SPREAD FOOTINGS. The term footing is usually under stood as meaning the bottom course or courses' of masonry which extend beyond the faces of the wall. It will be used here as applying to the material—whether masonry, timber, or iron—employed to increase the area of the base of the foundation. Whatever the character of the soil, footings should extend beyond the face of the wall (1) to add to the stability of the structure and lessen the danger of the work's being thrown out of plumb, and (2) to distribute the weight of the structure over a larger area and thus decrease the settlement due to the compression of the ground. To serve the first purpose, footings must be securely bonded to the body of the wall; and to produce the second effect, they must have sufficient strength to resist the transverse strain to which they are exposed. In ordinary buildings the distribution of the weight is more important than adding to the resistance to overturning, and hence only the former will be considered here.
There are four methods in more or less common use for increasing the width of footings: (1) extend the successive courses of the masonry at the bottom of the wall, (2) rest the wall or column upon a reinforced concrete slab, (3) use one or more layers of timbers or steel I-beams, or (4) support the structure upon inverted masonry arches.
To deduce a formula for the relation between these quantites, let P = the pressure, in tons per square foot, at the bottom of the footing course under consideration; R = the modulus of rupture of the material, in pounds per square inch; o = the greatest possible off-set or projection of the footing course, in inches; t = the thickness of the footing course, in inches; / = the factor of safety.
The part of the footing course that projects beyond the one above it, is a cantilever beam uniformly loaded. From the principles of
the resistance of materials, we know that the upward pressure of the earth against the part that projects multiplied by one half of the length of the projection is equal to the continued product of one sixth of the modulus of rupture of the material, the breadth of the footing course, and the square of the thickness. Expressing this relation in the above nomenclature and reducing, we get the formula Hence the projection available with any given thickness, or the thickness required for any given projection, may easily be computed by equation 7.
The margin to be allowed for safety will depend upon the care used in computing the loads, in selecting the materials for the footing courses, and in bedding and placing them. If all the loads have been allowed for at their probable maximum value, and if the material is to be reasonably uniform in quality and laid with care, then a comparatively small margin for safety is sufficient; but if all the loads have not been carefully computed, and if the job is to be done by an unknown contractor, and neither the material nor the work is to be carefully inspected, then a large margin is necessary. As a general rule, it is better to assume, for each particular case, a factor of safety in accordance with the attendant conditions of the problem than blindly to use the results deduced by the application of some arbitrarily assumed factor. Table 61 is given for the con venience of those who may wish to use 10 as a factor of safety.
Stone Footings. Strictly, the above computations when applied to stone-masonry footing courses are correct only for the lower off-set, and then only when the footing is composed of stones whose thickness is equal to the thickness of the course and which project less than half their length, and which are also well bedded. The resistance of two or more courses to bending, if bedded in good cement mortar, probably varies about as the square of their combined depth, and the bending due to the uniform pressure on the base increases as the square of the sum of the projections; and therefore the successive off-sets should be proportional to the thickness of the course; or, in other words, the values as above are applicable to any of the several projecting courses, provided no stone projects more than half its length beyond the end of the top course.