Although brick can be used as a footing course, the maximum possible offset (no matter how strong the brick may be) can only be a small part of the length of the brick—the brick being laid perpen dicular to the wall. One requirement of a footing course is that the blocks shall be so large that they will equalize possible variations in the density of the subsoil. This cannot he done by bricks or small stones. Their use should therefore be avoided in footing courses.
1S4. Beam Footings. Steel, and even wood, in the form of beams, are used to construct very wide offsets. This is possible on account of their greater transverse strength. The general method of calculation is identical with that given above, the only difference being that beams of definite transverse strength arc so spaced that one beam can safely resist the moment developed in the footing in that length of wall. Wood can be used only when it will he always under water. Steel beams should always be surrounded by concrete for protection from corrosion.
If we call the spacing of the beams 8, the length of the offset o, the unit-pressure from the subsoil P, the moment acting on one beam = Po' s. Calling w the width of the beam, t its thickness or depth, and R the maximum permissible fibre stress, the maximum permissible moment = R w P. Placing these quantities equal, we have the equation : P s w (3) Having decided on the size of the beam, the required spacing may be determined.
185. Example. An 18-inch brick wall carrying a load of 12,000 pounds per running foot, is to be placed on a soft, wet soil where the unit-pressure cannot be relied on for more than one-half a ton per square foot. What must be the spacing of 10 by 12-inch footing timbers of long-leaf yellow pine? Solution. The width of the footing is evidently 12,000 ÷- 1,000 = 12 feet. The offset o equals ; (12 — 1.5) = 5.25 feet = 63 inches. Since the unit of measurement for computing the transverse strength is the inch, the same unit must be employed throughout. Therefore 1,000 P ?• 1 = 1,200 pounds per square inch; w = 10 niches; and 144 t = 12 inches. Equatio'n (3) may be rewritten: R w s 3 P o2.
This shows that the beams must be spaced 20.9 inches apart, center to center, or with a clear space between them but little more than their width. Under the above conditions, the plan would probably be inadvisable, unless timber were abnormally cheap and no other method seemed practicable.
186. Steel I=Beam Footings. The method of calculation is the same as for wooden beams, except that, since the strength of I-beams is not readily computable except by reference to tables in the hand books published by the manufacturers, such tables will be utilized.
The tables always give the safe load which may be carried on an I-beam of given dimensions on any one of a series of spans varying by single feet. If we call IV the total load (or'upward pressure) to be resisted by a single cantilever beam, this will be one-fourth of the load which can safely be carried by a beam of the same size and on a span equal to the offset.
187. Example. Solve the previous example on the basis of using steel I-beams.
The offset is necessarily 5 feet 3 inches; at 1,000 pounds per square foot, the pressure to be carried by the beams is 5,250 pounds for each foot of length of the wall. By reference to the tables and interpolating, an 8-inch I-beam weighing 17.75 pounds per linear foot will carry about 28,880 pounds on a 5 foot 3 inch span. One fourth of this (or 7,220 pounds) is the load carried by a cantilever of that length. Therefore, 7,220 5,250 = 1.375 feet = 16.5 inches, is the required spacing of such beams. When comparing the cost of this method with the cost of others, the cost of the masonry concrete filling must not be overlooked.
188. Design of Pier Footings. The above designs for footings have been confined solely to the simplest ease of the footing required for a continuous wall. A column or pier must be supported by a footing which is offset from the column in all four directions. It is usually made square. The area is very readily obtained by dividing the total load by the allowable pressure per square foot on the soil. The quotient is the required number of square feet in the area of the footing. If a square footing is permissible (and it is usually prefer able), the square root of that number gives the length of one side of the footing. Special circumstances frequently require a rectangular footing or even one of special shape. The problem of designing a footing so that the center of pressure of the load on a column shall be vertical over the center of pressure of the subsoil, is usually even more complicated than the problem referred to in sec tion 1S9. A col umn_placed at the corner of a build ing which is lo cated at the ex treme corner of the property and which cannot ex tendover the prop erty line, must usually be sup ported by a canti lever (or by two of them at right an gles), balanced at the other end by the load on an other pier or col umn. While the general principle involved in such methods of.construction is very simple, a correct solution often requires the exercise of considerable ingenuity.