Optimum design of steel moment resisting frames

Optimum design of steel moment resisting frames PhD Thesis 2012

Muhammad Tayyab Naqash

University 'G. d'Annunzio' of Chieti‐Pescara


PhD Thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy On OPTIMUM DESIGN OF STEEL MOMENT RESISTING FRAMES In

XXV Cycle at the Department of Engineering and Geology

By

Muhammad Tayyab Naqash Ph.D. Supervisor Prof. Dr. Ing. G. DE MATTEIS

Ph.D. Co‐Supervisor Prof. Dr. Ing. A. DE LUCA


University of Naples “Federico II”

Ph.D. Coordinator Prof. Dr. Ing. M. VASTA University 'G. d'Annunzio' of Chieti‐Pescara

(2012)

UNIVERSITA’ DEGLI STUDI “G. d’Annunzio” Chieti-Pescara SCUOLA SUPERIORE “G. d’Annunzio” School of Advanced Studies

DOTTORATO DI RICERCA IN Progettazione e Ingegneria del sottosuolo e dell’ambiente costruito Curriculum: Structural Engineering

CICLO XXV

OPTIMUM DESIGN OF STEEL MOMENT RESISTING FRAMES PROCEDURE DI OTTIMIZZAZIONE PER IL DIMENSIONAMENTO DI TELAI IN ACCIAIO SISMORESISTENTI

Dipartimento di Ingegneria e Geologia Settore Scientifico Disciplinare ICAR/09

Dottorando

Coordinatore Prof.

Muhammd Tayyab Naqash

Prof. Nicola Sciarra Tutor Prof. Ing. Gianfranco De Matteis Co-Tutor Prof. Ing. Antonio De Luca

Anni Accademici 2010/2012

Naples 2012

University “G. d'Annunzio” of Chieti‐ Pescara

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Ph.D. thesis titled “Optimum design of steel moment resisting frames” by Tayyab Naqash

Dedications My parents (My beloved father and my mother): You being all my life, I cannot overlooked the tough times together with you all the way through my life who grown me up and who brought me to this stage. You deserve all my life. Higher thanks to my Father who constantly did it for all my family.

My old and new family: Thanks to all my family, to my brothers and my sisters for allowing me to rise among all of you. It could never be possible without your prayers and efforts. Bundle of thanks to the family of Mehwish Iqbal as well. My brother: Whom I cannot ignore in any step. You are not only a brother but also a companion with me who support me like a father, guide me like a friend and finally help me as a brother. My grandfather and my grandmother: Though did not go to school, still their unlimited love and prayers support me always. I missed my grandmother at the very end of this journey, who passed away on 11 Nov 2012. May Allah bless her soul with Peace. Ameen! My uncles, my Aunties, and my cousins:


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Acknowledgements I thank Allah THE Almighty for making my dream come true. His ceaseless blessings are upon me. Simply, I do not deserve a lot for what I am. If I would like to write about my Ph.D. supervisor Professor Gianfranco De Matteis, I do not have enough words to express my feelings for his curiosity, his inspiration, and his determined enthusiasm all the time long during my stay in Ph.D. with him. He truly is a unique guide for me. Kind thanks to Dr. Eng. Giuseppe Brando, the assistant of Prof. De Matteis for being beside whenever I need him. He really remained very much helpful during my Ph.D. studies. I am also indebted to my co supervisor Professor Antonio De Luca at the University of Naples “Federico II”, whose passion has inspired me to take my own desires always seriously, even though sometimes he is hard but still he is a great personality with a unique character. Thanks to the cooperation of Dr. Eng. Giuseppe Brandonisio, the assistant of Prof. De Luca who always remained very close friend. I would like to thank my family—my grandfather, my grandmother, my father, my mother, my sisters and my brothers—for their love and support during this long journey. Artists themselves, they have always encouraged and support me towards excellence. I am very grateful to my fiancée Mehwish Iqbal whose patience and true love lead me to the ending of my remaining research work more easily. Special thanks to Prof. Elena Mele, Prof. Federico Massimo Mazzolani, Prof. Bruno Calderoni, Dr. Eng. Giuseppe Brando, Dr. Eng. Giuseppe Brandonisio, and Dr. Eng. Antonio Formisano for their everlasting cooperation with me during my stay in Naples.


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I am very thankful to my friends, colleagues, and co‐workers at the University of Naples: Dr. Eng. Giuseppe Brandonisio, Eng. Maurizio Toreno, Eng. Giuseppe Lucibello, Dr. Eng. Carmine Castaldo, Eng. Vincenzo Macillo, Eng. Tony De Lucia, Eng. Gian Maria Montuori, Eng. Gianluca Sarracco, and Arch. Roberta Fonti, who are now scattered along the length of the coast. Without their company and their coffee and launch breaks, I would have been lost. How I can forgot Maurizio Toreno who always helped me without any hesitation. Many thanks to my colleagues Arch. Federica D'Agostino and Arch. Emanuela Criber at the University of Chiete Pescara for helping me whenever I need them in Pescara. My special friends Habib Rehman, Kashif Sarfraz, Asif Ahmed (Chata), Haiyl Alrawi, Shah Faisal, though physically not with me but still they support me by encouraging me all the time. I still remember my friends in Master “Design of Steel Structures” being scattered after the completion. I would also like to thank my Pakistani friends residing in Italy, Naveed Ahmad, Adnan Daud, Waqar Ahmed, with special thanks to Salim Khoso who remains very close to me. All of them did their part with high sincerity at Naples. I started this long journey from IMS & C Shabqadar fort, entering with GHS Battagram and then admitting in Pre‐engineering in NSDC Risalpur Cantt, with the graduation from QUEST Nawabshah and with Master from University of Naples and ending with University of Chieti‐Pescara. Therefore I am thankful to all those whom I meet throughout all my academics with special thanks to my teachers who were busy doing it till the end.


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Further, I humbly thanks to Prof. Zaheeruddin Memon at QUEST Nawabshah and General Manager Kamal Afridi at Water Management Center at PPAF Islamabad, who always contributed in many ways. Many thanks to Dr Naveed Ahmad, Asst. Professor at the Earthquake Engineering Center of UET Peshawar for providing me useful information on 1935 Quetta Earthquake. In the end, I am highly grateful to the Department of Structural Engineering of University of Naples “Federico II”, for allowing me to stay at their school and be a part of such a well‐known scientific group in Steel Structures all over the globe. The Neapolitan coffee and Pizza …...” MANY THANKS TO NAPOLI”


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Index Motivation ............................................................................................................... 1 Thesis organisation ................................................................................................. 2 Abstract ................................................................................................................... 6 Highlights ................................................................................................................. 7 Keywords ................................................................................................................. 8 Publications and reports ......................................................................................... 9 1.

INTRODUCTION AND OVERVIEW ON STEEL MOMENT RESISTING FRAMES . 11

1.1. General ..................................................................................................... 11 1.1.1. Major earthquakes in Pakistan .................................................................... 14 1.1.2. Seismic zonation of Pakistan ....................................................................... 17 1.1. Steel in seismic zones ................................................................................ 18 1.1.1. General ........................................................................................................ 18 1.1.2. Mechanical properties of structural steel ................................................... 19 1.2.

Philoshopical concepts ............................................................................... 22

1.3. Performance based design ......................................................................... 24 1.3.1. General ........................................................................................................ 24 1.3.2. PDB objectives and performance levels ...................................................... 24 1.3.3. Performance Based Design steps ................................................................ 26 1.3.4. PDB according to European and American codes ....................................... 28 1.4. Seismic resistant steel structural systems ................................................... 30 1.4.1. Moment resisting frames ............................................................................ 33 1.4.2. Eccentric braced frames .............................................................................. 34 1.4.3. Concentric braced frames ........................................................................... 36 1.5.

Pros and cons of steel moment resisting frames ......................................... 37


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1.6.

Modern building codes and their approach to seismic design ..................... 39

1.7. Overstrength and behaviour factors ........................................................... 40 1.7.1. Local overstrength ....................................................................................... 40 1.7.2. Global Overstrength .................................................................................... 42 1.7.3. Behaviour factor .......................................................................................... 42 1.8. Evaluation of behaviour factor ................................................................... 45 1.8.1. General ........................................................................................................ 45 1.8.2. Methods based on ductility factor theory ................................................... 45 1.8.3. Methods based on extension of the results concerning the dynamic inelastic response of simple degree of freedom systems .......................................... 46 1.8.4. Methods based on the energy approach .................................................... 48 1.9.

Structural characterization ......................................................................... 49

1.10.

General about behaviour factor ................................................................. 50

1.11. Ductility and its types ................................................................................ 52 1.11.1. Achieving global ductility ........................................................................ 53 2.

STATE OF THE ART ........................................................................................ 55

2.1. General ..................................................................................................... 55 2.1.1. Capacity design and SCWB .......................................................................... 55 2.1.2. Response modification factor, behaviour factor and overstrength factor .. 56 2.1.3. Seismic code comparisons ........................................................................... 57 2.1.4. Frame performance, non‐linear analysis, configurations and stiffness ...... 58 2.1.5. NEHRP Provisions on overstrength factor ................................................... 59 2.1.6. Ductility reduction factor ............................................................................ 60 2.1.7. Previous Studies on ductility factors ........................................................... 62 2.1.8. Redundancy factor ...................................................................................... 63 2.1.9. Previous studies on redundancy factor ....................................................... 64 2.1.10. NEHRP provisions on redundancy factor ................................................ 65 3. 3.1.

INFLUENCE OF CONNECTIONS IN MOMENT RESISTING STEEL FRAMES ....... 66 Introduction .............................................................................................. 66


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3.2.

Design approach ........................................................................................ 67

3.3. Requairments for structural behaviour ...................................................... 71 3.3.1. Strength ....................................................................................................... 72 3.3.2. Stiffness ....................................................................................................... 73 3.3.3. Deformation Capacity .................................................................................. 73 3.4.

Frame classification ................................................................................... 73

3.5.

Classification of joints ................................................................................ 75

3.6.

Frame verrsus connection behaviour ......................................................... 81

3.7.

Analysed substructure ............................................................................... 84

3.8.

Classfication as a basis for design ............................................................... 85

3.9. Strength design of connections .................................................................. 89 3.9.1. Calculation of Bolt Tension .......................................................................... 90 3.9.2. The Equivalent T‐stub concept .................................................................... 90 3.9.3. Multiple Bolt Rows ...................................................................................... 91 3.10.

Partial Strength Connections for Semi‐Continuous Framing ........................ 92

3.11. Plastic and elastic global analysis ............................................................... 93 3.11.1. What makes a connection suitable? ....................................................... 94 3.12.

Types of connections ................................................................................. 95

3.13.

T‐stub connections in steel ........................................................................ 97

3.14. EC3 approach for T‐stub connections ......................................................... 98 3.14.1. Failure mechanisms ................................................................................ 98 3.14.2. Effective length ....................................................................................... 99 3.15. Description and calibration of the model ................................................. 101 3.15.1. General ................................................................................................. 101 3.15.2. Modelling .............................................................................................. 102 3.16.

Numerical vs. experimental results .......................................................... 105


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3.17. Parametric analysis .................................................................................. 106 3.17.1. General ................................................................................................. 106 3.18.

Numerical results ..................................................................................... 108

3.19.

Numerical versus Eurocode 3 results ........................................................ 113

3.20.

Aluminium T‐stub connections ................................................................. 119

3.21.

Failure mechanisms (EC9 k‐method) ......................................................... 120

3.22. Description and calibration of the model ................................................. 122 3.22.1. General ................................................................................................. 122 3.22.2. Modelling .............................................................................................. 123 3.22.3. FEM sensitivity analysis ........................................................................ 125 3.23.

Numerical vs. experimental results .......................................................... 127

3.24. Parametric analysis .................................................................................. 129 3.24.1. General ................................................................................................. 129 3.24.2. Numerical results .................................................................................. 131 3.25. Comparison with Eurocode 9 results ........................................................ 133 3.25.1. Effective length evaluation for aluminium T‐stubs ............................... 137 3.26. 4. 4.1.

Conclusions ............................................................................................. 140 MAIN FEATURES OF THE U.S. CODES AND EUROCODES............................. 143 HISTORY of the codes ................................................................................. 143

4.2. Codes in the United States of America ..................................................... 144 4.2.1. Seismological considerations ..................................................................... 144 4.2.2. Evolution of code ....................................................................................... 145 4.2.3. Main code specifications ........................................................................... 146 4.3. History of main building codes in United States ........................................ 148 4.3.1. IBC and ASCE 7 provisions ......................................................................... 150 4.3.2. Seismic design prior to the blue book ....................................................... 150 4.3.2.1. Standards from ANSI and ASCE ........................................................ 150


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4.3.2.2.

The 2005 AISC specification ............................................................. 150

4.4. Codes in Europe ....................................................................................... 151 4.4.1. Seismological considerations ..................................................................... 151 4.4.2. Evolution of code ....................................................................................... 152 4.4.3. Main code specifications ........................................................................... 153 4.5.

Eurocode 8 and AISC seismic provisions ................................................... 153

4.6. EUROCODE 3 and AISC LRFD approach ........................................................ 154 4.6.1. European and American structural shapes................................................ 154 4.6.1. Material ..................................................................................................... 155 4.7. Synopsis of European and American codes ............................................... 156 4.7.1. General ...................................................................................................... 156 4.7.2. Synoptic tables .......................................................................................... 156 4.7.3. Material overstrength in the two codes .................................................... 162 4.7.4. Behaviour and response modification factor ............................................ 163 4.7.5. Cross section limitations ............................................................................ 165 4.8.

Capacity design rules ............................................................................... 168

4.9. Capacity design rules for MRFs ................................................................. 169 4.9.1. Structural overstrength for MRFs .............................................................. 171 4.9.1.1. Strong column weak beam concept in MRFs ................................... 173 4.9.1.2. MRF beam to column joints ............................................................. 175 4.9.2. ASCE 7‐10 Capacity Design Provisions ....................................................... 176 4.9.3. AISC Capacity Design Provisions ................................................................ 177 4.10. Desing rules: Synopsis (EC8 vs. AISC/ASCE) ............................................... 179 4.10.1. High ductility: DCH vs. SMF ................................................................... 179 4.10.2. Medium ductility: DCM vs. IMF ............................................................ 180 4.10.3. Low ductility: DCL vs. OMF ................................................................... 183 4.10.4. Elastic analysis ...................................................................................... 185 4.11. Modelling for Analysis ............................................................................. 186 4.11.1. Classification of frame response ........................................................... 186 4.11.1.1. Frame Mechanisms .......................................................................... 186 4.12.

Deformability requirements ..................................................................... 187


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4.12.1. 4.12.2. 5.

Criteria for P‐Delta effects .................................................................... 187 Inter‐story drift criteria ......................................................................... 189

STRUCTURAL ANALYSIS OF FRAMES ........................................................... 191

5.1. General ................................................................................................... 191 5.1.1. Representation of response spectra ......................................................... 191 5.1.2. Influence of different factors on spectra ................................................... 192 5.1.2.1. Structural damping .......................................................................... 192 5.1.2.2. Earthquake types ............................................................................. 192 5.1.2.3. Effects of soil conditions .................................................................. 193 5.1.3. Representation of seismic action .............................................................. 195 5.1.4. Basic principles of conceptual design ........................................................ 196 5.1.5. Importance classes and importance factors .............................................. 199 5.2. Structural analysis ................................................................................... 199 5.2.1. Modelling ................................................................................................... 199 5.2.2. Accidental torsional effects ....................................................................... 200 5.2.3. Torsional effects ........................................................................................ 200 5.2.4. Combination of the effects of the components of the seismic action ...... 201 5.2.4.1. Horizontal components of the seismic action .................................. 201 5.2.4.2. Load combination procedures used in MRS analysis ....................... 202 5.2.4.3. Accidental Torsion ............................................................................ 204 5.2.4.4. Orthogonal Load Effects ................................................................... 204 5.2.4.5. Vertical component of the seismic action........................................ 205 5.3. Seismic analysis procedures ..................................................................... 205 5.3.1. Main Characteristics .................................................................................. 205 5.3.2. Methods of Analysis .................................................................................. 206 5.3.3. Equivalent Static Analysis .......................................................................... 208 5.3.4. Response spectrum analysis: modal response method ............................ 208 5.3.5. Non‐linear static analysis: push‐over method ........................................... 209 5.3.5.1. Traditional push‐over procedure ..................................................... 210 5.3.5.2. Multimode load pattern of pushover procedure. ............................ 212 5.3.6. Non‐linear dynamic earthquake analysis .................................................. 214 6. 6.1.

RESEARCH MOTIVATION ............................................................................. 219 Need of research ..................................................................................... 219


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6.1.1. 6.1.2. 6.1.3. 6.1.4. 6.1.5. 6.1.6. 7.

General ...................................................................................................... 219 Outcomes on the comparisons of European and American code ............. 219 Overstrength factor ................................................................................... 229 Behaviour factor ........................................................................................ 229 Drift limitations .......................................................................................... 229 General remarks on overstrength ............................................................. 230

BUILDING CASE STUDIES ............................................................................. 233

7.1.

General ................................................................................................... 233

7.2.

Building description ................................................................................. 233

7.3. Analysed cases and results ....................................................................... 237 7.3.1. General ...................................................................................................... 237 7.3.2. Outcomes from the analysed cases ........................................................... 237 7.4. 8.

Vertical Loads acting on frames................................................................ 243 DESIGN CRITERIA AND DESIGN RESULTS .................................................... 244

8.1.

Design criteria ......................................................................................... 244

8.2.

Profile properties ..................................................................................... 245

8.3. Nomenclature of frame members ............................................................ 245 8.3.1. Beams profile matrix for combination 1 .................................................... 248 8.3.2. Columns profile matrix for combination 1 ................................................ 250 8.3.3. Beams profile matrix for combination 2 .................................................... 252 8.3.4. Columns profile matrix for combination 2 ................................................ 254 8.3.5. Beams profile matrix for combination 3 .................................................... 256 8.3.6. Columns profile matrix for combination 3 ................................................ 258 8.3.7. Beams profile matrix for combination 4 .................................................... 261 8.3.8. Columns profile matrix for combination 4 ................................................ 263 8.3.9. Beams profile matrix for combination 5 .................................................... 265 8.3.10. Columns profile matrix for combination 5 ............................................ 267 8.3.11. Beams profile matrix for combination 6 ............................................... 270 8.3.12. Columns profile matrix for combination 6 ............................................ 272 8.3.13. Beams profile matrix for combination 7 ............................................... 274


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8.3.14. 8.3.15. 8.3.16. 8.3.17. 8.3.18. 8.3.19. 8.3.20. 8.3.21. 8.3.22. 8.3.23. 8.3.24. 9.

Columns profile matrix for combination 7 ............................................ 276 Beams profile matrix for combination 8 ............................................... 278 Columns profile matrix for combination 8 ............................................ 280 Beams profile matrix for combination 9 ............................................... 283 Columns profile matrix for combination 9 ............................................ 285 Beams profile matrix for combination 10 ............................................. 287 Columns profile matrix for combination 10 .......................................... 289 Beams profile matrix for combination 11 ............................................. 291 Columns profile matrix for combination 11 .......................................... 293 Beams profile matrix for combination 12 ............................................. 295 Columns profile matrix for combination 12 .......................................... 297

ASSESSMENT OF FRAMES USING PUSHOVER ANALYSIS ............................ 301

9.1.

Non‐Linear static analysis (Pushover analysis) .......................................... 301

9.2.

Process of non‐linear static analysis ......................................................... 302

9.3.

Force deformation relationships .............................................................. 303

9.4. FEMA 356 acceptance criteria .................................................................. 304 9.4.1. Primary and secondary elements and components .................................. 305 9.4.2. Deformation‐controlled and force‐controlled behavior ........................... 306 9.5.

Beam & Column local slenderness and members capacities...................... 309

9.6.

Pushover analysis using FEMA procedure ................................................. 314

9.7.

Nomenclature and indications of the factors ............................................ 317

9.8.

Response parameters of pushover .......................................................... 319

9.9.

Moment resisting Frames ........................................................................ 320

10. OUTCOMES FROM THE ANALYSED FRAMES ............................................... 323 10.1. General ................................................................................................... 323 10.1.1. Basic pushover curves ........................................................................... 323 10.1.2. Pushover curves normalised to Vy : (∆u/∆y) ........................................... 327


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10.1.3. 10.2.

Pushover curves normalised to Vd: (∆u/∆d) ........................................... 331

overstiffness of the analysed frames ........................................................ 335

10.3. overstiffness of the analysed frames ........................................................ 338 10.3.1. Overstiffness for combination 1, 2 and 3 ............................................. 338 10.3.2. Overstiffness for combination 4, 5 and 6 ............................................. 339 10.3.3. Overstiffness for combination 7, 8 and 9 ............................................. 340 10.3.4. Overstiffness for combination 10, 11 and 12 ....................................... 341 10.3.5. General on elaboration of results ......................................................... 342 10.4.

Ductility factor ∆/∆y ............................................................................... 343

10.5.

Reserve overstrength from pushover analysis .......................................... 345

10.6.

Actual behaviour factor (qu,) ................................................................... 347

10.7.

Calculated overstrength (calc) ................................................................. 349

10.8.

Elastic overstrength (E) .......................................................................... 351

10.9.

Redundancy factor () ........................................................................... 353

10.10.

Global overstrength (E,) ................................................................... 355

10.11.

Alpha critical (CR) ............................................................................... 357

10.12.

Fundamental period (T in sec) ............................................................. 359

10.13.

Weight of frames (in kN) ..................................................................... 361

10.14.

Overstriffness (k) .............................................................................. 363

10.15.

Normalised base shear w.r.t weight (Vu/Ns Wt) .................................... 365

10.16.

Damageability ( = VΩ/Velastic) .............................................................. 367

10.17.

Fundamental period Normalised to code period .................................. 369

10.18.

Pushover global overstrengths normalised to the codified overstrength 371


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10.19.

Reserve overstrength from codified formulations (q_code) ................... 373

11. CONCLUSIONS AND OPTIMIZATION RULES ................................................ 375 11.1. Concluding remarks ................................................................................. 375 11.1.1. Behaviour factor of Eurocode: .............................................................. 375 11.1.2. Interstorey drift limitations of Eurocode 8 ........................................... 376 11.1.3. Overstrength factor of Eurocode 8 ....................................................... 377 11.1.4. Fundamental period ............................................................................. 378 11.1.5. Overstiffness ......................................................................................... 378 11.2. Proposed Methodology (Optimization rules) ............................................ 378 11.2.1. Damageability and ductility .................................................................. 378 11.2.2. Ductility classes ..................................................................................... 379 11.2.3. Damage limitation criteria .................................................................... 381 11.3.

Negotiation between damageability and ductility .................................... 381

11.4.

Proposed overstrength factors ................................................................. 384

11.5. Proposed rules ......................................................................................... 385 11.5.1. Steps for applicability of the proposed rules ........................................ 389 Future studies ....................................................................................................... 390 References ........................................................................................................... 391 Appendix A: Notations ........................................................................................ 407 Appendix B: List of Figures .................................................................................. 412 Appendix C: List of Tables ................................................................................... 427 Appendix D: List of Equations ............................................................................. 441 Appendix E: Unit Conversions ............................................................................. 446 Appendix F: Material Constants .......................................................................... 447 Appendix G: American standards steel grades ................................................... 448


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Appendix H: European standards steel grades ................................................... 449 Appendix I: Miscellaneous and Thumb rules ...................................................... 450 Printed and soft copies ....................................................................................... 451 Distribution ......................................................................................................... 452 Author’s vita ......................................................................................................... 453


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Motivation Devastating earthquakes has strong impacts on the society. It is a major natural cause of destruction, associated mainly to the type of material employed in the building construction e.g. stone masonry, etc. Such causes are also due to the adopted seismic load resisting system. In Pakistan, steel buildings with masonry infill has performed splendidly in 1935 Quetta earthquake in the past. The 1935 Quetta earthquake devastated almost whole the city with 30,000 causalities. Presently, the trend of use of steel as building construction material is not common, which might due to the deficiency of domain in such field. Before the independence of Pakistan in 1947 from the British, structures that were designed after the 1931 Earthquake by Eng. Kumar resisted the 1935 Quetta earthquake without damage. These structures had evidenced that with a modest design of steel structures, life safety can be assured in such earthquakes. Therefore, it is promising and true that these structures could be life saviour in future expected large earthquakes; Instead, of such recognition, steel building structures rarely constructed in Pakistan. The current research work is highly motivating because Pakistan is a high seismic zone; the October 2005 earthquake is a clear example. Further, it is believed and recommended by the design community that steel structures perform well in seismic regions, especially moment resisting frames. Therefore, it is of high interest to apply such advance engineering in Pakistan, using the modern building codes approaches. Hence, the presented research activity aims to allow the use of structural steel in the country and give awareness to the interested and involved technicians. Another encouraging motivation is the adoption or the background of official seismic code for steel structures in Pakistan and therefore the possible developments in the presently recommended code. This research work emerged from the study and critics on American codes (AISC/ASCE) and Eurocodes and highlighted the inconsistencies in the two codes in term of philosophical concepts and procedures.


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Thesis organisation The doctorate thesis “Optimum Design of Steel Moment Resisting Frames” composed of 11 chapters, in which as usual Chapter No. 1 is related to introduction and Chapter No. 11 to concluding remarks. Generally, the thesis deals with the wide field of Steel Moment Resisting Frames (SMRF). It starts with the introduction to the steel MRFs in chapter 1, where basic of MRFs are presented including some code philosophy for the use of behaviour factor and overstrength factor. This is followed by Chapter No. 2, in which a brief state of the art is presented. In the state‐of‐art, previous studies dealing with the MRFs are referenced. The issue of connections are addressed in Chapter 3 with special emphasis on T‐stub connections. Chapter No. 4 is interesting where comparison of the most modern codes related to the design of Steel moment resisting frames is presented. Chapter No. 5 deals with the modelling and type of analysis that are prescribed in Eurocode 8. In Chapter No. 6, the critical discrepancies of Eurocode 8 and AISC/ASCE for the design of steel moment resisting frames are addressed. Chapter No. 7, dealt with the case studies that are adopted for the analysis and design of MRFs following Eurocodes. Here useful combinations are adopted such that useful information can be collected, like the effect of overstrength, overstiffness etc. Chapter No. 8, the applied gravity loads are estimated on the frames and the designed profiles are reported. In Chapter No. 9, FEMA procedure for pushover analysis is described in detail, and in Chapter No. 10, all the assessment of the design frames through FEMA acceptance criteria is provided. The results of all 12 combinations from pushover analysis, which comprised of 144 cases, are elaborated carefully in this chapter as well. Chapter No. 11, deals with the conclusions and the thumb rules for the optimization of moment resisting frames. In Chapter No. 1, named as “Introduction and overview on steel moment resisting frames”, presents some the need of steel MRF in seismic zones, some major earthquakes like 1935 Quetta earthquake and 2005 Kashmir earthquakes are also presented. Then some basic philosophical concepts are given. Various conventional seismic resistant steel structural systems that include Moment resisting frames, Eccentric braced frames and Concentric braced frames are illustrated. The advantages of steel MRFs are drawn. The ductility concept is then presented which is the approach of modern building codes. In order to achieve ductility, the overstrength factors i.e. Local overstrength and Global Overstrength are also discussed. The historic review of behaviour factor and the simplified method for the evaluation of behaviour


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factor that’s is for example based on ductility factor theory, or based on extension of the results concerning the dynamic inelastic response of simple degree of freedom systems and which are based on the energy approach are presented and illustrated. Some attention is drawn to the structural characterization and at the end; general remarks are given for behaviour factor (ductility) and its types. Chapter No. 2, named as “State of the art review”, where previous work related to the research on MRFs is described. The most common topic that are important for such lateral load resisting system are Capacity design and SCWB, Response modification factor, behaviour factor and overstrength factor, Seismic code comparisons, connections and panel zone influence, Frame performance, non‐linear analysis, configurations and stiffness, all the related research is discussed in this chapter. In addition, NEHRP Provisions on overstrength factor is provided here. Some concept on the ductility reduction factor and previous studies on ductility factors, redundancy factor, and NEHRP Provisions on redundancy factor are discussed as well. In Chapter No. 3, “Influence of connections in moment resisting steel frames” reported. The classification of joints with respect to strength and stiffness is given. The T‐stub component is examined which represent the most important part in a moment connection. T‐stub behaviour is examined both with steel and aluminium material. Very interesting outcomes are presented when the influence of pitch of bolts and thickness of flange on effective length of T‐stub are examined. Chapter No. 4, is related to “Main features of the U.S. code and Eurocodes”. Therefore brief history of these codes is provided. The progress in seismic design codes and the evolution of seismic code in United States of America and in Europe are mentioned. The seismological considerations, the evolution and the main code specifications are also provided. Some paragraphs on building codes in United States and the current provisions, IBC and ASCE 7 (1998‐2009) and seismic design prior to the blue book (1927‐1959) is illustrated as well. The most interested part of this chapter is the general comparisons on European and American codes, where some synoptic tables are provided for both the codes. The deformability concepts in the two codes are also prescribed in this chapter. Chapter No. 5, “Structural analysis of frames” firstly deals with the seismic actions, response spectra, Representation of seismic action, modelling, accidental torsional effects and combination of the effects of the components of the seismic action. Then seismic analysis procedures and methods of


4


Analysis, for example: equivalent static analysis, response spectrum analysis, non‐linear static analysis (Pushover analysis) and non‐linear dynamic analysis are discussed.

