concentric rings. Additional rings also, are placed between columns through the section ordinarily occupied by the direct bands, and the central portion of the panel is similarly reinforced. This method of reinforcement is illustrated by the S. M. I. SYSTEM, invented and patented by Edward Smulski. Up to the Fig. 4. The Three-Way System. Typical Arrangement of Columns and Reinforcements. David W. Morrow, Inventor present time (1927), it has been used in about four hundred buildings, all of which, as far as known, have given satisfactory service. Figure 3 illustrates the essential features of this system. 5. The Three-Way System. This system, invented by David W. Fig. 5. The Three-Way System. Reinforcements over Column-Head Morrow, has been used very successfully where it has been feasible to arrange the columns as required by this method of design. In this system the columns in alternate rows are opposite each other, and in adjacent rows staggered with respect to each other, so that any four adjacent columns are located at the corners of a parallelogram, the four sides and short diagonal of which are of equal length. The reinforcing steel over a column-head is placed in three layers, and extends in three general directions, radiating into the surrounding slab and extending over the six adjacent columns, all of which are equidistant from the central one. All the reinforcing rods are lapped over the columnhead, the distance from center to center being the same in the three directions in which the reinforcing extends, and the amount of floor-space being the same over each group of rods. The rods, consequently, for all the interior panels are of the same size and length. Fig. 4 shows the typical arrangement of columns for a building, the outline of the uniformly and non-uniformly distributed areas, the location of the reinforcing steel, and the diamond-shape outline of the floor spaces carried by each band of steel. Fig. 5 shows, in plan and section, the reinforcements over a columnhead. 6. General Notation. The following notation, used in the discussion of girderless floor design, is taken from the report of the committee of the American Concrete Institute, Proceedings of 1920, page 297. w = total dead and live loads in pounds per square foot of floors; W l2 = = = total dead and live loads, in pounds on the entire panel under consideration, measured from center to center of columns; span in feet, measured from center to center of columns, parallel to sections for which the moments are considered; span in feet, measured from center to center of columns, perpendicular to sections for which the moments are considered; c = average diameter of column capital, in feet, at the plane where its thickness is 11⁄2 in; = q distance from center line of capital to center of gravity of the periphery of the half-capital, divided by c/2. For capitals circular in plan q may be considered 2% and for those square in plan, 34; t = total slab thickness, in inches; L average span in feet, measured from center to center of columns, but not less than nine-tenths of the greater span. The designations of the principal design-sections, used by both the American Concrete Institute and the Joint Committee on Standard Specifications for Concrete and Reinforced Concrete (1924), are shown in Figs. 6 and 7. These sections are determined for convenience in computing the bending moments, and are without relation to the location of the reinforcements. Corresponding moments are computed for similar sections at right angles to those shown. The New York City Building Code uses the designation of the American Concrete Institute, and Chicago follows that of the Joint Committee, except that the column-strip is referred to as Strip A and the middle strip as Strip B. 7. Structural Variations and Limitations. The following restrictions as to the application of the formulas used for flat-slab construction, and the minimum sections to be permitted, represent what in the author's opinion is conservative practice. The different systems of design and the formulas apply to girderless floors, continuous in each direction over three or more panels of approximately the same Fig. 6. Flat-Slab Construction. Flat-Slab, Column-Cap, and Panelled-Ceiling Designs. Designations of the American Concrete Institute size, in which the longer side is not more than four-thirds the shorter side and subjected to a uniformly distributed load. For structures having a width of less than three panels, or where the sizes of the panels are appreciably different, |