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Reference is made herein to my U.S. Pat. No. 4,001,964, Jan. 11, 1977,
which describes trapezoidal structures. Architectural structures composed
of triangles are shown in U.S. Pat. No. 3,346,998 and Canadian patent No.
653,204. Other structures of triangular elements are shown in U.S. Pat.
Nos. 2,164,966; 3,302,321 and 3,894,352.
This invention provides light weight architectural structures, suitable for
shelters for people or storage which can be erected easily and quickly
from identical repeating elements, or units, and which have high strengths
in relationship to their weights. The same elements and combinations may
be employed for making several different types of shelters; for instance,
these may be radial, arcuate or linear, as illustrated herein. The
elements may be hinged together (or a large sheet may be folded to form
the elements) at one site and put into a collapsed form for easy shipment
to the desired location where the collapsed structure may be expanded to
form the shelter.
While, as mentioned above, models of the structure may be made from
relatively small cardboard blanks, the architectural structure will of
course be of a size (e.g. having a height of 6 feet or more) such that
persons can be housed therein.
Suitable materials of construction include such materials as sheets or
panels of metal or plastic or metal-glass-or graphite fiber-reinforced
plastic. These may be hinged together at their edges, as by applying tape
(with suitable adhesive at the edges) or by forming a hinge in situ (e.g.
by applying a material that sets to a flexible plastic, such as an
elastomeric silicone, along the mating edges) or by providing mating hinge
elements along the edges and inserting hinge pins to secure the edges
together. A skeletal construction may be employed, in which there are rods
defining the edges of the polygonal elements and these rods are joined
together at common vertices of those elements by couplers each which may
have a plurality of sockets for receiving the rods; the sockets of each
coupler may be movable relative to one another for convenience in erecting
the structure. The skeletal structure may be covered with any suitable
material which may be of very light weight, e.g. canvas, plastic film or
sheet, thin metal sheeting, etc., appropriate to the environment in which
the shelter is to be employed.
The various configurations may be put to different uses. For instance, the
arcuate configurations discussed below may be used as portable stages for
theatrical performances, the radial structures may be used as on-site
shelters in harsh or unstable environments, e.g. in swampy areas, areas of
high snowfall, deserts, or even outer space. The canopy or base portions,
or both, of the structures may be enclosed, as by a ceiling or floor and
the structure may be made water tight as by application of suitable
sealing means or sealing compositions to the edges, while a suitable
access hatch may be provided in floor or ceiling. Many of the illustrated
structures are open on one side (e.g. the radial structures may have a
free middle zone); this may of course be enclosed.
One may employ materials and methods of construction like those described
(for triangular structures) in U.S. Pat. No. 3,346,998 and Canadian No.
653,204.
The invention is illustrated in the accompanying drawings in which
FIG. 1 is a diagram of a trapezoid, illustrating the nomenclature used;
FIG. 2 is a "blank" make up of a series of trapezoids;
FIG. 3 shows a portion of that blank after "folding";
FIG. 4 shows a portion that folded blank in collapsed condition;
FIG. 5 shows a radial structure made from that blank;
FIGS. 6 and 7 are views of a structure like that of FIG. 5 and showing an
added floor;
FIG. 8 shows part of another blank;
FIG. 9 shows how it is folded and FIGS. 10-11 are views of a radial
structure made therefrom;
FIG. 12 shows part of still another blank,
FIG. 13 shows how it is folded and FIGS. 14-15 show the corresponding
radial structures;
FIG. 16 shows part of a blank having asymmetrical trapezoids;
FIG. 17 shows how it is folded and FIGS. 18-19 show the corresponding
radial structures;
FIG. 20 shows part of a blank which provides a relatively greater free
height and FIG. 21 shows a radial structure made therefrom;
FIG. 22 shows part of a blank which provides an outwardly flaring core and
FIG. 23 shows a radial structure made therefrom;
FIG. 24 shows part of still another blank;
FIG. 25 shows a blank also containing rectangular elements and FIGS. 26-28
show a radial structure made therefrom;
FIG. 29 shows part of another blank having rectangular elements and FIGS.