Chapter No. 6, “Research motivation “is related to the previous criticism on the European and American codes, that were carried out previously is described. These are mostly related to the outcomes on the comparisons of European and American code, overstrength factor, behaviour factor and drift limitations Chapter No. 7, “Building case studies” is based on the previous chapter no. 5. In this chapter case study is developed that is based on several combinations, with q =6.5 (combination 1, 2 and 3), q =4.0 (combination 4, 5 and 6), q =3.0 (combination 7, 8 and 9) and q =2.0 (combination 10, 11 and 12). These cases are related to different number of storeys and several numbers of bays. These cases are analysed for all the drift limits as given by EC8. All these combinations give rise to 144 cases. Then the Loading (gravity and imposed) on 5 bay frames, 6 bay frames, 7 bay frames and 9 bay frames are shown. Chapter No. 8, “Design criteria, and design rules” deals the assumed design criteria and the outcomes in terms of design results. All the profiles (Beams and columns) obtained from the design are tabulated in this chapter. Chapter No. 9, “Assessment of frame (Pushover analysis)” deals with the Non‐ linear static analysis (Pushover analysis). The Assessment of frames using FEMA 356 acceptance criteria for Primary and secondary elements and components, deformation‐controlled and force‐controlled behavior are illustrated. Then Beam & Column Members capacities are provided for some European cross sections. Here the Nomenclature and indications of the factors and the response parameters of pushover are provided Chapter No. 10, deals with the results of Pushover analysis of the designed frames. Here the results are elaborated carefully and are presented in the form of tables, graphs and histograms for all the analysed and designed combinations. These contains: ductility factor (∆/∆y), reserve overstrength (q), actual behaviour factor (qu,), calculated overstrength (calc), elastic overstrength (E), Redundancy factor (), Global overstrength (E,) , Alpha critical (CR), fundamental period (T in sec), Weight (in kN), overstiffness (k), normalised base shear w.r.t weight (Vu/Wt), damageability VΩ/Velastic () and fundamental period normalised to code period. For each bay width set of graphs and a set of histograms are provided. Lastly, in” Chapter No. 11 “Conclusions and the optimization rules for optimum


5


design of MRFs”, the general conclusions and the optimization rules are presented.


6


Abstract Previously, Eurocode 8 and American codes were examined with the help of several case studies using short and long span moment resisting frames. The influences of the capacity design rules of the two codes are examined. Based on the observations, the current thesis deals with the diagnosis of the discrepancies presented in the design procedure of Eurocode 8, in order to optimally design steel moment resisting frames. Hence a parametric study is developed that deals with the seismic design of perimeter steel moment resisting frames of 9, 7 and 5 storeys with several span lengths (9.15m, 7.63m, 6.54m and 5.08m) designed according to Eurocode 8. Total 144 cases of steel moment resisting frames are managed; these are initially design using Ductility Class High (DCH) with behaviour factor of 6.5 and Ductility Class Medium (DCM) with behaviour factor of 4.0. These frames are also designed for DCL with behaviour factor of 2.0 according to EC3 where capacity design rules are eliminated and, further an additional case has been examined in order to examine the optimum design also compatible with the all Eurocode 8 recommended drift limitations, it is comprised of q equals 3.0. The designed frames therefore make able to shed light on the drift limitations of Eurocode 8. The results and the outcomes are elaborated carefully and the pros and cons of the design criteria and the influence of drift criteria on the capacity design rules of Eurocode 8 for the designed frames are analysed and criticised. In order to see the differences in design of the adopted ductility classes, the base shear are normalised with respect to the weight of each frame. The frame performances are measured in terms of overstrength and redundancy factors, strength demand to capacity, drift demand to capacity ratios and normalised base shear with respect to the weight of the frame thus allowing interesting conclusions to be drawn. The conclusion is followed by optimisation rules, where thumb rules are provided in order to optimally use the code behaviour factor with a defined drift limit. The influence of connections in Moment resisting frames is highlighted as well with specific emphasises on T‐stub connections. Parametric analysis are performed both for steel and aluminium T‐stub connections and the influence of different geometric parameters are investigated to examine the ultimate strength of T‐stub connections and the corresponding effective length.


7


Highlights o

Introduction to Moment resisting frames is addressed

o

State of the art of the related topics is written

o

Connection of moment resisting frames are highlighted with special emphasis on T‐stub connections in metal structures

o

Comparison of the most modern seismic codes is US and UE is drawn

o

Case studies (144 moment resisting frames) are analysed and designed

o

FEMA pushover procedure is described

o

All the cases are analysed through the use of Pushover analysis

o

Results are carefully elaborated in term of various outcomes

o

Conclusions is drawn for various parameters that includes, drift limits, overstrength factors and behaviour factor in Eurocode 8

o

Design optimization rules are presented for the optimum use of code limits

University “G. d'Annunzio” of Chieti‐ Pescara Ph.D. thesis titled “Optimum design of steel moment resisting frames” by Tayyab Naqash

Keywords Seismic codes, Moment resisting steel frames, Seismic resistance, Pushover analysis, Drift limitations, Behavioural factor, Ductility classes, Overstrength, Ductility class, Optimization rules, Connections in MRFs, T‐stub,

8


9


Publications and reports

[1].

M. T. Naqash, G. De Matteis, and A. De Luca, 2012, Critical overview on the seismic design of steel Moment Resisting Frames, In 45th IEP convention, Karachi.

[2].

G. De Matteis, M. T. Naqash, G. Brando,. 2012, Effective length of aluminium T‐stub connections by parametric analysis. Engineering Structures, 2012. 41: p. 548‐561.

[3].

M. T. Naqash, G. De Matteis, and A. De Luca, 2012, Seismic design of Steel Moment Resisting frames‐European versus American Practice. In NED University Journal of Research, Thematic Issue on Earthquake, 2012.

[4].

M. T. Naqash, G. De Matteis, and A. De Luca, .2012, Effect of Capacity design rules on the performance of Moment resisting frame in 15th World Conference on Earthquake Engineering, September 2012, Lisbon, Portugal.

[5].

M. T. Naqash, January 2012, Second year annual defence report on a): T‐stub connections, Parametric analysis for the evaluation of effective width b): Seismic design of steel Moment resisting frames (MRFs): European Versus American Practices.

[6].

M. T. Naqash, 2012, Research project in RELUIS 2010‐13, Technical report, “Optimum design of Moment Resisting Steel Frames according to Eurocode 8, Under (Riferimento codice selezione 84/2012‐ Dipartimento Ingegneria e Geotecnologie).

[7].

G. De Matteis, M. T. Naqash, G. Brando,. 2011, Parametric Analysis of Welded Aluminium T‐Stub Connections, in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil‐Comp Press, Stirlingshire, UK, Paper 162, 2011. doi:10.4203/ccp.96.162.


10


[8].

G. De Matteis, M.T. Naqash, G. Brando, 2011, Aluminium T‐stub connections: additional parametric analysis for the evaluation of effective width, in XXIII Italian steel conference. 2011. Lacco Ameno, Ischia, Naples.

[9].

M. T. Naqash, G. De Matteis, A. De Luca, 2011, European versus American practice for seismic design of steel moment resisting frames (MRFS), in XXIII Italian steel conference. 2011. Lacco Ameno, Ischia, Naples.

[10].

M. T. Naqash, January 2011, First year annual defence report on a): The influence of joints on metal structures b): Investigation and comparison of the Design methodologies for steel lateral load resisting structures following AISC and Eurocode approaches c): Interpretation of Aluminium Beam to Column Joint behaviour considering EC3 provisions.

[11]. M. T. Naqash, December 2010, annual report on Influence of Connections

on metal Moment Resisting Frames resisting frames following Eurocodes and American codes provisions Assegni Regionali per Attivita Di Ricerca E Tecnico‐Scientifiche (Re.C.O.Te.S.S.C.). Research activity financed by Re.C.O.Te.S.S.C. [12]. M. T. Naqash, 2009, Atelier 1 report “Design of Industrial building”, in II Level Master “Design of Steel Structures”, University of Naples “Federico II”, Naples. [13]. M. T. Naqash, 2009, Atelier 2 report “Design of multi‐storey building”, in II Level Master “Design of Steel Structures”, University of Naples “Federico II”, Naples. [14]. M. T. Naqash, G. De Matteis, and A. De Luca, 2012, Seismic design of steel Moment Resisting Frames according to seismic codes, IN REVIEW. [15]. M. T. Naqash, G. De Matteis, and A. De Luca, 2012, Optimum seismic design of steel moment resisting frames: negotiation between ductility and damageability, IN REVIEW

1.

CHAPTER

1

INTRODUCTION AND OVERVIEW ON STEEL MOMENT RESISTING FRAMES 1.1. GENERAL Pakistan is situated in a seismic‐prone zone and merely the past Earthquakes demonstrates its impact. The Pakistan‐Kashmir earthquake “magnitude 7.6” occurred on 8th October 2005 at the foothills of the Himalayas had been a devastating earthquake that took a heavy toll of more than 80,000 people. It is believed that, Muzaffarabad, Balakot and Bagh districts of Kashmir are underdeveloped are as therefore, the range of destruction in such regions is logical, but it was quite alarming and unimaginable to see the collapse of Margalla Tower (as evident from Figure 1) in the federal capital Islamabad; a modern city with newly constructed infrastructure. In order to prevent such disasters in future (remedy measure apart from the quality of construction with different methods and materials of construction) special techniques should be adopted. The use of ductile material such as steel might be very effective in such seismic zones if employed for conventional seismic load resisting systems, such as moment resisting steel frames.


12


Figure 1: Site of the Margalla Towers in Islamabad collapsed during the 2005 earthquake

Italy duly devotes energy and resources to the study of seismicity and seismic hazard as it is a high‐seismic Country. The seismic zones in Italy are shown in Figure 2 [1, 2]. Although not Like Pakistan, being a developed country but still Italy's worst earthquake in 30 years hit Abruzzo’s rough mountains at mid night, killed more than 150 people, and demolished exceptional ancient buildings (most of them are churches). More than 50,000 people were homeless in L’Aquila, 70 miles east of Rome. Since, the use of structural steel for building construction is not so common in Italy; therefore, it would be interesting and therefore fruitful to increase the trend of construction of building with structural steel. In the late 19th and early 20th centuries, engineers have accepted that steel structures have performed extremely well compared with structures constructed of other types of construction materials. Numerous factors have contributed to the growth of this market, and in the World, generally favourable performance of steel buildings in earthquakes prior to 1994, no doubt, played a significant role.

Chapter No. 1: Introduction and overview on seel moment resisting frames


13


Figure 2: Seismic zoning map of Italy

Specifically, four huge earthquakes in California and Japan (San Francisco, Kanto, Santa Barbara and Long Beach) gave engineers confidence in steel as a reliable material for seismic resistant design being steel a strong, lightweight, tough and ductile material. Consequently, it is capable to dissipate a huge amount of energy due to its high ductility, representing itself as an ideal material for using as a building material in seismic zones. During the aforementioned four seismic events, compared with other building material like concrete and masonry buildings of similar size and scale, fewer problems and less unreliable mechanisms were observed in steel structures [3, 4]. The concept of building steel structures to resist seismic events in the high seismic zones of Pakistan is very poor and most of the buildings are made of concrete and masonry. The presented research work would be valuable for the Country where few numbers of experts are working on steel structures and its Chapter No. 1: Introduction and overview on seel moment resisting frames


14


design. The importance of building standards to be used in the seismic zones of Pakistan can also be highlighted and the confidence level of the designers for the use of code adopted as the national code of the country might be increased due to the deep understanding and critics of the codes (European and American).

1.1.1. Major earthquakes in Pakistan The major earthquakes that occurred in Pakistan are mentioned below: o

In 1935 at 05 30 ‐ Quetta, Pakistan ‐ M 7.5 Fatalities 30,000

o

In 1945 at 11 27 ‐ Makran Coast, Pakistan ‐ M 8.0 Fatalities 4,000

o

In 1974 at 12 28 ‐ Northern Pakistan ‐ M 6.2 Fatalities 5,300

o

In 2005 at 10 08 – Kashmir Pakistan ‐ M 7.6 Fatalities 86,000

o

In 2008 at 10 28 ‐ Pakistan ‐ M 6.4 Fatalities 166

o

In 2011 at 01 18 ‐ Pakistan ‐ M 7.2 Fatalities 3

In the following, only the 1935 Quetta earthquake and the 2005 Kashmir earthquake are mentioned. These two earthquakes are the most devastating among all in term of the death toll, damages and collapse of structures. In general steel buildings are normally not constructed in Pakistan, although the huge earthquake that occurred in the City of Quetta (Capital of Baluchistan province) on May 31 1935 at local time 3:03AM [5‐7], some pictures demonstrated the behaviour and the response of steel structures. This earthquake had a magnitude of about 7.7, at a depth about couple of kilometres, with shaking caused by the earthquake lasted for about 120 sec. Devastating Earthquakes has strong impacts on the society, which is due to the main cause of construction material, e.g. stone, masonry or concrete buildings, etc. In Pakistan, steel buildings with masonry infill have performed better in the 1935 Quetta earthquake, which devastated almost whole city of Quetta. These building proved that even a modest design of steel structures saved lives in such earthquakes, which proves that these structures could be life saviour in future expected large earthquakes, nevertheless steel buildings rarely constructed despite of their excellent performance [8].



15


Figure 3: Some undamaged steel structures in 1935 Quetta Earthquake

Structures designed following the recommendation of Kumar withstood the 1935 Quetta earthquake without damage (see Figure 3). The structure form consisted of iron–rail frame provided with fired brick masonry infill in cement mortar, roof steel truss, and CI‐sheet roofing [7, 9, 10]. The earthquake of 1931 in Mach and 1935 in Quetta demonstrated an interesting development in the history of earthquake engineering in India (currently Pakistan). The earthquake of August 1931 in Mach in Baluchistan the largest of which was over magnitude 7 is of interest here. In this earthquake, the most highly engineered construction in the region and the railroad system had significant damage. After this earthquake Kumar, a young engineer working for the railroad was tasked for designing new earthquake resistant quarters (dwellings) for displaced railroad employees. In 1933, Kumar published some recommendations on earthquake resistant constructions which included seismic zonation map of India and a variation in seismic ratio from 5% to 15%, depending on both the seismic zone and the importance of the structure [10]. As mentioned by Reitherman [10‐12], Kumar was aware of the earlier work in Japan on the seismic ratio method, illustrating how influential that work was elsewhere. Reminiscent of the preference of Naito for steel‐reinforced‐ concrete was Kumar’s advocacy of a steel frame embedded in concrete or in masonry to reduce the cost. Actually, his first design incorporated iron rather than steel frames, because he used iron rails that were available within the railroad system at a time when steel rails were being phased in. Kumar devised connection details to use the rails for columns, beams, and roof truss members. Two other aspects of this account of early Indian earthquake engineering are similar to the story of Tachu Naito and the 1923 Kanto Earthquake. Kumar did not only design buildings with a particular seismic design method and lay out, the theory of his approach was published prior to 6 earthquakes, in addition Kumar’s buildings were soon tested by a major earthquake in 1935.



16


Figure 4: Structural damages of buildings caused by 1935 Quetta earthquake, built from material other than steel

In the magnitude 8 Quetta Earthquake on May 30, 1935 was a huge disaster that killed 30,000 people nevertheless Kumar’s buildings performed very well compared to the others in the vicinity which were badly damaged or collapsed. In India, the 1935 Quetta Earthquake marks the start of the first seismic regulations in the building code, an effect comparable to that of the Hawke’s Chapter No. 1: Introduction and overview on seel moment resisting frames


17


Bay Earthquake on construction standards in New Zealand. Figure 4, shows some damaged structures after 1935 Quetta earthquake, these were constructed from material other than steel. It included out–of–plane failure of walls in vertical bending and at building corners, complete collapse of structures, out–of–plane failure of structural and non–structural elements at the upper floors most probably due to structure and floor amplified ground motions.

1.1.2. Seismic zonation of Pakistan Since Pakistan is a developing Country, therefore the past quakes strongly influence the infrastructure in the corresponding areas and cause huge number of casualties and high damage to the building structures in particular, and to highways and transportation in general. Building Code of Pakistan (BCP) with the aid of “UBC‐97” [13]; is the recommend reference code adopted in the country which is recommended by Earthquake Reconstruction and Rehabilitation Authority [14] for the design of structures. The five seismic zones as shown in Figure 5 are adopted by BCP, mentioned in Table 1.

Figure 5: Seismic zoning map of Pakistan Chapter No. 1: Introduction and overview on seel moment resisting frames


18


Table 1: Seismic zonation in Pakistan S. No 1 2 3 4 5

Seismic zone 1 2A 2B 3 4

Horizontal Peak Ground Acceleration 0.05 to 0.08g 0.08 to 0.16g 0.16 to 0.24g 0.24 to 0.32g >0.32g

Damage cost Low Negligible Low Minor Medium Moderate Moderate Large Sever High Sever Collapse Huge

Hazard

Damage

NOTE: Where “g” is the acceleration due to gravity. The acceleration values are for Medium hard rock (SB) site condition with shear wave velocity (vs) of 760 m/sec.

1.1.

STEEL IN SEISMIC ZONES 1.1.1. General

In many ways structural steel represent itself as an ideal material for the design of earthquake‐resistant structures. It has distinct capabilities compared to other construction materials such as reinforced and pre‐stressed concrete, timber, brickwork etc. It is strong, lightweight, ductile, and tough, capable of dissipating extensive amount of energy through yielding when stressed into the inelastic range. Given the seismic design philosophy of present building codes, which is to rely on the inherent capability of structures to undergo inelastic deformation without failure, these are exactly the properties desired for seismic resistance [15]. Steel is a mixture of iron and carbon, with trace amounts of other elements, that includes primarily manganese, phosphorus, sulphur, and silicon. It is differentiated from the earlier cast and wrought iron by the reduced amounts of carbon relative to other alloys. The reduced amounts of other trace element making steel stronger and more ductile compare to cast and wrought irons, both are considered quite brittle. Compare to steel, as it is a modern material, iron alloys have been in use for centuries. Throughout the relatively brief history of their use, structural steel buildings have been among the best performing structural systems and, prior to January 1994 when previously unanticipated connection failures were discovered in some buildings. Following the Northridge earthquake (M 6.7), many engineers mistakenly regarded such structures as nearly earthquake‐proof. Inspection of steel buildings after the Northridge earthquake revealed the presence of cracks in welded moment frame connections. A year later, the Kobe earthquake (M 6.9) caused collapse of 50 steel buildings, confirming the potential vulnerability of these structures. This experience notwithstanding, structural steel buildings, if properly designed can provide outstanding earthquake performance. To assure good Chapter No. 1: Introduction and overview on seel moment resisting frames


19


behavior of steel structures, it is necessary to: o

Configure the structural steel system so that inelastic behavior is well distributed throughout the structure, rather than concentrated in a few stories or elements

o

Provide columns with sufficient strength to resist earthquake‐induced overturning loads without buckling

o

Provide adequate lateral bracing for flexural members to prevent lateral‐torsional buckling Proportion connections with sufficient strength so that inelastic behavior occurs in the members themselves

o

Select compact sections for those members intended to experience inelastic behavior to avoid local buckling and the rapid loss of strength that accompanies such behavior. In addition as with all structural materials, it is very important to assure that the structures are actually constructed as designed; quality is maintained in fabrication and field welding operations; and that the structure is maintained over its life.

1.1.2. Mechanical properties of structural steel The behavior of steel structures in earthquakes is dependent on key mechanical properties of the steel material, including its strength, ductility, and toughness. The properties of structural steel that are important to seismic performance are o

Yield strength

o

Tensile strength

o

Ductility and

o

Fracture toughness

Each of these properties depends on the metallurgy and thermo mechanical processing history, as well as the load application rate, temperature, and conditions of restraint at the time of load application. The mechanical properties that are important for design are determined from a standard tension test, where a machined specimen having standard cross section is loaded in a Universal Testing Machine (UTM) while load elongation data are recorded. These are then reduced in the form of a stress‐strain curve as shown in Figure 6. The initial straight‐line segment of the stress‐strain curve represents the specimen’s elastic behavior where stress is proportional to Chapter No. 1: Introduction and overview on seel moment resisting frames


20


strain and related by the Young’s Modulus (having value of 200, 000 MPa, or 29,000 ksi). As strain increases, the stress‐strain curve becomes nonlinear and the specimen experiences permanent plastic deformation. Many mild carbon steels exhibit a peak stress immediately after the stress‐ strain curve deviates from linearity, known as the yield point. Immediately after achieving the yield point, the stress dips with increasing strain, and then remains at a constant value, known as the yield strength, for considerable amounts of additional strain. Thereafter, the steel strain hardens with increasing stress until a peak or ultimate tensile strength is attain. With increasing strain beyond the tensile strength, the material exhibits necking and ultimately fractures.

Figure 6: Stress‐strain curve for structural steel: (a) typical and (b) S275 and S355 steel grades

Standard ASTM material specifications include controls on the yield strength or yield point of the material as well as the tensile strength and elongation of the material at fracture. Although yield point is of no engineering significance, ASTM specifications permit mills to report either yield point or yield strength. Therefore, it is possible that some material conforming to the ASTM material specifications will have slightly lower yield stress than the nominal value contained in the specification. More typically, due to variations in the production process, yield and tensile properties will substantially exceed the minimum specified values, sometimes by as much as 40% or more. In general, tensile properties of steel vary with temperature. Tensile data for various steels show that their yield strength and ultimate strength increase by approximately 410 Mpa (60 ksi) when the temperature decreases from 70°F to –320°F [16]. Similarly, when steel is elevated to about 900°F it loses about half of its room temperature strength and modulus of elasticity. However, for the Chapter No. 1: Introduction and overview on seel moment resisting frames


21


range of temperatures of interest for most structures (–60F 5.5 and Ms 4 only class 1 sections Limits λp to λps, i.e. to use class 1 sections are are allowed, for 2 5.5 and ii). Type 2 is for regions having moderate seismicity region with Ms 0.125

  h  E E    1.12 .  2.33  Ca    1.49  for  Ca  0.125 (48)    tw  Fy F y    Where Ca=Pu/(∅b.Py), Pu is the required compressive strength, Py is the axial yeild strength and φb is 0.9, h is the clear distance between flanges, tw is the thickness of web and Fy is the yield stress.

4.8. CAPACITY DESIGN RULES It is established that structures can be designed and constructed so as to satisfy various seismic performance criteria, most importantly that of preventing collapse during an exceptionally large earthquake. For most engineers seismic design is synonymous with the complex analysis of elastic or inelastic dynamic response to random ground excitations. This presentation, reflecting the views of a structural designer, attempts to contrast analysis with design strategies that are suited to overcome difficulties that stem from inevitable uncertainties in the prediction of ground motions. A deterministic design philosophy is advocated whereby the designer can, within certain limits, choose the seismic response of a structure that is safe, rational, predictable, and achievable in construction. The designer may thus enhance desirable, and suppress undesirable features of structural behavior. In this, the vital role of the quality of the design and detailing of critical regions of structural systems is emphasized because this alone can assure the very desirable characteristic of seismic response; tolerance with respect to the inevitable crudeness of predicting earthquake imposed displacements [81]. Capacity Design is a concept or a method of designing flexural capacities of critical member sections of a building structure based on a hypothetical behaviour of the structure in responding to seismic actions. This hypothetical behaviour is reflected by the assumptions that the seismic action is of a static equivalent nature increasing gradually until the structure reaches its state of near collapse and that plastic hinging occurs simultaneously at predetermined locations to form a collapse mechanism simulating ductile behaviour. The actual behaviour of a building structure during a strong earthquake is far from that described above, with seismic actions having a vibratory character and plastic hinging occurring rather randomly. However, by applying the Capacity Design concept in the design of the flexural members of the structure, it is believed that the structure will possess adequate seismic resistance, as has been proven in many strong earthquakes in the past. Therefore, many seismic Chapter No. 4: Main features of the U.S. codes and Eurocodes


169


design codes around the world, adopt the Capacity Design concept as a normative requirement. Most modern building codes employ capacity design principles to help ensure ductile response and energy dissipation capacity in seismic resisting systems. The design provisions are geared toward restricting significant inelastic deformations to those structural components that are designed with sufficient inelastic deformation capacity. Those are generally referred to as deformation‐controlled components. Other structural components, referred to as force‐controlled components, are designed with sufficient strength to remain essentially elastic. Capacity design provisions for force‐controlled components can be further differentiated between those that can be defined solely based on the strength of adjacent members, as the brace and brace connection example above, to those that require information of overall system behavior, such as columns in steel braced frames. The required axial strength for columns in seismic resistant steel frames is based on the load from all yielding members exerting demand on them, including the effects of material overstrength and strain hardening. The here mentioned codes (AISC/ASCE and EC8) are dealt here. Capacity design is an approach used to design structures for seismic resistance in which the strength of the members comprising the seismic load resisting system are proportioned such that inelastic behavior is accommodated in specific designated locations that are adequately detailed to accommodate this behavior. When these elements yield, they limit the force that can be transmitted to other elements, effectively shielding them from overstress and allowing them to resist design earthquake excitation while remaining elastic. This practice permits the elements that are not expected to yield or experience inelastic behavior to be designed and specified without rigorous detailing practices intended to provide ductile behavior. Many of the provisions contained in AISC 341 are intended to produce a capacity design of the seismic load resisting systems. As an example, Special Moment Frames must be proportioned such that inelastic behavior is accommodated through plastic hinging within the spans of the beams in moment frames, rather than the columns. As another example, Special Concentrically Braced Frames must be designed such that the connections and columns are stronger than the braces so that inelastic behavior is accommodated through yielding and buckling of the braces.

4.9. CAPACITY DESIGN RULES FOR MRFS EC8 recommends the capacity design approach for the design of members to have a global ductile behaviour of structure. In case of MRF, the weak beam Chapter No. 4: Main features of the U.S. codes and Eurocodes


170


and strong column concept should be followed. A flowchart for the prescribed design procedure is shown in Figure 102. From the flowchart, it is evident that the design is revised normally due to the re‐evaluation of overstrength factor (Ω) in Eurocode 8 as it is related to the plastic resistance of beams. For the beams of MRF with classes 1 and 2 cross sections, the inequalities, in Equation 49, Equation 50 and Equation 51 should be verified at the location where the formation of hinges is expected: Equation 49: Moment inequality for the design of beams

MEd  1.0 MPl ,Rd

(49)

Equation 50: Axial inequality for the design of beams

NEd  0.15 NPl ,Rd

(50)

Equation 51: Shear inequality for the design of beams

VEd  0.5 VPl ,Rd

(51)

Figure 102: Capacity design flowchart for steel MRFs using Eurocodes process

The columns shall be verified in compression considering the most unfavourable combination of the axial force and bending moments. In the checks, NEd, MEd, VEd should be computed using Equation 52, Equation 53 and Equation 54, respectively: Equation 52: Internal axial load combination for the design of columns

NEd  NEd ,G  1.1   Ov  Ω  NEd ,E

(52)

Equation 53: Internal moment combination for the design of columns

MEd  MEd ,G  1.1   Ov  Ω  MEd ,E

Chapter No. 4: Main features of the U.S. codes and Eurocodes

(53)


171


Equation 54: Internal shear load combination for the design of columns

VEd  VEd ,G  1.1   Ov  Ω VEd ,E

(54) The column shear force VEd resulting from the structural analysis should satisfy the following expression: VEd / Vpl, Rd ≤ 0.5. Being VEd =VEd, G +VEd, M ; NEd is the design axial force; (gravity +seismic), MEd is the design bending moment; VEd is the design shear; (gravity +seismic), Npl, Rd, Mpl, Rd, Vpl, Rd are design resistances in accordance with EC3, VEd, G is the design value of the shear force due to the non‐seismic actions (gravity only), VEd,M is the design value of the shear force due to the application of the plastic moments Mpl,Rd,A and Mpl,Rd,B with opposite signs at the end sections A and B of the beam. AISC suggests the use of load combinations for the design of members for the corresponding applicable building code used for the load definition, for ASCE to be an applicable building code the load combination as defined in section 3 of the current paper should be used. AISC “Seismic provisions” provides strength checks for members that should be fulfilled with the load combinations where overstrength factor is used for the capacity design criteria. A flowchart for the design procedure using AISC/ASCE is shown in Figure 103. The main difference in the flowchart using Eurocodes and American practices is the overpassing of the iteration for overstrength in the case of AISC/ASCE.

Figure 103: Capacity design flowchart for steel MRFs using AISC/ASCE process

4.9.1. Structural overstrength for MRFs Overstrength factor (reserve strength) is the ratio of “apparent strength” to the “design member strength”. The Ω factor is required to achieve the capacity design approach where a hierarchy is defined such that the ductile elements yield before other primary elements. In order to have a ductile behaviour of Chapter No. 4: Main features of the U.S. codes and Eurocodes


172


structure both ASCE and EC8 suggest the use of capacity design criteria (illustrated in section 6 of the current paper) which accounts in amplifying the seismic forces of some element by system overstrength factor (Ω). The overstrength factor has strong influence on the dimensions of member size and thus on the economy of the structure itself. A high value of Ω could cause oversizing of the members whereas smaller value of Ω could cause unexpected failure mechanisms. In EC8, Ω can be calculated as shown in Table 22. Table 22: Overstrength factors according to Eurocode 8 Seismic load resisting system All moment‐frame systems Concentrically Braced Frames (CBF) Eccentrically Braced Frames short links (EBF) Eccentrically Braced Frames intermediate and long links (EBF)

(Ω) Mpl,Rd,i/MEd,i 2 Npl,Rd, i/NEd,i 3 1.5Vp,link,i /VEd,i 4 1.5Mp,link,i/MEd,i 1

1

MEd, i is the design value of the bending moment in beam i in the seismic design situation and Mpl,Rd,i.is the corresponding plastic moment.

2

Npl, Rd, i is the design resistance of diagonal i; NEd,i is the design value of the axial force in the same diagonal i in the seismic design situation.

3

VEd, i, MEd,i are the design values of the shear force and of the bending moment in link i in the seismic design situation. 4

Vp, link, i, Mp, link, i are the shear and bending plastic design resistances of link i.

For any of the seismic load resisting system minimum value of Ω should be utilized in the calculation. Since, in Eurocode 8 minimum value of Ω has to be used in the capacity design, therefore the overall structural behaviour corresponds to the development of first plastic hinge in the beams and thus due to the redistribution of forces, columns will be subjected to higher forces and this could cause the formation of plastic hinges. On the contrary, maximum Ω will provide anticipated failures of beams than columns, but also will oversize the dimensions of the members and will lead to an uneconomical design. A modified value of Ω as shown in Equation 55 is suggested by (Elghazouli et al, 2010) [101], Equation 55: Modified overstrength factor suggested by Elghazouli et al

mod ,i 

Mpl ,Rd ,i  MEd ,G ,i MEd ,E ,i



Mpl ,Rd ,i  MEd ,G ,i MEd ,i  MEd ,G ,i

(55)

In modified Ω, bending moment due to reduced gravity forces are subtracted from both Mpl, Rd,i and MEd,i , which cause an increase in the code specified Ω. The value of Ω needs a more detailed study in order to assure a global ductile Chapter No. 4: Main features of the U.S. codes and Eurocodes


173


mechanism of the structure and not only on the first formation of plastic hinges in the beam. According to AISC the following overstrength values should be used as shown in Table 23, Table 23: Overstrength factors according to AISC/ASCE Seismic load resisting system All moment‐frame systems Eccentrically Braced Frames (EBF) All other systems

4.9.1.1.

