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RELATED APPLICATION 
       [0001]    This application claims the benefit under 35 U.S.C. §120 from U.S. application Ser. No. 13/371,774 filed Feb. 13, 2012, for “Cast Bodies With Tetrahedral Tube Reinforcement”. 
     
    
     BACKGROUND 
       [0002]    The present invention relates to the reinforcement of concrete and, in particular, to cost-effectively increasing the strength while reducing the overall weight or volume of concrete structures. 
       SUMMARY 
       [0003]    I have conceived a way of achieving this design objective using the invention described in my U.S. Pat. No. 3,237,362 “Structural Unit for Supporting Loads and Resisting Stresses,” the disclosure of which is hereby incorporated by reference. The construction-related technique disclosed therein can be adapted to improve the performance characteristics of concrete and other structures by substituting triangulated tubular cores for conventional reinforcing rods or bars (“rebar”). 
         [0004]    The present disclosure is preferably directed to a weight reduced and strength enhanced concrete structure comprising a continuous matrix of concrete reinforced with at least one tubular chain of integrally interconnected hollow tetrahedra, and to a method for reinforcing concrete. 
         [0005]    The tetrahedra have triangular planar faces that share common vertices and edges with neighboring tetrahedral in the chain and provide deep, angulated spaces that are filled with concrete. The cores in essence “float” within the concrete in that they are not mechanically fixed to anchors, panels, floors, or the like at the exterior surface of the concrete structure. However, as an option to further stiffen the reinforcement, the cores can be pre-tensioned and/or a plurality of cores can be affixed to each other. 
         [0006]    The use of triangulated tubular tetrahedra as reinforcement cores in a concrete matrix, offers a unique combination of advantages. The concrete matrix provides resistance to compression, but with the embedded cores the concrete structure becomes more resistant to tensile, torsional, torque and bending loads. Impact or other loads are distributed substantially isotropically, thereby diffusing the loads and reducing local stresses. Finally, this reinforcement and associated advantages can be achieved with cores that are lighter than the concrete material they displace or the rebar which they replace. 
         [0007]    Although not limited thereto, the most straightforward embodiment of the reinforced concrete structure would be as load bearing elements in the building and construction industries. In one embodiment, each core has a longitudinal centerline that is aligned in parallel with the longitudinal center line of the structure. The structure is intended for use where a compressive load is imposed on the structure at the longitudinal ends, in parallel with the centerlines of the cores, e.g., as in a structural column. In this embodiment, the cores reinforce the structure against torsional and bending forces that might arise over time or during transient loading. 
         [0008]    In another embodiment, the reinforcing cores area arranged along the length and/or width of a concrete beam or slab, to resist loads that are transverse to the length or width. For a horizontal beam supported at opposite ends, the cores are preferentially situated in the lower region of the beam to resist tensile bending stresses, whereas for a cantilevered beam the cores are preferentially situated in the upper region of the beam. 
         [0009]    The cores do not form a self-standing structural frame or skeleton, but rather merely reinforce a concrete structure. In the most common end use, a plurality of cores are independently arranged, i.e., one core is not rigidly connected to another core (although this does not preclude spacers or shims between cores to maintain spacing). For extra strength, the core members can be arranged with the tetrahedra of adjacent core members in closely spaced or connected registry, whereby confronting vertices or edges are in conforming contacting alignment and are rigidly joined directly or indirectly. 
