THE highlight of this trip to Barcelona, other than the SolidWorks events of course, have been a series of excursions out into the city to experience some of the most iconic architecture you will find anywhere, that of Antoni Gaudi. His name is where we get the word “gaudy”.
In the case of the arches that support the roof of Pedrera, he hung chains from supports that represented the bases on either side of the arch in such a way that the distance from the lowest point of the chain to the supports represented the height of the arch. The resulting shape, when inverted, represented the most efficient self-supporting arch shape. Because the chain is flexible, the joints between the links relieve any stress between the links. This creates a parabolic shape which is in fact optimized to support an evenly distributed load. The wieght of each link represents the weight of the building materials. The shape created by gravity represents the inverse of the shape required by gravity when the arch is rigid instead of fleible and goes up instead of down.
The spires of La Sagrada Familia were designed in a similar way, but the materials used to build them were heavier at the bottom than at the top. For this reason, the simple wieght of the chain links that simulate the use of bricks to build an arch could not be used for the spires. In this case, Gaudi used string with bags of varying numbers of shot pellets in them to represent varying weights of the building materials tied to the string at regular intervals. This very closely represents the finite element method in a physical way. A calculation of this type is actually faster than the fastest computer calculation, because the laws of physics, primarily gravity and strength of materials would recalculate the shape of the spire immediately if the ends of the strings or weights in the bags were changed. This natural, immediate, and error free method of calculation is something we tend to overlook these days, where if we can’t figure out how to do it on a computer, we think it can’t be done at all.