Commission of the European Communities

technical steel research

Properties and service performance

THE DEVELOPMENT OF RECOMMENDATIONS FORTHE DESIGN OF WELDED JOINTS BETWEEN

STEEL STRUCTURAL HOLLOW SECTIONS AND H-SECTIONS

Report EUR 9462 EN

Blow-up from microfiche original

Commission of the European Communities

technical steel research

Properties and service performance

THE DEVELOPMENT OF RECOMMENDATIONS FOR THE DESIGN OF WELDED JOINTS BETWEEN

STEEL STRUCTURAL HOLLOW SECTIONS AND H-SECTIONS

T.W. GIDDINGS

BRITISH STEEL CORPORATION 9, Albert Embankment GB-LONDON SE1 7SN

Contract No 7210-SA/814 (1.7.1980- 30.6.1983)

FINAL REPORT

Directorate-General Science, Research and Development

1985 EUR 9462 EN

Published by the COMMISSION OF THE EUROPEAN COMMUNITIES

Directorate-General Information Market and Innovation

L-2920 LUXEMBOURG

LEGAL NOTICE Neither the Commission of the European Communities nor any person acting on behalf of the Commission is responsible for the use which might be made of

the following information

ECSC-EEC-Euratom, Brussels Luxembourg

THE DEVELOPMENT OF RECOMMENDATIONS FOR THE DESIGN OF WELDED JOINTS BETWEEN STEEL STRUCTURAL HOLLOW

SECTIONS OR BETWEEN STEEL STRUCTURAL HOLLOW SECTIONS AND H-SECTIONS

F I N A L R E P O R T

Agreement No. 7 2 1 0 . S A / 8 I 4

T.W. Giddings Research Centre

Corby Works British Steel Corporation

EUR 9^62 EN

Summary This report contains the results of research carried out in the UK on the development of design recommendations for welded joints in steel structural hollow sections and forms part of an inter-national programme of research involving also France, Germany, Italy and The Netherlands. The UK programme examined three separate problems.

1. The effect on the strength of PHS K- joints of external loads applied at the joint.

2. The behaviour of FHS K- joints with bracings in two planes 90 to each other.

3. The influence of inplane moments and axial load/inplane moment interaction on CHS cross joints and Tee joints.

The work was carried out by the British Steel Corporation Tubes Division in co-operation with the University of Nottingham (PHS joints) and the Kingston Polytechnic (CHS joints). The results of all tests carried out are summarized. These com-prised 18 tests in part 1, 2 tests in part 2 and 27 tests in part 3. Recommendations are given to enable the designer to deal with external loads applied to PHS lattice frame joints and to deal with CHS cross joints and Tee joints subjected to axial load, inplane moment or a combination of axial load and inplane moment. Tentative conclusions only have been drawn from the two tests on PHS K- joints in two planes.

Sommaire

Le present rapport presente les resultats de recherches poursuivies au Royaume-Uni et portant sur la mise au point de recommandations en matire de conception des assemblages soudes de profils creux en acier utiliss en construction; il fait partie d'un programme international de recherches auquel participent galement la France, l'Allemagne, l'Italie et les Pays-Bas.

Les tudes menes au Royaume-Uni ont port sur trois aspects:-

1. L'effet sur la rsistance des joints en K pratiqus sur des profils creux rectangulaires, des charges extrieures s'exerant au niveau du joint.

2. Le comportement des joints en K des profils creux rectangulaires avec renforcements dans deux plans normaux l'un par rapport a 1'autre.

3. L'influence des moments de systmes plans et l'effet rciproque des charges axiales/moments de systmes plans sur les assemblages de profils creux ronds en T double et T simple.

Les travaux ont t conduits par la Division Tubes de la British Steel Corporation, en coopration avec l'Universit de Nottingham (assemblages de profils creux rectangulaires) et du Polytechnic de Kingston (assemblages de profils creux ronds).

Les recommandations labores ont pour but de permettre aux bureaux d'tudes d'arriver une plus grande prcision concernant les forces extrieures exerces sur les assemblages de poutres en treillis, ainsi que pour les assemblages de profils creux ronds en T double et T simple soumis une charge axiale, ou a une combinaison de charge axiale et de moment d'un systme plan. Les deux essais pratiqus sur les joints en K sur des profils creux rectangulaires en deux plans ont permis d'arriver a des conclusions qui ne sont encore que prliminaires.

n i

Zus flitmienf as sung Dieser Bericht en th l t die Ergebnisse der i n Grobritannien durchgefhrten Forschung zur Ausarbeitung von Modellempfehlungen fr geschweite Verbindungen zwischen Stahlbauhohlprofi len; dies s t e l l t e inen Te i l des in t e rna t iona len Forschungsprogramms dar , an dem auch Frankreich, Deutschland, I t a l i e n und die Niederlande b e t e i l i g t s ind .

Im Rahmen des b r i t i s c h e n Programmes wurden d r e i getrennte Probleme un te r such t . 1. Die Auswirkung ex te rner , auf die Verbindung wirkender Belastungen auf

die F e s t i g k e i t von KVerbindungen aus Hohlprofilen mit Rechteckquerschnit t . 2. Das Verhalten von KVerbindungen aus Hohlprofilen mit Rechteckquerschnitt

mit Versteifungen i n zwei um 90 gegeneinander ve r se tz t en Ebenen. 3 . Der Einflu von in e ine r Ebene wirkenden Momenten und der Wechselwirkung

zwischen Lngsbelastung und i n e ine r Ebene wirkendem Moment auf Querverbindungen und TVerbindungen aus Hohlprofilen mit Kre i squerschn i t t .

Die Arbeiten wurden von der B r i t i s h Steel Corporation, Unternehmensbereich Rhren in Zusammenarbeit mit der Univers i t t Nottingham (Verbindungen zwischen Hohlprofilen mit Rechteckquerschnit t) und dem Polytechnikum Kingston (Verbindungen zwischen Hohlprofilen mit Kre isquerschni t t ) durchgefhrt. Es e r fo lg t eine Zusammenfassung der Ergebnisse smtl icher Prfungen. Dazu gehrten 18 Prfungen i n Tei l 1, 2 Prfungen i n Tei l 2 und 27 Prfungen i n Te i l 3Es werden Empfehlungen gemacht, die dem Konstrukteur be i der Bearbeitung folgender Problemstellungen b e h i l f l i c h s ind: Bei auf Gitterrahmenverbindnngen zwischen Hohltrgern mit Rechteckquerschnitt wirkenden externai Belastungen, be i Lngsbelastungen ausgesetzten Quer und TVerbindungen zwischen Hohlprofilen mit Kreis que r s c h n i t t , be i i n e ine r Ebene wirkendem Moment oder e ine r Kombination aus Lngsbelastung und i n e ine r Ebene wirkendem Moment. Aus den beiden Prfungen an KVerbindungen zwischen Hohltrgern mit Rechteckquerschnitt in zwei Ebenen wurden l e d i g l i c h vorlufige Schlufolgerungen gezogen.

LIST OF CONTENTS

i) Summary ii) Symbols

Part 1: General Information T.W. Giddings, N.F. Yeomans British Steel Corporation, Tubes Division

Part 2: Influence of Purlin Loads on K- Joints M.G. Coutie, G. Davies, M. Bettison, J. Piatt The University of Nottingham

Part 3: The Strength of Three Dimensional PHS Joints M.G. Coutie, G. Davies, M. Bettison, J. Piatt The University of Nottingham

Part 4: The Strength of T- and X- Joints in CHS A. Stamenkovic, K.D. Sparrow The Kingston Polytechnic

A detailed list of contents is given at the beginning of each of the detailed parts of the report i.e. parts 2, 3 and 4.

vii

TABLE DES MATIERES

i) Sommaire

ii) Symboles

le Partie: Gnralits T.W. Giddings, N.F. Yeomans British Steel Corporation, Tubes Division

2e Partie: Effet des charges exerces par les pannes sur les joints en K M.G. Coutie, G. Davies, M. Bettison, J. Platt Universit de Nottingham

3e Partie: La rsistance des assemblages tridimensionnels de profils creux rectangulaires M.G. Coutie, G. Davies, M. Bettison, J. Platt Universit de Nottingham

4e Partie: La rsistance des assemblages en T double et T simple de.profils creux ronds A. Stamenkovic, K.D. Sparrow The Kingston Polytechnic

Une table des matires dtaille figure au dbut de chacune des parties dtailles du rapport, c'est--dire des 2e, 3e et 4e parties.

IX

INHALTSVERZEICHNIS

a) Zusammenfassung

b) Symbole

Tei l 1 : Allgemeine Angaben T.W. Giddings, N.F. Yeomans B r i t i s h Steel Corporation, Unternehmensbereich Rhren

Tei l 2: Einflu von Pfet tenbelastungen auf K-Verbindungen M.G. Coutie, G.Davies, M. Bet t i son , J . P l a t t Univers i t t Nottingham

Tei l 3* Die Fes t igke i t dreidimensionaler Verbindungen zwischen Hohlprofilen mit Rechteckquerschnitt M.G. Coutie, G.Davies, M. Bet t i son , J . P l a t t Univers i t t Nottingham

Tei l ]+: Die Fes t igke i t von T- und X-Verbindungen be i Hohlprofilen mit Kreisquerschni t t A. Stamenkovic, K.D. Sparrow Polytechnikum Kingston

Ein ausfhrl iches Inha l t sverze ichnis finden Sie am Beginn e ines jeden Ber ich tabschn i t t s , das heit zu Beginn von Teil 2, 3 und 1+.

X I

Symbols The symbols used are explained at the beginning of each part of the report.

Xlll

Acknowledgements

The Project Leader wishes to record his appreciation of the efforts and co-operation he has unceasingly received from the staff of the University of Nottingham and Kingston Polytechnic, and British Steel Corporation Tubes Division Technical Centre and of the valuable discussion, particularly at the formulation stage of the project, fron the Joints Working Group of CIDECT.

