Figure 1. Front View of Fabric Tension Apparatus
NTC Research: Phase 1
Architectural Fabric Structures:
Exploration, Modeling, and Implementation
Alexander Messinger
Csilla Z. Wollner
Christopher Pastore
Goal:
To develop an understanding of the mechanical behavior of nonlinear
anisotropic fabrics under tension and create a spatial vocabulary
and grammar for architectural structures.
Abstract:
In the initial phases of this program, four different experimental structures were assembled, digitized, and visualized, providing both physical and digital models of the systems. The structures combined different architectural configurations as well as different fabrics with different mechanical response. Apparati were designed and fabricated which allow quantitatively variable tension parameters in a consistent manner allowing equitable comparison amongst different fabric structures. Visualization was performed using photographic techniques as well as 3D rendering software.
Introduction
The Master Mason during the Gothic period was well educated in mathematics, geometry and philosophy. He approached stone using these skills and tried to maximize the ability of what the stone could do as an architectural element. He could look at the stone, see the vein, grain, and postulate how to cut the stone, and what its structural function would be within the building. Michelangelo could look at a piece of marble and seemingly defy gravity in work that reveals the inner beauty and maximizes the function of the stone as a sculptural element.
As technology developed, people looked for ways to mass-produce
building elements and created man-made objects, such as bricks
and tiles. These synthetic stones were intended to optimize the
use of the material to create structures greater than were conceived
before using irregular, natural materials. This was allowed because
the level of understanding of the material properties was increased,
and the uniformity and consistency of the materials allowed constructors
with less intimate knowledge of materials create satisfactory
results.
In the 19th Century, Inspired by Gothic cathedrals, Gaudi used
tiles to create composite structures. The way he modeled curvature
as well as the overall behavior of structures was to stretch fabrics
and observe their behavior to model stress flow.
At the turn of the 20th Century, using the technologies developed Gaudi, the Castovino Dome system of laminated composite tiles was first applied in Philadelphia, resulting in the first example in the world with nested domes one dome serving as the flooring for the rotunda contained within the outer dome.
For at least 5,000 years humans have been using membrane structures (skins or fabrics) to define space and create shelter. However membrane structures were not maximized for their performance. This was partly due to the fact that skins are inherently small, and that the materials available to them were not of high tensile strength. Fabrics were primarily used to an outer skin that drapes over a skeleton structure. The skeleton provides most of the structural performance.
The science of tensioned fabric structures was documented and pioneered by Frei Otto starting in 1957. Tension structures use fabrics as the primarily structural element. There is no draping over skeletons, rather the tension built up in the fabric membrane surface defines the space while providing shelter and other structural aspects. The guiding principle behind these structures is the minimal surface principle, such as that displayed by hyperbolic paraboloids (so called "monkey saddle") observed in materials such as soap bubbles and other minimal surface materials.
The study of soap bubbles was significant in the development of this field. Much tension structure follows this metaphor. A limitation of this approach is the inherent assumption that the membrane material is isotropic. Fabrics are not. The result of this is that much of the modeling of complex tension structures is wrong, as demonstrated in dramatic examples such as the Millennium Dome in London, wherein millions of dollars were spent correcting mistakes from analytical models.
To date, modeling in the industry is based on the assumption of isotropic, linear elastic materials. To exploit the potentials of tension structures, it is essential to develop more rigorous and correct models of fabric behavior. Such models allow a comprehensive investigation of the opportunities available. With such models, fabrics can be optimized for particular uses and new architectural forms can be generated.
Providing documentation of how different fabrics generate different forms yields a wide range of benefits:
Manufacturers: More fabric is sold in a wide range of styles
Architect/Engineer: More opportunities for creating 3D space are
available
User: More variety of spaces are available, providing increased
individualization of space
Apparatus
To generate three dimensional fabric forms in a reproducible manner, a device was designed and constructed that is analogous to a hollow cube. The apparatus allows variable vertical and horizontal location of stress points to tension the fabric. A front view of the apparatus is shown in Figure 1.
Support lines are connected to the vertical elements and to the fabric. Additional support lines can be connected to the horizontal plane (see Figure 2) and to the fabric.
Figure 3 shows a fabric structure attached to the apparatus. The tie lines can be seen in this figure.
Fabrics to be tested were cut and marked with a grid corresponding to the apparatus grid (see Figure 4). The grid allows for accurate measurement of individual points in the space. This grid was used for digitization (see below) and for measurements of strain and deflection.