         [0010]    Whether or not pre-tensioned, the reinforcing cores of the present invention self-anchor in the concrete and thus can remain entirely within the matrix. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0011]      FIG. 1  is a perspective view of a tubular blank shown partly crimped in the process of converting it into a structural tetrahedral chain core of square transverse outline in accordance with one embodiment of the present invention; 
           [0012]      FIG. 2  is a transverse section of the crimped tubular blank taken along the lines  2 - 2  of  FIG. 1 ; 
           [0013]      FIG. 3  is a transverse section of the crimped tubular blank taken along the lines  3 - 3  of  FIG. 1 ; 
           [0014]      FIG. 4  is a side elevation of a structure comprised of a tetrahedral chain core reinforced with tie rods along the rows of tetrahedral vertices in accordance with an optional feature; 
           [0015]      FIG. 5  is a transverse section of the reinforced core taken along the lines  5 - 5  of  FIG. 4 ; 
           [0016]      FIGS. 6 and 7  show longitudinal and cross sections, respectively, of a reinforced cylindrical concrete structure in accordance with one embodiment; 
           [0017]      FIG. 8  shows another embodiment, of a rectilinear concrete structure in which a first set of cores are aligned with the width direction and a second set of cores are interleaved with and aligned transversely to the first set; 
           [0018]      FIGS. 9 and 10  show a curved concrete structure and detail of how adjacent cores can optionally be connected together along confronting edges; 
           [0019]      FIG. 11  shows a concrete beam with a plurality of reinforcing cores offset below the centerline; 
           [0020]      FIG. 12  shows the beam of  FIG. 11  supported at both ends against a transverse load; 
           [0021]      FIG. 13  shows a beam supported at only one end against a transverse load at the other end, with a plurality of reinforcing cores offset above the centerline; 
           [0022]      FIGS. 14 and 15  show concrete slab having a plurality of reinforcing cores arranged perpendicularly below the center plane of the slab; and 
           [0023]      FIGS. 16A , B, and C are schematic representations of how a pre-stressed concrete beam can be fabricated with pre-tensioned cores. 
       
    
    
     DETAILED DESCRIPTION 
       [0024]      FIGS. 1-3  show a representative triangulated tubular tetrahedral core to be completely embedded in a solid matrix. An imperforate tubular blank  10  has a circular cross-section and specifically of cylindrical form made of bendable or deformable material such as metal, as for example, steel, copper and aluminum. The tubular blank can also be made of plastic material, and especially of thermoplastic material, so that it will be deformable upon heating. Other suitable materials may be paper and fibrous material embedded or bonded with plastic. 
         [0025]    The tubular blank  10  may be welded, glued, seamless or lock-seamed and is crimped at spaced transverse linear sections  11  and  12  in planes at right angles to the axis of the tubular blank to collapse this blank along these sections and to form a structural core or web  13 . This crimping operation may be performed while the tubular blank  10  is cold or hot according to the nature of the material from which the blank is formed and may be carried out in such a way that successive sections  11  and  12  are crimped in parallel planes but in different directions and alternate sections  11  or  12  are crimped in parallel planes and in parallel directions. Each of the crimped sections  11  and  12  is produced by collapsing the wall of the tubular blank  10  from diametrically opposite sides of the blank to an equal extent by a pinching action to form each crimped section substantially diametrically across the blank. In the specific form of the tube shown in  FIG. 1 , the two sets of crimped sections  11  and  12  extend in planes at right angles to each other, so that the transverse general outline of the core is square, However, the two sets of crimped sections  11  and  12  may extend in planes at an angle other than 90° to each other to define a transverse core outline which is of rectangular oblong shape. The crimped sections are shown as equally spaced and the distances between these sections are such in relation to the diameter of the tubular blank as to form regular tetrahedra, but this is not necessary. 
         [0026]    For producing the structural core or web  13 , the tubular blank  10  is first crimped in a plane at right angles to the axis of the blank in diametrically opposed directions near one end of the blank to form a first crimped section  11  at the region A and to close the blank; the blank is then crimped at a linear interval from the first crimped section at right angles to the axis of the blank in diametrically opposed directions transverse to the first mentioned directions and more specifically at right angles to the first mentioned directions to form a second crimped section  12  at the region B and to form thereby a hollow tetrahedron  14 . The blank is further crimped at the same linear interval at right angles to the axis of the blank in diametrically opposed directions parallel to the first mentioned directions to form a third crimped section  11  at the region C and thereby a second tetrahedron  15 . This crimping action is continued for successive sections in alternate directions until the tubular blank  10  has been shaped into a structural core  13  having the desired configuration. This core  13  will consist of a chain of tetrahedra  14  and  15  interconnected along the crimp sections  11  and  12  and arranged so that successive tetrahedra are mirror images of each other in the form of optical antipodes. 
