Memoirs 4. Folded Platesby Milo Ketchum
My first great love in shell structures and the first to be designed, were folded plates. The analysis was straight forward, used methods for which I was familiar, and the structural elements were those we used for other concrete structures. Also, the design of folded plates conditioned me for my approach to the design of barrel shells. It is possible to analyze folded plates with more precision that barrel shells.
My first acquaintance with folded plate structures was the appearance of the classic "Hipped Plate Construction" by George Winter and Minglung Pei, in the Journal of the ACI in January, 1947, pp. 505-531. I always disliked the name "hipped plate", and when I was chairman of an ASCE committee, I was at least partially responsible for changing the name to "folded plate". The theory we used involved only the initial stresses without consideration for deflection of the joints of the structure because we took care to avoid excessive deflections by proper support of the plates at the exterior valleys. I thought the use of simultaneous equations was very unsatisfactory, that time being well before the wide spread use of computers, and even a few equations took a long time to solve. I am not aware of who first suggested the use of moment distribution for obtaining the transverse moments, but it was a major breakthrough in my understanding, because it was a technique with which I was thoroughly familiar.
In 1952 we were approached by one of our best clients, Tom Moore, about the design of a roof for the State Home in Grand Junction, Colorado. It was a folded plate with a Z shape (tipped on it side, see Fig. 4.1), so that north light windows were provided. I had done my homework and was well prepared to design a typical structure but I was a little nonplused by this type. It was not until I saw a similar structure in Concrete and Constructional Engineering, published in England that I was fully convinced that the design was feasible. The roof consisted of elements of two spans, with four parallel elements. We completed the plans, and it was already to go out for bids, when the government agency responsible, saw the design and turned it down.
Tom Moore, not to be thwarted, talked his brother into using this type of design for his brothers new heavy equipment agency and shop, The H. W. Moore Equipment Company in Commerce City, an industrial suburb of Denver. The design in shown in Fig. 4.1, and subsequently was written up in a paper "Design and Construction of a Folded Plate Roof Structure", Journal of the ACI, January, 1955. There are three elements, a display area with a span of 38 feet and a cantilever span of 24 feet, with three bays each 36 feet wide, next a shop area with 80 foot spans, and 5 bays, 36 foot wide. Finally a parts area of Z elements with 75 foot spans and 22 foot overhangs with 11 bays each 18 feet wide, a huge building. It was reputed to be the first large folded plate building built in this country.
My memory was that we had no particular problems during the design. The analysis is straight forward, and is described in the paper just mentioned. The only area where a deflection analysis was required was the transition area between a low bay and a high bay in the shop area. After construction, we discovered a few facts about deflections with which we were not fully aware. The visual effects of are much exaggerated when viewed from a point that shortens the horizontal distance with reference to the vertical. Therefore in the next structures, if at all possible, we always placed columns to support the valleys of the end plates. This had a further advantage that it was not necessary to make a deflection analysis for the stresses, and the longitudinal reinforcing in the end plates could be reduced.
An incident occurred during construction. I met Felix Candela for the first time at an ACI meeting in Denver. I described my shell and he brought out a similar set of plans for a Z shell roof. I invited him to look at the construction, and after he took a look at the Z shells he said "There will be a crack here", indicating an point about at the quarter point of the span. There were indeed hairline cracks at these points.
We designed and had built, many folded plates in the next few years, and there is only room to comment on a few of the most interesting. We used a north light, Z shell, for the roof of the Casey Junior High School in Boulder, Fig. 4.2. The spans were continuous, of 40 feet, 20 feet and 65 feet, for a cafeteria, a hall, and a gymnasium, respectively. The bay spacing of the units was 15 feet. The whole structure was top lighted and gave an even north light without extra artificial lighting. The architect wanted to make the roof appear to float above the base, so the end of the plates were carefully detailed, and the usual beam stiffeners were replaced by slightly thickened areas over the supports.
Across the street from the Casey Junior High, we designed the gymnasium for St Mary's High School with spans of 75 feet and bay spacings of 35 feet, thus requiring horizontal spans of 17.5 feet for the slab element of the folded plate. See Fig. 4.3. This is a long span for the normal four inch slab, and we solved that problem by haunching the slab at the supports. This requires and extra analysis effort for the taper because the slab must be analyzed as a continuous haunched beam, and requires special stress distribution coefficients. In this case we put the end stiffeners below the plates.
As we designed more folded plates, we began to use more sophisticated design methods. The culmination was in the roof of the Arvada High School. The structural system was for two spans at about 60 feet on centers, with a bay spacing of about 30 feet. In order to eliminate the ties at the junction of the two spans, we supported the first valley and edge beam by additional columns at the center of each span. Then the horizontal thrusts that normally would be taken by a tie, can be carried by an effective horizontal beam which has a width of the edge plate plus the first inside plate, in this case, 15 feet plus 4 feet for a total of 19 feet. The visual effect is much more pleasing.
Other unusual structures were a folded plate with a portion of the plate replaced by a concrete truss to provide north light, a circular building for a church, using triangular plates supported by an arrangement of columns on a circle at the middle, and another church in Minnesota with triangular plates.
For the arrangement of shear reinforcing, we tried using both usual diagonal bar arrangement, and orthogonal patterns. The diagonal arrangement is better because the shear forces are carried directly in tension, but the other method has the advantage that the reinforcing is easier to place and requires only three layers. We used additional horizontal bars in the shear area to take some of the component of diagonal stress. After the Moore Equipment Company, we carried all of the shear in reinforcing, and did not allow any use of the concrete. This was the result of seeing the underside of even well placed concrete, which often had honeycombing areas where the concrete had hung up on the bars. It is also important to place the chair supports so this does not occur. For all of the many structures we designed and had built, I remember no real structural problems, and after a while, I began to have great confidence in shell structures. It is important to spend a lot of time studying the structure for possible adverse behavior, rather than do things by rote. Over confidence leads to problems.