Thanks are particularly due to the European Coal and Steel Community, Cometube International pour le Dveloppement et l'Etude de la Construction Tubulair and the Science and Engineering Research Council for their support which made the research possible.

Finally he wishes to thank Monsieur Descade, Chairman of Executive Committee F8 and Mr J. Ferron of the ECSC for their kindness and help during the presentation of the results of the work.

xv

Commission of European Communities Technical Steel Research

Final Project Report

DEVELOPMENT OF RECOMMENDATIONS FOR THE DESIGN OF WELDED JOINTS BETWEEN STEEL STRUCTURAL HOLLOW SECTIONS OR BETWEEN STEEL STRUCTURAL HOLLOW SECTIONS AND H SECTIONS

PART 1: GENERAL

T.W. GIDDINGS N.F. YEOMANS

British Steel Corporation Tubes Division Technical Centre Corby England

ECSC Agreement No: 7210.SA/814

Research carried out with the financial aid of the European Coal and Steel Community.

1. General 1.1 Introduction

Steel structural hollow sections (SUS) have an essential role to play in improving the aesthetics and economics of construction.

The use of steel SHS in construction has increased considerably in recent years even against a general decline in building activity. In many cases SHS have opened up new opportunities for steel that would otherwise be in other materials such as concrete or wood. An example of this is the use of concrete filled SHS columns in buildings that would traditionally be in reinforced concrete. This trend will encourage the use of steel products generally by leading the way to more steel intensive solutions.

Light SHS trusses are also the most serious competitor to wood applications such as roof trusses for housing.

The lack of comprehensive design reoommendations in some areas of SHS applications have proved to be a severe handicap to the con-tinuing development of the market. This is particularly so in the field of welded lattice girder construction where the particular properties of SHS can be used to their best advantage.

Based on research supported previously by ECSC and others, international design recommendations have been framed now and are being used in some of the EEC countries. However, from the information available it was found that a more detailed investigation was required in certain areas to increase the range of validity of the design reoommendations and to simplify them.

Some of these problems have been examined in a co-ordinated pro-gramme developed and undertaken by the major producers of structural hollow sections in the EEC under separate contracts with ECSC but under the general direction of the BSC Tubes Division.

The overall programme was undertaken by the companies listed below each of whcm will submit a report dealing with that part of the programme for which they were responsible.

Company Country ECSC Agreement

Mannesmannrohren-Vferke AG Federal Republic 7210.SA/109 of Germany

Valexy France 7210.SA/305 Dalmine Italy 7210.SA/410 Staal Centrum The Netherlands 7210.SA/606 British Steel Corporation UK 7210.SA/814

1.1

The conclusions and recommendations of each progranme will be pre-sented and co-ordinated in a summary report that will be prepared when all of the final reports are available.

1.2 Cbjectives

The objectives of this programme are:-

1. To provide the necessary experimental and theoretical data to enable rational and simple design recommendations to be developed in those areas of SHS welded joints not covered satisfactorily in existing work.

2. To provide evidence to enable existing design recaimendations to be simplified and extended to cover all of the parameters relevant to the range of manufactured structural hollow sections.

3. To identify the limits of parameters for which joint strengths do not have to be calculated.

4. To provide comprehensive recommendations on the design of welded joints in SHS and SHS and H sections to form the basis for future European recommendations and Euronorms.

1.3 Benefits

The development of comprehensive and efficient design recommend-ations for lattice girder construction using SHS will enable more economic designs to be produced and will encourage the greater use of steel products generally by encouraging steel intensive solutions. Thereby helping to safeguard the market for steel and hence employment in the industry.

1.4 UK Programme

The work carried out in the UK concentrated on three specific problem areas each of which is dealt with in a separate part of the report as follows.

Part 2 The effect on the strength of RHS K- joints of external loads applied at the joint.

Part 3 The behaviour of RHS K- joints with bracings in two planes at 90 to each other.

Part 4 The influence of inplane moments and axial load/inplane moment interaction on CHS cross joints and Tee joints.

The work was carried out by the British Steel Corporation Tubes Division in conjunction with the University of Nottingham (RHS joints) and the Kingston Polytechnic (CHS joints).

1.2

1.5 References 1. Wardenier, J and

Stark, J.W.B. The static strength of welded lattice girder joints in structural hollow sections in Commission of the European Communities, ECSC Agreement No. 6210-SA/6/604, Final Report 1980.

2. International Institute of Welding

Design reoommendations for hollow section joints, predominantly

statically loaded - IIW Document No. XV-491-81.

1.3

Commission of European Communities Technical Steel Research

Final Project Report

DEVELOPMENT OF RECOMMENDATIONS FOR THE DESIGN OF WELDED JOINTS BETWEEN STEEL STRUCTURAL HOLLOW SECTIONS OR

BETWEEN STEEL STRUCTURAL HOLLOW SECTIONS AND H SECTIONS

PART 2: JOINTS WITH LOCAL (XINCENTRATION LOADS

M.G.COUTIE G.DAVIES M.BETTISON J.PLATT

Department of Civil Engineering Nottingham University University Park NOTTINGHAM ND7 2RD

ECSC Agreement No: 7210.SA/814

December 1983

Research carried out with the finanical aid of the European Coal and Steel Community and the Science and Engineering Research Council

CONTENTS - PART 2

1. Introduction

2. Test Specimens

3. Material Properties

4. Test Rig and Testing Procedure

5. Measurements

6. Test Results (Joints with purlin loads)

6.1 General Description of Joint Behaviour Under Load 6.2 Modes of Failure 6.3 Branch-Chord Deflections 6.4 Failure Loads 6.5 Working Load Deflections 6.6 Forces and Moments 6.7 Summary and Conclusions

7. Development of Design Recommendations

7.1 Review of Previous Test Results 7.2 Corby Tests 7.3 Failure Modes 7.4 The Influence of Chord Preload on Ultimate Strength 7.5 Local Deflection 7.6 Comparison between Test Results and the Suggested CIDECT

Equation 7.7 Recommendat ions

References

Tables

Plates

Figures

2a

TABLE DES MATIERES - 2e PARTIE

1. Introduction

2. Eprouvettes

3. Proprits des matires

4. Montage d'essai et mode opratoire

5. Mesures

6. Rsultats des essais (assemblages subissant des charges exerces par les pannes)

6.1 Description gnrale du comportement de l'assemblage en charge

6.2 Mode de ruine 6.3 Flches des diagonales-membrures 6.4 Charges de ruine 6.5 Flches pour les charges de service 6.6 Forces et moments 6.7 Sommaire et Conclusions

7. Elaboration de recommandations en matire de conception

des 7.1 Examen des rsultats f\ essais prcdents 7.2 Essais de Corby 7.3 Modes de ruine 7.4 Effet de la pr-charge des membrures sur la rsistance

la rupture 7.5 Flche locale 7.6 Comparaison entre les rsultats des" essais et l'quation

propose par CIDECT 7.7 Recommandations

Rfrences Tableaux Photographies Chiffres

2b

INHALTSVERZEICHNIS - TEIL 2

1. Eirifhrung

2. Probestcke

3 Werkstoffeigenschaften

il. Prf Vorrichtung und Prfverfahren

5 Messungen

6. Prfergebnisse (Verbindungen mit Pfet tenbelastungen)

6.1 Allgemeine Beschreibung des Verhaltens der Verbindung unte r Last 6.2 Arten des Versagens 6.3 Abzweig/Gurt-Durchbiegungen 6.I4. Ausfallbelastungen 6.5 Durchbiegungen be i Arbei tsbelastung 6.6 Krfte und Momente 6.7 Zusammenfassung und Schlufolgerungen

7. Entwicklung der Modellempfehlungen

7.1 berblick ber frhere Prfergebnisse 7.2 C orby-Prfungen 7-3 Ausfallbelastungen 7.1+ Der Einflu der Gurt-Vorbelastung auf die maximale Fes t igke i t 7.5 Lokale Durchbiegung 7.6 Vergleich zwischen den Prfergebnissen und der vorgeschlagenen

CIDECT Gleichung 7.7 Empfehlungen

Literatur

Tabellen

Phot o graph! en

Abbildungen

2c

SYMBOLS

A^ cross sectional area (mm3) of member i

N load (kN) in member i

N0p pre-load (kN) or additional end load in chord due to other than the branch force components at the joint

N u ultimate load (kN) in member i Nlum Mean ultimate strut load (kN) from Wardenier's joint strength eguation

(Ref. 1) Nicr load (kN) at which crack initiation was first observed Nl%bo load (kN) at which a joint deformation of 1% chord width (b0) occurs

N*x joint design strength (kN) based on force in branch strut Nik characteristic joint strength (kN) based on strut

NpL 'purlin' load (kN)

a throat thickness (mm) of fillet weld

bi breadth (mm) of RHS member i perpendicular to plane of joint

e eccentricity (mm) between bracing and chord centre lines measured perpendicular to chord

g gap between the toes of the bracings (g' measured between toes of welds)

hj height (mm) of RHS member in plane of joint

i member number 0,1,2 for chord, strut and tie bracing respectively

s standard deviation

t wall thickness of member i

width ratio (compression bracing to chord)

y chord slenderness factor where y " bo/2t0

ym material or joint strength factor

0 local deflection - as measured by LVDTs shown in Fig. 7

2d

8 angle of inclination of bracing member (i = 1,2) relative to chord

0 average chord pre-load stress - Nop/A0

r0 gap shear stress (N/mm2) in chord Teo shear yield stress (N/mm2) in chord

o average stress (N/mm2) in member i

ei material yield stress (N/mm2) of member i

ou material ultimate stress (N/mm2) of member i

0 2 0.2% proof stress

. influence function for the axial stress in the chord on joint strength

LVDT linearly variable differential transformer

ERSG electrical resistance strain gauges

RHS rectangular hollow section

UB universal beam

SWG standard wire gauge

2e

ACKNOWLEDGEMENTS

The experimental part of this investigation was carried out under the direction of Dr. M.G. Coutie and Dr. G. Davies, at the laboratories of the Tubes Division of the British Steel Corporation, at Corby, Northants.

