Note: Descriptions are shown in the official language in which they were submitted.
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STRUCTURAL FRAME
Background Of The Invention
This invention relates in general to structures
such as load bearing frames and trusses and more
particularly to structures that provide an enhanced trade
off between the stress that can be safely carried in
relation to the amount of material required for the
structure.
This enhanced strength to weight ratio is a goal
of a large number of designs including many of those
proposed and constructed by Richard Buckminster Fuller. In
most contexts where load bearing frames and trusses are
employed, failure occurs because of a failure in tension
rather than in compression. Although the loads imposed
primarily induce compressive stress in the material, that
stress is resolved within the material by vectors which
introduce tension. For example, a dome subject to load
will tend to deflect in such a fashion as to introduce
tension along the trusses that constitute the dome.
Failure will occur because of a failure in tension. Much
attention has.been paid to developing materials which have
great tensile strength for use in load bearing structures
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in such a way as to employ the tensile strength of these
materials so that loads supplied will be resolved, at least
in part, by the tension created in these tension members.
Such an approach is outlined in the Buckminster Fuller U.S.
Patent No. 3,354,591 issued in 1967. A more recent
improvement on that structure is set forth in U.S. Patent
No. 4,207,715 issued in 1980. This combination of.tension
and compression members is also disclosed in the structure
shown in U.S. Patent No. 4,711,062 issued in 1987.
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Brief Description
This -invention is in a framework type of
structure composed of a plurality of struts. Each strut is
ideally equal in length and is deployed in such a fashion
as to cause the stress applied to the structure to be
resolved within the structure in a way that minimizes the
creation of tensile stress. The set of struts can be
analyzed as a plurality of interconnected sets of building
blocks. These building blocks which when interconnected
constitute the framework of this invention can be looked at
in three different ways. That is, depending upon where one
breaks apart the set of struts which constitutes the
framework of the invention, one can end up with any one of
three distinctly different sets of building blocks. Two of
these sets are true building blocks. The other is a bit
more abstract in that individual struts do double duty and
are considered as constituting edges of two or more of the
particular sub frames involved.
A first set is a twenty strut building block
which is called by Applicant a"Unicube". It is a frame in
which twelve struts define a cube. From each of the eight
corners of the cube, a single strut extends outward in such
a fashion as to form an equal angle with each of three
adjacent edge struts of the cube. A plurality of these
unicubes connected by the outboard ends of the struts which
extend from the corners of the cube creates a framework or
truss in accordance with the teachings of this invention.
A second set is composed of two buildings blocks.
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They are tetrax frames and cubic frames. Each tetrax frame
is the four struts which extend from the center point of a
tetrahedron to the four corners of a tetrahedron. Each
cubic frame is the twelve struts that define the edges of
a cube. The outboard end of each tetrax strut is connected
to the corner of a cubic frame and, correspondingly, each
corner of a cubic frame is connected to the outboard end of
a strut of a tetrax frame. Thus from the eight corners of
a cubic frame, eight tetrax frames will extend outwardly.
Correspondingly at the outboard ends the four struts of a
tetrax frame, there will extend four cubic frames each of
which is connected at its corner to the strut of the
tetrax. Since there are four outboard ends of a tetrax
frame and eight corners of a cubic frame, this arrangement
requires that there be twice as many tetrax frames as cubic
frames.
A third set is not exactly a building block. The
third set is the edge frame of the truncated rhombic
dodecahedron (TRD) that is disclosed in detail in the
referenced patent application. A structure composed of the
edge struts defining a plurality of truncated rhombic
dodecahedra will generate the frame of this invention.
However, it has to be understood that in a packed set of
TRDs each edge would be common to three of these TRDs. The
framework of this invention is a framework which
constitutes the common struts so that the three edges of
adjacent TRDs are represented by a single strut rather than
by three parallel coincident struts.
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FIGs. 1 through 6 illustrate these three sets or
building blocks. FIGs. 1 and 2 show two views of a
unicube. FIGS. 3 and 4 show the tetrax and cubic frame,
respectively. FIGs. 5 and 6 show two views of a TRD frame.
FIG. 5 shows an opaque TRD representing only the visible
edges of the TRD.
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Brief Description Of The Fi,Rures _
FIG. 1 is a perspective view of the unicube in
which the center cube is in opaque form so that only
visible struts can be seen.
FIG. 2 is a perspective view of the actual
unicube showing all twelve struts of the center cube and
the eight outwardly extending corner struts.
FIG. 3 shows two views of the four strut tetrax
which is also referred to herein as the tetrax frame.
FIG. 4 is a perspective view of a cubic frame;
this cubic frame being the center cube of a unicube.
FIG. 5 is a perspective view of an opaque
truncated rhombic dodecahedron (TRD) thereby representing
only the visible edges of an opaque TRD.
FIG: 6 is a perspective view of an actual TRD
showing all edges thereof.