30-33 show a radial structure made therefrom;
FIG. 34 shows part of still another blank having rectangular elements and
FIGS. 35 and 36 show a radial structure made therefrom;
FIG. 37 shows part of another version of a blank having rectangular
elements and FIGS. 38 and 39 show a radial structure made therefrom;
FIG. 40 shows part of another form of blank having rectangular elements;
FIG. 41 shows part of a blank having rectangular elements and cut-out
portions and FIGS. 42 and 43 show a radial structure made therefrom;
FIGS. 44 to 47 are views of a radial, sectorial structure made from a blank
like that of FIG. 37;
FIGS. 48 and 49 are views of another radial, sectorial structure, made by
joining two smaller arcuate structures;
FIG. 50 shows a structure like that of FIGS. 48 and 49, using other
trapezoid-separating elements;
FIG. 51 is a view of a ridge showing the relationship which results in
warping of trapezoids of the structure;
FIG. 52 is a view of a radial structure in which there are gores to reduce
the warping;
FIGS. 53 and 54 show structures in which triangular separating elements are
employed;
FIGS. 55-55C are details showing alternative arrangements at the edges of
the structure;
FIG. 56 shows a portion of a blank like that of FIG. 2 but with portions
(marked "X") eliminated;
FIG. 57A shows a blank and FIGS. 57-59 show an arcuate structure made
therefrom;
FIGS. 60, 61 and 62 illustrate a similar arcuate structure made from a
blank shown in FIG. 16;
FIGS. 63, 64 and 65 show other arcuate structures made from different
blanks;
FIGS. 66 and 67 show another arcuate structure made from a blank like that
of FIG. 29;
FIG. 68 shows a blank having only two sets of trapezoids;
FIGS. 69 to 71 and 73 show radial structures made with two sets of
trapezoids and FIG. 72 shows a portion of a blank used to make FIGS. 71
and 73 having two sets of trapezoids and rectangular separations;
FIGS. 74 and 75 show a rectilinear structure made from a blank as in FIG. 2
and FIG. 76 illustrates a floor shape; and FIG. 77 illustrates a roof
shape.
FIGS. 78 and 79 show one rectilinear structure having some rectangular
elements and FIG. 80 shows another such structure;
FIGS. 81 to 88 show rectilinear structures having their middle sets of
trapezoids uppermost;
FIGS. 89 and 90 show rectilinear structures having four sets of trapezoids;
FIGS. 91 to 96 show rectilinear structures in which the middle set of
trapezoids are more or less vertical;
FIG. 97 shows a portion of a blank in which the upper and lower sets of
polygons are triangles;
FIGS. 98-99 show a radial structure made therefrom;
FIGS. 100 and 101 show an arcuate structure made from a blank having upper
and lower sets of triangles;
FIG. 102 shows a portion of another blank having a set of triangular
elements and FIG. 103 shows a radial structure made therefrom;
FIG. 104 shows a portion of a blank having triangular elements and
rectangular separating elements and FIGS. 105-106 show a radial structure
made therefrom;
FIGS. 107 to 112 show blanks and structures in which the triangular
elements are isosceles;
FIG. 113 shows a radial structure made from a blank (partly drawn in FIG.
114) having a set of trapeziums;
FIGS. 115, 118 and 123, 125, 126 illustrate other blanks having trapezium
elements, FIGS. 116-117 show a radial structure made from the blank of
FIG. 115, FIGS. 119-120 show a radial structure made from the blank of
FIG. 118, FIG. 122 shows a radial structure made from the blank of FIG.
121 and FIG. 124 shows a radial structure made from the blank of FIG. 123.
The structures of this invention are built up from trapezoidal forms. In
describing the trapezoids the nomenclature shown in FIG. 1 will be used
herein. That is, the trapezoids have a long base LB, a parallel short base
SB and two angled sides, hereinafter called the "A-sides". The "altitude"
is, of course, the distance between the long base and the short base.
