Great idea! But how accurate is this translation of the catenary idea into 2D? What you really want is to hang a parallel array of chains all parallel to the X axis, and then hang another array of chains all parallel to the Y axis, and then adjust the length of each chain until all X chains touch all Y chains at all intersection points. This way, there is no assumption about the strength of the cloth. In other words, the problem with putting a non-elastic cloth into a catenary-type shape is that the cloth doesn't have enough degrees of freedom to assume the best position. Thus, when the dried concrete shape is turned over, the stresses will not all be tangential. A rubber sheet is somewhat better, but the thickness of the rubber is inverse to what you want: the highest stress will have the thinnest rubber, but that is where you want the thickest concrete. At 02:25 PM 12/27/2014, Allan Wechsler wrote:
The technique I heard about in the 70s was to hang a cloth sheet from a support the same shape as the intended foundation, let it settle into a nice catenary-like shape, and gradually spray it with concrete. You have to do it gradually, in thin, even layers, so that the heavy spots don't drag the cloth down and distort the shape. After it dries, you invert it. Perfect vaulted dome, ideal for bearing its own weight down to the foundation.