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The form finding of tensile membranes - a tool for architects and designers
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Content
THE FORM FINDING OF TENSILE MEMBRANES:
A TOOL FOR ARCHITECTS AND DESIGNERS
by
Kavita Rodrigues
A Thesis Presented to the
FACULTY OF THE SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF BUILDING SCIENCE
August 2008
Copyright 2008 Kavita Rodrigues
Table of Contents
List of Figures iv
Abstract viii
CHAPTER 1: The Problem 1
Why Tensile Structures? 1
Why Not Tensile Structures? 2
What is Needed 4
CHAPTER 2: Background 8
The History of Tensile Membranes 8
Form Finding of Tensile Membranes 16
The Role Played by Computer Applications in Form Finding 18
Conclusion 23
CHAPTER 3: Structural Principles 24
What is a Tensile Structure? 24
Anticlastic Stability 27
Edge Conditions 31
Pre-Stress 33
Surface Conditions and Shapes 35
Conclusion 37
CHAPTER 4: Materials 38
Fabric Properties 38
The Selection of Materials 48
Table 4.01 - Selection Table 52
Conclusion 53
CHAPTER 5: Program Structure 54
Form Finding 54
Structural Analysis 60
Cutting Pattern 61
Sample Structures 62
CHAPTER 6: Tutorial 64
The DXF File 64
Input 68
The Unloaded Form 73
Loads 75
In-Program Assistance 78
CHAPTER 7: Advantages and Disadvantages 82
The User Interface 82
User Input 83
Editing 84
Analysis 85
ii
CHAPTER 8: Areas for Future Work 86
Areas for Improvement in the Existing Program 86
Additions to the program 90
CHAPTER 9: Conclusions 92
GLOSSARY 95
BIBLIOGRAPHY 98
APPENDICES Appendix A – USC School Of Architecture Course Description 100
Appendix B – Force Density Method 103
Appendix C – Dynamic Relaxation Method 106
Appendix D – Common Assembly Properties 108
Appendix E – Fabric Selectors Guide 109
Appendix F – Code 139
iii
List of Figures
Figure 1.01 Tensile Structure Created by Graduate Building Science Students at USC 1
Figure 1.02 Fabric Structure at MOCA 2
Figure 1.03 Model of Tensile Structure Created by Graduate Building Science 4
Students at USC
Figure 1.04 Sketches Showing the Form Finding of a Simple Membrane Over 5
Crossed Arches
Figure 2.01 The Tipi 9
Figure 2.02 The Yurt 10
Figure 2.03 The Black Tent 10
Figure 2.04 Menai Strait Suspension Bridge 12
Figure 2.05 George Washington Bridge 12
Figure 2.06 Brooklyn Bridge 13
Figure 2.07 Burgo Paper Mill 13
Figure 2.08 Raleigh Arena North Carolina 14
Figure 2.09 Olympic National Stadia – Kenzo Tange 15
Figure 2.10 Munich Olympic Stadium 16
Figure 2.11 Clear Film Model 17
Figure 2.12 Stretch Fabric Model 17
Figure 2.13 Linear Load/Displacement Curve 19
Figure 2.14 Non Linear Load/Displacement Curve 19
Figure 2.15 Force Density Example 21
Figure 3.01 Cable Net – German Pavilion at Expo 67 Montreal 25
Figure 3.02 Air Supported Structure 26
Figure 3.03 Air Inflated Structure 26
Figure 3.04 Frame Supported Membrane 27
iv
Figure 3.05 Four Point Structure 28
Figure 3.06 Anticlastic Curvature 28
Figure 3.07 Explaining the Minimal Surface 30
Figure 3.08 The Hyperboloid 30
Figure 3.09 Multiple Hyperboloid Surfaces 31
Figure 3.10 Rigid Straight Edge 31
Figure 3.11a Rigid Compression Arch or Ring 32
Figure 3.11b Tensile Structure using Compression Arches 32
Figure 3.12a Flexible Curved Cable Edge 33
Figure 3.12b Tensile Membrane Installation at UT San Antonio with a Flexible Curved 33
Cable Edge
Figure 3.13 Membrane Stresses and Surface Tension 34
Figure 3.14 Saddle Shaped Membrane Surface 35
Figure 3.15 Wave Form of a Tensile Membrane 36
Figure 3.16a Arch Supported Membrane – Single Arch 36
Figure 3.16b Arch Supported Membrane – Multiple Arches 36
Figure 3.17a Point Supported 37
Figure 3.17b Tension Ring 37
Figure 3.17c Spherical Disc 37
Figure 3.17d Flexible Cable Eye 37
Figure 3.17e Flexible Looping Cable 37
Figure 4.01 Material Matrix 41
Figure 4.02 PVC Coated Polyester 42
Figure 4.03 PTFE Coated Glass Fiber 46
Figure 4.04 ETFE Foil 47
v
Figure 5.01a Elevation in AutoCAD 55
Figure 5.01b Plan in AutoCAD 55
Figure 5.02a Steel Strand 56
Figure 5.02b Wire Rope 56
Figure 5.03 Material Input Screen (Membrane Properties Page) 58
Figure 5.04 Display Screen 59
Figure 5.05 Saddle Shape 62
Figure 5.06 Four Point Structure 62
Figure 5.07 Multiple Four Point Structures 63
Figure 5.08 Repeating Surfaces 63
Figure 6.01 Design Sketch 64
Figure 6.02 Plan Drawing in AutoCAD 65
Figure 6.03 Elevation Drawing in AutoCAD 65
Figure 6.04 3D View in AutoCAD 66
Figure 6.05 Layers in the Drawing 67
Figure 6.06 Finished Drawing 67
Figure 6.07 Splash Screen 68
Figure 6.08 Import the DXF File 69
Figure 6.09 Membrane Tab in the Material Properties Window 70
Figure 6.10 Cable Tab in the Material Properties Window 72
Figure 6.11 Struts Tab in the Material Properties Window 73
Figure 6.12 Display Window Showing the Undeformed Shape of the Membrane 74
Figure 6.13 The Load Window 75
Figure 6.14 U.S. Annual Wind Power Resource and Wind Power Classes – 76
Contiguous U.S. States
Figure 6.15 Display Window 77
vi
Figure 6.16 The Help File 78
Figure 6.17 Guide to Selecting Fabric in the Help File 79
Figure 6.18 Glossary 80
Figure 8.01 Simple Four Point Structure 87
Figure 8.02 Shade Sail 87
Figure 8.03 Multiple Four Point Structure 88
Figure 8.04 Tensile Canopy 88
Figure 8.05 Shade Sail with Circular Opening 89
Figure 8.06 Multiple Conics – Ripleys Yatch Club South Carolina 89
Figure 8.07 Inverted Conic Shape – Hong Kong Jockey Club 90
Figure 9.01 Tensile Fabric Structure 92
Figure 9.02 Tensile Fabric Membrane 94
vii
Abstract
Lightweight structures have complex forms and are difficult to visualize and translate into two-
dimensional drawings. The stability and stiffness of such structures depends on the desired boundaries and
internal tension. Their precise shape depends on various factors such as the material used and its
properties, its pretension, curvature, and modulus of elasticity.
A useful tool for architects would be a program to generate a mesh for the membrane. The
program would compute the form using variable parameters and run a schematic structural analysis to test
the intended structural performance under both vertical and lateral loading. The third phase of the program
would generate a cutting pattern for the material.
The program, called ‘Form Finder’ was created in 2004 using Visual Basic 6.0. The tool
successfully accepted 3D geometry as input, along with edge conditions and material data and provided the
resulting 3D shape and a file containing the resulting stresses.
viii
CHAPTER 1: THE PROBLEM
1.1 WHY TENSILE STRUCTURES?
A well designed tensile structure is among the purest expressions of structure and materials. There
is no part of a lightweight structure that is superfluous or added on for any reason. Every part of these
structures is present by necessity – what you see is the essence of the structure. There are no massive
hidden structural fortifications; nothing in the structure has been added for decorative purposes. They are
minimalist, graceful and beautiful examples of how materials can be used in the most efficient manner
possible.
Fig 1.01 Tensile Structure Created by Graduate Building Science Students at USC (Photo: Douglas Noble c.2007)
These structures are captivating to people in part because of their obvious contrast to conventional
structures. Where conventional structures are sturdy, staid and obviously anchored to the ground, tensile
membranes are light, graceful and sometimes give you the impression that they could fly. They are the
complete antithesis to the tall concrete frames, the steel towers and trusses of everyday buildings.
This apparent lightness is the quality that makes them so appealing. They are beautiful, ingenious
and can have a quality of lightheartedness or fun. And in their most elaborate incarnations, they can be
awe-inspiring. Lightweight structures make people smile.
1
Tensile membranes are fascinating to architects. They present a beautiful solution for spanning
large distances and provide limitless possibilities when it comes to form and expression. In addition, due to
their nature, their very uniqueness, they have a tendency to become iconic buildings, and what architect
does not want his buildings to stand out and be memorable?
1.2 WHY NOT TENSILE STRUCTURES?
In view of these facts, it is surprising how few tensile structures, are currently being built. There are
a few important reasons for this mainly having to do with visualizing and simulating the final form. Tensile
membranes are beautiful in their simplicity, but this very simplicity in design makes their structural
implications difficult for architects to grasp.
The conventional architect sometimes designs a building in two dimensions, or designs on paper,
although this is increasingly less common. He works out his plan and his elevation (and section); he may
even build a scale model. Even if creating a digital model, it is usually just a schematic form. Only after he is
satisfied with what he wants the building to look like does he take it to his structural engineer. At this stage
the structural engineer is asked to create a structural system that will enable the building to look like the
architects vision.
Fig 1.02 Fabric Structure at MOCA (photo: Douglas Noble c.2007)
2
In the case of tensile membranes this two-dimensional design strategy is simply not possible. The
geometries of tensile structures are not conducive to a linear plan/elevation/section design method.
Scheurmann (1996) describes tension structures with their three dimensional curvature and curved edges
as ‘lack[ing] a predominant linear direction’. The implication of this observation is that any parallel projection
of these structures, such as a section, would change significantly if the section line was moved even a little.
On these types of line drawings curvature is impossible to depict and considerable additional information is
necessary. In this case, the computer is the best instrument with which to convey the information, but
convenient tools are not usually readily available for designing tensile structures.
Architects have a tendency to focus on form, the geometric shape of a building, and leave the
detailed structural implications to the engineers. For tensile membranes, this is not possible because of the
fundamental correlation of the two – geometry and structure. The architect must have a fairly sold grasp of
the forces in a tension structure in order to get the form close to correct. Small changes in the forces and
loading of a tension structure can make dramatic difference in the form and vice-versa. Subtle form changes
can create astonishingly different stress patterns. The unlimited number of shapes that can be arrived at by
changing a few parameters can be daunting. The precise shape of the tensile membrane is dependent on
the buildings boundary condition, the membrane form, and the properties of the materials used.
Light weight structures are thus difficult to visualize and translate into two-dimensional working
drawings. The subject is not often taught in schools, and very few research centers are devoted to the
research and development of tensile membranes, let alone teaching the principles of their design
1
.
The physics behind the structure and the mathematics that are involved tend to make architects
think twice about selecting this building type. The fact is that one cannot just draw a shape on paper and
rely on the knowledge that this will be the final result of the design. This is somewhat discouraging to
architects. Tension structures require considerable expertise. Architects only rarely find an incentive to use
these structures and this relies in a lack of experience. Architects often just do not have the confidence or
experience to design tensile membranes.
3
1
See Appendix A
1.3 WHAT IS NEEDED
Architects need to feel confident in their ability to design lightweight fabric structures. They are
visual people and need to be able to see something in three dimensions order to be satisfied with it. In
conventional design they do this by building scale models or even computer models. For the reasons
described in the following paragraphs this is not possible with tensile membranes. Scale models are difficult
to build and are not an accurate representation of the structure, and conventional 3D models may be
inadequate as they do not consider structural behaviour.
Fig 1.03 Model of tensile Structure created by Graduate Building Science Students at USC (Photo: Douglas Noble
c.2007)
2
It follows that a computer tool for conceptual design of tensile membranes would be very useful
indeed. It is the structural properties of tensile membranes make them difficult to conceptualize. Their
complex correlation of form and structural behaviour are contributing factors. Early pioneers in the design of
4 2
See Fig 1.01
tensile structures would construct physical models to study their behaviour. These models, while making
very effective presentation tools, were time-consuming to construct, fragile to use and not completely
accurate.
Fig 1.04 Sketches showing the Form Finding of a simple membrane over crossed arches.
3
5 3
http://www-ec.njit.edu/civil/fabric/shape.html
The advancement in computer technology makes the modern computer the most appropriate
medium for the study of tensile membranes. Modern computers are capable of carrying out billions of
calculations in the fraction of a second. They are also capable of producing beautiful 3d graphic images. A
computer tool that gave architects the ability to see in real time what effect the changes that they make to
the geometry have on the structure of the membrane would help de-mystify the design of tensile
membranes.
This form finding tool would need to have an easy to understand and easy to use graphic interface.
The program should be easy to learn. The information that would be required to be input should be simple
and easily obtainable.
Conventionally, computer programs that help the analysis and design of tensile structures are
developed by research facilities in universities or by firms that specialize in their design. To keep their
competitive edge and advantage in the market, these entities usually limit the availability of programs and
do not actively distribute their software (Shaeffer, 1996 p.5-13).
This form-finding tool would therefore be easily available to anyone who wanted to use it and help
in preliminary design in both schools and architectural firms.
The analysis that the tool conducts should be reasonably accurate. It would not be a complex tool,
but sufficiently accurate to demonstrate the initial design idea. The results that the tool should produce will
be a simple graphic representation of the geometry of the tensile membrane, and a representation of its
deflection under loading. It would display the load values used in the calculations to facilitate understanding
the design of tensile membrane structures.
This thesis is aimed at producing such a tool for the PC. It is a learning tool, aimed at aiding in the
conceptual design of tensile membrane structures and includes a tutorial demonstrating its use.
6
Chapter 2 covers the history of tensile structures. It describes their development from the early tent into the
modern tensile membrane structures. It describes the process of form finding and the role that computer
applications have played in this process.
Chapter 3 describes the structural principles of tensile structures. It defines and classifies each of the
principles and explains the appropriate physics underlying them.
Chapter 4 discusses the materials used in tensile membranes. It analyses their properties, advantages and
limitations.
Chapter 5 describes the new form finding computer program and its components. It describes how it is used
and the expected results.
Chapter 6 is a step by step description of the program. It is written in the form of a tutorial that covers each
aspect of the program in depth.
Chapter 7 describes additional advantages and disadvantages of the program not covered in Chapters 5
and 6. It covers the achievements and failings of the program and discusses why they are present.
Chapter 8 includes suggestions for further work in this area. It discusses the improvements that can be
made to this version of the program as well as supplemental tools that could be added to it.
Chapter 9 summarizes and concludes the report.
7
CHAPTER 2: BACKGROUND
This chapter describes the history of tensile structures and the methods that have been developed
to facilitate their design and analysis.
2.1 THE HISTORY OF TENSILE MEMBRANES
The tensile membrane in its most primitive form is the tent. It is one of the oldest man-made
dwelling types and evidence of the tent has been found as far back as 40,000 years ago.
The oldest constructed dwelling structures were stick-framed houses (Berger, 1996). These were
commonly built of tree branches or saplings stuck in the ground to form a circular or oval-shaped floor plan.
The saplings were bent over until they touched a central ridge beam supported by posts and laced to each
other to form arches along the length of the house. Other members were added to give the structure
integrity and the strength to support the enclosure surface. This enclosure consisted of thatching made from
natural materials such as reeds, grass, palm leaves or straw. Sometimes surface materials were made of
animal hides, bark or interwoven sticks covered with clay. Eventually tents were covered with woven
textiles.
These traditional stick-framed houses were easy to construct, often taking as little as a day to build.
However, for nomadic people who needed to move quickly and often, not only did the houses need to be
easy to construct, but they also had to be easily portable. The solution was to reduce the size and number
of rigid compression elements to a minimum, replacing them wherever possible with flexible, lightweight
tension elements. The result - the lightweight tent that developed was easy to transport and erect.
From the Native American Tipi to the Black Tent of the Bedouin, man has designed tents all over
the world and in all kinds of climatic conditions, illustrating the versatility of the tensile structure and its
adaptability to varying climate types.
8
2.1a A Brief Overview
The primitive tent was usually one of three types. The conical tent (for example the Tipi), the
cylindrical tent with a conical ceiling (e.g. the Yurt) or the saddle shaped tent (e.g. the Berber Tent or Black
Tent)
The simplest form of a tent is basically a square pyramid formed by the tent fabric that is supported
by a central mast or A-frame. An A-frame consists of two sticks crossed at the top supporting a curved
‘saddle piece’. The fabric is draped over the A-frame and four ropes anchored to the ground form the corner
ridges of a four-sided tent. The fabric is kept under stress to keep it from flapping in the wind.
The Tipi: The Tipi has an egg-shaped plan with its opening toward the end with the smaller radius.
To begin, three or four poles are laid on the ground and tied together near the top. Two poles are raised in
an A-frame using the additional pole or poles to create the basic structural shape. The positions of these
poles are adjusted to decide the location of the center point of the tent. This is usually toward the rear of the
tent to provide sufficient wind resistance. Additional poles are added to the frame by the simple method of
leaning them on the v-shape at the top and placing them at the right position in the plan. The enclosure is
traditionally made from animal hides sewn together in a semicircular piece and wrapped around the frame.
The tipi is easy to construct and can be adapted to various weather conditions. Flaps at the bottom can be
used as doors or can be lifted to open up the tent. At the top, flaps can serve for ventilation as well as wind
guides. In winter insulation can be filled between double skins to keep the interior warm.
Fig 2.01 The Tipi (Drawing by Author, 2004)
9
The Yurt: The Yurt has a circular latticed wall with a cone shaped roof. The roof has a
compression-ring skylight at the center and a tension band at the eaves. The walls form a base in tension
which when connected to the roof panels keeps them from pushing outward. The whole structure is covered
by large pieces of felt which are fastened by horse-hair rope.