In many of the structures shown herein one basic subcombination uses at
least two sets of trapezoids, having common A-sides. Thus in FIG. 2 the
trapezoids 2 and 3 have a common A-side 7. Here the trapezoids 2 (arranged
in the arc of a circle) may act as substantially vertical supports for the
trapezoids 3 (which extend outward substantially radially of that arc),
which may form a canopy as illustrated in FIG. 3 with their other A-sides
6 (hereafter termed their "end A-sides") at the outer surface of the
canopy. The spaces between those and A-sides 6 may be free, or filled in;
e.g. (as illustrated in FIGS. 2,3,5,6, and 7) they may be filled in with
pairs of triangles 4.
For convenience in visualization the drawings of this application will be
described in terms of structures that can be produced from small cardboard
blanks folded along predetermined score lines. It will be understood,
however, as discussed below, that those structures may be made of precut
individual panels, or groups or hinged panels, which may be later
assembled and joined together (e.g. at the construction site), with or
without forming intermediate sub-assemblies. The "blanks" illustrated in
the drawings thus are "maps" of flat projections of whole structures and
illustrate the relationships of the individual panels; the lines on the
blanks are, as previously indicated, score lines for folding such blanks.
The direction of each fold will be readily understood from the views of
the folded and/or unfolded structures.
The structures of FIGS, 5, 6, and 7 are composed of three sets of identical
trapezoidal elements 1,2,3 and two sets of identical triangular elements
4,5 connected together at their abutting sides. The corresponding "blank"
is shown in FIG. 2; its lines (score lines) correspond to the lines along
which the elements are connected. To construct the structure of FIG. 5
from this blank, the latter is folded along the score lines. The center
set of trapezoids 2 may be held vertical while the upper set of trapezoids
3 is folded down and the lower set of trapezoids 1 is folded up, so as to
attain the configuration illustrated (in part) in FIG. 3; that
configuration may be flattened or collapsed to the configuration shown in
FIG. 4 for storage or shipment. Then the opposite sides of the folded
structure are brought together and joined (in effect joining the opposite
ends 11a, 13a, 15a, 11b, 13b, 15b of the blank of FIG. 2 to make a new
fold line) to produce the structure shown in FIG. 5; from a 21.times.73/4
inch flat blank or rectangular blank (FIG. 2) of cardboard there is formed
a structure (of FIG. 5; about 7 inches in diameter, about 31/4 inches
high, with an open section, indicated by h.sub.F on FIG. 5, occupying
about 1/3 of the total height.
In FIG. 5 it will be seen that the connected long edges 15 of the lower
trapezoidal elements 1 are all substantially on the same level. A flat
horizontal floor (F in FIGS. 6 and 7) can be laid onto those edges to
cover the entire lower portion, including the triangular areas 23
available beween the connected vertical trapezoid elements 2. Similarly a
flat horizontal ceiling can, if desired, be placed on the corresponding
long edges 11 of the upper trapezoidal elements 3. It will be seen that
placement of the floor creates a set of bottom compartments below the
floor, while placement of the ceiling creates a similar set of upper
compartments. There is a small hollow central passage Y in the central
vertical core where the short edges 13 of the central trapezoids 2 come
together. For use as a floating structure the bottom compartments may be
sealed against entry of water, while the central passage Y may receive
anchoring means (e.g. an anchoring cable connected to an anchor, and
having a stop at its upper end, may pass through that passage).
When the blank shown in FIG. 2 (having 16 trapezoids, i.e. 8 pairs, in each
set) is formed into the circular structure of FIG. 5 the circumferences of
the structure are taut; that is, each pair of mirror-image triangles 4,4
(and 5,5) is substantially in a single plane the points 21, 20 thus cannot
be moved further apart. This locks the structure, making its "rotation"
(as described in my U.S. Pat. Nos. 3,894,352 and 4,001,964) practically
impossible. If FIG. 2 is modified to increase the number of trapezoids in
each set (e.g. to 9 pairs) the circumference of the resulting circular
structure is no longer taut and the structure is not as stable unless some
restraining means is added; such restraining means may be, for instance, a
floor or ceiling (as previously described) or other means such as devices
(e.g. pins or cables) for locking the short edges 13 together. With an
increase in the number of trapezoids per set, the diameter of the central
core may be increased and (in the middle set of trapezoids) adjacent
trapezoids having common short bases may not be back-to-back but at an
angle to each other. This may give a central core of still greater
resistance to collapse under vertical loads.
