

Figure 63: Parametric FEM modeiiing detaiis for single branch plate and through branch piate connections

A multi-linear mapping of the exact material properties (determined by duplicate tende coupon tests)

was used for the FEM models. The stress-main responses for the HSS material and branch plate matenal

are shown in Figure 6-4. Insofar as FEM modelling was concerned, the exact material properties of the

weld material was unimportant and thus the weld material was taken to be the same as the attached branch

plate matenal.

HSS 178 x 127 x 4.8 13.1 mm THK. PLATE 600 7 . . 1 . " . . . ' i " ' 600 , 1

t

i

Fv = 470 MPa Fy = 435 MPa

300

- Coupon 1 - Coupon I Coupon 2 Coupon t

0 FEM multi-linear o FEM muiti-linciu i mapping mapping

l , , , l . . , . l , . _ . / , . .

0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.10 0.75

Figure 6-4: Material stress-strain curves

The "engineering" stress-strain material curves were plotted in Figure 6-4. However, for large

defomtion analyses, ANSYS felease 5.5 (Swanson Analysis Systems Inc. 1998b) documents a

recommended "bue" stress-min conversion of:

Using Equations (6-1 and 6-2) a rnuti-linear mapping of the "true" stress-strain material response was used

as material property input for the FEM modeis.

6.1.4 FEM mode1 verijcation

Both geornetrical and material non-linearities were used in the solution of the FEM models. Figure 6-5

shows the loaddefomation curves for the experimental test series and corresponding FEM models. Two

deformation limits (Lu et al. 1994b, Zhao 1996) have been used to define the strength of the connection:

these are an ultimate deformation limit (3% bo) and a serviceability deformation limit (1% bo). The details

of the four connection experiments and corresponding FEM models are contained in Table 6-1. The FEM

models are verified by the experimental results within this deformation range.

- Longitudinal plates (experimental) I -- Through plates (expenmental)

O 10 20 30 40 50

Connection deformation, A (mm)

Figure 6-5: FEM and experimental loaddeformation curves for single branch plate and through branch plate connections

Table 6-1: Experimental test and FEM modelled results for single branch plate and through branch plate connections

Type: "X" or 'T" 1 T T 1 T T Soecimen Identitication

(a) Single 90LP 90LP2

c $ 5 c s

L VI

O .c!

g E O Z

YI - - $ - a - = z , .- X

tn - - a VI

E avg. = 2.1 2

Irl.'o.s(I

ib) Thmugh 90RP 9ORP2

z ,., -

hi [ml h 1 , = h I + 2 w [mm] b ' , = b 1 + 2 w [ m m ]

F,o Wal [ O [mm1 bo [mm]

2y,=bdio b', [mm]

P = b , l b o P ' = b ' l l b ' o

p , t%[kN1 P a w [ W

1 78 197 195 197 193 32.1 30.1 52.1 27.9

408 -1.8

178 127 178 117 37.1 26.5 37.1 26.5 173 122 173 127 0.07 O. 10 0.07 O. LO 0.19 0.25 0.19 0.23

38 44 66 97 75 87 127 171

Caiculated through plaie capacity = 2 x cqual sized (b', , h' ,) single plate calculated capacity

through platdsingle plate (P , ,,,JI 1.88 1 -89

(Eq. 1-9) Pr [ml P r +Pa 3%

through platdsingle plaie ( P , . , d through plaidsingle plate (P. ,,A

68 83 136' 166*

093 0.92 0.99 0.98

1.74 2.20 1.69 1.97

(Es. 1-9) P r [Hl Py+P,,% P ~ I K [ W P , r n [ W

68 83 136' 166'

0.91 O.% 1.07 0.97

41 58 88 122 73 90 137 170

through plaidsingle plate ( ~ , , , 3 ( 2.15 2.10

Table 6-1 lists the l%bo serviceability defomtion limit (P,.I#), and the 3%b0 ultimate deformation

limit (Pr3%) load levels obtained fiom the experimental and FEM loaddeformation results. From the four

experimental test specimens and corresponding FEM models, the strength of a through plate connection

can be reasonably approximated as having double the strength of an equivalent single plate connection.

Table 6-1 also lists the predicted yield strength [Pr using Equation (1-9)] of each connection. The

predicted yield sûength (Pr) corresponds well with the notional 3%bo ultimate deformation limit (pK,) load

level. Thus, the calculable connection yield strength (PY) can be used in lieu of the 3%bo ultimate

deformation limit (pK,%) load IeveI.

6.1.5 Parametric modelling programme

A parametric FEM study was undertaken to confirm the hypotheses that a through plate connection

can be designed as having double the strength of an equivalent single plate connection and that the

calculable connection yield strength (Pr) can be used in lieu of the 3%bo ultimate deformation Iimit (Pv,30k)

load level (where the latter can be determined from laboratory experiments or numerical analysis).

A comprehensive FEM study was done using CANKSA-G312.3-98 square HSS members as a

realistic parameter database. Table 6-2 shows the FEM modelling matrix and also illustrates some sampIe

FEM connections from the parametric modelling matrix. The width-to-thickness ratio of the HSS chord

(2yto) was varied in increments between a mauimum value of 39 and a minimum value of 13 (the HSS

wall thickness was held constant at 6.35mm).

Thus far, a branch plate length-to-HSS chord width ratio of unity has been used for the experirnental test

specimens and FEM parametric models. A FEM subset series using an HSS 152x152~6~35 section with a

variable branch plate length-to-HSS chord width ratio (q' = Hi/&) of 0.5, 1 .O, 1.5, and 2.0 was done for the

sake of verification and completeness (refer to Table 6-3).

Table 6-2: Parametrie FEM modelling natrix For a single branch plate and a correspondiog through branch plate connection

I Designation b o x h 0 x t o

HSS 254~254~6.35 2y', = 39.0

HSS203x203x6.35 Zy',, = 3 1.0

HSS 178x1 78~6.35 2f0 = 17.0

HSS 152~152~6.35 2f,, = 22.9

HSS 127~127~6.35 ?y',, = 19.0

HSS lO2xlO2x6.35 Zy'" = 15.1

HSS 89~89~6.35 - 2 6 = 13.0

Single plate I Through plate

Table 6-3: Parametric FEM modelling matrix for variable brancb plate kngth connections

HSS 152 r 152 x 6.35

Single plate Through plate

A total of seven different square HSS sizes were modelled as a single branch plate and a through

branch plate co~ection. The HSS wall thickness was held constant at 6.35 mm and a typical branch

plate length-to-HSS wicith ratio of unity was used initially. Figure 6-6 shows the loaddeformation

responses for this FEM parametric series.

Next the median HSS 152x1 52~6.35 section was chosen as a subset of the FEM parametric series

and modelled using a variable branch plate length-to-HSS chord width ratio (q' = Hl/&) of 0.5, 1 .O, 1.5,

and 2.0. Figure 6-7 shows the load-deformation responses for this FEM parametric subset series.

(a) Single plate (b) Through plate

HSS 254~254~6.35 -c- HSS 203xî03x6.35 + HSS 178~178~6.35 -a- HSS 152~152~6.35 + HSS 127~127~6.35 - HSS 102x1 02~6.35 - HSS 8 9 ~ 8 9 ~ 6 . 3 5

O 5 1 O 1s O 5 10 15

Connection deformation, A (mm) Connection defonnation, A (mm)

Figure 6-6: Loaddefomatioa response for FEM madelled single branch plate and corresponding thmugh branch plate connections

HSS 152~152~6.35 2y, = bol to = 23.9 Pr = 0.2 1

(a) Single plate (b) Through plate

0 1 2 3 4 5 6 7 8 9 1 0 0 1 2 3 4 5 6 7 8 9 1 0

Connection deformation, A (mm) Conneaion deformation, A (mm)

Figure 6-7: Load-deformation response for FEM modelled variable branch plate length connections

Table 6 4 and Table 6-5 lists the I%bo serviceability deformation Iimit (P,JY,), and the 3%bo ultimate

deformation Iimit (P&) Ioad levels obtained fiom the loaddefonation responses shown in Figures 6-6 and

6-7. Table 6-4 confms that for the ultimate deformation Ioad level (Pa3Y,), a through plate connection

results in double (avg. = 1.98, standard deviation = 6.0%) the capacity of a corresponding single plate

connection. The strength of a through plate versus a single plate comection ranged from slightly more than

double (= 2.09) for the more slender HSS 254x254~635 cross-section to slightly less than double (= 1.90)

for the very stocky HSS 8 9 ~ 8 9 ~ 6 . 3 5 cross-section. For design purposes, the ultimate deformation load Ievel

(Plr3%) of a through plate comection can shply be taken as double the strengih of a single plate connection.

Table 6-4 documents that the serviceability deformation ioad level (Pr,%) of a through plate connection

results in more than double (avg. = 2.15, standard deviation = 7.9%) the load level of a corresponding single

plate connection. The service load of a through plate versus a single plate co~ect ion ranged from more

chan double (=2.22) for the more slender HSS 2 5 4 ~ 2 5 4 ~ 6 . 3 5 cross-section to slightly more than double (=

2.04) for the very stocky HSS 89x89~635 cross-section. For design purposes, the serviceability load levet

(PJ.l%) of a througti plate connection can be consewatively taken as double the serviceability load level of a

single plate connection. in any event, the serviceability load b e l (P,!o4) is not as important as the ultirnate

limit state of the connection.