Fig 2.02 The Yurt (Drawing by Author, 2004)
The Black Tent: The Black Tent or Berber tent has poles located at the edges and center of the
plan. These poles support ropes which in turn support the woven fabric of the tent. Anchor ropes transfer
the load from the fabric to the stakes which pin down the structure.
Fig 2.03 The Black Tent (Drawing by Author, 2004)
Of all forms of the early tent the Black Tent of the Bedouin is the true predecessor of the modern
tensile structure. It is the only primitive tent that does not have its shape defined by its support system but
instead relies on the tension in its fabric to give it its anticlastic shape, thus providing structural stability for
its supports. The construction of the tent has remained important for various purposes throughout history.
10
But as man settled down in agricultural communities and started to build more permanent structures, tents
were relegated to the wings as ‘temporary’ structures and looked on as secondary forms of construction in
most societies.
In addition to army tents, the Romans developed other sophisticated tensile structures by studying
the sails of ships. The principle of using a mast and staying system to stabilize the sails of ships was
developed into retractable fabric shade structures called ‘Vela’. Vela consisted of a series of fabric panels
which were suspended from a horizontal mast which in turn was cantilevered from the supporting wall by a
system of stay-cables and struts. Vela are the predecessors of the tensile structural systems used to cover
the seating of today’s stadiums.
Thus the one area in which tents still formed an important part of construction was to house the
armies of the middle ages and indeed tents are as important in the military today.
2.1b The Evolution of the Tensile Structure
The evolution of the modern tensile structure began with the construction of long span suspension
bridges in the early 1800’s. Rope bridges have been built as far back as 4000 years ago in the Himalayas
and China, but it was the invention of wrought iron that paved the way for large-span suspension bridges in
Europe (Berger, 1996)
In 1826 Thomas Telford built the Menai Strait Suspension bridge in North Wales that spanned a
record breaking 580 feet. This was the first successful demonstration of the potential of the suspension
bridge. The roadbed for the Menai Strait Bridge is suspended from sixteen chains, in sets of four, each
made up of flat wrought iron eye-bars eight feet long linked by pins (Linda Hall Library 2002).
11
Fig 2.04 Menai Strait Suspension Bridge
4
Previously, bridges were predominantly masonry arch bridges, with no great spans. Telford’s
introduction of the suspension bridge using iron was a revelation and became the catalyst for change.
In the late 19
th
century the development of high-strength steel cables revolutionized the world of
bridge building. John Roebling, the inventor of the high strength cable was also the architect of the Brooklyn
Bridge (Berger, 1996)
Fig 2.05 George Washington Bridge
5
4
http://en.wikipedia.org/wiki/Image:Menai_Suspension_Bridge.jpg
12 5
http://commons.wikimedia.org/wiki/Image:Habs_gw_bridge1.jpg
Fig 2.06 Brooklyn Bridge
6
Completed in 1883, having taken fourteen years to build and spanning 1595 feet it was the
monument of its time. Only in 1929, forty-six years later, did the George Washington Bridge surpass it as
the longest span bridge, spanning 3400 feet.
The concepts involved in suspended bridges were for a long time regarded as the domain of civil
engineers. For one thing, the distances that they were used to span were very large and so of little
consequence to architects. However in 1958 Eero Saarinen used a simple hanging cable for the shape of
the Dulles Air Terminal. The use of cables in tension to suspend a bridge also inspired the design of a paper
mill in Mantua by Pier Luigi Nervi (Berger, 1996).
Fig 2.07 Burgo Paper Mill
7
6
http://en.wikipedia.org/wiki/Image:Brooklyn_Bridge_2004-01-11.jpg
13 7
Photograph - Yoshito Isono http://en.structurae.de/photos
The first air supported roofs were conceived in the early 1900’s but the first such structure to be
built was in 1946 by Walter Bird who introduced air supported enclosures to the engineering profession.
Fig 2.08 Raleigh Arena North Carolina
8
The first tensile structure of any significance was built in 1953 and was the Raleigh Arena in North
Carolina designed by Matthew Nowicki (Berger, 1996). The enclosure surface is shaped by two sets of
parabolic cables that intersect at right angles. One set of cables curves upward and the other curves
downward, their boundary formed by two intersecting inclined arches.
In the 1950’s and 1960’s many tensile structures were built on similar lines, but the most
noteworthy structures at that time were the Olympic National Stadia built in Tokyo in 1964 by Kenzo Tange.
The larger stadium has two splayed suspension cables supported by two concrete masts, which in turn are
tied back by extensions of the cables. The outer edge of the building is formed by a concrete ring beam. The
smaller stadium has one main support cable winding around its single mast in a spiral. Like the larger
building, the edge of this building has a concrete ring beam as well. Both stadia have roof surfaces
comprised of semi-rigid steel decking welded to rigid steel girders.
14 8
http://www.arcaro.org/tension/album/dorton.htm
Fig 2.09 Olympic National Stadia – Kenzo Tange
9
2.1c The Modern Tensile Structure
No discussion of these structures could be complete without mention of Frei Otto who is universally
acknowledged as the father of modern tensile architecture. As a prisoner of war during World War II, Frei
Otto worked in construction to repair damaged bridges. The shortage of material during the war contrasting
with the large number of laborers available, led to Otto investigating structures requiring a minimum of
materials to build. He quickly found that this was possible by increasing the number of tension members in a
structure (Drew 1976, p.6).
Frei Otto’s structural motivation was the investigation of lightweight structures for long spans
(Roland 1970, p.1). Structures loaded purely in tension or compression are more economical than structures
subject to bending. His first major building phase of lightweight structures started in about 1957. In 1967 he
built his first significant building – the German Pavilion at the World’s Fair in Montreal, Canada. From 1957
to 1971 he went through a period of alternate construction activity and theoretical investigation which
culminated in what is widely considered his masterpiece - the Munich Olympic stadium for the 1972 games
(Berger 1996, p.33). This stadium was designed by Guenter Behnisch with Frei Otto as consultant.
Here the interior edge of the roof is formed by anticlastic cable nets and a catenary. Flying masts
ride on suspension cables that span from the tall masts to this catenary and the whole is covered with semi-
rigid acrylic panels.
15
9
http://www.caroun.com/Architecture/Architects/K-Tange/KenzoTange.html
Fig 2.10 Munich Olympic Stadium
http://en.wikipedia.org/wiki/Image:Olympiastadion_Muenchen.jpg
In addition to being responsible for the development of new structural systems and founding the
Development Center for Lightweight Construction, one of Frei Otto’s most important contributions was
pioneering model techniques as design tools for developing the form and predicting the behaviour of tensile
structures. This work which was further developed by David Geiger and Horst Berger for air supported fabric
structures took the design of tensile structures to a new level of accuracy and more importantly,
accessibility.
Today, lightweight architecture has caught the imagination of the architectural profession and from
assembly-line, pre-fabricated, simple canopies to large-scale, unique designs; fabric architecture has
become an exciting and beautiful facet of modern architectural expression.
2.2 FORM FINDING OF TENSILE MEMBRANES
Horst Berger defined form finding as ‘the process of determining the equilibrium shape of a tensile
membrane for a given pre-stress, applied load and membrane properties’ (Berger 1996, p.170).
The shape of conventional buildings is arrived at by taking into consideration the building materials
used and the boundary or envelope conditions. Using finite element analysis the structure is analyzed by
applying external loads and solving for the resulting deflections. If the internal forces in the structure are
16
too large, or if the resulting deflections exceed the safety limits, the structure is revised. The most common
solution to this is to increase the mass of the structure. Thus the shape of the building does not change.
In contrast to conventional structures, membranes have low shear stiffness and cannot support
compressive stress. They undergo significant surface deflection in order to transmit loads. There is a close
interaction between the forces acting on them and the form that they take. Any structural analysis must
therefore take into account these relatively high displacements. Due to this nature of tensile membrane
structures, physical or numerical models are necessary to develop accurate representation of their final
form.
These models are used to predict the behaviour of full-scale structures. Both models of shape and
behaviour under loading are used which provide a simplified version of the structure and its behaviour.
2.2a Physical Models
Fig 2.11 Clear Film Model
10
Fig 2.12 Stretch Fabric Model
11
10
Berger, Horst. Light Structures - Structures of Light
17 11
Berger, Horst. Light Structures - Structures of Light
Frei Otto pioneered the idea of using soap film on a wire frame to represent a membrane structure.
He also developed methods of measuring the surface of these films photo-grametically (Schierle c.1968
p.23). The film forms a minimal surface which replicates a tensile membrane. Soap film however is much
too fragile for testing. One alternative to using soap film is to use a clear film that hardens into a rigid
surface.
Simple shapes for tensile structures can also be modeled by using a network of elastic strings, but
the best physical models are created by using stretch fabric. Physical models are useful for visualizing form
and for generating cutting patterns for the fabric membrane, but have their limitations when it comes to
structural analysis. They are simply not precise enough to analyze behaviour under loading.
2.2b Numerical Models
Horst Berger describes the surface form of a tensile membrane as-“a graphic representation of a
complex field of forces in equilibrium” (Berger 1996, p.167). Mathematically he describes it as a net of
intersecting force lines. When the net is correctly shaped the forces in all the lines intersecting at any one
node are in equilibrium with the weight of the structure acting at this node.
Numerical models most commonly visualize the surface of a membrane as a grid of distinct
elements connected by nodes. Numerical models though described as “graphic representations” should not
be confused with three-dimensional models. Numerical models are difficult for the layman to understand,
and architects in particular do not find it easy to use them in order to design their tensile structures. For
architects a much more visual approach is necessary.
2.3 THE ROLE PLAYED BY COMPUTER APPLICATIONS IN FORM FINDING
Tensile membranes exhibit geometric and material non-linear behaviour under loading. This means
that the actual displacement of the membrane is not directly proportional to the magnitude of the force
applied on it (Koch 2004, p102).
18
Fig 2.13 Linear Load/Displacement Curve
12
Fig 2.14 Non Linear Load/Displacement Curve
13
An important aspect of form finding is that the overall shape of the structure has to repeatedly be
altered in order for the structure to stay in equilibrium despite the changes in the forces in the surface,
boundary and supports caused by external loading. Repetition is an intrinsic part of this process. Referred to
as iteration, it is the mathematical process by which the solution to a problem is found in incremental steps
applied to a small portion of the total system (Berger 1996, p.170). This makes the computer the perfect tool
to carry out the process since they are capable of doing complex calculations in very small periods of time.
12
Koch, Klaus-Michael. Membrane Structures.
19 13
Koch, Klaus-Michael. Membrane Structures.
There are three widely used methods of form finding. They are:
1) The Force Density Method
2) The Finite Elements Method
3) Dynamic Relaxation
2.3a The Force Density Method
Form finding of a tensile membrane requires finding the state of equilibrium between the internal
forces of the structure and the externally applied loads. Essentially, for a structure to be in equilibrium the
internal forces and external forces must be balanced.
R.E. Shaeffer (1996, p.5-23) explains ‘force density’ as a term given to the ratio of forces to lengths
(cable force, divided by cable length); the higher the force density ratio, the shorter the element for a given
force. In addition, the higher the force density ratio, the bigger the element needs to be for a constant length.
The force density method finds the shape of a surface in equilibrium, with a given topology, given
support conditions and a set of force density ratios for the structure. Changing the force density ratios
changes the geometry of the surface.
R.E. Shaeffer (1996 p.5-24) explains that the force density ratio can be visualized as a rubber band
concept. If the cable element between two nodes is visualized as a rubber band, the bigger its force density
ratio, the stronger the rubber band is to link the two nodes. When the force densities for all elements around
a node are equal and uniformly distributed around the joint, i.e. in equilibrium, the surface created is a
minimal surface. In order to conduct this analysis, the continuous surface of the membrane is represented
by a grid of cables.
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A (0,1) E(6,1)
C D
21
B (0, -1) F=2kN F=1kn F(6,-1)
Fig 2.15 Force Density Example
The following example (Fig 2.15) is from ‘Tensioned Fabric Structures’ edited by R.E. Shaeffer (1996)
14
.
The first step is to solve for equilibrium at all unknown nodes.
Σx =0 and Σy =0 at node C and Σx =0 and Σx =0 at node D
These equations are solved by defining F/L=g where g is the force density, F is the force and L is
the length of cable, for each cable and substituting this in the equilibrium equations.
Once the node co-ordinates are known, the lengths and tensions of the elements can be
calculated. The unstressed lengths can be calculated by knowing the stressed length, the stress, and the
stress/strain relationship where:
L(unstressed) = L(stressed) – (1-F/AE)
2.3b The Finite Elements Method
The finite elements method is also referred to as the non-linear stiffness matrix analysis. In this
method of analysis the geometry of the membrane is represented by nodes, the location co-ordinates of
which are known. The nodes are then inter-connected by finite elements representing structural
components. Cables and beams are represented by lines and fabric is represented by triangular elements.
Any force or stress in an element is resolved into its component forces at the node, the sum of all
forces at each node being zero for the structure to be in equilibrium.
14
For entire calculation see Appendix B
In this analysis P = KU where
P(e) – equivalent forces at a node
U(e) – nodal displacement or deformation
K(e) – stiffness matrix calculated from the geometry and material properties (modulus of elasticity) of the
element being analyzed.
Using this equation, the deflection at each node is calculated. The stiffness matrix K(e) of all the
elements is assembled into a single stiffness matrix K for the entire structure. The deflections at all nodes
are calculated simultaneously so that the internal forces and the external forces are in equilibrium at every
node at each step in the process. Once the deflections at each node are determined, the stresses within the
elements are calculated. This process is reiterated until the forces at the nodes are equal to the desired pre-
stress (Koch, 2004).
Because modern computers are capable of carrying out instructions at extremely high speeds this
method is best suited to computing. A computer can solve the equation as many times as necessary in a
fraction of a fraction of the time that a human being can. In addition, programming a computer with the
algorithm to carry out this process enables the task to be accomplished by someone who may not even
understand the complex physics behind it (Siff n.d).
2.3c Dynamic Relaxation
In this analysis the geometry of the structures is represented by a mesh with the mass of the
structure assumed to be discretized and concentrated around the nodes. These masses oscillate about the
equilibrium position of each node for a certain period of time due to the residual internal forces in the
structure. This results in the dynamic behaviour of the mesh.
The nodes are returned to the equilibrium state by approximating kinetic damping at each node,
the residual force being equal to the sum of the internal forces, less the applied force at each node. The
residual forces are solved for geometrically and the velocities at each node are found based on the dynamic
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behaviour of the system. The new positions of the nodes are found based on the increment of time taken to
return to the equilibrium state. This process is reiterated until the residual forces in the mesh approach
zero
15
.
2.4 CONCLUSION
Thus, we can see that as history progressed, the tensile structure developed from a simple tent to
the complex fabric membrane structure that we know today. Along with this evolution the design process for
the structure has also become more complicated. Today the most effective way to design these structures is
to use the computer as a tool to help decipher the correlation between their form and structural behavior.
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15
For an example of the calculation see Appendix C
CHAPTER 3: STRUCTURAL PRINCIPLES
This chapter defines ‘tensile structure’, explains the physics behind such structures and classifies
the different types of tensile structures in accordance with their characteristics and shapes.
3.1 WHAT IS A TENSILE STRUCTURE?
A tensile structure is a structure that transfers forces from its main load bearing elements to the
support system, ground or foundation primarily by tension, without any compression or bending.
In most traditional frame or bearing wall structures, loads are transferred to the ground by compression or
bending. A tensile structure is supported by the tension applied to the structure through a surface
membrane or cable net.
Structures made of tensile members become more stable under increased stresses. Stress pulls at
each of the members increasing the tautness of the entire structure as a whole and therefore increasing its
stability. The loads are carried axially through the members by the most direct route available.
Tensile structures use less material than traditional structures and are therefore lighter than
conventional structures. In addition they are also flexible where traditional structures are rigid
3.1a Classification of Tensile Structures
Tensile structures can be made of membranes or a system of cables or both (Leonard 1988).
They are classified in two general categories:
a) Cable structures- in which the members are stressed in only one direction (uniaxially)
b) Membrane structures – in which the members are stressed in two directions (biaxially)
3.1b Cable Structures
Cable structures can be divided into four classes:
i) Single Cables: Single cable elements or line elements are subjected to loads in a single plane of action.
(e.g. guy ropes for tents)
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ii) Cable Trusses: Multiple pre-stressed elements are connected in the same plane and loaded in that
plane. (e.g. Cable truss bridges)
iii) Cable Nets: Multiple pre-stressed elements are connected in a curved plane. These elements are closely
spaced and orthogonal (or mostly orthogonal) to each other. The structure is loaded in a direction
perpendicular to its surface. (e.g. suspended roof)
Fig 3.01 Cable Net – German Pavilion at Expo 67 Montreal (Lightweight Structures Association)
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iv) Cable Network: Multiple pre-stressed elements are connected in a three dimensional framework. (e.g.
suspension network)
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3.1c Membrane Structures
Membrane structures can be divided into four classes:
i) Air Supported Structures: The enclosure of the structure is made from a membrane that is supported by
the pressurization of the interior space. These structures require air locks at openings to maintain the
internal pressure.
Fig 3.02 Air Supported Structure (LSA)
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ii) Air-inflated Structures: Highly inflated tubes and dual walled mats are used as beam, column or arch
members that are used to support an additional membrane enclosure.
Fig 3.03 Air Inflated Structure (LSA)
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iii) Frame Supported Structures or Pre-stressed Membranes: Fabric membranes are stretched over the
supporting structure that is made up of a rigid framework.
Fig 3.04 Frame Supported Membrane (LSA)
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iv) Hybrid Systems: hybrid systems have panels of membranes that span between pre-stressed cables and
rigid members.