In the structures shown in FIGS. 2,5,6 and 7 the free height (h.sub.F FIG.
5) between the canopy portion and the base portion is about one third the
total height, and the heights (h.sub.B and h.sub.C) of base portion and
canopy portion, respectively, are also about one third the total height.
The horizontal projections of the canopy and the base portions are
substantially congruent. As can be seen from FIG. 3 the heights of the
base portion and canopy portion will be determined by the altitudes of
trapezoids 1 and 3, respectively, (the altitudes of all the trapezoids in
this structure are identical) and the free height h.sub.F will be
determined by the length of the short base 13 of the upstanding middle
trapezoid.
A structure having an overhanging canopy (extending outwardly of the base
portion), such as illustrated in FIGS. 10 and 11 can be formed by
lengthening the upper set of trapezoids 28) as compared to the middle and
lower sets 27 and 26; this is also shown on the corresponding blank (FIG.
8 and folded collapsed structure (FIG. 9). The particular blank which is
shown (partly) in FIG. 8 differs from that of FIG. 2 in several other
respects. Thus, while all the angles between the bases of the trapezoids
and their A-sides are the same (45.degree. in each case) the altitudes of
the trapezoids are less in FIG. 8 and the number of sets of trapezoids is
greater (e.g. 13 pairs, as shown in FIG. 11, rather than 8). It will be
appreciated that, all other things being equal, one needs more sets in
order to obtain a canopy of greater circumference. If desired the
dimensions and number of sets may be such that the circumference of the
canopy is taut (while the smaller circumference of the base portion is
not); this provides a stability at the top against change in
configuration, as mentioned above, but stability can also be attained by
the use of a floor (as shown at F in FIGS. 10 and 11) or by other securing
means as previously described. It will be noted that the canopy in FIGS.
10 and 11 slopes downward from the center.
It will be understood from the drawings that the upper ridges 35 of the
canopy are the shorter bases of the upper trapezoids; the bases of the
valleys of the canopy are the longer bases 36 of those upper trapezoids;
the upstanding central core supporting the canopy is formed of the middle
trapezoids 27 whose long bases 37 form the outwardly projecting edges of
the core and whose short bases 38 form the inwardly projecting edges at
the center of that core; the structure rests on the short bases 39 (or
portions or points thereof) of lower trapezoids 26 and the floor rests on
the ridges formed by their long bases 40.
In the blanks shown in FIGS. 2 and 8 each of the trapezoids is symmetrical.
FIGS. 12, 13, 14 and 15 show blanks and structures which are like those of
FIGS. 8,9, 10 and 11 except that the trapezoids 45 of the top set are not
only more elongated but also asymmetrical (angle .alpha. being still
45.degree. but Angle .beta. being about 25.degree.), and there are 16
pairs of trapezoids in each set. The canopy portion here has a still
greater projected area (and circumference) and its overhang, past the
projected outer limits of the base portion, is greater than in the
structures of FIGS. 10 and 11.
It will be understood from the drawings that the upper ridges 48 of the
canopy are the short bases of the upper trapezoids; the bases of the
valleys of the canopy are the long bases 47 of those upper trapezoids; the
upstanding central core supporting the canopy is formed of the middle
trapezoids 27 whose long bases 37 form the outwardly projecting edges of
the core and whose short bases 38 form the inwardly projecting edges at
the center of that core; the structure rests on the short bases 39 (or
portions or points thereof) of lower trapezoids 26 and the floor rests on
the ridges formed by their long bases 40.
