Analyzing and Creating Forms: Rapid Generation of Graphic Statics Solutions through RhinoScript ...

189 Pages·2010·16.29 MB·English

Analyzing and Creating Forms: Rapid Generation
of Graphic Statics Solutions through RhinoScript
by
Michael S. Shearer
B.S. Civil and Environmental Engineering
Cornell University, 2009
SUBMITTED TO THE DEPARTMENT OF CIVIL AND ENVIRONMENTAL
ENGINEERING INPARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF
MASTER OF ENGINEERING IN CIVIL AND ENVIRONMENTAL
ENGINEERING
AT THE
ARCHNES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ASSACHUSETTS INSTUJTE
JUNE 2010 OF TECHNOLOGY
JUL 15 2010
@2010 Michael S. Shearer. All rights reserved.
LIBRARIES
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 7, 2010
Certified by.....................................
Joh sendorf
Associate Professor of Civil and Environmen al Engineering and Architecture
Thesis Super r
A ccepted by .................................
Daniele Veneziano
Chairman, Departmental Committee for Graduate Students

Analyzing and Creating Forms: Rapid Generation of
Graphic Statics Solutions through RhinoScript
by
Michael S. Shearer
Submitted to the Department of Civil and Environmental Engineering
on May 7, 2010, in partial fulfillment of the
requirements for the degree of
Master of Engineering in Civil and Environmental Engineering
ABSTRACT
Graphic statics is a method of structural analysis which relies solely on geometric
constructions to determine axial forces within members. Accordingly, any computer-
aided drafting (CAD) program may be utilized in the pursuit of a graphic statics
solution. This thesis presents a methodology which employs Rhinoceros 4.0 (Rhino)
in its capacity as such a program. Using RhinoScript, which provides access to Visual
Basic Scripting, or VBScript, within Rhino, the basic steps of graphic statics are
automated as scripts. The scripts are then compiled into RhinoStatics, a plug-in
module which facilitates graphic statics analyses.
The thesis focuses on three applications of graphic statics: determination of simply
supported reaction forces, funicular form-finding given restraints on the axial capacity
of the material being used, and determination of axial forces within a pin-jointed truss
loaded at its nodes. While only these three applications are explored in detail, the
developed scripts may be used in the pursuit of a wide range of graphical equilibrium
solutions, transforming Rhino into a highly specialized tool in the hands of a user with
knowledge of graphic statics techniques. Such users will be able to easily analyze a
host of two-dimensional cross-sections and forms, as well as generate new shapes given
loading and geometric constraints. Users familiar with VBScript could easily expand
on the documented script files to add functionality to suit their own needs.
In addition to providing worked examples of how to utilize the RhinoStatics plug-
in module, this thesis provides a brief overview of graphic statics in general. The
developed scripts are explained in detail, with fully documented RhinoScript code
provided in the appendices.
Thesis Supervisor: John Ochsendorf
Title: Associate Professor of Civil and Environmental Engineering and Architecture