Another form of tensile structure is the cable-and-strut structure. Here, a planar or curvilinear
structure is composed of short compression elements (struts) connected with tensile elements (cables) to
form a stable configuration. These structures are sometimes referred to as ‘Tensegrity Structures’.
3.2 ANTICLASTIC STABILITY
The components of a tensile structure require arrangement in a specific geometric form while they
are subject to a specific pattern of internal stresses (pre-stresses). Therefore the geometry of a tensile
structure is not in any way arbitrary, but follows strict engineering rules. Once the boundaries and support
positions have been decided on and a pre-stress level selected, there is only one possible surface shape
that can form.
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3.2a Why Curvature is Critical
Curvature is the critical aspect of a tensile structure. The stability of the structure comes from its
curvature. These structures are dynamic, where the flexibility of their elements helps them adjust to
changing load conditions.
The simplest form of a tensile membrane is a four point structure. Three points will generate a flat
plane; therefore four is the minimum number of supports required. Of these points at least one has to be in a
different plane to create curvature.
A simple four point structure can be formed by stretching a square piece of fabric or membrane out
of its plane to form the simplest form of saddle shape. The edges could be beams or catenaries and the
structure should be anchored down against wind uplift.
Fig 3.05 Four Point Structure (Drawing by Author, 2004)
Fig 3.06 Anticlastic Curvature (Drawing by Author, 2004)
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Anticlastic curvature is created by the two principle arcs of the structure curving in opposite
directions. The pre-tension in a fabric structure is developed by this anticlastic shape. The tension along one
curved element is resisted by the tension in the curved element that opposes it (Schierle c.1968 p.23).
3.2b What is a Minimal Surface?
The minimal surface is the smallest surface that can be formed within any closed boundary
condition. At any point on this minimal surface the sum of all radii of curvature (i.e. the positive and
negative) is zero. To form a minimal surface a membrane must be stressed equally in every direction
(Schierle c.1968, p.23).
A soap bubble is an example of a minimal surface that is familiar to everybody. Frei Otto used soap
film in wire frames to illustrate the minimal surface. The minimal surface is a very important concept in the
design of tensile membranes.
For a planar boundary the minimal surface is flat. For any non-planar configuration of a closed
boundary the minimal surface formed is always anticlastic. A synclastic surface – one that has both radii of
curvature in the same direction (for example, the surface of a dome) - is never a minimal surface.
If the stresses in the saddle shape change in only one direction this alters the curvature and
therefore the surface will exceed minimal size.
Therefore the conditions for a minimal surface are:
1) connections between boundaries with minimum surface area
2) the sum of the positive and negative radii of curvature at any point is zero.
3) Surface tension in all directions is zero.
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Fig 3.07 Explaining the Minimal Surface (Drawing by Author, 2004)
A minimal surface i.e. a saddle shape, has two directions of curvature; the positive and negative
that are perpendicular to each other and two directions of no curvature; perpendicular to each other at 45°
to the principal curvature.
Fig 3.08 The Hyperboloid (Drawing by Author, 2004)
In its purest form the saddle shape is the hyperboloid. The hyperboloid consists of intersecting
sets of parabolas. Though the surface formed is curved, the characteristic of the hyperboloid is that in the
two diagonal directions, the nodes are connected by straight lines. This makes its construction extremely
easy to carry out.
30
Fig 3.09 Multiple Hyperboloid Surfaces (Drawing by Author, 2004)
Four point structures can be constructed in many variations depending on the positions of the
supports and the amount of pre-stress. A number of four point structures can be combined to form larger
enclosures.
3.3 EDGE CONDITIONS
There are three different edge conditions commonly found in tensile structures, the rigid straight
edge, the compression arch or ring, and the flexible curved cable edge (Schierle c.1968).
3.3a The Rigid Straight Edge
A rigid straight edge is a structural edge such as a beam, girder or truss. This edge is subject to
considerable bending moments and therefore has a limited span due to its size.
Fig 3.10 Rigid Straight Edge (Drawing by Author, 2004)
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3.3b The Rigid Compression Arch or Ring
A compression arch or ring transfers loads from the membrane by compression. In addition to the
compression, a small amount of bending can occur.
Fig 3.11a Rigid Compression Arch or Ring (Drawing by Author, 2004)
Fig 3.11b Tensile Structure using Compression Arches
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3.3c Flexible Curved Cable Edge.
Flexible curved cables transfer loads through tension. The cable edge adjusts and deflects
according to the changing loading conditions. This deformation can be minimized by the pre-tensioning of
the membrane and the cable edge.
Fig 3.12a Flexible Curved Cable Edge (Drawing by Author, 2004)
Fig 3.12b Tensile Membrane installation at UT San Antonio with a Flexible Curved Cable Edge (photo Mahesh B.
Senagala)
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3.4 PRE-STRESS
3.4a Understanding Pre-Stress
Those forces and stresses present in an element when it is fully unloaded are known as the pre-
stresses. Pre-stresses are those stresses which concern the structural system while internal stresses
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concern the materials themselves. Internal stresses act in the absence of loads. A pre-stressed element is
assumed to have no dead weight and an unloaded structure does not transmit any forces or moments, even
its dead weight.
Membrane structures are stabilized by tension only. Compressive loads are applied on the
membrane and the resulting stresses reduce or balance the pre-stresses leaving a residual tensile force.
This means that the pre-stress in the material should be high enough to preserve a tensile force in the fabric
under all possible superimposed loads, static as well as dynamic. Non pre-stressed flexible elements such
as cables and membranes have no uniquely defined shape before loading. Their structural form is only
obtained under an adequate load (Berger 1996).
Fig 3.13 Membrane Stresses and Surface Tension (Drawing by Author, 2004)
Thus the pre-stress of a structure depends on the magnitude of the compressive loads on the
structure and the compressive stress induced by these loads. In a membrane structure there are two types
of stress, Membrane Stresses and Surface tension.
3.4b Membrane Stresses
Membrane stresses are defined as the surface stresses in the flexible enclosure fabric or shell. The
maximum membrane stress is equal to the pre-tensioning load plus the maximum tensile stress from the
superimposed load.
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3.4c Surface Tension
Surface tension for a membrane is defined as the force per unit cross-section. This is what is
known as active surface tension. Surfaces are evaluated in terms of rupture strength and strain, measured
as surface stresses. These are determined by rupture tests based on mono-axial stress of strips 30cm long
and 5cm wide. This is also known as strip tensile strength.
3.5 SURFACE CONDITION AND SHAPES
There are four basic shapes for tensile membrane structures: saddle shapes, wave shapes, arch
supported shapes and point supported shapes (Schierle c.1968).
3.5a Saddle Shapes
Saddle shapes are anticlastic surfaces defined by a membrane with an uninterrupted non-planar
boundary. These shapes are some of the simplest shapes that can be created as they are the basic four-
point structure. They are used often in multiples, creating undulating canopies over large areas.
Fig 3.14 Saddle Shaped Membrane Surface (Drawing by Author, 2004)
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3.5b Wave Shapes
Wave shapes are defined by a repetition of ridges curved in opposite directions or a series of non-
parallel straight ridges.
Fig 3.15 Wave form of a Tensile Membrane (Drawing by Author, 2004)
3.5c Arch Supported Shapes
The anticlastic surface of the membrane structure is defined by one or more supporting arches forming the
boundary for the membrane.
Fig 3.16a Arch Supported Membrane – Single Arch (Drawing by Author, 2004)
Fig 3.16b Arch Supported Membrane – Multiple Arches (Drawing by Author, 2004)
3.5d Point supported shapes.
The surface of the structure is defined by one or more supporting points that deform a membrane
of any boundary condition in one or more directions. Radial cables transfer membrane tension to the
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supporting point. A rigid tension ring can be used to eliminate a concentration of tension at the support. This
can also be achieved by using a spherical disc, flexible looping cable ring or a flexible cable eye.
Fig. 3.17a Point Supported Fig. 3.17b Tension Ring Fig 3.17c Spherical Disc
Fig. 3.17d Flexible Cable Eye Fig 3.17e Flexible Looping Cable
3.6 CONCLUSION
In summary, tensile structures are broadly classified into cable structures and membrane
structures. Membrane structures, which are the subject of this thesis, may have different boundary
conditions, surface conditions, shapes and pre-stress, but their common characteristic is their anticlastic
curvature without which they would have no stability.
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CHAPTER 4: MATERIALS
This chapter discusses materials used for membrane structures. In the first half it explains the
types of fabrics existing, the finishes available and their material properties. The second half of the chapter
details the selection criteria to be considered when choosing a fabric for a tensile membrane structure
4.1 FABRIC PROPERTIES
In a tensile structure, material properties, design, fabrication and installation are all equally
important to the resulting structural stability. Because a fabric structure transmits tension through the
surface membrane, the structural integrity and performance of the membrane material becomes vitally
important. The most important properties for any membrane material are its mechanical tensile strength and
elastic qualities.
4.1a Physical Properties
Fabrics used for tensile structures need to have great strength and a high modulus of elasticity.
4.1a.i Modulus of Elasticity
The modulus of elasticity of a material defines its stiffness. A high modulus of elasticity means that
the material has a greater ability to regain its original shape after a load has been applied to it. Materials
with a lower modulus of elasticity tend to deform over time, a phenomenon that is known as creep.
Polyester has a lower modulus of elasticity than glass fiber and thus has more of a tendency to
creep. The practical implications of this with regard to a tensile fabric structure, is that while glass fiber can
be pre-stressed up to 10% of its strip tensile strength, polyester can only be pre-stressed from 5% to 15% of
its strip tensile strength.
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4.1a.ii Types of Weaves
The strength of membrane fabrics depend on yarn size, twist and the type of weave used (National
Research Council (U.S.) Advisory Board on the Built Environment 1985).
Some common types of weaves are the following:
a) Flat weave – this weave results in uniform elastic properties.
b) Open weave – open weave fabrics tend to have lower strengths.
c) Tri-axial weave – yarn is woven at 60° angles. It is very stable especially in shear and has a high
tearing strength.
Fabrics tend to be stronger in the warp direction (along the length of the roll of fabric) than in the fill
direction. In the fill direction (across the roll of fabric) fabrics have more stretch and tend to elongate. Fabrics
are generally weak on the bias and loading them in this direction results in substantial stretching of the
membrane.
Thus, when the fabric is cut for a tensile membrane, the warp and fill should always follow the
principal lines of curvature of the structure. Correctly orienting the material in this manner minimizes stress
concentrations in the membrane.
4.1b Types of membranes
Fabrics can be coated or laminated with synthetic materials for greater strength, weatherproofing
and efficiency (Fabric Architecture March/April 2007, p.30-36). As a final process a top-coat may be applied
to the exterior or weathering surface.
The woven fabric provides the basic tensile strength for the membrane and also provides
resistance to tearing. The coat or laminate provides the protection against weather, resistance to UV
radiation, is the medium for creating joints and also increases the fire resistance of the membrane.
39
Commonly used substrates are (NRC 1985):
1) Polyamide – consisting of nylon filament yarns, it has high strength. However it has a low modulus
of elasticity thus having a tendency to creep. It also has poor dimensional stability which causes it
to stretch when cold and wet and shrink when hot and dry.
2) Polyester – woven polyester fabrics have the same high strength as nylon but with better
dimensional stability. They have a lower modulus of elasticity than nylon. ‘Hot stretching’ and ‘heat
setting’ (processes applying heat and pressure to the fabric) increase the elastic modulus of
polyester and thus increase its yield strength. The strip tensile strength of woven polyester fabric
ranges from 200 to 500 lbs/linear inch.
3) Glass fiber – Glass fiber has a high modulus of elasticity and extremely high strength. It has high
dimensional stability as well as high resistance to tearing. It also has a very high strip tensile
strength.
4) ETFE – A thin extremely durable film of polymer. ETFE has a high modulus of elasticity and is
extremely strong, although the film can be punctured rather easily.
4.1c Top-coating
Applying a top-coat to a membrane fabric creates what is known as the ‘self-cleaning effect’. This
coat allows dirt and dust that collects on the fabric surface to be cleaned away by normal rainfall. This
decreases the maintenance necessary to keep the fabric in good condition and also improves its
appearance. Adding a top-coat also increases the lifespan of the material by preventing atmospheric
pollutants from damaging it and by inhibiting the migration of plasticizers present in PVC, which prevent the
PVC from becoming brittle, blistering or delaminating (Rubb Building Systems n.d.). Top-coats may be
applied in different ways to the surface of the membrane fabric. This is dependent on the type of top-coat
required and its desired thickness. If a thin top-coat is required, a lacquer may be sprayed on, while thicker
layers may be applied by knife, or a process of lamination.
40
Widely used topcoats are
1) Chloroprene Chlorosulphinated Polyethylene (Elastomers)
2) Polyvinyl Chloride (PVC)
3) Fluorocarbon TFE resins (Teflon)
4) Silicone
The most commonly applied top-coatings are PVC or Silicone for woven polyester fabrics, or PTFE
or silicone in the case of woven fiberglass fabrics. Other top-coating materials include acrylic solutions,
PVDF solutions and PVF film laminations.
4.1d Commonly Used Membrane Materials
Thus the most commonly used membrane materials can be grouped into three distinct categories:
1) PVC – (Polyvinyl chloride) coated polyester fabric
2) PTFE – (Polytetrafluorethylene) coated glass fiber.
3) ETFE – (Ethylenetetrafluorethylene) foil
Fig 4.01 Material Matrix
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National Research Council (U.S.) Advisory Board on the Built Environment. Architectural Fabric Structures
PVC Coated Polyester Material.
Fig. 4.02 PVC Coated Polyester
23
Polyvinylchloride coated polyester membranes consist of woven or knitted polyester fabrics
laminated or coated with PVC. These fabrics are some of the most commonly specified membrane materials
(Koch, 2004).
Advantages:
PVC coated polyester material is extremely durable and strong and comes at a relatively
low cost.
The fabrics can be woven or knitted to pre-determined specifications to provide
appropriate fabric strength and consistency, with measurable properties of elasticity and strength.
This measurability allows engineers and designers to accurately predict the behaviour and
performance of the fabric before carrying out patterning and load analysis.
The PVC coating gives the fabric strength and waterproof properties. It also is available
in different colour choices.
The PVC coating allows adjoining panels of fabrics to be seamed by high frequency
welding. Joining panels of fabric with overlapping seams in this way, results in seam strengths that
exceed the strength of the fabric itself.
Disadvantages:
PVC has a hugely negative impact on the environment. A large number of toxic by-products
such as dioxins (which are carcinogenic) are created during the manufacturing process. In order to
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make a flexible vinyl, plasticizers known as phthalates are used which have been found to be a
considerable hazard on both health and environment. In addition, PVC is very difficult to recycle
and a very small percentage of all PVC products get recycled (Thornton 2002).
i) 100% PVDF Top-Coated Polyester.
The woven or knitted polyester fabric is coated with Polyvinylidene Fluoride. Commonly known as
PVDF, this coating is made up of 59% Fluorine, 38% carbon and 3% Hydrogen. PVDF coated Polyester has
a lifespan of fifteen to twenty years depending on site conditions.
Advantages:
The presence of carbon and fluorine in the top coat make it highly resistant to UV degradation
as well as atmospheric chemicals.
These coatings are highly flexible and resistant to cracking and also unsusceptible to mold.
They are self cleaning – that is, rainwater falling on the fabric is an effective enough cleaning
agent that only minimal maintenance is required for the material.
Disadvantages:
The nature of the polymers used and the chemical procedure of its manufacture limits the
range of colours that PVDF coated polyester is available in. The standard colour available is white
and while other colours are available, the selection is not very wide and they are more expensive.
Though its resistance to chemicals may be an advantage, it also means that the finished top-
coated material cannot be welded to itself. To create the weld the top-coat must be abraded off to
expose the PVC below it. This procedure requires a high level of skill and accuracy and increases
the cost of fabrication.
In addition, this makes site repairs difficult to administer accurately as they require manual
abrading of the membrane using sandpaper.
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ii) PVDF/PVC Top-coated Polyester.
The woven or knitted polyester fabric is coated with a PVDF/PVC top-coat which is a dilution of the
100% PVDF top-coat. These top-coats have a lifespan of ten to fifteen years depending on site conditions.
Advantages:
The dilution of the PVDF results in a top-coat that does not require the controlled abrasion for
welding that the 100% PVDF top-coat does. This makes PVDF/PVC coated polyester membranes
less expensive to produce and more economical to fabricate.
Disadvantages:
The dilution of the PVDF coating makes it less resistant to atmospheric pollutants and thus
decreases its life span.
iii) PVF Top-coated Polyester
The woven or knitted Polyester is laminated with a thin film of Polyvinyl Fluoride during its
manufacturing process. These fabrics have a life expectancy of about twenty-five years depending on site
conditions.
Advantages:
The finished fabric is thick and highly resistant to weathering and chemical attack. It also
completely eliminates the migration of plasticizers from the PVC base. It is self-cleaning and
resistant to graffiti, acid rain and bird droppings.
Due to its thickness it degrades at a much slower rate which increases its lifespan.
PVF top-coated membranes are extremely suitable and frequently specified for use in highly
industrialized areas, coastal regions with a high atmospheric-saline content, and desert regions.
They are available in a wide range of colours and are comparable in price to PVDF
membranes.
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Disadvantages:
The film layer is resistant to welding, therefore instead of abraded lap welds, the material must
be butt-welded. An extra welded seam also needs to be applied to the uncoated underside of the
material.
iv) Acrylic Top-coats
These commonly used finishes are manufactured by spray-applying acrylic in a thin solution to the
fabric, resulting in a transparent glossy finish.
Advantages:
Acrylics are widely available in addition to being very economical. The material is easy to
fabricate and repair using high frequency welding or hot air welding.
Acrylic top-coats are highly resistant to UV degradation which increases the lifespan of the
membrane.
They are ideal for fabrics that are used for temporary structures and demountable structures
such as marquees, circus tents, concert venues and warehouses.
