The amount that a course of timber may project beyond the one next above it can be determined by equation 7, page 356: Taking R in that equation gqual to 1,000—the value ordinarily used for oak or yellow pine—and / = 10, and solving, we obtain the following results for the safe projection: If the pressure on the foundation is 0.5 ton per sq. ft., the safe projection is 7.5 times the thickness of the course; if the pressure is 1 ton per square foot, the safe projec tion is 5.3 times the thickness of the course; and if the pressure is 2 tons per square foot, the safe projection is 3.7 times the thickness of the course.
The above method is not strictly correct, since, owing to the flexure of the timber beam, the pressure is not uniform as virtually assumed above, nor is the maximum moment• at the edge of the wall as assumed above.
The above method of computation is not applicable to two or more courses of timber, if one is transverse to the other, since the deflection of the timber materially affects the distribution of the pressure on the different courses of the footing. For references to methods of solving an analogous problem, see § 708.
This method of increasing the area of the footing was formerly much used at New Orleans. The custom-house at that place is founded upon a 3-inch plank flooring laid 7 feet below the street pavement. A grillage, consisting of timbers 12 inches square laid side by side, is laid upon the floor, over which similar timbers are placed transversely, 2 feet apart in the clear.
limestone footings resting on this crust were used, but they occupied valuable space and left no room for the necessary elevator and other machinery; and to meet these objections, a thin steel-grillage footing was devised, and has been called the raft or floating foundation. This steel-grillage foundation consisted of a row of steel beams placed side by side and embedded in rich concrete; and on top of this and at right angles to it is placed a shorter row, and above this, one and sometimes two other rows. At first, on account of the artificially high price of steel I-beams, railroad rails were used, but later I-beams have been employed, as they have a more economical cross section.
Steel is superior to timber for this purpose, in that the latter can be used only where it is always wet, while the former is not affected by variations of wetness and dryness. Twenty years' experience in this use of steel at Chicago shows that after a short time the surface of the metal becomes encased in a coating which prevents further oxidation. The most important advantage, however, in this use of steel is that the off-set can be much greater with steel than with wood or stone; and hence the foundations may be shallow, and not occupy the cellar space.
The proper projections for the steel beams can be computed by a formula somewhat similar to that of § 696; but the steel footing is appropriately a part of the steel-skeleton construction, and hence will not be considered here. For a description of a typical steel rail foundation and a presentation of the method of computations formerly employed in Chicago, see Engineering News, Vol. xxvi, page 122; and for adverse criticisms thereon, see ibid., pages 265, 312, 415, and Vol. xxxii, page 387. Concerning the effect of the strength of the base of the column, see Johnson's Modern Framed Structures, pages 444-46. For a discussion which considers the deflection of the several beams, see Engineering Record, Vol. xxxix, pages 333-34, 354-56, 383, 407-8. The last is the most exact method of analysis, and also secures the greatest economy of material.