Advanced analysis of steel frame structures comprising non compact sections

Advanced Analysis of Steel Frame Structures Comprising Non-Compact Sections By Philip Avery, B.Eng (Hons 1) A THESIS SUBMITTED TO THE SCHOOL OF CIVIL ENGINEERING QUEENSLAND UNIVERSITY OF TECHNOLOGY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY JULY 1998 QUT QUEENSLAND UNIVERSITY OF TECHNOLOGY DOCTOR OF PHILOSOPHY THESIS EXAMINATION CANDIDATE NAME Philip Avery CENTRE/RESEARCH CONCENTRATION Physical Infrastructure Centre PRINCIPAL SUPERVISOR Associa.te Professor Mahadeva ASSOCIATE SUPERVISOR(S) Associate Professor G Brameld THESIS TITLE "Advanced Analysis of Steel Frame Structures comprising non-compact sections" Mahendran Under the requirements of PhD regulation 9.2, the above candidate was examined orally by the Faculty The members of the panel set up for this examination recommend that the thesis be accepted by the University and forwarded to the appointed Committee for examination ~.: ~ ':\: ~ ~- ~:? ~ ~-~ -························ Name Panel Chairperson (Principal Supervisor) Name Signature QUT Verified Signature K~~-\-l VJ,Ji.w~ Signature QUT Verified Signature Panel Member Name .K\:\.r.v.\~, .Q\~··· · ··· Signatur QUT Verified Signature Panel Member G.~~~ ~ J -~- r.:~ -~-~- ~ -~- Name Panel Member QUT Verified Signature Under the requirements of PhD regulation 9.15, it is hereby certified that the thesis of the above-named candidate has been examined I recommend on behalf of the Thesis Examination Committee that the thesis be accepted in fulfillment of the conditions for the award of t he degree of Doctor of Philosophy Name ~N.,.\l/J./~ Signature Chair of Examiners (External Thesis Examinat C:\DA T A\MSWORDIPHD\NOMINA TIPHDCOA D OC QUT Verified Signature m Jz/~:? Statement of Original Authorship This thesis presents theoretical, numerical, and experimental work performed by the author All references to, and use of, work by other researchers are fully acknowledged throughout the text The remaining work described herein, to the best of my knowledge and belief, is original The work contained in this thesis has not been previously submitted, either in part or in whole, for a degree at this or any other university QUT Verified Signature Philip Avery Acknowledgements I would like to express my sincere gratitude to my supervisor, A/Prof Mahen Mahendran, for his expertise and guidance over the past three years I would also like to thank the Queensland University of Technology (QUT) and the Australian Institute of Steel Construction (AISC) for providing financial support of my project through the QUT Postgraduate Research Award (QUTPRA) and the AISC National Scholarship in Steel Structures Thanks also to the Physical Infrastructure Centre and the School of Civil Engineering at QUT for providing the necessary facilities and technical support Also deserving of thanks are the Structures Laboratory staff members for assistance with the experimental program, and BHP for providing the steel used to fabricate the test rig and frames Finally, I wish to thank my family, friends, and postgraduate colleagues for their support, encouragement, and patience P Avery: Advanced analysis of steel frame structures comprising non-compact sections • i Abstract During the past decade, a significant amount of research has been conducted internationally with the aim of developing, implementing, and verifying "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures Application of these methods permits comprehensive assessment of the actual failure modes and ultimate strengths of structural systems in practical design situations, without resort to simplified elastic methods of analysis and semi-empirical specification equations Advanced analysis has the potential to extend the creativity of structural engineers and simplify the design process, while ensuring greater economy and more uniform safety with respect to the ultimate limit state The application of advanced analysis methods has previously been restricted to steel frames comprising only members with compact cross-sections that are not subject to