Foundations

The necessity of keeping footings inside of party lines, and the desire to make the axis of load conform to the center of grav ity of area, sometimes results in the use of cantilever construction. These cantilevers are in some cases laid directly over the beams forming the grillage in the footing. This construction makes the actual point of application of the loads uncertain as any deflection would tend to throw the load on the outer beams. A better con struction is the use of a shoe with a pin bearing.

Improvement of Bearing Power.

The supporting power of all soils is improved by compacting, by mixing sand or gravel or by driving piles which prevent the spreading of the soil as well as compacting it. Drainage of a wet soil also greatly improves its bearing power.

The following table taken from Baker's " Treatise on Masonry Construction," gives values for general use in determining the bearing power of soils: The bearing power of clay depends largely upon the degree of moisture.

Foundations on clay, containing much water, and undrained, are liable to settlements from the escape of the water either by adjacent excavations, or by the squeezing out of the water.

Moist clay in inclined strata is liable to slide when loaded. Clay mixed with sand or gravel will bear more load than pure clay. Sand will bear more load than ordinary clay, and when in beds of sufficient thickness and extent to prevent running, will bear heavy loads with little settlement. Sand sufficiently fluid to run, as quicksand, cannot he easily employed to carry foundations. Grillage Foundations. The simple grillage foundation is illustrated by Fig. 151. The method of calculating the beams composing the grillage involves assumptions as to the conditions of distribution of loading and stresses. One method is given in Cambria, Page 2.63. This method involves the assumption that the beams can deflect from the line of axis of column. Such a condition, however, would lead to the cast-iron base bearing at its outer edges only ; this would involve strains for which these bases are rarely designed. Another assumption and one more in harmony with the assumption of the ordinary beam theory, is that the beams of the upper tier are fixed for the portion under the column hose. Under this assumption the load is distributed uni formly by the yapper tier and the stress in the free portion is calculated by the formula for a beam fixed at one end and free at the other.

Referring to Fig. 15:3 ; suppose the column load is P, and by the principles already given the extreme dimensions of footing are L and L' in feet. The length of the beams in the two tiers can be taken as L and L' also. Then if b and 1' are the dimen sions in feet of the column base, and the beams in the upper tier are placed the same width out to out of flanges as the column L — b base, — projection of the upper tier, and —— projection 2 of the lower tier. The load per square foot on the upper tier is

and on the lower tier is Ib' L L L' The moment in inch pounds, These formulas give the total moment borne by all the beams in the tier. The number of beams is generally determined by the dimensions of the footing, the beams of the upper tier being placed with their flanges generally not much more than 6 inches apart in the clear, and those of the lower tier from 6 inches to 12 inches. The number of beams being determined, the moment each bears is obtained by dividing the total moment by the num ber of beams ; and by dividing this individual moment by the allowable fibre stress the required moment of resistance and hence the size of beams is obtained. Since the concrete and steel act together, a higher fibre strain can be safely allowed ; this should in general be not more than 20,000 pounds per square inch, however.

Some trial and reproportioning of dimensions may sometimes be necessary to keep within the limits of depth and number of beams desired. Grillage beams in foundations should have the concrete thoroughly tamped around them, and it is preferable that the steel should be coated with neat cement instead of a coat of paint..

. I , .?, I i 1 Ark t, b ., The following problem will illustrate the method of proce dure in the case of combined footings.

Suppose two columns loaded and spaced as shown by Fig. 154, and let the allowable bearing on soil be 5,000 pounds per square foot. Let the dimensions of the footing be 20'— 0" X 11' — 0"=220 square feet. The determination of the size of base is largely a matter of judgment and depends upon the amount of load and the degree of spreading necessary to keep the size of grillage beams, or masonry offsets, within the limits which are economical. Suppose in this case the base is 3'—G" X The 1,100,000 load per square foot in the upper tier is therefore 20X 8.5 - 15,714 pounds. The moment on this tier will be a maximum either at one of the columns or at some point between them. The 600,000x 11 center of gravity of load is 1,100,000 = 6, or 6 feet from the lighter load. This fixes the projection of the footing beyond the loads as 4 feet from the light load and 5 feet from the heavy load. The beams between the column loads are in the condition of a beam fixed at the ends and loaded with a uniformly distributed load. The moment may therefore be taken as approximately of that for a beam simply supported. The moment between the columns will be a maximum where the shear is zero. To deter mine this start from one end, say the left-hand end, and deter mine the distance to the point of no shear by dividing the 600,000 concentrated load by the load per linear foot; =10.9.