Accept a total depth of 39 in and 11 %-in square bars at the interior face of the exterior footing. Vertical shear at the exterior face of the interior footing Checking the same section as governed by a positive bending moment equal to one-third of the maximum moment computed above, Accept a total depth of 24 in and six g-in square bars. Eleven -in square bars are placed in the top; of this number nine are straight, except for the bend beneath the exterior column, and two are bent down where indicated in Fig. 16. These two bars, together with the four straight -in bars in the bottom of the strap, give the six 8-in bars required at the exterior face of the interior footing. At both ends of the strap there is sufficient steel at both top and bottom to give a certain degree of security against unequal settlement. 17. Continuous Footings. As stated on page 220, the design of a continuous footing, supporting a line of columns, is exactly parallel to the design of a continuous beam carrying a uniform floor load. Ordinarily there is less probability of unbalanced loading, due to critical positions of the live load, than in work above ground. The proportion of dead load to live load, particularly under exterior columns, where this type of footing is most often encountered, is also greater than in floor-design. For these reasons it is often possible to employ design moments more closely approximating the theoretical values for conditions of definite loading. The possibility of a tendency toward unequal settlement, however, is nearly always a danger to be guarded against on soils of low bearing-value, which is the class for which this particular type of footing is best suited economically. Having these facts in mind, each design should Fig. 17. Arrangements of Bars in Continuous Footings under Wall-Columns be approached as a special problem with a full knowledge of the loads to be sustained and of the sub-soil conditions. The design illustrated in Fig. 17 is based on placing one-third of the computed steel area in the form of straight bars at the top of the footing, one-third in the form of straight bars at the bottom of the footing, and two-thirds bent at an angle of 45°, the center of the bend being located at the 1% point of the clear span between columns. This arrangement is suitable when it is desired to provide for equal positive and negative bending moments and to give some security against unequal settlement. For example, if the design moment determined upon requires 18 bars over supports, and the same steel area in mid-span, the arrangement would be as indicated, employing in all 24 bars of the required size. If conditions are such as to warrant the use of a positive Fig. 18. Alternate Cross- moment factor less than that of the negative moment, the sectional area required for the latter may be obtained by the usual method of lapping the reinforcement, the proportion of bent steel being varied to give the relative areas required. The DESIGN-PROCEDURE for a footing of this kind starts with the determination of the footing-area between column-centers, which depends upon the allowable soil-pressure. Having found the required area, the width is known, since the column spacing is fixed. If this width is considerably greater than that required by shear, based upon a desirable depth, the section may be made as shown in Fig. 18. Having computed the width of the footing, the design follows the procedure for rectangular or T beams subjected to uniform loads. CHAPTER X GIRDERLESS FLOORS 1. Codes and Systems. At present practically every large city has its own particular code governing GIRDERLESS OF FLAT-SLAB FLOOR CONSTRUCTION; and in addition to these there are the recommendations contained in the Standard Building Regulations for the Use of Reinforced Concrete, published by the American Concrete Institute (1920); * the Final Report of the Joint Committee on Concrete and Reinforced Concrete (1916); † and the Report of the Joint Committee on Standard Specifications for Concrete and Reinforced Concrete (1924). ‡ All of these have received considerable recognition. These codes, or recommendations, must be clearly differentiated from the many systems of design, which are methods of obtaining the required strength at the several design-sections, and which deal principally with the distribution of the reinforcement. Practically all systems can be made to conform to the requirements of any given code, and although the arrangement of the steel may vary considerably for the same problem, there is not much difference in the cost when all items of material and labor are considered. The CODE or RULING recommended when the design is not controlled by local building ordinances is that proposed by the American Concrete Institute (see example, page 279). Among the city building codes, there are also many which give satisfactory results and are widely applied even outside of their particular jurisdiction. Chief among these are the New York and Chicago codes. The different systems of flat-slab construction may be divided into four general classifications: (1) the TWO-WAY SYSTEM; (2) the FOUR-WAY SYSTEM; (3) the CIRCUMFERENTIAL SYSTEM; and (4) the THREE-WAY SYSTEM. There are at present no general patents in force in this country covering the TWO-WAY SYSTEM, the THREE-WAY SYSTEM or the FOUR-WAY SYSTEM of reinforcement. 2. The Two-Way System. In this system the reinforcement, placed in two directions (Fig. 1), comprises steel bands which are carried from column to column, and also a two-way reinforcement in the central, rectangular, portion of the panel between the bands, and running parallel to them. The slab is designed either with a PLINTH or DROP Over the column-capital, or with a uniform thickness throughout. Example (1), page 279, illustrates the general application of this system, which has been very widely and successfully used. *Proceedings American Concrete Institute, 1920, page 283. 3. The Four-Way System. In this system the reinforcement, placed in four directions (Fig. 2), comprises two steel bands carried directly from column to column, two other bands placed diagonally across the panel from column to column, and any supplementary reinforcement that the design may require. As in the TWO-WAY SYSTEM, the slabs may be designed either with or without drops over the columns. Example (4), page 286, illustrates this system, which, also, is extensively employed. 4. The Circumferential System. This system is so named because the reinforcement adjacent to the column-capital is in the form of radial rods and |