(Ωo) 3.0 2.5 2.0

Strong column weak beam concept in MRFs

For global ductility, columns must be stronger than beams therefore EC8 suggests that the condition in Equation 56 must be satisfied at all seismic beam to column joints: Equation 56: Global ductility check for SCWB criteria in Eurocode 8

MRc  1.3 MRb

(56)

Where ΣMRc and MRb is the sum of the design values of the moments of resistance framing the joint of the columns and beams respectively. The factor 1.3 takes into account the strain hardening and the material overstrength could be the multiplication of 1.1 γov and generally is taken as 1.3.

Figure 104: Capacity design approach, (a) Strong‐column‐weak‐beam good ductility and (b) Weak column strong beam‐poor ductility

In AISC Equation 57 need to be satisfied in the case of SMF at the column beam connections, Chapter No. 4: Main features of the U.S. codes and Eurocodes


174


Equation 57: Global ductility check for SCWB criteria in AISC

M*pc  1.0 M*bc

(57)

Where ΣM*pc is the sum of the moments in the column above and below the joint at the intersection of the beam and column centrelines and is calculated from Equation 58. Equation 58: Definition of sum of the moments in the column



P 



g

M*pc  Zc  Fyc  Auc 

(58)



ΣM*Pb is the sum of the moments in the beams at the intersection of the beam and column centrelines. Equation 59: definition of sum of the moments in the beams

M * pb   1.1Ry Fyb ZRBC  Muv 

(59)

Zc and ZRBS is the plastic section modulus of column and minimum plastic modulus at reduced beam section respectively Fyb and Fyc are the specified minimum yeild stress of beam and column respectively, Ry is the ratio of expected yeild stress to specified minimum yeild stress Puc is the required compressive strength using LRFD load combinations Muv is the additional moment due to shear amplification It is evident from Equation 59, where plastic moment of beam is amplified by a factor 1.1Ry which resembles Equation 56 as suggested by EC8. The value of Ry ranges from 1.1 to 1.5



175


(a)

(b)

Figure 105: Reduce beam section, (a) real example, and (b) sketch

4.9.1.2.

MRF beam to column joints

The beams to column joints of MRFs are generally full strength and rigid in order to resist the seismic forces and are therefore required to possess high strength with respect to the connected members such that the formation of the plastic hinge form in the beam rather than in the connection itself. The basic design criterion is based on the assumption that the joint should not be the dissipative component of a ductile frame. Local failure occurs in the steel frame when the rotation capacity of a beam exceeds a limit that cause local buckling of the cross section. For the use of beams end to be the dissipative zones beam‐to‐column connections should be designed for the required degree of overstrength taking into account the moment of resistance and the shear‐force of the connected beam. Eurocode 8 allows using dissipative semi‐rigid and/or partial strength connections if all of the following requirements are verified: a) The connections have a rotation capacity consistent with the global deformations; b) Members framing into the connections are demonstrated to be stable at the ultimate limit state (ULS); c) The effect of connection deformation on global drift is taken into account using nonlinear static (pushover) global analysis or non‐linear time history analysis.



176


The connection design should be such that the rotation capacity of the plastic hinge region θp is not less than 35mrad for structures of DCH and 25mrad for structures of DCM with q > 2. The rotation θp is defined as θp = δ / 0.5L and is shown in Figure 106. Where δ is the beam deflection at midspan, L is the beam span.

  L

Hinge

d

Hinge

L/2

L/2

Figure 106: Rotation capacity of connection

In AISC, the prescribed three frame types SMF, IMF and OMF offer three different levels of expected seismic inelastic rotation capability. SMF and IMF are designed to accommodate approximately 0.03 and 0.01 radian, respectively. OMFs are designed to remain essentially elastic and are assumed to have only very small inelastic demands. It is assumed that the elastic drift of typical MRFs is usually in the range of 0.01 radians and that the inelastic rotation of the beams is approximately equal to the inelastic drift. SMF, IMF and OMF are assumed to accommodate total interstorey drifts in the range of 0.04, 0.02 and 0.01 radian, respectively.

4.9.2. ASCE 7‐10 Capacity Design Provisions ASCE 7‐10 specifies the minimum design loads for seismic force resistant systems. To ensure economical design as well as ductile response and energy dissipation during seismic events, the elastic seismic forces (Veu) are reduced with the seismic response modification factor, R. The seismic force resistant system is then designed using the reduced forces, the seismic design forces (Vd), with the implication that inelastic deformations in components will occur under large ground motions. Selected components within the seismic force resistant systems are then designed based on the reduced forces (Vd) and therefore designed to deform in elastically. These components have been Chapter No. 4: Main features of the U.S. codes and Eurocodes


177


proven capable of significant inelastic deformation capacity and are referred to as deformation‐controlled components. Other components, i.e. the force‐ controlled components, are designed to remain elastic. To help ensure this desired behavior, the seismic design forces are multiplied by an overstrength factor, i.e. the Ω0 factor. Ω0 approximates the characteristic overstrength in seismic force resistant systems above the design strength (Vu) and by multiplying the seismic design force by Ω0, the maximum forces that the force‐ controlled components are likely to experience are approximated. Note that the term Ω0 applies to the overstrength factor for a class of structures, whereas Ω is the overstrength factor for a specific structure, as might be measured using a static pushover analysis. Figure 21 shows an inelastic force deformation curve where the aforementioned variables, Veu, Vd, Vu, R and Ω are shown. Ω0 is therefore meant capture the expected capacity of deformation‐controlled components and so the increased loads on force controlled members above the seismic design loads. The overstrength reflected by Ω0 arises due to the difference between member designs strengths and expected strengths (i.e., Rn versus Rexp) conservative biases in nominal strength equations, member overstrength due to drift limits and discrete member sizing, as well as the system’s redundancy and inelastic force re‐distribution. ASCE 7‐10 [39] limits the seismic design loads on force controlled components to not exceed the forces that can be delivered to them by yielding of deformation‐controlled components in the structure, using expected material properties and excluding resistance factors.

4.9.3. AISC Capacity Design Provisions The design requirements in the 2010 AISC Seismic Provisions generally follow the format of the AISC Specification [39] where the design strengths (resistance factor multiplied by the nominal resistance) of members or components should equal or exceed the required strengths. For force‐ controlled components proportioned following capacity design principles, the required strengths are generally based on capacities of deformation‐controlled components, which are adjusted to account for material overstrength, strain hardening, and other factors that increase strengths beyond their nominal values. The following is a summary of factors considered in the required design strength calculations: a) Expected versus Nominal Steel Yield Strength: The Ry accounts for the increase between the expected yield strength versus the minimum specified yield strength Fy, categorized according to ASTM steel material designations, steel grade, and application (e.g., plate versus Chapter No. 4: Main features of the U.S. codes and Eurocodes


178


rolled shapes). The factors specified in the AISC Seismic Provisions represent measured strengths from a representative sample of mill certificates. b) Expected versus Nominal Steel Tensile Strength: The Rt factor accounts for the difference between the expected ultimate strength versus the minimum specified ultimate strength, Fu, with the same categories as the Ry factors. The statistical basis for the Rt factors is the ratio of Fu/Fy evaluated by Liu [237]. c) Strain Hardening: Factors specified for strain hardening are not as well established on a statistical basis, since they depend on both the material properties and the level of strain demands in the deformation‐controlled components. Moreover, the strain hardening factors tend to be combined with other effects. Factors range from no allowance for strain hardening (e.g., for axial strength of brace connections, the required design strength is equal to the yield capacity) to values up to 1.25. The factors are typically specified as a simple coefficient (e.g.1.1 or 1.2), however, the AISC Prequalified Connection Requirements include the factor Cpr, that is based on a stress demand equal to the average between Fy and Fu. d) Other Adjustment Factors: Other adjustment factors are sometimes specified to account for a range of issues, which may or may not have a clear statistical basis. For example, the  factor to adjust for compression strengths of buckling restrained braces (BRBs) is based on BRB test data. On the other hand, factors for strength of columns are primarily on judgment as to the expectations regarding the inelastic deformation mechanisms, recognizing that forces in the steel columns and components may be limited by other factors such as foundation strengths. In the case of welded column splices, yet other factors based on judgment are introduced to account for fracture critical issues that are not explicitly considered in design. With regard to capacities, in most cases the AISC Seismic Provisions enforce use of the standard nominal strength criteria and resistance factors from the AISC Specification. For example, the Special concentric braced frames (SCBF) provisions require that the components of the brace connection will be proportioned such that the design strength for each of the possible modes of failure will be evaluated according to the AISC Specification. However, the AISC Seismic Provisions and the AISC Prequalified Connection Requirements do not always adhere to the standard design strength provisions of AISC Specification. Chapter No. 4: Main features of the U.S. codes and Eurocodes


179


For example, the AISC Prequalified Connection Requirements introduce alternative resistance factors and nominal strength equations to check certain limit states in prequalified connections. The AISC Seismic Provisions also apply some modifications to the standard design strength equations, such as in Eccentric Braced Frames, where the design strengths of beams outside the link region are increased by the Ry factor in recognition of the fact that the link and the beam are built of the same material. Similar modification is applied in net section failure of braces in SCBF, where the design strength of the net section is increased by the Rt factor in recognition of the fact that the demand is from the same member, i.e. the expected yield strength of the brace. Expected (as opposed to nominal) material strengths are used for some other design strength checks, where the material overstrength in the required design strengths and design strengths are correlated [238].

4.10.

DESING RULES: SYNOPSIS (EC8 VS. AISC/ASCE)

4.10.1. High ductility: DCH vs. SMF In order to provide a comparison of the capacity design rules and drift limitations in Eurocodes [32, 229] and AISC/ASCE [39, 54] for the design of MRF, the noticeable features provided by the relevant codes are illustrated briefly in the synoptic comparative scheme given in Table 24 [151]. Table 24: Capacity design rules and drifts limitations for EC3‐EC8 (DCH) and AISC‐ ASCE (SMF) Description

(EC3/EC8)‐DCH

Energy dissipation philosophy

Prescribed by means of DCH

Seismic load reduction factor

A behaviour factor (q) equal to 5αu/α1

Cross section limitations

For q > 4 only class 1 sections are allowed

Rotation capacity (local ductility concept)

Plastic hinge rotation is limited to 35 mrad

Overstrength factor



AISC/ASCE‐SMF Given by SMF, and are anticipated to undergo significant inelastic deformation A response modification factor (R) equal to 8 is given All beams and columns must be seismically compact. Therefore Limits λp to λps, i.e. to use seismically compact section and is obtained by modified slenderness ratio SMF are designed to accommodate plastic hinge rotation of 30mrad with inter‐ storey drifts in the range of 0.04 radians

Mpl ,Rd ,i

MEd ,i Ωo in EC8 is (1.1γov Ω)

Ωo equal to 3 for MRFs



180


Description Ratio of reduction/respons e modification factor to overstrength factor Strength checks for dissipative elements (Beam checks) Non‐dissipative elements (e.g. Columns checks in MRFs) Strong column weak beam (SCWB) philosophy Panel Zone philosophy

Panel Zone (PZ) (Stability check)

(EC3/EC8)‐DCH

AISC/ASCE‐SMF

q ? 

R 8   2.67  3

M E ,d M pl ,Rd

 1.0,

NE ,d Npl ,Rd

 0.15

VE ,d Vpl ,Rd

 0.5

N Ed  N Ed ,G  1.1 ov N Ed , E M Ed  M Ed ,G  1.1 ov  M Ed , E V V  1 .1  V Ed

Ed , G

M

Rc

ov

Ed , E

 1.3 MRb

Strong‐PZ with weak beam is recommended

hw 72 235 with    t fy  Where fy is in Mpa, and η is a factor with 1.2 as recommended value.

No additional checks are required except strength checks using AISC/LRFD Verification of strength with loads computed from special load combinations having Ωo

 M * pc  1.0  M * bc , Columns should have sufficient flexural strength Both weak/intermediate or strong PZ with weak beam are allowed

t

dz  wz where dz, wz and t 90

are length, width and thickness of PZ respectively. Brandonisio et al. [239]

Drift philosophy for occupancy category I and II (Reduction) Drift philosophy for occupancy category III and IV (Reduction) Drift criteria for MRFs (Limit 1) Drift criteria for MRFs (Limit 2) Drift criteria for MRFs (Limit 3) Height restriction and Recommendation for seismicity area

0.005h, where h is the storey height

No height limitation and recommended in all seismic prone areas (high and moderate)

No limitations

Connections

Connections should be full strength

Connections should be full strength

Spectrum is reduced by 2.0 Reduction factor is 1/(Cd/R=5.5/8=0.6875) = 1.45 Spectrum is reduced by 2.5

0.0075h, where h is the storey height 0.01h, where h is the storey height

0.02h (Occupancy I and II), 0.015h (Occupancy III) & 0.01h (Occupancy IV). where h is the storey height

4.10.2. Medium ductility: DCM vs. IMF In the following comparisons is provided between DCM and IMF in Table 25, similarly in Table 26 for DCL and OMF and lastly in Table 27 the elastic analysis Chapter No. 4: Main features of the U.S. codes and Eurocodes


181


checks for the two codes. Table 25: DCM vs. IMF (Ductility Class Medium versus Intermediate Moment Frame) Description Energy dissipation philosophy

(EC3/EC8)‐DCM

AISC/ASCE‐IMF Given by IMF, and are anticipated to undergo limited inelastic deformation

Prescribed by means of DCM

Seismic load reduction factor

A behaviour factor (q) equal to 4

Cross section limitations

for 2 2g; otherwise, they shall be classified as force‐controlled. Secondary component actions exhibiting Type 1 behavior shall be classified as deformation‐controlled for any e/g ratio. The Type 2 curve depicted in the Figure of ductile behavior where there is an elastic range (point 0 to point 1 on the curve) and a plastic range (points 1 to 2) followed by loss of strength and loss of ability to support gravity loads beyond point 2. Primary and secondary component actions exhibiting this type of behavior shall be classified as deformation‐controlled if the plastic range is such that e > 2g; otherwise, they shall be classified as force controlled.

Figure 148: Component forces versus deformation curves (FEMA 356)

The Type 3 curve depicted in Figure is representative of a brittle or nonductile behavior where there is an elastic range (point 0 to point 1 on the curve) followed by loss of strength and loss of ability to support gravity loads beyond point 1. Primary and secondary component actions displaying Type 3 behavior Chapter No. 9: Assesment of frames using pushover analysis


307


shall be classified as force‐controlled [37, 42, 260]. Table 270: Examples of possible deformation‐controlled and force‐controlled actions Component Deformation‐Controlled Action Force‐Controlled Action Moment frames Beams Moment (M) Shear (V Columns M Axial load (P), V 1 Joints ‐‐ V Shear walls M, V P Moment frames Braces P ‐‐ Beams ‐‐ P Columns ‐‐ P Shear links V P, M 3 Connections P, V, M P, V, M 2 Diaphragms M, V P, V, M Shear may be deformation controlled in steel moment resisting frame constructions If the diaphragm carries lateral loads from vertical seismic resisting elements above the diaphragm level, then M and V shall be considered force‐controlled actions Axial, shear, and moment may be deformation‐controlled actions for certain steel and wood connection

Acceptance criteria for nonlinear procedures, both in ATC‐40 [261] and in FEMA‐356 [42] are based on peak demands without explicit consideration of cumulative effects resulting from cyclic effects. To some extent, cyclic degrading effects can be implicitly included in the specification of the backbone envelope. To process the results of a nonlinear analysis, it is essential to define response measures that form the basis of acceptance criteria. Currently, the response measure of choice is the rotation demand at the plastic hinge. If a concentrated hinge model is used in the analysis, this is a relatively direct response quantity. However, if a spread‐plastic model or a fibre‐section model is used to represent material nonlinearities in the element, then the computation of plastic rotations is not straightforward. Either a plastic hinge length needs to be defined to integrate curvature estimates or alternative procedures need to be developed to estimate the plastic rotation demand. FEMA‐356 [42] and FEMA‐350 [41] define deformations in terms of chord rotations as shown in Figure 149. If the FEMA 356 definition of element rotation is used, then two possibilities exist for defining the plastic rotation. The first approach is to track the moment–rotation behavior at every connection and then compute the difference between the peak rotation and the recoverable rotation. In a nonlinear time‐history analysis, the recoverable rotation is more completely defined because member behavior is explicitly defined using constitutive material models or hysteresis models. Table 270 provides some examples of possible deformation‐ and force‐controlled actions in common framing systems.

Chapter No. 9: Assesment of frames using pushover analysis


308


For nonlinear static procedures, the recoverable rotation may be estimated using the initial stiffness path as the unloading path. Alternatively, the yield rotation can be predetermined using conventional concepts in structural mechanics. For example, FEMA suggests the following expression for steel frame members:

Figure 149: Definition of chord rotations to be used in calculating plastic rotation demands.

Following Equation 71 and Equation 72 are given in FEMA‐356, to calculate the yield rotation and yield moment of steel beams and similarly Equation 73 Equation 74 for columns. Equation 71: Definition of yield rotation of steel beams according to FEMA 356

for beams  y 

ZFye l b 6El b

(71)

Equation 72: Definition of yield moment of steel beams according to FEMA 356

M y  Z Fye

(72)

Equation 73: Definition of yield rotation of steel columns according to FEMA 356

for columns  y 

ZFye l c  P   1   6El c  Pye 

(73)

Equation 74: Definition of yield moment of steel columns according to FEMA 356

 P My  1.18 Z Fye  1   P ye 

   Z Fye 

(74)

where Z is the plastic section modulus, Fye is the yield stress of the material, l is the length of the member, EI is the flexural rigidity, P is the axial force in member (may be taken as zero for beams), and Pye is the expected axial capacity (Ag Fye). Chapter No. 9: Assesment of frames using pushover analysis


309


9.5. BEAM & COLUMN LOCAL SLENDERNESS AND MEMBERS CAPACITIES Steel moment frames develop their seismic resistance through bending of steel beams and columns, and moment‐resisting beam‐column connections. Such frame connections are designed to develop moment resistance at the joint between the beam and the column. To this end, the behavior of steel moment‐ resisting frames is generally dependent on connection configuration and detailing. In FEMA‐356, various connection types are identified as fully restrained or partially restrained. Along with the limits of web and flange slenderness, FEMA‐356 classified the beam & column members’ behavior; in this particular study, selected IPE sections for beams and HE sections for columns are within the limits of web & flange slenderness. For column and beam sections, pertinent ratios are smaller than the limits (Fye = 275Mpa = 39.9 Kips) For beams: Equation 75: Limit of bf/2tf for beams

bf 2 tf



52  8.23 Fye

(75)

Check Equation 76: Check of bf/2tf for beams  bf   2 tf

  

8.23

 1.0

(76)

Equation 77: Limit of h/tw for beams

h 418   66.2 tw Fye

(77)

Equation 78: Check of h/tw for beams

h    tw 

66.2

 1.0

(78)

For columns:



310


Equation 79: Limit of bf/2tf for columns

bf 2 tf



65  10.3 Fye

(79)

Check Equation 80: Check of bf/2tf for columns  bf   2 tf

  

10.3

 1.0

(80)

Equation 81: Limit of h/tw for columns h 640   101.3 tw Fye

(81)

Check Equation 82: Check of h/tw for columns h     tw 

101.3

1.0

(82)

Table 271: Beam & column member local slenderness ratio (HE‐profiles) designation HE 300 B HE 300 M HE 320 B HE 320 M HE 340 B HE 340 M HE 360 B HE 360 M HE 400 B HE 400 M HE 450 B HE 450 M HE 500 B HE 500 M HE 550 B HE 550 M HE 600 B HE 600 M HE 650 B

bf/2tf

h/tw

7.89 3.97 7.32 3.86 6.98 3.86 6.67 3.85 6.25 3.84 5.77 3.84 5.36 3.83 5.17 3.83 5.00 3.81 4.84

27.27 16.19 27.83 17.10 28.33 17.95 28.80 18.81 29.63 20.57 32.14 22.76 34.48 24.95 36.67 27.24 38.71 29.52 40.63

bf/2tf Beams ratios 0.96 0.48 0.89 0.47 0.85 0.47 0.81 0.47 0.76 0.47 0.70 0.47 0.65 0.46 0.63 0.46 0.61 0.46 0.59

h/tw

bf/2tf

0.41 0.24 0.42 0.26 0.43 0.27 0.44 0.28 0.45 0.31 0.49 0.34 0.52 0.38 0.55 0.41 0.58 0.45 0.61

Columns ratios 0.77 0.27 0.39 0.16 0.71 0.27 0.38 0.17 0.68 0.28 0.38 0.18 0.65 0.28 0.37 0.19 0.61 0.29 0.37 0.20 0.56 0.32 0.37 0.22 0.52 0.34 0.37 0.25 0.50 0.36 0.37 0.27 0.49 0.38 0.37 0.29 0.47 0.40


h/tw


311


designation HE 650 M HE 700 B HE 700 M HE 800 B HE 800 M HE 900 B HE 900 M HE 1000 B HE 1000 M

bf/2tf

h/tw

3.81 4.69 3.80 4.55 3.79 4.29 3.78 4.17 3.78

31.81 41.18 34.10 45.71 38.76 48.65 43.33 52.63 48.00

bf/2tf Beams ratios 0.46 0.57 0.46 0.55 0.46 0.52 0.46 0.51 0.46

h/tw

bf/2tf

0.48 0.62 0.52 0.69 0.59 0.74 0.65 0.80 0.73

Columns ratios 0.37 0.31 0.46 0.41 0.37 0.34 0.44 0.45 0.37 0.38 0.42 0.48 0.37 0.43 0.40 0.52 0.37 0.47

h/tw

The slenderness ratios of various profiles and the corresponding yield rotation, yield moment and yield axial force values calculated according to FEMA 356 equations are shown in the given tables for various profiles. These cross‐ sectional properties form a basis to the construction of behavior curves. Table 272: Beam & column member local slenderness ratio (IPE‐profiles) designation IPE 300 IPE O 300+ IPE 330 IPE O 330+ IPE 360 IPE O 360+ IPE 400 IPE O 400+ IPE 450 IPE O 450+ IPE 500 IPE O 500+ IPE 550 IPE O 550+ IPE 600 IPE O 600+

bf/2tf 7.01 5.98 6.96 6.00 6.69 5.85 6.67 5.87 6.51 5.45 6.25 5.32 6.10 5.25 5.79 4.67

h/tw 42.25 38.00 44.00 39.29 45.00 39.57 46.51 41.65 47.87 41.45 49.02 42.17 49.55 43.78 50.00 40.67

bf/2tf Beams ratios 0.85 0.73 0.85 0.73 0.81 0.71 0.81 0.71 0.79 0.66 0.76 0.65 0.74 0.64 0.70 0.57

h/tw 0.64 0.57 0.66 0.59 0.68 0.60 0.70 0.63 0.72 0.63 0.74 0.64 0.75 0.66 0.76 0.61

bf/2tf h/tw Columns ratios 0.68 0.42 0.58 0.38 0.68 0.43 0.58 0.39 0.65 0.44 0.57 0.39 0.65 0.46 0.57 0.41 0.63 0.47 0.53 0.41 0.61 0.48 0.52 0.42 0.59 0.49 0.51 0.43 0.56 0.49 0.45 0.40

Table 273: Beam, column yield quantities (HE profiles) Designation HE 300 B HE 300 M HE 320 B HE 320 M HE 340 B HE 340 M

Mpl 513.975 1121.45 590.975 1219.625 662.2 1297.45

Py 4100.25 8335.25 4435.75 8580 4699.75 8684.5

θ (4m) 0.0068 0.0063 0.0064 0.0060 0.0060 0.0057

θ (9.15m) 0.0156 0.0144 0.0146 0.0136 0.0138 0.0130

θ (7.63m) 0.0130 0.0120 0.0122 0.0114 0.0115 0.0108


θ (6.55m) 0.0111 0.0103 0.0105 0.0098 0.0099 0.0093

θ (5.08m) 0.0086 0.0080 0.0081 0.0076 0.0076 0.0072


312


Designation HE 360 B HE 360 M HE 400 B HE 400 M HE 450 B HE 450 M HE 500 B HE 500 M HE 550 B HE 550 M HE 600 B HE 600 M HE 650 B HE 650 M HE 700 B HE 700 M HE 800 B HE 800 M HE 900 B HE 900 M HE 1000 B HE 1000 M

Mpl 737.825 1371.975 888.8 1532.025 1095.05 1741.025 1324.125 1950.85 1537.525 2181.575 1766.875 2412.3 2013 2655.675 2289.925 2898.5 2813.25 3434.75 3459.5 3971 4086.5 4556.75

Py 4966.5 8767 5439.5 8959.5 5995 9223.5 6561.5 9468.25 6987.75 9746 7425 10001.75 7873.25 10276.75 8426 10532.5 9190.5 11118.25 10210.75 11649 11000 12215.5

θ (4m) 0.0057 0.0054 0.0051 0.0049 0.0046 0.0044 0.0041 0.0040 0.0037 0.0037 0.0034 0.0034 0.0032 0.0031 0.0030 0.0029 0.0026 0.0026 0.0023 0.0023 0.0021 0.0021

θ (9.15m) 0.0130 0.0123 0.0117 0.0112 0.0105 0.0101 0.0094 0.0092 0.0086 0.0084 0.0079 0.0077 0.0073 0.0072 0.0068 0.0067 0.0060 0.0059 0.0053 0.0053 0.0048 0.0048

θ (7.63m) 0.0109 0.0103 0.0098 0.0094 0.0087 0.0084 0.0079 0.0077 0.0072 0.0070 0.0066 0.0065 0.0061 0.0060 0.0057 0.0056 0.0050 0.0049 0.0045 0.0044 0.0040 0.0040

θ (6.55m) 0.0093 0.0088 0.0084 0.0080 0.0075 0.0072 0.0067 0.0066 0.0061 0.0060 0.0056 0.0055 0.0052 0.0051 0.0049 0.0048 0.0043 0.0042 0.0038 0.0038 0.0035 0.0034

θ (5.08m) 0.0072 0.0068 0.0065 0.0062 0.0058 0.0056 0.0052 0.0051 0.0048 0.0047 0.0044 0.0043 0.0040 0.0040 0.0038 0.0037 0.0033 0.0033 0.0030 0.0029 0.0027 0.0027

Table 274: Beam, column yield quantities (IPE profiles) Designation IPE 300 IPE O 300+ IPE 330 IPE O 330+ IPE 360 IPE O 360+ IPE 400 IPE O 400+ IPE 450 IPE O 450+ IPE 500 IPE O 500+ IPE 550 IPE O 550+ IPE 600 IPE O 600+

Mpl 172.81 204.545 221.1825 259.27 280.225 326.15 359.425 413.05 468.05 562.65 603.35 718.575 766.425 897.325 965.8 1229.525

Py 1479.5 1727 1721.5 1996.5 1999.25 2312.75 2323.75 2651 2717 3245 3190 3767.5 3685 4290 4290 5417.5

θ (4m) 0.0069 0.0068 0.0063 0.0062 0.0057 0.0057 0.0052 0.0051 0.0046 0.0046 0.0042 0.0041 0.0038 0.0038 0.0035 0.0035

θ (9.15m) 0.0158 0.0156 0.0143 0.0142 0.0131 0.0131 0.0118 0.0118 0.0106 0.0105 0.0095 0.0095 0.0087 0.0086 0.0080 0.0079

θ (7.63m) 0.0131 0.0130 0.0119 0.0119 0.0110 0.0109 0.0099 0.0098 0.0088 0.0087 0.0080 0.0079 0.0073 0.0072 0.0067 0.0066


θ (6.55m) 0.0113 0.0112 0.0103 0.0102 0.0094 0.0093 0.0085 0.0084 0.0076 0.0075 0.0068 0.0068 0.0062 0.0062 0.0057 0.0057

θ (5.08m) 0.0088 0.0087 0.0080 0.0079 0.0073 0.0072 0.0066 0.0065 0.0059 0.0058 0.0053 0.0053 0.0048 0.0048 0.0044 0.0044


313


2000

M [kN]

M [kN]

2000

IPE400

IPE600

L [9.15m] 1000

θ [rad] 0 ‐0.15

‐0.1

‐0.05

L [9.15m] 1000

L [7.63m]

0

0.05

0.1

0.15

L [5.08m] ‐0.15

H [4.0 m]

‐0.1

(a) M [kN]

0 0.05

0.1

0.15

M [kN]

‐0.15

H [4.0 m]

‐0.1

0.05

0.1

0.15

‐0.15

H [4.0 m]

‐0.1

L [5.08m]

0.15

H [4.0 m]

(d) M [kN]

HE500M L [9.15m] L [7.63m]

0 ‐0.05 0 ‐2000

L [6.55m] L [5.08m]

0.05

0.1

0.15

M [kN]

H [4.0 m]

6000

HE600M L [7.63m]

0.15

HE700M L [9.15m] L [7.63m]

2000

L [6.55m]

θ [rad]

L [5.08m] 0.1

M [kN]

4000

L [9.15m]

0.05

(f)

‐6000

‐0.15

H [4.0 m]

‐0.1

0 ‐0.05 0 ‐2000

L [6.55m] L [5.08m]

0.05

0.1

0.15

H [4.0 m]

‐4000

‐4000

(g)

‐6000

M [kN]

6000

L [9.15m]

θ [rad] 0 0.1

0.15

HE900M L [9.15m] L [7.63m]

2000

L [6.55m]

θ [rad] 0

L [5.08m] 0.05

M [kN]

4000

L [7.63m]

2000

(h)

‐6000

HE800M

4000

‐0.15

H [4.0 m]

‐4000 ‐6000

0.1

‐4000

θ [rad]

‐0.05 0 ‐2000

0.05

θ [rad]

(e)

2000

‐0.1

‐0.05 0 ‐1000

2000

L [6.55m] L [5.08m]

4000

‐0.15

L [6.55m]

4000

L [7.63m]

‐6000

6000

L [9.15m]

6000

‐4000

0 ‐0.05 0 ‐2000

HE400M

‐3000

L [9.15m]

