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On this basis, the area of the concrete footing must be 36 square feet, and therefore a concrete footing 6 feet square will answer the purpose. A concrete column 24 inches square will safely carry such a loading. Placing such a concrete column in the middle of a concrete footing will leave an offset 2 feet broad outside each face of the concrete column. We may consider a section of the concrete footing made by passing a vertical plane through one face of the concrete column. This leaves a block of the concrete footing 6 feet long and 2 feet• wide, on which there is an upward pressure of 12 X 7,000 = 84,000 pounds. The center of pressure is 12 inches from the section, and the moment is therefore 12 X 84,000 = 1,008,000 inch-pounds. Multiplying this by 4, we have 4,032,000 inch-pounds as the ultimate moment. Applying Equation 21, we place this equal to 397 bd2, in which b = 72 inches. Solving this for d, we have d = 11.9 inches. A total thickness of 15 inches would therefore answer the purpose. The amount of steel required per inch of width = .0084 d = .0084 X 11.9 = .100 square inch of steel per inch of width. Therefore i-inch bars spaced 5.6 inches apart will serve the purpose.

A similar reinforcing of bars should be placed perpendicularly to these bars. The above very simple solution would be theoretically accurate in the case of an offset 2 feet wide for the concrete footing of a concrete wall of indefinite length, assuming that the upward pressure was 7,000 pounds per square foot. The development, of such a moment uniformly along the section of our square concrete footing, implies a resistance to bending near the outer edges of the concrete slab which will not actually be obtained. The moment will certainly be greater under the edges of the concrete column. On the other hand, we have used bars in both directions. The bars passing under the concrete column in each direction are just such as are required to withstand the moment produced by the pressure on that part of the concrete footing directly in front of each face of the concrete column. It may be considered that the other bars have their function in tying the two systems into one plate whose several parts mutually support one another. If further justification of such a method is needed, it may be said that experience has shown that it practically fulfils its purpose. A more effective method of reinforcing a simple concrete footing is shown in Fig. 111. Two sets of the reinforcing bars are at aa and bb, and are placed only under the concrete column. To develop the strength of the corners of the concrete footings, bars are placed diagonally across the concrete footing, as at c-c and d-d. In designing this concrete footing, the projections of the concrete footing beyond the concrete column are treated as free cantilever concrete beams, or by the method discussed above.

The maximum shear occurs near the center; and therefore, if it is necessary to take care of this shear by means of reinforcement, it should be provided by using stirrups. Assume that a load of 300,000 pounds is to be carried by a concrete column 28 inches square, on a soil that will safely carry a load of 6,000 pounds per square foot. What should be the dimensions of the concrete footing and the size and spacing of the reinforcing bars? The bars are to be placed diagonally as well as directly across the concrete footing, as illustrated in Fig. 111. Also investigate the shear. The load of 300,000 pounds will evidently require an area of 50 square feet. This area of metal may be furnished by eight finch round bars, and therefore there should be eight finch round bars spaced about 3.5 inches apart under the concrete column in both directions. The mechanics of the reinforcement of the corner sections, which are each 28.5 inches square, is exceedingly complicated in its precise theory. The following approximation to it is probably sufficiently precise.

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