Where vaults of different width are near each other, you must remember to pay attention to the level of the floor above. Either you can level out the floor by making the smaller vaults have proportionately higher arches, or you can put extra material in between to keep the small vaults low—see ceiling height variety (190), or you can make steps in the floor above to correspond to changes in the vault sizes below.
Vaults on different floors do not have to line up perfectly with one another. In this sense they are far more flexible than column-beam structures, and for this reason also better adapted to structure follows social spaces (205). However, there are limits. If one vault is placed so that its loads come down over
the arch of the vault below, this will put undue stress on the lower vault. Instead, we make use of the fact that vertical forces, passing through a continuous compressive medium, spread out downward in a 45 degree angle cone. If the lower columns are always within this cone, the upper vault will do no structural damage to the vault below it.
The angle at which a vertical force sfreads downward.
To maintain reasonable structural integrity in the system of vaults as a whole, we therefore suggest that every vault be placed so that its loads come down in a position from which the forces can go to the columns which support the next vault down, by following a 45 degree diagonal.
Good ... . . . 110 good.
With all this in mind then, work out a vault plan for your building. We suggest that you try to keep the vaults aligned with the rooms, with occasional adjustments to suit a very big room, or a very small nook or alcove. The drawing on the next page shows a floor and ceiling layout for a simple building.
Each space that you single out for a vault may have either a two-way vault (a domical ceiling on a rectangular base) or a one-way vault (a barrel vault). The tw'o-way vaults are the most efficient structurally; but when a space is long and narrow, the domical shape begins to act like a barrel vault. We therefore
| CONSTRUCTION |
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| A version of floor-ceiling layout} shown in flan and section, for a simfle ultra-lightweight concrete building. |
suggest domical vaults for spaces where the long side is not more than twice the short side and barrel vaults for the spaces which are narrower.
We also suggest that you use barrel vaults for the rooms immediately under the roof. The roof itself is generally a barrel vault— see roof vault (220)—so it is most natural to give the ceiling of the space just under the roof a barrel vault as well.
The vaults described in floor-ceiling vaults (219) may
980 210 FLOOR AND CEILING LAYOUT
span from 5 to 30 feet. And they require a rise of at least 13 per cent of the short span.
Therefore:
Draw a vault plan, for every floor. Use two-way vaults most often; and one-way barrel vaults for any spaces which are more than twice as long as they are wide. Draw sections through the building as you plan the vaults, and bear the following facts in mind:
1. Generally speaking, the vaults should correspond to rooms.
2. There will have to be a support under the sides of each vault: this will usually be the top of a wall. Under exceptional circumstances, it can be a beam or arch.
3. A vault may span as little as 5 feet and as much as 30 feet. However, it must have a rise equal to at least 13 per cent of its shorter span.
4. If the edge of one vault is more than a couple of feet (in plan) from the edge of the vault below it—then the lower vault will have to contain an arch to support the load from the upper vault.
Put a perimeter beam (21 7) on all four sides of every vault, along the top of the bearing wall, or spanning openings. Get the shape of the vaults from floor-cf.iling vaults (219) and as you lay out the sections through the vaults, bear in mind that the perimeter beams get lower and lower on higher floors, because the
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columns on upper stories must be shorter (top floor columns about 4 feet, one below top 6 feet, two below top 6 to 7 feet, three below top 8 feet)—final column distribution (213). Make sure that variations in floor level coincide with the distinctions between quiet and more public areas—floor surface (233). Complete the definition of the individual spaces which the vaults create with columns at the corners (212). Include the smallest vaults of all, around the building edge, in thickening
THE OUTER WALLS (21 1) . . . .
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21 I THICKENING THE OUTER WALLS*
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. . . the arrangement of roof and floor vaults will generate horizontal outward thrust, which needs to be buttressed—cascade of roofs (116). It also happens, that in a sensibly made building every floor is surrounded, at various places, by small alcoves, window seats, niches, and counters which form “thick walls” around the outside edge of rooms—window place (180),
THICK WALLS ( I 97) j SUNNY COUNTER ( I 99) , BUILT-IN SEATS
(202), child caves (203), secret place (204). The beauty of a natural building is that these thick walls—since they need lower ceilings, always, than the rooms they come from—can work as buttresses.
Once the roof layout (209), and the floor and ceiling layout (210) are clear these thick walls can be laid out in such a way as to form the most effective butresses, against the horizontal thrust developed by the vaults.
We have established in THICK walls (197), how important it is for the walls of a building to have “depth” and “volume,” so that character accumulates in them, with time. But when it comes to laying out a building and constructing it, this turns out to be quite hard to do.
The walls will not usually be thick in the literal sense, except in certain special cases where mud construction, for example, lends itself to the making of walls. More often, the thickness of the wall has to be built up from foam, plaster, columns, struts, and membranes. In this case columns, above all, play the major role, because they do the most to encourage people to develop the walls. For instance, if the framework of a wall is made of columns standing away from the back face of the wall, then the wall invites modification—it becomes natural and easy to nail planks to the columns, and so make seats, and shelves, and changes there. But a pure, flat, blank wall does not give this kind of encouragement. Even though, theoretically, a person can always add things which stick out from the wall, the very smoothness of the
wall makes it much less likely to happen. Let us assume then, that a thick wall becomes effective when it is a volume defined by columns.
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| Thick walls made effective by columns. |
How is it possible for a wall of this kind to justify its expense by helping the structure of the building? The fact that the building is conceived as a compressive structure, whose floors and roofs are vaults—efficient structure (206), means that there are horizontal thrusts developed on the outside of the building, where the vaults do not counterbalance one another.
To some extent this horizontal thrust can be avoided by arranging the overall shape of the building as an upside down catenary—see cascade of roofs ( i 16). If it were a perfect catenary, there would be no outward thrust at all. Obviously, though, most buildings are narrower and steeper than the ideal structural catenary, so there are horizontal thrusts remaining. Although these thrusts can be resolved by tensile reinforcing in the perimeter beams—see perimeter beams (217)—it is simplest, and most natural, and stable to use the building itself to buttress the horizontal thrusts.