CHAPTER I - FOLDED PLATES It seems appropriate to start the presentation of examples of shapes and forms for shell structures with the folded plate because it is the simplest of the shell structures. The distinguishing feature of the folded plate is the ease in forming plane surfaces. Therefore, they are more adaptable to smaller areas than curved surfaces which require multiple use of forms for maximum economy. A folded plate may be formed for about the same cost as a horizontal slab and has much less steel and concrete for the same spans. Folded plates are not adapted to as wide bay spacings as barrel vaults. For widths of plate over, say, 12 feet, the thickness of the folded plate must be thicker than for a barrel vault. Some advantage may be gained by increasing the thickness of the slab just at the valleys so it will act as a haunched beam and as an I section plate girder.
BASIC ELEMENTS The principle components in a folded plate structure are illustrated in the sketch above. They consist of, 1) the inclined plates, 2) edge plates which must be used to stiffen the wide plates, 3) stiffeners to carry the loads to the supports and to hold the plates in line, and 4) columns to support the structure in the air. A strip across a folded plate is called a slab element because the plate is designed as a slab in that direction. The span of the structure is the greater distance between columns and the bay width is the distance between similar structural units. The structure above is a two segment folded plate. If several units were placed side by side, the edge plates sould be omitted except for the first and last plate. If the edge plate is not omitted on inside edges, the form should be called a two segment folded plate with a common edge plate. The structure above may have a simple span, as shown, or multiple spans of varying length, or the folded plate may cantilever from the supports without a stiffener at the end
THREE SEGMENT FOLDED PLATE This sketch shows a folded plate structure with three segments for each barrel. The end stiffeners are rigid frames rather than deep girders as in the last example. The forces from the reactions of the sloping plates on these rigid frames will be quire large and at an outside column they will not be balanced by thrusts from the adjacent plates. The size of the frames may be reduced by using a steel tie between the tops of the columns which can be concealed in the fenestration. The dimensions of the plates are dependent on both the width of the barrel and on the span. The depth of the shell should be about 0.10 times the span and the maximum slope of a plate should not be greater than 40 degrees. For example, assume for the above structure that the span is 60 feet and the bay width is 24 feet. The depth of the shell should be about 6 feet and the horizontal width of each plate with a three segment plate should be about 8 feet. The slope of the plates is 6/8, which is about 37 degrees and is satisfactory. The thickness of the plates could be about 3 ½ inches.
Z SHELL Each of the units above has one large sloping plate and two edge plates arranged with space between the units for windows. This form has been called a Z shell and is similar to the louver used for window ventilation. The architectural effect is very dramatic if the structure can be shown by a cantilever projected out beyond the support. The windows are normally open to the north but most of the light is actually reflected south light. To increase this effect, the roof surface can be painted with aluminum so light from the sun is reflected through the windows to the ceiling and the windows need not be very large. Adjacent units should be tied together by structural window mullions. In constructing the Z shell, movable forms need only be lowered a short vertical distance if construction is started on the right and proceeds to the left. The Z shell is not an efficient structural shape since it is discontinuous and its effective depth is much less than the actual vertical depth. Therefore, the spans are limited in comparison to the plates having a large number of units side by side
CANOPIES A folded plate structure for a small canopy at the entrance of a building is shown. This folded plate has four segments. A two segment structure is not desirable because it has very little torsional resistance. This instability can be demonstrated by a paper model having the ends of the model glued to vertical pieces of cardboard, acting as stiffening members. If it is absolutely necessary to have a two element
system, a torsion member can be placed in the valley which will carry the unbalanced loads. Stiffeners can often be hidden on the top surface so they are not in evidence and the shell will appear to spring from the vertical column. At the wall of the building there should also be a stiffener hidden in the wall construction. Provision should be made for drainage of the center valley.
TAPERED FOLDED PLATES Folded plate structures may be built with tapered elements and only one of the many possible combinations is shown here. Another possibility is to place the smaller depths all at one end so that the entire structure forms a circular ring. The height of the shells at the center of the span is the critical dimension for bending strength. Therefore, the structure is not very efficient and not suitable for long spans because of the excess height required for the large ends. Another weak element in this design is the transfer of shear from the small end of the triangular plate to the large end. If a large number of units are used in each span, the transfer of loads may be difficult. A folded plate may be used for walls as a thin structural element by casting each plate flat on the floor and grouting the joints full of concrete. A wall of this type can be made much thinner than a flat wall.
EDGE SUPPORTED FOLDED PLATES The usual upturned edge plate can be eliminated and the roof structure can be made to appear very thin if the edge plate is replaced by a series of columns. The slab between columns must be designed as a beam and it may be convenient to extend the main roof slab as a cantilever canopy. The beam element that carries the load of the roof between columns will then be wider and windows under the slab will have the same function as in the previous examples of folded plates. Note the vertical columns in the end walls at the crown of the gable. These take the reactions of the plates and the horizontal ties may be eliminated. Wind loads are taken by rigid frame action in the columns and stiffeners.
FOLDED PLATE TRUSS The term "folded plate truss" is intended to indicate the structural action of this structure. There are horizontal ties across the width only at the ends of the building and the structure acts as an edge supported shell as shown in the previous example. The thrusts from the triangular crossed arches are carried lengthwise to the ends. The top chord of the inclined truss is formed by the ridge member. The bottom chords are the ties at the base of the side gables and the diagonals are formed by the sloping valleys at the intersection of the gables and the triangular plates. The top longitudinal compression member may require some additional thickness to form a compression member of sufficient size to carry the compression force. This is truly a space structure and its structural action is not as obvious and, therefore, the architectural appearance is mote subtle that the usual shell structure.
FOLDED PLATE RIGID FRAME An arch with straight segments is sometimes called a rigid frame. It is not as efficient as the curved arch because the bending moments are greater. Ties across the plates are required at the knees and at the crown in order to distribute the forces at the ends of each segment.