The British Steel Corporation was responsible for the supply of materials and fabrication of joints to the specifications laid down and the supply and fixing of strain gauges. Recording of strains, and testing was carried out on Steel Corporation equipment. The operation of the testing machine was carried out by Tubes Division staff to the instruction of Nottingham personnel.

The authors acknowledge the ready co-operation of Tubes Division staff, and in particular that of Mr. T.W. Giddings and Mr. N.F. Yeomans.

Gratitude is also expressed to Professor R.C. Coates and in turn to Professor P.S. Pell, Heads of the Civil Engineering Department, University of Nottingham for their interest and cooperation. The support of the Science and Engineering Research Council has been of great encouragement.

Particular thanks are due to the European Coal and Steel Community for their sponsorship of this work.

2f

JOINTS WITH LOCAL CONCENTRATED LOADS

PREFACE

This report is the Final Report of the research programme "Influence of Purlin' Loads on K joints", subcontracted by the British Steel Corporation to Nottingham University. It covers the contents of four previously issued Intermediate Reports.

The investigation was divided into two phases:

PHASE I examined the effect of a varying magnitude of compressive 'purlin' load on the strength and stiffness of two dimensional Warren braced gap joints welded from rolled sguare hollow sections (RHS), of high chord wall slenderness. The effect of branch to chord width ratio and the level of preload was also considered.

PHASE II examined the effect of varying the eccentricity of the 'purlin' load in relation to the joint intersection. In addition two tests were carried out on three dimensional joints.

The Final Report of the investigation is presented in two parts: Part II, The Influence of Purlin type loads on K joints in RHS; Part III, Three dimensional joints in RHS. In addition appendices containing data and the results of individual tests are presented in a separate volume.

This investigation is part of an extensive international research programme entitled "Development of Recommendations for the Design of Welded Joints between Steel Structural Hollow Sections, or between Steel Structural Hollow Sections and 'H' Sections". It examines the strength of predominantly statically loaded welded lattice girder joints of different configurations, and made of different types of hollow sections or combinations of hollow and open sections.

2g

JOINTS WITH LOCAL CONCENTRATED LOADS

1* INTRODUCTION

As part of a previous investigation on the strength and stiffness of K joints involving RHS chord members, Wardenier & Stark (1) considered the effect of compression purlin loads on the behaviour of K joints with gaps, in their test series F. The joint and load parameters for these tests are indicated in Fig. 1, together with the loading method. Wardenier concluded that the purlin load did not have a significant effect on the joint strength, and that the results were contained within the normal experimental scatter for joints without purlin load. Packer (2) analysed these joints using a yield line analysis, excluding and allowing for membrane effects in the chord connecting wall in the gap and found that no significant variation in the strength was predicted, if the failure occurred in the connecting wall, or by shear in the sidewalls. It was, therefore, concluded that for normal purlin loads, the strength of the joint would be as predicted for the same joint without purlin loads.

All the Delft joints in the Series F tests were, however, carried out on relatively small chord members involving 100 100 RHS, with 25 < b0/t0 < 33, and it was considered prudent to extend the size of the chord and its slenderness into the range where buckling of the chord sidewalls might become a significant factor. The severity of the purlin loading was also increased to examine the effect of concentrated loads well in excess of that normally associated with purlin loads. Because of the increased slenderness it was considered appropriate to examine the effect of combined additional chord end load (or chord pre-load) and local concentrated load.

, TEST SPECIMENS

This investigation was based on a chord size of 250 250 6.3 RHS, with a slenderness b0/t0 - 40. The bracing/chord width ratio was varied from 0.4 < < 0.8, as shown in Table 1A, but a gap 'g' was kept constant at g - 0.2 b0. The local concentrated load was varied so that 0 < N P L < 0.8 H1 sin Sj. The tests were in sets of three local load (NPL) levels for each of three values of . Two tests

2.1

to examine the effect of chord preload (Nop) were included. These Phase I specimens also had one test WRR12, where both the branches acted as egually loaded strute, so that the joint really behaved as a modified cross joint. The effect of non-central purlin loading was investigated under Phase II, where the purlin was positioned opposite the intersection of the centre line of a branch and the inner face of the chord.

The proposed schedule of purlin load tests is given in Table 1A, while a general index of these tests is given in Table IB. Details of the nominal and measured dimensions of the RHS members are given in Table 2.

The full width purlin cleat shown in Figs 2 and 6 is a 250 mm long, RSJ stiffened to prevent web buckling but allowing application of a concentrated load without introducing bending moment. The cleat was fillet welded to the RHS chord, and was always present irrespective of whether a purlin load was added, or not.

Since the gap between the bracings was kept constant at 0.2 b0, the effect of varying the value of the branch-chord width ratio was to vary the eccentricity between - 41 < e < 29 mm, or - 0.164 < e/h0 < 0.116 as shown in Fig. 3. As will be indicated later the presence of secondary moments will cause a further variation in the effective eccentricity range.

In order to be able to fit this comparatively large joint into the testing rig it was necessary to shorten the strut bracing as shown in Fig. 2.

The fabrication of the joints was carried out in a special jig. The weld details specified are shown in Fig. 4, where the welds on three walls are always fillet welds, with a throat thickness egual to the wall thickness tx or t2 of the branch member. Only the wall adjacent to the gap is specially prepared, and this is also shown in Fig. 4, where the weld is specified as a butt weld. All specimens were welded with PHILLIPS 5 5 - 8 S.W.G. rods with a welding current of 180-200 amps and a voltage of 45 volts DC.

It became clear from some of the early tests that the preparation and butt welding at the tie toe had not been satisfactorily carried out (3), as illustrated by the early failure of WRR 4. The test was repeated on a replacement joint WRR 4A. Since the strength of other joints was not affected by the welding, further

2.2

re-testing was not considered necessary. The subsequent welding was carefully checked by sectioning, polishing and etching the welds, and found to comply with the specification.

The specimens were prepared and welded at the British Steel Corportion Laboratory Workshops, at Corby, Northants, from tube material either manufactured at Corby or Hartlepool. The welds were not x-ray tested, but checks on the quality of the weld were made by cutting the specimens after testing. Welds with a throat thickness 'a' < 4 mm were welded in one run, starting from the midside, while those with greater throat thickness were done in two runs.

3. MATERIAL PROPERTIES

The hot rolled hollow sections were specified as mild steel grade 43 C, according to BS 4360: Part 2: 1969 equivalent to Fe 430 C according to Euronorm 25-72, with a specified minimum yield stress 255 N/mma.

The cross sectional area was based on actual measured dimensions rather than nominal values, and was checked by weighing a given length (p - 7.860 gm/cm3). The yield stresses , ultimate stresses au and the elongation were derived from tensile coupons cut from the midside of the rectangular sections as specified in BS 4360: Part 2: 1969, or Euronorm 2-57, and tested according to BS 18: Part 4: 1971. The nominal and measured properties are recorded in Table 2. Some of the material used was below the grade 43C specification for yield stress ( - 255 N/mm2) and was known about before the joints were tested. It was considered acceptable for test purposes as the properties were known.

4_ TEST RIG AND TESTING PROCEDURE

A general view of the Corby Universal Test Rig is shown in Plate 1. Fig. 5 and Plate 2 show a typical Warren joint mounted horizontally in the rig. The end A of the chord was normally free, while the other end of the chord was supported by a knuckle joint, equivalent to a pin in compression, the end C of the tie bracing being bolted. Although these pins theoretically carry zero moment, friction and lack of fit result in some end moment being present both in and out of the joint

2.3

plane. The local concentrated or purlin load was also applied by hydraulic jack through the special loading cleat shown in Fig. 6, which is designed to avoid the application of moment. The strut load was effectively applied through a pin D although some lateral displacement (which was measured) also occured.

For the tests where chord precompression was applied by a hydraulic jack at A, the alignment of the jack was adjusted to ensure that the moment introduced into the chord due to its deflection under load was reduced to a minimum.

For each joint, preliminary elastic tests were carried out to ensure that the joint was properly aligned in the testing machine - where there were excessive in-plane or out of plane bending moments adjustments were carried out by shimming at the bolted supports to reduce these to a minimum. A check was also carried out to establish that the member forces derived from the system of strain gauges provided, were in reasonable eguilibrium with the external forces - see Secton 5.

The load was initially applied in steps of approximately 1/20 of the anticipated collapse load, and then at smaller intervals near failure. During this step by step loading, the strut bracing load, the deflection of the chord face and member strains were measured and recorded. The readings were also taken after failure, and unloading of the joint. The mode of failure of the joint was recorded, together with any indications of yielding or cracking.

5. MEASUREMENTS

During each stage of loading, the axial forces in the jacks were recorded by load cells, and the forces in the members calculated from electrical resistance strain gauges attached to the members well away from the joint intersection.

The deformation of the chord face was measured along the strut and tie centre-lines, and in the line of the local concentrated load on each side of the joint as shown in Fig. 7. This was similar to the approach used by Wardenier (1), but modified to ensure that the results were not affected by out of plane bending of chord walls. Dial gauges were also used to measure movement of the ends of the chord.

2.4

Electrical resistance strain gauges (TML type PLS-10) were attached as shown in Fig. 8, along the centre line of each face of each member at two cross sections, in order to check axial load and bending moment, (and thus allow an eguilibrium check) and to ascertain the magnitude of the secondary moment at the connection.

A program was written to process the results, and to plot load-deflection, strain curves up to failure.

In addition an X-Y plotter was used throughout the testing programme to record the outputs from the load cell and one displacement transducer (LVDT) on the compression bracing. This arrangement gave an immediate indication of specimen yielding during the course of the test, and also recorded the ultimate load which could be missed between the incremental scans of the data logger.

