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University of Sheffield Department of Civil And UNIVERSITY OF SHEFFIELD DEPARTMENT OF CIVIL AND STRUCTURAL ENGINEERING BUCKLING STRENGTH OF WELDED AND NON-WELDED ALUMINIUM MEMBERS BY Yuk Fai, Willy LAI (M.Eng) A Thesis Submitted to the University of Sheffield for tb,e Degree of Doctor of Philosophy October 1988 " -To Shirley and my parents 1 CONTENTS Contents i Aclmowledgements viii Declaration x Summary xi Notation xii 1 INTRODUCTION 1.1 Use of Aluminium . 1 1.2 Nature of Problem and Background . 2 1.3 Aim of Research . 3 1.4 Organisation of the Thesis . 4 References . ... 5 2 LITERATURE REVIEW 2.1 Introduction............. 6 Part A: Aluminium Alloys . 7 2.2 General Information . 7 2.2.1 Designation [ 2,3,4,5] ....•. 7 2.2.2 Welding Procedures [4,6] . .. 7 2.2.3 Different Theoretical Models of St-ress-strain Curve of Aluminium Alloy. .. .. 8. 2.2.4 Ramberg-Osgood Formula . .. 10 2.2.5 Elastic Limit Stress of Aluminium Alloy . .. 12 CONTENTS 11 Part B: Effects of Welding . • . .. 13 2.3 Background to the Effects of Welding . .. 13 2.3.1 Extent of Softening around a. Weld . 13 2.3.2 Mechanical Properties of Heat-affected Material ... 17 2.3.3 Residual Stress Distribution . 21 Part C: Structural Use of Aluminium . • . •. 27 2.4 Development of Structural Use of Aluminium .. 27 2.5 Resea.rchon Welded Aluminium Members 30 References . .. 32 3 IN-PLANE BEHAVIOUR OF ALUMINIUM MEMBERS 3.1 Description of the Program INSTAF . .. 41 3.1.1 Numerical Formulation of the Problem . .. 42 3.2 Comparison between INSTAF with Experimental and Theoretical Results .• '...................... 47 3.2.1 Comparison with Experimental Results ~ 47 3.2.2 Comparison with Theoretical Results . 48 3.3 Choice of Elimit •••••••••••••••••••••• 49 3.4 Parametric Studies of Transversely Welded Members . 50 3.4.1 Parametric Studies of Transversely Welded Columns 51 3.4.2 Parametric Studies of Transversely Welded Beams. 55 3.4.3 Parametric Studies of Transversely Welded Beam- columns . .. .. 57 3.5 FUrther Parametric Studies on Aluminium Members. 59 3.5.1 Effect of RSZ on Fixed Joints . 59 3.5.2 Studies on 7019 Aluminium Alloy . 60 CONTENTS iii 3.6 Conclusions . 63 References ... • . 64 4 TEST ON ALUMINIUM BEAMS WITH OR WITHOUT LOCAL TRANSVERSE WELDS 4.1 Introduction...... 65 4.2 Specimen . 66 4.2.1 Basic Dimensionsand Specimen Designations . 66 4.2.2 Welding........... 68 4.2.3 Initial Out-of-straightness . 68 4.3 Auxiliary Tests . 69 4.3.1 Tensile Coupon Tests [ 2] . 69 4.3.2 Coupon Results and Material Properties 70 4.3.3 Hardness Surveys and Extent of Reduced-strength Zone 72 4.4 Beam Tests . .. 74 4.4.1 Set-up of Beam Test with 1000 mm Span 74 4.4.2 Set-up of Beam Test with 2000 mm Span 75 4.4.3 Testing Procedure . 75 4.4.4 Beam Test Results and Computer Simulation Using Program INSTAF . .. 76 4.5 Discussion . .. 79 4.5.1 Test Results ... .. 79 4.5.2 Comparisons of Test Results . 82 4.6 Conclusions . • . • . 83 References .....•..•..•.•.•.. 84 CONTENTS iv 5 FLEXURAL-TORSIONAL BUCKLING OF ALUMINIUM MEMBERS 5.1 Description of the Program BIAXIAL. .. .. 85 5.1.1 General Formula.tion of the Program BIAXIAL .. .. 86 5.2 Comparisons with Theoretical and Experimental Results . .. 88 5.2.1 Comparison with the Program INSTAF 88 5.2.2 Comparison with the Experimental Column Results Obtained by Hill and Clark [ 6] 89 5.2.3 Compa.rison with the Tests on Beam-columns Subjected to Thrust and Biaxial Bending . .. 90 5.3 Parametric Studies of Aluminium Members 91 5.3.1 Parametric Studies of Aluminium Columns 92 5.3.2 Parametric Studies of Aluminium Beams . .. 98 5.3.3 Parametric Studies of Aluminium Beam-columns . 103 5A" Further Parametric Studies of Aluminium Members . 106 5A.l Study of Tee-section Aluminium Members 106 5A.2 Study of 5083-M Aluminium Columns 111 5.4.3 Study of 6061~TB Aluminium Columns 113 5.5 Conclusions . 114 References . 116 6 BIAXIAL BENDING OF ALUMINIUM BEAM-COLUMNS 6.1 Introduction.............................. 118 6.2 Factors Affecting the Solution of Biaxia.lly Loaded Beam- column "................ 119 CONTENTS v 6.3 Parametric Studies of Biaxially Loaded Aluminium Beam-columns 124 6.3.1 Parametric Studies of Non-welded Aluminium Beam-columns . 125 6.3.2 Parametric Studies of Longitudinally Welded Aluminium Beam- columns . .. 128 6.3.3 Parametric Studies of Transversely Welded Beam-columns 129 6.4 Conclusions . • . 130 References . 132 7 COMPARISON BETWEEN DRAFT BS 8118 WITH THE- ORETICAL RESULTS 7.1 Introduction............... 133 7.1.1 Basic Design Philosophy of Draft BS 8118 ... ... 133 7.1.2 Scope and Layout of this Chapter 134 7.2 Design of Aluminium Columns 135 7.2.1 Basic Principle and Design Procedures 135 7.2.2 Design of Columns Having Local Transverse Welds 136 7.2.3 Selection of Column Curves 137 7.2.4 Comparison between Design Column Curves of Draft BS 8118 with Theoretical Results of Columns . 139 7.3 Design of Aluminium Beams •.