Disadvantages:
Acrylic top-coats are not very durable, especially in comparison with a 100% PVDF top-coat.
v) PTFE coated Glass Fabric
Fabric Architecture magazine (March/April 2007, p.31) describes the base fabric for PTFE coated
glass fabric as made up of “glass fibers [that] are drawn into continuous filaments, which are bundled into
yarns”. The substrate is formed by weaving these yarns together after which it is then coated with PTFE or
Teflon.
45
Fig. 4.03 PTFE Coated Glass Fiber
24
Advantages:
The woven fiberglass base has high tensile strength and elasticity. This results in very little
stress relaxation (creep). The fiberglass base is also completely non-combustible.
The fabric has good light transmittance as a result of the glass scrim and the bleached
coating.
The PTFE or Teflon top-coat is also non-combustible and inert with a low coefficient of
adhesion. This results in quite a high self-cleaning ability in the coating.
Disadvantages:
Because of its poor flexural behaviour the material requires careful handling, failing which it is
extremely susceptible to cracking and self abrasion.
In the finished fabric the grainy surface of the membrane in tension creates minute
indentations in which airborne pollutants can accumulate, for which the self-cleaning properties of
the coating are not adequate protection.
The PTFE coated glass fabric is usually an off-white or brownish colour when manufactured
and only bleaches to white in the presence of UV radiation. Therefore in indoor applications pre-
bleaching is required. This bleaching effect gives the material its high light transmittance values.
The fabrication of PTFE membranes requires slow and specialized welding techniques under
controlled environmental conditions.
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The tensioning of PTFE glass fabrics is a slow process as they require incremental
adjustments over long periods on site. Additional tensioning hardware is needed for the finished
fabric structure.
These factors all contribute to the high cost of PTFE coated Glass Fabrics.
vi) ETFE Foil.
ETFE is a fluorocarbon based polymer that is spun into a thin extremely durable film (Koch 2004).
High performance foils made of ETFE are extruded and thus achieve a high quality and consistency of
material thickness.
Fig. 4.04 ETFE Foil
25
Advantages:
ETFE foils are extremely light, about 1/100
th
the weight of glass. Because of their light weight,
there are significant reductions in costs for their supporting structural systems.
They have a very high modulus of elasticity and are capable of being stretched to three times
their original length without losing their elasticity. As a result of the extrusion process these foils
have a high degree of transparency.
They also have very effective self-cleaning properties due to their chemical composition which
creates a non-stick, non-porous surface. Strips of ETFE can be heat-welded together to form much
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longer and wider pieces than glass. The foil membranes can also be easily patched with other
pieces of ETFE which again, are heat-welded on.
They are available in a number of different colours, finishes and can be easily printed on. They
are also completely recyclable and have low transportation costs due to the light weight of the foil.
Disadvantages:
ETFE Foils have very poor Acoustic insulating properties, transmitting more sound than either
wood or glass.
They are very easily punctured and are not very fire resistant as the foil softens and shrinks
when exposed to flames.
4.2 SELECTION OF MATERIALS
For a membrane material to be suitable for an architectural application, the fabric must meet the
demands of the structure
26
. When selecting a material for the tensile membrane, a number of factors should
be considered, including the structural design, installation, location and detailing of the structure. Other than
cost, some of the selection criteria to be considered are discussed below (Koch 2004).
4.2a Span
The span of a structure is limited by the physical properties of its membrane fabric. Alternatively,
the choice of membrane fabric is limited by the span of the structure.
The maximum span that a membrane structure can have depends on structural calculations, taking into
consideration the live and dead loads (wind and snow loads especially) on the structure.
48 26
For properties of common roof assemblies see Appendix D
4.2b Weight
Membranes vary in weight from about 0.2kg/m² to 1.5 kg/m². This extremely low weight makes it an
excellent material for large spans. The low weight also reduces the amount of structural support needed for
the membrane. Lower weights mean lower transportation costs. In addition to being lightweight, membrane
fabrics are less bulky than conventional building materials and take up less space in transportation. More
material can therefore be transported at the same time.
4.2c Buckling Resistance/Tolerance to Folding
Membrane materials should have good buckling strength. This is important during assembly. Also
for structures that are dismantled and re-deployed multiple times, buckling strength helps increase its
lifespan. In the case of structures that are re-deployed multiple times, the tolerance to folding is a very
important criterion, as membranes tend to weaken along edges of folds.
Coated and un-coated PTFE has the best resistance to buckling and tolerance of folding.
4.2d Life-Span
The lifespan of a membrane material is an important point to take into consideration while
designing the structure. Is this structure one that is going to be used for a short time and then taken down
never to be used again? Is it going to be deployed again and again in multiple locations? Where are these
locations going to be? Or is this structure going to be a permanent one, used extensively for the foreseeable
future?
The durability of a membrane depends on its resistance to UV radiation and the degradation that
this produces. Tolerance to bending and folding also greatly increases the life span of a membrane
especially for folding or retractable structures.
49
4.2e Resistance to Temperature Changes
Most membrane materials can be used in a wide range of temperatures, once installed they have a
high resistance to temperature change. The temperature during installation is most critical with assembly
temperatures lower than 5 deg. C. not being recommended.
4.2f Resistance to UV Radiation and Weathering
A membrane’s resistance to UV Radiation and weathering has a direct relationship with the
lifespan of that material. The better a material’s resistance to radiation and weathering, the longer is its
usable lifespan.
Both foils and coated fabrics are highly resistant to UV radiation and different weather conditions.
PTFE-coated glass fabric and PTFE foil are highly resistant to both. On the other hand extreme weather
conditions (such as hail) might damage some coated fabrics.
4.2g Transmission, Reflection and Absorption
Factors such as transmission, reflectance and absorption should be taken into account depending
on the use of the structure. Membrane structures that are used as exhibit spaces for example, could make
use of a high transmission co-efficient that allow the space to have natural diffused lighting. Sound
transmission is also important for structures that hold a large number of people, or are divided into several
spaces that have different functions. Membranes range from 0% transmission (an opaque fabric) to 95%
transmission (a transparent foil)
4.2h Fire Resistance
Most membrane fabrics are not very flammable (they have low flammability). Some membrane
materials, such as Teflon coated fiber glass, are even non-combustible.
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4.2i Self Cleaning Effect
The self-cleaning effect of membranes is useful in extending their useful life. These membranes
also require less maintenance. The self cleaning effect of membranes comes from their molecular structure
and surface qualities. ETFE, PTFE and PVDF all have excellent self-cleaning properties.
4.2j Thermal insulation
The low mass of membrane materials results in low thermal insulation. Different methods of
construction of the membrane fabric can increase thermal insulating values. For instance, the multi-layering
of fabric to include air-cavities, or cavities filled with thermal insulation greatly increases the thermal
insulating properties of a membrane. Thermal insulation layers can also be fitted to the membrane systems
but these generally make the membrane completely opaque.
4.2k Acoustics
Membranes have a very low mass, and therefore have very low acoustic insulation properties.
Acoustic behaviour is dependent on the material structure of the membrane. Absorption values can vary a
great deal for different types of membranes.
Coated and uncoated fabrics have good sound absorption properties and micro-perforated foils
also have excellent acoustic absorbency values.
4.2l Colour
Membrane fabrics are available in many different colours. Depending on the material chosen,
some colours may be more expensive to fabricate if they are not standard colour choices.
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4.2m Economic use of Resources and Recyclability
The low mass of membrane materials is an advantage when it comes to transportation and storage
of the material.
Many membrane materials can be completely recycled (e.g. ETFE foil) or largely re-used (PVC
coated polyester) or as a last resort many manufacturers have a buy-back policy until recycling facilities
become available.
By using a tensile membrane as a means of spanning a large area one achieves a structure that
uses considerably less material than a conventional building. Because the membrane itself is light, the
supporting structure is light; therefore precious resources are saved in its construction.
4.2n A Quick Guide to the Selection of Materials:
Table 4.01 Selection Table
27
(Author, 2004)
52 27
For the Lightweight Structures Association 2007 Fabric Specifier’s Guide see Appendix E
4.3 CONCLUSION
Membrane fabrics are available in a wide variety, and the technology is constantly improving. The
fabric used in a tensile membrane structure has quite a great impact on the behavior and aesthetic of that
structure. In the end, the selection of the membrane fabric for a project depends on the particular needs of
that project.
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CHAPTER 5: PROGRAM STRUCTURE
This chapter describes the form finding software program and its components. It describes how it is
used and explains the resulting output.
5.1 FORM FINDING
This program enables the user to derive the form of a tensile membrane structure, calculate its
response to loading, and determine the cutting pattern needed for the fabric.
5.1a Input
Typically a designer would have the basic shape of the tensile structure to be analyzed. This could
be in the form of plan and elevation, or even a 3-d model. For this computer program, the user would need
to provide the plan and elevation of the structure.
For the purpose of this thesis, it will be assumed that the user can create the plan and elevation of
his design in any 3d CAD software that has the capacity to export to DXF format. In the early experiments
while designing this tool AutoCAD 2000 was used. The origin of the file is not important as long as the DXF
file meets certain requirements. These requirements will be discussed at length in Chapter 6.
The user supplies a basic drawing in DXF format, consisting of the plan and rough profile of the
structure with the supports (fixed elements) specified.
54
Fig. 5.01a Elevation in AutoCAD
Fig. 5.01b Plan in AutoCAD
55
Supply variables for the desired materials in the following manner:
For the Cable elements:
Elastic Modulus:
The elastic modulus E is also called Young’s modulus. It is the ratio of stress to strain for a
particular material, and defines stiffness.
The Elastic modulus of a steel strand is 25,000 ksi (170 kN/mm²)
The Elastic modulus of a wire rope is 16,000 ksi (112 kN/mm²)
Pre-stress:
Membrane structures are stabilized by tension only. Compressive loads are applied on the
membrane and the resulting stresses reduce or balance the pre-stresses leaving a residual tensile force.
The user should note that this implies that the pre-stress in the material should be high enough to
preserve a tensile force in the fabric under all possible superimposed loads, static as well as dynamic.
Thus the pre-stress depends on the magnitude of the compressive loads and the compressive
stress induced by these loads. The maximum membrane stress is equal to the pre-tensioning load plus the
maximum tensile stress from the superimposed load.
Cross sectional area:
This is the area of cross section of the cable. Steel cables are typically made up of several strands
twisted together. Each strand in turn is made up of several wires. The collection of strands is sometimes
known as a wire rope.
56 Fig. 5.02a Steel Strand Fig 5.02b Wire Rope
For the Membrane:
Elastic Modulus:
The elastic modulus of a membrane will vary according to the material used. The modulus of
elasticity defines the stiffness of the material and a higher modulus of elasticity implies less of a tendency of
a material to creep, that is, to deform over a period of time.
For instance polyester has a lower modulus of elasticity and a higher tendency to creep than glass
fiber fabric, which the user will realize means that while glass fiber can be pre-stressed up to 20% of its strip
tensile strength, polyester can only be pre-stressed from 5 to 15% of its strip tensile strength.
The elastic modulus of a typical fabric is 6000 pli.
Strip Tensile Strength:
The strip tensile strength of membrane fabric is the measure of the fabric's resistance to tensile
failure; it usually ranges from 200 to 800 lb/in
28
.
Pre-stress:
Pre-stress in the membrane can be applied by stretching it from the edges by the cable supports.
Dimensions in the Warp and Fill directions:
The term warp refers to the yarn running in the direction of the roll of fabric. The term fill refers to
the yarn running across the roll of fabric (the fabric has more stretch in this direction). Fabrics tend to be
stronger and suffer less elongation in the warp direction than in the fill direction. If loaded on the bias they
are much weaker and the membrane stretches substantially.
Seam Allowance:
This refers to the allowable width of the seams. An alternative to the seam allowance is the usable roll
width. This is width of fabric that can be used to define the panel widths excluding the allowances left for
seams and can be obtained from the manufacturer’s specifications.
57 28
See Appendix :Air Tent & Tensile Structures – 2007 Fabric Specifier’s Guide
For the Struts:
Elastic modulus:
The elastic modulus E is also called Young’s modulus. It is the ratio of stress to strain for a
particular material, and defines stiffness.
The elastic modulus of steel is 30,000,000 psi.
Area of Cross Section:
The cross sectional area of the steel strut.
Fig. 5.03 Material Input Screen (Membrane Properties Page)
5.1b Calculations
Using an iterative process (convergence tolerance) the program interpolates the positions of the
various points of the membrane (from the drawing) in three dimensional space. This is a repetitive
procedure until the minimal surface of the given structure is arrived at.
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5.1c Output
The program will then display the form of the structure which could also be exported as a DXF file
which would allow it to be opened in a program such as AutoCAD.
At this point the user would be given the option to change the parameters he entered in the beginning and
recalculate the form or to go on to the analysis.
Fig. 5.04 Display Screen
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5.2 STRUCTURAL ANALYSIS
5.2a Input
The user specifies the dead load and the parameters for wind uplift (wind speed, q factor)
i) Dead load
Dead loads are static loads. They are the weight of the structure and materials and any items
permanently attached to it. They are also known as gravity loads.
ii) Wind Load
Wind loads are lateral loads. They are also static loads consisting of pressure on the windward
side of a structure and suction on the leeward side of a structure. Wind uplift is the upward force created by
wind travelling over the membrane structure. For the purposes of this program, the parameters required to
define the wind uplift force are the wind velocity defined in mph and the ‘q’ factor, which is defined as the
velocity pressure in psf.
i.e. q = 0.00256 V²(H/33) raised to 2/7 where H is the height in feet of the structure.
(Usual wind pressure p=20 psf)
5.2b Generation of load pattern
i) Gravity load
Using the specified dead load the program calculates the tributary area using a grid superimposed on
the membrane, and thus the load at each node on the surface.
ii) Wind uplift
The surface area for each node is calculated along with the directional vector to arrive at the wind
uplift on the surface of the membrane.
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5.3 CUTTING PATTERN
5.3a Input
The user selects the appropriate fabric sizes and seam allowances. Fabrics tend to be stronger
and suffer less elongation in the warp direction than in the fill direction. If loaded on the bias they are much
weaker and the membrane stretches substantially.
While generating the cutting pattern, care must be taken such that the warp and fill follow the
principle lines of curvature of the structure. The correct orientation of the material minimizes stress
concentrations
5.3b Development
From the generated surface of the structure the program develops the cutting pattern for the
membrane panels.
This part of the program has not been implemented yet. It is described in detail in Chapter 7:
Future Work.
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5.4 SAMPLE STRUCTURES
Some examples of the structures that can be analyzed by this program are shown below.
Fig 5.05 Saddle Shape
Fig 5.06 Four Point Structure
62
Fig 5.07 Multiple Four-Point Structures.
Fig 5.08 Repeating Surfaces
63
CHAPTER 6: A TUTORIAL
This chapter is a step by step description of how the program works. It also explains the data
necessary to use it. At any point during the use of the program, clicking on Help will open the help file. This
contains instructions on the use of the program, and also definitions and a glossary.
6.1 PREPARING THE DXF FILE
Most design ideas start out with a basic sketch such as the one in the diagram shown below. The
designer knows the perimeter of the building that needs a tensile roof, and also has an image of what he
would like the form of the roof to be.
Fig 6.01 Design Sketch
6.1a Drawing in AutoCAD
The first step in the process would therefore be to translate the idea from the rough sketch into a
basic drawing in a 3-D CAD program.
In this example, AutoCAD2000 was used to create the drawing. The designer gives two supports a
positive height with two supports at ground level. The membrane surface itself is drawn as a grid with the
perimeter of the structure acting as the edge cables.
64
Fig 6.02 Plan Drawing in AutoCAD
Fig 6.03 Elevation Drawing in AutoCAD
65
Fig 6.04 3D View in AutoCAD
6.1b Layers
In order for the program to recognize the various elements of the structure, they must be
differentiated between in the AutoCAD drawing. This is done by assigning each element of the structure to a
different layer. The order in which the layers are listed is very important as the program reads the different
layers and parses the information in this order. The colours and names of the layers on the other hand do
not matter.
The layers must be read in the order:
1) Support nodes
2) Cables in the X-direction
3) Cables in the Y-direction
4) Membrane element in the X-direction
5) Membrane element in the Y-direction
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Fig 6.05 Layers in the Drawing
The support nodes must be marked with a circle, with the center of each circle at the center of the
corresponding support.
The drawing at this point is just a graphical representation of the undeformed membrane and as
such it is just a collection of grid points. In the course of analysis the shape of the membrane will be defined
by loading it with concentrated forces, uniformly distributed loads and the displacements that occur.
At this point in the process the drawing looks like this:
Fig 6.06 Finished Drawing
67
As can be observed, the supports are indicated by the red circles, the edge cables run around the
perimeter of the structure, and the membrane is divided into a grid in the X and Y direction. At this point the
drawing is ready to be exported to a DXF file and saved.
6.2 INPUT
The purpose of this program is to help derive the form of a tensile membrane, given the boundary
conditions and material properties of the various elements.
That is, to translate a design idea into a structurally feasible and architecturally desirable solution.
Once the user has copied formfinder.exe on to your computer, he must start the program by double clicking
the file icon. This will bring up the splash screen. The user presses ‘Start’ to begin.
Fig 6.07 Splash Screen
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6.2a Importing the DXF file
The first step in the program is to import the DXF file that has already created.
The first window that appears in the program therefore is the ‘import DXF’ window.
Fig 6.08 Import the DXF File
Using the ‘Browse’ button will locate the DXF file which is loaded by clicking ‘Open’ The DXF file
will be loaded into the program.
The ‘View’ menu can be used to view the imported file. Pressing ‘Continue’ will take the user on to
the next step.
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6.2b Material Properties
The next step in the program is to give the different materials in the structure their physical
properties.
6.2b.i The Membrane
The program begins with the fabric of the membrane.
Fig 6.09 Membrane Tab in the Material Properties Window
At this stage, there are two different steps the user can take. The simplest step is to select a
membrane type. The program has a library of common membrane fabrics. These are: Expanded PTFE,
PTFE coated Fiberglass, Silicone coated Fibreglass, PVC coated polyester, ETFE and HDPE. Selecting a
membrane type in the drop-down menu will load the material properties of that fabric type into the program.
