Source: http://www.google.com/patents/US4794742?ie=ISO-8859-1
Timestamp: 2015-04-25 19:05:59
Document Index: 728504684

Matched Legal Cases: ['art 27', 'art 27', 'art 161', 'ART0', 'ART0', 'arts 117', 'arts 118', 'arts 119', 'arts 120', 'arts 121', 'arts 122', 'art 118', 'art 117']

Patent US4794742 - Multi-conic shell and method of forming same - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inAdvanced Patent SearchPatentsA multi-conic shell and a process of creating multi-conic shells from flat materials which are bent and thereby forced into the configuration of continuous regions from oppositely oriented, tangential cones to create variably configured building structures and variably configured lightweight structural...http://www.google.com/patents/US4794742?utm_source=gb-gplus-sharePatent US4794742 - Multi-conic shell and method of forming sameAdvanced Patent SearchPublication numberUS4794742 APublication typeGrantApplication numberUS 06/841,501Publication dateJan 3, 1989Filing dateMar 19, 1986Priority dateMar 19, 1986Fee statusLapsedPublication number06841501, 841501, US 4794742 A, US 4794742A, US-A-4794742, US4794742 A, US4794742AInventorsCharles E. HendersonOriginal AssigneeHenderson Charles EExport CitationBiBTeX, EndNote, RefManPatent Citations (20), Non-Patent Citations (1), Referenced by (7), Classifications (13), Legal Events (8) External Links: USPTO, USPTO Assignment, EspacenetMulti-conic shell and method of forming same
US 4794742 AAbstract
A multi-conic shell and a process of creating multi-conic shells from flat materials which are bent and thereby forced into the configuration of continuous regions from oppositely oriented, tangential cones to create variably configured building structures and variably configured lightweight structural panels. The process of creating multi-conic shells from connecting cone segments corresponding to a theoretical array of regular (opening downward) and inverted (opening upward) cones provides an unlimited number of variations for the design of building structures and the design of structural panels. Such multi-conic structures achieve excellent strength to weight ratios by distributing loads into tension and corresponding tetrahedron structures which propogate throughout the shell. One embodiment is a building structure wherein a number of generally two-dimensional panels constructed of plywood or other flat materials are raised and forced into multi-conic surface positions by the use of winches, or other mechanical devices thus creating one or more multi-conic shells. Another embodiment is a structural panel manufactured by bending flat panels or stamping, vacuum forming, or casting materials into multi-conic shells which attach to one or more panel surfaces to create a sandwich type structural panel.
1. A shell congruent to a surface, said surface comprising:a first convex region of a first cone; and a second concave region of a second cone; said first region and said second region each having positive area, said first cone being oppositely oriented to said second cone, said first cone being tangent to said second cone along a line segment, said line segment being common to a generator line of said first cone and a generator line of said second cone, said line segment being a portion of the perimeter of said first and said second regions, said shell, by virtue of being congruent to said surface, therefore comprising a first convex portion congruent to said first region and a second concave portion congruent to said second region, said first and said second portions including a common linear portion congruent to said line segment, said first and said second portions together forming a portion of said shell congruent to the union of said first and said second regions. 2. A shell as in claim 1, further comprising means for restraining movement of said shell, said means of restraining movement contacting said shell so as to maintain congruent of said first poriton of said shell to said first region.
This invention relates to building structures and structural panels constructed from thin materials to create shell structures, and in particular to multi-conic shell structures.
The increasing cost of building materials and the increasing global populations which lack sufficient housing has created the need for permanent structures built with a minimum of materials. Further, the increasing cost of delivering payloads to orbital and sub-orbital platforms has created the need for ultra-lightweight structures and structural support componens. An approach now common in the design of architectural structures is to create thin shells which are congruent to curved surfaces. Examples include the hyperbolic paraboloid (hy-par), the geodesic dome and other domed structures, the Quonset hut and other cylindrical structures, and conical shaped structures. An approach now common in the design of lightweight support structures, such as in air and space craft, is to create truss frameworks or sandwich structural panels. Examples include the octahedron-tetrahedron (oct-tet) truss and hexagonal or honey-comb sandwich panels. Typical design elements for both minimum-material building structures and lightweight structural panels include the transformation of stress loads into tension and compression forces within the structure, and the distribution of stress loads throughout the structure.
In contrast to the above structures, the present invention comprises multi-conic shells which can be variously designed and used for building structures and panel structures.
FIG.1 is a perspective view of a building constructed according to the teachings of and expressing a possible configuration of the present invention;
FIG. 18 is an oblique view of a regular cone with tri-part and projected base angle divided into increments θn ' and θn respectively, the tri-part is also shown in its uncurved and flat configuration;
The invention concerns thin curved shell structures which can be variously connected to existing structures or other likewise curved shell structures to create an improved load supporting structural component for use as a building structure as shown in FIG. 1, or structural panel as shown in FIG. 20. The advantage of curved shell structures built or manufactured in accordance with the teachings of the invention lies in increased strength per unit weight and ease of manufacture. The strength of the shell structure results from the distribution of loading forces throughout the entire structure via the conversion of compression and bending forces into tension forces. Ease of manufacture of these curved shell structures arises from the ability to use common two-dimensional materials such as plywood, sheetmetal, fiberglass, plastic sheeting, or other flat materials in their construction as will presently be described.