Table 6-4 also lis& the predicted yield strength [Pr using Equation (1-9)] of each connection. The

predicted yield strength (Pr) corresponds well (avg. = 1.03, standard deviation = 6.9%) with the notional

3%b0 ultimate deformation Iimit ( P , 4 load level. ïhus, the calculable connection yield strength ( P r ) c m

k used in lieu of the 3%bo ultimate deformation limit (Pu.3%) load level.

Table 6-4: FEM results for single branch plate and corrosponding through branch plate connections

(a) Single plate (b) Througb plate

Noies: [AI Pr using Eq. (1-9) where: (F,,=408 MPa, O = 90". hV,lb',= 1.00) [BI CalcuIated ihrough plate capacity = 2 x equal sized (b',, hW,) sbgle plate calculatcd capacity

HSS -iJx154x6.35

HSS 103~203~6.35

HSS178x178x6.35

HSS152~1~6.35

HSS I27xI27x6.35

HSS lO?xIO26.35

HSS 89~85~6.35

Std. Dcviation 9.5%

COV 9.3%

I

(a) Sin& plate . Defmatron

Limit Siaus

P r . 1 ~ P m - (W (W

46 95

57 1ûO

64 105

74 112

89 122

108 139

121 154

TLroRgkdrcc Si**&

P . Pm= --- PLI% P m

Z T 2.09 221 200 2.22 2-00

2 2 1 198

2.11 1.95

2.06 1.93

204 1.90 U S 1911

Sid. &viarion 6.9%

COV 6.m

(b) Tbmugh plaie

C a l c u l d

C ~ P ~ W P r - P T (W

note [A]

108 1.14

1 IO 1.10

t 12 1.06

116 1.04

120 0.99

128 0.92

135 0.88

Avaagc 1.02

7.996 6.0%

3.7% 3.Wo

Detormntion

Limit Stavs

P . P w s (W (W)

IO? 198

125 200 143 210

164 21

188 2.37

23 268

247 292

Cdculûtcd

Capacity P r P r

(W pi-

nole PI. [BI 216 1 .O9 "O 1.10

224 1.07

232 f.05

240 1-01

256 0.95

270 0.92

Average 1.03

For the sake of completeness, the median HSS 152~152~6.35 section was chosen as a subset of the

FEM parametric series and modelled using a variable branch plate length-to-HSS chord width ratio (q' =

hl/bo) of 0.5, 1.0, 1.5, and 2.0. Table 6-5 contains the results of this FEM subset series and confirms the

relative independence of the branch plate length-to-HSS width ratio.

[n summq, the tesults of a parametric FEM study of seven different square HSS sizes confinned the

hypothesis that a through plate connection cm be designed as having double the strength of an equivalent

single plate connection. Furthemore, the calculabIe connection yield strength [Py using Equation (I-9)]

can be used in lieu of the 3%bo ultimate deformation lirnit (PiL3%) load level.

Table CS: FEM rcsulb for variable branch platc kngth connections

E f k l i v e branch plate Iength-to-HSS width ratio q' = h',l b',, = (h , + 2w)/(b,- I , , )

r 1

ho HSS I5Zx 152~6.35 I L

I I

(a) Single plate (b) Thmugb plate

t I (b) Tbroigb plate TLmsb d i t e (a) Single plale SLik iilrtt

Calculatcd I Dcfomiion Calculaicd

Limit Staics Cnpacity I no* [Al noie [Al. [BI

95 1.08 120 165 190 L i 5 2.18 1.89

IL6 1.04 164 221 232 f .OS 221 1.98

136 1.00 209 ni 272 1.00 2.24 199

157 0.97 257 322 314 0.98 2.40 t.98 Avcagc 1-02 Average 1.M 2 . 2 6 136

[A] P r using Eq. (1-9) whcre: (F, , = 408 MPa, 0 = 90a, BI = 0.21) [BI CaicuIated through piate cipafity = 2 x e q d s k d (b ',, h',) single plate caicubxl q a c i t y

Figure 7-1 shows some typical welded HSS connections with circular HSS or rectangular HSS

members. In the case of failure modes involving an HSS comecting face failure, a cleariy defined peak-

load, or even yield-load, is ofien not exhibited by the loaddefonnation response of the connection. In

these instances, the connections are inherently flexible and large deformations facilitate additional load-

carrying capacity due to membrane-action in the chord and strain hardening in the material. These large

deformations are usually intolerable in real structures. Furthermore, the initiation of local punching

shear-type cracking may occur at higher deformation levels associated with membrane-action and strain-

hardening. Therefore, a deformation critenon can be used to define the capacity of such connections.

(a) Transverse branch plate-[O-circuIar :#. and -rectangular HSS c o h conneaion

(b) 1-beams-to-circular and -rectangular HSS column connection

(c) Axially loaded X- and T-type connections in rectangular HSS mernberç

Figure 7-1: Typicrl welded B S connections fmm Lu et al. (1994b)

For HSS connections, several specific notional ultimate deformation Iimits have been proposed by

various researchers. Mouty (1976, 1977) observed that the yield load predicted by yield line analysis

agreed well with the experimentally obtained load corresponding to a connection face deformation of l?h

of the main HSS member width (bo) for 12 symmetrical rectangular HSS K-type gapped connections.

Thus, Mou9 (1976, 1977) suggested that the design ultimate load of a rectangular HSS connection could

be based on a connection face defonnation limited to 1% of the main HSS member width (bo). However,

one should note that K-connections are much Less flexible than the connection ypes generally covered in

this thesis. Yura et al. (1980,198 1) suggested that the ultimate connection face deformation limit for a

circular HSS cmnection should be Limited to twice the branch member yield deformation (= V'E)

where the bmch member length (L) is taken to be 30 times its diameter. Korol and Mirza (1982)

suggested that the ultimate connection face deforrnation limit for a rectangular HSS connection shouId be

limited to 25 times the deformation at the elastic limit of the connection. KoroI and Mirza (1982) showed

that this ultimate connection face deformation limit was generally about 1.2 times the main HSS member

connecting face wall thickness (to).

A single generalised ultimate deformation Iimiî, to cover al1 types of welded HSS connections was

proposed by Lu et al. (1994b). They proposed that the load corresponding to a deformation of 3% of the

member widih (bo) or diameter (do) would be deemed to be the "ultimate load" of the connection. This

3%b0 (or 3%do) ultimate deformation limit was subsequently adopted by the International lnstitute of

Welding (IIW) Subcomrnission XV-E. Also, a l%bo (or 10/odo) defonnation limit has historically been

used as a serviceability deformation limit and has also k e n adopted by the International Institute of

Welding (nW) Subcommission XV-E. This corresponds to the typical out-of-flamess (convexity or

concavity) tolerance for rectangular HSS wall faces imposed on manufacturers.

Currently, the ultirnate defonnation limit of 3%b0 proposed by Lu et al. (1994b) and adopted by the

International institute of Welding (ITW) Subcommission XV-E is the most widely accepted deformation

limit being used by tesearchers ta define and compare the strength of welded HSS connections, However,

as this 3%b0 (or 3a/od0) ultimate deformation limit gains wider acceptance in the international research

community, the original development of this ultimate deformation limit should be reviewed to prevent its

misuse.

7.1 -1 Developmeni of the 3%bo utrimore deformion limit

A notional deformation limit is essentially used to define the strength of connections that do not

exhibit a pronounced peak or yield load. Thus, the toad corresponding to a particular deformation limit is

deemed to be the ultimate capacity of the connection. Lu et al. (1994b) chose a 3%bo (or 3%do) ultimate

deformation limit based on two premises.

First, it was found that for welded HSS connections that did exhibit a peak load, a corresponding local

indentation of the chord face of between 2.5% - 4% bo (or 2.5% - 4% do for circular HSS chord

members) was obtained. This observation was made based on the loaddeformation curves from both

experimental and numerical tests mainly performed at Delft University of Technology as shown by van

der Vegte (199 1), de Winkel(1993) and Yu (1994). Therefore, for connections that do not exhibit a peak

ioad, a deformation limit of 3%bo (or do), which is roughly equivalent to the deformation level for

connections that did exhibit a peak load, was suggested by t u et al. (1994b).

The second premise is derived specifically from an FEM study of transverse branch plate-to-

rectangular HSS colurnn connections. Lu et al. (1994b) observed that for these connections, the

deformation limit of 3%bo is very close to where the loaddeformation curves cross each other. Lu et al.

(1994b) show three loaddeformation c w e s to illustrate this observed trend. Lu and Wardenier (1995)

show five loaddeformation curves that contain the same three load-deformation curves cited in Lu et al.

(1994b). These curves are reproduced in Figure 7-2 with some additional annotation.