In the structure shown in FIGS. 16,17,18 and 19, all three sets of
trapezoids 56, 57, 58 are asymmetrical, though congruent. The final
structure has a central core (formed of the middle trapezoids 57) which
flares outward upwardly; that is, in that structure the lower ends 53
(FIG. 17) of the short bases 64 of these middle trapezoids are close
together or in contact while the upper ends 54 of those same short bases
are spaced apart (uniformly). The long bases 63 of the core-forming middle
trapezoids are similarly at angle to the vertical, and the canopy (formed
by the upper trapezoids 58 whose short bases 66 form the upper ridges and
whose long bases 65 form the bottoms of the valleys of the canopy)
overhangs the base portion (formed by lower trapezoids 56 on whose short
bases 62 the whole structure is supported and whose long bases 61 form
floor-supporting ridges). Triangles 60 are so shaped, in this case, that
their outer edges 74 take a position on substantially the same level as
the ridges formed by long bases 61.
FIGS. 20 and 21 show structures like those of FIGS. 2,3,5,6 and 7 except
that the free height h.sub.F between the canopy and the base portion is
greatly increased by making the trapezoids 75 of the middle set much
longer while all other relationships are unchanged. In these Figures the
long bases 77 and short bases 76 of the middle, core-forming, trapezoids
are substantially vertical as in FIGS. 5,6,7.
An increased height between canopy and base portion may also be obtained in
the structures having outwardly flaring cores (shown, e.g., in FIG. 18) by
lengthening the middle trapezoids. This is illustrated in FIGS. 22 and 23
in which the asymmetrical trapezoids 58, 56 of the upper and lower sets,
respectively, are of identical shape, while the trapezoids 78 of the
middle, core-forming, sets are uniformly longer. Thus the (long bases 79
of the middle trapezoids 78 are longer than the corresponding (long) bases
61 65 of the upper and lower trapezoids; and the (short) bases 80 of the
middle trapezoids are longer than the corresponding (short) bases 66,62.
(Here again the outer edges of 74 of the edge triangles are at angle to
each other, for reasons described in connection with FIG. 16 above). It
will be noted that in this case, unlike that of FIGS. 20 and 21, the
increase in the length of the middle trapezoids results in an increase in
the circumference of the canopy portion (and in its overhang with respect
to the base portion) and thus may require an increase in the number of
pairs of trapezoids as compared to those in FIGS. 16,17,18 and 19.
FIG. 24 shows a blank like that of FIG. 2 except that the lengths of the
upper, middle and lower trapezoids are unequal (in FIG. 24, upper
trapezoids 83 are longer than middle trapezoids 82 which in turn are
longer than lower trapezoids 81). It will be understood that this blank
will form a structure with an overhanging canopy structure. While that
structure may be radially symmetrical about a central core (as in the
structures of FIGS. 10,11,14,15, 18,19,21 and 23), it may also (like
those) take other forms, as will be discussed below.
The trapezoidal elements may be combined with other elements, e.g. of
rectangular configuration. Thus, in the blank shown in FIG. 25 there are
the same pairs of upper trapezoids 3, middle trapezoids 2 and lower
trapezoids 1, as in FIG. 2. But there are also rows of rectangles (such as
100,99,98 and 106,105,104) between adjacent rows of such pairs of
trapezoids. The structure shown in FIGS. 26,27 and 28 is formed like that
of FIGS. 5-7, by folding the blank along the illustrated score lines,
unfolding it and securing its ends 11a, 13a, 15a, 11b, 13b, 15b together.
It will be seen that the use of the trapezoid-separating rectangles makes
for a central core area of larger diameter (as compared to FIGS. 5-7). In
the illustrated embodiment, both the rectangles 105 are cut out (i.e. 105
represents an empty space); this provides two areas of access to the
central core area. The presence of the rectangles 99 creates interior
compartments, or bays, as can be seen in FIG. 26. In the illustrated
embodiment there are (a) eight pairs of sets of trapezoids forming 8
spaced canopy peaks, 6 bays and 8 spaced lower support structures; and (b)
8 files of rectangles including (b.1) 6 files of narrower rectangles
(100,99,98) forming 6 radially extending horizontal canopy portions
(between the peaks), 6 inner walls of the bays and 6 radially extending
horizontal base portions which may be just below the floor F or may form
part of the floor, and (b.2) two files of wider rectangles (106,105,104)
forming two aligned diametrically extending horizontal canopy portions,
two open areas between bays and two aligned diametrically extending
horizontal base portions which may be just below the floor F or may form
part of the floor.
