We could find great resemblance between spider web and simpler tensile structure, such as the radial tent shown in the following example.
Project
Purpose
The purpose of this project is
to design four large stores, covered with candy-striped tent roofs. The
question is how to develop the exact shape and curvature of the tensile
structure, so that it could maintain equilibrium for a given pattern of
stresses.
Design
The final design is a radial geometry
plan layout similar to a spider web. In the resulting net, radial lines
represents radial cables. These are straight in the plan layout, spaced
at equal angles of 15 degrees. Ring lines, located on horizontal planes,
represent the fabric stretched between the radial cables. A mast, pushing
the hub of the net upward, would give it its three-dimensional shape, the
one basic deviation from the spider web.
How
to Find Exact Geometry
The challenge is to find the exact
geometry of this tensile structure shape, in which the fabric and cable
forces would be predictable, and the surfaces smooth and regular.
Designers start with an approximate
net geometry, giving each node a set of starting coordinates. The condition
for checking and adjusting each node point is the requirement that the
internal horizontal forces needed to attach the rings to the radials in
each node have to be equal and opposite in order to achieve equilibrium
in the net.
Iteration
What makes the process easy is
the discovery that the correction could be done in steps, one node at a
time, assuming for that particular step that the four adjacent nodes are
fixed. Making this adjustment for every node in the net, one at a time,
and repeating it until no further corrections are required, leads to the
final shape. In mathematics, this process is called iteration, and it is
really similar the construction procedure of a spider building her net.
Final Apperearance
