form finding of tensile membranes

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The Form Finding of Tensile Membranes: A Computer Tool for Archi tects and Designers

Kavita RodriguesJune 15, 2008

Thesis Committee:

G. Goetz Schierle, FAIA, Ph.D (Chair)Douglas Noble, FAIA, Ph.D

Karen Kensek

A well designed tensile structure is among the purest expressions of structure and materials. Every

part of these structures is present by necessity – what you see is the essence of the structure. 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.

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?

Thus 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)

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.

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.

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 (See Fig 1.01) created by Graduate Building Science Students at USC (Photo: DouglasNoble c.2007)

Program Description

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

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.

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 ofcalculations 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.

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.

The form finding tool created has an easy to understand and easy to use graphic interface. The

program is easy to learn. The information that is required to be input is 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 is reasonably accurate. It is not a complex tool, but sufficiently

accurate to demonstrate the initial design idea. The results that the tool produces are a simple graphic

representation of the geometry of the tensile membrane, and a representation of its deflection under

loading. It displays the load values used in the calculations to facilitate understanding the design of tensile

membrane structures. It is a learning tool, aimed at aiding in the conceptual design of tensile membrane

structures.

InputTypically 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.

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.

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.

The variables for the desired materials are supplied as follows:

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.

Fig. 5.02a Steel Strand Fig 5.02bWire 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

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.

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 Screens

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.

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.

Fig. 5.04 Display Screen

Structural Analysis



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)

Generation of the 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.

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.

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.

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

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.



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



Fig 5.07 Multiple 4-point structures.

Fig 5.08 Repeating Surfaces

form finding of tensile membranes

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