0

‐0.1

M [kN]

0

HE500B

θ [rad]

‐0.15

(b)

‐2000

2000

6000

H [4.0 m]

L [7.63m]

(c)

4000

‐0.05 0 ‐2000

0.15

θ [rad]

L [5.08m]

‐3000

‐0.1

0.1

1000

L [6.55m]

‐2000

‐0.15

0.05

2000

L [7.63m]

θ [rad]

6000

0

3000

L [9.15m]

1000

‐0.05 0 ‐1000

‐0.05

‐2000

HE400B

2000

‐0.1

L [5.08m]

0

‐1000

‐2000

‐0.15

L [6.55m]

θ [rad]

‐1000

3000

L [7.63m]

L [6.55m]

‐0.1

‐0.05 0 ‐2000

L [6.55m] L [5.08m]

0.05

0.1

0.15

H [4.0 m]

‐4000

(i)

‐6000

(j)

Figure 150: Moment, axial and rotational capacity curves for 4.0m, 9.15m, 7.63m, 6.55m and 5.08m (1kN = 225 Ib & 1m= 3.28ft), (a) IPE400, (b)IPE600, (c)HE400B, (d)HE400M, (e)HE500B, (f)HE500M, (g)HE600M, (h)HE700M, (i) HE800M and (j) HE900M



314


Table 275: Moment (kN‐m), axial capacity (kN) and Plastic rotation (rad) for some beam/column members Designation HE 400 B HE 400 M HE 500 B HE 500 M HE 600 B HE 600 M HE 700 M HE 800 M HE 900 M HE 1000 M IPE 400 IPE 500 IPE 600

Mpl

Py

θ (4m)

θy(9.15m) θy(7.63m) θy(6.55m) θy(5.08m)

888.8 1532.025 1324.125 1950.85 1766.875 2412.3 2898.5 3434.75 3971 4556.75 5621 359.425 603.35

5439.5 8959.5 6561.5 9468.25 7425 10001.75 10532.5 11118.25 11649 12215.5 14415.5 2323.75 3190

0.005136 0.004906 0.004117 0.004017 0.003444 0.003387 0.002934 0.002587 0.002321 0.002103 0.002059 0.00518 0.004173

0.011749 0.011222 0.009418 0.009188 0.007879 0.007748 0.006712 0.005917 0.005308 0.00481 0.004711 0.011849 0.009545

0.009798 0.009357 0.007854 0.007662 0.00657 0.006461 0.005597 0.004934 0.004427 0.004011 0.003928 0.00988 0.007959

0.008411 0.008033 0.006742 0.006577 0.00564 0.005546 0.004804 0.004236 0.0038 0.003443 0.003372 0.008482 0.006833

0.006523 0.00623 0.005229 0.005101 0.004374 0.004302 0.003726 0.003285 0.002947 0.002671 0.002615 0.006578 0.005299

9.6. PUSHOVER ANALYSIS USING FEMA PROCEDURE Static nonlinear analysis has been carried out for evaluating the lateral load resisting performance of the frames. For this reason, triangular distribution (unit load at roof level) of static incremental loads has been applied and the displacement at the roof level has been controlled. For the ultimate rotation capacity of an element, acceptance criteria are defined according to FEMA 356. These are represented as IO (immediate occupancy), LS (life safety), and CP (collapse prevention) as indicated in Figure 151. Mechanical non‐linearity of the members has been assumed concentrated in plastic hinges at the ends (lumped plasticity) of the elements as shown in Figure 147b. The effect of geometric nonlinearity due to large deflections and second order effects are considered automatically in the analysis.by the programme The current approach to performance based design relies on component‐based evaluation as delineated in the FEMA‐356 [42]and ASCE 41 documents. In the component‐based approach, each component of the building is assigned a normalized force/moment – deformation/ rotation relation such as shown in Figure 152. In the same Figure, segment “AB” indicates elastic behavior, point “C” identifies the onset of loss of capacity, segment “DE” identifies the residual capacity of the component, and point “E” identifies the ultimate inelastic deformation/rotation capacity of the component. Chapter No. 9: Assesment of frames using pushover analysis


315


Figure 151: Idealised performance curve for structure

(a)

(b)

(c)

Figure 152: Generalized component force‐deformation relations in FEMA‐356 and ASCE 41‐06 documents: (a) deformation (b) deformation ratio and (c) component or element deformation acceptance criteria



316


The acceptance criteria according to FEMA 356 is illustrated in Table 276. Table 276: Modelling parameters and acceptance criteria for nonlinear procedures for structural steel components Modelling parameters Plastic Residual rotation strength angle ratio (radians)

Component/Action

(a)

(b)

(c)

Acceptance criteria Plastic rotation angle (radians)

IO

Primary

Secondary

LS

CP

LS

CP

Beam‐flexure

a.

bf h 418 52  and  tw 2t f Fye Fye

9θy

11θy

0.6

1θy

6θy

8θy

9θy

11θy

b.

bf 65  or 2t f Fye

4θy

6θy

0.2

0.25θy

2θy

3θy

3θy

4θy

h 640  tw Fye

Linear interpolation between the values on lines a and b for both flange slenderness shall be performed, and the lowest resulting value shall be used

c. Other Column‐flexure For P/Pcl 1.0 means that the design is governed by strength and frame is considered overstiff.

o

The frames with overstiffness close to 1.0 are optimally design with stiffness (SLS).

o

If drift limitation govern, q cannot be optimally used and leads to uneconomical design situation, thereby, paying extra due to the assumed ductility together with paying for deformability.

PROPOSED METHODOLOGY (OPTIMIZATION RULES)

11.2.1. Damageability and ductility In the following optimization rules are provided for the design of steel moment resisting frames when dealing with Eurocode 8 [32]. The rules are based on large bulk of parametric analysis in which 144 different frames are designed according to Eurocode 8 provisions, using modal response spectrum analysis [256] followed by non‐linear static analysis with the application of FEMA 356 [42] acceptance criteria. The adopted frame cases are summarized in Table 295. Chapter No. 11: Conclusions and optimization rules


379


Table 295: Analysed cases for 9, 7 and 5 storeys frames No. of Storys (Height)

No. of Bays (Width)

behaviour factor (q)

∆ /h L1 (0.01h) ‐ Relax limit L2 (0.0075h) ‐ Intermediate limit

5 (H=20m)

7 (H=28m)

5 (9.15m) 6 (7.63m) 7 (6.54m) 9 (5.08m)

Ductility Class High (q=6.5) Ductility Class Medium (q=4) Ductility Class Conventional (q=3) Ductility Class Low (q=2)

9 (H=36m)

L3 (0.005h) ‐ Stringent limit L1 (0.01h) ‐ Relax limit L2 (0.0075h) ‐ Intermediate limit L3 (0.005h) ‐ Stringent limit L1 (0.01h) ‐ Relax limit L2 (0.0075h) ‐ Intermediate limit L3 (0.005h) ‐ Stringent limit

All these frames are designed using Eurocode methodology [32, 229] as prescribed in Figure 236.

Figure 236: Eurocode proposed capacity design flowchart for steel MRF

11.2.2. Ductility classes For moment resisting frames the ductility classes given by Eurocode 8 correspond to the reduction of elastic spectrum by a suggested q factor in order to account for the in‐elastic response of the framing system. Ductility is a key parameter in seismic design, as it permits the design of structures possess reduce strength (designed using q factor) for resisting strong earthquake shaking in elastic range but still persist such strong quaking through the inelastic response. Structures that do not have ductility will fail when subjected to ground motion that deforms them beyond their elastic limit. In MRFs, the ductility is achieved by assuming beams to be dissipative zone and therefore the formation of hinges is allowed at the end of the beams. Whereas columns are supposed to be non‐dissipative zone and therefore are designed for relatively high strength than the one required from the seismic combination. According to Eurocode 8, No collapse or Ultimate Limit States (ULS) must be Chapter No. 11: Conclusions and optimization rules


380


respected and where the specified ductility classes of the codes are employed for design purpose: No collapse or ULS is the state against which the structure should be designed according to the Eurocode 8 “Basis of Structural Design” [32]. It entails protection of life under a rare seismic action, through prevention of collapse of any structural member and retention of structural integrity and residual load capacity after the event. Eurocode 8 allows the use of three ductility classes, High, Medium, and low as mentioned below: o

Ductility Class High (DCH): For DCH, code suggests the use of q=5(αu/α1), αu/α1 is termed as redundancy factor and the recommended value according to EC8 for multiple bays with multiple Storys as 1.6. Therefore, the suggested behaviour factor for DCH according to Eurocode 8 is 6.5. The required cross sectional class to be use in high ductility class where q is always greater than 4 is “Class 1”.

o

Ductility Class Medium (DCM): In the case of DCM, the code prescribes the reduction of elastic spectrum by q, which equals 4.0. As like in DCH, the beams are supposed dissipative and the column is considered to be non‐dissipative elements. The same philosophy of using overstrength for the design of columns is applicable here. The only difference is the assured ductility in the case of high ductility class (specially the detailing of connections). Unlike DCH, where only Class 1 cross sections are allowed, in DCM, class 2 cross sections are also allowed.

o

Ductility Class Low (DCL): DCL, in Eurocode 8 correspond to elastic analysis, where no concept of dissipative and non‐dissipative elements needs to be apply and further the allowable behaviour factor is 2.0, the provision of ductility is not mandatory. The entire elements of the structure are designed for higher forces as during the earthquake excitation, they are assumed to be in the elastic state. Further, class 1, class 2, and class 3 cross sections are allowed in this class of ductility. According to Eurocode 8, the use of Low Ductility Class is recommended only for low seismicity. The low seismicity cases are those seismic zones where design ground acceleration (ag) on type A soil is not greater than 0.08g (0.78m/sec2) or where the product agS is not greater than 0.1g

Chapter No. 11: Conclusions and optimization rules


381


(0.98m/sec2).

11.2.3. Damage limitation criteria The main aim of this criterion is to mitigate the loss of property during frequent earthquakes. It can be achieved by the imitation of structural and non‐structural damage. After frequent earthquake, structural elements are supposed to have no permanent deformation, retain their full strength and stiffness, and need no repair. Experience shows that non‐structural items perform badly. In the case, when non‐structural elements suffer some damage, they can be easily and economically repaired later. According to Eurocode 8, damage limitation shows the role of the Serviceability Limit State (SLS) against which the structure should be designed. The damage limitation performance level is achieved by limiting the overall deformations (lateral displacements) of the building to levels acceptable for the integrity of all its parts (including non‐structural ones). More specifically, interstorey drift ratios (defined as the difference between the mean lateral displacements of adjacent storeys divided by the interstorey height) are limited to the following values: Eurocode 8 suggests the use of three different drift limits.

o

o

Relax drift limit (L1=0.01h): where non‐structural elements follow the deformations of the structural system.

o

Intermediate drift limit (L2=0.0075h): where the non‐structural elements of a given storey are ductile

Stringent drift limit (L3=0.005h): where the storey has brittle non‐ structural elements attached to the structure (notably, ordinary masonry infills).

11.3. NEGOTIATION BETWEEN DAMAGEABILITY AND DUCTILITY According to Patton [265], when the drift limits dictate the design of the frames, the designer has to use limited ductility. No such restrictions exists in the present version of the Eurocode 8, even though from the presented study it is evidenced that there is no compatibility between the code prescribed ductility classes and the interstorey drift limits, therefore as like Patton suggested, at least such restrictions has to be adopted in Eurocode 8. Now, the issue arises how to limit the ductility class and how to adopt a suggested drift Chapter No. 11: Conclusions and optimization rules


382


limit for an assume ductility class or which type of non‐structural elements should be used. In the present version of Eurocode 8, no such rules exist in clarifying these issues. From the parametric analysis it has been observed that drift limit (L2 and L3) are not compatible with high ductility class. Similarly, drift limit L3 is found not compatible with medium ductility class, whereas all the drift limits are almost compatible if a conventional ductility class (DCC) defined by behaviour factor of 3 is used, and also the drift limits are satisfied when elastic analysis is performed. Based on these observations in the following some suggestions are provided. Table 296: Drift limit versus assumed ductility class S.No

Ductility class

1 2

DCH (q=6.5)

3 4 5

DCM (q=4.0)

6 7 8

DCC (q=3.0)

9 10 11 12

DCL (q=2.0)

Compatible drift limits Description Drift limit Relax drift limit L1(0.01h) Intermediate drift L2(0.0075h) limit Stringent drift limit L3(0.005h) Relax drift limit L1(0.01h) Intermediate drift L2(0.0075h) limit Stringent drift limit L3(0.005h) Relax drift limit L1(0.01h) Intermediate drift L2(0.0075h) limit Stringent drift limit L3(0.005h) Relax drift limit L1(0.01h) Intermediate drift L2(0.0075h) limit Stringent drift limit L3(0.005h)

Remarks

Suggestions

Convenient

Optimum q Un‐economical

NOT convenient NOT convenient Convenient Convenient NOT convenient Convenient Convenient Less convenient Less convenient Less convenient convenient

Un‐economical Optimum q Optimum q Un‐economical Less economical Less economical Un economical Less economical Less economical Less economical

Further, it is still difficult to decide the assumed conventional ductility class (q equals 3.0) for satisfying drift limit L3, as the obtained elastic overstrength is too high which give rise to uneconomical design situation. Therefore, when drift limit L3 is required the better choice is the use of elastic analysis. All these observations are evident by Figure 237 (5 and 6 bays) and Figure 238 (7 and 9 bays) where the overstiffness of all the cases is recorded.



383


3.5

5

5 Bays

Ωk

7

3.0

9 2.5

3.5

Ωk

7

2.0

(a1)

L2

2.0

(b1)

L2 L3

L3

1.5

9

L1

2.5

L1

5

6 Bays

3.0

1.5

1.0

1.0

0.5

0.5

Comb

Comb

0.0

0.0 0

5

10

15

0

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

5

10

15

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

Figure 237: Graphs showing overstiffness factor for 5 bays (a1) and for 6 bays (b1) 3.5

Ωk

5

7 Bays

9 L1

2.5

3.5 3.0 2.5

(c1)

L2

2.0

L1

(d1)

2.0

L2

L3

1.5

5 7 9

9 Bays

Ωk

7

3.0

L3

1.5

1.0

1.0

0.5

0.5

Comb

0.0

Comb

0.0 0

5

10

15

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

0

5

10

15

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

Figure 238: Graphs showing overstiffness factor for 7 bays (c1) and for 9 bays (d1)

Figure 239: Graphs showing overstiffness factor for: 5 bays (a), 6 bays (b), 7 bays (c), and 9 bays (d)



384


The overstiffness values are also shown in the graphs (see Figure 239), where they are grouped according to the behaviour factor for the corresponding bay.

11.4. PROPOSED OVERSTRENGTH FACTORS In this section, relevant information is given to find a better compromise between q factor and the suggested drift limits of Eurocode 8. Question arises, which global overstrength should be used as its value drastically changes and depends on the governing condition of the design e.g., if it is strength base or stiffness. The codified overstrength is convenient only in the cases when the strength govern the design. As highlighted already that the optimum and ideal scenario is attained only when elastic overstrength is unity. Another interesting fact is when the gravity load govern the design (it is not always factual that the drift govern the design as the seismic forces might not that much high to size the beams). In such circumstances, fixed values might be applicable as the codified formulation give higher overstrength. In any case, if the codified formulation gives less overstrength than the proposed one, then it is convenient to use the overstrength obtained from the codified formulation. Table 297: Drift limit, behaviour factor and proposed elastic overstrength S.No

Ductility class

q

Compatible drift limits

Remarks

(ΩE)

L1(0.01h)

Convenient

1.6

Intermediate drift limit

L2(0.0075h)

NOT convenient

2.2

3

Stringent drift limit

L3(0.005h)

NOT convenient

3.3

4

Relax drift limit

L1(0.01h)

Convenient

1.3


L2(0.0075h)

Convenient

1.5


L3(0.005h)

NOT convenient

2.0

1 2

5

DCH

DCM

6.5

4.0

6 7

Description

Drift limit

Relax drift limit

Relax drift limit

L1(0.01h)

Convenient

1.3


L2(0.0075h)

Convenient

1.4

9


L3(0.005h)

Less convenient

1.6

10

Relax drift limit

L1(0.01h)

Less convenient

1.1


L2(0.0075h)

Less convenient

1.1


L3(0.005h)

convenient

1.1

8

11 12

DCC

DCL

3.0

2.0

The compatible combinations (between q factor and the drift limits) are shown in Table 297; in addition, elastic overstrength is also reported here.



385


6

E

5 L1 L2

4

6

5 7 9

5 Bays

L3

L1

4

3

3

2

2

1

1

L3

L2

(b1)

Comb

Comb

0

0 5

5 7 9

6 Bays

5

(a1)

0

E

10

0

15

5

10

15

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

Figure 240: Graphs showing elastic overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2)

Figure 240 (5 and 6 bays) and Figure 241 (7 and 9 bays), shows the overstiffness of the analysed frames. 6

E

5 7 9

7 Bays

5

5 7 9

9 Bays

E

5 L1

L1

4

6

L2

4

L3

(c1)

3 2

L3

L2

(d1)

3 2

1

1 Comb

Comb

0

0 0

5

10

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

15

0

5

10

15

6.5 4 3 2 6.5 4 3 2 6.5 4 3 2

Figure 241: Graphs showing elastic overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2)

11.5.

PROPOSED RULES

As an ideal scenario in the design, the elastic overstrength (ΩE) might be unity, which is mostly not possible to achieve, anyway reaching to the nearest value is always acceptable. Since the resistance moment of beam profiles must not be less than the corresponding design moment, therefore ΩE is always at least one. As shown previously, ΩE varies with the changing in drift limit. For instance, it increases when the drift limit varies from the more relaxed one (0.01h) to the stringent one (0.005h). Consequently, for the cases where the drift limits are dictating the design, the value of this overstrength needs to fix; Chapter No. 11: Conclusions and optimization rules


386


otherwise, the resulted profiles of columns would be drastically huge, thereby making the design un‐economical therefore, inconvenient. In the cases where beams are sized considerably in excess of the minimum requirement, the structure will start to yield at a lateral force considerably greater than that effectively assumed in the analysis due to the drift limitations. Therefore, the column forces will also be greater than predicted by the analysis as these are normally factored by ΩG,E (Global overstrength). The factor 1.375 is used to allow for strain hardening in the beam plastic hinges, and to provide some degree of additional reserve strength. In the following some suggested values of the elastic overstrength are given based on the parametric analysis. Such values would help to fix the rest of the factors as well, for example, the redundancy factor and the reserve overstrength factor for an assumed ductility class. Redundancy exists when multiple elements must yield or fail before a complete collapse mechanism forms, therefore, it is believed that structures possess low inherent redundancy are required to be stronger and more resistant to damage and therefore seismic design forces are amplified. Hence, it is assumed that structures having high ductility exhibits high redundancy and vice versa. In order to account for the width of bay (long, intermediate, and short span) and number of storeys, the elastic overstrength factor obtained from the pushover analysis are averaged for each combination. Table 298 shows the q factor with compatible drift limits and overstrength factors for different materials overstrength. It is to be mentioned here that when the suggested elastic overstrength values are less than 3.0 for a given combinations as shown in Table 298, the proposed q factor and drift limit are supposed to be convenient. Furthermore, minimum of the overstrength obtained from Eurocode 8 formulation and the suggested one must be adopted in the design of columns. In fact, the proposed values are differing than the AISC/ASCE recommended values as the interstorey drift limits and the assumed behaviour factors or response modification factors are different. The proposed method can be easily demonstrated by Figure 244, in which the re‐evaluation of overstrength factor is overpassed and therefore an un‐iterated design approach is proposed. In Table 299, q factors are related to compatible drift limits and then the overstrength factors are provided. These are shown for DCH (L1=0.01h) in Figure 242.a, for DCM (L1=0.01h) in Figure 242.b, and for DCM (L2=0.0075h) in Figure 242.c. Similarly, these are shown in Figure 243.a, Figure 243.b and Figure 243.c for DCC (L1=0.01h), DCC (L2=0.0075h), and DCC (L3=0.005h), Chapter No. 11: Conclusions and optimization rules


387


respectively. Table 298: Drift limit, behaviour factor and global overstrength with material overstrength S.No

Ductility class

q

2

DCH

65

γov =1.25

γov =1.2

γov =1.1

γov =1.0

Drift limit

(ΩE)

(Ωp)

(ΩE,p)

L1(0.01h)

1.6

1.3

2.08

2.9

2.7

2.5

2.3

L2(0.0075h)

Global overstrength (ΩG,E)

2.2

1.3

2.86

3.9

3.8

3.5

3.1

3

L3(0.005h)

3.3

1.3

4.29

5.9

5.7

5.2

4.7

4

L1(0.01h)

1.3

1.3

1.69

2.3

2.2

2.0

1.9

L2(0.0075h)

1.5

1.3

1.95

2.7

2.6

2.4

2.1

6

L3(0.005h)

2

1.3

2.6

3.6

3.4

3.1

2.9

7

L1(0.01h)

1.3

1.2

1.6

2.1

2.1

1.9

1.7

L2(0.0075h)

1.4

1.2

1.68

2.3

2.2

2.0

1.8

9

L3(0.005h)

1.6

1.2

1.92

2.6

2.5

2.3

2.1

10

L1(0.01h)

1.1

1.1

1.21

1.7

1.6

1.5

1.3

L2(0.0075h)

1.1

1.1

1.21

1.7

1.6

1.5

1.3

L3(0.005h) 1.1 1.1 1.21 ΩG,E = (ΩE,p)×1.1×γov, represent the global overstrength

1.7

1.6

1.5

1.3

5

DCM

8

DCC

11

DCL

4

3

2

12

Table 299: Drift limit, behaviour factor, proposed global and reserve overstrength S.No

Ductility class

q

DCH

6.5

DCM

4.0

DCC

3.0

1

Drift limit

(ΩE)

(Ωp)

(ΩE,p)

(ΩG,E)

(ΩReserve)

L1(0.01h)

1.6

1.3

2.08

2.9

2.3

L2(0.0075h) L3(0.005h)

2.2 3.3

1.3 1.3

2.86 4.29

3.9 5.9

1.7 1.1

L1(0.01h) L2(0.0075h) L3(0.005h) L1(0.01h)

1.3 1.5 2 1.3

1.3 1.3 1.3

1.69 1.95 2.6

2.3 2.7 3.6

1.7 1.5 1.1

1.2

1.56

2.1

1.4

L2(0.0075h)

1.4

1.2

1.68

2.3

1.3

9

L3(0.005h)

1.6

1.2

1.92

2.6

1.1

10

L1(0.01h)

1.1

1.1

1.21

1.7

1.2

DCL 2.0 11 12 ΩG, E = (ΩE,p)×1.1×γov with γov as 1.25

L2(0.0075h) L3(0.005h)

1.1 1.1

1.1 1.1

1.21 1.21

1.7 1.7

1.2 1.2

2 3 4 5 6 7 8



388


Figure 242: Proposed global overstrength and reserve overstrength for DCH and DCM

In this case for completeness, γov is assumed 1.25, the factor 1.1 is used to take into account the strain hardening. ΩE denotes elastic overstrength whereas ΩG,E denotes global overstrength. As like American code, where the reserve overstrength decreases when the ductility of the resisting system decreases, the same philosophy is provided here. Additionally as studied in [90] by Elnashai and Mwafy, that higher ductility level buildings display higher reserve strength and is directly attributed to the use of a higher force reduction factor, which causes a reduction in the design forces thus magnifying the effect of gravity loads. This statement holds for a structural system explicit of the material and therefore the same approach and philosophy is obtained and adopted here.

Figure 243: Proposed global overstrength and reserve overstrength for DCC

NOTE: For completeness of the task, it is recommended that when strength governs the design minimum value of global overstrength between the assumed one and the one obtained from codified formulation of Eurocode 8 should be employed in the design. The suggested rules allow pre‐deciding of drift limit for an assumed ductility class. Since, the rules are fixed and as the suggested rules are fixed; therefore, unknown iterations are not be required to satisfy the capacity design rules. Chapter No. 11: Conclusions and optimization rules


389


Figure 244: Proposed capacity design flowchart for steel MRFs

11.5.1. Steps for applicability of the proposed rules The overstrength factor is also related to the number of bays and to the number of storeys. The following procedure can be used for optimum design of MRFs.



Design frame for gravity loading



Find overstrength factor using Eurocode 8 formulation and use the minimum between the code value and of the one of the proposed method



Check beams for siesmic condition



If beams are influenced by seismic condition, find overstrength again and use the minimum between the code value and of the one of the proposed method



Design columns for the capacity design combinations



Check drift

From the optimization rules of frames, interesting remarks are drawn, some suggestions together with thumb rules for the optimum design of steel moment resisting frames are provided. The thumb rules are based on the previously 144‐designed frames, these are analysed with static pushover analysis. From the obtained results, it is therefore, concluded that when a ductility class for the primary members is defined a suitable drift limit should be chosen such that the two limit states does not indulge each other. This misperception of the designer about moment resisting frames that they are quite deformable (not comparing with the other lateral load resisting systems) and that drift criterion is governing, holds when the adopted drift limit is not compatible with the behaviour factor. Therefore, when the designer choose a behaviour factor that Chapter No. 11: Conclusions and optimization rules


390


at the end cannot be achieved due to the deformability criteria leads to have an inconvenient design of steel moment resisting frames. Therefore, at the end it is suggested to preliminary choose a proper interstory drift limit before choosing the ductility of the frame. Another way could be the adoption of the cladding system when a ductility class is assumed, for example, when high ductility is assumed for the framing system (primary member), this is inconvenient to decide a cladding system that is defined as brittle. Similarly, if a brittle system of cladding is assumed; it is inappropriate to decide the primary element to be highly ductile as they can be designed with elastic analysis for a frequent earthquake. For completeness, in the end, it needs to be underlined that, use of high ductility with brittle material at façade is a choice that leads to pay two times by the owner; this means that the choice of structural elements and non‐structural elements are directly related to each other. Further, it is also concluded that the overstrength of the frames in Eurocode 8 is defined well and is convenient when the seismic situation govern the design for strength, when the design of frame is governed by drift due to the inconvenient choice of drift; the Eurocode 8 definition of overstrength does not hold any stability and vary drastically. The proposed methodology will not only allow the designers to use Eurocode 8 optimally for the seismic design of frames but will also let a consistent design approach without un‐necessary iteration.

FUTURE STUDIES The presented study evolved interesting results and to the point suggestions for the technicians involved in the design for moment resisting frames. The study is aimed to be continued in order to suitably apply the optimization rules and therefore to check the extent of its applicability. Further, the consequences of connections are also intended to be investigated in the future studies. As the foreseen observations are for rigid connections, therefore one can think for the Eurocode 8 provisions when semi‐rigid connections are provided, as they are more flexible.



391


References [1]

[2]

[3]

[4] [5]

[6]

[7]

[8] [9]

[10]

[11] [12] [13] [14]

[15]

C. Meletti, E. Patacca, and P. Scandone, "Construction of a seismotectonic model: the case of Italy," Pure and Applied Geophysics, vol. 157, pp. 11‐35, 2000. G. Solomos, A. Pinto, and S. Dimova, "A review of the seismic hazard zonation in national building codes in the context of Eurocode 8," European Commission, EUR, vol. 23563, p. 72, 2008. S. Cutcliffe, "On Shaky Ground: A History of Earthquake Resistant Building Design Codes and Safety Standards in the United States in the Twentieth Century," Bulletin of Science Technology and Society, vol. 16, pp. 311‐328, 1996. S. H. Cutcliffe, "Earthquake resistant building design codes and safety standards: The California experience," GeoJournal, vol. 51, pp. 259‐262, 2000. T. Rossetto and N. Peiris, "Observations of damage due to the Kashmir earthquake of October 8, 2005 and study of current seismic provisions for buildings in Pakistan," Bulletin of Earthquake Engineering, vol. 7, pp. 681‐699, 2009. R. O. Hamburger. (2009). Facts for Steel Buildings Number 3 ‐ Earthquakes and Seismic Design. Available: http://www.aisc.org/store/p‐1995‐facts‐for‐steel‐ buildings‐number‐3‐earthquakes‐and‐seismic.aspx N. Ahmad, "A Note on The 2012 Emilia‐Romagna Earthquake, Italy," International Journal of Earth Sciences and Engineering, vol. Vol 5. No.3 p. 1, 2012. R. Jackson, Thirty Seconds at Quetta. The story of an earthquake. [With plates.]: Evans Brothers, 1960. N. Ahmad, "Seismic risk assessment and loss estimation of building stock of Pakistan," PhD PhD thesis, ROSE School‐IUSS Pavia, University of Pavia, Pavia, 2011. S. L. Kumar, "Theory of Earthquake Resisting Design With a Note on Earthquake Resisting Construction in Baluchistan," Punjab Enginering Congress, 1933. R. Reitherman, "Effects of Significant Earthquakes On the Development of Earthquake Engineering," presented at the 2006 NZSEE, New Zealand, 2006. S. K. Jain and N. C. Nigam, "Historical developments and current status of earthquake engineering in India," 2000. UBC‐1997, "International Conference of Building Officials,," ed. Whittier, California 1997. Building Code of Pakistan (BCP), "Building Code of Pakistan (Seismic Provisions‐2007)," in Ministry of Housing and Works, ed. Islamabad: Pakistan Engineering Council, 2007. R. O. Hamburger and N. A. Nazir, "Seismic design of steel structures," ed: CRC Press, Boca Raton, Florida, 2003.