the effects of local buckling This precluded the use of advanced analysis from the design of steel frames comprising a significant proportion of the most commonly used Australian sections, which are non-compact and subject to the effects of local buckling This thesis contains a detailed description of research conducted over the past three years in an attempt to extend the scope of advanced analysis by developing methods that include the effects of local buckling in a non-linear analysis formulation, suitable for practical design of steel frames comprising non-compact sections Two alternative concentrated plasticity formulations are presented in this thesis: the refined plastic hinge method and the pseudo plastic zone method Both methods implicitly account for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling The accuracy and precision of the methods for the analysis of steel frames comprising non-compact sections has been established by comparison with a comprehensive range of analytical benchmark frame solutions Both the refined plastic hinge and pseudo plastic zone methods are more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations For example, the pseudo plastic zone method predicts the ultimate strength of the analytical benchmark frames with an average conservative error of less than one percent, and has an acceptable maximum unconservati_ve error of less than five percent The pseudo plastic zone model can allow the design capacity to be increased by up to 30 percent for simple frames, mainly due to the consideration of inelastic redistribution The benefits may be even more significant for complex frames with significant redundancy, which provides greater scope for inelastic redistribution The analytical benchmark frame solutions were obtained using a distributed plasticity shell finite element model A detailed description of this model and the results of all the 120 benchmark analyses are provided The model explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling Its accuracy was verified by comparison with a variety of analytical solutions and the results of three large-scale experimental tests of steel frames comprising non-compact sections A description of the experimental method and test results is also provided P Avery: Advanced analysis of steel frame structures comprising non-compact sections + ii Publications Avery, P (1996), "Advanced analysis of steel frames comprising non-compact sections", Ph.D literature review, School of Civil Engineering, Queensland University of Technology, Brisbane, Australia Mahendran, M., Avery, P., and Alsaket, Y (1997), "Benchmark solutions for steel frames structures comprising non-compact sections", Proceedings of the International Conference on Stability and Ductility of Steel Structures, Nagoya, Japan Avery, P., Alsaket, Y., and Mahendran, M (1997), "Distributed plasticity analysis and large scale tests of steel frame structures comprising members of non-compact cross-section", Physical Infrastructure Centre Research Monograph 97-1, Queensland University of Technology, Brisbane, Australia Avery, P and Mahendran, M (1998), "Advanced analysis of steel frames comprising non-compact sections", Proceedings of the Physical Infrastructure Centre's Conference on Infrastructure for the Real World, Queensland University of Technology, Brisbane, Australia Avery, P and Mahendran, M (1998), "Advanced analysis of steel frame structures comprising non-compact sections", Proceedings of the Australasian Structural Engineering Conference, Auckland, New Zealand Avery, P and Mahendran, M (1998), "Large scale testing of steel frame structures comprising non-compact sections", Physical Infrastructure Centre Research Monograph 98-1, Queensland University of Technology, Brisbane, Australia Avery, P and Mahendran, M (1998), "Distributed plasticity analysis of steel frame structures comprising non-compact sections", Physical Infrastructure Centre Research Monograph 98-2, Queensland University of Technology, Brisbane, Australia Avery, P and Mahendran, M (1998), "Analytical benchmark solutions for steel frame structures