From Figure 7-2 it can be seen that for a transverse plate width-to-rectangular HSS chord width ratio

(p) of 0.30 and 0.50, the loaddeformation curves for connections to HSS main members with varying

wall slenderness (2yo) simultaneously cross each other at a deformation of 3% bo. However, for a

transverse plate width-to-rectangular HSS chord width ratio (P) of 0.18 and 0.73, the loaddeformation

curves cross each other at multiple locations ranging from 3%bo to 4.3%bo. For a transverse plate width-

to-rectangular HSS chord width ratio (P) of 0.93, the loaddeformation curves do not cross each other.

Ultimately, the physical phenomenon or importance underlying the point (or range of points) where the

loaddeformation curves for transverse plate-to-HSS column connections cross one another (or do not

cross one another for B = 0.93) is vague. However, at that connection deformation the connection loads

are fairly similar for a considerable range of main member HSS wall slendemess (2yo) values.

(a) LoaddefomitiOn CUWU for P = 0.18 (b) Lord-dtformrtion cuwes for = 0.30

O 5 10 1s 20 Connection de formation, A (mm)

(e) Load-defornition curvm for p = 030

O 5 10 15 ?O Connection deformation, A (mm)

(e) LoiddeConition cuntr for P = 0.93

" O 5 10 1s 20 Conneciion de formaiion, & (mm)

O 5 IO 1s 20 Cannection deformation. A (mm)

[d) Load-dtfarmation cuncs for 0 = 0.73

O 5 I O 15 20 Conneciion de formation. A (mm)

Figure 7-2: FEM load-Mormation curves Cor transverse branch plate-to-ASS column connections tom Lu and Wardtnkr (1995)

In summary, the 3%bo deformation limit proposed by Lu et al. (1994b) is usefil as an analysis tool

but not resolute. A single set of intemationally-agreed deformation criteria such as the l %bo serviceability

deformation Iimit and the 3%bo ultimate deformation limit adopted by the International Institute of

Welding (IIW) Subcommission XV-E is best suited for a consistent cornparison of results within a

database or behveen databases of various researchers. As a cautionary note, Wardenier (2000) shows in

Figure 7-3 that for different deformation limits different influences of parameters are obtained. ïhus. the

choice and scope of applicability for any particular deformation limit should always be considered.

Transverse bmch plate-to-rectangular h - - HSS member connections d

k.' Y

P) a O Deformation Iirnit .- cn uY 0 Defornation lirnit

E

0.0 0.02 0.04 0.06 0.08

Normalised comection deformation, A / 6,

Figure 7-3: Effwt of a deformation limit on observed parameter influences from Wardenier (2000)

7.2 Exhîing methods for determining the yield load from loaddeformation curves

Previously in Section 7.1, a notional deformation limit based criterion was described to determine the

capacity of welded HSS connections that do not exhibit a clearly defined peak-load or even yield load.

Alternatively, several methods for determining the "yield load" fiom loaddeformation curves that do not

exhibit a distinct yield load have been proposed. This so-called yield load can then be used to define the

Iimit state capacity of the connection. Figure 7-4 shows a sample experimentai loaddeformation curve

for a welded HSS T-type connection exhibiting a ductile chord flange failure mode. in this case, the load-

deformation curve can be approximated by two straight lines. The yield load (labelled as Pnetd in Figure

7-4) is defined as the load at the intersection of the hvo Iines, representing the "kink" in the curve where

an abrupt change in stiffness occurs. This bi-linear approximation of the yield load has been used since

the 1970's.

Connection deformation, A (mm)

Figure 7-4: Example of the ciassical bi-linear tangent yield load approximation method [Zhao and Hancock (1991)l

Packer et al. (1980) developed a formula to calculate the "yield" strength of gapped joints in

rectangular HSS trusses based on yield-line anatysis. However, they noted that there was no agreement

on how to define the yield load of a HSS lattice girder joint fiom the experimental load-deformation

curves. Packer et al. (1980) resorted to the aforementioned classical bi-iinear approximation of the yield

load as shown in Figure 7-5.

Vertical deformation of HSS connecting face beneath compression branch member, as a percentage of the main HSS rnember width, AJbQ

Figure 7-5: Example of the classical bi-linear tangent yield load approximation method [Parker et al. (1980)l

Figure 7-6 shows two different loaddeformation curves ("A" and "B") plotted on a log-log scale. In

this case the yield load fiom the load-deformation curve was detennined using a procedure proposed by

Kurobane et al. (1984). The procedure once again requires that the loaddeformation curve be

approximated by two straight lines. For the case of Curve "A", the yield strength is defined as the load at

the intersection of the two lines, representing a point of maximum curvature variation of the load-

deformation curve. However, in cases where the loaddeformation curve cm not be approximated by hvo

straight lines as illustrated in curve B of Figure 7-6, Kurobane's method uses an offset scatter band of 0.25

compared with the initial dope of the loaddeformation curve. The load at the intersection of this line and

the load-deformation c w e is defined as ihe log of the yield load.

b

Naturai logarithni of connection deformation, h(A)

Figure 7-6: Definition of yield Ioad by Kurobane et al. (1983)

Kamba and Taclendo (1998) studied experimental specimens and FEM models of transverse branch

plate-to-circular HSS member connections and defined the yield load as it relates to the initial stiffhess of

the loaddeformation curve. Figure 7-7 illusirates the yield load as defined by Kamba and Taclendo

(1998). Karnba and Taclendo (1998) idealised the overall Ioaddeformation curve as a tnlinear model

connecting the origin, points A, B, and C as shown in Figure 7-7. First, the yield load (P.,*) is taken to

be the location ("point B") on the load-deformation curve where the tangent stifhess reduces to one third

of the initial stifhess. Using this one third initial tangent stifhess method to define the yield load (Pycld),

Kamba and Taclendo (1998) observed that the maximum load (Pu) of four experimental test results

ranged fiom between 1 .28PPeld to 1 .35P,,id, with an average value of 1.3 1 PyCId. Thus, the generalised

ultimate load (Pu) "point C" was defined as the location on the load-deformation curve where the Ioad (P)

equals 1.3 1 times the defined yield load (Pyield), Finally, "point A" was defined as the location aIong the

initial tangent stiffness (&) line where the load (P) equals two thirds of the aforernentioned defined yield

-

Connection deformation, A (mm)

Figure 7-7: Definition of yield load by Kamba and Taclendo (1998)

Each method for determining the yield-load from a load-deformation curve has its merits. However,

similar to a notional deformation limit state based approach, certain methods are undemined by

necessary but somewhat adventitious provisions. For example, a breakpint stifhess of one third in the

case of Kamba and Taclendo (1998), and a contingent scatter band in the case of Kurobane et al, (1984)

are discretionary in nature.

7 3 Proposed FEM-based approach for determining the yield load from loaddeformation curves

A novel FEM-based approach is proposed to determine the yield load from a load-deformation curve.

A general T-type rectangular HSS connection is shown schematically in Figure 7-8.

~o&ing Sagging Yield Lines field Lines

Figure 7-8: Rectangular HSS T-type connection

The stiffened branch plate-to-rectangular HSS member FEM model, used in Chapter 5, c m be used to

approxirnate a generalised T-type (or X-type) connection. By using a relatively thick ("effectively-rigid")

stiffening plate, the footprint of the stiffening plate and ifs weld would behave sirnilarly to the rectangular

HSS T-type connection show in Figure 7-8. A pararnetric FEM study containing eight different square

HSS chord cross-sections, and four different branch width-to-rectanguiar HSS chord width ratios kvas

carried out to demonstrate the overall load-deformation behaviour of T- or X-type connections ehibiting

a chord flange failure mode. The parametric range of FEM test specimens is listed in Table 7-1. The

analytical model given by Equation (1-9) is proposed to be used to predict the yield load (Pr) of welded

rectangular HSS connections exhibiting a chord flange failure mode, based upon verification against

experirnental results demonsûated earlier in the thesis. The FEM parametric study, presented in this

section, is used to further illustrate some of the existing methods for detennining the "yield" load from

loaddeformation cwes. Finally, this chapter presents a novel approach for determining the "yield" load

fiom FEM-based loaddefonnation curves.

Table 7-1: Parametric FEM modelling matrix for a generaiised rectangular HSS T-type connection

(mm) (mm) note [A]

178 x 178 x 6351 127 x 127 x 6.351 Class I

sS16.1-94 Cl= of HSS Section

P' P r (W

note [B

0.4 120

0.5 136

0.6 161

0.7 19:

. -

[BI P r using Eq. (1-9) where: (F, ,=350 MPa. 0=9O0 . n =O. h ',ib ', = 1.00)

Figure 7-9(a) shows the toad-deformation response curves for seven different rectangular HSS cross-

sections with a constant connection effective branch width-to-chord width ratio of /3' = 0.4 and a constant

effective branch and stiffener plate length-to-HSS width ratio of q' = 1.0. Using the analytical mode1

described by Equation (1-9), each of the connection response curves should exhibit the sarne yield load

(PY) of 120 kN. Using the double tangent rnethod of approximating the loaddeformation response by two

straight lines, the defined yield load varies between 60 kN and 110 kN [see Figure 7-9(b)]. This

represents a large range of values that, overall, does not agree well with the analytical yield load (Pr) of

Effective branch plate length-to-HSS width ratio, 7' = 1 .O EKective stiffener plate width-to-HSS width ratio, P' = 0.4

-c HSS 305.~305~6.35 * HSS 254~254~6.35 -t. HSS 203.~203~6.35 -P- HSS 178~178~6.35 -t HSS 127~127~6.35 - HSS 102.u102x6.3S -t HSS 89~89x6,35

O 1 4 6 8 1 0 1 2 1 4 O 2 4 6 8 1 3 1 2 1 4

Connection deformation, A (mm) Connection deformation, 4 (mm)

Figure 7-9: Bi-linear tangent method for determiaation o f connection yield load

Figure 7-10(a) shows the same ioad-deformation response curves s h o w in Figure 7-9(a) but plotted on a

log-log scale as recommended by Kurobane et al. (1984). Using the bi-linear tangent method of

approximating the loaddeformation wponse, the defined yield Ioad varies between 55 kN and 90 kN

[see Figure 7-10(b)]. Once again this represents a large range of values that, overall, does not agree well

with the analytical yield load of 120 kN predicted by Equation (1 -9).