During the final testing of each specimen, modes of failure, initial yielding, local buckling, initiation of cracks etc., were observed and recorded. Various possible modes of failure are indicated in Fig. 9, taken from Ref. 1. Failure or maximum test loads are shown for two typical load-deflection curves in Fig. 10. In many cases the maximum test load is the highest recorded, the specimen still exhibiting some positive stiffness as shown in Fig. 10b, but where considerable and excessive local deflection has occurred.

A considerable amount of information with regard to the fabrication of each specimen was recorded before testing commenced and typical information sheets are given in Appendix Al. The pertinent data is given for all specimens in Table 2.

Difficulty occurred on occasions due to the malfunctioning of the data logging and control systems which considerably extended the time taken to carry out tests and results analysis. It was necessary to edit punched tape data to allow for known discrepancies before the load-strain and load-deflection curves were plotted.

Preliminary tests were carried out and graphical output obtained for elastic runs before the joint was loaded to failure. Based on these results any faulty strain gauges were replaced, and excessive out of plane stresses were reduced by shimming the flanged supports, as described in Section 4.

An examination of the strain gauge outputs and graphs showed that there were

2.5

often differences between the estimates of axial load from various pairs of gauges on the same member, and also with the expected force obtained from the calibrated load cell. This is discused in greater detail in Section 6.6.1. This could occur for various reasons e.g. St. Venant effect due to the nearness of the support affecting one of the gauges, local bending of member walls and pitting of the steel surface. The most serious disagreements occured in the chord member, where insufficient distance to end plate or branch connection was available.

A simple check on joint eguilibrium for forces and bending moments both in and out of the joint plane was made, and sometimes a significant lack of equilibrium was found, although great care had been taken in setting-up. In order to examine this affect a computer program was written which is described by Piatt (4) elsewhere. This was based on a least squares approach for an over determined set of results, where weightings were given for each strain gauge output. Force diagrams for axial load, shear and bending moments have been derived at each load increment and joint. Bending moment diagrams based on raw results, and modified for equilibrium are presented with the results for each joint.

In order to observe initiation and development of yielding of the joint a coating of whitewash was provided in the critial areas before the commencement of the test.

6. TEST RESULTS (Purlin Loading)

6.1 General Description of Joint Behaviour Under Load

Test results for each joint are presented in modular form in Appendix A2, consisting of

(i) comment on test (ii) sketches of joint dimensions and position of strain gauges

(iii) photographic plates of failed joints (iv) load-strain curves (v) load-deflection curves (vi) bending moment and axial force distribution in members (iv) load-strain curves

Specific detailed reference is omitted in this section.

2.6

With the application of the test load the top face of the chord deflected inwards in the area below the compression bracing and outwards at the tie bracing. This was accompanied by an outwards deflection of the sidewalls of the chord, which was confined largely to the section below the compression bracings. Little deformation was present under the tension bracing.

The first local yielding, indicated by flaking of the whitewash coating, usually occurred in the chord material, at the gap, close to the corners of the compression bracing welds. As the loading increased, the local yielding spread gradually around the strut/chord connection, above and below the weld.

At the tie/chord connection the local yielding, similar to but less extensive than that at the strut, began in the chord material at the weld corners and spread into the gap, parallel to the weld at the toe of the tie.

The specimen was considered to have failed when the chord deformation became excessive or when a significant increase in the strut load could not be obtained. Usually at this stage, the chord face deformation was so great that the material in the gap had been pulled parallel to the tie bracing.

At the end of the tests the bracings were undamaged except for some local yielding in the vicinity of the welds. Similarly the purlin bracket and the bottom face of the chord were undamaged.

6.2 Modes of Failure

The most common mode of failure (see Fig. 9) was identified as G4, associated with large deflections of the chord connecting wall and sidewalls, under the strut. One joint WRR 4 failed because of inadequate toe welding of the branch tie and is identified as G2b (or G2w) as the failure occured at the edge of the weld and tie wall. In no other tests did weld failure occur. However, in many other cases local fracture of the chord connecting wall adjacent to the tie branch toe occured (G2c) but this was usually after extensive deformation of the G4 variety with the gap wall almost parallel to the tie centre line. Cracking initiated in the significantly bent region adjacent to the tie weld. In many cases the test was stopped while there was still some positive stiffness as the deformations were

2.7

exceedingly large. The modes of failure shown in Table 2 are therefore dominated by G4, although G2c may be the final trigger of failure.

6.3 Branch-Chord Deflections

The branch to chord load-deflection curves, incorporating preliminary testa and accidental damage are summarised in Figs 11-17. Accidental damage occurred in two cases either while the joint was being positioned in the rig or due to loss of load control during a test. In order that elastic deflection comparisons can be made the strut force (N^) and tie force (N) are presented in kN in (a) and (b), while in (c) and (d) are non-dimensional to include the yield stress variation which occurs from test to test.

The branch-chord deflections are given for each joint in Appendix A2 on Frames 10-13 or Frames 12-15, for the final test to failure. These frames do not show the preliminary tests. The load is recorded as a percentage of the maximum strut test load N^u. Frame 10 records the deflections of the six LVDTs while Frame 9, records the mean strut, tie and purlin deflections. Frames 12 and 13 repeat the information but with the deflection recorded as a percentage of the chord width b0.

For WRR 1-3, with = 0.8 the deflections (Fig. 11) remain small nearly up to failure, the tie deflection being progressively reduced as the purlin load proportion is increased. The load-deflection relation is linear for a substantial proportion of the maximum load. There is no significant difference in the 3trut deflection with increasing purlin load proportion.

For WRR 4-6, with = 0.6, the deflections (Fig. 12) are significantly larger indicating a more flexible joint, with non-linearity commencing at a much lower load. The load-deflection curves take the characteristic bi-linear form shown in Fig. 10(b). The outward deflection of the tie is reversed with an increasing proportion of purlin load. For low loads where elastic behaviour can be expected Fig. 12(a) shows that there is little difference in the four joints tested. Until weld failure in WRR 4 there is little difference in behaviour between it and the retested joint WRR 4A. However, if account is taken of the differing chord yield stress in each case then the non-dimensional results shown in Fig. 12(c) for these joints differ significantly. Joint WRR 6 was the first tested and the sharp knee

2.8

in the curve may indicate that the preliminary test was taken to too high a load with resulting permanent set, which was not recorded. If this were the case this would indicate a small increase in strut deflection with increasing proportion of purlin load for WRR 5 and WRR 6. For the highest values of purlin load ratio, the purlin LVDTs also record significant deflections - see Appendix A2. The 1% b 0 strut deflection is approximately 50% of the failure loads - but higher for the low strength WRR 4.

For WRR 7-9 with 0.4 the deflections (Fig. 13) are significantly more nonlinear than for higher values of and the joints noticeably more flexible. Fig. 13(a) shows the cumulative deflections, allowing for preliminary runs and accidental damage, as outlined in Appendix A2. The difference between Fig. 13(a) and the corresponding deflections in Appendix A2 is important to realise, particularly as accidental over-loading is possible. The influence of this on 1% b 0 deflection loads is of course great. Both Fig. 13(a) and (c) indicate the growing influence of purlin load ratio on local strut deflection, with the corresponding reduction of 1% b 0 deflection loads. The variation of tie deflection is very clearly indicated in Fig. 13(b) and (d), where increasing purlin load ratio results in the tie deflection changing to inward deflection under maximum purlin effect.

Fig. 13 also shows the effect of varying Np^ from 0 up to 2, the last case being for WRR 12 where the branch load should be equally compressive. It can be seen that there is a profound effect on the strut as the tie ceases to be tensile. Again the photographic plates illustrate this point clearly.

The effect of purlin position is shown in Fig. 14 and 15 for - 0.6. For NpL/N^ sin = 0.5, Fig. 14(a) shows a progressive increase in strut deflection as the purlin eccentricity moves from being under the tie to under the strut. This is not reflected in Fig. 14(c) where the difference of chord yield stress in WRR 5 changes its relative position. However, the tie pull-out changes consistently with eccentricity, there being push-in for WRR 13 rather than pull out. For the higher value of purlin load ratio the load deflection curves are shown in Fig. 15. Fig. 15(a) shows little difference between WRR 15 and WRR 16 for low loads, although WRR 15 exhibits larger strut deflections for high loads. In this case WRR 6 with zero eccentricity shows the lowest deflection, although this may be exaggerated due to an accidental permanent set before final testing. In Fig. 15(c) where the effect

2.9

of yield stress is allowed for, a significant difference is observed throughout the deflection range. Fig. 15(d) clearly illustrates the increasing inwards deflection of the tie associated with purlin eccentricity towards the strut side. This effect is also clearly illustrated in the photographic plates associated with these tests and shown in the Appendix A2.

All previous tests were carried out on joints with no preload. Tests WRR loll were designed to examine whether there was any interaction between preload and purlin load. As is described in the section on the individual joints, considerable difficulty was experienced in the setting up of the preload such that large deflections did not occur at the free end of the chord, and hence introduce significant preload eccentricity moments. The initial test WRR 10 was repeated viz WRR 10A, in an effort to get a proper basic comparison test for no purlin loads. In both WRR 10 and 10A there was a noticeable reduction in strength due to preload compared with the identical joint WRR 7 which had no chord preload. With the purlin load level set at NpL/Ni =0.5 sin ^ in WRR 11, the strength of the joint is seen to be greater than either WRR 10 or WRR 10A. It is not completely clear whether this is due to restriction on the free movement of the free end of the chord - Fig. 18, thus reducing the eccentricity of the preload or not.

The load-deflection diagrams for these joints are given in figs 16 and 17. It can be seen that initial deflections of varying degree occur with the application of the preload only, but that the initial stiffness of each joint with strut load is very similar. Joints WRR 10 and 10A show a long plastic plateau, while WRR 11 preserves a positive stiffness for a greater range.

6.4 Failure Loads

A comparison with Wardenier's results shows that the joints at both Delft and Corby were deformed to about the same level i.e. a strut deflection of the order of 10% b0. This is important in making comparisons of maximum loads with residual positive stiffness, as in Fig. 10(b).