comprising non-compact sections", Physical Infrastructure Centre Research Monograph 98-3, Queensland University of Technology, Brisbane, Australia Avery, P and Mahendran, M (1998), "Refined plastic hinge analysis of steel frame structures comprising non-compact sections", Physical Infrastructure Centre Research Monograph 98-4, Queensland University of Technology, Brisbane, Australia 10 Avery, P and Mahendran, M (1998), "Pseudo plastic zone analysis of steel frame structures comprising non-compact sections", Physical Infrastructure Centre Research Monograph 98-7, Queensland University of Technology, Brisbane, Australia 11 Avery, P and Mahendran, M (1999), "Large scale testing of steel frame structures comprising non-compact sections", Engineering Structures (under review) P Avery: Advanced analysis of steel frame structures comprising non-compact sections • iii 12 Avery, P and Mahendran, M (1999), "Distributed plasticity analysis of steel frame structures comprising non-compact sections", Engineering Structures (under review) 13 Avery, P and Mahendran, M (1999), "Analytical benchmark solutions for steel frame structures comprising non-compact sections", Journal of Structural Engineering, ASCE (under review) 14 Avery, P and Mahendran, M (1999), "Refined plastic hinge analysis of steel frame structures comprising non-compact sections I: Formulation", Journal of Structural Engineering, ASCE (under review) 15 Avery, P and Mahendran, M (1999), "Refined plastic hinge analysis of steel frame structures comprising non-compact sections II: Verification", Journal of Structural Engineering, ASCE (under review) 16 Avery, P and Mahendran, M (1999), "Pseudo plastic zone analysis of steel frame structures comprising non-compact sections", Journal of Structural Engineering, ASCE (in preparation) P Avery: Advanced analysis of steel frame structures comprising non-compact sections • iv Table of Contents Acknowledgements i Abstract ii Publications iii Table of Contents v List of Figures .ix List of Tables .xiv Notation xvii Abbreviations xvii Symbols xvii Chapter Introduction Chapter Literature Review .4 2.1 Advanced analysis of steel frame structures 2.1.1 Distributed plasticity analysis 2.1.2 Concentrated plasticity analysis 2.1.3 Design considerations 15 2.2 Local buckling 19 2.2.1 Local buckling fundamentals 19 2.2.2 Quantifying local buckling effects 21 2.3 Design of steel frame structures comprising non-compact sections 25 2.3.1 AS4100 25 2.3.2 AISC LRFD 28 2.3.3 Comparison of the AS4100 and AISC LRFD design specifications 30 Chapter Large Scale Frame Testing 31 3.1 Test specimens 31 3.2 Test setup and instrumentation 36 3.3 Test procedure 43 3.4 Test results and discussion 45 3.4.1 Test frame (non-compact universal beam) 45 3.4.2 Test frame (slender rectangular hollow section) 52 3.4.3 Test frame (slender welded 1-section) 57 3.5 Summary 63 P Avery: Advanced analysis of steel frame structures comprising non-compact sections • v Chapter Distributed Plasticity Finite Element Analysis 65 4.1 Model description 65 4.1.1 Elements 66 4.1.2 Discretization of the finite element mesh 67 4.1.3 Material model and properties 68 4.1.4 Loads and boundary conditions 69 4.1.5 Initial geometric imperfections 70 4.1.6 Residual stresses 72 4.1.7 Analysis 76 4.2 Verification 76 4.2.1 Vogel frames comprising compact sections 77 4.2.2 Test frames comprising non-compact sections 86 4.3 Analytical benchmarks and parametric studies 97 4.3.1 Modified Vogel frames 98 4.3.2 Series 1: Fixed base sway portal frames (major axis bending) 102 4.3.3 Series 2: Pinned base sway portal frames (major axis bending) 112 4.3.4 Series 3: Leaned column sway portal frames (major axis bending) 113 4.3.5 Series 4: Pinned base non-sway portal frames (major axis bending) 114 4.3.6 Series 5: Pinned base sway portal frames (minor axis bending) 115 4.4 Summary 116 Chapter Concentrated Plasticity Refined Plastic Hinge Analysis 117 5.1 Formulation of the frame element force-displacement relationship 118 5.1.1 Second-order effects 120 5.1.2 Section capacity 122 1.3 Gradual yielding and distributed plasticity 126 5.1.4 Hinge