If the user does not want to use a material from the membrane library, the program gives him the
option to create a custom membrane. In this case, press the ‘Custom’ button.
70
This will clear all the material properties from their windows and allow the user to enter values of his own
choosing. The material properties for the membrane fabric that will be required are:
In the warp direction:
1) Elastic modulus
2) Pre-stress
3) Area of cross section
4) Capacity
In the fill direction
1) Elastic modulus
2) Pre-stress
3) Area of cross section
4) Capacity
6.2b.ii The Cables
The cable elements for the purposes of this program are the boundary elements of the structures.
The program assumes steel cables which are the default values already entered in the relevant boxes.
Again, the user has the ability to input values of his own choosing.
The properties required to be entered are the following:
1) Elastic modulus
2) Pre-stress
3) Area of cross section
4) Capacity.
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Fig 6.10 Cable Tab in the Material Properties Window
If needed the help file (described later in this chapter) will provide the user with definitions and
explanations of any concepts he is unfamiliar with
29
.
6.2b.iii The Struts.
The struts in this program are the support elements for the structure. These are the compression
elements of the structure.
The physical properties the user needs to enter for the struts are the following:
1) Elastic modulus
2) Area of cross section
3) Capacity
72 29
See Chapter 6, Section 6.5 for a description of the Help file.
Fig 6.11 Struts Tab in the Material Properties Window
6.3 UNLOADED FORM
At this point with all the material properties entered and the DXF file imported the program is ready
to run. Pressing ‘Continue’ will take the user on to the next stage.
At this point if desired, the user may also look at what the structure looks like at this stage in the
proceedings. Using the ‘View’ menu will now enable the user to preview the undeformed shape of the
tensile membrane.
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Fig 6.12 Display Window Showing the Undeformed Shape of the Membrane
The unloaded shape of the structure is due to the self weight of the membrane, and the support
and boundary conditions. In order to understand how the structure will behave under loading, the user now
needs to specify the loads to be applied.
Pressing the ‘Next’ button will progress the user to the Loading section of the program.
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6.4 Loads
In this section of the program, loads for the structure will have to be defined.
Fig 6.13 The Load Window
The variables required for gravity loading are:
1) Dead load
2) Live load
The variables required for wind loading are:
1) Wind uplift
2) Wind speed
75
If the user is uncertain of wind speeds at the site location the ‘Look Up’ button will direct him to the
Wind Energy Resource Potential page of the Wind and Hydropower Technologies Program run by the U.S.
Department of Energy, where wind maps of the U.S can be found.
Fig 6.14 U.S. Annual Wind Power Resource and Wind Power Classes – Contiguous U.S. States
30
Once the loads have been specified, the program is now ready to move on to the next and final
step. The button marked ‘Continue’ takes the user to the next step.
76 30
U.S. Department of Energy – Energy Efficiency & Renewable Energy, Wind & Hydropower Technologies Program
Fig 6.15 Display Window
The program will now display the form of the tensile membrane resulting from its physical
characteristics as well as the applied loads.
Using the ‘Change Parameters’ Option, the user may now go back to any of the Input Screens
and manipulate the values to change the form of the structure.
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6.5 IN-PROGRAM ASSISTANCE
6.5a The Help File
Fig 6.16 The Help File
At any time in the process, should he require it, the user will find a Help file available. This file is
useful for definitions should he need any and basic explanations of the various concepts he need to
understand.
The help file will provide him with material types and properties that are not pre-loaded into the
program. To help select a material that is suitable for the project there is a basic table that compares the
different fabrics.
The user can find for each of the different types of membrane materials, physical properties such
as weight, elastic modulus, allowable pre-stress and capacity.
78
Fig 6.17 Guide to Selecting Fabric in the Help File
In addition to these structural properties, there is also information available to help make good
design choices. This is information such as life expectancy, whether it is possible to get a warranty for that
fabric and if so, for how long. Also available is data concerning the usable width of a fabric which is useful
79
for creating the cutting pattern for the structure. It also lists colours that are available for different fabrics and
their light transmission, reflection and absorption values. These are properties that may not have an effect
on the structural performance of the structure but are important for the overall performance of the
membrane structure as a piece of architecture.
Fig 6.18 Glossary
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6.5b Glossary
The last part of the help file is the Glossary. This provides the user with definitions and simple
explanations of concepts that may be needed through the use of the program. The complete Glossary is
included at the end of this report.
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CHAPTER 7: ADVANTAGES AND DISADVANTAGES
Chapter 6 described the operation of the program and included descriptions of most of the features
and capabilities of the software. This chapter outlines several additional advantages of the program and
includes descriptions of some of the most important disadvantages of this version of the tool.
7.1 USER INTERFACE
The program has been designed to be easy and intuitive to use. The program structure follows the
recognizable form of common applications, with a familiar menu structure and help-file.
It is also not a rigidly linear program. For instance, at any point during its use the user has the
ability to move between the material property specification page and the display page. There is always the
provision for going back and changing the information supplied at any stage during the analysis. This allows
the user to tweak his design to get the results he wants.
This aspect of the program is also helpful as a learning tool. For example, an inexperienced
designer can see almost instantly the result of using different fabric materials. He can also see how
changing one aspect of the design can result in changing the shape of the structure.
There are many more sophisticated programs available but these require a certain level of
experience in order to use them. They have a steep learning curve and can be quite complicated to the first
time user. This tool in contrast is designed for the beginner and so is much easier to grasp.
Existing form finding software is usually one of two types, easy to use software designed for the
architect that offer spatial modeling tools with no ability to predict structural behavior, or complex full-
featured programs aimed at the structural engineer. These types of engineering software require the input to
have a level of detail that is much too complex for an architect. The time that it would require for an architect
to familiarize himself with this information and learn to use the program is much too long for this to be
feasible.
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7.2 USER INPUT
This program has been designed for a user who has little basic knowledge of tensile structures.
However, the user is assumed to have the ability to use some 3D CAD software in order to generate the
basic information that the program requires.
The disadvantage of needing the initial sketch in DXF format is that a casual user would not be
able to use the program. The ability to create a sketch within the program itself would be a big advantage to
this casual user. Also, the user might not have CAD software available at that moment and thus would not
be able to use the program.
In this sense, some preparation is necessary in order to use the form finding program and the
disadvantage is that it excludes spur-of the moment design ideas.
The advantage of using a CAD based format for the initial input is that AutoCAD or other CAD
programs are common in the architectural profession and most of the projected users of this program would
be familiar with creating drawings with them. In addition to the ease in creating these drawings, they are
extremely easy to convert to DXF format.
The DXF file however, has to be prepared with some care, with the precise information laid out as
specified in the instructions in the help file. If this is not done as specified, there are errors generated when
loading the file and the program will not work as intended.
Another aspect of the CAD drawing is that the more complex the grid that is created in AutoCAD,
the more comprehensive the analysis is, and the more accurate the resulting shape will be. This can require
a good deal of work in AutoCAD, as each segment between the nodes of the grid has to be a separate line
in order for the program to pinpoint each grid point. The more complicated the design, the more difficult this
initial drawing will be.
An advantage to the program is that it already has preset material properties. It comes pre-loaded
with the specifications of common membrane materials. This enables the user to get his first results very
quickly by just choosing one of the fabric types from the pull-down menu. Once he has a basic idea of the
83
behavior of the structure he can go back to the material properties page and be more specific about the type
of material he wants to use. In this sense the program is a very effective learning tool.
7.3 EDITING
There is another disadvantage to not having the ability to draw within the program. This becomes
apparent after the user has run the program the first time and he or she wants to change the basic
parameters of the design, such as the outline of the boundary, or the heights of the supports. In this case, it
becomes necessary for the user to edit their original CAD drawing, or export the resulting drawing from the
program back to AutoCAD and edit it there. This is not a major flaw but certainly an important
inconvenience.
Recent advances in BIM tools suggest that perhaps in the future it will be better to have just one
source of the geometry, and the idea of having a separate geometry modeler in the program may not be
much of a benefit.
At the moment the ability to edit the drawing right there in the program itself would be quite
convenient. Once the drawing has been edited in CAD, it has to be exported to DXF once again, and then
re-imported to the program before it can be analyzed again.
If however, the user only wants to change the material properties, for example the type of fabric he
is using or pre-stress, he can do it very easily. At any point during the analysis, the user has the ability to re-
define the material properties of the membrane, cables and struts by going back to the materials input form.
In addition, as long as the project has been saved, or the program not been shut down between
exporting the DXF file to AutoCAD and re-importing it, the material properties that were specified will be
retained and there is no need to specify them all over again.
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7.4 ANALYSIS
The analysis of this program focuses on the shape of the structure. It is a tool to show the form that
the structure will take with the parameters that are specified. Thus, it is easy to change those parameters
and see how that affects the overall form of the tensile membrane.
The basic output from the analysis is easy to read and understand. The most immediate form of
output is displayed as a 3-dimensional view of the resulting structure. The program also produces an
AutoCAD script file which can be run in AutoCAD to display the three dimensional geometry of the structure.
In addition to this the program creates a text file containing a matrix showing the resulting position of each
node and the stresses in each element.
While the program produces a text file showing the stresses in each element, this information is not
always helpful to the user. That is, the information is never displayed in the geometry that is created. Thus
the user cannot look at the form that is created and deduce the areas that are being excessively stressed or
strained, or those areas that do not have enough pre-stress. The resultant output from the program only
shows the deformed shape which is an important structural criteria.
It is unfortunate that the program does not take into account openings in the membrane. The
membrane has to be a continuous surface in order for the tool to work.
The program is also not structured to inform the user if there is a flaw in his or her design. The
program will produce a result no matter how unrealistic the design is. In this sense, it does help that the user
has a little basic knowledge of tensile structures.
In addition to the tool itself, the only other software required is AutoCAD or some other 3d CAD
program that enables the user to create the DXF file. The output scrip file and the text file will be created in
the same folder as the executable file. At this time the user is unable to specify a destination for these files.
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CHAPTER 8: AREAS FOR FUTURE WORK
This chapter outlines improvements that could be made to the program. It also outlines areas that it could be
developed further in order to increase its scope in the design process.
8.1 AREAS FOR IMPROVEMENT IN THE EXISTING PROGRAM
8.1a Drawing Ability
One area for improvement in the program would be the ability to draw within the user interface.
This would enable the user to make a basic sketch in the program itself and would eliminate the need for the
DXF file.
This ability to draw could be kept simple, with the user being able to draw three types of elements:
supports, cables, and membrane grid elements. This would make the program a great design tool for a
person that wanted to quickly visualize what his design would look like.
However, the ability to import the DXF file should remain, as much more complex shapes could be
created in AutoCAD. It would not be productive to try and replicate the complexity of an already existing,
very reliable software application. In addition to this, in the future more complex BIM Software could be used
to create the initial drawings.
In addition to adding basic drawing capabilities, there should also be added the capacity to edit the
drawing form within the user interface. This would then eliminate the need for exporting and importing the
cad files multiple times and increase the program’s efficiency.
8.1b Display of Results
Another area for improvement could be the display of results. At the present time, the display
shows the resultant shape of the structure. While this is quite adequate from the designer’s viewpoint as an
aesthetic issue, it would be quite useful for the program to display the stresses and strains created in the
membrane. This would be helpful for a learning tool, as the user would be able to see the areas of greater
and lesser strain and learn how manipulating various parameters could change this.
86
The program already computes stress and strain but only reflects the resulting deflection in its
display. The stress and strain calculations could be shown as colour gradients on the membrane gird.
Conventionally, lines in red show areas of high stress and lines in blue show areas of low stress, with these
colors gradually changing from red through orange, yellow and green to blue.
8.1c Additional shapes
At this time the program analyses and displays simple shapes such as the ones below:
Fig 8.01 Simple Four Point Structure
Fig 8.02 Shade Sail (Lightweight Structures Advisory Service)
31
87 31
http://www.ltwsas.com.au/
Fig 8.03 Multiple Four Point Structures
Fig 8.04 Tensile Canopy (Lightweight Structures Advisory Service)
32
88 32
http://www.ltwsas.com.au/
In a future version of the program, it should be able to analyze more complex structures as shown below:
Fig 8.05 Shade Sail with Circular Opening (Lightweight Structures Advisory Service)
33
Fig 8.06 Multiple Conics – Ripleys Yatch club South Carolina (Lightweight Structures Advisory service)
89 33
http://www.ltwsas.com.au/
Fig 8.07 Inverted Conic Shape – Hong Kong Jockey Club (Lightweight Structures Advisory Service)
8.2 ADDITIONS TO THE PROGRAM
8.2a A Cutting Pattern Generator
A useful addition to the program would be a cutting pattern generator. This would take the program
from a learning tool and basic design tool, towards being a useful practical tool.
A cutting pattern generator would use the deformed shape of the membrane grid and the usable
fabric widths specified in the materials editor, to generate the shape of the individual fabric panels used to
create the membrane canopy
The ability to go back from the cutting pattern generator to the structural analysis in order to
optimize the material use would be an interesting idea to explore. This would help the user to adjust his
design to take advantage of the available dimensions of the fabric he has selected.
90
8.2b Fabric Selector Tool
In its present version the program has a library of fabrics with a comparison chart of their relative
merits. The cutting pattern generator might include a tool that helps select the fabric available that is most
suitable to the pattern generated. In addition, the selector tool could take into account the location of the
project and its function
8.2c Teaching Handbook
At this time the software has a ‘Help’ function which provides an overview of tensile structures and
their properties. It also lists and describes common fabric materials. The next version of the program could
also include a tutorial on designing fabric structures, which could take the user through the process step by
step. An accompanying teaching handbook would be a useful addition.
8.2d Accessibility
The program cannot be accessed as yet from the internet; the file has to be downloaded into a
folder of the user’s choice in which the output files will be generated. An online version of the program would
be step in making the tool more accessible and easy to use.
8.2e Improved Ability to Read Meshes
In the present version of the software the program is unable to analyze membranes with holes in
them. In future versions this ability could be added. In addition, at the present time only structures with
rectangular meshes can be analyzed, and not those with radial meshes. In the future the ability to read
radial meshes, or to switch from rectangular meshes to radial meshes might be useful.
91
CHAPTER 9: CONCLUSIONS
Tensile structures have always had a certain appeal to architects. A well designed tensile
structures is a beautiful thing –structure expressed explicitly in form.
Fig 9.01 Tensile Fabric Structure (LSA)
34
Tensile membranes can have exciting shapes, graceful geometries and appealing aesthetics. They
can have large clear spans and ample natural lighting. Lightweight tensile structures use fewer materials
than conventional structures and are less energy intensive. With the present day focus on sustainable living,
fabric structures could be a viable solution to the search for resource-efficient building materials.
The stumbling block for many architects who have limited experience in designing lightweight
tension structures is that they are difficult to analyze structurally. Their structural behavior is non-linear and
difficult to calculate. Prior to the development of computer applications geared toward their analysis,
architects and designers depended on scale models to study these structures. These models were difficult
to construct and not always completely accurate. These issues created an artificial barrier preventing many
architects from selecting tensile structures for new projects. Architects need to have confidence in their
ability to design a structure that can be built.
92 34
http://www.lightweightstructures-ifai.com/component/option,com_zoom/Itemid,43/)
The development of computer applications to analyze tensile structures was an important step in
the advancement of the design process. Models could now be created and analyzed much faster than
before. However, the drawback to this was that most programs that are available are quite complicated and
difficult to use. The early versions of software created to analyze tensile structures were aimed at
engineering professionals who needed full-featured programs. This meant that the software was capable of
doing complete structural analysis, but the programs required far too detailed and complicated data input for
the normal needs of an architect. The architect needs to know if the idea is generally possible and
reasonable. He needs to know that the fundamental geometries and loads can be managed. He is seeking
“ballpark” estimates on loads, vectors and geometries, and typically is not prepared to provide the full range
of inputs needed for a full analysis. They lengthy training period for the full-featured software is offset when
a fabric structure engineer is conducting the analysis regularly. For an architect that may only design one or
two fabric structures, spending hours or days learning a software program is not viable.
The form finding tool described in this thesis has been designed to be easily used.
The program is aimed at helping beginners, such as students to design simple structures and discover how
the structures actually behave.
The tool could be used as a design tool in schools, or for schematic design in the real world. There
are some programs available which are much more sophisticated and enable a user to analyze their
structure to a much greater degree of detail, but they have a rather steep learning curve and require the
user to be extremely knowledgeable and have a comprehensive grasp of the fundamentals of tensile
membrane design. Other programs available are easier to use but only offer spatial modeling tools, with no
ability to predict structural behavior.
93
Fig 9.02 Tensile Fabric Membrane (LSA)
35
The form finding tool is in many ways the opposite of these programs. It gives the user an easy
way to estimate what their structure is going to look like, without having to spend a long time learning to use
the software. It works in conjunction with software that is already familiar to the target user so eliminates the
need to master a new application. All the user has to do is supply the basic information about their design in
order to achieve a result.
Thus, this form finding tool could be an invaluable aid to the architect or student beginning to
explore the endless possibilities present in the design of lightweight tensile structures.
94 35
http://www.lightweightstructures-ifai.com/component/option,com_zoom/Itemid,43/
GLOSSARY
Absorption - The process in which incident radiated energy is retained without reflection or transmission on
passing through a medium.
Adhesion Strength - The resistance of the fabric membrane to delamination.
Adhesive Seam - A seam created by the use of an adhesive as the sealing agent
Air Inflated structure - A structure in which highly pressurized tubes or dual walled mats are used as the
structural elements
Air Supported Structure - A structure in which the enclosing membrane is supported by an air pressure
differential.
BIM - Building Information Modeling.
