The previous shells have all been basic types: the folded plate, the cylindrical barrel shell, the dome of revolution, and the folded plate domes. The next category is made up by combining portions of the previous types arranged to form more stable combinations than the individual elements alone. The most appropriate name is "intersection shell" because the surfaces that produce the shell appear to meet at an intersection. Any of the basic types may be used in this manner but the barrel shell is the most familiar and useful.
The structural efficiency of the intersection shell depends on the angle of the intersection of the surfaces. If the angle is small (called here for descriptive purposes, sharp), then a natural rib is formed by the adjacent elements of the basic shells which is much stiffer than the adjacent shells on each side. An itersection for which the angle is very large is called here a shallow intersec@on. An intersec@on of 90 degrees is the op@mum value because it gives a stiff rib. On large structures with shallow intersections, massive ribs may be necessary which are very evident and detract from the light appearance.
INTERSECTION SHELL - SQUARE IN PLAN SHALLOW INTERSECTION
This structure is a dome formed by using triangular pieces of a cylindrical shell arranged in the form of a square. The drawing, however, conveys more than the description.
The word "shallow" has been used to indicate that the angle between the components is rather small, especially if the rise of the shell is small. With four sides, however, the ribs formed by the intersection should provide an adequate structural member. It is the best type of dome to cover a square area and maintain a level parapet around the building. The structural action is essentially that of a short shell. Loads are carried by the cross ribs formed by the intersection and by the stiffening element created by the edge beam. The bottom of the shell requires tensile reinforcement as in a short shell.
This structure can be inverted and supported from a central column similar to the "umbrella shell" described in the chapter on warped surfaces.
INTERSECTION - POLYGONAL PLAN, SHALLOW INTERSECTION
This form is suitable for a dome of large span which must be nearly circular in plan. If more than six sides are used, the rib formed by the shell gets rather shallow so a rib is added above the shell surface. Columns are shown in this sketch at the center of each panel rather than at the ribs. This would be suitable only for a small structure since it produces additional bending in the lowest part of the shell. As in other types of domes, a skylight may be placed at the crown of the dome. A thrust ring must be added to take the forces in the ribs. Windows may be placed in the shell except at the lowest points.
GROINED VAULT - SQUARE IN PLAN
The groined vault is an intersection shell composed of four triangular pieces of cylindrical shells, arranged in a cross form so that there are arches on each of the sides. This is one of the most ancient of masonry arch structures and still used for underground water reservoirs of concrete without any reinforcing.
The usual vault is a continuous structure but only a single unit is shown here. The structure obtains its rigidity by the large angle between the shell components at the intersections which creates a very strong rib.
The size of these structures is almost unlimited because the form is inherently very strong and is stiffened by six complete arches. In order to take advantage of the rigs, it is necessary to have the center of the abutments at the center of the effective rib. Otherwise, an additional heavy rib is required which impairs the appearance of the groined vault.
GROINED VAULT - POLYGONAL PLAN
This structure is similar to the previous groined vault, square in plan, except that there are five triangular cylindrical elements instead of four. The shells which form the dome all have axes perpendicular to the vertical axis. Again, an excellent structural rib is formed by the intersection.
Arched stiffening ribs are required around the outside of the structure and these ribs exert thrusts at their abutments. Therefore, either a steel tie is required at this level (it can be hidden by the window), or if the area must be open, thrust abutments can be used. There are, of course, many possible variations on the structure sketched here. If six sides are used, a continuous series of shells my be constructed and units of this type could alternate with those having a shallow intersection.
INTERSECTION SHELL - CROSS FORM
Four cylindrical barrels intersect to form a central dome. The structure is supported by four columns at the corners of the intersection so that part of the barrel cantilevers from the central dome. Provision must be made for thrusts from the barrels and the central dome at the column. There are several alternates: 1) the columns may be made very heavy, 2) short lengths of walls in an angle shape may be used at the corners instead of individual columns, 3) diagonal members may be placed in each of the walls, or 4) @es may be place between tops of columns. The latter solution might be unsightly if the interior of the building should be clear.
Shell thicknesses for this structure should correspond to those used for barrel shells. The cantilever span of the barrels should not be made too large to take the bending forces. The architectural advantage of this structure is that it appears to float in the air. Therefore, windows should be located so that this illusion is preserved.
INTERSECTION SHELL - FOLDED PLATE
A two element folded plate is shown here as an intersection shell and is similar to the previous example. Almost all the combinations used for curved shells may be used for folded plates, the resulting forms are almost unlimited. In the above sketch, a cross form is used. The columns may be place so that there is no column at the corner and the central dome is suspended from four cantilevers. However, it is better to put the column in the corner so that the central intersection may be used as the stiffening element. The resulting thrusts can be carried by diagonal braces in the plane of the outside walls and may be concealed by the wall construction. The same effect is achieved by a solid concrete wall in each corner. Ties around the barrel would be very unsightly in this structure.