A building 20 formed according to the teachings of the first embodiment of the present invention is illustrated in FIG. 1. Building 20 has a multi-conic shell roof/wall portion 21 shaped like (i.e. congruent to) a multi-conic surface as previously discussed. The multi-conic shell 21 is mounted on multiple support beams including beams g1-g7 (other support beams are not shown in FIG. 1). Support beams g1 and g7 act as rigid supports of the perimeter of the multi-conic shell 21 and support beams g2-g6 act as rigid intermediate supports for the multi-conic shell 21. Support beams g1-g4 meet and are joined together at vertex h1 and support beams g4 and g5 meet at vertex h2. Support beams g5-g7 meet at vertex h3. Support beams (such as g2-g5) serve as strut lengths of tripod (tetrahedron) supports (the other strut lengths of the tripods are not shown in FIG. 1). Support tripods generally exist throughout the structure (see FIGS. 8a-8f). These tripod supports act as rigid support for multi-conic shell 21. In such a configuration the vertices of inverted cones which correspond to the multi-conic shell, such as h1 and h3, form foundation support points 22, and the vertices of regular cone surfaces such as h2, h4 and h5 form top vertex points of the roof/wall structure 20. Vertical side walls i1-i3 extend from foundation level 23 to roof/wall structure 21 to complete the building. At the vertices corresponding to regular cones (such as h2, h4 and h5) a skylight (24-26 respectively) may be included, if desired.
Theoretical Array of Regular and Inverted Cones
Significant strength in supporting structural loads is realized when multi-conic shells correspond to an array of intersecting regular (opening downward) and inverted (opening upward) theoretical cones. The nature of this array, and structures built corresponding to it will now be discussed in detail.
As shown in FIG. 16 when designing a multi-conic shell that corresponds to the theoretical array the designer must determine the height ht of the multi-conic shell. He also must determine the vertex angle vt of the cones in the theoretical array (twice the interior angle ia between the cone axis ax and the cone surface cs from the vertex). Both the height ht and vertex angle vt are design considerations and are determined by aesthetic and/or space requirements. From the height ht and vertex angle vt the length lg of all primary generators (distance from vertex of a regular cone to the vertex of a tangent inverted cone) can be calculated as follows: ##EQU1## where: ht =desired vertical height of cones in array
vt =vertex angle of all cones in array
Given the vertex angle vt as shown in FIG. 16 of all cones in the array, the surface angle sh (FIG. 17) between generator lines for a hex-part 27 and the surface angle st between generator lines for a tri-part (not shown) when unflexed and in their respective flat configuration (e.g. hex-part 27' in FIG. 17) can be calculated as follows: ##EQU2## Thus the surface angles sh and st between primary generators of hex-part and tri-part perimeter are determined.
STEP ONE: The Designer selects the vertex angle vt and height ht (FIG. 16) of the cones in the theoretical array of cones and determines the length of primary generators lg (distance between the vertices of adjacent regular and inverted cones) in the theoretical array of cones. All cones in the array, both inverted and regular, have identical vertex angles vt and identical primary generator lengths lg.
STEP TWO: Solve for the lengths lthn (as shown for a tri-part in FIG. 18) between the vertex 163 of the parent cone and the hyperbolic curve line 162 at base angle increments θn. For a hex-part (not shown in FIG. 18) (60 degree base angle) and tri-part 161 (120 degree base angle) increments of 3.75 degrees are recommended as providing sufficient accuracy in the construction of a building structure although smaller increments may be used if greater accuracy is desired. In general, ##EQU3## where: lg =length of primary generator bordering the cone segment
Increment n and repeat calculation until 16 or 33 lengths lthn have been calculated for the hex-part and tri-part respectively (assuming a 3.75 degree increment). The lengths lthn are then the appropriate surface lengths in the planar configuration when the hex-part or tri-part is made flat; however the surface vertex angle θn ' for each length lthn must be calculated from the base angle θn.