References


392


[16] [17] [18] [19] [20] [21] [22] [23]

[24]

[25]

[26]

[27] [28] [29]

[30] [31]

[32]

[33]

J. Barsom and S. Korvink, "Through‐thickness properties of structural steels," Journal of Structural Engineering, vol. 124, pp. 727‐735, 1998. W. F. Chen and C. Scawthorn, Earthquake engineering handbook vol. 24: CRC, 2002. F. Naeim, The seismic design handbook: Springer, 1989. A. Hayward, F. Weare, and A. Oakhill, Steel detailers' manual: Wiley‐Blackwell, 2011. M. B. Wong, Plastic analysis and design of steel structures: Butterworth‐ Heinemann, 2009. N. S. Trahair, M. A. Bradford, D. A. Nethercot, and L. Gardner, The Behaviour and Design of Steel Structures to EC3 4E: Taylor & Francis, 2008. H. A. Nageim, Steel structures: practical design studies: Taylor & Francis, 2005. Scott M. Adan and R. O. Hamburger. (2010) Steel Special Moment Frames: A Historic Perspective. STRUCTURE. Available: http://www.structuremag.org/Archives/2010‐6/C‐StructPerf‐Adan‐June10.pdf C. W. Roeder and E. P. Popov, "Inelastic behavior of eccentrically braced steel frames under cyclic loadings," NASA STI/Recon Technical Report N, vol. 78, p. 20375, 1977. A. Derecho, M. Iqbal, S. Ghosh, M. Fintel, W. Corley, and A. Scanlon, "Structural walls in earthquake‐resistant buildings: Dynamic analysis of isolated structural walls. Development of design procedure: Design force levels," Final Report Portland Cement Association, Skokie, IL. Construction Technology Labs., vol. 1, 1981. S. El‐Bahey and M. Bruneau, "Bridge piers with structural fuses and bi‐steel columns. II: Analytical investigation," Journal of Bridge Engineering, vol. 17, pp. 36‐46, 2011. M. Bruneau, C. M. Uang, and A. S. Whittaker, Ductile design of steel structures: McGraw‐Hill Professional, 1998. E. D. Booth and D. Key, Earthquake design practice for buildings: Thomas Telford Services Ltd, 2006. A. Mirzaei, H. Estekanchi, and A. Vafaei, "Application of Endurance Time Method in Performance‐Based Design of Steel Moment Frames," Scientia Itanica, 2010. S. T. Bungale, "Wind and Earthquake Resistant Buildings Structural Analysis and Design," ed: Marcel Dekker, USA, 2005, 892 p, 2005. T. Margaret, Eduardo Castro., P. Flavio, B. Andrzej, and E. Mohammed. (2008) Performance‐Based Design with Application to Seismic Hazard. STRUCTURE. Available: http://www.structuremag.org/Archives/2008‐6/C‐StrDesign‐ ettouney‐etal‐June‐08.pdf EN‐1998‐1, "Eurocode 8, Design of Structures for Earthquake Resistance, Part 1: General rules, seismic actions and rules for buildings," in European Committee for Standardization, CEN, ed. 36 B‐1050, Brussels, 2005. M. N. Fardis, Seismic design, assessment and retrofitting of concrete buildings: based on EN‐Eurocode 8 vol. 8: Springer Verlag, 2009.

References


393


[34]

[35] [36] [37] [38] [39] [40] [41]

[42] [43]

[44]

[45] [46]

[47] [48]

[49]

[50]

[51]

J. Diebold, K. Moore, T. Hale, and G. Mochizuki, "SEAOC Blue Book: Seismic Design Recommendations 1959 to 2008," ed: International Association for Earthquake Engineering, 2008. A. K. Chopra, Dynamics of structures vol. 1: Prentice Hall, 1995. M. N. Fardis, Advances in performance‐based earthquake engineering vol. 13: Springer Verlag, 2010. S. K. Kunnath, "Chapter 5: Performance‐based seismic design and evaluation of building structures," ed, 2006. V. Gioncu and F. M. Mazzolani, Ductility of seismic resistant steel structures vol. 1: Taylor & Francis, 2002. ANSI/AISC‐341‐10, "Seismic provisions for structural steel buildings," ed. Chicago, Illinois 60601‐1802: American Institute of Steel Construction, 2010. ANSI/AISC‐360‐10, "Specification for structural steel buildings," ed. Chicago, Illinois 60601‐1802: American Institute of Steel Construction, 2010. P. FEMA‐350, "Recommended seismic design criteria for new steel moment‐ frame buildings FEMA‐350," in FEMA‐350, Rich mond, Calif, ed. Washington, DC, 2000. P. FEMA‐356, "Commentary for the seismic rehabilitation of buildings, FEMA‐ 356," in Federal Emergency Management Agency, ed. Washington, DC, 2000. NEHRP‐1998, "NEHRP recommended provisions for seismic regulations for new buildings [1997 ed.]," in Federal Emergency Management Agency, FEMA vol. 302, ed, 1998, p. 337. P. FEMA‐273, "NEHRP Guidelines for the Seismic Rehabilitation of Buildings‐ FEMA‐273," in Federal Emergency Management Agency, ed. Washington, DC, 1997. M. Brescia, "Rotation capacity and overstrength of steel members for seismic design," Universita’ degli Studi di Napoli Federico II, 2008. Scott M. Adan and Ronald O. Hamburger. (2010) Steel Special Moment Frames. STRUCTURE. Available: http://www.structuremag.org/Archives/2010‐ 11/C‐StrucPerformance‐Adan‐Nov10.pdf G. Metelli, "Theoretical and experimental study on the cyclic behaviour of X braced steel frames," Engineering Structures, vol. 46, pp. 763‐773, 2013. G. Brandonisio, M. Toreno, E. Grande, E. Mele, and A. De Luca, "Seismic design of concentric braced frames," Journal of Constructional Steel Research, vol. 78, pp. 22‐37, 11// 2012. H. Moghaddam, I. Hajirasouliha, and A. Doostan, "Optimum seismic design of concentrically braced steel frames: concepts and design procedures," Journal of Constructional Steel Research, vol. 61, pp. 151‐166, 2005. P. Uriz and S. A. Mahin, "Seismic performance assessment of concentrically braced steel frames," in Proceedings of the 13th world conference on earthquake engineering, 2004, p. 6. E. M. Marino, M. Nakashima, and K. M. Mosalam, "Comparison of European and Japanese seismic design of steel building structures," Engineering structures, vol. 27, pp. 827‐840, 2005.

References


394


[52]

[53] [54]

[55]

[56] [57] [58] [59]

[60]

[61] [62]

[63]

[64] [65] [66]

[67] [68] [69]

E. M. Marino and M. Nakashima, "Seismic performance and new design procedure for chevron‐braced frames," Earthquake engineering & structural dynamics, vol. 35, pp. 433‐452, 2006. D. Key, "Seismic Design Codes: Philosophy» Application and Effectiveness," 1993, pp. 273‐83. ASCE/SEI‐7‐10, "Minimum design loads for buildings and other structures," ed. 1801 Alexander Bell Drive Reston, Virginia 20191: American Society of Civil Engineers, 2010. I. B. Code, "Internationa Building Code 2009 (IBC‐2009)," ed. 4051 West Flossmoor Road, Country Club Hills, Illinois 60478. U.S.A: International code council, 2009. NBCC, "National Building Code of Canada," Institute for Research in Construction, 2005. NZS‐code, "Code of practice for general structural design and design loadings for buildings," NZ Standards Association, Wellington, 1992. Australian Standards (A.S), "Part 4: Earthquake Loads," in Minimum Design Loads on Structures, , ed, 1993. J. Humar and M. Rahgozar, "Concept of overstrength in seismic design," presented at the Eleventh world conference on earthquake engineering (11WCEE), ACAPULCO, MEXICO, 1996. T. Balendra and X. Huang, "Overstrength and ductility factors for steel frames designed according to BS 5950," Journal of Structural Engineering, vol. 129, p. 1019, 2003. !!! INVALID CITATION !!! H. Krawinkler and M. Zohrei, "Cumulative damage in steel structures subjected to earthquake ground motions," Computers & Structures, vol. 16, pp. 531‐541, 1983. G. H. Powell and R. Allahabadi, "Seismic damage prediction by deterministic methods: concepts and procedures," Earthquake engineering & structural dynamics, vol. 16, pp. 719‐734, 1988. A. S. Veletsos and N. M. Newmark, "Effect of inelastic behavior on the response of simple systems to earthquake motions," 1960. J. Penzien, "Elasto‐Plastic Response of Idealized Multi‐Story Structures Subjected to a strong Motion Earthquake, II WCEE," ed: Tokyo, 1960. N. M. H. Newmark, W. J., "Seismic design criteria for nuclear reactor facilities,," in Building Practices for Disaster Mitigation, National Bureau of Standards, , ed. United States: U. S. Department of Commerce,, 1973, pp. 209‐ 236. S. A. Mahin and V. V. Bertero, "An evaluation of inelastic seismic design spectra," Journal of the Structural Division, vol. 107, pp. 1777‐1795, 1981. V. Piluso, Theory and design of seismic resistant steel frames: Taylor & Francis, 1996. G. Ballio, ECCS approach for the design of steel structures to resist earthquakes: IABSE, 1985.

References


395


[70] [71] [72] [73] [74] [75] [76] [77]

[78] [79] [80]

[81] [82] [83] [84] [85]

[86]

[87]

[88]

V. Petrini, P. Setti, and R. Zandonini, "Inelastic behaviour of steel frames subjected to strong earthquakes," 1982. H. Krawinkler, "New trends in seismic design methodology," 1995. E. Miranda and V. V. Bertero, "Evaluation of strength reduction factors for earthquake‐resistant design," Earthquake Spectra, vol. 10, pp. 357‐357, 1994. P. Fajfar, "Capacity spectrum method based on inelastic demand spectra," Earthquake engineering and structural dynamics, vol. 28, pp. 979‐994, 1999. G. W. Housner, "Behavior of structures during earthquakes," 1959. M. Como and G. Lanni, "Aseismic toughness of structures," Meccanica, vol. 18, pp. 107‐114, 1983. B. Kato and H. Akiyama, "Seismic design of steel buildings," Journal of the Structural Division, vol. 108, pp. 1709‐1721, 1982. SEAOC Seismology Committee. (2008) A Brief Guide to Seismic Design Factors. STRUCTURE. Available: http://www.structuremag.org/Archives/2008‐9/C‐ GuestCol‐SeismicDesign‐SEAOC‐Sept08.pdf C. M. Uang, "Establishing R (or Rw) and Cd factors for building seismic provisions," Journal of Structural Engineering, vol. 117, pp. 19‐28, 1991. V. Gioncu, "Framed structures. Ductility and seismic response: General Report," Journal of Constructional Steel Research, vol. 55, pp. 125‐154, 2000. M. Esposto, "PTED beam‐to‐column connections for steel moment resisting frames: structural identification based on numerical analyses," PhD, Department of Structural Engineering, Faculty of Engineering, University of Naples, Federico II, Naples, 2008. T. Paulay and M. J. N. Priestley, Seismic design of reinforced concrete and masonry buildings: Wiley Online Library, 1992. M. J. N. Priestley, Myths and fallacies in earthquake engineering, revisited: IUSS press, 2003. A. Plumier, "General report on local ductility," Journal of Constructional Steel Research, vol. 55, pp. 91‐107, 2000. M. Rahgozar and J. Humar, "Accounting for overstrength in seismic design of steel structures," Canadian journal of civil engineering, vol. 25, pp. 1‐15, 1998. D. Mitchell, R. Tremblay, E. Karacabeyli, P. Paultre, M. Saatcioglu, and D. L. Anderson, "Seismic force modification factors for the proposed 2005 edition of the National Building Code of Canada," Canadian journal of civil engineering, vol. 30, pp. 308‐327, 2003. V. V. Bertero, A. E. Aktan, F. A. Charney, and R. Sause, "US–Japan cooperative earthquake research program: earthquake simulation tests and associated studies of a 1/5 th scale model of a 7‐story reinforced concrete test structure," 1984. C. M. Uang and V. V. Bertero, Earthquake simulation tests and associated studies of a 0.3‐scale model of a six‐story concentrically braced steel structure vol. 86: Earthquake Engineering Research Center, College of Engineering, University of California, 1986. A. S. Whittaker, V. V. Bertero, and C. Thompson, Earthquake simulator testing

References


396


[89]

[90]

[91] [92] [93] [94]

[95]

[96]

[97] [98]

[99]

[100]

[101]

[102]

[103]

of steel plate added damping and stiffness elements vol. 89: Earthquake Engineering Research Center, University of California at Berkeley, 1989. J. Osteraas and H. Krawinkler, "The Mexico earthquake of September 19, 1985—Behavior of steel buildings," Earthquake spectra, vol. 5, pp. 51‐88, 1989. A. S. Elnashai and A. M. Mwafy, "Overstrength and force reduction factors of multistorey reinforced concrete buildings," The structural Design of Tall Buildings, vol. 11, pp. 329‐351, 2002. J. Kim and H. Choi, "Response modification factors of chevron‐braced frames," Engineering Structures, vol. 27, pp. 285‐300, 2005. A. J. Kappos, "Evaluation of behaviour factors on the basis of ductility and overstrength studies," Engineering Structures, vol. 21, pp. 823‐835, 1999. A. A. Nassar and H. Krawinkler, "Seismic demands for SDOF and MDOF systems," Engineering, vol. 95, 1991. V. V. Bertero, Design guidelines for ductility and drift limits: review of state‐of‐ the‐practice and state‐of‐the‐art in ductility and drift‐based earthquake‐ resistant design of buildings vol. 91: Earthquake Engineering Research Center, University of California at Berkeley, 1991. R. L. Sanchez and A. Plumier, "Parametric study of ductile moment‐resisting steel frames: A first step towards Eurocode 8 calibration," Earthquake Engineering & Structural Dynamics, vol. 37, pp. 1135‐1155, 2008. G. Ballio, C. A. Castiglioni, and F. Perotti, "On the assessment of structural design factors for steel structures," 9th WCEE, Tokyo, vol. 5, pp. 1167‐1171, 1988. F. Mazzolani and V. Piluso, "ECCS manual on design of steel structures in seismic zones," ECCS, TC, vol. 13, 1994. M. Nakashima and P. Chusilp, "A partial view of Japanese post‐Kobe seismic design and construction practices," Earthquake Engineering and Engineering Seismology, vol. 4, pp. 3‐13, 2003. M. Nakashima, C. W. Roeder, and Y. Maruoka, "Steel moment frames for earthquakes in United States and Japan," Journal of Structural Engineering, vol. 126, p. 861, 2000. L. M. Rand, J. P. Fleming, and L. G. Archuleta, "A comparative parametric study of the AISC 1978, DIN 18–800 (1) and BS5950 steel design codes," Finite Elements in Analysis and Design, vol. 4, pp. 91‐114, 1988. A. Elghazouli, "Assessment of European seismic design procedures for steel framed structures," Bulletin of Earthquake Engineering, vol. 8, pp. 65‐89, 2010. S. Paul, C. Murty, and S. K. Jain, "State‐of‐the‐art Review of Seismic Design of Steel Moment Resisting Frames–Part I: General Considerations and Stability Provisions," Journal of Structural Engineering, vol. 27, pp. 23‐32, 2000. S. Paul, C. Murty, and S. K. Jain, "State‐of‐the‐art review of seismic design of steel moment resisting frames Part II+: Strength and Drift criteria," Journal of Structural Engineering, vol. 27, p. 117, 2000.

References


397


[104]

[105]

[106]

[107]

[108] [109] [110] [111]

[112] [113]

[114]

[115]

[116] [117]

[118] [119]

[120]

E. Mele, A. De Luca, and L. Di Sarno, "Design aspects affecting the seismic behaviour of steel MRF buildings: analysis of three case studies," presented at the 12th World Conference on Earthquake Engineering, Auckland, N.Z., 2000. E. Mele, L. Di Sarno, and A. De Luca, "Seismic behaviour of perimeter and spatial steel frames," Journal of earthquake engineering, vol. 8, pp. 457‐496, 2004. T. Hasegawa, K. Takahashi, and T. Nagao, "Comparison of seismic performance between U.S. Steel perimeter frame and Japanese spatial moment resisting frame," presented at the 12th World Conference on Earthquake Engineering (WCEE), Auckland, N.Z., 2000. D. Özhendekci and N. Özhendekci, "Seismic performance of steel special moment resisting frames with different span arrangements," Journal of Constructional Steel Research, vol. 72, pp. 51–60, 2011. A. Gupta and H. Krawinkler, "Seismic demands for the performance evaluation of steel moment resisting frame structures," Stanford University, 1998. R. K. Goel and A. K. Chopra, "Period formulas for moment‐resisting frame buildings," Civil and Environmental Engineering, p. 62, 1997. R. K. Goel and A. K. Chopra, "Evaluation of modal and FEMA pushover analyses: SAC buildings," Earthquake spectra, vol. 20, p. 225, 2004. S. Y. Yun, R. O. Hamburger, C. A. Cornell, and D. A. Foutch, "Seismic performance evaluation for steel moment frames," Journal of Structural Engineering, vol. 128, pp. 534‐545, 2002. D. A. Foutch and S. Y. Yun, "Modeling of steel moment frames for seismic loads," Journal of Constructional Steel Research, vol. 58, pp. 529‐564, 2002. K. Lee and D. A. Foutch, "Seismic performance evaluation of pre‐Northridge steel frame buildings with brittle connections," Journal of Structural Engineering, vol. 128, p. 546, 2002. S. Mahin, J. Malley, and R. Hamburger, "Overview of the FEMA/SAC program for reduction of earthquake hazards in steel moment frame structures," Journal of Constructional Steel Research, vol. 58, pp. 511‐528, 2002. S. A. Mahin, J. O. Malley, R. O. Hamburger, and M. Mahoney, "Overview of the US program for reduction of earthquake hazards in steel moment‐frame structures," Earthquake Spectra, vol. 19, p. 237, 2003. S. A. Freeman, "Prediction of response of concrete buildings to severe earthquake motion," pp. 589‐605, 1978. P. Fajfar and M. Fischinger, "N2‐A method for non‐linear seismic analysis of regular buildings," presented at the Proceedings of 9th World Conference on Earthquake Engineering (WCEE), Tokyo Japan, 1988. P. Fajfar, "A nonlinear analysis method for performance‐based seismic design," Earthquake Spectra, vol. 16, pp. 573‐592, 2000. M. O. Eberhard and M. A. Sozen, "Behavior Based Method to Determine Design Shear in Earthquake Resistant Walls," Journal of Structural Engineering, vol. 119, pp. 619‐640, 1993. H. Krawinkler and G. Seneviratna, "Pros and cons of a pushover analysis of

References


398


[121]

[122] [123] [124]

[125]

[126]

[127]

[128] [129]

[130]

[131]

[132]

[133]

[134]

[135]

seismic performance evaluation," Engineering structures, vol. 20, pp. 452‐464, 1998. W. Tso and A. Moghadam, "Pushover procedure for seismic analysis of buildings," Progress in Structural Engineering and Materials, vol. 1, pp. 337‐ 344, 1998. A. Mwafy and A. S. Elnashai, "Static pushover versus dynamic collapse analysis of RC buildings," Engineering structures, vol. 23, pp. 407‐424, 2001. S. K. Kunnath and B. Gupta, "Validity of deformation demand estimates using nonlinear static procedures," 2000. F. M. Mazzolani and V. Piluso, "Plastic design of seismic resistant steel frames," Earthquake engineering & structural dynamics, vol. 26, pp. 167‐191, 1997. S. W. Choi and H. S. Park, "A Study to Reduce the Inter‐story Drifts of Steel Moment Frames Subjected to Seismic Load," Procedia Engineering, vol. 14, pp. 325‐328, 2011. M. Fathi, F. Daneshjoo, and R. E. Melchers, "A method for determining the behaviour factor of moment‐resisting steel frames with semi‐rigid connections," Engineering Structures, vol. 28, pp. 514‐531, 2006. C. A. Castiglioni and A. Zambrano, "Determination of the behaviour factor of steel moment‐resisting (MR) frames by a damage accumulation approach," Journal of Constructional Steel Research, vol. 66, pp. 723‐735, 2010. V. Gioncu and F. M. Mazzolani, Earthquake engineering for structural design: Taylor & Francis, 2009. G. De Matteis, "Effect of lightweight cladding panels on the seismic performance of moment resisting steel frames," Engineering structures, vol. 27, pp. 1662‐1676, 2005. G. De Matteis, R. Landolfo, and F. Mazzolani, "Seismic response of MR steel frames with low‐yield steel shear panels," Engineering Structures, vol. 25, pp. 155‐168, 2003. G. De Matteis, F. Mazzolani, and S. Panico, "Pure aluminium shear panels as dissipative devices in moment‐resisting steel frames," Earthquake Engineering & Structural Dynamics, vol. 36, pp. 841‐859, 2007. G. Della Corte, De Matteis, G., Landolfo, R., Mazzolani, FM., "Seismic analysis of MR steel frames based on refined hysteretic models of connections," Journal of Constructional Steel Research, vol. 58, pp. 1331‐1345, 2002. J. D. a. K. Osteraas, H.,. (1990). Strength and Ductility Considerations in Seismic Design ‐ Report No 90. Available: https://blume.stanford.edu/sites/default/files/TR90_Osteraas.pdf P. FEMA‐450, "NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (FEMA 450)," in Building Seismic Safety Council of the National Institute of Building Sciences, ed. Washington, DC, 2003. C. K. Kang and B. J. Choi, "Statistical study and evaluation of ductility factors for elastic perfectly plastic SDOF systems in stiff soils," International Journal of

References


399


[136] [137]

[138]

[139] [140] [141] [142]

[143] [144] [145]

[146]

[147] [148]

[149] [150] [151]

[152]

[153]

Steel Structures, vol. 4, pp. 15‐24, 2004. S. S. P. Lai and J. M. Biggs, "Inelastic response spectra for aseismic building design," Journal of the Structural Division, vol. 106, pp. 1295‐1310, 1980. R. Riddell and N. M. Newmark, "Statistical analysis of the response of nonlinear systems subjected to earthquakes," Illinois Univ., Urbana (USA). Dept. of Civil Engineering1979. R. Riddell, P. Hidalgo, and E. Cruz, "Response modification factors for earthquake resistant design of short period buildings," Earthquake spectra, vol. 5, pp. 571‐590, 1989. E. Miranda, "Site Dependent Strength Reduction Factors," Journal of Structural Engineering, vol. 119, p. 3503, 1993. B. Borzi and A. S. Elnashai, "Refined force reduction factors for seismic design," Engineering Structures, vol. 22, pp. 1244‐1260, 2000. H. Furuta, M. Shinozuka, and J. T. P. Yao, "Probabilistic and fuzzy representation of redundancy in structural systems," ed, 1985. Applied Technology Council (ATC), "Structural Response Modification Factors (ATC‐19)," 1995 ed. Redwood City, California 94065: APPLIED TECHNOLOGY COUNCIL, 1995. D. M. Frangopol and J. P. Curley, "Damage States, Redundancy and System Strength," 1987. J. Tang and J. Yao, "Evaluation of Structural Damage and Redundancy," 1987. N. F. G. Youssef, D. Bonowitz, and J. L. Gross, "A survey of steel moment‐ resisting frame buildings affected by the 1994 Northridge earthquake," The National Institute of Standards and Technology (NIST) 1995. S. L. Wood, "Performance of reinforced concrete buildings during the 1985 Chile earthquake: Implications for the design of structural walls," Earthquake spectra, vol. 7, pp. 607‐638, 1991. F. Moses, "Reliability of structural systems," Journal of the Structural Division, vol. 100, pp. 1813‐1820, 1974. NEHRP, "NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (FEMA 450)," ed: Building Seismic Safety Council of the National Institute of Building Sciences Washington, DC, 2003. NEHRP, "Strategic Plan for the National Earthquake Hazards Reduction Program," FEMA, NIST, USGS report 20082008. F. M. Mazzolani, "3D aluminium structures," Thin‐Walled Structures, vol. 61, pp. 258–266, 2012. M. T. Naqash, G. De Matteis, and A. De Luca, "Seismic design of Steel Moment Resisting frames‐European Versus American Practice," NED University Journal of Research, vol. Thematic Issue on Earthquake, pp. 45‐59, October 2012 2012. M. T. Naqash, "Optimum design of Steel Moment Resisting Frames using Eurocode 8," PhD Doctorate Thesis, Department of Engineering and Geology, University of Chiete and Pescara, Pescara, 2012. F. Mazzolani, Aluminium alloy structures: Taylor & Francis, 1994.

References


400


[154]

[155] [156] [157] [158] [159] [160]

[161]

[162] [163]

[164]

[165]

[166] [167]

[168]

[169]

[170] [171]

S. A. Mahin, "Overview of the U.S. Program for Reduction of Earthquake Hazards in Steel Moment‐Frame Structures," Earthquake Spectra, vol. Vol. 19, 2003. B. Dowswell, "Steel Connection Design—What You Didn’t Learn in School," in 2006 Structural Engineering and Public Safety, 2006, pp. 1‐10. B. Dowswell, "Calculation of Transfer Forces in Steel Structures," in Structures 2004—Building On The Past@ sSecuring The Future, 2004, pp. 1‐7. M. T. Naqash, "Atelier I "Design of Industrial building"," Department of Structural Engineering University of Naples "Federico II"2009. M. T. Naqash, "Atelier II "Design of Multisotry building"," Department of Structural Engineering University of Naples "Federico II"2009. L. A. Soltis and T. L. Wilkinson, Bolted‐connection design: US Department of Agriculture, Forest Service, Forest Products Laboratory, 1987. EN‐1993‐1‐8, "Eurocode 3. Design of steel structures. Part 1‐8: Design of Joints ", ed. 36 B‐1050, Brussels: European Committee for Standardization, CEN, 2005. C. Faella, V. Piluso, and G. Rizzano, "A new method to design extended end plate connections and semirigid braced frames," Journal of Constructional Steel Research, vol. 41, pp. 61‐91, 1997. C. Faella, V. Piluso, and G. Rizzano, Structural steel semirigid connections: theory, design, and software: CRC press, 1999. F. Iannone, M. Latour, V. Piluso, and G. Rizzano, "Experimental analysis of bolted steel beam‐to‐column connections: Component identification," Journal of Earthquake Engineering, vol. 15, pp. 214‐244, 2011. M. Latour, V. Piluso, and G. Rizzano, "Cyclic Modeling of Bolted Beam‐to‐ Column Connections: Component Approach," Journal of Earthquake Engineering, vol. 15, pp. 537‐563, 2011. C. Faella, V. Piluso, and G. Rizzano, "Cyclic behaviour of bolted joint components," Journal of Constructional Steel Research, vol. 46, pp. 433‐434, 1998. G. De Matteis, "Title," unpublished|. C. Faella, V. Piluso, and G. Rizzano, "Connection influence on the elastic and inelastic behaviour of steel frames," in International workshop and seminar on behaviour of steel structures in seismic areas, STESSA, 1994. G. Della Corte, G. De Matteis, and R. Landolfo, "Influence of connection modelling on seismic response of moment resisting steel frames," Moment resistant connections of steel buildings frames in seismic areas, E. & FN Spon, London, pp. 485‐512, 2000. L. Calado, G. De Matteis, and R. Landolfo, "Experimental response of top and seat angle semi‐rigid steel frame connections," Materials and Structures, vol. 33, pp. 499‐510, 2000. EN‐1999‐1‐1, "Design of aluminium structures," in European Committee for Standardization, CEN, ed. 36 B‐1050, Brussels, 2007. G. De Matteis, R. Landolfo, and L. Calado, "Cyclic behaviour of semi‐rigid angle

References


401


[172]

[173]

[174]

[175] [176] [177]

[178]

[179]

[180]

[181]

[182]

[183]

[184]

[185]

connections: A comparative study of tests and modeling," Behaviour of Steel Structures in Seismic Areas, pp. 165‐174, 2000. L. Calado, G. De Matteis, R. Landolfo, and F. Mazzolani, "Cyclic Behavior of Steel Beam‐to‐Column Connections: Interpretation of Experimental Results," in SDSS’99 Stability and Ductility of Steel Structures, Proc. 6th International Colloquium, 1999, pp. 211‐220. E. Cosenza, A. De Luca, and C. Faella, "Elastic buckling of semi‐rigid sway frames," Elsevier Applied Science, Structural Connections. Stability and Strength, pp. 253‐295, 1989. M. De Stefano, A. De Luca, and A. Astaneh‐Asl, "Modeling of cyclic moment‐ rotation response of double‐angle connections," Journal of Structural Engineering, vol. 120, pp. 212‐229, 1994. P. Zoetemeijer, "A design method for the tension side of statically loaded bolted beam‐to‐column connections," Monogr. Heron, vol. 20, 1974. EN‐1993‐1‐8, "Design of steel structures " in Part 1.8: Design of joints, ed. 36 B‐1050, Brussels: European Committee for Standardization, CEN, 2005. G. De Matteis, R. Landolfo, and F. Mazzolani, "Experimental Analysis of Aluminium T‐stubs: framing of the research activity," in Proc. of the 8th Int. Conf. on Joints in Aluminium (INALCO 2001), Munich (Germany), 2001, pp. 28‐ 30. The Steel Construction Institute, Joints in Steel Construction Moment Connections. Silwood Park London, England: The Steel Construction Institute, 1995. A. M. Girão Coelho, Bijlaard, F.S.K., Gresnigt, N., Simões da Silva, L., "Experimental assessment of the behaviour of bolted T‐stub connections made up of welded plates," Journal of Constructional Steel Research, vol. 60, pp. 269‐311, 2004. G. De Matteis, A. Mandara, and F. M. Mazzolani, "T‐stub aluminium joints: influence of behavioural parameters," Computers & Structures, vol. 78, pp. 311‐327, 2000. G. De Matteis, M. T. Naqash, and G. Brando, "Effective length of aluminium T‐ stub connections by parametric analysis," Engineering Structures, vol. 41, pp. 548‐561, 2012. G. De Matteis, Brescia, M., Formisano, A., Mazzolani, F.M., "Behaviour of welded aluminium T‐stub joints under monotonic loading," Computers & Structures, vol. 87, pp. 990‐1002, 2009. V. Piluso and G. Rizzano, "Experimental analysis and modelling of bolted T‐ stubs under cyclic loads," Journal of Constructional Steel Research, vol. 64, pp. 655‐669, 2008. V. Piluso, C. Faella, and G. Rizzano, "Ultimate behavior of bolted T‐stubs. I: Theoretical model," Journal of Structural Engineering, vol. 127, pp. 686‐693, 2001. V. Piluso, C. Faella, and G. Rizzano, "Ultimate behavior of bolted T‐stubs. II: Model validation," Journal of Structural Engineering, vol. 127, pp. 694‐704,

References


402


[186] [187] [188]

[189]

[190]

[191] [192] [193] [194] [195]

[196] [197] [198]

[199]

[200]

[201] [202] [203]