softening 138 5.2 Assembly and solution of structure force-displacement relationship 140 2.1 Coordinate transformation 140 5.2.2 Solution method 141 5.3 Sensitivity of analytical model parameters 142 5.3 Initial load increment size 143 5.3.2 Number of elements per member 145 5.3.3 Effective section properties 146 5.3.4 Section capacity interaction function 147 5.3.5 Tangent modulus 148 5.3.6 Flexural stiffness reduction parameter 149 5.3.7 Method of analysis 150 5.4 Verification of the refined plastic hinge method 152 5.4.1 Modified Vogel frames 152 5.4.2 Series 1: Fixed base sway portal frames (major axis bending) 154 5.4.3 Series 2: Pinned base sway portal frames (major axis bending) 162 5.4.4 Series 3: Leaned column sway portal frames (major axis bending) 164 5.4.5 Series 4: Pinned base non-sway portal frames (major axis bending) 167 5.4.6 Series 5: Pinned base sway portal frames (minor axis bending) 170 5.5 Summary 172 P Avery: Advanced analysis of steel frame structures comprising non-compact sections • vi Chapter Concentrated Plasticity Pseudo Plastic Zone Analysis 174 6.1 Stub beam-column model analysis 174 6.1.1 Description of the stub beam-column model 175 6.1.2 Analytical results and discussion 176 6.2 Formulation of the pseudo plastic zone frame element force-displacement relationship 182 6.2.1 Plastic strength, section capacity and initial yield 183 6.2.2 Section tangent moduli 186 6.2.3 Hinge softening 189 6.2.4 Imperfection reduction factor 191 6.2.5 Second-order effects 192 6.2.6 Flexural stiffness reduction parameter 193 6.3 Verification of the pseudo plastic zone analytical method 194 6.3.1 Series 1: Fixed base sway portal frames (major axis bending) 195 6.3.2 Series 2: Pinned base sway portal frames (major axis bending) 201 6.3.3 Series 3: Leaned column sway portal frames (major axis bending) 203 6.4 Summary 206 Chapter Conclusions 208 Appendix A Benchmark Load-Deflection Results 211 Al A2 A3 A4 A5 Benchmark series load-deflection results 212 Benchmark series 2load-deflection results 221 Benchmark series load-deflection results 223 Benchmark series load-deflection results 229 Benchmark series load-deflection results 231 Appendix B Comparison of Load-Deflection Curves 232 B Benchmark series load-deflection curves 233 B2 Benchmark series load-deflection curves 239 B3 Benchmark series load-deflection curves 243 B4 Benchmark series 4load-deflection curves 247 B5 Benchmark series 5load-deflection curves 249 Appendix C Comparison of Strength Curves 251 Cl Benchmark series strength curves 252 C2 Benchmark series strength curves 258 C3 Benchmark series strength curves 260 C4 Benchmark series strength curves 264 C5 Benchmark series strength curves 266 Appendix D Abaqus Residual Stress Modules 267 Dl Abaqus module used to define membrane residual stress in hot-rolled!sections 268 D2 Abaqus module used to define membrane residual stress in welded!sections 269 D3 Abaqus module used to define membrane and bending residual stress in cold-formed rectangular hollow sections 270 P Avery: Advanced analysis of steel frame structures comprising non-compact sections • vii fprintf ( fout, "\n\ "out-of-plane\", \"horizontal load (V IH=15) \", \"vertical load (VIH=15)\"], [0, 0, @"); fprintf(fout,"\nO, 0, 0], \"\", 0., FALSE)"); fprintf ( fout, "\nloadcase_create ( \ "V IH=3 \", \"Static\", \" \"' [\"fixed base\", \"more out-of-plane\", @"); fprintf (fout, "\n\ "out-of-plane\", \"horizontal load (VIH=3) \", \"vertical load (V IH=3) \"] , [ 0, 0, 0, @") ; fprintf(fout,"\n 0, 0], \"\", 0., FALSE)"); I* equivalence grids *I fprintf(fout,"\nREAL fem_equiv_all_x_equivtol"); fprintf(fout,"\niNTEGER fem_equiv_all_x_segment"); fprintf ( fout, "\nfem_equi v_all_group3 ( [ \" \"] , 0, FALSE, fem_equiv_all_x_equivtol, @"); fprintf(fout,"\nfem_equiv_all_x_segment )"); \" \", 1, 5, I* create MPCs *I fprintf(fout,"\nfem_create_mpc_nodal( 1, \"Rigid (Fixed)\", 0., 2, [TRUE, FALSE], [0., 0.], [ @"); fprintf(fout,"\n\"Node 3:146 148:295 297:304 306:313 315:322 324:331 333:340 342:349 351:35\" II @"); fprintf(fout,"\n\"8 360:367 369:376 378:385 387:394 396:403 405:412 414:421423:430 