the unit shearing-stress around the perimeter of the column-capital by one of the following formulas, V2 = V/bd (New York City, 1926) (6) (7) in which V is the total load on the panel, in pounds, less that on the area inclosed by the perimeter of the column-capital; b the perimeter of the column-capital, in inches; j equal to 0.875; and d the effective depth of the drop, in inches. The stress is usually limited to 120 lb per sq in for 2 000 lb concrete.* The shearing-stress around the periphery of the drop is then computed by Formula (1), Chapter IV, v = V/vjd in which V is the total load on the panel, in pounds, less that on the area inclosed by the perimeter of the drop; b the perimeter of the drop, in inches; j equal to Fig. 12. The Two-Way System. Column-Cap, Drop, and Slab. Shear-Computations, American Concrete Institute Ruling, 1920 0.875; and d the effective depth of the slab, in inches. This stress is usually limited to 60 lb per sq in for 2 000 lb concrete. In both cases, in order to permit these unit stresses, it is assumed that the longitudinal reinforcement is thoroughly anchored and designed to fully resist all stresses due to positive and negative bending moments. The American Concrete Institute (1920), recommends that the unit shearingstress, governing diagonal tension, computed between the compression face of the slab or drop, and the level of the center of gravity of the reinforcing steel, be determined over the surface of a frustum of a cone or pyramid, passing through the periphery of the column capital and having a base angle of 45°. This stress is limited to 0.035f'c, or 70 lb per sq in for concrete showing an ultimate compressive strength of 2 000 lb per sq in, when tested at the end. of 28 days. (See Example 1, page 280, and Fig. 12.) This requirement applies *This conforms to both the New York City and Chicago codes. to flat-slab construction both with and without drop-panels. The shearingstress around the periphery of the drop in drop-panel construction, is computed as above by Formula (7) and limited to 0.03f', or 60 lb per sq in for the same quality of concrete. This same ruling proposes another method for computing the shearing stress as a measure of the diagonal tension using the formulas v = 0.25W/bjd for slabs without drops and v = 0.30W/bjd for drop-construction. In these equations b = L/2. The punching shear is then computed on the full depth around the perimeters of both column capital and drop-panel by the formula, v = 1.25V/bd. In this equation V is the portion of the total panel load lying outside of the section under consideration. The value of v is limited to 120 lb per sq in for 2 000 lb concrete. The Report of the Joint Committee (1924), proposes the following formula for the limiting value of the unit shearing-stress in flat-slab construction: v = 0.02f'(1+r) with the added limitation that it shall not exceed 0.03f'c. (8) The shear adjacent to the periphery of the column-capital is then computed on a vertical section which has a depth, in inches, of (t1 - 11⁄2) and which lies at a distance, in inches, of t1 - 11⁄2 from the edge of the column-capital. Adjacent to the periphery of the drop the shear is computed on a vertical section which has a depth, in inches, of (t2 - 11⁄2), and which lies at a distance, in inches of tą 11⁄2 from the edge of the drop. t is the thickness of a flat-slab without dropped panels, or the thickness of both slab and drop where such are used. tą is the thickness of a flat-slab with dropped panels at points away from the dropped panel. (See Fig. 7.) In computing the shearing-stress adjacent to the column capital, r is the proportional amount of negative reinforcement within the column-strip crossing the column-capital. In computing that adjacent to the perimeter of the drop, r is the proportional amount of negative reinforcement within the column-strip crossing entirely over the dropped panel. In no case is a value less than 0.25 given to r. 14. Bond. The bond-stresses in girderless floor construction are seldom critical; they may be investigated, however, by the usual formula given on page (60). 15. Design-Procedure for Girderless Floors. Having at hand a sketch showing the over-all dimensions of the building and the locations of the columns, the following are determined or computed: (1) The average center-to-center span, L, for any particular panel. (2) The slab thickness. (3) The size of the drop, if used. (4) The size of the column-capital. (5) The thickness of the slab or total thickness of slab and drop across the column-head. (6) From the maximum bending moments at the several design-sections, the cross-sectional area of the reinforcement, and the number, size and length of bars required. 16. Typical Design of Interior Panel, Two-Way System. American Concrete Institute Ruling, 1920.