Fig. 19(a) shows a non-dimensional plot of these maximum loads for central purlin joints in terms of the branch/chord width ratio . The results (except for joints 10-12) generally fall within the scatter band of the results for gap joints

2.10

without purlin loads, or on the safe side - as for joints with = 0.4. The plot in Fig. 19(b) shows the deviation from the Wardenier gap equation for all joints tested.

The variation of strength at maximum load based on the strut load N^u with purlin load ratio is shown in Fig. 20(a) for each case of , while the effect of eccentricity up to 0.52 b 0 is shown in (b).

No significant trend can be detected with the value of Npj^/Nj sin ^, while a tie force exists, but a significant reduction in strength can occur once both branches are in compression, as signified by test WRR 12 where NpL/N^ sin ^ = 2. However, a decrease in strength can be detected for any non-zero purlin eccentricity.

The effect of chord preload is indicated in Fig. 21 and Fig. 19. The reduction in joint strength with chord load is greater than that given by Wardenier's reduction factor = 1.3 - 0.4(/)//? for compressive chord forces. This may be due to the eccentricity of chord preloading caused by rigid body movement and chord bending associated with the Corby testing rig. In this case failure is noticeably magnified by the large strut-chord punch-in, which reduces the effective properties of the cross-section, exacerbating failure adjacent to the strut as shown by the reversal of chord face end deflection in Fig. 18. The photographic plates for these tests also clearly display the mode of failure.

6.5 Working Load Deflections

Not only must the joint be of sufficient strength under ultimate load conditions, it must also behave satisfactorily under service conditions. For gap joints local deflections of the chord, particularly under the strut must be such as not to be too large or significantly non-linear under such working loads.

It is clear from Figs 11, 12, 13, 14, 15 that the 1% b 0 deflection level represents a fair amount of non-linearity in all joints tested and it is unlikely that values in excess of this would be permitted. Indeed bearing in mind that the deflection normal to the chord face is likely to be approximately a factor of

2.11

(l/sin ) greater than this, it is probable that this should be considered the limit.

The 1% b 0 values of Nj_ are plotted in Fig. 22 on the basis of either the maximum load N^u, or the average strength of the joint derived from the Wardenier equation, for various branch/chord width ratios . The points lie on a curve which indicates the importance of the value of .

If the margin of safety between failure and working loads is to be say 2.0, then the intersection of the horizontal line of Ni%Do/Nlu = 0.5 in Fig. 22(a) represents the limit of = 0.6 at which joints with lower 's will have excessive local deflection unless the working load is reduced below 0.5 N^Q. However, since joints would normally be designed on the basis of strength, the values of N]*jj0 are plotted as a ratio of the design strength - illustrated in terms of the Wardenier equation in Fig. 22(b). As can be seen there is more scatter of the results, but the curve lies marginally higher. It can also be seen that joints with higher or eccentric purlin loads give the worst results.

Fig. 23 shows the variation of the l%b0 deflection on the basis of purlin load ratio. There is very little variation in strut deflection up to a central purlin load ratio of 0.8 for > 0.6, but there is indication of a fall off after a ratio of 0.5 for = 0.4, as indicated in the joint WRR 9, and joint WRR 12. The effect of eccentricity of the purlin load on the local deflection limit of l%b0 is shown in Fig. 24.

6.6 Forces and Bending Moments

6.6.1 General

The results of strain gauge output were used to calculate axial load on the basis of (a) each pair of gauges at each cross section (b) mean of four gauges at each cross section (c) mean of eight gauges on both cross sections for each member and compared with the load predicted by the strut load cell. In this way it was possible to isolate the more doubtful gauges.

2.12

Axial load, bending moment and shear force distribution in both planes were then plotted for each joint by computer as shown in Fig. 25 - the actual graphical output has been offset from the intersection point for clarity. Significant out-of-plane bending was eliminated by shimming, during preliminary tests. The plots shown are for final tests only, and the resulting effects are based on the gauge values at the beginning of the test to failure.

Even though considerable care was taken in setting up the joint and eliminating undesirable effects, it is clear that the resulting force distribution can only be approximate. To reduce this to a realistic level, account is taken of the fact that there is a surplus of gauges for the unique determination of strain distribution, and the over determined set of equations obtained is used to satisfy equilibrium, and to modify the results to their likely level, using a least squares procedure described by Piatt (4). Two sets of moment distribution are presented for each joint in Appendix A2, the raw set, and the adjusted set. It can be seen that there are often very big differences. The problem of lack of equilibrium is illustrated from Fig. 25, for Joint WRR 1, and load increment 10.

Out of balance moment at intersection of branch centre lines = M0 + N0(e) + + M2 - 6.0 + 349.7 (0.04) - 9.9 - 7.6 = 2.49 kNm.

It is important to note that the unadjusted raw results in this case indicate an out-of-balance moment, which is an appreciable proportion of the measured member moments. In other joint tests the out-of-balance moment was of the order of the largest measured moment in the joint. Clearly in such cases only general observations are likely to be useful and valid, and therefore it is not proposed to dwell on detail.

Good agreement is generally obtained for axial load in the strut, as derived by load cell and strain gauge measurement based on measured cross sectional area.

For the tie the tensile force can vary by up to 10% from that calculated assuming a pinned joint, the value based on strain gauges being usually less.

The form of the bending moment diagrams approximately conform with the positions of the knuckle joints (pins) in both strut and chord, while the point of

2.13

contraflexure in the tie is usually well outside the fixed flange supports.

6.6.2 Joints WRR 1-9, 12

In joints WRR 1-3 ( = 0.8) the bending moments at the end of the branch members are considerably greater than that in the chord. For this group of tests the joint eccentricity is + 40 mm, i.e. e = 0.16 h 0 - see Fig. 3. Nevertheless the chord bending moment is dominated by the secondary stress effect, rather than eccentricity, and the bending stresses under the tie are still compressive. The effective load eccentricity in the chord at centre line intersection varies from -0.05 h 0 to -0.10 h 0 with increasing purlin load. The actual moment remains fairly constant, but the chord load reduces with increase of purlin load proportion. The maximum strut moment is approximately 0.25 My for the section.

In joints WRR 4-6 ( = 0.6) the bending moments at the end of the branch members are less than that in the chord member - sometimes considerably less than the recorded values, but of the same order as the adjusted values. The eccentricity of centre line intersection for this group is + 6 mm i.e. + .025 h0, which is almost axial loading. Nevertheless, the chord adjusted moments are much the same as for WRR 1-3 and the effective chord load eccentricity lies -0.20 h 0 < e < -0.12 h 0 increasing with purlin load ratio. The maximum moment recorded for the strut is approximately 0.25 My for the branch section.

In joints WRR 7-9, 12 ( -= 0.4) the bending moments at the ends of the branch members are considerably less than that in the chord. The eccentricity of the centre line for this group is - 28 mm i.e. - 0.11 h0- Apart from WRR 7 which indicates very large chord moments - probably associated with the initial overloading referred to earlier the maximum, chord bending moments are again of the order of 8-10 kN.m. The effective chord eccentricity at the joint noding is, however, -0.3 < e/h0 < -0.2. There is, however, no clear evidence that there is a significant change of effective chord eccentricity with purlin load ratio. It is worth noting that the chord moment has reversed completely for the high purlin load indicated in WRR 12, where the behaviour is equivalent to that of a Croas Joint. This is of course by virtue of the method of testing in the Corby Rig. The maximum adjusted moment recorded for the strut is approximately 0.55 My for the branch.

2.14

In summary the following comments can be made:

The ratio of maximum branch to chord moment decreases significantly as the ratio reduces. If = 0.8, the branch moments are greater than those in the chord, while at = 0.4 they are considerably less. This is probably not only a effect, but is also associated with the geometrical eccentricity of intersection. The actual moment in the chord will be algebraic sum of the moments associated with the geometrical eccentricity and the secondary moment of the joint.

At zero eccentricity the chord moment is still equivalent to an effective chord force eccentricity varying between - 0.1 h 0 and - 0.2 h0.

For the higher joints this effective chord force eccentricity appears to increase in magnitude, but in a negative sense with increasing purlin load ratio. For 0.4 it is not possible to discern a trend, but the value of effective eccentricity appears to be between -0.3 < e/h0 < -0.2. The effective eccentricity in the chord at the heel of the tie would of course be less and about 2/3 of the above values for 0.4.

6.6.3 WRR 14-16 Eccentric Purlins

The effect of eccentric load is to be seen in the adjusted Bending Moment Diagrams, e.g. the effect of moving from WRR 13 to 14 (Table IB) is to apply an anticlockwise moment NpL (2 ePL) to the joint in addition to the moments existing in WRR 13. This increases the moments in the strut and tie but reduces the moment in the chord. Similarly for WRR 15 and 16 with the higher purlin ratio the moment in the chord not only reduces, it actually reverses. There is reasonable indication that the moment due to purlin eccentricity is approximately distributed according to member stiffness, as shown in Table 3, even though members are not rigidly interconnected. The majority of the moment is transferred to the chord, of course, so that in a design situation most of the eccentric purlin moment would be associated with the chord.

2.15

6.6.4 WRR 10-11 Chord Preload or Additional End Load in Chord (Nop - Fig 2)

Considerable effort was made to ensure the proper alignment of the preload jack - it being offset initially to ensure that when the end of the chord deflected the offset decreased so that near collapse the preload was almost axial. The extent to which this was successful can be gauged from the bending moment diagrams for WRR 10. It can be seen that the eccentricity was probably about right, but that the jack alignment produced significant bending moments in the chord under both strut and tie. The maximum unadjusted moment indicated is about 40 kN.m, compared with 128 kN.m to produce yield. However, with a preload ratio oop/aeo =

0.495, the maximum moment required to produce yield is reduced to 64 kN.m. The jack end of the chord deflected in the direction of the force N for the low values of N^ but reversed near to collapse - see Fig. 18. This reversal can be explained in terms of the yielding of the inside face of the chord due to large local deflection adjacent to the strut connection and the chord end load movement. As the local deflection increased the middle of the chord wall was unable to sustain the large compressive stresses due to chord end force, and it was transferred to the two inside corners. When the corners yielded the loss of stiffness on the inside face caused failure which reversed the direction of the end movement. In these circumstances it was not possible to predict safely the joint capacity using the strength reduction formula.