2001. M. E. Lemonis and C. J. Gantes, "Incremental modeling of T‐stub connections," Journal of Mechanics of Materials and Structures, vol. 1, pp. 1135‐1159, 2006. G. Stamatopoulos, "Influence of the T‐stub Flexibility on Its Strength," International Journal of Steel Structures, vol. 10, pp. 73‐79, 2010. E. Mistakidis, C. Baniotopoulos, C. Bisbos, and P. Panagiotopoulos, "Steel T‐ stub connections under static loading: An effective 2‐D numerical model," Journal of Constructional Steel Research, vol. 44, pp. 51‐67, 1997. A. M. G. Coelho, L. S. da Silva, and F. S. K. Bijlaard, "Finite‐element modeling of the nonlinear behavior of bolted T‐stub connections," Journal of structural engineering, vol. 132, pp. 918‐928, 2006. E. Efthymiou, M. Zygomalos, and C. C. Baniotopoulos, "On the structural response of aluminium T‐stub joints under tension," Trans FAMENA. v30 i1, pp. 45‐58, 2006. G. De Matteis and F. M. Mazzolani, "Behaviour of Welded Aluminium T‐Stub Connections: Experimental Analysis and Interpretative Models," 2006. M. Bahaari and A. Sherbourne, "Computer modelling of an extended end‐ plate bolted connection," Computers & structures, vol. 52, pp. 879‐893, 1994. M. R. Bahaari and A. N. Sherbourne, "Behavior of eight‐bolt large capacity endplate connections," Computers & Structures, vol. 77, pp. 315‐325, 2000. A. N. Sherbourne and M. R. Bahaari, "3D simulation of end‐plate bolted connections," Journal of Structural Engineering, vol. 120, pp. 3122‐3136, 1994. O. Bursi and J. P. Jaspart, "Calibration of a finite element model for isolated bolted end‐plate steel connections," Journal of Constructional Steel Research, vol. 44, pp. 225‐262, 1997. R. Douty and W. McGuire, "High strength bolted moment connections," Journal of the Structural Division, ASCE, vol. 91, pp. 101‐128, 1965. H. Agerskov, "High‐strength bolted connections subject to prying," Journal of the Structural Division, vol. 102, pp. 161‐175, 1976. J. Packer and L. Morris, "A limit state design method for the tension region of bolted beam‐column connections," The Structural Engineer, vol. 55, pp. 446‐ 458, 1977. D. Moore and P. Sims, "Preliminary investigations into the behaviour of extended end‐plate steel connections with backing plates," Journal of Constructional Steel Research, vol. 6, pp. 95‐122, 1986. W. Grogan and J. Surtees, "Experimental behaviour of end plate connections reinforced with bolted backing angles," Journal of Constructional Steel Research, vol. 50, pp. 71‐96, 1999. J. A. Swanson and R. T. Leon, "Bolted steel connections: Tests on T‐stub components," Journal of Structural Engineering, vol. 126, pp. 50‐56, 2000. ABAQUS/Standard: User's manual vol. 1: Hibbitt, Karlsson & Sorensen Inc., 2007. EN‐1999‐1‐1, "Design of aluminium structures – Part 1‐1: general structural rules," ed. 36 B‐1050, Brussels: European Committee for Standardization, CEN,

References


403


[204]

[205]

[206]

[207]

[208]

[209] [210] [211] [212] [213]

[214]

[215] [216] [217] [218]

[219] [220]

2007. A. De Martino, R. Landolfo, and F. Mazzolani, "The use of the Ramberg‐ Osgood law for materials of round‐house type," Materials and Structures, vol. 23, pp. 59‐67, 1990. Wikipedia. (2012). Building code ‐‐‐ Wikipedia The Free Encyclopedia. Available: http://en.wikipedia.org/w/index.php?title=Building_code&oldid=494319986 Wikipedia. (2012). Structural engineering ‐‐‐ Wikipedia The Free Encyclopedia. Available: http://en.wikipedia.org/w/index.php?title=Structural_engineering&oldid=510 546730 J. O. Malley, C. J. Carter, and C. M. Saunders, "Seismic Design Guidelines and Provisions for Steel‐Framed Buildings: FEMA 267/267A and 1997 AISC Seismic Provisions," Earthquake Spectra, vol. 16, p. 179, 2000. Wikipedia. (2012). New Madrid Seismic Zone ‐‐‐ Wikipedia The Free Encyclopedia. Available: http://en.wikipedia.org/w/index.php?title=New_Madrid_Seismic_Zone&oldid =511255249 D. R. Bonneville and R. E. Bachman, "The evolving process of US seismic code development," 2002. T. D. M. Sheckler, M.G., "The World of Earthquake Building Codes, Standards and Provisions: A View According to FEMA," 2002, p. 395. S. Ghosh, "Seismic design provisions in US codes and standards: A look back and ahead," PCI journal, vol. 47, pp. 94‐99, 2002. E. Popov, "U. S. seismic steel codes," Engineering Journal‐3rd quarter, vol. 28, pp. 119‐128, 1991. H. Hwang, "Comments on Design Earthquake Specified in the 1997 NEHRP Provisions," presented at the 12th World Conference of Earthqauke Engineering (WCEE), Auckland, Newzealand, 2000. T. G. Atkinson and P. J. Kiland. (2004). The evolution and history of SEAOC, a celebration of 75 years of history, 1929 to 2004 (January 18, 2010 ed.). Available: http:http://www.seaosc.org/about_history.cfm Applied Technology Council, Tentative Provisions for the Development of Seismic Regulations for Buildings: National Bureau of Standards, 1978. N. H. Heck, H. O. Wood, and M. W. Allen, "Earthquake history of the United States," US Coast and Geod. Surv. Publ., Serial, 1938. IBC and ICC, "International building code 2000," International Code Council, Washington, DC, 2000. B. S. S. Council, "NEHRP recommended provisions for seismic regulations for new buildings [1997 ed.]," in Federal Emergency Management Agency, FEMA vol. 302, ed, 1998, p. 337. ASCE‐7‐98, "Minimum Design Loads for Buildings and Other Structures," ed: American Society of Civil Engineers, 1998. IBC and ICC, "International building code 2006," International Code Council,

References


404


[221] [222] [223]

[224]

[225] [226] [227] [228] [229]

[230] [231]

[232] [233]

[234] [235] [236] [237]

[238]

Inc.(formerly BOCA, ICBO and SBCCI), vol. 4051, pp. 60478‐5795, 2006. ASCE‐7–05, "Minimum Design Loads for Buildings and Other Structures, ," ed. Reston, VA: American Society of Civil Engineers, 2005. R. Bjorhovde, "The 2005 American steel structures design code," Journal of Constructional Steel Research, vol. 62, pp. 1068‐1076, 2006. ANSI, "ANSI A58.1.," in American standard building code requirements for minimum design loads in buildings and other structures, ed. New York: American National Standards Institute, 1945. J. E. Beavers, "A review of seismic hazard description in US design codes and procedures," Progress in Structural Engineering and Materials, vol. 4, pp. 46‐ 63, 2002. Allowable Stress Design (ASD). "Plastic Design Specifications for Steel Buildings," AISC, Chicago, 1989. A. Marcellini, R. Daminelli, M. Pagani, and F. Riva, "Seismic hazard of the Mediterranean area," 1999. G. I. N. d. G. e. V. Vannucci, An atlas of Mediterranean seismicity: Editrice Compositori, 2004. M. N. Fardis, "Current developments and future prospects of the European code for seismic design and rehabilitation of buildings: Eurocode 8," 2004. EN‐1993‐1‐1, "Eurocode 3. Design of steel structures, Part 1‐1: General rules and rules for buildings," in European Committee for Standardization, CEN, ed. 36 B‐1050, Brussels, 2005. EN‐1990, "Eurocode 0, Basis of structural design," in European Committee for Standardization, CEN, ed. 36 B‐1050, Brussels, 2002. EN‐1991‐1‐1, "Eurocode 1, Actions on structures ‐ Part 1‐1: General actions ‐ Densities, self‐weight, imposed loads for buildings," in European Committee for Standardization, CEN, ed. 36 B‐1050, Brussels, 2004. D. Lam, P. Ang, and S. P. Chiew, Structural steelwork: design to limit state theory: Elsevier Butterworth‐Heinemann, 2004. R. L. Brockenbrough and F. S. Merritt, Structural Steel Designer’s Handbook: AISC, AASHTO, AISI, ASTM, AREMA, and ASCE‐07 Design Standards: ASCE, 2006. M. Bangash, Structural detailing in steel: a comparative study of British, European and American codes and practices: Thomas Telford, 2000. ASTM International. (1898). ASTM (American Society for Testing and Materials). Available: http://www.astm.org/Standard/index.shtml USGS. (Established since March, 1879). United States Geological Survey (USGS). Available: http://www.usgs.gov/pubprod/ D. Liu, W. M. Gho, and J. Yuan, "Ultimate capacity of high‐strength rectangular concrete‐filled steel hollow section stub columns," Journal of Constructional Steel Research, vol. 59, pp. 1499‐1515, 2003. R. O. Hamburger and S. SE, "Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications, ANSI/AISC 358‐05," 2006.

References


405


[239]

[240] [241] [242] [243] [244]

[245] [246] [247] [248]

[249]

[250]

[251]

[252]

[253]

[254]

[255]

G. Brandonisio, A. De Luca, and E. Mele, "Shear instability of panel zone in beam‐to‐column connections," Journal of Constructional Steel Research, vol. 67, pp. 891‐903, 2011. A. Elghazouli, Seismic design of buildings to EC8: Taylor and Francis, 2009. F. A. Charney, Seismic Loads: Guide to the Seismic Load Provisions of ASCE 7‐ 05: Amer Society of Civil Engineers, 2010. A. King (2000). Earthquake Loads & Earthquake Resistant Design of Buildings. Available: http://www.branz.co.nz/cms_display.php R. K. Mohammadi and M. H. EL NAGGAR, "Modifications on equivalent lateral force method," 2004. ESDEP Lecture Note. (2008). Structural Analysis for Seismic Actions (Work group‐17). Available: http://www.fgg.uni‐ lj.si/kmk/esdep/master/wg17/l0400.htm S. Kim and E. D'Amore, "Pushover analysis procedure in earthquake engineering," Earthquake spectra, vol. 15, p. 417, 1999. R. Pinho, "Using Pushover Analysis for Assessment of Buildings and Bridges," Advanced Earthquake Engineering Analysis, pp. 91‐120, 2007. R. S. Lawson, V. Vance, and H. Krawinkler, "Nonlinear static push‐over analysis‐why, when, and how?," 1994. R. Almeida and R. Carneiro‐Barros, "A new multimode load pattern for pushover analysis: the effect of higher modes of vibration," Advances in earthquake engineering, pp. 3‐13, 2003. A. K. Chopra and R. K. Goel, "A modal pushover analysis procedure to estimate seismic demands for buildings: theory and preliminary evaluation," Civil and Environmental Engineering, p. 55, 2001. A. K. Chopra and R. K. Goel, "A modal pushover analysis procedure for estimating seismic demands for buildings," Earthquake engineering & structural dynamics, vol. 31, pp. 561‐582, 2002. C. Chintanapakdee and A. K. Chopra, "Evaluation of modal pushover analysis using generic frames," Earthquake engineering & structural dynamics, vol. 32, pp. 417‐442, 2003. V. Papanikolaou, A. S. Elnashai, and J. F. Pareja, "Limits of applicability of conventional and adaptive pushover analysis for seismic response assessment," Mid‐America Earthquake Center, Civil and Environmental Engineering Department, University of Illinois at Urbana‐Champaign, 2005. S. Lee, "Non‐linear dynamic earthquake analysis of skyscrapers.," presented at the 8th World Congress of Council on Tall Buildings and Urban Habitat, Dubai, 2008. M. T. Naqash, G. De Matteis, and A. De Luca, "European versus American practice for seismic design of steel Moment Resisting Frames (MRFs)," in XXIII Italian steel conference (CTA 2011), Lacco Ameno, Ischia, Naples, 2011, pp. 599‐610. M. T. Naqash, G. De Matteis, and A. De Luca, "Effects of capacity design rules on seismic performance of steel moment resisting frames," in 15 World

References


406


[256]

[257] [258]

[259] [260] [261] [262] [263]

[264] [265]

Conference on Earthquake Engineering (WCEE), Lisbon Portugal, 2012, pp. 1‐ 10. Computer and Structures Incorporation (CSI), "General purpose civil engineering software SAP 2000 Users Manual," ed. Berkeley, California, USA: Computer and Structures, Inc.,1978‐2011, 1978. COMFLOR 46. (2012). Composite floor decking. Available: http://www.comflor‐uk.com/ P. FEMA‐273, "273‐NEHRP Guidelines for the Seismic Rehabilitation of Buildings‐FEMA‐273," in Federal Emergency Management Agency, ed. Washington, DC, 1997. P. FEMA‐440, "Improvement of Nonlinear Static Seismic Analysis Procedures," in Federal Emergency Management Agency, ed. Washington DC, 2005. A. Ghobarah, "Performance‐based design in earthquake engineering: state of development," Engineering structures, vol. 23, pp. 878‐884, 2001. California Seismic Safety Commission and A. T. Council, "Seismic evaluation and retrofit of concrete buildings," ATC‐40, 1997. A. Elghazouli, "Assessment of capacity design approaches for steel framed structures," Journal of Steel Structures, vol. 5, pp. 465‐475, 2005. A. Elghazouli, "Seismic Design of Steel‐Framed Structures to Eurocode 8," presented at the 14th World Conference on Earthquake Engineering (14WCEE), Beijing, China, 2008. M. R. Horne and W. Merchant, The stability of frames vol. 156: Pergamon Press, 1965. R. N. Patton, "Section B: Analysis and design methods," Bulletin of the New Zealand National Society for Earthquake Engineering vol. Vol 18, 1985.

References


407


Appendix A: Notations ad

= Design acceleration

δd

= Maximum displacement evaluated by applying ad

wy

= Elastic strain energy stored by the system in the yield state

wu

= Total energy stored and dissipated up to structural failure

Vw

= Actual base shear set up by the applied dynamic loading

Veu

= Equivalent base shear

E

= Effect of horizontal and vertical earthquake induced forces,

QE

= Effect of horizontal seismic forces

SDS

= Design spectral response acceleration parameter at short periods

D

= Effect of dead load

Ω0

= System overstrength factor

fy

= Nominal yield strength

γov

= Material overstrength

Fy

= Minimum specified yield strength

Fu

= Minimum specified tensile strength

Gk,j

= Dead load acting in EC8

Qk,i

= Live or variable load in EC8

D

= Dead load in AISC/ASCE

S

= Snow load

L

= Live load

QE

= Seismic load

ρ

= Redundancy factor

Ωo

= Overstrength factor

SDS

= Design spectral response acceleration parameter at 1.0sec period

Appendix A: Notations


408


Ss

= Mapped spectral response acceleration parameter at short period

Ptot

= Total vertical load acting on the level under consideration

dr

= Design story drift resulting from Vtot

Vtot

= Total seismic storey shear force

h

= Interstorey height

NEd

= Design axial force; (gravity +seismic)

MEd

= Design bending moment; (gravity +seismic)

VEd

= design shear; (gravity +seismic)

Npl, Rd

= Design resistances in accordance with EC3

Mpl, Rd


Vpl, Rd


VEd,G

= Design value of the shear force due to the non‐seismic actions (gravity only)

MEd,i

= Design value of the bending moment in beam i in the seismic design situation

Npl,Rd,i

= Design resistance of diagonal i

NEd,i

= Design value of the axial force in the same diagonal i in the seismic design situation

VEd,i

= Shear force in link i in the seismic design situation

MEd,i

= Bending moment in link i in the seismic design situation

Vp,link,i

= Shear design resistances of link i

Mp,link,i

= Bending plastic design resistances of link i

Puc

= Compressive strength using LRFD load combinations

Fyb

= Specified minimum yeild stress of beam

Fyc

= Specified minimum yeild stress of column

Ry

= Ratio of expected yeild stress to specified minimum yeild stress



409


Muv

= Additional moment due to shear amplification

Z

= Plastic section modulus

Fye

= Yield stress of the material

l

= Length of the member

EI

= Flexural rigidity

P

= Axial force in member (may be taken as zero for beams)

Pye

= Expected axial capacity (Ag Fye)

H

= Overall depth of profile

bf

= Flange width

tf

= Flange thickness

tw

= Web thickness

Fye

= Expected yield strength of material

θy

= Yield rotation

P

= Axial force in the member computed from nonlinear dynamic analyses

PCL

= Lower bound compressive strength of the column

Muc

= Ultimate moment of the connection

Mpb

= Plastic moment of the connected beam

ε

= Strain of steel material

σ

= Stress of steel material

E

= Young's modulus of elasticity of steel

u

= Ultimate strain

f0,haz

= Ultimate strength of the heat affected zone

MConn

= Moment of connection

Mpl,1, Rd

=

Mpl, 2, Rd

= Plastic moments of the flange cross sections when failure “mode 2” arises

leff

= Effective lengths defined according to the failure mode and

Plastic moments of the flange cross sections when failure “mode 1” arises



410


the yield line developing (circular or non‐circular pattern) in the preceding section m

= Distance of the weld seams from the centre of bolts

n

= Minimum between 1.25m

fub

= Ultimate stress of the bolt material

As

= Resisting area of the bolt

(Mu,1)w

= Plastic moment of the critical flange cross sections, located close to the T‐stub web

(Mu,1)b

= Plastic moment of the critical flange cross sections, located close to the bolt rows

M0,2

= Elastic moment at 0.2% proof strength

Mu,2

= Plastic moment of the flange when the failure type is “mode 2”

f0.2

= Conventional yield stress

fu

= Conventional ultimate stress

f0,haz

= Ultimate strength of the heat affected zone

∆/∆y

= Ductility factor

q

= Reserve overstrength

qu,

= Actual behaviour factor

calc

= Calculated overstrength

E

= Elastic overstrength



= Redundancy factor

E,

= Global overstrength

CR

= Alpha critical

T

= Fundamental period (in sec)

Wt

= Weight (in kN)

k

= Overstiffness

Vu/Wt

= Normalised base shear w.r.t weight



= Damageability VΩ/Velastic


University “G. d'Annunzio” of Chieti‐ Pescara Ph.D. thesis titled “Optimum design of steel moment resisting frames” by Tayyab Naqash

L2

= Drift limit (0.0075h)

L3


L1


DCH

= Ductility Class High (q=6.5)

DCM

= Ductility Class Medium (q=4)

DCC

= Ductility Class Conventional (q=3)

DCL

= Ductility Class Low (q=2)


411


412


Appendix B: List of Figures Figure 1: Site of the Margalla Towers in Islamabad collapsed during the 2005 earthquake ..................................................................................................................... 12 Figure 2: Seismic zoning map of Italy ............................................................................. 13 Figure 3: Some undamaged steel structures in 1935 Quetta Earthquake ...................... 15 Figure 4: Structural damages of buildings caused by 1935 Quetta earthquake, built from material other than steel ....................................................................................... 16 Figure 5: Seismic zoning map of Pakistan ....................................................................... 17 Figure 6: Stress‐strain curve for structural steel: (a) typical and (b) S275 and S355 steel grades ............................................................................................................................. 20 Figure 7: Strain and stress distributions in symmetric cross section at various levels of plasticity .......................................................................................................................... 21 Figure 8: Steel member behaviour ................................................................................. 22 Figure 9: Steps of performance based design ................................................................ 27 Figure 10: Performance and damage levels (Gioncu and Mazzolani) ............................ 30 Figure 11: Different lateral load resisting schemes ........................................................ 32 Figure 12: Different lateral load resisting schemes ........................................................ 32 Figure 13: Moment resisting frames: general scheme (a) and global collapse mechanism (b) ................................................................................................................ 34 Figure 14: Eccentrically braced frames: general scheme (a) and collapse mechanism (b) ........................................................................................................................................ 35 Figure 15: Eccentrically braced frame (a) and Moment resisting steel frame (b) .......... 35 Figure 16: Target failure mechanism of: moment resisting steel frame: (a), concentrically braced frame (b) and eccentrically braced frame (c) .............................. 36

Appendix B: List of figures


413


Figure 17: Concentrically Braced Frames: (a) general scheme; (b) collapse Mechanism ........................................................................................................................................ 37 Figure 18: Evaluating of behaviour factor based on ductility (Ballio and Setti).............. 46 Figure 19: Evaluating q based on the response of SDOF systems (a), Ductility factor theory (b), and Equivalence energy theory (c) ............................................................... 47 Figure 20: Multiplier of horizontal forces versus displacement relationship ................. 49 Figure 21: Inelastic response of a SDOF moment‐resisting frame. ................................ 51 Figure 22: Types of ductility ............................................................................................ 53 Figure 23: Rigid frame (a), Plastic hinges in beams (b) and Plastic hinges in columns (c) ........................................................................................................................................ 54 Figure 24: Principle of capacity design by Paulay T. in 1992 .......................................... 56 Figure 25: Fracture of a column flange and web at a moment connection ................... 68 Figure 26: Typical fractures of beam‐to‐column connections (a) fracture at fused zone, and (b) column flange ‘‘divot’’ fracture. ......................................................................... 68 Figure 27: Strength, Stiffness, and deformation capacity of steel and connections ...... 71 Figure 28: Moment rotation diagram of a beam‐to‐beam connection (M‐⏀ curve) ..... 72 Figure 29: Analysis of the forces on the connection (a) Schematization of structure, (b) connection analysis ........................................................................................................ 72 Figure 30: Moment versus rotation curve ...................................................................... 75 Figure 31: Connection classification on behalf of stiffness ............................................ 78 Figure 32: Definition of full‐strength and partial‐strength connections ........................ 79 Figure 33: Connection classification on behalf of strength ............................................ 79 Figure 34: Classification of connections by strength (Moment resistance) ................... 79 Figure 35: Classification of connections by rigidity (rotational stiffness) ....................... 80 Figure 36: Classification of connections by ductility (rotational capacity) ..................... 80 Appendix B: List of figures


414


Figure 37: Global behaviour due to the beam‐to‐connection resistance ratio .............. 84 Figure 38: The simplified model: substructure extracted from an actual frame ............ 85 Figure 39: Moment rotation diagrams (M‐⏀ curves)..................................................... 86 Figure 40: Schematization of rotational stiffness ........................................................... 87 Figure 41: Various forms of M‐⏀ curves ........................................................................ 87 Figure 42: Possible idealizations for M‐⏀ curves: (a) Non‐linear, (b) Bi‐linear, and (c) tri‐ linear ............................................................................................................................... 88 Figure 43: Critical components in moment connection ................................................. 89 Figure 44: Stiffening and Strengthening possibilities; (a) conventional horizontal stiffeners, (b) k‐pattern, (c) Morris stiffener (with compression stiffener), and (d) supplementary web plates ............................................................................................. 90 Figure 45: Failure mechanisms of steel T‐stub connections ........................................... 91 Figure 46: Bending moment diagram for a beam in a semi‐continuous braced frame .. 92 Figure 47: End plate connections for semi‐continuous construction ............................. 94 Figure 48: Controlled yielding of end plate protects brittle components (bolts and welds) from overloading ................................................................................................. 95 Figure 49: Influence of end plate thickness on connection behaviour and failure modes ........................................................................................................................................ 95 Figure 50: Idealization and schematization of T‐stub ..................................................... 97 Figure 51: Geometrical characteristics of tested T stub specimens; (a) IPE‐300, (b) HEB‐ 220 ................................................................................................................................ 102 Figure 52: T‐stub model with complete assembly for calibration process, (a) Geometry and (b) FEM .................................................................................................................. 103 Figure 53: T‐stub model with symmetry for validation and parametric analysis, (a) Geometry and (b) FEM model ...................................................................................... 104



415


Figure 54: Material adopted for models used in calibration process according to Bursi and Jaspart experimental tests; (a) IPE300, and (b) HEB220 ........................................ 104 Figure 55: Numerical versus Bursi and Jaspart results (experimental and numerical) for; (a) NON‐preloaded IPE300 model (NPL1), and (b) for preloaded IPE300 model (PL1) 105 Figure 56: Numerical versus Bursi and Jaspart results (experimental and numerical) for; (a) NON‐preloaded HE220 model (NPL2), and (b) for preloaded HE220 model (PL2) . 106 Figure 57: Geometry and controlling points for failure identification of the T‐stubs; (a) Plan view, and (b) Sectional at A‐A ............................................................................... 108 Figure 58: Variation of adopted parameters in parametric analysis ............................ 108 Figure 59: Force versus displacement graphs for the analysed profiles: (a) HEA‐200, (b) HEA‐400, (c) HEA‐600, (d) HEA‐800 and (e) HEA‐1000 ................................................. 109 Figure 60: Failure mechanisms identification for the analysed profiles with bolt pitch of 40mm ............................................................................................................................ 110 Figure 61: Failure mechanisms identification for analysed profiles with bolt pitch of 60mm ............................................................................................................................ 110 Figure 62: Failure mechanisms identification for analysed profiles with bolt pitch of 80mm ............................................................................................................................ 110 Figure 63: Failure mechanisms identification for analysed profiles with bolt pitch of 100mm .......................................................................................................................... 110 Figure 64: Failure mechanisms identification for analysed profiles with bolt pitch of 120mm .......................................................................................................................... 111 Figure 65: Failure mechanisms identification for analysed profiles with bolt pitch of 160mm .......................................................................................................................... 111 Figure 66: Stress contours from analysed HEA‐1000 profile (tf=31mm) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm .............. 111 Figure 67: Stress contours from analysed HEA‐800 profile (tf=28mm) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm .................... 112 Figure 68: Stress contours from analysed HEA‐600 profile (tf=25mm with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm .................... 112 Appendix B: List of figures


416


Figure 69: Stress contours from analysed HEA‐400 profile (tf=19mm) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm .................... 113 Figure 70: Stress contours from analysed HEA‐200 profile (tf=10mm) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm .................... 113 Figure 71: Tangency lines showing ultimate strength obtained from numerical analysis and Eurocode 3 formulations with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm ............................................................................. 114 Figure 72: Histograms showing ultimate strength obtained from Numerical analysis and Eurocode 3 formulations with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm ............................................................................. 114 Figure 73: Effective length from numerical analysis (failure mode 1) and Eurocode formulations 3 (non‐circular pattern) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm, (e) 120mm and (f) 160mm ............................................................ 115 Figure 74: Effective length from numerical analysis (steel and aluminium T‐stubs) and Eurocode 3/Eurocode 9 formulations (non‐circular pattern) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm and (d) 120mm ............................................................... 116 Figure 75: Effective length from numerical analysis (failure mode 1) and Eurocode 3 (non‐circular pattern) formulations for flange thicknesses: (a) 10mm, (b) 19mm, (c) 25mm, (d) 28mm and (e) 31mm .................................................................................. 116 Figure 76: Monitored points along the mid‐section of T‐stub representing average stress values for 10mm thick flange and pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm (e) 120mm and (f) 160mm .............................................................................. 117 Figure 77: Contour of monitored mid‐section for 10mm thick flange and pitch of: (a) 40mm, (b) 60mm, (c) 80mm, (d) 100mm (e) 120mm and (f) 160mm .......................... 118 Figure 78: Monitored points along the mid‐section of T‐stub representing average stress for 80mm bolt pitch with flange thicknesses of: (a) 10mm, (b) 19mm, (c) 25mm, (d) 28mm (e) and 33mm ............................................................................................... 118 Figure 79: Contour of monitored mid‐section for 80mm bolt pitch with flange thicknesses of: (a) 10mm, (b) 19mm, (c) 25mm, (d) 28mm (e) and 33mm .................. 119 Figure 80: Failure modes of aluminium T‐stubs prescribed by EC9 .............................. 120



417


Figure 81: T‐stub, (a) Geometry and (b) FEM model .................................................... 124 Figure 82: Experimental and true stress/strain curves for: (a) Flange, (b) Web, (c) HAZ, (d) 4.8 steel bolts, (e) 7075 aluminium bolts, and (f) 10.9 steel bolts .......................... 125 Figure 83: Sensitivity analysis for mesh size (a) 3mm, (b) 4mm, and (c) 5mm ............. 126 Figure 84: Sensitivity analysis for: (a) T‐stub mesh, (b) Bolts mesh, and (c) Contacts .. 127 Figure 85: Deformed shapes of (a) Test specimen A, (b) Test specimen B and (c) Test specimen C ................................................................................................................... 128 Figure 86: Deformed shapes and stress contour of (a) FEM specimen A, (b) FEM specimen B and (c) FEM specimen C ............................................................................ 128 Figure 87: Experimental vs numerical results for: (a) 4.8 steel bolts, (b) 7075 aluminium bolts, and (c) 10.9 steel bolts ........................................................................................ 128 Figure 88: Ultimate resistance versus displacement graphs related to different bolt pitches: T‐stub with 4.6 steel bolts and (a1) tf=8mm (a2) tf=10mm (a3) tf=12mm; T‐stub with 6082 aluminium bolts and (b1) tf=8mm (b2) tf=10mm (b3) tf=12mm .................. 131 Figure 89: Ultimate resistance versus displacement graphs: for 10.9 bolt grades with different pitches (a) tf=8mm (b) tf=10mm (c) tf=12mm (d) tf=15mm ........................... 132 Figure 90: Monitored points in the model for the identification of failure modes ...... 132 Figure 91: Failure mechanisms identification for 4.6 steel bolts: (a1) tf=8mm , p40; (a2) tf=10mm , p40; (a3) tf=12mm , p40; (b1) tf=8mm , p60; (b2) tf=10mm , p60; (b3) tf=12mm , p60; (c1) tf=8mm , p80; (c2) tf=10mm , p80; (c3) tf=12mm , p80; (d1) tf=8mm , p120; (d2) tf=10mm , p120; (d3) tf=12mm , p120; ..................................................... 134 Figure 92: Failure mechanisms identification for 6082‐alloy aluminium bolts: (a1) tf=8mm , p40; (a2) tf=10mm , p40; (a3) tf=12mm , p40; (b1) tf=8mm , p60; (b2) tf=10mm , p60; (b3) tf=12mm , p60; (c1) tf=8mm , p80; (c2) tf=10mm , p80; (c3) tf=12mm , p80; (d1) tf=8mm , p120; (d2) tf=10mm , p120; (d3) tf=12mm , p120; ....... 135 Figure 93: Failure mechanisms identification for 10.9 steel bolts: (a1) tf=8mm , p40; (a2) tf=10mm , p40; (a3) tf=12mm , p40; (a4) tf=15mm , p40; (b1) tf=8mm , p60; (b2) tf=10mm , p60; (b3) tf=12mm , p60; (b4) tf=15mm , p60; (c1) tf=8mm , p80; (c2) tf=10mm , p80; (c3) tf=12mm , p80; (c4) tf=15mm , p80; (d1) tf=8mm , p120; (d2) tf=10mm , p120; (d3) tf=12mm , p120; (d4) tf=15mm , p120; ...................................... 136 Appendix B: List of figures