432:439\" II@"); fprintf(fout,"\n\" 441:448 450:457 459:466 468:475 477:484 486:493 495:502 504:511 513:520 \" II @"); fprintf(fout,"\n\"522:529 531:538 540:547 549:556 558:565 567:574 576:583 585:592 594:597\", @"); fprintf(fout, "\n\"Node 1\"], [\"\", \"\"] ) "); fprintf(fout,"\nfem_create_mpc_nodal( 2, \"Rigid (Fixed)\", 0., 2, [TRUE, FALSE], [0., 0.], [ @"); fprintf(fout,"\n\"Node 598:741 743:890 892:899 901:908 910:917 919:926 928:935 937:944 946:\" II @"); fprintf(fout,"\n\"953 955:962 964:971 973:980 982:989 991:998 1000:1007 1009:1016 1018:1025\" II @"); fprintf(fout,"\n\" 1027:1034 1036:1043 1045:1052 1054:1061 1063:1070 1072:1079 1081:1088 10\" II@"); fprintf(fout, "\n\"90:1097 1099:1106 1108:1115 1117:1124 1126:1133 1135:1142 1144:1151 1153:\" II@"); fprintf(fout,"\n\"1160 1162:1169 1171:1178 1180:1187 1189:1192\", \"Node 2\ 11 11 ] , [ \" \", \" \ 11 ] ) ) ; I* mesh columns and beam *I fprintf(fout,"\niNTEGER fem_create_mesh_surfa_num_nodes"); fprintf(fout,"\niNTEGER fem_create_mesh_surfa_num_elems"); fprintf(fout,"\nSTRING fem_create_mesh_s_nodes_created[VIRTUAL]"); fprintf(fout,"\nSTRING fem_create_mesh_s_elems_created[VIRTUAL]"); fprintf ( fout, "\nfem_create_mesh_surf_2 ( \" IsoMesh \", 0, \"Surface \", 1, [%f], \"Quad4\", @",cmesh); fprintf(fout,"\n\"10001\", \"10001\", \"Coord 0\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout,"\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout,"\nfem_create_mesh_s_elems_created) "); fprintf ( fout, "\nfem_create_mesh_surf_2 ( \" IsoMesh \", 0, \"Surface \", 1, [%f], \"Quad4\", @",cmesh); fprintf(fout,"\n\"20001\", \"20001\", \"Coord 0\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout,"\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout,"\nfem_create_mesh_s_elems_created) "); P Avery: Advanced analysis of steel frame structures comprising non-compact sections • 278 fprintf ( fout, "\nfem_create_mesh_surf_2 ( \ "IsoMesh\", \", 1, [%f], \"Quad4\", @",cmesh); fprintf(fout,"\n\"30001\", \"30001\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout, "\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout, "\nfem_create_mesh_s_elems_created) "); fprintf(fout,"\nfem_create_mesh_surf_2( \"IsoMesh\", \", 1, [%f], \"Quad4\", @",cmesh); fprintf(fout,"\n\"40001\", \"40001\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout, "\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout, "\nfem_create_mesh_s_elems_created) "); fprintf ( fout, "\nfem_create_mesh_surf_2 ( \ "IsoMesh \", 13 \", 1, [%f], \"Quad4\", @",bmesh); fprintf(fout,"\n\"50001\", \"50001\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout, "\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout, "\nfem_create_mesh_s_elems_created ) "); fprintf ( fout, "\nfem_create_mesh_surf_2 ( \ "IsoMesh \", 1415 \", 1, [%f], \"Quad4\", @",bmesh); fprintf(fout,"\n\"70001\", \"70001\", \"Coord 0\", fem_create_mesh_surfa_num_nodes, @"); fprintf(fout, "\nfem_create_mesh_surfa_num_elems, fem_create_mesh_s_nodes_created, @"); fprintf(fout, "\nfem_create_mesh_s_elems_created ) "); /* equivalence grids */ fprintf ( fout, "\nfem_equiv_all_group3 ( [ \" \"], FALSE, fem_equiv_all_x_equivtol, @"); fprintf(fout, "\nfem_equiv_all_x_segment )"); 0, 0, \"Surface \"Coord 0, \"Surface \"Coord 0, 0\", \"Surface \"Coord \" \", 0\", \"Surface \"Coord 0, 0\", 1, 0\", 5, fprintf(fout, "\n"); fclose(fout); } P Avery: Advanced analysis of steel frame structures comprising non-compact sections • 279 Appendix F Equation Derivations P Avery: Advanced analysis of steel frame structures comprising non-compact sections • 280 Fl Derivation of the refined plastic hinge model's hinge softening equation (5.1-42) The incremental force-displacement relationship for the refined plastic hinge formulation is shown in Equation F1-1 ¢+-::(H.)] MA MB = EJ = -0.5 + ~0.25 + 2e P Avery: Advanced analysis of steel frame structures comprising non-compact sections (F2-5) • 283 Equation F2-6 represents a simple generalised form of equations F2-4 and F2-5 which is valid for any end moment ratio ({3) Note that Equation F2-6 reduces to F2-4 for f3 = -1, and to F2-5 for f3 =