Base Fabric - The woven material used as the fabric of the membrane
Butt Seal- A seam created by placing the material edge to edge and welding
Cable - Tension elements. Cables are either structural strands or structural rope. A strand consists of steel
wires wound helically around a center wire in symmetrical layers. A rope consists of a number of
strands wound helically around a core
Canopy - A canopy is an architectural fabric projection that provides weather protection, identity, and/or
decoration and can be ground-supported in addition to being supported by the building to which it
is attached. The term also can refer to a small tent, a tent without sidewalls or an awning
Clearspan Structures - A structure without internal supports
Coating Material - The coat or laminate that provides the membrane with a seal against weather,
resistance to ultra violet light, provides the medium to create joints and also helps in increasing the
fire resistance of the membrane
Elastic Modulus - The ratio of stress to strain for a particular material, the measure of stiffness
Fill - The yarn running across the roll of fabric (the fabric has more stretch in this direction)
French Hem - A hem that encloses the seams edge to prevent unraveling
Geometry - The shape or form of a surface, solid or frame
HDPE - High Density Polyethylene
Heat-seal Seam - A seam created by heat-welding it to fuse the membrane seams in a permanent,
watertight seal
95
Laminate - A material produced by bonding together layers of material
Lap Seal - See overlap seal
Lb/in - Pounds per inch
LDPE - Low Density Polyethylene
Membrane - A very thin pliable layer of material
Overlap Seal - A seal in which two edges of a material are joined together inner surface to outer surface
PES - Polyester Fabric
Plf - Pounds per linear foot
Pli - Pounds per linear inch
Pole Tent - A tent created by arranging a set of poles beneath a fabric structure which then support and
define the tent's shape. The fabric is tensioned over the poles with ropes attached
around the tent's edges. The ropes are then anchored to the ground with stakes or augers.
Pre-stress - The internal stresses that are introduced in a structural element to counteract the stresses that
will result from an applied load.
Pre-stressing forces - Pre-stressing forces, such as edge loads, self weight and pressure, are those forces
which act on a predominant configuration of static equilibrium for a structure. They stabilize the
structure and provide stiffness against further deflection.
Pre-tension- Internal tensile stress that is introduced in structural elements to counteract stresses that will
result from an applied load.
PTFE- Polytetrafluoroethylene
PVC- Poly Vinyl Chloride
Reflectance- The ratio between the amount of light that is reflected from a surface to the amount of light
that was incident on that surface.
RF Seam - A sealing that fuses two or more vinyl substrates using pressure and radio waves to create a
seam or fabric joint.
Strip Tensile Strength - The measure of the fabric's resistance to tensile failure, it usually ranges from 200
to 800 pli.
Strut - Refers to compression elements.
96
Tear Strength- The resistance of the fabric membrane to abrasion and tears.
Tensile Structure- Structure which relies primarily on the tensile strength of its components for its strength
and stability. The main load carrying members transmit loads to the foundation or support system
by tensile stresses with no compression or flexure allowed.
Tension Tent- A temporary fabric structure that shares some characteristics with the pole-supported tent,
but relies more on the tensioning of the fabric roof for its structural integrity and shape. The use of
tensioned fabric to resist applied loads and to shape the fabric membrane means less of a
traditional support structure is needed to maintain it.
Tpi - Threads per inch
Transmittance- The ratio of light that passes through an object to the amount of light that was incident on
that object.
Usable Roll Width The width of fabric that can be used to define the panel widths excluding the allowances
left for seams.
Warp- the yarn running in the direction of the roll of fabric.
Yarn Count- the number of threads in the fabric warp and fill per square area.
97
BIBLIOGRAPHY
‘Air, Tent & Tensile Structures: 2007 Fabric Specifier’s Guide’ Fabric Architecture,
November/December 2007, p.100
Berger, Horst 1996, Light Structures - Structures of Light. Birkhauser-Verlag, Basel,
Switzerland.
Drew, Philip 1996, Frei Otto: Form & Structure. Westview Press Inc. Boulder Colorado.
‘Getting Down to Basics – Fabric Facts that all Designers Should Know’, Fabric Architecture,
March/April 2007, p.30
Grundig, Lothar- Moncrieff, Erik- Singer, Peter and Strobel, Deiter 2000, A History of the
Principal Developments and Applications of the Force Density Method in Germany 1970-1999.
IASS-IACM 2000
Koch, Klaus-Michael 2004, Membrane Structures: Innovative Building with Film and Fabric.
Prestel Verlag, Munich.
Leonard, John William 1988, Tension Structures – Behavior & Analysis. McGraw-Hill Book
Company, New York.
Lewis, W.J. 2003, Tension Structures: Form and Behaviour. Thomas Telford, London.
National Research Council (U.S.) Advisory Board on the Built Environment 1985, Architectural
Fabric Structures- The use of Tensioned Fabric Structures by Federal Agencies. National
Academy Press, Washington, D.C.
Onouye, Barry & Kane, Kevin 2002, Statics and Strength of Materials for Architecture and
Building Construction. Pearson Education, Inc. New Jersey.
Otto, Frei (Ed.) 1967, Tensile Structures design, Structure, and calculation or buildings of
cables, nets and membranes V.2. The M.I.T Press, Cambridge, MA.
Roland, Conrad 1970, Frei Otto: Tension Structures. Praeger Publishers, New York.
Rubb Building Systems, Technical Specifications: High Strength Architectural Membrane,
viewed 21 June 2008, http://www.rubb.com/technical-high-strength-architectural-
membrane.asp
Sanchez, J. and Morer, P.2004, Surface Fitting Approach for Tensile Membrane Design. IASS
2004 Symposium Montpellier.
Scheurmann, Rudi 1996, Tensile Architecture in the Urban Context. Reed Educational and
Professional Publishing Ltd, Oxford.
98
Schierle, G.G. c.1968 Lightweight Tension Structures. U.C. Berkeley Design Research
Laboratory, Berkeley.
Schodek, Daniel L 2001, Structures. Prentice-Hall, Inc. New Jersey.
Senagala, Mahesh B, ‘UTenSAils: A Design-Develop-Build Project’, Texas Architect, Texas
Society of Architect/AIA, viewed 21 June 2008, http://www.texasarchitect.org/ta200701-
studio.php
Shaeffer, R.E. (Ed.) 1996, Tensioned Fabric Structures. American Society of Civil Engineers.
New York.
Siff, Michael, What is Computer Science? Sarah Lawrence College, viewed 21 June 2008,
http://science.slc.edu/~msiff/what-is-cs.php
Thornton, Joe 2002, Environmental Impacts of Polyvinyl Chloride Building Materials, Healthy
Building Network, viewed 21 June 2008,
http://www.healthybuilding.net/pvc/ThorntonPVCSummary.html
University of Stuttgart, Institute for lightweight Structures 1975, Nets in Nature and Technics,
Stuttgart-Vaihingen.
99
APPENDIX A – USC SCHOOL OF ARCHITECTURE COURSE DESCRIPTION
Prof. G G Schierle
Benjamin Ball
Gaston Nogues
COURSE DESCRIPTION
A GENERAL
1. Course: Architecture 499, 2 units
2. Title: Fabric Structure Design and Construction
3. Class meetings: One two hour meeting per week (Thursday 11am to 1 pm)
4. Student hours: 6 hours per week, including class time For the prototype design and
construction additional times will be scheduled as needed.
B OBJECTIVES
Study design principles, materials and methods of membrane structure construction. Study
schematic design, structural design/analysis, design development, and construction of fabric
structures. Students are encouraged to also enroll in Arch 513: Advanced Structures, to broaden
the theoretical base.
C SUBJECT MATTER
Design, analysis, design development and construction of fabric and cable net structures. Loads
acting on fabric structures: gravity, seismic, and wind load, including wind gust factor; design
considerations for flutter and large deformations. The term project will be design, analysis, and
construction by students of an actual fabric structure, to develop hands-on experience for critical
details and the construction process.
D TEACHING METHODS
Weekly lecture presentations and reading assignments about architectural and structural
design/analysis, design development, manufacture, and erection. The term project,
design/analysis, manufacture, and construction, will provide valuable hands-on experience.
E BASIS FOR COURSE GRADE
Assigned projects: 50%; class participation: 50%
Grading scale: A = 90 -100%; B = 80 - 89%; C = 70 - 79%; D = 60 - 69%
Any Student requesting academic accommodations based on a disability is required to register with
Disability Services and Programs (DSP) each semester. A letter of verification for approved
accommodations can be obtained from DSP. Please be sure the letter is delivered to your
professor during the first 3 weeks of each semester. DSP is located in STU 301 and is open 8:30
am to 5:00 pm, Monday through Friday. The DSP phone is 213-740-0776.
F READING LIST
Required text (notably chap. 13, 14, 24)
Schierle (2005) Architectural Structures, USC Custom Publishing
Additional Reading:
ASCE (1995) Tensioned Fabric Structures, ASCE, Structural Division
Fabric Architecture, IFAI (International magazine – Schierle on Advisory Board)
Holgate (1997) The Art of Structural Engineering, Menges
Berger (1996) Light Structures Structures of Light, Princeton Arch
Koch (2004) Membrane Structures, Prestel
Otto (1954) Das Haengende Dach, DVA
Otto (1966) Zugbanspuchte Konstruktionen, Ullstain
Otto (1973) Tensile Structures, MIT Press
Roland (1965) Frei Otto – Spannweiten, Ullstein
Schierle (1968) Lightweight Tension Structures, UCB
Schlaich, Bergermann (2003) Light Structures, Prestel
100
G COURSE OUTLINE
Th 24 Introduce course objectives, teaching method, and expected results.
Historic background of membrane structures Overview of fabric and cable net
structures, pretress effect and requirements
August
Th 31 Minimal surface criteria and form-
finding Minimal surface equations
(Schierle, 1977)
September
Th 7 Typology of membrane structures. Boundary conditions: cable,
arch, beam, frame. Surface conditions: Saddle shape, arch shape, wave
shape, point shape
Th 14 Form-finding methodologies
Soap film models, stretch fabric models
Computer form-finding
Th 21 Structural design and analysis Manual
computation for schematic design Computer
aided design and analysis, test models
Th 28 Pattern design Manual model methods of
fabric strips Computer methods using triangular
development
October
Th 5 Sustainability issues
Translucency and natural lighting
Thermal performance of fabric Fabric
durability and maintenance issues
Th 12 Sustainability issues
Translucency and natural lighting
Thermal performance of fabric
Fabric durability and maintenance
Th 19 Fabric details: welded, stitched, and laced
seams Fabric joints: fabric/cable;
fabric/arch/beam/frame Cable end fittings – fixed and
adjustable for prestress Foundations and sol anchors
Th 26 Prototype design
November
Th 2 Field trip to fabric manufacturer
Th 9 Prototype pattern development
Th 16 Prototype manufacture
Th 23 Prototype assembly and erection
Th 30 Prototype testing, review, and evaluation
101
ARCH 499: Fabric Structure Design and Construction - proposed 2 unit course Fall 2006
Faculty: Prof. G. Goetz Schierle and Benjamin Ball, Gaston Nogues
This course would study design principles, materials and methods of construction for membrane
structures. Students will learn about schematic design, structural design/analysis, design
development, and construction of membrane structures. Several graduate and undergraduate
students have asked about a course like this where they can actually build something. Students
are encouraged to also enroll in Arch 513: Advanced Structures, to broaden the theoretical base.
Prof. Schierle has hands-on practical experience with large tension structures, and conducted
courses similar to this one in which students actually built structures of fabric and wire mesh at
USC, UC Berkeley, and University of British Columbia. Benjamin Ball and Gaston Nogues have
designed and built an innovative fabric structure.
Topics:
• Historic background
• Overview of membrane structures
• Minimal surface criteria
• Minimal surface governing equations (Schierle, 1977)
• Typology of membrane structures
• Form-finding: soap film, stretch fabric, computer aided design
• Structural design/analysis: schematic calculations and computer analysis
• Pattern design: model patterns and computer methodology
• Fabric properties: strength, stiffness, durability, etc.
• Sustainability issues: natural lighting, thermal performance, etc
• Cable net structures
• Construction issues
• Detailing and connections
• Support elements: mast, arch, frame, etc.
• Foundations and soil anchors
• Manufacture and erection
• Field trip to fabric contractor
• Design and construction of a small fabric structure as class term project
Saddle shape Wave shape Arch shape Point shape
102
APPENDIX B – FORCE DENSITY METHOD
103
104
Excerpt from: ‘Tensioned Fabric Structures: A Practical Introduction’ R.E. Shaeffer, 1996,
American Society of Civil Engineers. New York.
105
APPENDIX C – DYNAMIC RELAXATION METHOD
106
Excerpt from: ‘Tensioned Fabric Structures: A Practical Introduction’ R.E. Shaeffer, 1996,
American Society of Civil Engineers. New York.
107
APPENDIX D – COMMON ASSEMBLY PROPERTIES
Excerpt from: ‘Tensioned Fabric Structures: A Practical Introduction’ R.E. Shaeffer, 1996,
American Society of Civil Engineers. New York
108
APPENDIX E – FABRIC SELECTOR’S GUIDE
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
‘Air, Tent & Tensile Structures – 2007 Fabric Specifier’s Guide’ Fabric Architecture, Nov/Dec 2007
138
APPENDIX F – CODE
VERSION 5.00
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BackColor = &H00000000&
BorderStyle = 3 'Fixed Dialog
ClientHeight = 5790
ClientLeft = 255
ClientTop = 1410
ClientWidth = 7110
ClipControls = 0 'False
ControlBox = 0 'False
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KeyPreview = -1 'True
LinkTopic = "Form2"
MaxButton = 0 'False
MinButton = 0 'False
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ShowInTaskbar = 0 'False
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Begin VB.CommandButton Command1
Caption = "START"
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TabIndex = 0
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Begin VB.Image Image1
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Left = 0
Picture = "frmSplash.frx":000C
Stretch = -1 'True
Top = 720
Width = 5280
End
End
139
Attribute VB_Name = "frmSplash"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub Command1_Click()
Unload frmSplash
Load frmMaterials
frmMaterials.Show
End Sub
VERSION 5.00
Object = "{BDC217C8-ED16-11CD-956C-0000C04E4C0A}#1.1#0";
"TABCTL32.OCX"
Object = "{F9043C88-F6F2-101A-A3C9-08002B2F49FB}#1.2#0";
"comdlg32.ocx"
Begin VB.Form frmMaterials
Caption = "FormFinder"
ClientHeight = 5400
ClientLeft = 60
ClientTop = 2115
ClientWidth = 7110
LinkTopic = "Form1"
ScaleHeight = 5400
ScaleWidth = 7110
StartUpPosition = 2 'CenterScreen
Begin MSComDlg.CommonDialog CommonDialog2
Left = 3240
Top = 4800
_ExtentX = 847
_ExtentY = 847