418


Figure 94: Ultimate strength obtained from FEM analyses and EC9 formulation for analysed cases: (a) p= 40mm, (b) p= 60mm (c) p= 80mm and (d) p= 120mm ............. 137 Figure 95: FEM vs. EC9 results in terms of tendency lines: (a) p= 40mm, (b) p= 60mm (c) p= 80mm and (d) p= 120mm ........................................................................................ 138 Figure 96: Von Mises stress contours for the T‐stub flanges of models with steel 10.9 bolts: (a1) tf=8mm , p=40mm; (a2) tf=10mm , p=40mm; (a3) tf=12mm, p=40mm; (b1) tf=8mm , p=60mm; (b2) tf=10mm , p=60mm; (b3) tf=12mm, p=60mm; (c1) tf=8mm, p=80mm; (c2) tf=10mm , p=80mm; (c3) tf=12mm, p=80mm; (d1) tf=8mm , p=120mm; (d2) tf=10mm , p=120mm; (d3) tf=12mm, p=120mm ................................................... 139 Figure 97: Effective length of aluminium T‐stub from FEM and EC9 approach using 10.9 grade steel bolts (a) tendency lines and (b) limit curve for safe evaluation of effective length ............................................................................................................................ 140 Figure 98: Effective length from numerical analysis (steel and aluminium T‐stubs) and Eurocode 3/Eurocode 9 formulations (non‐circular pattern) with bolt pitch of: (a) 40mm, (b) 60mm, (c) 80mm and (d) 120mm ............................................................... 141 Figure 99: Type of structural steel sections; (a) Wide‐flange, (b) Standard profile, (c) Standard channel, (d) Angle, (e) Structural Tee, (f) Pipe section, (g) Hollow structural Tube .............................................................................................................................. 155 Figure 100: Response spectra for: EC8 (a) and ASCE (b) .............................................. 161 Figure 101: Moment vs. rotation (M‐φ) curve for steel cross sections ........................ 166 Figure 102: Capacity design flowchart for steel MRFs using Eurocodes process ......... 170 Figure 103: Capacity design flowchart for steel MRFs using AISC/ASCE process ......... 171 Figure 104: Capacity design approach, (a) Strong column weak beam‐good ductility and (b) Weak column strong beam‐poor ductility .............................................................. 173 Figure 105: Reduce beam section, (a) real example, and (b) sketch ............................ 175 Figure 106: Rotation capacity of connection ................................................................ 176 Figure 107: Failure mechanisms of moment resisting frames ...................................... 187 Figure 108: Deformed vertical axis of structure due to seismic forces ........................ 189



419


Figure 109: Elastic (left) and displacement (right) spectra ........................................... 192 Figure 110: Recommended Type 1 (Ms> 5.5) elastic response spectrum for ground types A to E (5% damping) ............................................................................................ 193 Figure 111: Recommended Type 2 (Ms ≤ 5.5) elastic response spectrum for ground types A to E (5% damping) ............................................................................................ 194 Figure 112: Achieving structural simplicity, (a) subdividing the building and (b) adding seismic joints ................................................................................................................ 197 Figure 113: Example of structure with nonparallel system irregularity ....................... 197 Figure 114: Slender plan building possess weak and strong axis ................................. 198 Figure 115: Torsion effect ............................................................................................. 198 Figure 116: Sixteen basic lateral load cases.................................................................. 202 Figure 117: Static Load cases for torsion and MRS analysis. ........................................ 203 Figure 118: Schematization of accidental torsion ........................................................ 204 Figure 119: Schematization for simultaneous action in two directions ....................... 204 Figure 120: Examples of several ground motion records during various earthquakes (From Chopra, A.K. 2000) ............................................................................................. 216 Figure 121: Typical floor plan of the building (a) and Frame elevation (b) .................. 220 Figure 122: Pushover curves‐12 storeys (a, b), Pushover curves normalised to Vy (c, d), Pushover curves normalised to Vd (e, f) for AISC/ASCE‐SMF and EC8‐DCH frame configurations ............................................................................................................... 221 Figure 123: Pushover curves‐6 storeys (a, b), Pushover curves normalised to Vy (c, d), Pushover curves normalised to Vd (e, f) for AISC/ASCE‐SMF and EC8‐DCH frame configurations ............................................................................................................... 222 Figure 124: Fig. 7: Pushover curves‐3 storeys (a, b), Pushover curves normalised to Vy (c, d), Pushover curves normalised to Vd (e, f) for AISC/ASCE‐SMF and EC8‐DCH frame configurations ............................................................................................................... 222



420


Figure 125: (a) Typical floor plan of the building with perimeter MRFs and (b) perimeter frame elevation ............................................................................................................ 224 Figure 126: (a) Typical floor plan of the building with spatial MRFs and (b) spatial frame elevation ....................................................................................................................... 224 Figure 127: Pushover curves of frames: (a) Perimeter, (b) Spatial external and (c) Spatial internal .............................................................................................................. 225 Figure 128: Pushover curve of frames normalized to Vy (a) Perimeter, (b) Spatial external and (c) Spatial internal ................................................................................... 226 Figure 129: Pushover curve of frames normalized to Vd (a) Perimeter, (b) Spatial external and (c) Spatial internal ................................................................................... 226 Figure 130: Comparative parameters in the two codes: (a) Base shear [KN], (b) D/C of base shear among different frame configurations ....................................................... 227 Figure 131: Pushover results: (a) design base shear; (b) base shear at first plastic hinge; (c) roof displacement at ultimate base shear; (d) redundancy factors; (e) overstrength factors; (f) roof displacement at first plastic hinge (1kN = 225 Ib & 1mm= 0.04 inch) . 227 Figure 132: Structural weight for the analysed frame configurations (1kN = 225 Ib) .. 228 Figure 133: Reserve overstrength according to AISC/ASCE for (a) SMFs and (b) IMFs 231 Figure 134: (a) Typical floor plan of 5 Bays perimeter MRFs and (b) perimeter frame elevation (1m = 3.28ft) ................................................................................................. 234 Figure 135: (a) Typical floor plan of 6 Bays perimeter MRFs and (b) perimeter frame elevation (1m = 3.28ft) ................................................................................................. 234 Figure 136: (a) Typical floor plan of 7 Bays perimeter MRFs and (b) perimeter frame elevation (1m = 3.28ft) ................................................................................................. 235 Figure 137: (a) Typical floor plan of 9 Bays perimeter MRFs and (b) perimeter frame elevation (1m = 3.28ft) ................................................................................................. 235 Figure 138: Loads on roof and typical floor for 5 bays (a) Gravity, and (b) Imposed ... 243 Figure 139: Loads on roof and typical floor for 6 bays (a) Gravity, and (b) Imposed ... 243 Figure 140: Loads on roof and typical floor for 7 bays (a) Gravity, and (b) Imposed ... 243 Appendix B: List of figures


421


Figure 141: Loads on roof and typical floor for 9 bays (a) Gravity, and (b) Imposed ... 243 Figure 142: Eurocode 8 design spectra for various q factors ....................................... 245 Figure 143: Nomenclature for profiles for 5 bays frame members .............................. 246 Figure 144: Nomenclature for profiles for 6 bays frame members .............................. 246 Figure 145: Nomenclature for profiles for 7 bays frame members .............................. 247 Figure 146: Nomenclature for profiles for 9 bays frame members .............................. 247 Figure 147: Generalised component force‐deformation curve .................................... 303 Figure 148: Component forces versus deformation curves (FEMA 356) ...................... 306 Figure 149: Definition of chord rotations to be used in calculating plastic rotation demands. ...................................................................................................................... 308 Figure 150: Moment, axial and rotational capacity curves for 4.0m, 9.15m, 7.63m, 6.55m and 5.08m (1kN = 225 Ib & 1m= 3.28ft), (a) IPE400, (b)IPE600, (c)HE400B, (d)HE400M, (e)HE500B, (f)HE500M, (g)HE600M, (h)HE700M, (i) HE800M and (j) HE900M ........................................................................................................................ 313 Figure 151: Idealised performance curve for structure ................................................ 315 Figure 152: Generalized component force‐deformation relations in FEMA‐356 and ASCE 41‐06 documents: (a) deformation (b) deformation ratio and (c) component or element deformation acceptance criteria .................................................................... 315 Figure 153: Nomenclature of the factors obtained from pushover analysis ................ 318 Figure 154: Definitions of the ultimate displacement: (a) based onload reduction capacity and (b) based on ultimate plastic rotation ..................................................... 320 Figure 155: Pushover curves for combination 1 (q= 6.5, L1) ‐ High ductility ................ 324 Figure 156: Pushover curves for combination 2 (q= 6.5, L2) ‐ High ductility ................ 324 Figure 157: Pushover curves for combination 3 (q= 6.5, L3) ‐ High ductility ................ 324 Figure 158: Pushover curves for combination 4 (q= 4, L1) ‐ Medium ductility ............ 324 Figure 159: Pushover curves for combination 5 (q= 4, L2) ‐ Medium ductility ............ 325 Appendix B: List of figures


422


Figure 160: Pushover curves for combination 6 (q= 4, L3) ‐ Medium ductility ............ 325 Figure 161: Pushover curves for combination 7 (q= 3, L1) ‐ Conventional ductility ..... 325 Figure 162: Pushover curves for combination 8 (q= 3, L2) ‐ Conventional ductility ..... 325 Figure 163: Pushover curves for combination 9 (q= 3, L3) ‐ Conventional ductility ..... 326 Figure 164: Pushover curves for combination 10 (q= 2, L1) ‐ Low ductility.................. 326 Figure 165: Pushover curves for combination 11 (q= 2, L2) ‐ Low ductility.................. 326 Figure 166: Pushover curves for combination 12 (q= 2, L3) ‐ Low ductility.................. 326 Figure 167: Pushover curves normalised to Vy for combination 1 (q= 6.5, L1) ............. 327 Figure 168: Pushover curves normalised to Vy for combination 2 (q= 6.5, L2) ............. 327 Figure 169: Pushover curves normalised to Vy for combination 3 (q= 6.5, L3) ............. 327 Figure 170: Pushover curves normalised to Vy for combination 4 (q= 4, L1) ................ 328 Figure 171: Pushover curves normalised to Vy for combination 5 (q= 4, L2) ................ 328 Figure 172: Pushover curves normalised to Vy for combination 6 (q= 4, L3) ................ 328 Figure 173: Pushover curves normalised to Vy for combination 7 (q= 3, L1) ................ 328 Figure 174: Pushover curves normalised to Vy for combination 8 (q= 3, L2) ................ 329 Figure 175: Pushover curves normalised to Vy for combination 9 (q= 3, L3) ................ 329 Figure 176: Pushover curves normalised to Vy for combination 10 (q= 2, L1) .............. 329 Figure 177: Pushover curves normalised to Vy for combination 11 (q= 2, L2) .............. 329 Figure 178: Pushover curves normalised to Vy for combination 12 (q= 2, L3) .............. 330 Figure 179: Pushover curves normalised to Vd for combination 1 (q= 6.5, L1) ............. 331 Figure 180: Pushover curves normalised to Vd for combination 2 (q= 6.5, L2) ............. 331 Figure 181: Pushover curves normalised to Vd for combination 3 (q= 6.5, L3) ............. 331 Figure 182: Pushover curves normalised to Vd for combination 4 (q= 4, L1) ................ 332 Appendix B: List of figures


423


Figure 183: Pushover curves normalised to Vd for combination 5 (q= 4, L2) ................ 332 Figure 184: Pushover curves normalised to Vd for combination 6 (q= 4, L3) ................ 332 Figure 185: Pushover curves normalised to Vd for combination 7 (q= 3, L1) ................ 332 Figure 186: Pushover curves normalised to Vd for combination 8 (q= 3, L2) ................ 333 Figure 187: Pushover curves normalised to Vd for combination 9 (q= 3, L3) ................ 333 Figure 188: Pushover curves normalised to Vd for combination 10 (q= 2, L1) .............. 333 Figure 189: Pushover curves normalised to Vd for combination 11 (q= 2, L2) .............. 333 Figure 190: Pushover curves normalised to Vd for combination 12 (q= 2, L3) .............. 334 Figure 191: Notation of drift limit ................................................................................. 337 Figure 192: Overstiffness for combination 1 (q=6.5, L1) ‐ High ductility (strength controls) ........................................................................................................................ 338 Figure 193: Overstiffness for combination 2 (q=6.5, L2) ‐ High ductility (stiffness controls) ........................................................................................................................ 338 Figure 194: Overstiffness for combination 3 (q=6.5, L3) ‐ High ductility (stiffness controls) ........................................................................................................................ 338 Figure 195: Overstiffness for combination 4 (q=4, L1) ‐ Medium ductility (strength controls) ........................................................................................................................ 339 Figure 196: Overstiffness for combination 5 (q=4, L2) ‐ Medium ductility (strength/stiffness controls) ......................................................................................... 339 Figure 197: Overstiffness for combination 6 (q=4, L3) ‐ Medium ductility (stiffness controls) ........................................................................................................................ 339 Figure 198: Overstiffness for combination 7 (q=3, L1) ‐ Conventional ductility (strength controls) ........................................................................................................................ 340 Figure 199: Overstiffness for combination 8 (q=3, L2) ‐ Conventional ductility (strength controls) ........................................................................................................................ 340



424


Figure 200: Overstiffness for combination 9 (q=3, L3) ‐ Conventional ductility (strength/stiffness controls) ......................................................................................... 340 Figure 201: Overstiffness for combination 10 (q=2, L1) ‐ Low ductility (strength controls) ........................................................................................................................ 341 Figure 202: Overstiffness for combination 11 (q=2, L2) ‐ Low ductility (strength controls) ........................................................................................................................ 341 Figure 203: Overstiffness for combination 12 (q=2, L3) ‐ Low ductility (strength controls) ........................................................................................................................ 341 Figure 204: Ductility factors for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ........... 343 Figure 205: Ductility factors for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ........... 344 Figure 206: Reserve overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) .. 346 Figure 207: Reserve overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) .. 346 Figure 208: Actual behaviour factor for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ...................................................................................................................................... 347 Figure 209: Actual behaviour factor for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ...................................................................................................................................... 348 Figure 210: Graphs showing calculated overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ........................................................................................................... 349 Figure 211: Graphs showing calculated overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ........................................................................................................... 350 Figure 212: Graphs showing elastic overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................... 351 Figure 213: Graphs showing elastic overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................... 352 Figure 214: Graphs showing redundancy factor for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................... 353 Figure 215: Graphs showing redundancy factor for 7 bays (c1 and c2) and for 9 bays (d1 and d2) .......................................................................................................................... 354 Appendix B: List of figures


425


Figure 216: Graphs showing global overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................... 355 Figure 217: Graphs showing global overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................... 356 Figure 218: Graphs of alpha critical for 5 bays (a1 and a2) and for 6 bays (b1 and b2)358 Figure 219: Graphs of alpha critical for 7 bays (c1 and c2) and for 9 bays (d1 and d2) 358 Figure 220: Graphs showing fundamental period for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................... 360 Figure 221: Graphs showing fundamental period for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................... 360 Figure 222: Graphs showing weight for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ...................................................................................................................................... 361 Figure 223: Graphs showing weight for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ...................................................................................................................................... 362 Figure 224: Graphs showing overstiffness for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................................. 363 Figure 225: Graphs showing overstiffness for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................................. 364 Figure 226: Graphs showing normalised base shear w.r.t weight for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ............................................................................................ 365 Figure 227: Graphs showing normalised base shear w.r.t weight for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ............................................................................................ 366 Figure 228: Graphs showing damageability for 5 bays (a1 and a2) and for 6 bays (b1 and b2) .......................................................................................................................... 367 Figure 229: Graphs showing damageability for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................................. 368 Figure 230: Modal analysis period normalised to code prescribed period for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ............................................................................... 369



426


Figure 231: Modal analysis period normalised to code prescribed period for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ............................................................................... 370 Figure 232: Pushover global overstrength normalised to the codified overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................. 371 Figure 233: Pushover global overstrength normalised to the codified overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................. 372 Figure 234: Reserve overstrength obtained from codified formulation for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ............................................................................... 374 Figure 235: Reserve overstrength obtained from codified formulation for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ............................................................................... 374 Figure 236: Eurocode proposed capacity design flowchart for steel MRF ................... 379 Figure 237: Graphs showing overstiffness factor for 5 bays (a1) and for 6 bays (b1) .. 383 Figure 238: Graphs showing overstiffness factor for 7 bays (c1) and for 9 bays (d1) .. 383 Figure 239: Graphs showing overstiffness factor for: 5 bays (a), 6 bays (b), 7 bays (c), and 9 bays (d) ............................................................................................................... 383 Figure 240: Graphs showing elastic overstrength for 5 bays (a1 and a2) and for 6 bays (b1 and b2) ................................................................................................................... 385 Figure 241: Graphs showing elastic overstrength for 7 bays (c1 and c2) and for 9 bays (d1 and d2) ................................................................................................................... 385 Figure 242: Proposed global overstrength and reserve overstrength for DCH and DCM ...................................................................................................................................... 388 Figure 243: Proposed global overstrength and reserve overstrength for DCC ............ 388 Figure 244: Proposed capacity design flowchart for steel MRFs .................................. 389



427


Appendix C: List of Tables Table 1: Seismic zonation in Pakistan ............................................................................. 18 Table 2: Matrix of performance objectives .................................................................... 25 Table 3: Effective lengths of an unstiffened column flange ......................................... 100 Table 4: T‐stub tested specimens used for calibration of the proposed models ......... 101 Table 5: Mechanical features of the materials used in parametric analyses ............... 106 Table 6: Geometrical parameters (mm) and ultimate force (kN) for the analysed T‐stubs ...................................................................................................................................... 107 Table 7: T‐stub tested specimens used for calibration of the proposed models ......... 123 Table 8: Mesh size of T‐stub model, related number of elements and nodes ............. 126 Table 9: Mesh size for bolt model, related number of elements and nodes ............... 126 Table 10: Different contact combinations .................................................................... 127 Table 11: Mechanical features of the materials used in parametric analyses ............. 129 Table 12: Values of geometrical parameters (mm) for analysed T‐stubs ..................... 130 Table 13: Failure modes for 12 mm and 15 mm thick flanges using 10.9 steel bolts ... 133 Table 14: Effective lengths for T‐stub from FEM and EC9 ............................................ 139 Table 15: Improvements in UBC editions after the occurrence of an earthquake event ...................................................................................................................................... 147 Table 16: Synthetic comparison scheme for EC8/EC3 and AISC/ASCE provisions ........ 157 Table 17: Synthetic comparison scheme for EC8/EC3 and AISC/ASCE provisions ........ 158 Table 18: ASCE and EC8 soil profile .............................................................................. 161 Table 19: Behaviour factor for MRF and Dual system in Eurocode 8 ........................... 164 Table 20: Design factor for structural steel systems .................................................... 164 Appendix C: List of tables


428


Table 21: Cross section limitation for behaviour factor ............................................... 166 Table 22: Overstrength factors according to Eurocode 8 ............................................. 172 Table 23: Overstrength factors according to AISC/ASCE .............................................. 173 Table 24: Capacity design rules and drifts limitations for EC3‐EC8 (DCH) and AISC‐ASCE (SMF) ............................................................................................................................ 179 Table 25: DCM vs. IMF (Ductility Class Medium versus Intermediate Moment Frame) ...................................................................................................................................... 181 Table 26: DCL vs. OMF (Ductility Class Low versus Ordinary Moment Frame) ............. 183 Table 27: Elastic analysis ............................................................................................... 185 Table 28: EC8 interstorey drift limitations .................................................................... 189 Table 29: ASCE interstorey drift limitations .................................................................. 189 Table 30: Values of the parameters describing the recommended Type 1 elastic response spectrum ....................................................................................................... 193 Table 31: Values of the parameters describing the recommended Type 2 elastic response spectrum ....................................................................................................... 193 Table 32: Ground types prescribed in Eurocode 8 ....................................................... 195 Table 33: Sixteen basic lateral load cases ..................................................................... 201 Table 34: The analysed cases for 6.6m span frames .................................................... 220 Table 35: Analysed cases for 9.15m span frames ......................................................... 225 Table 36: Analysed cases for 9, 7 and 5 storey frames ................................................. 236 Table 37: Adopted cases for combinations with q = 6.5 (combinations 1, 2 and 3) ..... 238 Table 38: Adopted cases for combinations with q = 4 (combinations 4, 5 and 6) ........ 239 Table 39: Adopted cases for combinations with q = 3 (combinations 7, 8 and 9) ........ 241 Table 40: Adopted cases for combinations with q = 2 (combinations 10, 11 and 12) .. 242

Appendix C: List of tables


429


Table 41: Sectional and material properties for the profiles used ............................... 245 Table 42: Profile matrix for beam B1 for combination 1 (q=6.5, L1) ............................ 248 Table 43: Profile matrix for beam B2 for combination 1 (q=6.5, L1) ............................ 248 Table 44: Profile matrix for beam B3 for combination 1 (q=6.5, L1) ............................ 248 Table 45: Profile matrix for beam B4 for combination 1 (q=6.5, L1) ............................ 249 Table 46: Profile matrix for beam B5 for combination 1 (q=6.5, L1) ............................ 249 Table 47: Profile matrix for beam B6 for combination 1 (q=6.5, L1) ............................ 249 Table 48: Profile matrix for beam B7 for combination 1 (q=6.5, L1) ............................ 249 Table 49: Profile matrix for beam B8 for combination 1 (q=6.5, L1) ............................ 249 Table 50: Profile matrix for beam B9 for combination 1 (q=6.5, L1) ............................ 250 Table 51: Profile matrix for column C1 for combination 1 (q=6.5, L1) ......................... 250 Table 52: Profile matrix for column C2 for combination 1 (q=6.5, L1) ......................... 250 Table 53: Profile matrix for column C3 for combination 1 (q=6.5, L1) ......................... 250 Table 54: Profile matrix for column C4 for combination 1 (q=6.5, L1) ......................... 251 Table 55: Profile matrix for column C5 for combination 1 (q=6.5, L1) ......................... 251 Table 56: Profile matrix for column C6 for combination 1 (q=6.5, L1) ......................... 251 Table 57: Profile matrix for column C7 for combination 1 (q=6.5, L1) ......................... 251 Table 58: Profile matrix for column C8 for combination 1 (q=6.5, L1) ......................... 252 Table 59: Profile matrix for column C9 for combination 1 (q=6.5, L1) ......................... 252 Table 60: Profile matrix for column C10 for combination 1 (q=6.5, L1) ....................... 252 Table 61: Profile matrix for beam B1 for combination 2 (q=6.5, L2) ............................ 252 Table 62: Profile matrix for beam B2 for combination 2 (q=6.5, L2) ............................ 252 Table 63: Profile matrix for beam B3 for combination 2 (q=6.5, L2) ............................ 253 Appendix C: List of tables


430


Table 64: Profile matrix for beam B4 for combination 2 (q=6.5, L2) ............................ 253 Table 65: Profile matrix for beam B5 for combination 2 (q=6.5, L2) ............................ 253 Table 66: Profile matrix for beam B6 for combination 2 (q=6.5, L2) ............................ 253 Table 67: Profile matrix for beam B7 for combination 2 (q=6.5, L2) ............................ 254 Table 68: Profile matrix for beam B8 for combination 2 (q=6.5, L2) ............................ 254 Table 69: Profile matrix for beam B9 for combination 2 (q=6.5, L2) ............................ 254 Table 70: Profile matrix for column C1 for combination 2 (q=6.5, L2) ......................... 254 Table 71: Profile matrix for column C2 for combination 2 (q=6.5, L2) ......................... 254 Table 72: Profile matrix for column C3 for combination 2 (q=6.5, L2) ......................... 255 Table 73: Profile matrix for column C4 for combination 2 (q=6.5, L2) ......................... 255 Table 74: Profile matrix for column C5 for combination 2 (q=6.5, L2) ......................... 255 Table 75: Profile matrix for column C6 for combination 2 (q=6.5, L2) ......................... 255 Table 76: Profile matrix for column C7 for combination 2 (q=6.5, L2) ......................... 256 Table 77: Profile matrix for column C8 for combination 2 (q=6.5, L2) ......................... 256 Table 78: Profile matrix for column C9 for combination 2 (q=6.5, L2) ......................... 256 Table 79: Profile matrix for column C10 for combination 2 (q=6.5, L2) ....................... 256 Table 80: Profile matrix for beam B1 for combination 3 (q=6.5, L3) ............................ 256 Table 81: Profile matrix for beam B2 for combination 3 (q=6.5, L3) ............................ 257 Table 82: Profile matrix for beam B3 for combination 3 (q=6.5, L3) ............................ 257 Table 83: Profile matrix for beam B4 for combination 3 (q=6.5, L3) ............................ 257 Table 84: Profile matrix for beam B5 for combination 3 (q=6.5, L3) ............................ 257 Table 85: Profile matrix for beam B6 for combination 3 (q=6.5, L3) ............................ 258 Table 86: Profile matrix for beam B7 for combination 3 (q=6.5, L3) ............................ 258 Appendix C: List of tables


431


Table 87: Profile matrix for beam B8 for combination 3 (q=6.5, L3) ............................ 258 Table 88: Profile matrix for beam B9 for combination 3 (q=6.5, L3) ............................ 258 Table 89: Profile matrix for column C1 for combination 3 (q=6.5, L3) ......................... 258 Table 90: Profile matrix for column C2 for combination 3 (q=6.5, L3) ......................... 259 Table 91: Profile matrix for column C3 for combination 3 (q=6.5, L3) ......................... 259 Table 92: Profile matrix for column C4 for combination 3 (q=6.5, L3) ......................... 259 Table 93: Profile matrix for column C5 for combination 3 (q=6.5, L3) ......................... 259 Table 94: Profile matrix for column C6 for combination 3 (q=6.5, L3) ......................... 260 Table 95: Profile matrix for column C7 for combination 3 (q=6.5, L3) ......................... 260 Table 96: Profile matrix for column C8 for combination 3 (q=6.5, L3) ......................... 260 Table 97: Profile matrix for column C9 for combination 3 (q=6.5, L3) ......................... 260 Table 98: Profile matrix for column C10 for combination 3 (q=6.5, L3) ....................... 260 Table 99: Profile matrix for beam B1 for combination 4 (q=4, L1) ............................... 261 Table 100: Profile matrix for beam B2 for combination 4 (q=4, L1) ............................. 261 Table 101: Profile matrix for beam B3 for combination 4 (q=4, L1) ............................. 261 Table 102: Profile matrix for beam B4 for combination 4 (q=4, L1) ............................. 262 Table 103: Profile matrix for beam B5 for combination 4 (q=4, L1) ............................. 262 Table 104: Profile matrix for beam B6 for combination 4 (q=4, L1) ............................. 262 Table 105: Profile matrix for beam B7 for combination 4 (q=4, L1) ............................. 262 Table 106: Profile matrix for beam B8 for combination 4 (q=4, L1) ............................. 262 Table 107: Profile matrix for beam B9 for combination 4 (q=4, L1) ............................. 263 Table 108: Profile matrix for column C1 for combination 4 (q=4, L1) .......................... 263 Table 109: Profile matrix for column C2 for combination 4 (q=4, L1) .......................... 263 Appendix C: List of tables


432


Table 110: Profile matrix for column C3 for combination 4 (q=4, L1) .......................... 263 Table 111: Profile matrix for column C4 for combination 4 (q=4, L1) .......................... 264 Table 112: Profile matrix for column C5 for combination 4 (q=4, L1) .......................... 264 Table 113: Profile matrix for column C6 for combination 4 (q=4, L1) .......................... 264 Table 114: Profile matrix for column C7 for combination 4 (q=4, L1) .......................... 264 Table 115: Profile matrix for column C8 for combination 4 (q=4, L1) .......................... 265 Table 116: Profile matrix for column C9 for combination 4 (q=4, L1) .......................... 265 Table 117: Profile matrix for column C10 for combination 4 (q=4, L1) ........................ 265 Table 118: Profile matrix for beam B1 for combination 5 (q=4, L2) ............................. 265 Table 119: Profile matrix for beam B2 for combination 5 (q=4, L2) ............................. 265 Table 120: Profile matrix for beam B3 for combination 5 (q=4, L2) ............................. 266 Table 121: Profile matrix for beam B4 for combination 5 (q=4, L2) ............................. 266 Table 122: Profile matrix for beam B5 for combination 5 (q=4, L2) ............................. 266 Table 123: Profile matrix for beam B6 for combination 5 (q=4, L2) ............................. 266 Table 124: Profile matrix for beam B7 for combination 5 (q=4, L2) ............................. 267 Table 125: Profile matrix for beam B8 for combination 5 (q=4, L2) ............................. 267 Table 126: Profile matrix for beam B9 for combination 5 (q=4, L2) ............................. 267 Table 127: Profile matrix for column C1 for combination 5 (q=4, L2) .......................... 267 Table 128: Profile matrix for column C2 for combination 5 (q=4, L2) .......................... 267 Table 129: Profile matrix for column C3 for combination 5 (q=4, L2) .......................... 268 Table 130: Profile matrix for column C4 for combination 5 (q=4, L2) .......................... 268 Table 131: Profile matrix for column C5 for combination 5 (q=4, L2) .......................... 268 Table 132: Profile matrix for column C6 for combination 5 (q=4, L2) .......................... 269 Appendix C: List of tables


