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For some reason, this is the most loaded, the most emotional question, that can be asked about building construction. In all our investigations of patterns, we have not found any other pattern which generates so much discussion, so much disagreement, and so much emotion. Early childhood images play a vital role; so does cultural prejudice. It is hard to imagine an Arab building with a pitched roof; hard to imagine a New England farmhouse with a Russian onion roof over a tower; hard to imagine a person who has grown up among pitched steep wooden roofs, happy under the stone cones of the trulli.
CONSTRUCTION
For this reason, in this pattern we make our discussion as fundamental as we can. We shall do everything we can to obtain the necessary features which we can treat as invariant for all roofs, regardless of people or culture—yet deep enough to allow a rich assortment of cultural variations.
We approach the problem with the assumption that there are no constraints created by techniques or availability of materials. We are merely concerned with the optimum shape and distribution of materials. Given a roughly rectangular plan, or plan composed of rectangular pieces connected, what is the best shape for the shell of the roof which covers them?
The requirements influencing the shape are these:
1. The feeling of shelter—sheltering roof (117). This requires that the roof cover a w'hole wing (that is, not merely room by room). It requires that some of the roof be highly visible— hence, that it have a fairly steep slope—and that some of the roof be flat and usable for gardens or terraces.
2. The roof must definitely contain lived-in space—that is, not just sit on top of the rooms which are all below—see sheltering roof (117). This means it needs rather a steep slope at the edge—because otherwise there is no headroom. This requires an elliptical section dome, or a barrel vault (which starts going up vertically at the edge), or a very steep slope.
3. In plan, each individual roof is a very rough rectangle, with occasional variations. This follows from the way the roofs of a building must, together, follow the social layout of the plan—
ROOF LAYOUT (2O9).
4. The roof shape must be relaxed—that is, it can be used in any plan layout—and can be generated very simply from a few generating lines which follow automatically from the plan—that is, it must not be a tricky or contrived shape which needs a lot of fiddling around to define it—structure follows social SPACES (205).
5. Structural considerations require a curved shell, dome or vault to eliminate as much bending as possible—see efficient structure (206) and good materials (207). Of course, to the extent that wood or steel or other tension materials are available, this requirement can be relaxed.
6. The roof is steep enough to shed rain and snow in climates
| 220 ROOF VAULTS |
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where they occur. Obviously, this aspect of the roof will vary from climate to climate.
These requirements eliminate the following kinds of roofs:
1. Flat roofs. Flat roofs, except roof gardens ( i i 8), are already eliminated by the psychological arguments of sheltering roofs ( i i 7) and, of course, by structural considerations. A flat roof is necessary where people are going to walk on it; but it is a very inefficient structural shape since it creates bending.
2. Pitched Roofs. Pitched roofs still require materials that can withstand bending moment. The most common material for pitched roofs—wood—is becoming scarce and expensive. As we have said in good materials (207), we believe it is most sensible to keep wood for surfaces and not to use it as a structural material, except in wood rich areas. Pitched roofs also need to be very steep, indeed, to enclose habitable space as required by sheltering roof (11 7)—and hence rather inefficient.
3. Dutch barn and mansard roofs. These roofs enclose habitable space more efficiently than pitched roofs; but they have the same structural drawbacks.
4. Geodesic domes. These domes cover essentially circular areas, and are not therefore useful in their ordinary form— cascade of roofs (116), structure follows social spaces (205). In the modified form, which comes when you stretch
CONSTRUCTION
the base into a rough rectangle, they become more or less congruent with the class of vaults defined by this pattern.
5. Cable nets and tents. These roofs use tensile materials instead of compressive ones—they do not conform to the requirements of good materials (207). They are also very inefficient when it comes to enclosing habitable space—and thus fail to meet the requirements of structure follows social spaces (205).
The roofs which satisfy the requirements are all types of rectangular barrel vaults or shells, with or without a peak, gabled or hipped, and with a variety of possible cross sections. Almost any one of these shells will be further strengthened by additional undulations in the direction of the vault. Examples of possible cross sections are given below. (Remember that this does not include those flat roof gardens (118) built over floor-ceiling vaults
(219)0
Possible roof vaults.
We have developed a range of roof vaults which are rather similar to a pitched roof—but with a convex curve great enough to eliminate bending, in some cases actually approaching barrel vaults. One is shown in the drawing opposite3 another is shown below.
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| Another version of a roof vault, built by Bob Harris in Oregon. |
Wc build the roof vault very much like the floor vaults:
1. First span the wing to be roofed with pairs of lattice strips which are securely nailed at their ends to the perimeter beam, and weighted at their apex so that the two pieces become slightly curved.
2. Make the frame for the ceiling under the roof frame at the same time according to floor-ceiling vaults (219).
3. Repeat this frame every 18 inches, until the entire wing 3s
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| A type of roof vault, similar to the floor-ceiling vault, made from lattice strips, burlapy chicken-wire and ultra-lightweight concrete, but with an apex, and a pilchy and undulations for strength. |
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framed. The outer one will be the same, while the inner frame for the ceiling may change according to the rooms under it.
4. Now lay burlap over the ceiling frame, then resin, then 1J/2 inches of ultra-lightweight concrete—as for floor-ceiling vaults (219).
5. Now lay burlap over the roof frame, tacking it onto the lattice strips so that there is a 3-inch scallop in between the ribs— to form structural undulations in the skin. Again, paint the burlap with resin; lay chickenwire and put a layer of lightweight concrete over the entire roof.
We have analyzed a 48-foot roof of this type by means of a computerized finite element analysis similar to the one described for floor-ceiling vaults (219). The analysis shows that the maximum membrane compressive stress in the roof is 39.6 psi; the maximum membrane tensile stress is 2.5 psi, and the maximum diagonal membrane stress which develops from the maximum shear of 41.7 psi is 1 5.2 psi. These stresses are within the capacity of the material (See allowable stresses given in floor-ceiling vault (219)). The maximum membrane bending moment is 46 inch pounds per inch which is higher than the capacity of the unreinforced section, but extrapolations from our data show that this will be comfortably taken care of by the reinforcing which is needed anyway for shrinkage. Roofs with smaller spans, for a typical wing of light (106), will be even stronger.