GEODESIC PROPERTIES                                                               

                                                 
PERFORMANCE

A good index to the performance of any building 
is structural weight required to shelter a square foot of floor 
(from the weather).

In a conventional building it is often 50 lbs per sq. ft.

By constructing a frame of generally spherical form 
in which main structural elements are interconnected 
in a geodesic pattern of approximately great circle arcs 
intersecting to form a three-way grid 
& covering (lining) this frame work with a plastic skin 
a wt./ft of approx. 0.78 lbs/sq. ft can be achieved.

Geodesic spherical structures 
which are inherently omni-triangulated 
framed entirely of great circle chords, 
give the strongest structure per weight
of material employed. 

With the tensegrity structure, 
we see that we have broken through 
to a structural knowledge & technique 
which permits a progressively decreasing relative weight of structure 
as proportional to linear gain.

It is statable that the higher the frequency, 
the more ephemeral the tensegrity complex  
& the lesser the total weight of the structure 
per given level of performance 
& the less vulnerable is the whole structure 
by total violations 
by any or many inwardly or outwardly originating impinging forces.

TENSEGRITY

Tensegrity is a contraction of "TENSional intEGRITY" structuring.

The word integrity points to their structural completeness.

In a tensegrity, the continuity is in the tensional network;
a sort of stressed cage in which compressions float.

The great structural systems of the universe are accomplished 
by islanded compression & omni-continuous tension.

All geodesic domes are tensegrity structures 
whether or not the tension/islanded compression differentiations 
are visible to the observer.

Geodesic domes are designed as enclosing tensile structures 
to meet discretely,
ergo non-redundantly,
the patterns of outward forces.

The tensegrity compressional chords are restrained 
by the spherical tensional integrities closed network of connectors 
which alone can complete the great circle paths 
between the ends 
of the entirely separate,
non-directly interconnecting
compressional chords.

In the geodesic tensegrity sphere, 
each of the entirely independent compressional chord struts 
represent 
2 oppositely directioned & force paired molecules.

The tensegrity compressional chords do not touch one another; 
they operate independently 
each trying to escape outwardly from the sphere.

The tension lines clearly show 
that the struts each pull away 
from each other (nearest neighbor) 
& strain to escape radially outward of the system.

Were the chordal struts 
to be pushing circumferentially from the sphere
their ends would touch one another or slide by one another.
The paired-outward caroming of the 2 chord ends 
produces 
a single,
radially outward 
force of each chord strut.


LOAD DISTRIBUTION

Structural strength 
at the surface of a structure 
is not provided 
by the "solid" quality of the exterior shell, 
but by the triangularly inter-stabilized lines of force 
operative 
within that shell 
(ergo you can perforate the shell 
between the force lines 
without strength decrease ).

The pattern of triangulated force lines 
peppered 
with triangular holes in the hollowed-out structural shell 
is 
what is called a truss.

The three-way grid 
of structural members in a geodesic dome
results 
in substantially uniform stressing 
of all members.

The framework itself 
acts 
almost as a membrane 
in absorbing & distributing loads.

If the structural members 
are aligned 
with the lines of geodesic grids 
then 
the resulting framework 
will be characterized 
by more uniform stressing of the individual members 
than is possible 
with any construction 
heretofore known.

In geodesic tensegrities, 
all tension members 
cross one another 
in great circle chorded triangulations, 
thus providing 
the highest possible dimensional stability.

Great circle arcs 
represent the limit 
of structural transformative tendency 
of outward surface tensing 
by internal pressure.

Great circle segment chords 
represent the limit structural optimum 
for axis of compression-resisting columns 
opposing 
external pressure 
by surface spreading.

As Vertices & trussed faces 
multiply 
at a given diameter, 
there are greater numbers 
of shorter compression columns 
to share the load - 
to be realized progressively with more economical slenderness ratios.

An increased number of vertices & edges 
provide 
more & dispersed structural interactions 
for resisting 
concentrated loads from more directions.

If a further approach 
to the congruence of all-trussed chordal polyhedra
with arc-structured spheres 
can be accomplished, 
not only 
will the vertices & trussed facets (penetration points) 
multiply, 
it provides 
increased advantage 
in more directions 
against concentrated loads & more directions of penetration.

As the number of trussed facets increase, 
the convex vertexial interactions 
approach a zero attitude condition,
which, 
though ideal for tension or internal pressure, 
tends 
to allow concentrated external loads 
to push the convex chordal vertices inside-out 
(i.e. to a dimpled or concave condition).

In the dimpled or concave condition, 
continuing concentrated external pressure 
will be resisted 
by a tension increase in omni-surface direction 
(eg. as a rubber ball 
draws on its skin 
as it resists punching in 
& gains reaction 
& springs back 
causing bounce).

This behavior 
was dramatical demonstrated to the author (amk)
when he climbed 
a 4 Frequency, 16 ft radius dome 
constructed of 1/2" electrical metal conduit (emt).
This material is not strong enough 
to support my weight in the middle of the strut, 
though the vertices are 
& show no deflection when loaded with my weight.
I had climbed to the 3rd level from the ground
& was beginning to retreat 
when I stepped 
into the middle of a strut with great force 
severely bending the strut.
This initiated a failure by pulling a vertex 
in toward the center of the dome.
I began to sink as several other vertices were pulled inward.
This failure stopped 
& I was buoyed up 
by the surrounding unsunken dome 
as though in a net .
AMEN to that, 
Thank God & Bucky.

EXPANSION / CONTRACTION

An impressive behavioral characteristic 
of tensegrity spheres, 
witnessed at low frequencies, 
is 
that when any two islanded struts 
180 degrees apart around the sphere
are pulled outward from one another 
the whole sphere expands symmetrically.

When the same two struts 
are pushed toward one another 
the whole sphere contracts symmetrically.

When the solar pushing together or pulling apart ceases 
the tensegrity sphere 
assumes a radius 
halfway between the radii of the most pullingly expandable
& pushingly contractible conditions
(i.e. it will rest in dynamic equilibrium).
The equilibrium state 
which tensegrity spheres spontaneously assume 
is 
the state wherein all parts 
are most comfortable 
but are always subject to spherical oscillability.

The tightening of any one tension member 
or increasing the length of any one strut 
tightens the whole system uniformly 
as is tunably demonstrable.

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