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 intersection. An intersection of 90 degrees is the optimum 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.