FIGS. 29, 30 and 31 illustrate a structure in which there is one file of
trapezoid-separating rectangles for three files of pairs of trapezoids.
The trapezoids used in this particular embodiment have a smaller altitude
(in relation to their other dimensions) than those of FIG. 25. In the
illustrated embodiment there are a total of b 24 files of trapezoids
118,117,116 (12 pairs, arranged in groups of three identical pairs) and 4
identical files of rectangles 137,136,135. When the rectangles 136 are
actual elements, the central core of the structure is a closed rectangular
tube formed by the four vertically arranged rectangles 136 (see FIG. 32)
each of whose vertical sides is secured to four joined short bases of
trapezoids 117. One, two, three or all four of the rectangles 136 may be
cut out giving a corresponding number of access openings to the central
core. The configuration of the structure may be secured in any suitable
manner, as previously discussed, as by the use of a floor F (illustrated)
and/or ceiling.
Incidentally, in FIG. 33 the lines joining the triangles 130 of each
triangle pair in the base portion are folded outward revealing the
interiors of the hollow compartments below the floor.
FIGS. 34,35 and 36 illustrate a structure in which there is one row of
trapezoid-separating rectangles for two files of pairs of trapezoids. The
trapezoids used in this particular embodiment have a still smaller
altitude (in relation to their other dimensions) than those of FIG. 29. In
the illustrated embodiment there are a total of 28 per files of trapezoids
148,147,146 (14 pairs, arranged in groups of two identical pairs) and 7
identical files of rectangles 167,166,165, all the rectangles 166 being
cut out. The configuration of the structure may be stably secured in any
suitable manner, as previously discussed, as by the use of a floor F
(illustrated) and/or ceiling.
The structures shown in FIGS. 37,38 and 39 are like those of FIGS. 29,30-33
except that identical files of rectangular separations are positioned
between files of single pairs of identical trapezoids. In the illustrated
embodiment there are a total of 20 files of trapezoids 118,117,116 (10
pairs forming ten radially extending canopy peaks and a corresponding ten
support structures and ten inwardly extending bay walls, for five bays)
and 10 identical files of rectangles 137,136,135, five of the middle
rectangles 136 are cut out so that there are five accesses to the central
areas, while the other five rectangles 136 form the inner walls of the
five bays. Also outer wall elements (which may be rectangles 172) may be
applied to any portions, or all, of the perimeter of the free space
between the canopy and the base portion of the structure; this, of course,
may also be done with any of the other structures (such as those
previously described).
In FIGS. 40 the middle trapezoids 75 are longer than the upper and lower
trapezoids as in FIG. 20 with arrangement of rectangles and trapezoids
like that of FIG. 37 except that the middle trapezoids 75 (and middle
rectangles 173) are much longer than the upper and lower trapezoids 3 and
1 and upper and lower rectangles 100 and 98. This gives structures whose
free height is proportionately increased (or whose canopy and base
diameters are decreased).
FIGS. 41,42 and 43 illustrate an arrangement in which there is a row of
trapezoid-separating rectangles on both sides of each row of trapezoids
118,117,116. It will be apparent that there are two sets of files of
rectangles. One set (files 137,136,135) is like those previously
described. The other set (files 177,176,175) has the effect of providing
(a) intervening flat tops 177 (FIG. 42) at the upper ridge-forming short
bases 124 of the upper trapezoids 118 (b) corresponding intervening flat
bottoms 175 of the downwardly projecting supports formed by the short
bases 120 of the lower trapezoids 116 and (c) intervening flat vertically
arranged flat panels 176 at the outer edges formed by the long bases 121
of middle trapezoids 117. In addition these latter rows of rectangles may
include rectangles 178 and 174 which intervene between pairs of triangles
129,129 and 130,130. The result may be viewed as a flattening of all
angles at ridges and valleys as well as at edges of core-forming
vertically arranged trapezoids. Also shown is a variation in which,
instead of cutting out all of a middle rectangle, only part thereof is cut
out (in 136) so as to form a restricted doorway to the core area. It will
be understood that one may form structures that are not radially
symmetrical (e.g. structures having the general appearance, in plan view,
of a sector of a circle, or more properly, of a sector of a polygon) by
using fewer rows of the elements (and not joining the blanks end-to-end).