+ HSS 102~102~6.35 -t HSS 89~89~6.35

-O- HSS 305~305~6.35 -0- HSS 254~254~6.35

o. 1 1 10

Conneaion deformation, A (mm)

HSS 203X203x6.35 +r- HSS 178x178x6.35

0.1 1 I O

Connection deformation, A (mm)

Effective branch plate length-to-HSS width ratio, II' = 1.0 Effective stiffener plate width-to-HSS width ratio, Pt = 0.4

Figure 7-10: Log-Log plotting method for determination of connection yield load

-O- HSS 127~127~6.35

Figure 7-1 l(a) shows the same load-deformation response curves as in Figure 7-9(a) but Figure 7-1 I(b) is

ploned on a normalised deformation d e . The connection deformation (A) is divided by the width of the

HSS connecting face (bo) to obtain a dirnensionless deformation measure. Figure 7-1 l(b) is annotated

with the notional l%bo serviceability and the 3%bo ultimate deformation limits. Using the 3%bo ultimate

defonnation limit, the "mngth" of the connection varies fiom between 1 15 kN and 130 kN which agrees

very wetl with the analytical yield load of 120 kN predicted by Equation (1-9). Theoretically however, a

yield-line based analytical rnodel d m not predict a specific (Le. 3x60) deformation-based load

determination.

Effmive branch plate 1engt.h-to-HSS width ratio, q' = 1 .O Effective stiffener plate widh-to-HSS width ratio, B' = 0.4

- HSS 305~305~6.35 - HSS 254~254~6.35 -t HSS 203~203~6.35 - HSS 178~178~6.35 - HSS 127~127~6.35 ++ HSS 102~102~6.35 -+ HSS 89~89~6.35

O 2 4 6 8 1 0 1 2 1 4 0.00 0.01 0.02 0.03 0.04 0.05 0.06

Comection deformation, A (mm) Normalised connection deformation. A / b,

Figure 7-11: Notional delormation Iimit method for determination of conneetion yield load

A simple but novel FEM-based approach can be used to conclusively define the "strength" and

determine the so-called yield Ioad of welded HSS connections that do not exhibit a pronounced peak or

yield l a d . The validity of a FEM model is usually defined by how well the FEM results match physical

experimental test results. To this end, the FEM model aims to ideally match the physical experimental

rnodel in al1 respects (Le. geometry, material properties, boundary conditions etc.). The validity of an

analytical model is then usuafly defmed by how well the analytical model predicts the results of either the

physical experimental model or the verified FEM-simulated experimental model. However, just as the

FEM mode1 aims to simulate the physical experirnental model, so tw could a separate FEM model aim to

simulate the analytical model. The "validity" of an analytical model can only be detennined by FEM

analysis insofar as the FEM model duplicates the assumptions underlying the analytical model. The

"applicability" of the analytical model is a separate question that is anwered by how well the analytical

madel predicts the results of either the physical experimental model or the verified FEM-simulated

experimental model.

Analytical models based on fusterder yield-line theory are based on a ngid, perfectly-plastic rnaterial

response and so too should the FEM models k ing used as a basis for their validation. Figure 7-I2(b)

shows the load-deformation response curves when an "effectively-@id" elastic modulus of E x is

used. The original loaddeformation curve in Figure 7-12(a) is plagued by a non-pronounced peak and

yield load. This non-pronounced peak andior yield load led to the use of a defined ultimate Ioad level

determined by a notional 3%bo ultimate deformation limit state. Altematively, the so-called yield load

coutd be deduced by a variety of somewhat discretionary methods from the load-deformation curves.

However, the use of a rigid, perfectly-plastic material model leads to a clearly defined yield plateau as

evidenced in Figure 7-12(b). The simplified analytical model defined by Equation (1-9) predicts that each

of the seven connections should share a conunon yield load (Pr) of 120 kN. Figure 7-I2(b) finally

illustrates this similarity where al1 other methods of determining the soçalled ultimate load level or yield

Ioad Ievel have failed. Furthemore, the validity or effïcacy of other yieid-line based analytical models

cm more rationally be compared with this rigid, perfectly-plastic determination of the yield load.

1 Effective branch plate length-to-HSS widih ratio. q' = 1 .O 1 1 Effective stiffener date width-CO-HSS width ratio. i3' = 0.4 1

(a) Elastic, Perfectly-Plastic [E = 200 000 MPa]

-e HSS 305~305~6.35 - HSS 254~254~6.35 -t HSS 203~203~6.35 -i~- HSS 178~178~6.35 + HSS 127~127~6.35 -a- HSS 102~102~6.35 -t HSS 89~89~6.35

(b) Infinitely-Elastic, Perfectly-Plastic [E = 200 000 x lo3 MPa]

180 1 1

Comectioa defonnation, A (mm) Comection deformation, A (mm)

Figure 7-12: Proposed rigid, perfectly-plastic yield load determination metbod

Table 7-2 documents the complete results of the parametric FEM series outlined in Table 7-1. The

FEM test series included both an applied branch plate tension load as well as an applied branch plate

compression load case. The branch plate compression load case resulted in approximately 10% less

conservative loads for the 3%bo load level as compared with the tension load case. The rigid, perfectty-

plastic yield load determination resuked in almost identical (within 1%) values for the branch plate

tension versus branch plate compression load case. The analytical model, represented by Equation (1-9),

is not dependent on the sense (Le. tension or compression) of the applied branch plate load.

In Table 7-2, the notional 3%bo dtimate defonnation limit based load level (PUII%) is cornpared with

the yield load (PY) predicted by Equation (1-9). The 3%bo ultimate deformation limit based load level

(Pu3r.) compares well with the calculated yield load (Pr) predicted by Equation (1-9) [PrIPuS~ = 0.90 for

the branch plate tension load case and 1.03 for the branch plate compression load case]. Earlier in the

thesis, it was also shown that the 3%bo ultimate deformation limit based load level (Pu,3v.) also compared

well with the calculated yield load (Pr) predicted by Equation (1-9) for longitudinal branch plate,

longitudinal through branch plate, transverse branch plate, and stiffened branch plate connections. Thus,

the analytical yield load (Pr) predicted by Equation (1-9) agrees well with the notional 3%bo ultimate

defonnation limit based load (PUJv.) currently k ing used by the international research community.

A proper validation of the analytical yield load (Pr) predicted by Equation (1-9) is obtained by its

cornparison with the newly-defined, rigid, perfectly-plastic, yield load determination (Pngd.phtic). From

Figure 7-12(b), it can be seen that by using a rigid, perfectly-plastic, material model, the overall load-

deformation response exhibits a clearly defined yield plateau. As the material properties used in the FEM

model were only effectively-rigid (E = 200 000 x 10' ma), the overall loaddeformation response is not

exactly rigid, perfectly-plastic. From Figure 7-12(b) it can be seen that the initial slope of the load-

deformation curves are not vertical and the yield plateau are not perfectly horizontal. Thus, a tangent

line along the near-horizontal yield plateau of a load-deformation curve was drawn to intersect the

vertical load axis. The vertical load axis represents a n'gid initial slope and its intersection with the near-

horizontal yield plateau tangent line was defined to be the yield load (Pngid-plariic) of the connection. An

elastic modulus more closely approaching infinity (e.g. E x IO', 10 '... etc.) would result in a more ideal

rigid, perfectly-plastic overall loaddeformation response. However, increasing the value of the elastic

modulus beyond E x lo3 (i.e. E x lo4) resulted in only a negligibly better loaddeformation response at the

expense of increasing the numerical convergence problems with the FEM solution. As such, an otherwise

near-horizontal tangent line drawn along the yield plateau, resulting from an elastic modulus thee orders

of magnitude greater than the actual value, is sufficient to define this soîalled rigid, perfectly-plastic

yield load (Prigidplanis).

