This section is from the book "The Building Trades Pocketbook", by International Correspondence Schools. Also available from Amazon: Building Trades Pocketbook: a Handy Manual of reference on Building Construction.
These are used on compressible soils to bring the load per square foot within the safe bearing power of the soil. They may be made of timber, in wet soils, alternate courses being laid transversely; of layers of I beams or rails, laid in concrete; or of concrete with several transverse courses of twisted iron rods (a patented method). These are shown at (a), (6), and (c), Fig. 5. In the first two cases, it is necessary to figure the safe length of the projecting portion.
For example, determine the size of the timber footing, Fig. 5 (a), for a wall having a load of 40,000 lb. per ft. in length. The ground is wet and not safe to load over 3,000 lb. per ft.; consequently, the footings must be 13 1/3 ft. wide. The stepped-out foundation is 32 in. wide, making the projection L 5 ft. 4 in. on each side. To find what size timber is required, consider either side as ac, a cantilever beam, 1 ft. wide, uniformly loaded, supported at c, and resisting the upward reaction of the earth w of 3,000 lb. per sq. ft.; for 5 ft. 4 in. it
L w = 16,000 lb.; call this W. According to Table XXVI, page 113, the bending moment is M = WL / 2 = (16,000x5.33) / 2
= 42,667 ft.-lb.; or 512,000 in.-lb.
The resisting moment (see page 114) M1= QS, S being the safe unit fiber stress, and Q the section modulus, which for a rectangular beam is, from Table XII, page 83, bd2 / 6; b is the width and d the depth. Suppose that the timber is spruce and that the safe bending stress is 1,000 lb. per sq. in.; let the beam be 12 in. wide; its depth remains to be determined.
Then, M1 = (1000x12xd2) / 6. Since the safe resisting moment should equal the bending moment,
M1=M, or (1000x12xd2) / 6 = 512,000; whence, = 16 in.
Hence, 12" X 16" timbers, set side by side, with cross-layers of planks above and below, shown in Fig. 5 (a), would be used.
The principles are the same when the footing consists of I beams, or rails, but other values are used for Q and S, on account of the different cross-sections and material. (See page 118 for rolled-steel beams.) The safe offsets for stone footings may also be figured in the same manner. In general, it is beat to make the offset in each course of stonework brickwork not greater than the depth of the course. For calculation of stone beams, as flagstones, lintels, etc., see page 119.