         [0027]    Another alternative procedure for forming the tetrahedral chain core or web  13  is to crimp one end and at a linear interval corresponding to two successive tetrahedra, the blank is crimped in diametrically opposed directions parallel to the diametrically opposed first crimping directions to form a hollow pillow-shaped body between end crimp sections. A third crimp is then formed in the middle of the pillow-shaped body between these crimped sections but in diametrically opposed directions transverse to and specifically at right angles to the first crimping directions. This third crimp deforms the pillow-shaped body into two hollow tetrahedra  14  and  15 . 
         [0028]    Each of the tetrahedra  14  and  15  is bounded by four substantially plane triangular faces  16  and will contain six edges  17 , two of which are at opposite ends of the tetrahedron along successive crimped sections  11  and  12  and four vertices  18  located at the ends of these crimp sections. These vertices  18  are arranged in four parallel linear rows extending along the core  13  and encompassing a rectangular area transverse to the core and more specifically a square area. A tie rod or cord can be welded to successive vertices in each row of vertices. Such ties in conjunction with successive triangular plane sections  16  of the tetrahedra form chains of interconnected triangular trusses. 
         [0029]    In  FIGS. 4 and 5 , the ties between the vertices of the core  13  are shown constituting steel rods or wires  20 , brazed, welded or otherwise affixed to the core  13  at all vertices  18  in accordance with the nature of the core material, so that these rods or wires constitute parallel chords forming part of the structure unit. These chordal rods  20  serve to further rigidize the core  13  and to form a composite unit. 
         [0030]    Although the core unit  13 ,  20  has been deformed or prebuckled into a series of continuous tetrahedra, it is still a tubular structure and still retains the high torsional or twist resistance of a tube. Moreover, the structure  13 ,  20  is isotropic in character. Its plane face sections  16  are equally strong and are oriented in different directions, so that the structure can stand stresses in all directions and will distribute stress applied in any region in all directions. The core structure  13  can be manufactured with ease from tubular stock of from ⅛″ diameter to as much as 6″ or more in diameter. 
         [0031]    The composite unit  13 ,  20  has an unusually high strength to weight ratio because of the mutually braced triangular planes and because tetrahedra have the highest ratio of surface area per unit volume of any regular polyhedrons, and consequently are the most stable of all polyhedrons. By combining this property of the tetrahedra with the high twist resistance of the original tube, a very stable structure created. 
         [0032]      FIGS. 6 and 7  show a first embodiment  100  of a reinforced concrete structure, in the form of a cylinder having a length L.  FIG. 6  is a longitudinal section and  FIG. 7  is a cross section. The reinforcing core  102  is embedded within a solid matrix  104 . The circular outer surface  106  of the concrete structure is continuously contoured about the axis, and the centerline  108  of the core is at the center of the surface, i.e., congruent with the axis. These figures show only one core embedded longitudinally within an elongated matrix, but in some embodiments a plurality of cores could be provided in a circular pattern around the central core (not shown). It should be understood that the matrix and thus the concrete structure can have any uniform or non-uniform cross sectional shape and can taper longitudinally. Generally, the resulting concrete structure would be used as a construction element, such as a column, whereby the longitudinal ends would be under compression (as indicated by the axially directed arrows). 
         [0033]    Especially when the concrete structure will be subjected to a potentially corrosive natural or man-made (e.g., industrial) climate, a metal tube blank can be externally galvanized or treated with an organic material before crimping. 
         [0034]      FIG. 8  shows another embodiment  200  of a rectilinear concrete structure having length L, width W and thickness T. A first plurality of cores  202   a  and  202   b  are aligned with the width direction and a second plurality of cores  202   c  and  202   d  are interleaved with and aligned transversely to the first plurality. This configuration reinforces the matrix  204  against stresses applied anywhere and in any direction on the surface  206  of the concrete structure  200 .  FIG. 8  also shows that when viewed along the centerline  208  of each core, each tetrahedron envelopes a relatively large internal volume  210  of air. 
