Static structures (e.g. – buildings) – Compound curve structure – Geodesic shape
Reexamination Certificate
2001-06-11
2002-10-01
Canfield, Robert (Department: 3635)
Static structures (e.g., buildings)
Compound curve structure
Geodesic shape
C052S081300, C052S660000, C052S664000, C245S005000
Reexamination Certificate
active
06457282
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of specialized structures and, more particularly, to a skeletal building structure in spherical or hemispherical form similar to a geodesic dome. It is comprised of resiliently flexible rings that are interwoven. The resulting structure is curved to approximate the shape of a sphere or a hemisphere with each of the rings remaining in tension. The resulting skeletal structure achieves incredibly great strength and yet is extremely lightweight. Further related aspects of the invention are that because the curved surface is comprised solely of interwoven rings normally lacking fixed point to point connection, the entire area circumscribed by the ring is available for openings to the structure, and any one of the rings may be opened at its closure point and readily removed from the skeletal structure.
2. Description of the Prior Art
Ever since man has been building structures, he has chiefly relied on vertical components like posts in combination with horizontal components like beams. The posts achieve their function in compression while beams achieve their function with both tension and compression. That is, when a beam is supported by two posts, the space between the posts tends to sag due to the force of gravity with the result that the top side of the beam is compressed while the lower side is tensioned. This was a severe limiting factor because early materials used for construction were frequently dense materials such as stone, which are strong in compression, but considerably weaker in tension. Furthermore, dense material is inefficient for supporting weight as beams are expected to do. That is, the weight of stone is such that is has very little capacity for supporting anything but itself.
The ineffectiveness of beams made from such material was partially overcome sometime around the time of the Romans by engineers who developed archways that distributed sideways the load at the center of the arch to posts on either side. This had the additional advantage of utilizing a structure in which more space could be disposed between the posts, since the span length of beams made from materials that were weak in tension was necessarily limited, resulting in greatly reduced floor space in such structures.
The difficulty with such arches, particularly when constructed of such dense materials, is a tendency of the arch to collapse outwardly. This problem was overcome with the aqueducts because all the arches were placed end to end and supported each other laterally. In the construction of many of the great cathedrals, outward collapse of arches was prevented by exterior structures known as flying buttresses. When the arch concept is revolved about an axis at its center, a dome results and the problem of the external collapse of the dome was then sometimes solved by surrounding the base of the dome with a large chain. The dome at St. Peter's Basilica in the Vatican employs this technique thereby avoiding the necessity for flying buttresses such as are used at the Notre Dame Cathedral in Paris.
As engineering and building materials improved, such building construction resolved into skeletal structures of wood or steel, simple beams were replaced in many instances by trusses and the skeletal structures were covered by surfaces that acted as a skin and played little or no part in the support of the structure.
In the relatively recent past, structures that rely more on tension than compression have been developed. Consider, for example, a balloon in which the entire surface is in tension and there is no supporting skeleton or framework utilizing members which are in compression. This concept has been employed in the extreme case to temporary structures which are supported almost entirely by air trapped inside, any losses from which are supplied by a blower. Such losses can be minimized by the use of airlocks for ingress and egress.
The concept of using tension as the principal force can also be employed in structure utilizing a framework or skeleton, particularly when the surfaces of those structures are curved in more than one dimension. Since a balloon in its simplest form is geometrically described as a sphere, portions of a sphere referred to as sections can be employed in structures which principally rely on tension forces for support. In modern architecture, certain domed structures rely principally on tension for support, and thereby are employed most commonly where large areas are sought to be enclosed without any central supporting posts. Examples particularly include structures in which athletic activities occur like domed stadiums, in which no internal posts can be utilized.
The use of surfaces in the design of structures that curve in two dimensions leads to other complications, however, since construction materials are not naturally found or easily fabricated into such shapes. Complex mathematical and geometric relationships result from the efforts to employ essentially planar and linear building materials in the construction of curved structures. This is frequently achieved by subdividing a curved surface, a sphere, or a section of a sphere, into a multiplicity of small planar surfaces that fit together into a regular and coherent pattern, which surfaces, when small enough in comparison to the diameter of the structure, approximate a curved surface. To understand how this is achieved, it is important to examine the geometry of various polygons that can be employed as the small planar surfaces to approximate a curved surface.
The simplest regular polygon is an equilateral triangle, since it employs the fewest number of sides that can enclose a surface area in a symmetrical form. Since our objective is to achieve three dimensional structures, it is also important to consider the construction of convex polyhedra utilizing polygons. Four equilateral triangles joined together at their edges form the simplest regular polyhedron, a regular tetrahedron.
The next regular polygon is a square, and six squares joined at their edges form the regular polyhedron known as a cube.
The following regular polygon is a pentagon having five equal length sides and five corners with equal interior angles. If regular pentagons are employed to form a three dimensional regular convex polyhedron, it has been established that twelve regular pentagons joined at all their edges will form a regular polyhedron known as a dodecahedron. It is so named because it has twelve faces all of which are identical regular pentagons.
The next regular polygon is a hexagon. However, the regular hexagon cannot be employed to form three dimensional convex polyhedra because three regular hexagons fitted closely together at one corner of each of them produce a flat surface. This results from the fact that the inside angle at any corner of a hexagon is 120 degrees, which in each of the three interior angles of the hexagons attached at one of their corners results in 360 degrees or a complete circle about the point of the three corners. Of course a flat surface cannot be used to form a convex polyhedron because regardless of how many hexagons are used, the surface remains flat. For the same reason, any regular polygon having more than six sides cannot even been joined together at a common corner, so the pentagon is the polygon with the largest number of sides that can be used to form a regular convex polyhedron if no other polygon is employed.
It is noted generally that the triangle can be used to form two other regular convex polyhedra besides the tetrahedron. Eight equilateral triangles formed together at their edges will form a regular convex polyhedron called a octahedron. One other regular convex polyhedron is possible, and it is a icosahedron. It is comprised of twenty equilateral triangles all joined at their edges. These are the only regular convex polyhedra that can be constructed. For an explanation and more information concerning this fact, reference should be made to Polyhedra A Visual Approach by Anthony Pugh, publ
Canfield Robert
Van Der Wall Robert J.
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