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Begin VB.CommandButton cmdMaterialsCONTINUE
Caption = "CONTINUE"
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TabIndex = 27
140
Top = 4800
Width = 1215
End
Begin TabDlg.SSTab SSTab1
Height = 4335
Left = 120
TabIndex = 0
Top = 360
Width = 6855
_ExtentX = 12091
_ExtentY = 7646
_Version = 393216
Tabs = 4
TabsPerRow = 4
TabHeight = 520
TabCaption(0) = "Import DXF FILE"
TabPicture(0) = "frmMaterials.frx":0000
Tab(0).ControlEnabled= -1 'True
Tab(0).Control(0)= "Label1"
Tab(0).Control(0).Enabled= 0 'False
Tab(0).Control(1)= "Text1"
Tab(0).Control(1).Enabled= 0 'False
Tab(0).Control(2)= "cmdBrowse"
Tab(0).Control(2).Enabled= 0 'False
Tab(0).Control(3)= "CommonDialog1"
Tab(0).Control(3).Enabled= 0 'False
Tab(0).ControlCount= 4
TabCaption(1) = "Membrane"
TabPicture(1) = "frmMaterials.frx":001C
Tab(1).ControlEnabled= 0 'False
Tab(1).Control(0)= "Frame2"
Tab(1).Control(1)= "Frame1"
Tab(1).Control(2)= "cmdCustom"
Tab(1).Control(3)= "cboMembranes"
Tab(1).Control(4)= "Label2"
Tab(1).ControlCount= 5
TabCaption(2) = "Cables"
TabPicture(2) = "frmMaterials.frx":0038
Tab(2).ControlEnabled= 0 'False
Tab(2).Control(0)= "Text5"
Tab(2).Control(1)= "txtCabEM"
Tab(2).Control(2)= "txtCABPrestress"
Tab(2).Control(3)= "txtCabCAP"
Tab(2).Control(4)= "Label30"
Tab(2).Control(5)= "Label29"
Tab(2).Control(6)= "Label28"
Tab(2).Control(7)= "Label27"
141
Tab(2).Control(8)= "txtCabArea"
Tab(2).Control(9)= "Label14"
Tab(2).Control(10)= "Label13"
Tab(2).Control(11)= "Label12"
Tab(2).ControlCount= 12
TabCaption(3) = "Struts"
TabPicture(3) = "frmMaterials.frx":0054
Tab(3).ControlEnabled= 0 'False
Tab(3).Control(0)= "txtStrutArea"
Tab(3).Control(1)= "txtStrutEM"
Tab(3).Control(2)= "txtStrutCAP"
Tab(3).Control(3)= "Label33"
Tab(3).Control(4)= "Label32"
Tab(3).Control(5)= "Label31"
Tab(3).Control(6)= "Label17"
Tab(3).Control(7)= "Label16"
Tab(3).Control(8)= "Label15"
Tab(3).ControlCount= 9
Begin MSComDlg.CommonDialog CommonDialog1
Left = 5160
Top = 2880
_ExtentX = 847
_ExtentY = 847
_Version = 393216
End
Begin VB.TextBox txtStrutArea
Height = 375
Left = -71400
TabIndex = 38
Text = "6"
Top = 2040
Width = 1575
End
Begin VB.TextBox txtStrutEM
Height = 375
Left = -71400
TabIndex = 37
Text = "29000"
Top = 1560
Width = 1575
End
Begin VB.TextBox txtStrutCAP
Height = 375
Left = -71400
TabIndex = 36
Text = "0"
Top = 1080
142
Width = 1575
End
Begin VB.TextBox Text5
Height = 375
Left = -71400
TabIndex = 31
Text = "0.3"
Top = 2520
Width = 1575
End
Begin VB.TextBox txtCabEM
Height = 375
Left = -71400
TabIndex = 30
Text = "16000"
Top = 2040
Width = 1575
End
Begin VB.TextBox txtCABPrestress
Height = 375
Left = -71400
TabIndex = 29
Text = "0"
Top = 1560
Width = 1575
End
Begin VB.TextBox txtCabCAP
Height = 375
Left = -71400
TabIndex = 28
Text = "23000"
Top = 1080
Width = 1575
End
Begin VB.Frame Frame2
Caption = "FILL"
BeginProperty Font
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Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
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EndProperty
Height = 2295
Left = -71520
143
TabIndex = 8
Top = 1320
Width = 3135
Begin VB.TextBox txtFillEM
Height = 285
Left = 1680
TabIndex = 17
Top = 1440
Width = 735
End
Begin VB.TextBox txtFillPrestress
Height = 285
Left = 1680
TabIndex = 16
Top = 1080
Width = 735
End
Begin VB.TextBox txtFillCAP
Height = 285
Left = 1680
TabIndex = 15
Top = 720
Width = 735
End
Begin VB.TextBox txtFillSTS
Height = 285
Left = 1680
TabIndex = 14
Top = 360
Width = 735
End
Begin VB.Label Label26
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 50
Top = 1440
Width = 375
End
Begin VB.Label Label25
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 49
Top = 1080
Width = 375
End
144
Begin VB.Label Label24
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 48
Top = 720
Width = 375
End
Begin VB.Label Label23
Caption = "lb/in"
Height = 255
Left = 2520
TabIndex = 47
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Width = 375
End
Begin VB.Label Label11
Caption = "Elastic Modulus"
Height = 255
Left = 120
TabIndex = 26
Top = 1440
Width = 1215
End
Begin VB.Label Label10
Caption = "Pre-Stress"
Height = 255
Left = 120
TabIndex = 25
Top = 1080
Width = 1215
End
Begin VB.Label Label9
Caption = "Capacity"
Height = 255
Left = 120
TabIndex = 24
Top = 720
Width = 1095
End
Begin VB.Label Label8
Caption = "Strip Tensile Strength"
Height = 255
Left = 120
TabIndex = 23
Top = 360
Width = 1695
145
End
End
Begin VB.Frame Frame1
Caption = "WARP"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 2295
Left = -74760
TabIndex = 7
Top = 1320
Width = 3135
Begin VB.TextBox txtWarpWidth
Height = 285
Left = 1680
TabIndex = 13
Top = 1800
Width = 735
End
Begin VB.TextBox txtWarpEM
Height = 285
Left = 1680
TabIndex = 12
Top = 1440
Width = 735
End
Begin VB.TextBox txtWarpPrestress
Height = 285
Left = 1680
TabIndex = 11
Top = 1080
Width = 735
End
Begin VB.TextBox txtWarpCAP
Height = 285
Left = 1680
TabIndex = 10
Top = 720
Width = 735
End
Begin VB.TextBox txtWarpSTS
146
Height = 285
Left = 1680
TabIndex = 9
Top = 360
Width = 735
End
Begin VB.Label Label22
Caption = "in"
Height = 255
Left = 2520
TabIndex = 46
Top = 1800
Width = 255
End
Begin VB.Label Label21
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 45
Top = 1440
Width = 255
End
Begin VB.Label Label20
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 44
Top = 1080
Width = 375
End
Begin VB.Label Label19
Caption = "pli"
Height = 255
Left = 2520
TabIndex = 43
Top = 720
Width = 375
End
Begin VB.Label Label18
Caption = "lb/in"
Height = 255
Left = 2520
TabIndex = 42
Top = 360
Width = 375
End
Begin VB.Label Label7
147
Caption = "Usable Roll Width"
Height = 375
Left = 120
TabIndex = 22
Top = 1800
Width = 1335
End
Begin VB.Label Label6
Caption = "Elastic Modulus"
Height = 255
Left = 120
TabIndex = 21
Top = 1440
Width = 1335
End
Begin VB.Label Label5
Caption = "Pre-Stress"
Height = 255
Left = 120
TabIndex = 20
Top = 1080
Width = 1095
End
Begin VB.Label Label4
Caption = "Capacity"
Height = 255
Left = 120
TabIndex = 19
Top = 720
Width = 1335
End
Begin VB.Label Label3
Caption = "Strip Tensile Strength"
Height = 255
Left = 120
TabIndex = 18
Top = 360
Width = 1695
End
End
Begin VB.CommandButton cmdCustom
Caption = "CUSTOM"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
148
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = -70200
TabIndex = 6
Top = 720
Width = 1335
End
Begin VB.ComboBox cboMembranes
Height = 315
ItemData = "frmMaterials.frx":0070
Left = -73080
List = "frmMaterials.frx":0083
TabIndex = 5
Text = "Select Membrane Material"
Top = 720
Width = 2535
End
Begin VB.CommandButton cmdBrowse
Caption = "BROWSE"
Height = 375
Left = 5160
TabIndex = 3
Top = 1800
Width = 855
End
Begin VB.TextBox Text1
Height = 375
Left = 2400
TabIndex = 2
Top = 1800
Width = 2415
End
Begin VB.Label Label33
Caption = "sq in"
Height = 375
Left = -69600
TabIndex = 57
Top = 2040
Width = 375
End
Begin VB.Label Label32
Caption = "psi"
Height = 375
Left = -69600
149
TabIndex = 56
Top = 1560
Width = 495
End
Begin VB.Label Label31
Caption = "lb/in"
Height = 375
Left = -69600
TabIndex = 55
Top = 1080
Width = 495
End
Begin VB.Label Label30
Caption = "sq in"
Height = 255
Left = -69720
TabIndex = 54
Top = 2640
Width = 495
End
Begin VB.Label Label29
Caption = "psi"
Height = 375
Left = -69720
TabIndex = 53
Top = 2160
Width = 375
End
Begin VB.Label Label28
Caption = "lb/in"
Height = 375
Left = -69720
TabIndex = 52
Top = 1680
Width = 495
End
Begin VB.Label Label27
Caption = "lb/in"
Height = 375
Left = -69720
TabIndex = 51
Top = 1200
Width = 495
End
Begin VB.Label Label17
Caption = "Area of Cross Section"
Height = 375
150
Left = -73320
TabIndex = 41
Top = 2160
Width = 1815
End
Begin VB.Label Label16
Caption = "Elastic Modulus"
Height = 375
Left = -73320
TabIndex = 40
Top = 1680
Width = 1575
End
Begin VB.Label Label15
Caption = "Capacity"
Height = 375
Left = -73320
TabIndex = 39
Top = 1200
Width = 1935
End
Begin VB.Label txtCabArea
Caption = "Area of Cross Section"
Height = 375
Left = -73320
TabIndex = 35
Top = 2640
Width = 1815
End
Begin VB.Label Label14
Caption = "Elastic Modulus"
Height = 375
Left = -73320
TabIndex = 34
Top = 2160
Width = 1575
End
Begin VB.Label Label13
Caption = "Pre-Stress"
Height = 375
Left = -73320
TabIndex = 33
Top = 1680
Width = 1695
End
Begin VB.Label Label12
Caption = "Capacity"
151
Height = 375
Left = -73320
TabIndex = 32
Top = 1200
Width = 1935
End
Begin VB.Label Label2
Caption = "Membrane Type"
Height = 255
Left = -74640
TabIndex = 4
Top = 720
Width = 1335
End
Begin VB.Label Label1
Caption = "Specify File To Import"
Height = 375
Left = 600
TabIndex = 1
Top = 1800
Width = 1935
End
End
Begin VB.Menu mnuFile
Caption = "File"
Begin VB.Menu mnuFileOpen
Caption = "Open"
End
Begin VB.Menu mnuFileSave
Caption = "Save"
End
Begin VB.Menu mnuFileSaveAs
Caption = "Save As"
End
Begin VB.Menu mnuFileBar
Caption = "-"
End
Begin VB.Menu mnuFileExit
Caption = "Exit"
End
End
Begin VB.Menu mnuWindow
Caption = "Window"
Begin VB.Menu mnuWinUnloaded
Caption = "Unloaded Form"
End
Begin VB.Menu mnuWinLoads
152
Caption = "Loads"
End
Begin VB.Menu mnuWinResults
Caption = "Results"
Enabled = 0 'False
End
End
Begin VB.Menu mnuHelp
Caption = "Help"
Begin VB.Menu mnuHelpContents
Caption = "Contents"
End
Begin VB.Menu mnuHelpBar
Caption = "-"
End
Begin VB.Menu mnuHelpAbout
Caption = "About"
End
End
End
Attribute VB_Name = "frmMaterials"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub cboMembranes_Click()
If cboMembranes.Text = "PVC Coated Polyester" Then
txtWarpSTS.Text = 440
txtFillSTS.Text = 435
txtWarpCAP.Text = 110
txtFillCAP.Text = 108.75
txtWarpPrestress.Text = 36.6
txtFillPrestress.Text = 36.2
txtWarpEM.Text = 4000
txtFillEM.Text = 6000
txtWarpWidth.Text = 70
End If
If cboMembranes.Text = "Expanded PTFE" Then
txtWarpSTS.Text = 510
txtFillSTS.Text = 510
txtWarpCAP.Text = 127.5
txtFillCAP.Text = 127.5
txtWarpPrestress.Text = 42.5
txtFillPrestress.Text = 42.5
txtWarpEM.Text = 4000
153
txtFillEM.Text = 6000
txtWarpWidth.Text = 71
End If
If cboMembranes.Text = "PTFE Coated Fiberglass" Then
txtWarpSTS.Text = 640
txtFillSTS.Text = 640
txtWarpCAP.Text = 160
txtFillCAP.Text = 160
txtWarpPrestress.Text = 54
txtFillPrestress.Text = 54
txtWarpEM.Text = 4000
txtFillEM.Text = 6000
txtWarpWidth.Text = 150
End If
If cboMembranes.Text = "Silicone Coated Fiberglass" Then
txtWarpSTS.Text = 610
txtFillSTS.Text = 600
txtWarpCAP.Text = 152.5
txtFillCAP.Text = 150
txtWarpPrestress.Text = 51
txtFillPrestress.Text = 50
txtWarpEM.Text = 4000
txtFillEM.Text = 6000
txtWarpWidth.Text = 60
End If
If cboMembranes.Text = "HDPE, LDPE Coated" Then
txtWarpSTS.Text = 275
txtFillSTS.Text = 255
txtWarpCAP.Text = 68.75
txtFillCAP.Text = 63.75
txtWarpPrestress.Text = 23
txtFillPrestress.Text = 21.25
txtWarpEM.Text = 4000
txtFillEM.Text = 6000
txtWarpWidth.Text = 144
End If
End Sub
Private Sub cmdBrowse_Click()
CommonDialog1.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog1.FilterIndex = 1
CommonDialog1.ShowOpen
If CommonDialog1.FileName <> "" Then
Open CommonDialog1.FileName For Input As #1
file = Input(LOF(1), #1)
154
Close #1
End If
filetoopen.Text = file
filetoopen.SetFocus
End Sub
Private Sub cmdMaterialsCONTINUE_Click()
Unload frmMaterials
Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
Private Sub mnuFileExit_Click()
Unload Me
End Sub
Private Sub mnuFileOpen_Click()
CommonDialog2.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog2.FilterIndex = 1
CommonDialog2.ShowOpen
If CommonDialog2.FileName <> "" Then
Open CommonDialog2.FileName For Input As #1
file = Input(LOF(1), #1)
Close #1
End If
filetoopen.Text = file
filetoopen.SetFocus
End Sub
Private Sub mnuFileSaveAs_Click()
Dim WhatFile As String
CommonDialog2.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog2.FilterIndex = 1
CommonDialog2.ShowSave
WhatFile = CommonDialog2.FileName
End Sub
Private Sub mnuWinLoads_Click()
Unload frmMaterials
Load frmLoads
frmLoads.Show
End Sub
Private Sub mnuWinUnloaded_Click()
Unload frmMaterials
155
Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
Option Base 1
Private Type StrutDatascapacity As Singlesprest As
Singlesemod As Singlesarea As Single
End Type
Private Type CableDataccapacity As Singlecprest As
Singlecemod As Singlecarea As Single
End Type
Private Type MembraneDatamemname As Stringstenswarp As
Singlestensfill As Singlecapacityw As Singlecapacityf
As Singleprestwarp As Singleprestfill As Singleemodwarp As
Singleemodfill As Singlewidthwarp As Single
End Type
Dim limit As IntegerDim mem(50) As MembraneData 'defines
membrane arrayDim cab(50) As CableData ' defines cable
arrayDim str(50) As StrutData 'defines strut array
Private Sub browse_Click()CommonDialog.ShowOpen
End Sub
Private Sub cablenew_Click()cabcap.Text = ""cabpstr =
""ecab = "" areacab = ""
limit = limit + 1
End Sub
Private Sub cableok_Click()
cab(limit).ccapacity = cabcap.Textcab(limit).cprest =
cabpstr.Textcab(limit).cemod =
ecab.Textcab(limit).carea = areacab.Text
End Sub
Private Sub continue_Click()mprops.Unloaddxffile.Load
End Sub
'clears all fields for user entry
Private Sub custom_Click()memTypes.Text = ""stswarp.Text =
""stsfill.Text = "" capwarp.Text = ""capfill.Text
= ""pstrwarp.Text = ""pstrfill.Text = ""Ewarp.Text =
""Efill.Text = "" dwarp.Text = ""
limit = limit + 1
End Sub
Private Sub Form_Load()Dim strdata As StringDim numdata As
Singlefile = "C:\data.txt" limit = 0 'reads from
array to load the form
Open file For Input As #1While Not EOF(1)
limit = limit + 1 Input #1, strdatamem(limit).memname =
156
strdataInput #1, numdatamem(limit).stenswarp =
numdataInput #1, numdatamem(limit).stensfill = numdataInput
#1, numdatamem(limit).capacityw = numdataInput
#1, numdatamem(limit).capacityf = numdataInput #1,
numdatamem(limit).prestwarp = numdataInput #1,
numdatamem(limit).prestfill = numdataInput #1,
numdatamem(limit).emodwarp = numdataInput #1,
numdatamem(limit).emodfill = numdataInput #1,
numdatamem(limit).widthwarp = numdata
Wend Close
For i = 1 To limit memTypes.AddItem mem(i).memnameNext i
'populates combobox
End Sub
Private Sub Form_Unload(Cancel As Integer)file =
"C:\data.txt" Open file For Output As #1For j = 1 To limit
Print #1, mem(j).memname; ","; mem(j).stenswarp; ",";
mem(j).stensfill; ","; mem(j).capacityw; ",";
mem(j).capacityf; ","; mem(j).prestwarp; ",";
mem(j).prestfill; ","; mem(j).emodwarp; ",";
mem(j).emodfill;
","; mem(j).widthwarp
Next jClose 'stores user data in txt file
filecable = "c:\cable.txt" Open filecable For Output As
#2For k = 1 To limit
Print #2, cab(k).ccapacity; ","; cab(k).cprest; ",";
cab(k).cemod; ","; cab(k).careaNext k Close 'stores cable
data in txt file
filestrut = "C:\strut.txt" Open filestrut For Output As
#3For l = 1 To limit Print #3, str(l).scapacity; ",";
str(l).sprest; ","; str(l).semod; ","; str(l).sareaNext l
Close 'stores strut data in txt file
End Sub
Private Sub memTypes_Click()choice =
memTypes.ListIndexchoice = choice + 1 stswarp.Text =
mem(choice).stenswarpstsfill.Text =
mem(choice).stensfillcapwarp.Text =
mem(choice).capacitywcapfill.Text =
mem(choice).capacityfpstrwarp.Text =
mem(choice).prestwarppstrfill.Text =
mem(choice).prestfillEwarp.Text =
mem(choice).emodwarpEfill.Text =
mem(choice).emodfilldwarp.Text = mem(choice).widthwarp
'reads from text file to fill out boxes when the membrane
type is changed
End Sub
Private Sub mprops_DblClick()
End Sub
157
Private Sub okmem_Click()mem(limit).memname =
memTypes.Textmem(limit).stenswarp =
stswarp.Textmem(limit).stensfill =
stsfill.Textmem(limit).capacityw =
capwarp.Textmem(limit).capacityf =