The test was repeated (WRR10A), again taking even greater care with both the eccentricity and alignment of the chord preload jack. Although the chord moments were reduced so that the line of action can be considered more axial, the same reversal of bending moments is observed. The load-deflection curves are similar for both WRR 10 and 10A, although the loads are a little enhanced in the latter. It is, however, clear that the low failure load with much smaller moments cannot be accounted for by the proposed chord load reduction formula.

In WRR 11 where the joint has a purlin load, the same precautions were taken, but the chord tip deflections were reduced by the presence of the purlin load. The chord bending moments are small on the free section and show a considerable reversal towards failure load so that the chord connecting face has a compressive stress level less than the average. The strength of this joint is enhanced above that of WRR 10 and 10A, but insufficiently to bring it to the safe strength predicted as shown by Fig. 19.

2.16

In summary it can be said that chord preload has produced a significant reduction in the joint strength, much in excess of that suggested by the Wardenier chord load reduction factor for - 0.4. To some extent it can be argued that this is associated with the bending moments inevitable with the application of the chord preload in the Corby testing rig. However, this is only partly true in view of the small chord moments in WRR 10A, and the reverse moments in WRR 11. Some recent experimental results for similar large joints carried out in Norway by Strmmen (7) also indicate a greater than predicted reduction in strength even though the joints were prestressed and each branch was independently loaded. Care should therefore be taken in discussing these preload results as being inappropriate for lattice girders.

Sul Conclusions

These tests on large joints show good agreement of joint strength with the predictions of the Wardenier equation, although the predictions for 0.4 tend to be conservative.

There appears to be little variation in joint strength with increase in the central purlin load as long as the tie branch remains in tension. However, if both branch members are in compression, then the reduction can be significant.

Eccentricity of purlin loading appears to produce weaker joints irrespective of the direction of the eccentricity.

The strength of joints subject to chord preload were significantly less than the Wardenier prediction, even when no purlin load was present. This may, however, have been a function of the testing method. The effect of simultaneous chord preload and purlin load was to strengthen the joint, but still well under that predicted. The wisdom of using gap joints of large chord slenderness and low branch/chord width ratio is debatable in the presence of large chord forces.

The 1% b 0 deflection limit (in the direction of the branch) for these joints of large chord slenderness is likely to result in initial non-linearity, associated with some permanent set. It is likely to represent the upper limit on local

2.17

deflection under working load conditions, with some permanent set on the initial loading.

For branch/chord width ratio's less than 0.6 and a factor of safety of 2, the Wardenier mean joint strength equation will require reducing to limit the local joint deflection to 1% b 0 under service conditions. Further reduction is likely to be necessary for joints with large purlin load ratios or eccentricities of the order discussed.

7.0 DEVELOPMENT OF DESIGN RECOMMENDATIONS

7.1 Review of Previous Te3t Results

The only previous testing programme in which localised joint loads have been applied to K gap joints in RHS is that of Wardenier (1). Wardenier tested six joints, and the results are shown in Fig. 1 and Fig. 27(a), together with the results of similar joints carrying no localised loads. Among these twelve test results three different values were used and two b0/t0 ratios - approximately 26 and 32. It can be seen from Fig. 27(b) that there is no definite trend discernable among the results. For instance, at a ratio of 0.4, the two joints with b0/t0 of 27 show an increase of strength with increasing local load (NPL) while the joints having b0/t0 > 30 show a decrease of strength. The average is a constant joint strength. The results for = 0.6 show a consistant decrease in strength while those for = 1.0 tend to show an increase. Wardenier concludes 'concentrated loads of about 35-55% of N^u sin reduce the strength of joints with low ratios by about 20% compared with the results for joints not loaded by concentrated loads'. This conclusion appears to be based on one result only - that for joint 151 (b0/t0 = 30). Joint 150 (b0/t0 = 27) shows an increase of 17%.

In the Delft report the exact method by which the 'purlin' load was applied is not clear. A load-deflection graph such as that in Fig. 28 suggests that the joint was loaded initially without a local load and that only after a considerable proportion of the ultimate load had been applied was the local load added. This difference in loading method may make valid comparisons difficult.

2.1!

7.2 Corby Te3ts

In the current Corby test series nine comparable joints have been tested. The results for these tests, plotted in a similar manner to those for the Delft series, are shown in Fig. 29(a). It can be seen that a rather flatter line than the Delft choice of (0.5 + 10.3 ) would be more appropriate, but the scatter is very similar. The trend with N P L is shown in Fig. 29(b). As with the Delft results there is no clear trend, and there is no support from these tests for Wardenier's contention that "concentrated loads of about 35-55% of N^u.sinei reduce the strength of joints with low ratios by about 20% compared with the results of joints not loaded by concentrated loads". It must be remembered that all the Corby joints had a b0/t0 of approximately 40.

7.3 Failure Modes

A study of failure modes shows no clear pattern among either the Delft or Corby results. In most cases the recorded failure mode in the presence of a local load differs from that in its absence, but there is no consistency. Joint 4A (NpL = 0) failed by mode G2C, while the similar joint 6 (NpL = 261 kN) failed by G4. However, joint 3 in the Delft series failed by G4 (NpL - 0) while joint 146 (NpL -0) failed by G2C. The picture is to some extent confused by the fact that all joints were not tested to the same level of local deformation, and that there may well be an overlap between one form of mode of failure and another. Generally, however, for the Corby tests local deformation at maximum load was always present in the G4 mode, but higher levels of deflection could give way to chord failure (G2C) at the toe of the tie branch particularly where the tie force was high i.e. for low purlin loads.

2- The Influence of Chord Preload on Ultimate Strength

No joints with chord preload were tested in the Delft series. Three such joints were tested at Corby (10, 10A and 11) and the results have already been shown in Fig. 21, together with that for joint 7 which had no preload. Only joint 11 carried a local load, and the failure load is seen to be higher than that for joints where Np L - 0 (10 and 10A). One disturbing feature of this graph is that the strength reduction due to chord force appears to be much greater than that

2.19

predicted by the Delft formula . 1.3 - 0.4(0/0)//}. This may, however, be due to the manner of preloading adopted in the Corby tests. Comment has already been made in section 6.6.4 on the eccentricity of loading produced by the chord jack, and the low value of the resulting failure load could to some extent be due to the additional bending moment produced.

7.5 Local Deflection

Comparisons between the results obtained at Corby and those obtained at Delft are shown in Fig. 30(a). In Fig. 30(a) the results are plotted against Ni%bo/Nlu and in Fig. 30(b) the results are plotted against N^^/N^um- ^ium used here is the joint strength determined from Wardenier's empirical equation (Ref. 1, equation la).

9 R 1 + s i n Nlum * eo V < W (4 + 8-5/?) , .

2 sin where . = chord force function = 1.3 - ' I I

fi aor, eo

In both cases the influence of the thin joints tested at Corby is clear, with the results falling below those from Delft. The loading arrangements seemingly used at Delft and refered to earlier are likely to reduce the value of comparisons based on deflection. It appears from the Delft results (Fig. 28) that the l%b0 deflection value occurred before the purlin load was applied in joints having < 1.0, and the figure is not therefore comparable with that obtained in the Corby series.

In Fig. 31(a) the influence of 'purlin' load is demonstrated for both the Corby and Delft tests. For the higher ratios the results are in agreement with the Delft tests for = 1.0 above the Corby tests for - 0.8. This follows the trend of the Corby results on their own (Fig. 23). However, the remaining results show a much less well ordered pattern. Although generally all Delft results fall in value with decreased , they do not give the same approximately horizontal lines shown by the Corby results.

2.20

The general conclusion is that there is a decrease of the strut load at which the local deflection reaches l%b0 of the chord width, as a proportion of the failure value, with decreasing ratio. The purlin load does appear to decrease the ratio further in some cases, but there is no clear pattern.

The influence of chord preload (Corby tests 10, 10A and 11) is clearly to reduce N^u considerably, but to increase deflections to a much smaller extent.

Deflections are only of significance at working loads. If the maximum working load is taken as being some 50% of ultimate load, then only for joints having the ratio Ni%bo/Nlu less than 0.6 does deflection have to be considered. Hence from Fig. 30(b) all joints with > 0.6 (b0/t0 = 40) automatically satisfy a l%b0 deflection limit criterion for working load. The equivalent figure for b0/t0 32 from the Delft results is > 0.4. Purlin load appears to have little effect on these values, whether placed centrally, or eccentrically to the joint.

7.6 Comparison between Test Results and the Suggested CIDECT Equation

The Wardenier equation, based as it was on the results of a large ECSC sponsored test programme, provided the best available method of predicting joint strength at the time (1978). It was, however, based entirely on the results of his own tests, and did not take into account tests performed elsewhere. These other tests, although small in number, did illustrate aspects of joint design not fully examined by the Delft series. Since 1980 CIDECT has been engaged in the production of design recommendations that would take account of all test results, and be of use internationally. In the CIDECT Monograph No. 6 (5) to be published shortly, an equation providing the characteristic strength for K and N joints, is given as

2 bl + b2 + hl + h2 1 0 5 N1Ic - t 9.8 (_i i t 1) ___ yu-* f(n) K e ok 4b. sin ,

where the chord force function f(n) has the value _ .

f(n) = 1.3 - 111. I _f_ I and y = (b /2t ) o o " eo

2.21

This form of equation has been developed from Wardenier's equation by a) simplification of his expression of (0.4 + 8.5/3) to 9, as he suggested b) modification of the angle function to 0.85/sin 9Q_, to take better account of

joints c) replacement of by (bj + b 2 + h^ + h2)/4b0 to allow for rectangular bracings.