* fe 2 000 lb per sq in v = 60 lb per sq in (shearing unit stress around periph ery of drop) 70 lb per sq in (shearing unit stress around periph- Panel-data: Dimensions, center to center of columns, 20 ft by 20 ft. Drops are to be used. The diagrams, Figs. 8, 9, and 10, illustrate the application of the TWO-WAY SYSTEM to the recommendations of the American Concrete Institute. Example 1 is given in complete detail in order that every step may be clearly understood, but in practice the computations, except under unusual conditions, can of course be greatly abbreviated. In order to determine the load, w, a slab-thickness of 8 in and an approximate weight per square foot is assumed. Then, in which (4 × 80) is the periphery of the drop and 6.75 the effective depth of the slab, both in inches. As 60 lb per sq in is permitted, a square drop with the side equal to 6 ft 8 in is accepted. *For the American Concrete Institute's designation of sections, see Fig. 6. to flat-slab construction both with and without drop-panels. The shearingstress around the periphery of the drop in drop-panel construction, is computed as above by Formula (7) and limited to 0.03f'c or 60 lb per sq in for the same quality of concrete. This same ruling proposes another method for computing the shearing stress as a measure of the diagonal tension using the formulas v = 0.25W/bjd for slabs without drops and v = 0.30W/bjd for drop-construction. In these equations b = L/2. The punching shear is then computed on the full depth around the perimeters of both column capital and drop-panel by the formula, v 1.25V/bd. In this equation V is the portion of the total panel. load lying outside of the section under consideration. The value of vis limited to 120 lb per sq in for 2 000 lb concrete. The Report of the Joint Committee (1924), proposes the following formula for the limiting value of the unit shearing-stress in flat-slab construction: v = 0.02f'e(1+r) with the added limitation that it shall not exceed 0.03f'c. (8) The shear adjacent to the periphery of the column-capital is then computed on a vertical section which has a depth, in inches, of %(t1 - 11⁄2) and which lies at a distance, in inches, of t1 11⁄2 from the edge of the column-capital. Adjacent to the periphery of the drop the shear is computed on a vertical section which has a depth, in inches, of %(t2 — 11⁄2), and which lies at a distance, in inches of t2- 11⁄2 from the edge of the drop. t is the thickness of a flat-slab without dropped panels, or the thickness of both slab and drop where such are used. tą is the thickness of a flat-slab with dropped panels at points away from the dropped panel. (See Fig. 7.) In computing the shearing-stress adjacent to the column capital, r is the proportional amount of negative reinforcement within the column-strip crossing the column-capital. In computing that adjacent to the perimeter of the drop, r is the proportional amount of negative reinforcement within the column-strip crossing entirely over the dropped panel. In no case is a value less than 0.25 given to r. 14. Bond. The bond-stresses in girderless floor construction are seldom critical; they may be investigated, however, by the usual formula given on page (60). 15. Design-Procedure for Girderless Floors. Having at hand a sketch showing the over-all dimensions of the building and the locations of the columns, the following are determined or computed: (1) The average center-to-center span, L, for any particular panel. (2) The slab thickness. (3) The size of the drop, if used. (4) The size of the column-capital. (5) The thickness of the slab or total thickness of slab and drop across the column-head. (6) From the maximum bending moments at the several design-sections, the cross-sectional area of the reinforcement, and the number, size and length of bars required. 16. Typical Design of Interior Panel, Two-Way System. American Concrete Institute Ruling, 1920.* Specification-data: f. 18 000 lb per sq in Panel-data: = = 2 000 lb per sq in v = 60 lb per sq in (shearing unit stress around periphery of drop) 70 lb per sq in (shearing unit stress around periph- Dimensions, center to center of columns, 20 ft by 20 ft. Drops are to be used. The diagrams, Figs. 8, 9, and 10, illustrate the application of the TWO-WAY SYSTEM to the recommendations of the American Concrete Institute. Example 1 is given in complete detail in order that every step may be clearly understood, but in practice the computations, except under unusual conditions, can of course be greatly abbreviated. In order to determine the load, w, a slab-thickness of 8 in and an approximate weight per square foot is assumed. Then, in which (4 × 80) is the periphery of the drop and 6.75 the effective depth of the slab, both in inches. As 60 lb per sq in is permitted, a square drop with the side equal to 6 ft 8 in is accepted. *For the American Concrete Institute's designation of sections, see Fig. 6. |