Table 7-2: FEM results for the proposcd rigid, perfectly-plastic yield load determination method

HSS Member theoretical Elastic, Perfectly-Plastic

Pmperties Comection Smngth E = 200,000 MPa F, = 350 MPa

Taision load Compression load b O x h o x r o RHS h l l b ' ~ P' P r PWIK P r Pu.lrc P r (mm) Clas (mm) (mm) (W IlrN) P.,Y. (W P,JY,

89 x 89 x 6.351 1 83 83 305 x 305 x 6.35) Class 3 1 299 299

note [BI

D.4 120

0.5 1 136

1 2 5 5 0,77 204 0.97 1 Average 0.90 1 .O3

Rigid, Perfectly-Plastic

E = 200.000( x 10') ma F.. = 350 MPa

227 0.87 224 0.88 Average 0.94 0.94 SL Dev. 5.2% 5.1%

COV 5.6% 5.4%

[A] CANICSA-S 16.1-94 Class oFHSS section

[BI P using Eq. ( 14) where: (Fyo=350 MPa @=Wu. n 4)

It is the author's opinion that this FEM-based rigid, perf'ectly-plastic yield load (Pn,d.,~,l,,) represents

the most rational yield andor ultimate limit state load determination for welded HSS connections that do

not otherwise exhibit a clearly defined yield andfor peak load. Furthemore, the relative validity of

various yield-line based analytical models should undoubiedly be judged relative to this so-called rigid,

perfectly-plastic yield load (PnBidgk,).

Table 7-2 documents that the aoalytical yield load (Pr) predicted by Equation (1-9) agrees very well

with the newlydefined rigid, perfectiy-plastic yield load (&$d,Mc). For both the applied branch plate

tension load as well as the applied branch plate compression load cases, the ratio of the analytically-

calculated yield load (Py) predicted by Equation (1-9), to the FEMdetermined, rigid, perf'ectly-plastic

yield load (Pn,ebic) is 0.94 with a standard deviation of only 5%.

8. CONCLUSI~NS & RECOMMENDATIONS FOR FURTHER RESEARCH

A conventional longitudinal branch plate-to-rectangular HSS member connection exhibits excessive

distonion or plastification of the HSS connecting face at relatively low loads. In an effort to better mode1

this connection, and to recommend alternatives that would reduce the inherent flexibility of longitudinal

branch plate connections, a comprehensive study consisting of longitudinal branch plate, through branch

plate, transverse branch plate, and stiffened longitudinal branch plate-to-rectangular HSS member welded

connections was presented in the thesis. This snidy included ptiysical experimental testing, analytical

models, and FEM analysis. A total of 22 labotatory tests on isolateci connections have been perfonned

and 48 1 FEM-modelled connections have been studied.

Specifically, the thesis serves to develop cornprehensive, rational, limit m e s design procedures and

equations that encornpass, and wherever possible consolidate, the multitude of branch plate-to-rectangular

HSS connection types available to designers. The thesis has shown that, for the failure mode of HSS

connecting face plastification which was the focus of this thesis, these different connection types can be

grouped under the generaiised case of a rectangular-to-rectangular HSS connection and designed as such.

8.2 General design formula for HSS connecting face plastification

A traditional yield line based formula [given by Equation (1-9)1 and reproduced below as Equation

(8-1) can effectively be used to determine the yield strength (Pr) of a11 the branch plate-to-HSS welded

connections described above, for the failure mode of flexure/pliutification of the HSS connecting face.

A resistance factor (4) of 1.0 can be applied to Equation (8-1) fur limit States design because the

connection is deflection critical and the calculated comection yield l a d (PI-) is welI below the comection

tiacture load. A notional 3% ultimate deformation limit (Pd%) load level is currently k ing used by the

international research community to define the capacity of such connections. This approach is not suited for

design purposes because a loaddefomation cuve would need to be generated, using either an experimental

test or an FEM-based simulation, for each connection geometry. However, the thesis has shown that the

calculable connection yield load (Pr) satisfies, and can be used in lieu of the 3%bo ultimate deformation

limit (Pd%) load level.

8.2.1 Influence of main member preload

The term \lz in Equation (8-1) aceounts for a reduction in connection strength due to the influence

of an applied stress (fiom axial load andor bending moment) in the connecting face of the main HSS

member. For non-90' branch member connections, the component of the branch member force acting

parallel to the HSS connecting face wouid cause an additional axial stress in the HSS co~ect ing face.

However, this additional axial stress is transferred locally at the branch member-to-HSS connecting face

region and can not be simplified as a uniform axial m s . The term J s in Equation (8-1) d a s not

include the effects of this possible additionai stress but the results of this thesis have show the overall

eficacy of the simplifkd Jztertn. Thus for a tende or compressive normal stress in the ClSS

connecting face:

applied net stress (F, ) n = (8-2)

yield stress (Fyo )

The idealised theoretical yield load of the connection [Pr using Equation (8-l)] is not dependent on the

force sense of the applied loads. In terrns of the main HSS member, either a compressive or a tensile

normal stress would result in an equivalent premature yielding of the connection. Similarly, the strengih

of the connection is independent of the branch king taaded in compression or tension. In both instances,

the assumed yield-line pattern that dwelops would be equivalent with only the sense of each yield line

(i.e. hogging versus sagging) changing.

The thesis has s h o w that only one of the four possible loading combinations (simultaneous branch

plate tension combined with main member comecting face tension) would be considered overly

conwrvative if designed using the JI-n' reduction factor in Equation (8-l), in conjunction with the

interpretation of Equation (8-2). Also, considering the uncertainty of the exact loading combination and

perhaps a load reversa1 that may occur in the field, it would be prudent to propose the overall use af the

Js reduction factor in Equation (8-1) for ail losd direction cases.

8.2.2 Serviceability condition

For HSS connections a connecting face deflection of 1% of the main member width (l%bo) has

generally been used as a serviceabiiity deformation limit (using unfactored loads), and a co~ec t ing face

deflection of 3% of the main member width (3%b0) has generally been used as an ultimate deformation

limit (using factored loads) as given by the international Institute of Welding (1989).

The I%bo serviceability deformation limit (Px,Ieh) load level typically lies between the elastic and

plastic portions of the loaddeformation response. Thus, neither an elastic analytical model nor a plastic

analytical model can be used to express this load level. Instead, a defomtion-based analytical formula that

models the interaction between the elastic and plastic response of the connection would be required to

calculate this load level. Such an analytical model, even if it were developed, would presumably be very

complex and unsuitable for design purposes. In any event, an empirical rnodel can be used to calculate the

l%bo serviceability deformation limit (P.r.l./i) load level as it relates to the calculable yield load [P, using

Equation (8-l)]. Developed in Section 4.2.2 of the thesis, the relationship between the connection yield

load (Pr) and the connection serviceability load (PI.lYi) for Class 1, 2, and 3 sections (defined by

CANICSA-S 16.1-94 for example) takes the form:

For C I ~ S 2 (t i 32) PSsl% = PY 2.0 - 1.258'

Now, both the yield load [Pr calculated using Equation (8-l)] and the serviceability load [ P , J ~ using

Equation (8-3), (8-4), or (8-S)] of a branch plate-to-rectangular HSS member connection can be

calculated. The governing strength or serviceability Iimit condition is detennined using accepted Lirnit

States Design principles. The calculated yield load of the connection (Pr) is compared with the total

applied factored load (PJ The calcülated serviceability load of the connection (Pr.lK) is compared with

the total specified, unfactored load (P). Thus, the goveming strength or serviceability condition is no

longer based on a standard ratio of 1.5 (as is the case with a notional PvJw versus a 1.5P,rv, connection

strength determination) for the factored to the unfactored load level. Instead, the strength or serviceability

governing condition is rationally determined using the actual factored and unfactored Ioads.

8 3 Design considerations for specific conaectioa types

8.3.1 Single branch plate versur through brunch plate connections

The results of an experimental and FEM mdy of single longitudinal branch plate and through branch

plate connections confirm the hypothesis that a through branch plate comwtion can be designed as having

two times the strength [Pr calculated using Equation (8-t)] of an equivalent single branch plate connection.

On a general note, longitudinal and through branch plate connections are characterised by iow P ratios

(= 0.1 to 0.25) resulting in a relatively low connection yield load (Pr)- For such connections, a

comprehensive FEM study has concluded that the non-unifonn stress distribution in the connecting

branch plate (typically treated using an effective width factor) is of negligible consequence for practical

connections at the branch plate load level cornmensurate with the connection yield load ( P r ) . Thus a

reduction in the branch plate effectiveness (or effective width) need not be considered in the branch plate

design.

8.3.2 Si@ened longitudinal branch plate connections

A stiffened branch plate connection cm ultimately achieve a much higher design resistance

equivalent to the enlarged "footprint" of the stiffening plate as opposed to the modest footprint of the

branch plate itself. In order to achieve the design yield load [Py calculated using Equation (8-t)] the

stiffening plate must be "effectively-rigid" with respect to the HSS connecting face so that a plastificahon

mechanism does not occur in the stiflening plate itself.

The author developed an empirical formula in Chapter 5 to produce the minimum required

"effectively-rigid" bound for the stiffening plate thickness, td,,, and is reproduced below as Equation

(8-6):

Equation (8-6) was developed to be a single consolidated design equation that satisfies both the strength

(Pr) and serviceability limit state (P,,J#) conditions. Finally, using the results of a comprebensive FEM

analysis, a generalised 20% reduction factor at the yield limit state (or a 0.80 effective width factor) is

recommended to be applied to the design of the connecting branch plate to account for a non-uniform

stress distribution along the branch plate width.