FIG. 7 is a two dimensional aggregation of the
FIG. 1 unicubes showing the connection of the outwardly
extending struts 14 of adjacent unicubes in essentially a
shell which is shallow with respect to the plane of FIG. 8
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Defmitions
Applicant hereby adopts the following terms.
These terms are used in the specification and the claims in
accordance with the following definitions.
Unicube.
A unicube consists of twenty equal struts
connected to one another. Twelve of the struts define the
edges of a cube and thus are a cubic frame. Eight of the
struts extend outward from the eight corners of the cube in
a direction so that each of these outwardly extending
struts forms an equal angle with each of the three cubic
frame struts to which it is connected. The twelve struts
that define the cube are called cubic struts and the eight
struts that extend outward from the corners of the cube are
called outwardly extending struts. The outwardly extending
struts of a single unicube each have an outer end. FIG. 2
illustrates a unicube.
Cubic Frame.
A cubic frame consists of a set of struts
defining the twelve edges of a cube. A cubic frame
constitutes one of two
building blocks of an optimum structure of this invention.
The other building block is the tetrax, defined below. A
cubic frame is illustrated in FIG. 4.
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Tetrax.
The tetrax is the four equal sized axes extending from
the center point of a tetrahedron to the four corners of
the tetrahedron. The mutual angle between any two of the
struts or legs of the tetrax is 109.47 . A plurality of
tetraxes and a plurality of cubic frames can be combined to
create an optimum structural frame of the invention. This
tetrax is also called a tetrax frame herein. FIG. 3
illustrates a tetrax.
Tetrax Structure.
A tetrax structure is a four strut structure or
building block that approximates a tetrax. The four struts
are all connected to a common point. But the struts may
not be equal in length and may deviate somewhat from the
109_.47 angle between any two of the struts. A tetrax
structure may be used as a building block in an embodiment
of the invention which is less than optimum. The limits of
how much a tetrax structure can deviate from a tetrax frame
and still be usable in some embodiment of this invention is
discussed in greater detail under the detailed description.
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Truncated Rhombic Dodecahedron (TRD).
This is the term applied to a rhombic
dodecahedron in which the six vertices that have four edges
extending therefrom are truncated. Truncating each of the
six four-edge vertices of each rhombic dodecahedron at
approximately the midpoint of the edge and removing the
truncated portions provides the TRD as defined herein. A
more extensive discussion of the TRD appears in U.S. Patent
No. 5, 615, 528.
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Description Of The Preferred Embodiments
FIGs. 1 and 2 illustrate one form of the building
block of- this invention. It is referred to herein as a
unicube 10. As shown in FIG. 1, there are.twelve struts 12-
which form the edges of a cube. There are eight struts 14
which extend outward from the eight corners of the cube.
Each outwardly extending strut 14 forms an equal angle with
each of the three cube edge struts 12 that form the corner
from which the strut 14 extends. The struts 14 and 12 are
all equal in length.
In order to facilitate viewing this unicube 10
building block, FIG. 1 shows the cube as opaque. Since the
structure itself is a series of struts, FIG. 2 is the more
accurate representation. In building the framework of this
invention from the FIG. 1 unicube, the outboard ends 14E of
each of the struts 14 is attached to an outboard end 14E of
three other unicubes. FIG: 7 is designed to illustrate and
suggest this arrangement. In FIG. 7 only three, not four,
ends 14E are illustrated as being connected in order to
provide a clearer presentation.
A plurality of the FIG. 2 unicubes 10 connected
by their strut ends 14E to each other will create an
optimum frame embodiment of this invention. It should be
noted that each end 14E is connected to three other ends
14E of three other unicubes. Thus any set of four
connected unicubes will share only one common point.
FIGs. 3 and 4 illustrate another form of the
building blocks of this invention.
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One of the building blocks is a cubic frame 16
shown in FIG. 4 and the other is a tetrax frame 18 shown in
FIG. 3. Each cubic frame consists of twelve struts 12
defining the edges of a cube. Each cubic frame 16 has
eight corners. Each tetrax frame 18 is constituted by four
struts 14 which comprise the corner axes of a tetrahedron.
The four struts are equal in length, extend out from a
center point 14E to which all four struts are connected and
in which any two of the struts have a mutual angle of
109..47 . That is, there are six angles involved in these
four struts, taking two at a time. Each angle has a value
of 109.47 . If the four end points 14C of these four
struts are considered to be the four vertices of a regular
tetrahedron, then these four struts are the four lines
which extend from the center of the tetrahedron to the four
vertices of the tetrahedron.
The end point 14C of each tetrax is connected to
a corner of a cubic frame and the corner of each cubic
frame is connected to an end point 14C of a tetrax. Since
there are four end points 14C to each tetrax and eight
corners to a cubic frame, there are,twice as many tetrax
frames as there are cubic frames in the structure of this
invention.
In the preferred embodiment, the tetrax frame is
a true tetrax in which each strut is equal in length and
has internal angles of 109.47 . The internal angle is the
angle between any two of the four struts.
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Relation Between Unicube, Cubic Frame and Tetrax.