Thus the "semi-circular" structure shown in FIGS. 44,45,46, and 47 is
essentially one half that shown in FIGS. 37,38 and 39. Any suitable means
may be employed for stably securing the elements together in their
unfolded condition; this securing function is served, for instance, by a
flat central roof R attached to the inwardly disposed edges of the
elements of the canopy portion and a floor F resting on the base portion
and serving to keep the upstanding elements 117 in predetermined spaced
relationship.
Combinations of such sectorial-type structures may be produced. One such
embodiment is shown in FIGS. 48 and 49, formed of two identical
sectorial-type structures S and S' joined at their narrow sides by a roof
R and floor F. Each of the structures S and S' is formed of the same
elements as in FIGS. 44-47 except that fewer rows are used, so that each
structure fans out only about 90.degree. instead of about 180.degree..
The trapezoid-separating elements need not be rectangular. Thus in FIG. 50
(which shows a structure otherwise identical to FIG. 48, the horizontally
disposed trapezoid-separating elements 185 are roughly trapezoidal
themselves, being narrower at the outer, longer, circumference (at 139)
and wider at the inner core (at 140).
In all the structures described so far the various originally parallel
identical trapezoidal elements are placed in non-parallel relationship.
This can be seen in FIG. 51 (which illustrates a portion of the structure
shown in FIGS. 2 and 7), for instance, by considering two adjacent upper
trapezoids 3, having A-sides 6a, 7a and 6b, 7b, and a common short base
10. In FIG. 51 the A-sides 6a and 6b are brought into substantial
coincidence and are both in the same plane as the common short base 10,
but the other A-sides (7a and 7b) are flared outward from the outer-end of
that short base 10. As a result the upper trapezoids 3 are in a warped,
stressed non-planar smooth-curved condition, to a greater or lesser
degree. The same is true of the lower trapezoids 1. It is contemplated
that the materials of construction of the trapezoids (e.g. thin metal such
as aluminum or fiber glass-reinforced sheets, cardboard, etc.) will be
flexible enough to accommodate such warping. If desired the construction
may be such as to diminish, or avoid, the warping, as by using triangular
gores 187 illustrated in FIG. 52) and appropriate panels 186 to substitute
for or modify, the end triangles; this introduces additional connections
or hinges and additional panels, and increases the expense. Other
arrangements such as use (FIGS. 53,54) of outwardly flaring triangles, to
separate trapezoids 3 and 1, of the upper and lower sets, may be employed
(in FIG. 53 this enables use of less trapezoids per set to form the
radially symmetrical structure). It will also be understood that the
separations such as elements 137 and 177 in FIG. 43 need not be
rectangular but may be tapered to flare outwardly, thereby reducing the
warping.
The illustrated structures have pairs of triangular elements at the free
ends of the upper and lower trapezoids (e.g. elements 5 and 4 in FIGS.
2,3,4-7,20,21,25,26,27,28, and 40; elements 29 and 30 in FIGS. 8,9,10 and
11; elements 46 and 30 in FIGS. 12,13,14 and 15; elements 59 and 60 in
FIGS. 16,17,18,19,22 and 23, elements 84,85 in FIG. 24; elements 129,130
in FIGS. 29-33,37,38,39,41-50; elements 149,150 in FIGS. 34,35 and 36). As
indicated earlier the use of such pairs of triangles constitutes one
convenient way to fill in the spaces at the free ends of the trapezoids,
but those spaces may be filled in as well by single triangles such as 113
(as shown in FIG. 55) or may be left unfilled particularly when the spaces
between the free ends of those trapezoids are maintained by other suitable
means such as the elements 113a (FIG. 55c), which may be struts (acting in
compression and/or tension, or tensiond elements such as cables or guy
wires. As shown in FIG. 13, for instance, the angle .beta. at the free
ends of the upper and/or lower trapezoids may be different from the angle
.alpha. at the opposite end; other angles .beta. are shown in FIG. 55A
(90.degree.) and FIG. 55B (obtuse and, if desired, the complement of
.alpha. so that the A-sides are parallel).