Where the width ratio of the "rigid" stiffening plate to the HSS is approximately unity, the additional

failure mode of chord side wall failure ought to also be checked. Similarly, when this width ratio is 0.85

or greater the failure mode of punching shear ought to be checked too, providing the "rigid" stiffening

plate is theoretically capable of punching through the HSS connecting face between the inside of the two

HSS side walls. These potential failure modes associated with very high stiffening plate-to-HSS width

ratios are beyond the scope of this thesis and design criteria can be found in Packer and Henderson

( 1997).

83.3 Transverse brunch plate connedians

A transverse branch plate to rectangular HSS member connection is significantly stiffer (due to a higher

p ratio) and hence has a higher design resistance than a longinidinaily-oriented branch plate. A transverse

branch plate with a low to medium P ratio will develop a plastification mechanism in the connecting face

whose yield load (Pr) can be predicted using Equation (8-1). The two transverse plate connections tested in

this study included a moderate P = 0.4 (p = 0.52) and a relatively high p = 0.8 (P' = 0.9 1 ) ratio. In bath

cases, the connection yield load can be detennined using Equation (8-1). However, aside from the

behaviour of the HSS connecting face, the design strength of transverse plate connections may also be

governed by an "effective width" criterion applied to the branch plate (reviewed in Section 1,7.5), which

accommodates the highly non-uniform stress distribution in the plate. This branch plate effective width

criterion has been shown by de Koning and Wardenier (1985) to be the critical failure mode for P < 0.85.

Where the width ratio of the transverse plate to the HSS is approximately unity, the additional failure

mode of chord side wall failure ought to be checked. Similarly, when this width ratio is 0.85 or greater

the failure mode of punching shear ought to be checked too, providing the transverse plate width is less

than the chord width minus mice the HSS wall thickness. These potential failure modes associated with

very high transverse plate-to-HSS width ratios are beyond the scope of this thesis and design criteria can

be found in Packer and Henderson (1997).

8.4 Rnage of applicability

Each of the equations presented in this chapter contain an inherent range of applicability limited to the

extent of the parametric testing programmes presented in the thesis. The details and extent of each

parametric testing programme are contained within the thesis. However, an overview of the proven

experimental and numerical range of applicability is worth noting in this section.

Overall, the traditional yield line based formula [given by Equation (8-l)] was experimentaIly proven

and numerically verified (using FEM anaiysis) to be effective for detennining the yield strength (PY) of a

variety of branch plate-to-rectangular HSS member connections including longitudinal branch plate-to-HSS,

through longitudinal branch plate-to-HSS, transverse branch plate-to-HSS, and the so-called "effectively-

rigid" stiffened longitudinal branch plate-to-HSS member connections.

The term a contained in Equation (8-1) and isolated in Equation (8-2) accounts for a reduction in

comection strength due to the influence of an applied stress (From axial load andor bending moment) in the

c o m t i n g face of the main HSS member. This term d l w a s verified experimentally for both 90" and

non-90" (45" experimental test series) connections, under a maximum axial compression preioad of 54% of

the column squash load, for an HSS cross-section with a siendemess ratio (2yo = bdto) of 23. This term

was verifed using FEM numerical analysis for both colurnn axial tension and colurnn axial

compression. The FEM parametric programme included a full range of HSS cross-sections with slenderness

ratios (2yo) of 20,24,28,32, and 40.

Equations (8-3,8-4, and 8-5) describe the relationship between the connection yield load (Pr) and the

connection serviceability load (Pr,146) for Class 1, 2, and 3 sections (defined by CANICSA-S16.l-94).

These equations have been verified both experimentally and numerically (using FEM anaiysis). The

experimental results contained a variety of branch plate-to-recîangular HSS member connections including

longitudinal branch plate-to-HSS (2yo = 26 and 37), through longitudinal branch plate-to-HSS ( 3 0 = 26 and

37), transverse branch plate-to-HSS (2y0 = 37), and the so-called "effectively-rigid" stiffened longitudinal

branch plate-to-HSS (2yo = 37) connections. The FEM results contained the so-called "effectively-rigid"

stiffened longitudinal branch plate-to-rectangular HSS member connections with a full range of HSS cross-

sections with slendemess ratios (2y0) of 12, 14, 16,20,28,32,40 and 48.

Equation (8-6) describes an empirical formula to produce the minimum required "effeçtively-rigid"

bound for the stiffening plate thickness [rH&,] for the so-called "effectively-rigid" stiffened longitudinal

branch plate-to-recîangular HSS connections. The experimental results contained an HSS cross-section

with a slendemess (2yo) of 37, stiffening plate-to-HSS width ratios (P) of 0.4 and 0.8, and two different

stiffening plate thicknesses (to). nie FEM results contained a full range of HSS cross-sections with

slendemess ratios (2y0) of I l , 13, 15, 19, 27, 31, 39 and 48, a full range of stiffening plate-to-HSS width

ratios (B) between 0.2 and 0.8, and a full range of stiffening plate thickness parameter ratios (2y'wl) between

1 .O and 10.0.

In ternis of material pmperties, the yield strength of the HSS main member (&) for the experimental

test specimens was either 394 MPa or 408 MPa The material properties of the FEM numerical models

either matched the properties of the experimental test specimens or a generic (CMSA-G40.20-98) 350W

structural steel with a yield strength (F@) of 350 MPa was used.

8.5 Recommeadations for further research

The current international specification (international Institute of Welding 1989) for the static strength of

HSS connections is only applicable to HSS with a nominal yield strength of up to 355 W a as this has been

the common grade of steel used. In Canada for example, the common grade of 350W steel has a nominal

yield strength of 350 MPa As such, both the experimental and FEM numerical analyses presented in this

thesis were based on this steel grade. Moreover, the bulk of research done intemationally and the design

recommendations set forth by CiDECT (Comité International pour le Développement et l'Étude de la

Construction Tubulaire) are based on HSS with a nominal yield strength of up to 355 MPa. The

modifications required to current static strength design expressions for HSS connections fabricated from

high strength steels (e,g. 420 MPa, 460 ma, 550 MPa nominal yield strength steel grades) are the subject

of discussion amongst international researchers. As the use of higher strength steels becomes more

prevalent, the behaviour of HSS connections fabricated from these high sîrength steels represents an area

where further research is required.

Another bmad area of M e r study relates to the use of yield line theory. It is the author's opinion that

analytical formulae based on yield-line theory can only be validated by a rational determination of the yield

load fiom experimental results. Such a rationai cornparison is then complicated by the inability to

conciusively detennine the yield load h m load-deformation cwes. EKisting methods for determining the

yield load fiom loaddeformation curves are discretionary in nature. The author believes that an FEM-based

rigid, perfectly-plastic, yield load (P"pidple) determination as presented in Chapter 7 of the thesis,

represents the most rationai yieldlultimate Ioad for connections that do not otherwise exhibit a cleariy

defined yield andlor peak load. This newly postulated ri& perfectly-plastic yield load (PrigidplPmc)

determination cm be used by other researchers, and may be applicable to other types of connections that

also lack a clearly defuied yield andlor peak load.

A5AQUS version 5.6 (1996). Hibbit, Karlsson, & Sorenson Inc. Pawtucket, R.I.

AiSC (1993). "Load and resistance factor design specification for structural steel buildings," American

Institute of Steel Construction, Chicago, Illinois, U.S.A.

Ariyoshi, M., and Makino, Y. (1999). "Loaddeformation relationships for gusset-plate to CHS tube joints

under compression loads." Proc. Ninth Internafional mshore and Polar Engineering Conference, Vol.

IV, Brest, France, pp. 54-62.

Bakker, M.C. (1990). "Yield line analysis of pst-collapse behaviour of thin-walled steel members."

Heron, Vol. 35, No. 3.

CANICSA-G40.20-98 (1998). "General Requirements for Rolled or Welded Structural Quality Steel."

Canadian Standards Association, Toronto, Canada.

CANICSAG40.2 1-98 (1998). "Structural Quality Steels," Canadian Standards Association, Toronto,

Canada.

CAN/CSA-G3 12.3-98 (1998). "Metric dimensions of structural steel shapes and hollow stnictural

sections," Canadian Standards Association, Toronto, Canada.

CANKSA-S 16.1-94 (1994). "Limit States Design of Steel Structures," Canadian Standards Association,

Toronto, Canada.

Cao, JJ., Packer, J.A. and Kosteski, N. (1998a). "Design Guidelines for Longitudinal Plate to HSS

Connections," Journal of Structural Engineering, ASCE, Vo1.124, No.7, pp.784-79 1.

Cao, J J., Packer, J.A. and Yang, GJ. (1998b). 'Yield line aoalysis of RHS connections with axial loads." J:

Consh?6ctional Steel Research, Vol. 48, pp. 1-25.