This equation is intended for design, and is to be based on nominal dimensions and the characteristic yield stress of the materials specified. The factor of 9.8 takes into account the variability of actual dimensions and yield stresses observed by Wardenier (6).

The values of N^ j for the Corby tests are plotted against the measured ultimate loads in Fig. 32, with a dashed line drawn to indicate the mean joint strength on which the characteristic value is based. (Characteristic - 0.90 mean). This figure shows that most points lie close to or above the mean line -that is, they are safe. The specimen '4' failed prematurely, due to defective welding and could be discarded. Similarly, the points 1, 2 and 3 (on the 500 kN line) could also be rejected as the material was below specification - the measured minimum in three tests was 237 N/mm2 against a specified minimum of 255 N/mm2

although this was known before testing (section 3). Points on the characteristic line are acceptable, however, as the assumption is that only 95% of all points need lie above the line. In this figure the strength of joint 12 is computed as that of a cross joint.

The characteristic strength for a cross-joint is given in Ref. 5 as:-

2 r 2hl / .5. N.. - a t [ + 4(1-/3) ] Ik eo o Lr _ ._ v ~' J b sin . (1->) sin .

If a Warren joint carrying two compressive bracing members is visualised as a cross joint, the strength can be based on one bracing member only. On this basis, the strength of joint WRR12 is 109 kN (hx = 99.9 mm, - 45).

If the two Warren bracings are taken to form a single branch with normal force component 2N^ sin (= Np^), and h = (2h^/sin ^ + g) then the above equation reduces to:-

2.22

2 hl - + g

9 s i n Nlk - eo V [ - + 2(1-^) ] b (1-0) sin .

For this case the strength of joint WRR12 is 74 kN, against the measured ultimate loads of 170 kN in the strut and 150 kN in the tie (both compression).

The experimental ultimate strengths for all joints tested at Corby and carrying purlin loads are compared with the computed values in Fig. 34. It 'is seen that the joint strength based on the Wardenier K joint equation over estimates the experimental value, while the equivalent cross joint based on two bracings under estimates the strength significantly, which is in keeping with previous observations for cross joints with low and high chord slenderness b0/t0. The joint strength based on the single bracing equation gives a result more in keeping with the other results based on joint predictions. Unfortunately, it does not idealise the joint correctly.

Local deflections are often a problem for cross joints with low , but here it is not the case, since N^% is well above the working load as seen in Fig. 31(b). The presence of chord load would lower both N ^ and N^u.

Figure 32 indicates that the allowance in the joint strength equation for chord force (function f(n)) above is not adequate - results 10, 10A and 11. Of these three tests, only joint 11, with the highest failure load carried a purlin load.

In Fig. 33 the values of Nllc are shown plotted against the Njjj values. As the deflection limit is a working load level criterion of serviceability the dashed line shown corresponds to working load, here taken as characteristic divided by 1.7 (5). All points lying above the dashed line have a deflection of less than 1% b 0 at working load - the values for 0 0 . 8 and those for - 0.6, close to the line, are therefore quite satisfactory. The joints having 0 - 0 . 4 are well below the assumed working load line, and therefore can be regarded as too flexible in practice. This type of joint would be likely to lead to early fatigue failure in the case of cyclic loading.

2.23

7.7 Recommendations

(a) The scatter of experimental results from these tests with purlin load is similar to that previously obtained without purlin load, and on which the characteristic strength equation given in CIDECT Monograph No. 6 was based. For purlin loads less than 0.6 N^u in magnitude no account need be taken of the effect of purlin load. This conclusion can be applied to joints with chord slenderness ratio b0/t0 up to 40. The purlin may be eccentric from the bracing intersection by up to 0.5 b0. Compressive purlin loads only have been considered. Joints should be checked for punching shear and bearing failure, as discussed in Ref. 5 and Ref. 6, and the welding must be adequate to transfer the loads involved.

(b) The chord force factor of Monograph 6 is not adequate to explain the strength reductions found in the present tests although the differences could be explained by the loading procedure. More tests should be carried out.

(c) It is considered that the equivalent cross joint strength (2 bracings) gives a realistic although conservative estimate of strength of a K joint with NPL/ Nl s i n el = 2' ano- ensures that the working load deflection is satisfied. However, it should be noted that this is based on one test result only.

(d) Joints having b0/t0 as high as 40 and with less than about 0.6 are generally too flexible and should be avoided. If they are used, the working load ought to be regarded as no more than approximately 0.35 of the characteristic strength of the Wardenier joint equation estimate (at 0 = 0.4).

2.24

REFERENCES

1. Wardenier, J. and Stark, J.W.B. The static strength of welded lattice girder joints in structural hollow sections - Part 4: Joints made of rectangular hollow section. Report No. BI-78-20.0063.43.470, Delft University of Technology, March 1978.

2. Packer, J.A. Theoretical behaviour and analysis of welded steel joints with RHS chords - Final Report. CIDECT Report No. 5U-78/19, 1978.

3. Davies, G. and Bettison, M. Report on quality of member preparation and welding of joints WRR 1, 4, 5 and 6. University of Nottingham, 1981.

4. Piatt, J. Sidewall behaviour in full-width rectangular hollow section joints. Ph.D. Thesis, University of Nottingham, to be published.

5. CIDECT CIDECT Monograph No. 6 - Welded Joints. To be published.

6. Strating, J. The interpretation of test results for a level-1 code. Annual Assembly, International Institute of Welding, Lisbon, 1980, (IIW Doc. XV-462-80).

7. Strmmen, E.N. Ultimate strength of welded K-joints of rectangular hollow sections. University of Trondheim, Norwegian Institute of Technology.

8. Wardenier, J. and Davies, G. The strength of predominantly statically loaded joints with a square or rectangular hollow section chord. Annual Assembly, International Institute of Welding, Opato, 1981, (IIW Doc. XV-492-81).

2.25

NOTTINGHAM UNIVERSITY PHASE 1 - INFLUENCE OF 'PURLIN LOADS' ON K JOINTS

TEST No.

WRR1 WRR 2 WRR 3

WRR 4 WRR S WRR6 WRR 7 WRR 8 WRR 9 WRR 10 WRR11

WRR12

CHORD SECTION

250 X

250

250

250 250 250 250 250 250 250 250

250 6.3 250 6.3 250 6.3

250 6.3 250 6.3 250 6.3 250 6.3 250 6.3 250 6.3 250 6.3 250 6.3

250 250 6.3

BRACING SECTION

200 200 200

150 150 150 100 100 100 100 100

200 6.3 200 6.3 200 6.3

150 6.3 150 6.3 150 6.3 100 6.3 100 6.3 100 6.3 100 6.3 100 6.3

100 100 6.3

0.8 0.8 0.8

0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4

0.4

" 39.7 39.7 39.7

39.7 39.7 39.7 39.7 39.7 39.7 39.7 39.7

39.7

pi

0 .5 Feu .8 Feu

0 .5 Feu .8 Feu 0 .5 Feu .8 Feu 0 .5 Feu

2 Feu

Sin Sin .

Sin Sin

Sin ; Sin ;

Sin

Sin

REMARKS

These tests are designed to compliment the work of Mr. Wardenier by providing evidence for the effect of purlin loads

on chord sections with a high value of > o

ratio of 1.0 not considered because it is unusual in practice and a special case as far as failure modes are concerned.

= 0.6 op eo

= 0.8 op eo

TABLE 1A TESTS PROPOSED FOR THE NOTTINGHAM SUB-CONTRACT

PHASE

I

I

II

I

I

II

I

N PL N, sin 1 1

0

0.5

0.8'

2.0

op o eo

0

0.5

0

0.5

0

0

er,r/ h PL o

0

0

+ 0.52

- 0.52

0

0

+ 0.52

- 0.52

0

bi + bo = b /b= * 1 o 2b0 0.4

WRR 7

WRR 10/WRR 10A

WRR 8

WRR 11

WRR 9

WRR 12

0.6

WRR 4/WRR 4A

WRR 5

WRR13

WRR 14

WRR 6

WRR 15

WRR 16

0.8

WRR 1

WRR 2

WRR 3

A l l chord RHS: : 250 250 6.3 grade.43 s t e e l ; _o _ ^\4

g = 0.2 b o TABLE IB Index of 'Purlin' Load Tests Carried Out Under Phases I and II

2.27

to M 00

TEST SPECIMEN

WRR i WRR 2. WSR 3 WRR i WRR 5 WRR 6 WRR 7 WRR 8 WRR 9

1 WiJR. / o

WRR /OA

KJRR i l U K R 12

WRR >fA

WRC 13

WRR 14 WRR IS WR lia

s I

Dimension chord (mm) NOMINAL

* % ho V t A

2 m m

MEASURED b % o ho / l w

A 2

mm *

2 5 0

"

l

'1

'

H

l\

M

1'

I I

A 2 mm '

Zoo

l |

K

ISO

i l

II

I0O

II

I I

,, II

V

(S"0

j

l i

M

,.

2

' 1

ISO

I t

'00

n

,, ,, II

lt

ISO

,,

6 3

,( . .. .,

I I

,,

.,

,, ,.

6 3

.,

4fco

M

I I

2>(*0O

/

' 1

2 3 f o

1

n

I I

I

?Goo

1117 I"?*1?

mi 14-1-5

I f f l 141-0 no

99s 994

99 4

a 1

' .

f i* 4 ! I

45

5

4 4_

4 R _

45. .

4 4 i

45

o

TEST SPECIMEN

WRR 1 WRR 2.

WRR 3

WRR f

WRR S

WRR 6

/RR 7 __________________

WRR8

WR 9

BASED ON MEASURED DIMENSIONS N deform.! %)

' ' . bL(d0)

N ' U 2

' 0 W i%b /N_

t 9/ 9o

?2 4

5 0

41 4 0

28

> too

> lOo

y 100

91 >/00

72 _

~?loo

26 ,

WR? /O g o VJRR /OA WRR l |

UlRR 12

WRR + A

WR2 3 Lv'QR 14

? + 4' 4/

5o

455 +q

1 I WRR IS \ So WW /& 41

j _ !