Structures
Two different knit fabrics were used to create the first set of
structures. Each fabric was deployed on a test apparatus in two
different configurations, resulting in four different architectural
structures.
The first set of structures were anisotropic hyperbolic paraboloids, or "monkey saddles." These are also designated as "two up, two down" or 2/2 configurations, referring to the number of tension points which act away from gravity and towards gravity. Figures 5 and 6 show the two different fabrics in the 2/2 configuration.
The second structure employed 4 up and 4 down points, which results in a concatenation and intersection of hyperbolic paraboloids, creating a "compound monkey saddle." These structures were assembled and can be seen in Figures 7 and 8.
Digitization
Once the fabric models were assembled a physical three-dimensional
digitizer was constructed. This device included a gravity driven
planar locator and a vertical rule for determining the z-coordinate.
The digitizer was aligned with the grid on the fabric using a
penetration probe to ensure proper placement. Using this device
the x, y, and z coordinates were recorded for each corresponding
intersection mark on the fabric.
Meshwork, a three-dimensional trimesh modeling program
for Macintosh was used to transfer the data obtained from each
model to a digitized picture. The coordinates obtained from the
models were entered into a document file as the vertices or vertex
points in three-dimensional space. In order to obtain the edges
and faces of the model a computer program was written to calculate
the connection between two vertices and further connect three
edges to form a triangle. After the output of the computer program
and the coordinates were completed the file produced a three-dimensional
digitized model in Meshwork. This model can now be viewed
in several angles as well as rotated and texture mapped to show
the original fabric used in the models. Renderings from the digitized
data for the beige fabrics are shown below in Figures 9-10.
Figure 9. Beige 4/4 rendering using MeshWork
Figure 10. Beige 2/2 Rendering using MeshWork.
Comparative Analysis
Initial modelling efforts have been focused on experimental measurements.
The techniques described are applicable to any fabrics. Future
work will develop predictive models of fabric response to load
based on material properties. These predictions will be compared
with experimental results such as are described below.
A predictive model of load-deformation response of the fabric subject to external loads will allow visualization of the three dimensional space defined by the tensioned fabric.
The digitized data were used to determine deformations and strains on the fabric. The strains were calculated as
ewi,j = ri,j ri,j+1/r°i,j r°i,j+1
where ewi,j is the strain in the warp direction, ri,j is the position vector of grid point i,j before deformation, and r°i,j is the position vector of grid point i,j after deformation.
Fill direction strain was calculated in a complementary manner:
efi,j = ri,j ri+1,j/r°i,j r°i+1,j
The shear deformation angle was determined by considering the corner angles as follows:
cos(gi,j) = (ri+1,j ri,j) o (ri,j+1 ri,j)
where gi,j is the deformation angle at grid point i,j and o is the dot product of the vectors.
For the beige 4/4 construction, the warp strains were calculated
as shown in Figure 11. As can be seen in this figure, there are
negative strains apparent near the left edge. Some of the negative
value may be caused by Poisson's effect from the fill direction
strain, some of this is due to the coarse nature of the digitization,
in that curvature of individual grid blocks can appear as contraction,
and some of this suggests wrinkling. An observation of the actual
structure reveals some small wrinkling in this area, consistent
with the calculated strains.
Figure 11. Calculated warp direction tensile strains in beige
4/4 fabric.
The fill direction tensile strains are shown in Figure 12 and
the deformation angles in Figure 13.
Figure 12. Calculated fill direction tensile strains in beige
4/4 construction.
As can be seen by comparing Figures 11 and 12, the fabric is
highly anisotropic with substantially higher strains in
the fill direction compared to the warp direction despite similar
tensions applied.
Figure 13. Calculated shear deformation angles in beige 4/4
construction.
As can be seen in Figure 13, the main surface of the fabric has relatively low shear, with maximum values located near the tension points.
Future Objectives
Understanding the creation of three dimensional spaces using
tensioned membranes is the objective of this research. Forms
define these spaces. The available forms are governed by the
fundamental nature of the fabric from which they are constructed.
Thus specific fabric properties ultimately define a unique 3D
form. A model that can translate fabric properties into the potential
unique 3D forms inherent to the fabric under consideration provides
a strong link between the nature of the material with the creative
potential of designers who plan to use these materials.