Acknowledgments
It goes without saying that any major project such as a thesis is not completed in a
vacuum, nor solely through the efforts of the author. With that in mind, I would like
to thank the following individuals for their contributions to the successful completion
of this thesis:
John Ochsendorf for his support, guidance, and encouragement through the entire
thesis process. Perhaps most importantly, he introduced me to the concept of
graphic statics, a true "twenty-fifth century method" which just happened to
be first developed in the eighteenth century. Throughout the development of
the RhinoStatics plug-in, he was an invaluable sounding board, always looking
to possible future applications and trying to push the project as far as it would
go. It has been a privilege to have him as my advisor, and I look forward to
future collaborations.
Patrick McCafferty (Arup) for recommending John as a thesis advisor and for
challenging me to develop my project into something truly original. Pat first
suggested expanding the thesis from a series of case studies into a full-fledged
program capable of performing graphic statics. Without his influence, this whole
project would have looked very different, and with his continued influence, it
may evolve even further.
Tom Chatt (Cornell University, ECE MEng 2010) for helping me though my
largest programming endeavor to date and for providing support even after
the scripting was complete. From I4TEX assistance to proofreading of the final
draft, I am indebted to Tommy for the high quality of my finished thesis, both
its content and its visual appeal.
My family and friends for their constant love and unflagging support through
what have been a grueling nine months. The constant workload and long hours
were made easier by having people in my life with whom I could share both the
highs and the lows.
The Schoettler Scholarship Fund for providing me with the full tuition scholar-
ship which allowed me the freedom to pursue this Master of Engineering degree.
Though rigorous and demanding, obtaining this degree has been immensely re-
warding.
In pursuing the Master of Engineering degree, I sought to improve myself as an
engineer by broadening the tools at my disposal. At the beginning of this program, I
had never even heard of graphic statics; however, as my time at MIT draws to a close,
I believe learning to harness it may have been the most important skill I gained. For
that, I am immensely grateful to everyone who assisted in this endeavor.
This thesis was typeset using the MiKTEX 2.8 implementation
of LATEX for Windows and the mitthesis template provided on
Athena. TEXnicCenter served as the text editor and compiler.
Contents
1 Introduction
1.1 Problem Statement . . . . . . . . . . . .
1.2 Literature Review . . . . . . . . . . . . .
1.3 RhinoStatics . . . . . . . . . . . . . . . .
2 Review of Graphic Statics Methodology
2.1 Definitions . . . . . . . . . . . . . . . . .
.
2.2 Bow's Notation . . . . . . . . . . . . . .
.
2.3 Load Line Construction . . . . . . . . .
.
2.4 Simply Supported Reactions . . . . . . .
.
2.5 Force and Funicular Polygons . . . . . .
.
2.5.1 Funicular Shapes . . . . . . . . . .
2.5.2 Truss Analysis . . . . . . . . . . .
3 RhinoScript Programming Methodology
3.1 Why Rhinoceros? . . . .
3.2 Script-Level Routines
3.2.1 GetLoadScale
3.2.2 GetPlane . . . .
3.2.3 GetBowsSize
3.2.4 GetForceScale
3.2.5 GetForceSize
3.2.6 GetAxialSize
3.2.7 MakePoint . . . .
3.2.8 MakeLabel . . . .
3.2.9 LabelOverlap
3.2.10 IntersectLines
3.2.11 SlopeVector . . .
3.2.12 MakeParallelLine
3.2.13 DrawPin . . . . .
3.2.14 DrawRoller . . .
3.3 User-Level Routines . . .
3.3.1 AddSupports . .
3.3.2 ApplyLoads . . .
3.3.3 MakeLineOfAction . . .
3.3.4 AddBows . . . . .
3.3.5 MakeLoadLine
3.3.6 MakePole . . . . . . . . 52
3.3.7 ConnectPole . . . . . . . 52
3.3.8 MakeFunicular 52
3.3.9 MakeClosingString 55
3.3.10 CloseLoadLine . . . 55
3.3.11 MakeForce . . . . . . . . 58
3.3.12 LabelForcePoly . . . . . 58
3.3.13 GetForceLabel . . . . . . 61
3.3.14 ViewGlobals . . . . 64
3.4 Concluding Thoughts . . . . . . 64
4 Implementation Examples
4.1 Simply Supported Reaction Forces . . . . .
4.2 Analysis of Ideal Truss Loaded at Joints . .
4.3 Form-Finding with Material Restraints . . .
4.4 Optimization of Truss Under Vertical Loads
5 Conclusion
5.1 Discussion . . . . . . . . . . . . . . . . . . .
5.2 Recommendations for Further Development
5.2.1 Functionality in Any 2D Plane . . . .
5.2.2 Parametric Linkages . . . . . . . . .
5.2.3 Automated Structural Optimization .
5.2.4 Increased Robustness . . . . . . . . .
5.2.5 Improved Graphic Interface . . . . .
A RhinoScript Code for Script-Level Routines 103
A.1 DrawPin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
A.2 DrawRoller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.3 GetAxialSize . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.4 GetBowsSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.5 GetForceScale . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.6 GetForceSize . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.7 GetLoadScale . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A.8 GetPlane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.9 IntersectLines . . . . . . . . . . . . 114
A.10 LabelOverlap . . . .. .... 118
A.11 MakeLabel . . . . . . . . . . . . . . 120
A.12 MakePoint . . . . . . . . . . . . . . 121
A.13 MakeParallelLine . . . . . . . . . . 122
A.14 SlopeVector . . . . . . . . . . . . . 124
B RhinoScript Code for User-Level Routines 125
B.1 AddBows ................................ . 126
B.2 AddSupports ........ ............................... 130
B.3 ApplyLoads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B.4 CloseLoadLine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
B.5 ConnectPole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B.6 GetForceLabel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.7 LabelForcePoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
B.8 MakeClosingString . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B.9 MakeForce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.10 MakeFunicular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B.11 MakeLineOfAction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
B.12 MakeLoadLine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
B.13 MakePole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.14 ViewGlobals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
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