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Evaluating the Use of Particle-Spring Systems in the Conceptual Design of Grid Shell Structures By Evaluating the Use of Particle-Spring Systems in the Conceptual Design of Grid Shell Structures by Trevor B. Bertin B.S. Civil Engineering Worcester Polytechnic Institute, 2011 SUBMITTED TO THE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING IN THE PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF 1 MASTER OF ENGINEERING IN CIVIL AND ENVIRONMENTAL ENGINEERING AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2013 ©2013 Trevor Bertin. All Rights Reserved The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of Author: _____________________________________________________________ Department of Civil and Environmental Engineering May 10, 2013 Certified by: ___________________________________________________________________ John A. Ochsendorf Professor of Building Technology and Civil and Environmental Engineering Thesis Supervisor Accepted by: ___________________________________________________________________ Heidi M. Nepf Chair, Departmental Committee for Graduate Students 2 Evaluating the Use of Particle-Spring Systems in the Conceptual Design of Grid Shell Structures by Trevor B. Bertin Submitted to the Department of Civil and Environmental Engineering on May 10, 2013 in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in Civil and Environmental Engineering ABSTRACT 3 This thesis evaluates particle-spring systems as conceptual design tools in an effort to create efficient grid shell structures. Currently many simulation tools are available to create representations of intricate geometries and forms. However, these forms can become highly complex and challenging upon their realization. A lack of understanding of these forms leads to structures that cannot support their corresponding loads due to their shape, boundary conditions or edge conditions. To create successful grid shells, designers must understand the design principles behind these forms. The goals of this research were achieved through a parametric study that involved manipulating the topology and topography of three global grid shell geometries. It was determined that the ability of particle-spring form finding methods to create good structures is highly dependent on both the mesh type used and the structure’s global geometry. A list of implications has been developed and is presented in this work. Thesis Supervisor: John Ochsendorf Title: Professor of Building Technology and Civil and Environmental Engineering 4 Acknowledgements I would like to thank Professor John Ochsendorf for his advice and invaluable insight in supervising this work. Professor Ochsendorf’s interest and enthusiasm was an unwavering source of encouragement. I would also like to thank Professor Jerome Connor who has shared his incredible knowledge and passion for structural engineering throughout my time at MIT. Thank you to my girlfriend Courtney for her constant love, support and understanding. Lastly thank you to my family, who have always believed in me and encouraged me in everything I do. 5 Table of Contents Acknowledgements ......................................................................................................................... 5 Table of Contents ............................................................................................................................ 6 List of Figures .................................................................................................................................. 8 List of Tables ................................................................................................................................. 10 1 Introduction ........................................................................................................................... 11 1.1 Definition of Form Finding ............................................................................................. 11 1.2 Definition of Particle-Spring System .............................................................................. 12 1.3 Definition of ‘Good Structure’ ........................................................................................ 13 1.4 Motivation ...................................................................................................................... 14 6 1.5 Problem Statement ........................................................................................................ 14 1.5.1 Thesis Goals ............................................................................................................ 14 1.5.2 Approach ................................................................................................................. 15 1.5.3 Outline of Chapters ................................................................................................. 16 2 Literature Review .................................................................................................................. 17 2.1 Introduction.................................................................................................................... 17 2.2 History of Form Finding .................................................................................................. 17 2.3 Grid Shells ....................................................................................................................... 18 2.4 Process of Design with Form Finding ............................................................................. 20 2.5 Particle-Spring Systems as Design Tool .......................................................................... 21 2.5.1 CADenary ................................................................................................................ 23 2.5.2 Rhinoceros/Grasshopper/Kangaroo ....................................................................... 24 2.5.3 Commercial Design Tools ........................................................................................ 26 2.6 Summary ........................................................................................................................ 27 3 Methodology ......................................................................................................................... 29 3.1 Overview ........................................................................................................................ 29 3.2 Procedure of Parametric Study ...................................................................................... 29 3.2.1 Parameters and Test Geometries ........................................................................... 30 3.2.2 Form Finding Process .............................................................................................. 32 3.2.3 Analysis Process ...................................................................................................... 35 3.3 Summary ........................................................................................................................ 37 4 Results .................................................................................................................................... 39 4.1 Introduction.................................................................................................................... 39 4.2 Spherical Cap .................................................................................................................. 39 4.3 Rectangular Hanging Mesh ............................................................................................ 44 4.4 Double Curved Barrel Vault ............................................................................................ 48 7 4.5 Discussion ....................................................................................................................... 51 4.6 Rhinoceros/Grasshopper/Kangaroo Critique................................................................. 54 4.7 Summary ........................................................................................................................ 57 5 Conclusions ............................................................................................................................ 59 5.1 Summary of Contributions ............................................................................................. 59 5.2 Future Work ................................................................................................................... 60 References .................................................................................................................................... 63 Appendix A: Grasshopper Script ................................................................................................... 65 Appendix B: Spherical Cap ............................................................................................................ 72 Appendix C: Rectangular Hanging Mesh....................................................................................... 79 Appendix D: Double Curved Vault ................................................................................................ 87 List of Figures Figure 1.1: Hanging cable to particle-spring network .................................................................. 13 Figure 1.2: Good structure ............................................................................................................ 13 Figure 1.3: Bad structure .............................................................................................................
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