Memoirs 6. Hyperbolic Paraboloids and Domes

by Milo Ketchum
circa 1990

I had seen the many inverted umbrella hyperbolic paraboloids (hypars) built by Candela in Mexico City, but there never was a chance to design one. The first hypar we designed was the First Methodist Church building in Boulder, Fig. 6.1, and it was not an orthodox hypar. The width of the building was small, only 45 feet. The length of the shell units was 26 feet, were supported by arches on the sides of the building, and by rigid frames across the 45 foot span. The outside arches were higher than the center, so the ribs from the top of the arch to the center were not level, but sloped downward. This caused a lot of head scratching, but it was concluded that the structure carried most of its load by the parabolic crossed arches, and was therefore stable. The justification for the architectural solution with the exposed arches on the street facade, was to reproduce the slope of the original church building. The walls were glass brick, in colors, alternating with concrete block, a truly handsome building. The structure was the first shell that we designed that was built with shotcrete.

The next large hypar was at the Broadmoor Hotel in Colorado for the International Center, Fig 6.2. At that time it was reputed to be the largest hypar constructed in America. It was a typical four-gabled hypar with spans of 185 feet in both directions, or as we liked to say a three inch shell spanning 260 feet (diagonally). As it was under design, we made simple models to study the structural problems. It soon became evident to me that it looked exceedingly boxy. The solution was to make the external ribs quite thin at the edges and project then outward so that the length of the apparent top ridge was the same as the sloping distance of the exterior ribs., Fig 6.3. At the same time, this solution provided a very thin edge that gave a lightness to the entire structure. It was proposed to hang a heavy curtain across the structure at the middle, and we were asked if the shell would carry it. Our solution was to prestress the top rib for moment, and to make it triangular so it could be roofed over, and not be so prominent. This was a case where we, as structural engineers, were responsible for one of the most important architectural features.

We then decided to prestress the other ribs. Our overriding consideration was the deflection of the thin rib. Afterward, we were criticized for this decision because these members are in compression, and therefore prestressing was not necessary. What was not fully realized at that time, is that the ribs are also subjected to high torsional stresses, so afterward we were very glad that we used this system.

We also designed the structure of the St. Louis Planetarium, Fig. 6.3, for the firm of Hellmuth, Obata, and Kassabaum. Fig. 6.3. It was a hyperboloid of one sheet, a large circular dome shaped structure similar to the cooling towers now used. At the center of the building there was a spherical metal dome to house the viewing screen for the projections of stars, and space for the seating spectators. This dome was surrounded by a lobby with stairs to the roof. The roof was a platform so the stars could be viewed in actuality. The design of the dome was an exercise in statics with the exception of the supporting ring at the base, which was triangular in shape tapering to the thickness of the shell. We analyzed this element of the structure by finite difference methods, and there was very little moment.

The largest building we designed using domes, was for a discount store called Fan-Fair, Fig 6.4. The structure consisted of a series of 50 foot square translation shells, 2.5 inches thick; there were 9 rows of 4 units, so it covered a large area. The domes were formed with stock bowstring trusses, so the forms could be lifted in one piece and moved to the next row. Also the trusses could be resold to cut the cost of the forming. There were no ties at the tops of the columns, but external diagonal thrust members were used to support the domes at exterior edges. Again the acoustics were a consideration, and when the building was unoccupied, the reverberation time was very long, however, when all the furniture was placed, the acoustics were acceptable. The contractor, who was the owner, reported very low costs, less than structures with other materials.

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