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Accuracy of a Simplified Analysis Model for Modern Skyscrapers

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Accuracy of a Simplified Analysis Model for Modern Skyscrapers Brigham Young University BYU ScholarsArchive Theses and Dissertations 2013-06-11 Accuracy of a Simplified Analysis Model for Modern Skyscrapers Jacob Scott Lee Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Civil and Environmental Engineering Commons BYU ScholarsArchive Citation Lee, Jacob Scott, "Accuracy of a Simplified Analysis Model for Modern Skyscrapers" (2013). Theses and Dissertations. 4055. https://scholarsarchive.byu.edu/etd/4055 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Accuracy of a Simplified Analysis Model for Modern Skyscrapers Jacob S. Lee A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Richard J. Balling, Chair Paul W. Richards Fernando S. Fonseca Department of Civil and Environmental Engineering Brigham Young University June 2013 Copyright © 2013 Jacob S. Lee All Rights Reserved ABSTRACT Accuracy of a Simplified Analysis Model for Modern Skyscrapers Jacob S. Lee Department of Civil and Environmental Engineering, BYU Master of Science A new simplified skyscraper analysis model (SSAM) was developed and implemented in a spreadsheet to be used for preliminary skyscraper design and teaching purposes. The SSAM predicts linear and nonlinear response to gravity, wind, and seismic loading of "modern" skyscrapers which involve a core, megacolumns, outrigger trusses, belt trusses, and diagonals. The SSAM may be classified as a discrete method that constructs a reduced system stiffness matrix involving selected degrees of freedom (DOF's). The steps in the SSAM consist of: 1) determination of megacolumn areas, 2) construction of stiffness matrix, 3) calculation of lateral forces and displacements, and 4) calculation of stresses. Seven configurations of a generic skyscraper were used to compare the accuracy of the SSAM against a space frame finite element model. The SSAM was able to predict the existence of points of contraflexure in the deflected shape which are known to exist in modern skyscrapers. The accuracy of the SSAM was found to be very good for displacements (translations and rotations), and reasonably good for stress in configurations that exclude diagonals. The speed of execution, data preparation, data extraction, and optimization were found to be much faster with the SSAM than with general space frame finite element programs. Keywords: Jacob S. Lee, skyscraper, structural analysis, optimization, preliminary design ACKNOWLEDGEMENTS I wish to express my sincere appreciation and thanks to my advisor, Dr. Richard J. Balling, for his help and dedication that went into our research. I am grateful for his motivation and encouragement in stretching my mind in ways I never thought possible. I was blessed with the opportunity he gave me to explore an area of structural engineering that inspires me and share that experience alongside him. I am indeed indebted to him for making it possible to travel to China to study the skyscrapers there and collaborate with the engineers behind their designs as part of his Megastructures class. That unforgettable experience has given me a wider perspective of what structural engineering has to offer and excites me about my future career aspirations in engineering. I would also like to thank my committee members, Dr. Paul W. Richards and Dr. Fernando S. Fonseca, who have truly been inspirational professors to me in my academic life at BYU. I would like to thank my family and friends who have supported me throughout this endeavor and my graduate degree, and who have instilled in me the values of one who strives to emulate the pure love of Christ. I would also like to thank my fellow colleagues for their hard work and insight during this project. TABLE OF CONTENTS LIST OF TABLES ...................................................................................................................... vii LIST OF FIGURES ...................................................................................................................... x 1 Introduction ........................................................................................................................... 1 2 Literature review................................................................................................................. 13 2.1 Continuum Methods for Low/Medium-Rise Buildings ................................................ 13 2.2 Continuum Method for Framed Tubes ......................................................................... 16 2.3 Inherent Problems with Continuum Methods ............................................................... 17 2.4 Discrete Outrigger Methods .......................................................................................... 20 2.5 Discrete Substructuring Methods .................................................................................. 22 3 Simplified Skyscraper Analysis Model ............................................................................. 24 3.1 Determination of Megacolumn Areas ........................................................................... 24 3.2 Construction of the Stiffness Matrix ............................................................................. 27 3.3 Calculation of Lateral Forces/Displacements ............................................................... 39 3.4 Calculation of Stresses .................................................................................................. 44 3.5 Rapid Trial-and-Error Optimization ............................................................................. 52 4 Space frame model .............................................................................................................. 54 4.1 Nodes ............................................................................................................................ 54 4.2 Members ....................................................................................................................... 55 4.3 Supports ........................................................................................................................ 58 4.4 Loads ............................................................................................................................. 59 4.5 Output ........................................................................................................................... 59 5 Results .................................................................................................................................. 60 5.1 Configuration #1 – core+megacolumns ........................................................................ 61 v 5.2 Configuration #2 – core+megacolumns+outriggers ..................................................... 65 5.3 Configuration #3 – core+megacolumns+belts .............................................................. 68 5.4 Configuration #4 – core+megacolumns+diagonals ...................................................... 72 5.5 Configuration #5 – core+megacolumns+outriggers+belts ........................................... 76 5.6 Configuration #6 – core+megacolumns+outriggers+belts+diagonals .......................... 81 5.7 Configuration #7 – core+megacolumns+outirgger at one level only ........................... 85 6 Conclusions .......................................................................................................................... 89 REFERENCES ............................................................................................................................. 91 APPENDIX A. SSAM Excel Spreadsheet (Configuration #6) ............................................. 95 vi LIST OF TABLES Table 3-1: Stiffness matrix - contribution of the core and megacolumns ..............................29 Table 3-2: Stiffness matrix - contribution of outriggers ........................................................32 Table 3-3: Stiffness matrix - contribution of the belt trusses .................................................35 Table 3-4: Stiffness matrix - contribution of diagonals .........................................................37 Table 5-1: Configuration #1 - design variables and calculated megacolumn areas ..............61 Table 5-2: Configuration #1 - lateral core translation (m) .....................................................62 Table 5-3: Configuration #1 - core rotation (rad) ..................................................................62 Table 5-4: Configuration #1 - vertical megacolumn translation minus vertical core translation .............................................................................................................63 Table 5-5: Configuration #1 - core stress (KPa) ....................................................................63 Table 5-6: Configuration #1 - megacolumn stress (KPa) ......................................................64 Table 5-7: Configuration #2 - design variables and calculated megacolumn areas ..............65 Table 5-8: Configuration #2 - lateral core translation (m) .....................................................65 Table 5-9: Configuration #2 - core rotation (rad) ..................................................................65 Table 5-10:
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