The present invention directed to a web structure, and more particularly to a web structure that could be utilized to form structural elements.
Architects, civil and structural engineers conventionally utilize various web structures for supporting, for example, trusses, floors, columns, etc. Typically, web structures form various lattices or framework that support underlying or overlying supports. In this regard, structural engineers are quite familiar with a “Fink truss” (FIG. 2), the geometry of which encodes an approximation of a “Sierpinski triangle” (also known as a 2-web) (FIG. 1).
It has recently been observed that the geometry of the hardest substance known to man, namely diamonds, and the modern roof truss encode and represent the approximations to certain fractals. The Fink truss (FIG. 2) is an engineering design that is a level-1 2-web. In the nature, carbon-carbon bonding in diamond encodes a level-1 3-web.
A structure resembling the Sierpinski triangle has been useful to structural engineers because each member or edge 110, 112 and 114 at level-0 (FIG. 1) can be braced at its midpoint 116, 118 and 120, respectively, (level-1 represents the “midpoint bracing” of level-0.) For example, consider a standard wooden 8-foot 2″×4.″ As a stud in the wall of a house, it will buckle at a certain load L. But the (engineering) buckling equations explain that when that same 2×4 is braced in the middle, it can carry as much as four times the load L. In other words, with very little extra material, we can make a much stronger column by simply bracing in the middle. It is noted, however, that the Sierpinski triangle is the limit curve of this bracing in the middle process, e.g., a level-2 approximation (FIG. 3) is obtained by bracing each member (in the middle) of the level-1 approximation, a level-3 approximation (FIG. 4) is obtained by further bracing each member (in the middle) of the level-2 approximation, and so on ad infinitum.
Turning to diamonds, I recently observed that the diamond lattice encodes the “Sierpinski Cheese,” which is also called a 3-web (FIG. 7). Relative to the 2-web, we can think of the diamond lattice as encoding four “Fink trusses” (level-1 2-webs), one in each face of a tetrahedron—in FIG. 8, the bracing members 122(A-C), 124(A-C), 126(A-C) and 128(A-C) expose four level-1 2-webs (Fink trusses).
The macro-scale observation that bracing in the middle greatly increases strength may also be observed on the micro scale. In the case of diamonds, the cabon-cabon bonding distance (distance between two carbon atoms that share a covalent electron) is 154.1 pm (one pm=10−12 meters). In contrast, silicon exhibits the same diamond lattice structure as diamond, but the silicon-silicon bonding distance is 235.3 pm. Thus, again strength in the case of compressive and tensile forces is directly related to distance (compression and tension at these scales are virtual, i.e., the edges in the diamond lattice (FIG. 7) resist being made shorter (compression) and resist being made longer (tension). The bonding provides “electrostatic balance.”
All of these fractals, the 2-web (limit of Fink truss concept), the 3-web (limit of the diamond lattice concept) provide for adjusting the distances of the compression and tension members by middle bracing. It is a mathematical fact (since we are dealing with line segments) that we can middle brace and never worry about the braces at one level obstructing the braces at the next level. In practice, however, the scales and sizes of the materials used for edges may affect the limit of these fractal designs.
In summary, the Fink truss, which is a level-1 Sierpinski triangle, has been utilized for many years in constructing various support structures. To date, diamond which has the geometry of a level-1 Sierpinski cheese as its basic building structure is known to be the hardest structure. The inventor of the present invention has discovered a geometrical structure that represents the next step.