         [0035]      FIG. 9  shows a section view of a portion of a curved concrete structure  300 , in which the centerlines  308  of adjacent reinforcing cores  302  extend in the length direction L of the structure while embedded in a concrete matrix  304  that defines the overall shape  306 . The depiction in  FIG. 9  can be considered an arc section of a large concrete conduit or the like that extends along an axial length L (only a portion of which is shown). The tetrahedra in the core envelope volumes  310 . Adjacent cores such as  302   a  and  302   b  can be rigidly connected to each other directly along confronting edges  312   a  and  312   b  (as shown in  FIG. 10 ) or the vertices  314   a,    314   b  can be connected indirectly by mutual connection to a common rigid support such as longitudinally extending tie rods or angled strips. 
         [0036]    For the preferred embodiment such as shown in  FIG. 1 , the succession of triangle planes or faces are equal and opposite, forming regular tetrahedra. Triangulated, tetrahedral reinforcing cores not only greatly increase the volume to weight ratio, but also the strength to weight ratio relative to a cylinder made entirely from concrete. The cores resist stresses by distributing tension, torsion, and bending forces imposed on the structure, while the concrete resists compressive forces. 
         [0037]      FIG. 11  shows a rectilinear concrete beam  22  having a length L, width W, and thickness T. The beam has an upper surface  24  and a lower surface  26 , with a centerline or center plane  28  extending longitudinally midway between the upper and lower surfaces, from the left or front end  30  to the back or right end  32 . In this embodiment, a plurality of reinforcing cores  13 A,  13 B and  13 C extend in spaced apart, parallel relationship offset from and below the centerline  28 . Thus, the reinforcing cores  13  are situated in the portion of the matrix  34  that is below the centerline  28 . 
         [0038]      FIG. 12  shows the beam  22  anchored  36  at the left end  20  and anchored  38  at the right end  32 , as commonly found in building and other constructions. The beam is designed to support a local or distributed load indicated by force F, which would tend to bend the beam  22  downwardly, thereby compressing the matrix closer to the upper surface  24  while inducing a tensile stress in the matrix portion  34  closer to bottom surface  26 . According to the present embodiment, the cores  13  located below the centerline  28  resist the tensile force in the lower region  34  and thereby enable the beam  22  to bear a higher load F than would be possible without such reinforcement. 
         [0039]    It should further be appreciated that the reinforcing cores  13  need not be anchored at the ends  30 ,  32  of the beam  22 . Due to the large surface areas presented by the planes of the plurality of tetrahedra in intimate contact with the surrounding matrix, the cores are in effect self-locking in place within the matrix portion  34 . Thus, the reinforcing core remains in fixed relation to the matrix material. 
         [0040]      FIG. 13  represents another configuration that can be found in building construction or the like, where the beam  22 ′ is anchored  36  only at one end  30 , with the other end  32  unsupported, i.e., cantilevered. If the load F is imparted toward the free end  32 , the upper surface  24  experiences a tensile stress whereas the material closer to the lower surface  26  experiences a compressive stress. In this configuration, the reinforcing cores  13  are situated longitudinally above the centerline  28 . Thus, the upper region  40  of the matrix closer to the upper surface  24  is reinforced against the tensile loads on the concrete. 
         [0041]      FIGS. 14 and 15  show a different configuration  42 , of a concrete slab  44 , such as would be used for flooring in a building, supported in four corners by columns or posts  46 A,  46 B,  46 C and  46 D. Alternatively, at least two of the sides are supported along their full length (as would also be represented by  FIG. 12 ). The length L and width W are shown as different, but could be of equal dimensions. Because in a slab  44  the length and width are generally somewhat similar, reinforcement is needed in both directions. A first plurality of reinforcing cores  13 D extend in laterally spaced apart relation in the length direction and another plurality of reinforcing cores  13 E and  13 F extend in the width dimension, in alternation above and below the cores  13 D. Because in general a slab as shown would only need to bear loads imposed on the top surface, only the region of the slab below the center plane need be reinforced. 