capfill.Textmem(limit).prestwarp =
pstrwarp.Textmem(limit).prestfill =
pstrfill.Textmem(limit).emodwarp =
Ewarp.Textmem(limit).emodfill =
Efill.Textmem(limit).widthwarp = dwarp.Text
memTypes.AddItem mem(limit).memname
'assigns variable names to the numbers that the user fills
inEnd Sub
Private Sub okstrut_Click()str(limit).scapacity =
strcap.Textstr(limit).sprest =
strpstr.Textstr(limit).semod = estr.Textstr(limit).sarea =
areastr.TextEnd Sub
Private Sub strutsnew_Click()strcap.Text = ""strpstr.Text =
""
estr.Text = "" areastr = "" limit = limit + 1 End Sub
frmMaterials - 1
Private Sub cboMembranes_Click()
If cboMembranes.Text = "PVC Coated
Polyester" ThentxtWarpSTS.Text =
440txtFillSTS.Text = 435
txtWarpCAP.Text = 110txtFillCAP.Text
= 108.75 txtWarpPrestress.Text =
36.6txtFillPrestress.Text = 36.2
txtWarpEM.Text = 4000txtFillEM.Text =
6000 txtWarpWidth.Text = 70
End If
If cboMembranes.Text = "Expanded PTFE"
ThentxtWarpSTS.Text =
510txtFillSTS.Text = 510
txtWarpCAP.Text =
127.5txtFillCAP.Text = 127.5
txtWarpPrestress.Text =
42.5txtFillPrestress.Text = 42.5
txtWarpEM.Text = 4000txtFillEM.Text =
6000 txtWarpWidth.Text = 71End If
If cboMembranes.Text = "PTFE Coated
Fiberglass" ThentxtWarpSTS.Text =
640txtFillSTS.Text = 640
txtWarpCAP.Text = 160txtFillCAP.Text
= 160 txtWarpPrestress.Text =
158
54txtFillPrestress.Text = 54
txtWarpEM.Text = 4000txtFillEM.Text =
6000 txtWarpWidth.Text = 150End If If
cboMembranes.Text = "Silicone Coated
Fiberglass" ThentxtWarpSTS.Text =
610txtFillSTS.Text = 600
txtWarpCAP.Text =
152.5txtFillCAP.Text = 150
txtWarpPrestress.Text =
51txtFillPrestress.Text = 50
txtWarpEM.Text = 4000txtFillEM.Text =
6000 txtWarpWidth.Text = 60End If
If cboMembranes.Text = "HDPE, LDPE
Coated" ThentxtWarpSTS.Text =
275txtFillSTS.Text = 255
txtWarpCAP.Text =
68.75txtFillCAP.Text = 63.75
txtWarpPrestress.Text =
23txtFillPrestress.Text = 21.25
txtWarpEM.Text = 4000txtFillEM.Text =
6000 txtWarpWidth.Text = 144End If End
Sub
Private Sub
cmdBrowse_Click()CommonDialog1.Filte
r = "DXF
Files(*.dxf)|*.dxf"CommonDialog1.Fil
terIndex = 1CommonDialog1.ShowOpenIf
CommonDialog1.FileName <> "" Then
Open CommonDialog1.FileName For Input
As #1file = Input(LOF(1), #1)Close #1
End If
frmMaterials - 2
filetoopen.Text =
filefiletoopen.SetFocusEnd Sub
Private Sub
cmdMaterialsCONTINUE_Click()Unload
frmMaterials Load frmDXFunloaded
frmDXFunloaded.Show End Sub
Private Sub mnuFileExit_Click()Unload
Me
End Sub
Private Sub
mnuFileOpen_Click()CommonDialog2.Fil
ter = "DXF
Files(*.dxf)|*.dxf"CommonDialog2.Fil
terIndex = 1CommonDialog2.ShowOpenIf
CommonDialog2.FileName <> "" Then
159
Open CommonDialog2.FileName For Input
As #1file = Input(LOF(1), #1)Close #1
End If
filetoopen.Text =
filefiletoopen.SetFocusEnd Sub
Private Sub mnuFileSaveAs_Click()Dim
WhatFile As
StringCommonDialog2.Filter = "DXF
Files(*.dxf)|*.dxf"CommonDialog2.Fil
terIndex =
1CommonDialog2.ShowSaveWhatFile =
CommonDialog2.FileNameEnd Sub
Private Sub mnuWinLoads_Click()Unload
frmMaterials Load frmLoads
frmLoads.Show
End Sub
Private Sub
mnuWinUnloaded_Click()Unload
frmMaterials Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
VERSION 5.00
Object = "{F9043C88-F6F2-101A-A3C9-08002B2F49FB}#1.2#0";
"comdlg32.ocx"
Begin VB.Form frmDXFunloaded
Caption = "FormFinder"
ClientHeight = 5370
ClientLeft = 60
ClientTop = 2115
ClientWidth = 7080
LinkTopic = "Form1"
ScaleHeight = 5370
ScaleWidth = 7080
StartUpPosition = 2 'CenterScreen
Begin MSComDlg.CommonDialog CommonDialog1
Left = 720
Top = 4680
_ExtentX = 847
_ExtentY = 847
_Version = 393216
End
Begin VB.CommandButton cmdDXFchangepars
Caption = "CHANGE PARAMETERS"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
160
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 2880
TabIndex = 2
Top = 4800
Width = 2295
End
Begin VB.PictureBox Picture1
BackColor = &H00404040&
Height = 4215
Left = 240
ScaleHeight = 4155
ScaleWidth = 6435
TabIndex = 1
Top = 360
Width = 6495
End
Begin VB.CommandButton cmdDisplayDXFcontinue
Caption = "CONTINUE"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 5400
TabIndex = 0
Top = 4800
Width = 1215
End
Begin VB.Menu mnuFile
Caption = "File"
Begin VB.Menu mnuFileOpen
Caption = "Open"
Enabled = 0 'False
End
Begin VB.Menu mnuFileSave
Caption = "Save"
161
End
Begin VB.Menu mnuFileSaveAs
Caption = "Save As"
End
Begin VB.Menu mnuFileBar
Caption = "-"
End
Begin VB.Menu mnuFileExit
Caption = "Exit"
End
End
Begin VB.Menu mnuWindow
Caption = "Window"
Begin VB.Menu mnuWinMaterials
Caption = "Material Properties"
End
Begin VB.Menu mnuWinLoads
Caption = "Loads"
End
Begin VB.Menu mnuWinResults
Caption = "Results"
Enabled = 0 'False
End
End
162
Caption = "Help"
Begin VB.Menu mnuHelp
Begin VB.Menu mnuHelpContents
Caption = "Contents"
End
Begin VB.Menu mnuHelpBar
Caption = "-"
End
Begin VB.Menu mnuHelpAbout
Caption = "About"
End
End
End
Attribute VB_Name = "frmDXFunloaded"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub cmdDisplayDXFcontinue_Click()
Unload frmDXFunloaded
Load frmLoads
frmLoads.Show
End Sub
Private Sub cmdDXFchangepars_Click()
Unload frmDXFunloaded
Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuFileExit_Click()
Unload Me
End Sub
Private Sub mnuFileSaveAs_Click()
Dim WhatFile As String
CommonDialog1.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog1.FilterIndex = 1
CommonDialog1.ShowSave
WhatFile = CommonDialogue1.FileName
End Sub
Private Sub mnuWinLoads_Click()
Unload frmDXFunloaded
Load frmLoads
frmLoads.Show
End Sub
Private Sub mnuWinMaterials_Click()
Unload frmDXFunloaded
Load frmMaterials
frmMaterials.Show
End Sub
frmDXFunloaded - 1
Private Sub
cmdDisplayDXFcontinue_Click()Unload
frmDXFunloaded Load frmLoads
frmLoads.Show End Sub
Private Sub
cmdDXFchangepars_Click()Unload
frmDXFunloaded Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuFileExit_Click()Unload
Me
163
End Sub
Private Sub mnuFileSaveAs_Click()Dim
WhatFile As
StringCommonDialog1.Filter = "DXF
Files(*.dxf)|*.dxf"CommonDialog1.Fil
terIndex =
1CommonDialog1.ShowSaveWhatFile =
CommonDialogue1.FileNameEnd Sub
Private Sub mnuWinLoads_Click()Unload
frmDXFunloaded Load frmLoads
frmLoads.Show
End Sub
Private Sub
mnuWinMaterials_Click()Unload
frmDXFunloaded Load frmMaterials
frmMaterials.Show
End Sub
VERSION 5.00
Object = "{F9043C88-F6F2-101A-A3C9-08002B2F49FB}#1.2#0";
"comdlg32.ocx"
Begin VB.Form frmLoads
Caption = "FormFinder"
ClientHeight = 5370
ClientLeft = 60
ClientTop = 2115
ClientWidth = 7080
LinkTopic = "Form1"
ScaleHeight = 5370
ScaleWidth = 7080
StartUpPosition = 2 'CenterScreen
Begin MSComDlg.CommonDialog CommonDialog1
Left = 5880
Top = 4200
_ExtentX = 847
_ExtentY = 847
_Version = 393216
End
Begin VB.CommandButton cmdLoadChangepars
Caption = "CHANGE PARAMETERS"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
164
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 2880
TabIndex = 16
Top = 4800
Width = 2295
End
Begin VB.CommandButton cmdLoadscontinue
Caption = "CONTINUE"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 5400
TabIndex = 15
Top = 4800
Width = 1215
End
Begin VB.Frame Frame2
Caption = "Wind Loads"
Height = 1695
Left = 240
TabIndex = 1
Top = 2880
Width = 4455
Begin VB.TextBox txtWindspeed
Height = 285
Left = 2040
TabIndex = 6
Top = 960
Width = 975
End
Begin VB.TextBox txtWinduplift
Height = 285
Left = 2040
TabIndex = 5
Top = 360
Width = 975
End
Begin VB.Label Label9
165
Caption = "mph"
Height = 375
Left = 3120
TabIndex = 14
Top = 960
Width = 375
End
Begin VB.Label Label8
Caption = "psf"
Height = 255
Left = 3120
TabIndex = 13
Top = 360
Width = 375
End
Begin VB.Label Label5
Caption = "Wind Speed"
Height = 255
Left = 720
TabIndex = 10
Top = 960
Width = 975
End
Begin VB.Label Label4
Caption = "Wind Uplift"
Height = 255
Left = 720
TabIndex = 9
Top = 480
Width = 975
End
End
Begin VB.Frame Frame1
Caption = "Gravity Loads"
Height = 1815
Left = 240
TabIndex = 0
Top = 840
Width = 4455
Begin VB.TextBox txtLiveload
Height = 285
Left = 2040
TabIndex = 4
Top = 1080
Width = 975
End
Begin VB.TextBox txtDeadload
166
Height = 285
Left = 2040
TabIndex = 3
Top = 600
Width = 975
End
Begin VB.Label Label7
Caption = "psf"
Height = 255
Left = 3120
TabIndex = 12
Top = 1080
Width = 495
End
Begin VB.Label Label6
Caption = "psf"
Height = 375
Left = 3120
TabIndex = 11
Top = 600
Width = 375
End
Begin VB.Label Label3
Caption = "Live Load"
Height = 255
Left = 720
TabIndex = 8
Top = 1200
Width = 975
End
Begin VB.Label Label2
Caption = "Dead Load"
Height = 375
Left = 720
TabIndex = 7
Top = 600
Width = 1095
End
End
Begin VB.Label Label1
Caption = "LOADING"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
167
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 255
Left = 240
TabIndex = 2
Top = 360
Width = 1455
End
Begin VB.Menu mnuFile
Caption = "File"
Begin VB.Menu mnuFileOpen
Caption = "Open"
Enabled = 0 'False
End
Begin VB.Menu mnuFileSave
Caption = "Save"
End
Begin VB.Menu mnuFileSaveAs
Caption = "Save As"
End
Begin VB.Menu mnuFileBar
Caption = "-"
End
Begin VB.Menu mnuFileExit
Caption = "Exit"
End
End
Begin VB.Menu mnuWindow
Caption = "Window"
Begin VB.Menu mnuWinMaterials
Caption = "Material Properties"
End
Begin VB.Menu mnuWinUnloaded
Caption = "Unloaded Form"
End
Begin VB.Menu mnuWinResults
Caption = "Results"
End
End
Begin VB.Menu mnuHelp
Caption = "Help"
Begin VB.Menu mnuHelpContents
Caption = "Contents"
End
Begin VB.Menu mnuHelpBar
Caption = "-"
168
End
Begin VB.Menu mnuHelpAbout
Caption = "About"
End
End
End
Attribute VB_Name = "frmLoads"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub cmdLoadChangepars_Click()
Unload frmLoads
Load frmMaterials
frmMaterials.Show
End Sub
Private Sub cmdLoadscontinue_Click()
Unload frmLoads
Load frmResult
frmResult.Show
End Sub
Private Sub mnuFileExit_Click()
Unload Me
End Sub
Private Sub mnuFileSaveAs_Click()
Dim WhatFile As String
CommonDialog1.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog1.FilterIndex = 1
CommonDialog1.ShowSave
WhatFile = CommonDialogue1.FileName
End Sub
Private Sub mnuWinMaterials_Click()
Unload frmLoads
Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuWinResults_Click()
169
Unload frmLoads
Load frmResult
frmResult.Show
End Sub
Private Sub mnuWinUnloaded_Click()
Unload frmLoads
Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
frmLoads - 1
Private Sub cmdLoadChangepars_Click()Unload frmLoads Load
frmMaterials frmMaterials.Show
End Sub
Private Sub cmdLoadscontinue_Click()Unload frmLoads Load
frmResult frmResult.Show
End Sub
Private Sub mnuFileExit_Click()Unload Me
End Sub
Private Sub mnuFileSaveAs_Click()Dim WhatFile As
StringCommonDialog1.Filter = "DXF
Files(*.dxf)|*.dxf"CommonDialog1.FilterIndex =
1CommonDialog1.ShowSaveWhatFile = CommonDialogue1.FileName
End Sub
Private Sub mnuWinMaterials_Click()Unload frmLoads Load
frmMaterials frmMaterials.Show
End Sub
Private Sub mnuWinResults_Click()Unload frmLoads Load
frmResult frmResult.Show
End Sub
Private Sub mnuWinUnloaded_Click()Unload frmLoads Load
frmDXFunloaded frmDXFunloaded.Show
End Sub
VERSION 5.00
Object = "{F9043C88-F6F2-101A-A3C9-08002B2F49FB}#1.2#0";
"comdlg32.ocx"
Begin VB.Form frmResult
Caption = "FormFinder"
ClientHeight = 5370
ClientLeft = 60
ClientTop = 2115
ClientWidth = 7080
LinkTopic = "Form1"
170
ScaleHeight = 5370
ScaleWidth = 7080
StartUpPosition = 2 'CenterScreen
Begin MSComDlg.CommonDialog CommonDialog1
Left = 1800
Top = 4800
_ExtentX = 847
_ExtentY = 847
_Version = 393216
End
Begin VB.CommandButton cmdResultChangepars
Caption = "CHANGE PARAMETERS"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 2880
TabIndex = 2
Top = 4800
Width = 2295
End
Begin VB.CommandButton cmdExit
Caption = "EXIT"
BeginProperty Font
Name = "MS Sans Serif"
Size = 8.25
Charset = 0
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height = 375
Left = 5400
TabIndex = 1
Top = 4800
Width = 1215
End
Begin VB.PictureBox Picture1
BackColor = &H00404040&
Height = 4215
171
Left = 240
ScaleHeight = 4155
ScaleWidth = 6435
TabIndex = 0
Top = 360
Width = 6495
End
Begin VB.Menu mnuFile
Caption = "File"
Begin VB.Menu mnuFileOpen
Caption = "Open"
Enabled = 0 'False
End
Begin VB.Menu mnuFileSave
Caption = "Save"
End
Begin VB.Menu mnuFileSaveAs
Caption = "Save As"
End
Begin VB.Menu mnuFileBar
Caption = "-"
End
Begin VB.Menu mnuFileExit
Caption = "Exit"
End
End
Begin VB.Menu mnuWindow
Caption = "Window"
Begin VB.Menu mnuWinMaterials
Caption = "Material Properties"
End
Begin VB.Menu mnuWinUnloaded
Caption = "Unloaded Form"
End
Begin VB.Menu mnuWinLoads
Caption = "Loads"
End
End
Begin VB.Menu mnuHelp
Caption = "Help"
Begin VB.Menu mnuHelpContents
Caption = "Contents"
End
Begin VB.Menu mnuHelpBar
Caption = "-"
End
Begin VB.Menu mnuHelpAbout
172
Caption = "About"
End
End
End
Attribute VB_Name = "frmResult"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Private Sub cmdExit_Click()
Unload Me
End Sub
Private Sub cmdResultChangepars_Click()
Unload frmResult
Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuFileExit_Click()
Unload Me
End Sub
Private Sub mnuFileSaveAs_Click()
Dim WhatFile As String
CommonDialog1.Filter = "DXF Files(*.dxf)|*.dxf"
CommonDialog1.FilterIndex = 1
CommonDialog1.ShowSave
WhatFile = CommonDialogue1.FileName
End Sub
Private Sub mnuWinLoads_Click()
Unload frmResult
Load frmLoads
frmLoads.Show
End Sub
Private Sub mnuWinMaterials_Click()
Unload frmResult
Load frmMaterials
173
frmMaterials.Show
End Sub
Private Sub mnuWinUnloaded_Click()
Unload frmResult
Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
frmResult - 1
Private Sub cmdExit_Click()Unload Me
End Sub
Private Sub
cmdResultChangepars_Click()Unload
frmResult Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuFileExit_Click()Unload Me
End Sub
Private Sub mnuFileSaveAs_Click()Dim
WhatFile As String
CommonDialog1.Filter = "DXF
Files(*.dxf)|*.dxf"CommonDialog1.FilterInd
ex = 1CommonDialog1.ShowSaveWhatFile =
CommonDialogue1.FileName
End Sub
Private Sub mnuWinLoads_Click()Unload
frmResult Load frmLoads frmLoads.Show
End Sub
Private Sub mnuWinMaterials_Click()Unload
frmResult Load frmMaterials
frmMaterials.Show
End Sub
Private Sub mnuWinUnloaded_Click()Unload
frmResult Load frmDXFunloaded
frmDXFunloaded.Show
End Sub
174
Abstract (if available)
Abstract
Lightweight structures have complex forms and are difficult to visualize and translate into two-dimensional drawings. The stability and stiffness of such structures depends on the desired boundaries and internal tension. Their precise shape depends on various factors such as the material used and its properties, its pretension, curvature, and modulus of elasticity.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Rodrigues, Kavita
(author)
Core Title
The form finding of tensile membranes - a tool for architects and designers
School
School of Architecture
Degree
Master of Building Science
Degree Program
Building Science
Publication Date
07/30/2008
Defense Date
04/01/2004
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
form finding,OAI-PMH Harvest,tensile membranes
Language
English
Advisor
Schierle, G. Goetz (
committee chair
), Kensek, Karen (
committee member
), Noble, Douglas (
committee member
)
Creator Email
kavitar@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1453
Unique identifier
UC184550
Identifier
etd-Rodrigues-20080730 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-98623 (legacy record id),usctheses-m1453 (legacy record id)
Legacy Identifier
etd-Rodrigues-20080730.pdf
Dmrecord
98623
Document Type
Thesis
Rights
Rodrigues, Kavita
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
form finding
tensile membranes