433


Table 133: Profile matrix for column C7 for combination 5 (q=4, L2) .......................... 269 Table 134: Profile matrix for column C8 for combination 5 (q=4, L2) .......................... 269 Table 135: Profile matrix for column C9 for combination 5 (q=4, L2) .......................... 269 Table 136: Profile matrix for column C10 for combination 5 (q=4, L2) ........................ 269 Table 137: Profile matrix for beam B1 for combination 6 (q=4, L3) ............................. 270 Table 138: Profile matrix for beam B2 for combination 6 (q=4, L3) ............................. 270 Table 139: Profile matrix for beam B3 for combination 6 (q=4, L3) ............................. 270 Table 140: Profile matrix for beam B4 for combination 6 (q=4, L3) ............................. 271 Table 141: Profile matrix for beam B5 for combination 6 (q=4, L3) ............................. 271 Table 142: Profile matrix for beam B6 for combination 6 (q=4, L3) ............................. 271 Table 143: Profile matrix for beam B7 for combination 6 (q=4, L3) ............................. 271 Table 144: Profile matrix for beam B8 for combination 6 (q=4, L3) ............................. 271 Table 145: Profile matrix for beam B9 for combination 6 (q=4, L3) ............................. 272 Table 146: Profile matrix for column C1 for combination 6 (q=4, L3) .......................... 272 Table 147: Profile matrix for column C2 for combination 6 (q=4, L3) .......................... 272 Table 148: Profile matrix for column C3 for combination 6 (q=4, L3) .......................... 272 Table 149: Profile matrix for column C4 for combination 6 (q=4, L3) .......................... 273 Table 150: Profile matrix for column C5 for combination 6 (q=4, L3) .......................... 273 Table 151: Profile matrix for column C6 for combination 6 (q=4, L3) .......................... 273 Table 152: Profile matrix for column C7 for combination 6 (q=4, L3) .......................... 273 Table 153: Profile matrix for column C8 for combination 6 (q=4, L3) .......................... 274 Table 154: Profile matrix for column C9 for combination 6 (q=4, L3) .......................... 274 Table 155: Profile matrix for column C10 for combination 6 (q=4, L3) ........................ 274 Appendix C: List of tables


434


Table 156: Profile matrix for beam B1 for combination 7 (q=3, L1) ............................. 274 Table 157: Profile matrix for beam B2 for combination 7 (q=3, L1) ............................. 274 Table 158: Profile matrix for beam B3 for combination 7 (q=3, L1) ............................. 275 Table 159: Profile matrix for beam B4 for combination 7 (q=3, L1) ............................. 275 Table 160: Profile matrix for beam B5 for combination 7 (q=3, L1) ............................. 275 Table 161: Profile matrix for beam B6 for combination 7 (q=3, L1) ............................. 275 Table 162: Profile matrix for beam B7 for combination 7 (q=3, L1) ............................. 276 Table 163: Profile matrix for beam B8 for combination 7 (q=3, L1) ............................. 276 Table 164: Profile matrix for beam B9 for combination 7 (q=3, L1) ............................. 276 Table 165: Profile matrix for column C1 for combination 7 (q=3, L1) .......................... 276 Table 166: Profile matrix for column C2 for combination 7 (q=3, L1) .......................... 276 Table 167: Profile matrix for column C3 for combination 7 (q=3, L1) .......................... 277 Table 168: Profile matrix for column C4 for combination 7 (q=3, L1) .......................... 277 Table 169: Profile matrix for column C5 for combination 7 (q=3, L1) .......................... 277 Table 170: Profile matrix for column C6 for combination 7 (q=3, L1) .......................... 277 Table 171: Profile matrix for column C7 for combination 7 (q=3, L1) .......................... 278 Table 172: Profile matrix for column C8 for combination 7 (q=3, L1) .......................... 278 Table 173: Profile matrix for column C9 for combination 7 (q=3, L1) .......................... 278 Table 174: Profile matrix for column C10 for combination 7 (q=3, L1) ........................ 278 Table 175: Profile matrix for beam B1 for combination 8 (q=3, L2) ............................. 278 Table 176: Profile matrix for beam B2 for combination 8 (q=3, L2) ............................. 279 Table 177: Profile matrix for beam B3 for combination 8 (q=3, L2) ............................. 279 Table 178: Profile matrix for beam B4 for combination 8 (q=3, L2) ............................. 279 Appendix C: List of tables


435


Table 179: Profile matrix for beam B5 for combination 8 (q=3, L2) ............................. 280 Table 180: Profile matrix for beam B6 for combination 8 (q=3, L2) ............................. 280 Table 181: Profile matrix for beam B7 for combination 8 (q=3, L2) ............................. 280 Table 182: Profile matrix for beam B8 for combination 8 (q=3, L2) ............................. 280 Table 183: Profile matrix for beam B9 for combination 8 (q=3, L2) ............................. 280 Table 184: Profile matrix for column C1 for combination 8 (q=3, L2) .......................... 280 Table 185: Profile matrix for column C2 for combination 8 (q=3, L2) .......................... 281 Table 186: Profile matrix for column C3 for combination 8 (q=3, L2) .......................... 281 Table 187: Profile matrix for column C4 for combination 8 (q=3, L2) .......................... 281 Table 188: Profile matrix for column C5 for combination 8 (q=3, L2) .......................... 282 Table 189: Profile matrix for column C6 for combination 8 (q=3, L2) .......................... 282 Table 190: Profile matrix for column C7 for combination 8 (q=3, L2) .......................... 282 Table 191: Profile matrix for column C8 for combination 8 (q=3, L2) .......................... 282 Table 192: Profile matrix for column C9 for combination 8 (q=3, L2) .......................... 282 Table 193: Profile matrix for column C10 for combination 8 (q=3, L2) ........................ 283 Table 194: Profile matrix for beam B1 for combination 9 (q=3, L3) ............................. 283 Table 195: Profile matrix for beam B2 for combination 9 (q=3, L3) ............................. 283 Table 196: Profile matrix for beam B3 for combination 9 (q=3, L3) ............................. 283 Table 197: Profile matrix for beam B4 for combination 9 (q=3, L3) ............................. 284 Table 198: Profile matrix for beam B5 for combination 9 (q=3, L3) ............................. 284 Table 199: Profile matrix for beam B6 for combination 9 (q=3, L3) ............................. 284 Table 200: Profile matrix for beam B7 for combination 9 (q=3, L3) ............................. 284 Table 201: Profile matrix for beam B8 for combination 9 (q=3, L3) ............................. 284 Appendix C: List of tables


436


Table 202: Profile matrix for beam B9 for combination 9 (q=3, L3) ............................. 285 Table 203: Profile matrix for column C1 for combination 9 (q=3, L3) .......................... 285 Table 204: Profile matrix for column C2 for combination 9 (q=3, L3) .......................... 285 Table 205: Profile matrix for column C3 for combination 9 (q=3, L3) .......................... 285 Table 206: Profile matrix for column C4 for combination 9 (q=3, L3) .......................... 286 Table 207: Profile matrix for column C5 for combination 9 (q=3, L3) .......................... 286 Table 208: Profile matrix for column C6 for combination 9 (q=3, L3) .......................... 286 Table 209: Profile matrix for column C7 for combination 9 (q=3, L3) .......................... 286 Table 210: Profile matrix for column C8 for combination 9 (q=3, L3) .......................... 287 Table 211: Profile matrix for column C9 for combination 9 (q=3, L3) .......................... 287 Table 212: Profile matrix for column C10 for combination 9 (q=3, L3) ........................ 287 Table 213: Profile matrix for beam B1 for combination 10 (q=2, L1) ........................... 287 Table 214: Profile matrix for beam B2 for combination 10 (q=2, L1) ........................... 287 Table 215: Profile matrix for beam B3 for combination 10 (q=2, L1) ........................... 288 Table 216: Profile matrix for beam B4 for combination 10 (q=2, L1) ........................... 288 Table 217: Profile matrix for beam B5 for combination 10 (q=2, L1) ........................... 288 Table 218: Profile matrix for beam B6 for combination 10 (q=2, L1) ........................... 288 Table 219: Profile matrix for beam B7 for combination 10 (q=2, L1) ........................... 289 Table 220: Profile matrix for beam B8 for combination 10 (q=2, L1) ........................... 289 Table 221: Profile matrix for beam B9 for combination 10 (q=2, L1) ........................... 289 Table 222: Profile matrix for column C1 for combination 10 (q=2, L1) ........................ 289 Table 223: Profile matrix for column C2 for combination 10 (q=2, L1) ........................ 289 Table 224: Profile matrix for column C3 for combination 10 (q=2, L1) ........................ 290 Appendix C: List of tables


437


Table 225: Profile matrix for column C4 for combination 10 (q=2, L1) ........................ 290 Table 226: Profile matrix for column C5 for combination 10 (q=2, L1) ........................ 290 Table 227: Profile matrix for column C6 for combination 10 (q=2, L1) ........................ 290 Table 228: Profile matrix for column C7 for combination 10 (q=2, L1) ........................ 291 Table 229: Profile matrix for column C8 for combination 10 (q=2, L1) ........................ 291 Table 230: Profile matrix for column C9 for combination 10 (q=2, L1) ........................ 291 Table 231: Profile matrix for column C10 for combination 10 (q=2, L1) ...................... 291 Table 232: Profile matrix for beam B1 for combination 11 (q=2, L2) ........................... 291 Table 233: Profile matrix for beam B2 for combination 11 (q=2, L2) ........................... 292 Table 234: Profile matrix for beam B3 for combination 11 (q=2, L2) ........................... 292 Table 235: Profile matrix for beam B4 for combination 11 (q=2, L2) ........................... 292 Table 236: Profile matrix for beam B5 for combination 11 (q=2, L2) ........................... 292 Table 237: Profile matrix for beam B6 for combination 11 (q=2, L2) ........................... 293 Table 238: Profile matrix for beam B7 for combination 11 (q=2, L2) ........................... 293 Table 239: Profile matrix for beam B8 for combination 11 (q=2, L2) ........................... 293 Table 240: Profile matrix for beam B9 for combination 11 (q=2, L2) ........................... 293 Table 241: Profile matrix for column C1 for combination 11 (q=2, L2) ........................ 293 Table 242: Profile matrix for column C2 for combination 11 (q=2, L2) ........................ 294 Table 243: Profile matrix for column C3 for combination 11 (q=2, L2) ........................ 294 Table 244: Profile matrix for column C4 for combination 11 (q=2, L2) ........................ 294 Table 245: Profile matrix for column C5 for combination 11 (q=2, L2) ........................ 294 Table 246: Profile matrix for column C6 for combination 11 (q=2, L2) ........................ 295 Table 247: Profile matrix for column C7 for combination 11 (q=2, L2) ........................ 295 Appendix C: List of tables


438


Table 248: Profile matrix for column C8 for combination 11 (q=2, L2) ........................ 295 Table 249: Profile matrix for column C9 for combination 11 (q=2, L2) ........................ 295 Table 250: Profile matrix for column C10 for combination 11 (q=2, L2) ...................... 295 Table 251: Profile matrix for beam B1 for combination 12 (q=2, L3) ........................... 296 Table 252: Profile matrix for beam B2 for combination 12 (q=2, L3) ........................... 296 Table 253: Profile matrix for beam B3 for combination 12 (q=2, L3) ........................... 296 Table 254: Profile matrix for beam B4 for combination 12 (q=2, L3) ........................... 296 Table 255: Profile matrix for beam B5 for combination 12 (q=2, L3) ........................... 297 Table 256: Profile matrix for beam B6 for combination 12 (q=2, L3) ........................... 297 Table 257: Profile matrix for beam B7 for combination 12 (q=2, L3) ........................... 297 Table 258: Profile matrix for beam B8 for combination 12 (q=2, L3) ........................... 297 Table 259: Profile matrix for beam B9 for combination 12 (q=2, L3) ........................... 297 Table 260: Profile matrix for column C1 for combination 12 (q=2, L3) ........................ 298 Table 261: Profile matrix for column C2 for combination 12 (q=2, L3) ........................ 298 Table 262: Profile matrix for column C3 for combination 12 (q=2, L3) ........................ 298 Table 263: Profile matrix for column C4 for combination 12 (q=2, L3) ........................ 298 Table 264: Profile matrix for column C5 for combination 12 (q=2, L3) ........................ 299 Table 265: Profile matrix for column C6 for combination 12 (q=2, L3) ........................ 299 Table 266: Profile matrix for column C7 for combination 12 (q=2, L3) ........................ 299 Table 267: Profile matrix for column C8 for combination 12 (q=2, L3) ........................ 299 Table 268: Profile matrix for column C9 for combination 12 (q=2, L3) ........................ 300 Table 269: Profile matrix for column C10 for combination 12 (q=2, L3) ...................... 300



439


Table 270: Examples of possible deformation‐controlled and force‐controlled actions ...................................................................................................................................... 307 Table 271: Beam & column member local slenderness ratio (HE‐profiles) .................. 310 Table 272: Beam & column member local slenderness ratio (IPE‐profiles) ................. 311 Table 273: Beam, column yield quantities (HE profiles) ............................................... 311 Table 274: Beam, column yield quantities (IPE profiles) .............................................. 312 Table 275: Moment (kN‐m), axial capacity (kN) and Plastic rotation (rad) for some beam/column members ............................................................................................... 314 Table 276: Modelling parameters and acceptance criteria for nonlinear procedures for structural steel components ......................................................................................... 316 Table 277: Steel Moment frame connection types ...................................................... 321 Table 278: Acceptance criteria at different levels of performance for steel MRFs according to FEMA 356 ................................................................................................. 322 Table 279: Ductility factor for all the analysed cases ................................................... 343 Table 280: Reserve overstrength for all the analysed cases ......................................... 345 Table 281: Actual behaviour factor for all the analysed cases ..................................... 347 Table 282: Calculated overstrength for all the analysed cases .................................... 349 Table 283: Elastic overstrength for all the analysed cases ........................................... 351 Table 284: Redundancy factor for all the analysed cases ............................................. 353 Table 285: Global overstrength for all the analysed cases ........................................... 355 Table 286: Alpha critical for all the analysed cases ...................................................... 357 Table 287: Fundamental period (T) in sec for all the analysed cases ........................... 359 Table 288: Weight in kN for all the analysed cases ...................................................... 361 Table 289: Overstiffness for all the analysed cases ...................................................... 363



440


Table 290: Normalised base shear w.r.t weight Vu/Wt for all the analysed cases ........ 365 Table 291: Damageability () VΩ/Velastic for all the analysed cases ............................... 367 Table 292: Modal analysis period normalised to code prescribed period ................... 369 Table 293: Normalised global overstrength (pushover overstrength to the codified overstrength) ................................................................................................................ 371 Table 294: Values of reserve overstrength obtained from codified formulation ......... 373 Table 295: Analysed cases for 9, 7 and 5 storeys frames ............................................. 379 Table 296: Drift limit versus assumed ductility class .................................................... 382 Table 297: Drift limit, behaviour factor and proposed elastic overstrength ................ 384 Table 298: Drift limit, behaviour factor and global overstrength with material overstrength ................................................................................................................. 387 Table 299: Drift limit, behaviour factor, proposed global and reserve overstrength ... 387



441


Appendix D: List of Equations Equation 1: Definition of q factor based on energy approach ....................................... 48 Equation 2: Definition of ductility factor ........................................................................ 50 Equation 3: Response modification factor ..................................................................... 50 Equation 4: Definition of q factor according to European approach .............................. 52 Equation 5: Seismic combination with additive gravity load .......................................... 60 Equation 6: Seismic combination with counteractive gravity load ................................ 60 Equation 7: Ductility factor definition ............................................................................ 60 Equation 8: Displacement ductility ................................................................................. 60 Equation 9: Ductility reduction factor ............................................................................ 61 Equation 10: Ductility reduction factor as a function of period ..................................... 61 Equation 11: Ductility reduction factor with  equals 1.0 (Elastic behaviour) ............... 61 Equation 12: Ductility reduction factor with T = 0 (Rigid structures) ............................. 61 Equation 13: Ductility reduction factor with T →  (Flexible structures) ...................... 62 Equation 14: Non‐dimensional stiffness parameter ....................................................... 77 Equation 15: Non‐dimensional strength parameter....................................................... 77 Equation 16: Non‐dimensional rotational parameter .................................................... 78 Equation 17: Strength parameter ................................................................................... 81 Equation 18: Strength parameter for un‐braced frames ................................................ 81 Equation 19: Strength parameter for braced frames ..................................................... 81 Equation 20: Beam‐to‐column stiffness ratio ................................................................. 84 Equation 21: Non‐dimensional rotational stiffness ........................................................ 84 Appendix D: List of equations


442


Equation 22: Non‐dimensional ultimate flexural resistance of the connection ............. 85 Equation 23: Ultimate resistance of the T‐stub failure modes 1 .................................... 98 Equation 24: Ultimate resistance of the T‐stub failure modes 2 .................................... 99 Equation 25: Ultimate resistance of the T‐stub failure modes 3 .................................... 99 Equation 26: Plastic moment of the T‐stub failure modes 1 .......................................... 99 Equation 27: Plastic moment of the T‐stub failure modes 2 .......................................... 99 Equation 28: Bolt pretension ........................................................................................ 103 Equation 29: Ultimate resistance of the aluminium T‐stub failure modes 1 ................ 120 Equation 30: Ultimate resistance of the aluminium T‐stub failure modes 2a .............. 121 Equation 31: Ultimate resistance of the aluminium T‐stub failure modes 2b .............. 121 Equation 32: Ultimate resistance of the aluminium T‐stub failure modes 3 ................ 121 Equation 33: Plastic moments of the critical flange cross sections close to web ......... 121 Equation 34: Plastic moments of the critical flange cross‐sections close to bolt ......... 121 Equation 35: Plastic moment of the flange when the failure type is “mode 2” ........... 121 Equation 36: Elastic moment at 0.2% proof strength ................................................... 121 Equation 37: Definition of k‐factor adopted by EC9 ..................................................... 122 Equation 38: Factor used in the definition of k‐factor ................................................. 122 Equation 39: Ramberg Osgood law .............................................................................. 129 Equation 40: Ultimate strain approximation ................................................................ 129 Equation 41: Definition of SDS ....................................................................................... 162 Equation 42: Definition of SD1 ....................................................................................... 162 Equation 43: bf/tf for non‐seismic regions .................................................................... 167 Equation 44: bf/tf for seismic regions ........................................................................... 167 Appendix D: List of equations


443


Equation 45 : h/tw for non‐seismic regions for Ca  0.125 ............................................ 167 Equation 46: h/tw for non‐seismic regions for Ca > 0.125 ............................................. 167 Equation 47: h/tw for seismic regions for Ca  0.125 .................................................... 167 Equation 48: h/tw for seismic regions for Ca > 0.125 .................................................... 168 Equation 49: Moment inequality for the design of beams ........................................... 170 Equation 50: Axial inequality for the design of beams ................................................. 170 Equation 51: Shear inequality for the design of beams ................................................ 170 Equation 52: Internal axial load combination for the design of columns ..................... 170 Equation 53: Internal moment combination for the design of columns ...................... 170 Equation 54: Internal shear load combination for the design of columns ................... 171 Equation 55: Modified overstrength factor suggested by Elghazouli et al ................... 172 Equation 56: Global ductility check for SCWB criteria in Eurocode 8 ........................... 173 Equation 57: Global ductility check for SCWB criteria in AISC ...................................... 174 Equation 58: Definition of sum of the moments in the column ................................... 174 Equation 59: definition of sum of the moments in the beams ..................................... 174 Equation 60: Definition of θ according to EC8 .............................................................. 188 Equation 61: Definition of θ according to AISC ............................................................ 188 Equation 62: Definition of θmax according to AISC ........................................................ 188 Equation 63: Simplified definition of accidental torsional effects according to EC8 .... 200 Equation 64: Amplified accidental torsional effects according to EC8 ......................... 200 Equation 65: Overstrength factor definition according to EC8 .................................... 230 Equation 66: Reserve overstrength for special MRFs ................................................... 231 Equation 67: Reserve overstrength for Intermediate MRFs ......................................... 231 Appendix D: List of equations


444


Equation 68: Reduction factor for drift limits for SMFs ................................................ 231 Equation 69: Reduction factor for drift limits for IMFs ................................................ 231 Equation 70: Slenderness factor ................................................................................... 234 Equation 71: Definition of yield rotation of steel beams according to FEMA 356 ....... 308 Equation 72: Definition of yield moment of steel beams according to FEMA 356 ....... 308 Equation 73: Definition of yield rotation of steel columns according to FEMA 356 .... 308 Equation 74: Definition of yield moment of steel columns according to FEMA 356 .... 308 Equation 75: Limit of bf/2tf for beams .......................................................................... 309 Equation 76: Check of bf/2tf for beams ........................................................................ 309 Equation 77: Limit of h/tw for beams ............................................................................ 309 Equation 78: Check of h/tw for beams .......................................................................... 309 Equation 79: Limit of bf/2tf for columns ....................................................................... 310 Equation 80: Check of bf/2tf for columns ..................................................................... 310 Equation 81: Limit of h/tw for columns ......................................................................... 310 Equation 82: Check of h/tw for columns ....................................................................... 310 Equation 83: Definition of ductility reduction factor qu, ............................................. 317 Equation 84: Definition of redundancy factor Ω ......................................................... 317 Equation 85: Definition of elastic overstrength factor ΩE ............................................ 318 Equation 86: Definition of global overstrength factor ΩE, .......................................... 318 Equation 87: Definition of Reserve ductility (q) .......................................................... 318 Equation 88: Definition of behaviour factor qd ............................................................. 319 Equation 89: Definition of Reserve ductility (q) in term of global overstrength ........ 319

Appendix D: List of equations


445


Equation 90: Definition of ductility reduction factor qu, in term of redundancy factor ...................................................................................................................................... 319 Equation 91: Formulation for overstiffness .................................................................. 335 Equation 92: Limit of cr for elastic analysis ................................................................. 335 Equation 93: Limit of cr for plastic analysis ................................................................. 335 Equation 94: Formulation of cr as defined by the code .............................................. 336 Equation 95 Formulation of cr evaluated using stiffness of frame from pushover .... 336 Equation 96 Formulation of cr evaluated using required deformability of frame from code .............................................................................................................................. 336 Equation 97: Presented interstory drift withstand by the frame ................................. 336

Appendix D: List of equations


446


Appendix E: Unit Conversions Length Conversion Imperial/USA unit Metric (SI) unit Inch 2.54 centimetres Foot 30.48 centimetres Yard 0.91 meters Mile 1.61 kilometres

Metric (SI) unit Centimetre Meter Meter Kilometre

Imperial/USA unit 0.39 inches 3.28 feet 1.09 yards 0.62 miles

Weight (or mass) conversion Imperial/USA unit Ounce (weight) Pound UK ton (2240 pounds) US ton (2000 pounds)

Metric (SI) unit 28.35 grams 0.45 kilograms 1.02 metric tons 0.91 metric tons

Metric (SI) unit Gram Kilogram Metric ton (1000 kg.) Metric ton (1000 kg.)

Imperial/USA unit 0.035 ounces 2.21 pounds 0.98 UK tons 1.10 US tons

Load (Force)

1 kip 1 tonne

= 1,000 Ib. = 1,000 kgf = 2,205 lb. = 9.807 kN

1 kgf

= 2.2046 Lb & 1 Lb = 0.4536 kgf

1 N 1 kN Force per running length 1 kN/m 1 tonne/m Stress (Pressure) 1 psi

= kg‐m / sec2

1 kPa

1 tsm

1 MPa 1 ksi

Appendix E: Unit conversions

= 1,000 N = 68.52 Lb/ft. = 672 Lb/ft. = 144 psf = 0.14504 psi = 6.895 kPa (1 kPa = 1 kN/m2) = 20.885 psf = 0.70307 tsm (tonne/m2) = 9.807 kPa = 1.422 psi = 204.82 psf = 145 psi = 0.145 ksi = 20,885 psf = 101.97 tsm = 6.895 Mpa


447


Appendix F: Material Constants Properties

Carbon Steels

Alloy Steels

Aluminium

Reinforce Concrete

Density (1000 kg/m3)

7.85

7.85

2.6‐2.8

2.3 – 2.4

Elastic Modulus (GPa)

190‐210

190‐210

70‐79

17‐31

Tensile Strength (MPa)

276‐1882

758‐1882

230‐570

12 ‐ 15

Yield Strength (MPa)

186‐758

366‐1793

215‐505

Poisson's Ratio

0.27‐0.3

0.27‐0.3

0.33

0.1‐0.2

10‐32

4‐31

10‐25%

Thermal Expansion (10 /K)

11‐16.6

9.0‐15

23

10 ‐ 12

Melting Point (°C)

1510

1510

660

Thermal Conductivity (W/m‐K) 24.3‐65.2

26‐48.6

20.4‐25.0

Specific Heat (J/kg‐K)

450‐2081

452‐1499

910

Electrical Resistivity (10 ‐m)

130‐1250

210‐1251

26

Hardness (Brinell 3000kg)

86‐388

149‐627

Percent Elongation (%) ‐6

‐9

Appendix F: Material constants


448


Appendix G: American standards steel grades

Yield strength Re MPa [ksi]

Tensile strength Rm MPa [ksi]

Grade 36 Grade 42 Grade 50 Grade 55 Grade 60 Grade 65

≥250 [36] ≥290 [42] ≥345 [50] ≥380 [55] ≥415 [60] ≥450 [65]

A588‐05

Grade B Grade C

A709‐07

Standard

Grades

Minimum elongation A min. 200 mm [8 in] %

min. 50 mm [2 in] %

400‐550 [58‐80] ≥415 [60] ≥450 [65] ≥485 [70] ≥520 [75] ≥550 [80]

20 20 18 17 16 15

21 24 21 20 18 17

≥345 [50] ≥345 [50]

≥485 [70] ≥485 [70]

18 18

21 21

Grade 36 Grade 50 Grade 50S

≥250 [36] ≥345 [50] 345‐450 [50‐65]

400‐550 [58‐80] ≥450 [65] ≥450 [65]

20 18 18

21 21 21

A913‐04

Grade 50 Grade 65

≥345 [50] ≥450 [65]

≥450 [65] ≥550 [80]

18 15

21 17

A992‐06a

Grade 50

345‐450 [50‐65]

≥450 [65]

18

21

A36‐05

A572‐07

Appendix G: American standards steel grades


449


Appendix H: European standards steel grades Minimum yield strength (MPa) Nominal thickness (mm)

Standard Grades ≤16

Minimum elongation (%)

Nominal thickness (mm) Nominal thickness (mm)

>16 >40 >63 >80 >100 >3 ≤40 ≤63 ≤80 ≤100 ≤125 ≤ 100

S235JR S235J0 235 225 215 S235J2 S275JR S275J0 S275J2 EN S355JR 10025‐2: S355J0 2004 S355J2 S355K2 S450J0 E295 E335 E360

Tensile strength (MPa) >100 ≤125

>3 >40 >63 >100 ≤40 ≤63 ≤ 100 ≤125

195 360‐510 350‐500

26 25

24

22

275 265 255 245 235 225 410‐560 400‐540

23 22

21

19

355

345 335 325 315 295 470‐630

450‐600

22 21

20

18

450 295 335 360

430 285 325 355

530‐700 450‐610 550‐710 650‐830

17 20 19 16 15 11 10

18 14 9

16 12 8

410 275 315 345

390 265 305 335

380 255 295 325

380 245 275 305

Appendix H: European standards steel grades

550‐720 470‐610 570‐710 670‐830


450


Appendix I: Miscellaneous and Thumb rules Structural depth System Slab Steel beams Steel Joist (Floor) Steel Joist (Roof) Plate girder Joist girder Steel truss Space frame

L/D (Length to depth) 40 to 50 20 to 28 20‐25 25‐35 15 12 12 12 to 20

Span range Up to 75ft (23 m) 8ft to 144ft (2.5m to 44m) 40ft to 100ft (12m to 30.5m) 20ft to 100ft (6m to 30.5m) 40ft to 300ft (12m to 91.5m) 80ft to 300ft (24m to 91.5m)

Loads 2

System Weight (kN/m ) Floor finished (screed) 1.8 Ceiling and service loads 0.5 Removable light weight partitions 1.0 Blockwork partition 2.5 External walls‐ Curtain walling and glazing 0.5 on Elevation Cavity walls (Light weight blocks/bricks) 3.5 Composite floor slabs 2.5 to 3.5 Precast concrete slabs 2.5 to 4.0 From Manual for the design of steel work building structures

Appendix I: Miscellaneous and thumb rules


451


Printed and soft copies Ph.D. Candidate: Muhammad Tayyab Naqash (Printed and soft formats), Ph.D. Supervisor: Prof. Gianfranco De Matteis (Printed and soft formats), Ph.D. Co‐Supervisor: Prof. Antonio De Luca (Printed and soft formats), Ph.D. Coordinator: Prof. Marcello Vasta (Printed and soft formats), Department of Engineering and Geology, University “G. d'Annunzio” of Chieti‐ Pescara (Printed and soft formats),

Printed and soft copies


452


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Author’s vita Muhammad Tayyab Naqash was born in Charsadda (KPK) Pakistan. After completing his schooling, from Battagram Charsadda, he entered for his intermediate studies at Nisar Shaheed Degree College Risalpur Cantt Nowshera, where he completed his Pre‐Engineering; he was awarded with silver medal for obtaining second position in Engineering group from the Board of Intermediate and Secondary Education Mardan. During the years of 2003 to 2007, he attended Quaid‐e‐Awam University of Engineering Sciences and Technology (QUEST) Nawabshah Sindh and achieved Bachelor’s degree in Civil Engineering. He was awarded with triple honour (Gold Medal for faculty top in 03 Batch, Gold Medal for best graduate in 03 Batch and silver medal for first position in 03 Civil) in the fourth convocation of the University held in 2012. After bachelor, he worked as Production Engineer for a year at MobiServe Pakistan (Pvt) Limited Islamabad and then joined Pakistan Poverty Alleviation Fund (PPAF) Pakistan as Management Executive at Water Management Centre Islamabad. He was offered full scholarship at the University of Naples “Federico II”, Naples, Italy in the Second Edition of the Master (Design of Steel Structures) being at the top of the list in September 2008. He obtained Master’s Degree in “Design of Steel Structures” and was awarded with maximum evaluation 110/110 in November 2009. He entered in the 25th cycle of Ph D. at the Department of Engineering, University ‘‘G. D’Annunzio’’ of Chieti‐Pescara, Pescara, Italy. During his Ph D. studies, he worked on metal connections and seismic design of steel structures, in such fields he has several publications in International Journals and conferences. He also remained in the organising committee for the “Design of Steel Structures” in collaboration with the University of Naples “Federico II”, together with the participation in the courses as an assistant with professors. The current thesis is aimed to conclude his Ph.D. studies at the University ‘‘G. d’ Annunzio’’ of Chieti‐Pescara. Contacts: [email protected], [email protected] The Author typed and composed this thesis. Distributions