         [0042]      FIGS. 16A , B and C illustrate schematically a variation by which a concrete beam or slab can be pre-stressed with the reinforcing cores. One core  48  has a succession of tetrahedra  50  connected together via successive crimps or webs  52 ,  54 , which alternate in perpendicular relationship, (i.e.,  52  is vertical and  54  is horizontal). Each tetrahedron has four triangular planes  56 , as previously described in connection with  FIG. 1 . An arbitrary number of tetrahedra can be provided on any given core, with the first tetrahedron indicated at  50 A and the last indicated at  50 B. The core is tensioned (i.e., pulled in opposite directions along the axis) as indicated by the arrows at P, thereby elastically straining the core to some extent. 
         [0043]    While the core is in tension, concrete is poured around the core  48 , preferably with the lead and trailing tetrahedra  50 A,  50 B outside the matrix  58 , as one way of providing convenient surfaces for devices represented by P to maintain the tension in the core while the matrix cures. Upon curing of the matrix  58 , the tension on the device is released, and the end tetrahedra  50 A,  50 B removed as by cutting, thereby creating a reinforced beam, pole, or the like, in which the core retains restorative forces indicated at  62 . These forces  62  tend to compress the concrete at the concrete interface. The triangular planes do not move, and thereby provide great strength for resisting bending loads on the beam  60 . The deep notches formed by successive tetrahedra are filled with concrete and provide a much higher surface area in contact with concrete, which resists longitudinal displacement of the core relative to the concrete, to a much greater degree than ribs or the like on rebar. Moreover, this self-locking maintains the core in a pre-stressed condition, especially deep within the matrix, without external anchoring of the core. In essence, the core is internally anchored at every tetrahedron. 
         [0044]    The cores are very strong in resisting tension, in part because the webs formed by the crimps are aligned with the core axis so cannot readily be strained longitudinally and tensile forces would not act across the web to separate the closely compacted walls formed the crimp. Furthermore, the any tensile forces that act on the core would tend to urge the planes against and thereby compress the concrete in the notches. 
         [0045]    For an especially rigid reinforcement, each core can have tie rods  20  or the like as shown in  FIGS. 4 and 5 , connecting successive vertices, and thereby assure longitudinal alignment of the vertices at the four corners as indicated in  FIG. 5 . If each core  13  is horizontally oriented as shown in  FIG. 5 , the crimped webs  11 ,  12  will be oriented obliquely to the centerlines or center planes of the beams. Since the beams will bear vertical loads, none of the crimped webs will be subjected to a perpendicular load, and thus the cores will be doubly strong, i.e., due to the connection of the tie means at the four corners, as well as the minimization of the load acting perpendicular to the crimped webs. 
         [0046]    It should thus be appreciated that with the present invention, concrete structures or bodies of a given size can be strengthened while reducing the average density (and thus overall weight), relative to a structure or body of that given size made of homogenous concrete or rebar-reinforced concrete. Alternatively, a desired degree of strength can be achieved with a smaller and/or lighter structure than if made of homogenous concrete or rebar-reinforced concrete. If very high strength is desired, each core can be stiffened by connecting successive vertices with a tie rod or the like, while the weight of the tie rods. Is offset to some degree by hollow nature of the tetrahedra. Concrete structures or bodies can be reinforced with a substantially uniform pattern or array of individual, unconnected tetrahedral cores, or the cores can be arrayed non-uniformly.

Summary:
A weight reduced and strength enhanced concrete structure in which at least one tubular reinforcing core is embedded in a solid concrete matrix. Each core is a chain of integrally interconnected hollow tetrahedra. Each tetrahedra has triangular faces connected at common edges and vertices. The planar faces of adjacent tetrahedra are spaced from each other, and concrete fills the spaces. The cores are suspended within the concrete and self-anchored, without anchors at the exterior surface of the structure. With the embedded cores the concrete structure becomes more resistant to compressive, tensile, and bending loads. For even greater strength of the structure, the cores can be tensioned and thereby pre-stress the concrete. Impact or other loads are distributed substantially isotropically, thereby reducing local stresses. These advantages can be achieved with cores that are lighter than the concrete material they displace or rebar they replace.