STEP THREE: Solve for the vertex angle θn ' measured on the surface of the cone from the base angle θn. Since the cone segment is a developable surface, the vertex surface angles θn ' will remain unchanged when the cone segment (e.g. 161) is in a flat two-dimensional configuration (e.g. 161'). ##EQU4## where: vt =vertex angle of all cones in the array
The calculations have been performed for a theoretical array where all cones have a vertex angle vt of 97.1808 degrees as shown below. The calculations have been performed for both hex-parts and tri-parts. A primary generator length lg of 1.0 has been used in the calculations which follow:
______________________________________LENGTHS FROM VERTEX TO HYPERBOLIC CURVE LINECALCULATED AT 3.75 DEGREE INCREMENTS        vertex surface        angle &#952;n '        (also correct        for uncurved        and therefore                    length lthn        flat surface)                    on surfacebase angle   where       from parent&#952;n        vt = 97.1808�                    cone vertex______________________________________HEX-PART0.00         0.00        1.0000     (lg)3.75         2.81        .96567.50         5.62        .937311.25        8.43        .914515.00        11.25       .896518.75        14.06       .882922.50        16.88       .873526.25        19.69       .867930.00        22.50       .866033.75        25.31       .867937.50        28.13       .873541.25        30.94       .882945.00        33.75       .896548.75        36.56       .914552.50        39.38       .937356.25        42.19       .965660.00        45.00       1.0000     (lg)TRI-PART0.00         0.00        1.0000     (lg)3.75         2.81        .89107.50         5.62        .821311.25        8.43        .758315.00        11.25       .707118.75        14.06       .665022.50        16.88       .630226.25        19.69       .601330.00        22.50       .577633.75        25.31       .557537.50        28.13       .541241.25        30.94       .528045.00        33.75       .517648.75        36.56       .509852.50        39.38       .504356.25        42.19       .501160.00        45.00       .500063.75        47.81       .501167.50        50.62       .504371.25        53.44       .509875.00        56.25       .517678.75        59.06       .528082.50        61.88       .541286.25        64.69       .557590.00        67.50       .577693.75        70.31       .601397.50        73.13       .6302101.25       75.94       .6650105.00       78.75       .7071108.75       81.56       .7583112.50       84.38       .8213116.25       87.19       .8910120.00       90.00       1.0000     (lg)______________________________________
STEP FIVE: Scribe or otherwise mark each alculated length lthn at corresponding angular increments (θn ') on the surface of the flat (two-dimensional) panel. Draw a smooth line connecting all points so marked. Cut along smooth line.
Example of Building Structure Built to Correspond to the Theoretical Array
FIGS. 19a thru 19c-11 depict a roof-wall portion of a building structure which can be constructed to correspond to the theoretical array. FIG. 19a is a plan view of a structure that can be derived from the theoretical array and built according to the teachings of the invention. FIG. 19b is an oblique view of the same structure with shadows projected vertically downward from the, edge of the roof/wall. As can be seen in the plan view of FIGS. 19c-1 thru 19c-11 the structure is made of connected cone segments which are identified as regular tri-parts 117, inverted tri-parts 118, regular tri-parts 119 extended beyond the hyperbolic curve perimeter, regular hex-parts 120, inverted hex-parts 121, and regular hex-parts 122 extended beyond the hyperbolic curve perimeter. No extended inverted hex-parts or extended inverted tri-parts are shown as part of this example structure. In FIG. 19b opening skylights 123 are shown for the upper corner of an inverted tri-part 118 and the upper corner of a regular tri-part 117. FIG. 19c shows a plan view of the same building structure 180 as in FIG. 19b with each component flat panel j1-j10 shown in its respective two-dimensional orientation and with the appropriate perimeter j1a-j10a dimension to scale as they would appear prior to being flexed and thus curved into a shape corresponding to a multi-conic shell of the depicted roof/wall structure as shown in FIGS. 19a thru 19c-11.
Method of Forming a Structural Panel
A second embodiment of the invention is a structural panel such as panel 130 as shown in FIG. 20 and a method of forming same. The structural panel 130 of FIG. 20 is comprised of a plurality of connected multi-conic shells 129 attached on one or both sides to a flat panel such as panel 131 and/or panel 132, to create a sandwich panel. Such a structural panel 130 can be used for wall construction, foundation support, or other structural membranes. As in the multi-conic shell building structure disclosed above, the multi-conic shell structural panel provides increased structural support and loading capacity per unit weight by virtue of the radial distribution of loading forces into tension and compression forces throughout the multi-conic shell structure. Additionally, if a pattern of cone segments is employed so that an interlocking network of tetrahedron structures is expressed within the multi-conic shell(s) and top and/or bottom flat panels (as in the structural panel 130, an example tetrahedron 133 is illustrated in multi-conic shell 129 connecting vertices 135a, 135b, 135c, and 135d), further gains in strength per unit weight are provided. Structural panels may be constructed of sheet metal, plastic, concrete, wood, or other suitable material.
Alternatives to the Regular Array
Although the theoretical array, and functional multi-conic shell designs that can be derived from it, are the most structurally stable and provide the greatest strength per unit weight for building structures and structural panels constructed under the teachings of this invention, it may be desirable to, in some instances, utilize other patterns of intersecting regular and inverted cones. However, for the purposes of creating special shaped, lightweight structures, the theoretical array can be altered somewhat without greatly compromising the inherent strength of the equilateral triangular (and therefore tetrahedron based) theoretical array. Such an alteration may be useful for inclusion in the interior portion 142 of an aircraft wing 143 an example of which is shown in FIG. 22, or for inclusion in the roof/wall surface (e.g. 144-147) of a building structure such as building structures 148-151 in FIGS. 21a thru 21d, to conform to steep or uneven terrain. Other applications of the invention may require further modifications in the theoretical array. A method of altering the theoretical array to accommodate various shapes will now be discussed.
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