It will be noted that when the trapezoids are warped the opposite bases of
a warped trapezoid may no longer be parallel, e.g. the long base may be
horizontal while the short base is at a small angle to the horizontal.
Thus the ridges 14 of the base portion shown in FIGS. 5 and 6 tilt upward,
so that (if the structure is resting on relatively firm ground) the
support may be mainly at the lowermost, inward, portions of those ridges,
i.e., at point 24; the rigidity provided by the interaction of the
elements of the structure makes it strong enough to carry a considerable
weight substantially on those points.
In many of the structures previously discussed there are portions in which
paired elements are doubled-up face-to-face. For instance, in the
structure shown in FIGS. 5 and 6 each pair of middle trapezoids 2 having
common long bases 13, has its paired trapezoids in face-to-face
relationship. To save material one of the trapezoids of all (or some) of
such pairs may be eliminated in each of these structures. Thus, in the
(portion of a) blank illustrated in FIG. 56 half (marked "X") of the
middle trapezoids 2 are omitted; in making the structure of FIGS. 5-7 from
such a blank the A-sides 7c and 7d are secured together as are the A-sides
8c and 8d. In the oppositely unfolded structure such as those of FIGS.
57-59 there are pairs of triangles 5 and 4 (see FIG. 2) which are
doubled-up and located under the inwardly projecting A-sides 9 and 6 of
upper and lower trapezoids 3 and 1; those triangles may be eliminated
entirely and those A-sides (of adjacent trapezoids having common short
bases) may be secured together.
One way of making other structures is to unfold the blank from its
collapsed position (e.g. a position like that in FIGS. 3 and 4, in the
opposite direction; that is, the unfolding is such as to separate the
edges 122 (i.e. the short bases of the middle trapezoids) instead of
keeping them together, and (conversely) to keep together the edges 121,
which are the long bases of the middle trapezoids. This converts the
folded blank into an arcuate structure such as the semicircular structures
shown in FIGS. 57-59 made from the blank shown in FIG. 57A. In that
structure the short bases 122 of trapezoids 117 form the outer ridges of
the semicircular arc and their long bases 121 project inwardly
substantially radially of that arc. The upper trapezoids 118 also project
radially inwardly and their end A-sides 128 may be secured together in
pairs, that is, the pair of triangles 129 adjacent those end A-sides 128
may be brought face-to-face so that those end A-sides meet (it will be
understood that in such a case the triangles 129 are essentially
superfluous and may be eliminated from the structure). The tips T of the
long bases 123 of the inwardly projecting upper trapezoids 118 may be
brought together in a semi-circular internal ring. The same arrangement
may be used for the radially projecting lower trapezoids 116 so that pairs
of adjacent end A-sides 125 thereof are joined (triangles 130 being
eliminated as superfluous) and the tips T' of the long bases 119 are
brought together in the same type of semi-circular internal ring. A floor
F may be supported on the long bases 119 of the lower trapezoids; also a
ceiling may be positioned against the long bases 123 of the upper
trapezoids. Various securing means may be used to stabilize the structure.
For instance the degree of unfolding about the inwardly projecting long
bases 121 of the middle trapezoids may be fixed, as by having the floor
fit into the triangular inwardly directed spaces H between the middle
trapezoid. It will be understood that the final configuration need not be
semicircular; the structure may be unfolded to a greater extent, e.g.
270.degree. or even 360.degree. (with addition of trapezoids to each set);
in the latter case a fully enclosed structure is formed and one or more of
the elements 117 may have appropriate cutouts to serve as windows and/or
doorways.
FIGS. 60,61 and 62 illustrate a similar arcuate structure made from the
blank shown in FIG. 16. It will be seen that the middle trapezoids form an
inwardly flaring ring in this arrangement.
It will also be understood that the relative lengths of either (or both) of
the upper and lower trapezoids may be increased so as to reduce the radius
of the arcuate internal ring to any desired deg | | |