55 y joo

y f00

7o

y yioo

S3 >/>>

N c r o c k > n % N 2 u

> 100

>IOO

yioo

100

>ioo

> 100

00

s4 ? loo

7/00 y/00 100

? loo

^ s . * _ __ 'PL -- _

\ / + vT

'PU

Li

I cm4

1 mm

i/l--* mm

Distribution Factor

=

kN.m

WRR 13 M13

M , + . 13 *

WRR 14 M14

Strut

1236

883

1.40

.155

Tie

1236

1383

.894

.100

Chord

6049

895

6.76

.747

2 eT = 2 46.7 .13 kN.m = 12 kN.m PL PL

for Load Increment No. 9/8 See Moment Diagrams in Appendix 2. ai - - 1.9 4=-1.2 -M5=-9.0

-4.2

-6.1

-8.1

-4.7

-5.9

-6.3

+ 14.3

+5.3

+7.6

TABLE 3 ECCENTRIC PURLINS

Distribution of Purlin Moment for WRR 13-14

2.31

WRR 4A

WRR 17

WRR 18

WRR 7

WRR 17

WRR 18

.595

.597

.598

0.394

0.399

0.399

b /t o o

41.2

39.8

40.2

39.8

39.8

40.2

eo N/mm2

291

291

291

260

291

291

o N/mm2

100

154

25

75

154

25

o eo

0.344

0.529

.086

.288

.529

.086

U

1.0

.946

1.0

1.0

.771

1.0

N 1 lum

= 1 kN 457

482

474

302

334

328

, N. lum lu kN expt

kN 457 445

456 400

474 440

302 352

258 289

328 330

lu expt lum

.974

.877 (.83)

.928

1.165

1.12 (.865)

1.006

Wardenier (2) Mean Strength Equation for RHS Gap Joints

lum , 0 . 5 ^ 1 . 5 , . . _ _, 1 + sin = b t 0.4 + 8.513 -r ; - Eq. 1 eo o o 2 sin , , 0.4 ,o .

where = 1.3 ( )

eo TABLE 4 COMPARISON OF 3D JOINT STRENGTH WITH TWO DIMENSIONAL JOINTS

2.32

PIATE 1 : Corby Universal Testing Rig

PLATE 2 : Typical joint in Universal Testing Rig, showing joint deflection gauges, and electrical resistance gauges.

2.33

SERIES F11):INFLUENCE ADDITIONAL LOAD ON ULTIMATE STRENGTH

NpL

-o O + -o

X T II

ca

a

b

c

LO

062 I

07

0-38 I

0-42

NpL= 0

W-RR-1

W-RR-3

W-RR-6

W-RR-7

WITH NpL

W-RR-U4

W-RR-H2

W-RR-V.6

W-RR-14 7

W-RR-150

W-RR-151

Ratio _ 2 _ _ chord 33 ' o

SERIES F

10 o

in

y KJ JQ

A

J * A

Ratio chord of other testpieces cv 25 t o

* ) Sections normalised

g=20

f_3M^_-i. . _ . Oh

concentrated bad

local buckling of JK_l\ccmpr. bracing

NpL VARIED FROM 35% TO 55% OF N^ 'S IN N 1 u = t P o 5 'o %o 105.10.3)

_ _ u 2 5 l t bo I' 'PL

+ r 33 'o

RELATION BETWEEN 1u

b0-5 t1-5 6 uo To Qeo

OS

AND

b vb2 10

______ 2 b n

r 2 b 0 FOR WRR JOINTS WITH

CONCENTRATED LOAD AND WITHOUT CONCENTRATED LOAD

Q) testpieces with eccentricity +025h0< e 0510 FIG.l TESTS PREVIOUSLY CARRIED OUT ON WRR JOINTS WITH LOCAL CONCENTRATED

LOADS (1)

2.34

N,

= 900

32L_Z : R > , s

- * > * -900 N PL

203x133 U.B.

N,

FIG.2 ARRANGEMENT OF JOINTS

\ / \

Y \

/ / '

4 Y :__./.-. 4__ :-*_ \ *-^e i I POSITIVE

ECCENTRICITY ZERO

ECCENTRICITY

\ \

/

-\ l-4-

/ ____-/_zp7

NEGATIVE ECCENTRICITY

FIG.3 DEFINITION OF ECCENTRICITY

2.35

1 S max (a) BRANCH SIDE WALL FILLET WELD

a=t (c) BRANCH HEEL FILLET WELD

(b) BRANCH TOE BUTT WELD

FIG.4 WELD DETAILS

HYDRAULIC JACKS

FIG.5 PLAN OF THE CORBY UNIVERSAL TEST RIG, AS SET UP FOR WRR JOINTS WITH LOCAL LOADING

2.36

HYDRAULIC RAM

LOAD CELL

6mm STIFFENER PLATES

1

-v FIG.6 DETAILS OF APPLICATION OF LOCAL CONCENTRATED LOAD

LVDTs

FIG.7 JOINT DEFLECTION GAUGES

2.37

FIG.8 TYPICAL ARRANGEMENT OF STRAIN GAUGES

KEY: L INWARD DEFORMATION OUTWARD DEFORMATION

^__%4^_^__^_j PP 3-^ O O O

CHORD FACE CHORD FACE AND CHORD SHEAR CRACK LEADING FAILURE WALL FAILURE AROUND MODE OF TO DIAGONAL

THE JOINT WITH OR FAILURE FAILURE WITHOUT CRACKS

TYPE G1| TYPE GA TYPEG2^ TYPE G3 TYPEG5r-

WkAi O O gg. o o

LOCAL BUCKUNG COMPR. BRACING LEADING TO BRACING FAILURE

CHORD CHORD FACE CHORD WALL BUCKLING AND CHORD BUCKLING

WALL FAILURE AROUND TENSION BRACING

ITYPEGSI |TYPEG7| |TYPEGfl |TYPEG9|

F I G . 9 MODES OF JOINT FAILURE

2 . 3 8

() Deformation (b) Deformation

FIG.10 LOAD - DEFORMATION RELATION, SHOWING MAXIMUM LOAD CAPACITY

2.39

LOAD-DEFLECTION PATHS CAILURE WRR 1:2:1

( a ) STRUT

2 3 t

CCHPRESSiON 3?AC rLCCTiON [.V.b]

LEGEND 95 1 rfRR 2

SCALE' ABSCISSA: . 3

U _ . _ . _ . . ! a

I OTOjNATS 1.22

! NOTES

FRAHE No. < i ) LOADDEFLECTION PATHS TO FAILURE WRR 1 :2=3

_ l _ Z I e I 2

T I E 8RACE DEFLECTION [ * )

LEGEND

SCALES ABSCISSA:

W I v 2 ! VSR 3 i

I I

I u ORDINATE: .ca

S3

NOTES

J iea ise :

( b ) TIE FIG 11 LOAD-DEFLECTION CURVES FOR JOINTS WRR 1-3 ( = 0.8)

2.40

8

n ' s 0

.

2 ? o , LU Ci 1 , i l l ! 2 * LO ( a I

o 1

I I

LOADDEFLECTION PATHS TO FAILURE WRR 1

" ^ ^ ^ ^ . i i i f f

I I I I I ! I . I : 2 3 -j G 7 'j a

COHPRESSION BRACE DEFLECTION C>.b03

: 2 : 3

! LEGEND

I _,_

C-CALC,

A5SCSSA!

e

0' :

e

! NOTES

I i ! i

j

-

WP 2

VRR 3

j i i

. 8 3

.tu

2 ]

|

t J

(c ) STRUT

FRAME No. <

fl IP O IO Si' 0

0 t? \ 2 Q < O _1 LU O < a m LU t

I 1

i ) LOADDEFLECTION PATHS TO FAILURE WRR

8

7

G

S

1

3

2

< 1

e

y /

; J a y

> I )

I I I I

3 2 1 8 I 2 3 1

TIE BRACE DEFLECTION l>.b0J

1 : 2 : 3 LEGEND

_

SCALES AescrssA

e ORO I NATE:

1 1 8 1

NOTES

WRR I

WRR 2 WRR 3

.ea

1

1 .Hi!

1 2

(d ) TIE

FIG 11 (CONT) NON-DIMENSIONAL LOAD-DEFLECTION CURVES FOR JOINTS WRR1-3 ( = 0.8)

2.41

LOAD-OrFLCCTiN PATHS TO FAILURE WRR 4:5 N

->"__.J

_!_ _ l _ __ _ l _ 2 3 1 5 S 7 COriPRESSION BRACE DEFLECTION i"/:b0]

LEGEND WRR '.

WRR 3

* 9 0 C

WRR A

SCALES AQ'XJYA:

0 1

1 .W5

.ea

1

1 5 ea

NOTES

( a ) STRUT

FRAME No. < 2> LOADDEFLECTION PATHS TO FAILURE WRR 4 : 5 : G

2

Cl < o

_L. _L 2 1 2

TIE BRACE DEFLECTION CV.LO

LEGEND WRR 1

WRR 5

V R R S

V R R

SCALES ABSCISSA:

I . . . . . . . . . . . . . . 8

ORDINATS:

e sa ac is

NOTES

( b ) TIE FIG 12 LOADDEFLECTION CURVES FOR JOINTS WRR46 (3 = 0.6)

2.42

LOAD-DEFLECTION PATHS TO FAILURE WRR 4:5:6 LEGEND

7

WRR-

WRR-

WRR-

WRR-

"> 5

6

SCALES

ABSCISSA: .ea

a

ORDINATE: 1 .?B

1

NOTES

2 3 1 5 6 7

COMPRESSION BRACE DEFLECTION [v.b-]

( c ) STRUT

FRAME No. < 2) LOAD-DEFLECTION PATHS TO FAILURE WRR 4 : 5