•••••.••••..•.•••.•. 148 7.3.1 Basic Principle and Design Procedures [ 7] 148 7.3.2 Comparison between Draft BS 8118 with Theoretical Results of Beams I· .' e. • • • • • • • • • • • • • • • • • • • • • • • • 151 7.4 Design of Aluminium Beam-columns .. 157 7.4.1 Basic Principle, and Design Procedures .•............ 157 CONTENTS vi 7.4.2 Comparison between Draft BS 8118 with Theoretical Results of Beam-columns ••••••.•••..•••••.••.. 159 7.4.3 Comparison between Draft BS 8118 with Theoretical Results of Beam-columns under Biaxial Bending .....•.... 164 7.5 Discu.ssion . 168 7.5.1 Discussion on the Design of Aluminium Columns 168 7.5.2 Discussion on the Design of Aluminium Beams 169 .: 7.5.3 Discussion on the Design of Aluminium Beam-columns . 173 7.6 Proposed Design Recommendations for Transversely Welded Mem- bers 174 7.6.1 Proposed Design Method for Transversely Welded Columns . 175 7.6.2 Proposed Design Method for Transversely Welded Beams . 176 7.6.3 Proposed Design Method for Transversely Welded Beam.-col umns . 177 7.7 Comments on Draft BS 8118. • . • . 178 7.8 Conclusions . .... 179 References ..... ... 181 8 CONCLUSIONS 8.1 General Summary of Present Study . • . • . • . 183 8.2 Conclusions . 185 8.2.1 Theoretical Studies ...•.•..•................ 185 8.2.2 Tests on Aluminium Beams • • • • • • • • • • • • • • • • • • • • 187 8.2.3 Design of Aluminium Members Using Draft BS 8118 .. 188 CONTENTS w 8.3 Further Worb 190 8.4 Application of Present Research Work •.........•.... 191 A VARIOUS PROPOSALS ON STRESS-STRAIN RELATION- SHIP OF ALUMINIUM A.l Stress-strain Relationships of Aluminium in Continuous Form of (/'= /(e) 193 A.I.! Stress-strain Relationship Proposed by Baehre 194 A.l.2 Stress-strain Relationship Proposed by Mazzolani . • • . • . 195 A.l.3 Stress-strain Relationship Proposed by Hong .•..•.....• 198 A.1.4 Stress-strain Relationship Proposed by Frey •••••••••.• 199 A.2 Stress-strain Relationships of Aluminium in Continuous Form of e=f(u) ...••....•.•••................ 201 A.2.1 Stress-strain Relationship Proposed by Ramberg and Osgood . 201 A.2.2 Comments to the Four Proposals for the Determination of Knee FK'tor," 206 A.3 Numerical Example for the Comparison between the Different Proposals on the Stress-strain Rela.tionships of Aluminium Alloy207 References • • • . • . • • • . • . • . • . • • • • . • . 209 B CAMBRIDGE RESIDUAL STRESS MODEL B.l Cambridge Residual Stress Model ..•............... 210 References • • • • • • • • . • • • . • • . • • • • • . • . • . • . • 212 viii ACKNOWLEDGEMENT The work described in this thesis was carried out at the University of Sheffield, Department of Civil and Structural Engineering between October 1985 and September 1988. The author would like to express his sincere gratitude to Dr. D A Nethercot for his supervision, valuable guidance, encouragement and general interest throughout the study. The author also wishes to thank Professor T H Hanna (Hea.dof the Department) and all his academic staff for their support. The research work was made possible by the financial support of the Royal Armament Resea.rch and Development Establishment (R.A.R.D.E.). Iwould like to thank Dr. P S Bulson, Mr. J B Dwight and Mr. D Webber of R.A.R.D.E. for their interest and sound ideas. I am indebted to the sta1f of the Structures Laboratory for assisting with experiments. In particular I should mention Mr. S Walters, Mr. J D Web- ster, Mr. G B Anthony and Mr. T Robinson for their advice and help with instrumentation. My thanks go to Miss. S Y Tung for typing this thesis and everybody else who has contributed to the work either with practical help or interesting ideas. ~~------------------------------~ ACKNOWLEDGEMENT. IX Finally, the author wishes to express his deepest apprecia.tion to his family, especially to his parents and his two sisters, Anita. and Sabina, for their support encouragement and understanding throughout his many years of academic study. x DECLARATION The author wishes to declare that,exeeptfor commonly understoodandac- cepted ideas, or where specific reference is made, the .work reported in this thesis is his own. The work has not previously been submitted in part or in whole to any University for any degree, diploma or other qualification. 5 Y FW LA! Xl SUMMARY High strength aluminium alloys when welded suffer a loca.lloss of strength due to heat-affected zone (HAZ) effects. The influence of such loca.1.ised strength loss on structural behaviour of columns, beams and beam-columns is studied using numerical technique. Two programs INSTAF and BIAXIAL, previously developed for the use of steel structures, have been modified to incorporate the special features of the aluminium problem. The general in- plane behaviour of aluminium frames or members is studied by using program INSTAF. The general 3-D behaviour of aluminium members is simulated by the program BIAXIAL.
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