C DECT (1 986). "The strength and behaviour of staticalty loaded welded connections in smcttaaI hoUow

sections", Monograph No. 6, Comité International pour le Développement et l'Étude de la Construction

Tubulaire, Cohy, UX.

Davies, G. and Packer, JA. (1982). "Predicting the strength of branch plate - RHS connections for

punching shear." Canadiun Journal of Civil Engineering, Vol. 9, pp. 458467.

Davies, P., Kemp, K.O., and Waiker, A.C. (1975). "An analysis of the failure mechanism of an auially

loaded simply supported steel plate." Proceedings-institution of Civil Engineers, Part 2, Vol. 59, pp.

645-658.

Dawe, J.L. and Guravich, S.J. (1993). "Branch plate to reinforced HSS connections in tension and

compression." Canadian Journal of Civil Engineering, Vol. 20, pp, 63 1-64 1.

Dawe, J.L. and Mehendale, S.V. (1995). "Shear connections using stub tees between W beams and HSS

columns." Canadian Journal ofCivil Engineering, Vol. 22, pp. 683-69 1.

Eekhout, M. (1 996). "Tubular structures in architecture." Comité International pour le Développement et

l'Étude de la Construction Tubulaire (CIDECïJ.

Eurocode 3 (1992). "Design of steel structures. Part 1.1: General rules and rules for buildings", European

Committee for Standardisation, EMr 1993-1-1 : 1992E, British Standards Institution, London, England.

Fung, T.C., Chan, T.K. and Soh, C.K. (1999). "Ultimate capacity of doubler plate-reinforced tubular

joints," Journal of Sfruchaal Engineering, ASCE, Vol. 125, N d , pp. 89 1-899.

International Institute of Welding (IIW). (1989). "Design recomrnendations for hollow section joints - predominantly statically loaded." IIWDoc. XV-701-89,Znd ed, iIW Subcommission XV-E, Helsinki,

Finland.

Jatrett, N.D., and Malik, A.S. (1993). "Fin plate connections between RHS columns and 1-beams." Proc.

Fifh International Symposium on Tubular Structures, Nottingham, U.K., pp. 23 1-240.

Jubb, J.E.M. and Redwood, R.G. (1966). "Design ofjoints to box sections!' Conference on Industrial

Buildmg and the Strucmal Engineer, institution of Structural Engineers, U.K.

Kamba, T., and Taclendo, C. (1998). "CHS column connections without stiffeners." Proc. Eighth

International Symposium on Tubular Structures, Singapore, pp. 567-576.

Kapp, R.H. (1974). "Yield line analysis of a web connection in direct tension," Engineering Jomal,

American Institute of SteeI Construction, Vol.11, No2, pp. 38-41.

Kato, B., and Nishiyama, 1. (1979). "The static sûength of RR.-joints with large P ratio." CDECT prog.

SY Repofi Department of Architecture, University of Tokyo, Japan.

Koning, C.H.M. de, and Wardenier, J. (1985). "ïhe static strength of welded joints between structural

hollow sections or between structural hollow sections and H-sections. Part 2: joints between rectangular

hollow sections." Stevin Report 6-84-19, Delfi University of Technology, Delft, The Netherlands.

Korol, R.M. and Mirza, F.A. (1982). "Finite element analysis of RHS T-joints." Journal of the Structural

Division, ASCE, Vol. 108, No. 9, pp. 2081-2098.

Korol, R.M., El-Zanaty, M., and Brady, F.J. (1977). "Unequal width connections of square hollow sections

in Vierendeel trusses." Canadian Journal of Civil Engineering, Vol. 4, pp. 190-20 1.

Korol, R.M., Mitri, H., and Mirza, FA. (1982). "Plate reinforced square hollow section T-joint. of unequal

width." Canadian Journal of Civil Engineering, Vol. 9, pp. 143- 148.

Kurobane, Y., Makino, Y., and Ochi, K., (1984). "Ultimate resistmce of unstiffened tubular joints." Journal

of Structural Engineering, ASCE, Vol.110, No.2, pp.385-400.

Lu, L.H. (1997). "The static strength of 1-beam to rectangular hollow section column connections." Ph.D.

thesis, Del fi University of Technology, Delft, The Netherlands.

Lu, L.H. and Wardenier, J. (1995). "Parametric study on the static süength of uniplanar and multiplanar

plate to RHS column connections." Proc. Fijh International ûjj'shore anà Polar Engineering

Conference, Vol. IV, The Hague, The Netherlands, pp. 21-28.

Lu, LH., Puthli, R.S. and Wardenier, J. (1993). "Semi-rigid connections between plates and rectangular

hollow section columns." Proc. Fifh International Symposium on Tubulm S m u r e s , Nomngham

U.K., pp. 723-73 1.

Lu, L.H., Puthli, R.S., and Wardenier, J. (1994a). "Ultirnate deformation criteria for uniplanar connections

between 1-beams and RHS columns under in-plane ùending." Proc. Foiarh International qshore and

Polar Engineermg Conference, Osaka, Japan.

Lu, L.H., de Winkel, GD., Yu, Y. and Wardenier, J. (1994b). "Defornation limit for the ultimate strength

of hollow section joints." Proc. Skth International Symposium on Tubular Snuctures, Melbourne.

Australia, pp. 341-347.

Mouty, J. (1976). "Calcul des charges ultime des assemblages soudés de profiles creux carrés et

rectangulaires." Construction Métallique, Paris, France, No.2, pp. 37-58.

Mouty, J. (1977). "Theoretical prediction of welded joint strength." Proc. of the International Svmposium

on Hollow Struchnal Sections, Toronto, Canada.

Packer, J.A. and Henderson, J.E. (1992). "Design guide for hoilow sfructural secrion connections",

Canadian Institute of Steel Construction, Toronto, Canada.

Packer, J.A. and Henderson, J.E. (1997). "Hollow structural secrion connections and m s e s - cl design

guide", 2nd Edition, Canadian lnstitute of Steel Construction, Toronto, Canada.

Packer, J.A.. Davies. G.. and Coutie. M.G. (1980). "Yield strength of gapped joints in rectangular hollow

section trusses." Proceedings-Institution of Civil Engineers, Part 2, Vol. 69, pp. 995- 10 13.

Rolloos, A. (1969). "The effective weld length of beam to column connections without stiffening plates."

Stevin Report 6-69-7-m, Delfi University of Technology, Del& The Netherlands. (also: International

Institute of Welding, [IW ïkc. XV-276-69).

Saidani, M., and Nethercot, D.A., (1994). "Design of fui plate connections to SHS." Proc. Strrh

International Symposium on Tubular Structures, Melbourne, Australia, pp. 335-340

Sherman, D.R. (1996). "Designing with structural tubing." Engirreermg Jounta~, AISC, Vol. 33, No, 3, pp.

101-109.

Swanson Analysis Sysîems (1 !Ma). ANSYS Release 5.5, Houston, U.S.A.

Swanson Analysis Systems (1998b). "Structural analysis guide.", 4th Edition, Houston, U.S.A.

Vegte, G.J. van der, Puthli, RS., and Wardenier, J. (1991). "The static strength and stifiess of uniplanar

tubular steel X-joints." Proc. International Conjeence on Steel und Alumntium Structures, Singapore.

Wardenier, J. (1982). " H o l h section jointsn, Delfi University Press, Delft, The Netherlands.

Wardenier, J. (2000). "How to irnprove the conceptual design of tubular structures." Proc. Tenth

International ûj5hore and Polar Engineering Conference, Vol. IV, Seattle, U.S.A., pp. 1 -7.

Wardenier, J. , Davies, G., and Stolle, P. (1981). "The effective width of branch plate to RHS chord

connections in cross joints." Stevin Report 6-81-6, Delft University of Technology, DelQ The

Netherlands.

White, R.N., and Fang, P.J. (1966). "Framing connections for square structural tubing." Journal of the

S ~ u r a l Division, ASCE, Vol. 92, No. 2, pp. 1 75-194.

Winkel, G.D. de, Rink, H.D., Puthli, R.S., and Wardenier, J. (1993). "The behaviour and the static strength

of unstiffened 1-beam to circular column connections under rnuItiplanar in-plane bending moments."

Proc. Third International mshore and Polar Engineering Confirence, Singapore.

Wood, R.H. (196 1). "Plastic and elastic design of slabs andplates", Thames & Hudson, London, England.

Yeomans, N.F. (2001). "1-bearn to rectangular hollow section column T-connections." Proc. Ninth

International Symposium on Tubular S m u r e s , Düsseldorf, Gemany, pp. 1 19-1 26.

Yu, Y., and Wardenier, J. (1994). "Influence of the types of welds on the static strength of RHS T- and X-

joints loaded in compression." Proc. Sixrh International Symposium on Tubuiar Structures, Melbourne,

Australia.

Yura, J.A., Zettlernoyer, N. and Edwards, I.F. (1980). "Ultimate capacity equations for tubular joints."

Proc. Wshore Technology Conjërence, Houston, Texas, Vol. 1, Paper No. 3690.

Yura, J.A., Zettlemoyer, N . and Edwards, I.F. (1981). "Ultimate capacity of circular tubular joints."

