This project is an exploration of Statics vs. Statistics. That is to say it is a refutation of the ideal “truss” structure, which is statically determinate, in favor of alternatives based on a logic of statistical probability. While the logic of the truss is very efficient, it is not necessarily the most effective for unpredictable load patterns. The statistical approach, in which material is allocated according to where stress is most likely to occur, is closer to the structural logic that has evolved in living systems.
Fiber structures are common in Nature. Monodirectional structures such as bones or tree trunks use oriented fibers to resist axial loads . Multidirectional structures, like those shown below, use fibers in a random pattern to resist multiple loads. They often act as membranes because they can deform without breaking. Their resiliency is due, in part, to the redundancy of their overlapping members.
type I collagen
These structures are called statically indeterminate because it is impossible to determine the load path using statics: the hand calculations that have been used by structural engineers since the 1800′s. Today we have computers and nonlinear analysis to solve for complex structures, but buildings are still designed and constructed in terms of the old methods. In the words of Karl Chu: “Architecture has still yet to incorporate the architecture of computation into the computation of architecture” *
The goal of this project is to create a building method that relies on redundancy and statistical probablity as a structural logic instead of efficiency and static determinacy. I used Grasshopper to create a randomized fiber membrane on a base surface in the following steps:
First, points are located on the surface using a probability algorithm in which areas of higher curvature are more likely to be populated (surface is color-coded for gaussian curvature in these screenshots). This should yeild a higher density of material in those areas.
Next, the points are used as origins for randomly oriented strips of material based on “plank line” geometry (see earlier post), which conforms to the curvature of the surface but can be fabricated using perfectly straight strips of material.
Finally, the length of the strips is set to achieve the proper overlap. Individual strip lengths adjust to curvature as well: shorter pieces where curvature is more intense. Holes are placed at the intersections for attachment and the strips are unrolled for fabrication.
This project is designed to address structural requirements in a statistical manner rather than a determinant one. That is to say without exhaustive analysis of the stresses in each member. As in many living systems, more material is allocated where more stress is most likely to occur, and where more strength is needed to maintain the surface’s intended shape.
This method could be modified by adding structural analysis of the base surface instead of simple curvature analysis. Finite element analysis programs like NASTRAN or ANSYS will analyze a simple shell and output a deformation map similar to the curvature map shown here. All that is needed is to apply the bitmap to the surface, then vary point density by color, rather than by the native curvature graph.
*For an insightful analysis of design/construction paradigms in flux, see Karl Chu’s essay: “The Metaphysics of Genetic Archtecture” in Arquitecturas Geneticas-II