Each strut 14 of a tetrax is an outwardly
extending strut of a unicube in the assembled structure.
FIG. 7 may aid in seeing this relationship. Thus the same
reference number "1411 is used for the struts. Similarly,
the cubic struts 12 of the unicube are the cubic frame 16
in the assembled structure. Thus the end point 14E of the
strut 14 in the unicube is the center point of the tetrax
struts. And the end point 14C of the tetrax struts is the
corner point of the cubic frame 16.
Similarly the center point of the cubic frames 16
is the center point of the cubes of the unicube.
The center point of all of the_cubic frames 16 is
a set of points having a relationship to each other such
that each member of this set of center points will be equal
distant from the twelve neighboring members of the set of
points. This relationship is important because that set of
points must always be spaced from the set of struts.12, 14
so as to avoid transmission of forces along a strut through
those points. By avoiding the transmission of forces
through the set of center points, the forces are steered in
such a fashion as to minimize the development of tension.
The closer the arrangement is to the preferred
embodiment, the less tension will be developed. However,
some deviation in uniform length of struts 12, 14 and in
the center angle of the tetrax 18 as well as in the right
angle of the cube 16 can be tolerated while still obtaining
much of the improvement of this invention which improvement
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is to minimize the development of tension in the struts of
the structure. Accordingly, the term tetrax structure is
used herein to refer to a four strut structure based on the
tetrax 18 but having less than ideal equal length struts
and/or less than ideal internal angles. Thus a te'trax
structure is a tetrax modelled structure that provides a
significant improvement in the stress steering.
FIG. 7 illustrates a panel approximately two
unicubes deep constructed in accordance with the teachings
of this invention. This network of struts 12, 14 can be
used to produce a number of a wide range of building
structures such as a wall truss, a floor truss, a dome and
an arch as well as many other structural components. The
structures can be made extremely light compared to
comparable structures made by other techniques because they
resolve loads in terms of compression rather_than in terms
of tension. Thus the structures take full advantage of the
high compressive strength to weight ratios as opposed to
much lower tensile strength to-weight ratios. -
It might be noted that the struts can be made of
any suitable material such as steel, aluminum, fiber,
reinforced plastic or ordinary plastic struts. The strut - -
material as well as its length and cross-sectional size
will be a function of the particular design requirements
--of the structure, involved. The struts can be joined to one
another using any known technique such as bolting, welding,
or being cast as integral cubic and tetrax building blocks.
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The surface of the structural frame created in
accordance with this invention would normally be closed and
preferably smooth in some sense. Thus at the boundary, the
struts 12 or 14 will connect to some structure that is not
part of the structural frame of this invention.
Hypothesis as to Stress Steering.
The framework of this invention steers stresses
due to loads in such a fashion as to minimize the
development of tension and resolve these stresses as
stresses in compression.
Applicant believes that an understanding of why
this occurs may best be obtained from a consideration of
the TRD arrangement shown in FIGs.-5 and 6. The TRD is a
closed structure having six square frames and twelve
hexagon frames. Pairs of-these square frames and pairs of
the hexagon frames are parallel to one another. All edges
are exactly equal in length. The set of struts 12, 14 that
form an optimum embodiment of this invention (that is, true
cubic frames and tetraxes with all equal struts) will also
define TRDs. The TRDs are not strictly building blocks
because each strut 12 and 14 will be common to three TRDs.
It is believed significant that- the volume of
this truncated rhombic dodecahedron (TRD) is very nearly
equal to the volume of a regular sphere_which would be
inscribed within the TRD. An aggregation of independent
spheres would transmit -forces only in compression. Of
course, they would fly apart unless they were constrained
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at their ends. Viewing the frame of this invention as
composed of interconnected TRDs is believed to suggest why
the frame steers stresses in a fashion similar to that
which would occur if they were independent spheres. But
because of the interconnection of the TRDs, they do not fly
apart.
It is believed that additional reinforcing struts
that do not conform to the pattern of the struts described
above will normally provide no useful benefit and will
usually result in some degradation from optimum
performance. For example, a diagonal strut along the
surface of the cubic frame 16 might appear to provide _
additional rigidity and strength. Applicant believes =that
the main result of such an additional strut would be to
deflect the optimum force steering created by the struts
12, 14 of this invention and thereby increase the
development of tension in certain strut members. At the
best such additional struts would provide no improvement in
reducing tension yet create additional cost and weight.
Furthermore, additional struts that go through
the center of the cubic frames 16 or through points defined
by the center of the cubic frames would undercut the
objectives of this structure by causing forces to be
resolved in a fashion that would tend to increase the
- tension developed rather than minimize the tension.
The tetrax and cubic frame strut building blocks
are so connected that each end point of a tetrax leg or
strut is connected to a corner of a cubic frame strut and
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each corner of a cubic frame strut is connected to an end
point of a tetrax strut.
It should be noted that this description of
combining cubic frame and tetrax building blocks-does not
literally apply to the surface zone of the framework. That
is, the framework has to come to an end some place.
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