Journai of the Sn?rctural Division, ASCE, Vol- 107, No. 1 O! pp. 1965-1985.

Zhao, X.L. (1996). "Verifkation of the defornation limit for T-johts in coid-formed RHS sections." Proc

Seventh International Symposium on Tubular Siruciures, Miskolc, Hungary, pp. 2 13-220.

Zhao, X.L. (2000). "Defonation Iimit and ultimate strength of welded T-joints in cold-formed RHS

sections," JournaI of Constructional Steel Research, Voi. 53, pp. 149-165.

Zhao, X.L., and Hmcock, GJ. (1991). "T-joinîs in rectangular hollow sections subject to cornbined

actions," Jourml of S n u c ~ a l Enginemmg, ASCE, Vol. 1 17, No.8, pp.2258-2277.

APPENDIX A: Material properties

Table Al: Measured material properties

IDENTIFICATION Measured Mechanical Promrties

Young's Modulus, E ( m a ) Yield Stress, F, (MPa)

Static Yicld Stress, Fy ( m a ) Ultimate Stress, F, ( m a )

FY (UmC)' Fy l Ductility. E,,,,-

,Cieasured Geometrical Promrries [note Al thickness, i (mm)

[note BI Cross-Srctional Area, .l (mm') Outside Corner Radius, R-= (mm)

Rectanmilar HSS 17Ibt127x7.6 178~127~4.8

Steel Plates 13.1 9.4 6.3

13.06 9.42 6.34

NIA NIA NIA NIA N/A NIA

[A] measured diredy using an average of three micrometer measuremenrs on the "Rat" [BI back calculared using measured section weight and length (using steel density = 7,850 kglm3)

457 mm 11 8 inches) coupon length

64 mm (2.5") gauge length

Figure Al: Typical coupon taken from rectangular HSS and steel plate stock

weld seam

Figure A2: Duplicate rectangular HSS coupon locations

c .- g zoo

l ' " ' I r T r ' i 1 " ' l i " '

- Coupon 1

Coupon 2

F, = 506 MPa - 1 1

i l I l ~ 1 1 1 ~ 1 1 ~ " a ' i

Fy = 394 MPa

Fy(static) = 378 MPa

1 L u -t 4 i

1 ' 1 1 ' ' ' ' ~ 1 ' ' 1 1 ' 1 ' 0.015 0.020

, IJ 0.000 0.005 0.010 0.025 :

1 1 1 1 1 1 1 1 1 1 1 1 2 . I 1 ( -

0.00 0.05 0.10 0.15 0.20 O 25

Figure A3: HSS 178~127~7.6 tensile coupon curves

i - Coupon I Coupon 2

500

Figure A4: HSS 178~127~4.8 tensile coupon Cumes

Figure AS: 13.1 mm plate stock tende coupon cuwes

, . I r 1 Coupon l Coupon 2

Figure A6: 9.4 mm piate stock tcnsüe coupon curvrs

Figure Al: 6.3 mm plate stock tensile coupon cuwes

APPENDIX B: Deformation profide and stress détribution plots

90" TEST SERIES

Figure BI: HSS connecting face deformation profile for specimen 90LPO Figure B2: Branch plate stress distribution for specimen 90LP0

note: refer to Figures 2-15 and 2-17 for specimen 90LP20

Figure B3: HSS connecting face deformation profile for specimen 90LP4O Figure B4: Braneb plate stress distribution for specimen 90LPd0

Figure BS: HSS connecting face deformation profile for specimen 90LP60 Figure B6: Branch plate stress distribution for specimen 90LP60

d5O TEST SERIES

Figure 87: HSS connecting face deformation profile for specimen J5LPO Figure 88: Branch plate stress distribution for specimen 45LPO

Figure B 9 HSS eonneeting face deformation profile for specimen JSLPZO Figure B10: Branch plate stress distribution for specimen 45LP2O

Figure BI 1: HSS connecting face defonnation profile for specimen 45LP40 Figure Bl2: Brancb plate stress distribution for specimen 45LP40

note: refer to Figures 2-16 and 2-18 for specimen 45LP60

30° TEST SPECIMEN

Figure B13: HSS connccting face deformation profile for specimen 30LPO Figure B14: Brancb plate stress distribution for specimen 30LPO

600 TEST SPECIMEN

F i i r e BIS: HSS conaccting lace deformation profile for specimen 60LPO Figure 816: Branch plate stress distribution for specimen 60LPO

Tension Load (kN) Soecimen 90LPO

Left side Centre of connection Right side

Position along HSS connecting face centre line (mm)

Figure BI: HSS connecting face deformation profile for specimen 90LPO

300 Tension Load (kN1

367 (failure load) Broken both ends -

-90 -75 -60 -45 -30 -15 O 15 30 45 60 75 90 Left end Plate centre Right end

Position along branch plate widtfi (mm)

Figure BZ: Branch phte stress distribution for specimen 90LPO

Tension Load (kN) S~ecimen 90LP40

LeR side Cenire of connection Right side

Position along HSS connecting face centre line (mm)

Figure B3: HSS connecting face deformation profile for specimen 9OLP4O

Sbecimen 90LP40

Tension Load (kN)

: 17 (Failure load) Broken both e n d s

-90 -75 -60 -45 -30 -15 O 15 30 45 60 75 90

Left end Plate centre Right end

Position along branch plate width (mm)

Figure 84: Bnnch pIate stress distribution for specimea 90LP40

Tension Load (kN) Snecimen 90LP60

Left side Centre of co~ection Right side

Position along HSS connecting face centre line (mm)

Figure BS: HSS connecting face deformation profile for specimen 90LP60

Soecimen 90LP60

308 (failure load) .. . ..

Tension Load (kN)

not broken / '- / ) "O

-90 -75 60 -45 -30 -15 O 15 30 45 60 75 90

Left end Plate centre Right end

Position along branch plate width (mm)

Figure 86. Branch plate stress distribution for specimen 90LP60

Broken at toe --- 350

300

250 200 1 O0

3 0

Toe Heel

- - - 25 -

Left side Centre of connection Right side

Position along HSS connecting face cenue line (mm)

Figure B7: HSS connecting face delormation profile for specimen 4SLPO

Tension Load (kN) Specimen 45LPO

-

-90 -75 -60 -45 -30 -15 O 15 30 45 60 75 90 Left end Plate centre Eüght end

- S~ecimen 45LPO Tension Load (W)

P - - - - 420 (failure load) - 350 - - Broken at toe

300

250

200

Position along branch plate width (mm)

- - - -

Figure BS: Branch plate stress distribution for specimen 45LPO

l l ~ l l ~ l l I I I 1 I l 1 1 1 I i I ) l l I I I I

Tension Load OrN)

Broken at toe i 1 350

1 A

300 - 250 200 1 O0

---- Toe Hrel

Lefi side Centre of connection Right side

Position along HSS connecting face centre line (mm)

Figure 89: HSS connecting face deformation profile for specimen 45LP20

- - note: branch plate stresses should be higher at the bmch plate S~ecirnen 45LPîO - ends. Specimen 4SLP20 does not follow the same trend - as the ofier specimens. Strain gauge channels may have

+ ken mislabelled dunng testing. - - - - -

l

I

I

3 C .- E 9 V1

X 9 - 3 a ,- - I

I

I

l

I I ) I t

-30 -15 # 30 45 60 75 90

Letl end Plate cenw Right end

Position dong branch plate width (mm)

Figure B10: Braneh piate stress distribution for specimen 45LP20

Broken at toe -- - -

Tension Load (1<N) S~ecimen 45LP40

Left side Centre of connection Right side

Position along HSS connecting face centre line (mm)

Figure Bll: HSS connecting face deformation profile for specimen 45LP40

400 S~ecimen 45LP40 Tension Load (kN)

-90 -75 4 4 5 -30 -15 O 15 30 45 60 75 90

Lefi tw end Plate centre Right heeI end

Position along branch plate widdi (mm)

Figure B12: Brnnch plate stress distribution for specimen 45LP40

4' Tension Load &N) Soecimen 30LW

500 CI

i Toe Heel

-200 -150 -100 -50 O 50 1 O0 150 100

Lefi end Plate centre Right end

Position along HSS connecting face centre Iine (mm)

Figure B13: HSS connecting face deformation profile for specimen 30LW

Tension Load (kN) Specimen 3OLPO

-90 -75 6 0 -45 -30 -15 O 15 30 45 60 75 90

Lefi toe end Plate centre Right heel end

Position dong branch plate width (mm)

Figure B14: Branch plate stress distribution for specimen 30LPO

i Tension Load (kN) Soecimen 60L W 30

Left side Centre of connection Right side

Position along HSS connecting face centre line (mm)

Figure BIS: HSS connecting face deformation profile for specimen 60LPO

h 3 O0

B E

250 U

L "00 9 a - L C 0 150 z 2 P 0 LOO B e X

50

O

Soecimen 60LPO Tension Load (kN)

P

-90 -75 -60 -45 -30 -15 O 15 30 45 60 75 90

Leîl toe end Plate centre Right hee l end

Position dong branch plate width (mm)

Figure 816: Branch plate stress distribution for specimen 60LPû