When you try to apply this pattern to floor plan, you will find a certain type of difficulty. Since the corners of rooms may already be fixed by columns at the corners (212), it is not always possible to space the stiffeners correctly within the wall of any given room. Naturally this does not matter a great deal; the stiffeners only need to be about right; the spacing can comfortably vary from room to room to fit the dimensions of the walls. However, on the whole, you must try and put the stiffeners closer together where the rooms are small and further apart where rooms are large. If you do not, the building will seem odd, because it defies one’s structural intuitions.
Consider two rooms on the same floor, one twice as large as the other. The larger room has twice the perimeter, but its ceiling generates four times the load; it therefore carries a greater load per unit length of wall. In an ideal efficient structure, this means that the wall must be thicker; and therefore, by the arguments already given, it will need stiffeners spaced further apart than the smaller room which carries less load and has thinner walls.
We recognize that few builders will take the trouble to make wall thicknesses vary from room to room on one floor of the building. However, even if the wall is uniformly thick, we believe that the stiffeners must at least not contradict this rule. If, for reasons of layout, it is necessary that the spacing of stiffeners varies from room to room, then it is essential that the larger spacings of the stiffeners fall on those walls which enclose the
IOOI
| CONSTRUCTION |
|---|
 |
| The final column distribution in a jour story building, built according to our -patterns for columns, walls and vaults. |
larger rooms. If the greater spacing of stiffeners were to coincide with smaller rooms, the eye would be so deceived that people might misunderstand the building.
One important note. All of the preceding analysis is based on the assumption that walls and stiffeners are behaving as elastic plates. This is roughly true, and helps to explain the general
1002
213 FINAL COLUMN DISTRIBUTION
phenomenon we are trying to describe. However, no wall behaves perfectly as an elastic plate—least of all the kind of lightweight concrete walls we are advocating in the rest of the construction patterns. We have therefore used a modified form of the elastic plate theory, calibrated according to the AC1 code, so that the numbers in our analysis are based on the elastic behavior of concrete (and fall within the limits of its tension and compression). However, when the plate goes out of the elastic range and cracks, as it almost certainly will in a concrete design, other factors will enter in. We therefore caution the reader most strongly not to take the actual numbers presented in our analysis as more than illustrations. The numbers reflect the general mathematical behavior of such a system, but they are not reliable enough to use in structural computations.
Therefore:
Make column stiffeners furthest apart on the ground floor and closer and closer together as you go higher in the building. The exact column spacings for a particular building will depend on heights and loads and wall thicknesses. The numbers in the following table are for illustration only, but they show roughly what is needed.
in stories ground floor 2nd floor 3rd floor 4th floor
2''5'
1
2
3
4
Mark in these extra stiffening columns as dots between the corner columns on the drawings you have made for different floors. Adjust them so they are evenly spaced between each pair of corner columns; but on any one floor, make sure that they are closer together along the walls of small rooms and further apart along the walls of large rooms.
1003
CONSTRUCTION
v w w~
floor by floor variation
s/
To the extent consistent with ceiling height variety (190), make walls and columns progressively shorter the higher you go in the building to keep slenderness ratios low.
And make wall thicknesses and column thicknesses vary with the height—-see wall membrane (218). Our calculations, for a typical lightweight concrete building of the kind we have been discussing, suggest the following orders of magnitude for wall thicknesses: Top story—2 inches thick; one below top story—3 inches; two below top story—4 inches; three storys below top (ground floor on a four story building)—5 inches. Of course these numbers will change for different loads, or for different materials, but they show the type of variation you can expect.
Column thicknesses must be proportional to wall thicknesses, so that the thinnest walls have the thinnest columns. If they are very thin, it will be possible to make them simply by placing boards, or one thickness of material, outside the outer skins which form the wall membrane—see wall membrane (218). If the walls are thick, they will need to be full columns, twice as thick as the walls, and roughly square in section, built before the walls, but made in such a way that they can be poured integrally with the walls—box columns (216). . . .
fut stakes in the ground to mark the columns on the site} and start erecting the main jrame according to the layout oj these stakes;
| 214. | ROOT FOUNDATIONS |
| 215- | GROUND FLOOR SLAB |
| 216. | BOX COLUMNS |
| 10 1—< | PERIMETER BEAMS |
| 218. | WALL MEMBRANES |
| 219. | FLOOR-CEILING VAULTS |
| 220. ROOF VAULTS | |
10 MAGIC OF THE CITY
desirable to have as many centers as possible, we propose that the city region should have one center for each 300,000 people, with the centers spaced out widely among the population, so that every person in the region is reasonably close to at least one of these maj or centers.
To make this more concrete, it is interesting to get some idea of the range of distances between these centers in a typical urban region. At a density of 5000 persons per square mile (the density of the less populated parts of Los Angeles) the area occupied by 300,000 will have a diameter of about nine miles; at a higher density of 80,000 persons per square mile (the density of central Paris) the area occupied by 300,000 people has a diameter of about two miles. Other patterns in this language suggest a city much more dense than Los Angeles, yet somewhat less dense than central Paris—four-story limit (21), density rings (29). We therefore take these crude estimates as upper and lower bounds. If each center serves 300,000 people, they will be at least two miles apart and probably no more than nine miles apart.
One final point must be discussed. The magic of a great city comes from the enormous specialization of human effort there. Only a city such as New York can support a restaurant where you can eat chocolate-covered ants, or buy three-hundred-year-old books of poems, or find a Caribbean steel band playing with American folk singers. By comparison, a city of 300,000 with a second-rate opera, a couple of large department stores, and half a dozen good restaurants is a hick town. It would be absurd if the new downtowns, each serving 300,000 people, in an effort to capture the magic of the city, ended up as a multitude of second-class hick towns.