This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
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 are 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 be always under water. Steel beams should always be surrounded by concrete for protection from corrosion.
If we call the spacing of the beams s, the length of the offset o, the unit-pressure from the subsoil P, the moment acting on one beam = 1/2 Po2 s. Calling w the width of the beam, t its thickness or depth, and R the maximum permissible fibre stress, the maximum permissible moment = 1/6 Rwt2. Placing these quantities equal, we have the equation:
1/2Po2s = 1/6Rwt2...(3)
Having decided on the size of the beam, the required spacing may be determined.
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 1/2 (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
P= 1,000 ; R = 1,200 pounds per square inch; w = 10 inches; and 144 t = 12 inches. Equation (3) may be rewritten: s = R wt2
3 P o2
Substituting the above values, we have: s= 1,200X10X144 =20.9 inches
3 x 1,000 x 3,969 144
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.