15. RULES COVERING THE DESIGN OF REINFORCED Definitions. (In Effect 1926) (1) Flat slabs as understood by this ruling are reinforced concrete slabs, supported directly on reinforced columns with or without plates or capitals at the top, the whole construction being hingeless and monolithic without any visible beams or girders. The construction may be such as to admit the use of hollow panels in the ceiling or smooth ceiling with depressed panels in the floor. (2) The column capital shall be defined as the gradual flaring out of the top of the column without any marked offset. (3) The drop panel shall be defined as a square or rectangular depression around the column capital extending below the slab adjacent to it. (4) The panel length shall be defined as the distance center to center of columns of the side of a square panel, or the average distance center to center of columns of the long and short sides of a rectangular panel. Columns. (5) The least dimension of any concrete column shall be not less than onetwelfth (12) the panel length, nor one-twelfth (2) the clear height of the column. Slab Thickness. (6) The minimum total thickness of the slab in inches shall be determined the panel, measured center to center of columns. (7) In no case shall the thickness be less than one thirty-second of the panel length (L/32) for floors, nor one-fortieth of the panel length (L/40) for roofs (L being the distance center to center of columns). (8) In no case shall the thickness of slab be less than six inches (6") for floors or roofs. Column Capital. (9) When used the diameter of the column capital shall be measured where its vertical thickness is at least one and one-half inches (11⁄2"), and shall be at least two hundred and twenty-five thousandths (.225) of the panel length. The slope of the column capital shall nowhere make an angle with the vertical of more than forty-five degrees. Special attention shall be given to the design of the column capital in considering eccentric loads, and the effect of wind upon the structure. Drop Panel. (10) When used, the drop panel shall be square or circular for square panels and rectangular or elliptical for oblong panels. (11) The length of the drop shall not be less than one-third of the panel length (L/3) if square, and not less than one-third of the long or short side of the panel respectively, if rectangular. (12) The depth of the drop panel shall be determined by computing it as a beam, using the negative moment over the column capital specified elsewhere in this ruling. (13) In no case, however, shall the dimensions of the drop panel be less than required for punching shear along its perimeter, using allowable unit shearing stresses specified below. Shearing Stresses. (14) The allowable unit punching shear on the perimeter of the column. capital shall be three-fiftieths (30) of the ultimate compressive strength of the concrete as given in section 533 of the building ordinance. The allowable unit shear on the perimeter of the drop panel shall be three one-hundredths (100) of the ultimate compressive strength of the concrete. In computing shearing stress for the purpose of determining the resistance to diagonal tension the method specified by the ordinance shall be used. Panel Strips. (15) For the purpose of establishing the bending moments and the resisting moments of a square panel, the panel shall be divided into strips known as strip A and strip B. Strip A shall include the reinforcement and slab in a width extending from the center line of the columns for a distance each side of this center line equal to one-quarter (1⁄44) of the panel length. Strip B shall include the reinforcement and slab in the half width remaining in the center of the panel. At right angles to these strips, the panel shall be divided into similar strips A and B, having the same widths and relations to the center line of the columns as the above strips. These strips shall be for designing purposes only, and are not intended as the boundary lines of any bands of steel used. (16) These strips shall apply to the system of reinforcement in which the reinforcing bars are placed parallel and at right angles to the center line of the columns, hereinafter known as the two-way system, and also to the system of reinforcement in which the reinforcing bars are placed parallel, at right angles to and diagonal to the center line of the columns hereinafter known as the fourway system. (17) Any other system of reinforcement in which the reinforcing bars are placed in circular, concentric rings and radial bars, or systems with steel rods arranged in any manner, whatsoever, shall comply with the requirements of either the two-way or the four-way system herein specified. Bending Moment Coefficients, Interior Panel, Two-way System. (18) In panels where standard drops and column capitals are used as above specified, the negative bending moment taken at a cross-section of each strip A at the edge of the column capital or over it, shall be taken as WL (19) The positive bending moment taken at a cross-section of each strip A midway between column centers, shall be taken as WL (20) The positive bending moment taken at a cross-section of each strip B in the middle of the panel shall be taken as WL (21) The negative bending moment taken at a cross-section of each strip B on the center line of the columns shall be taken as WL (22) In the formulas hereinabove given total live and dead load on the whole panel in pounds, panel length, center to center of columns. Bending Moment Coefficients, Interior Panel, Four-way System. (23) In panels where standard drops and column capitals are used as above specified, the negative bending moment taken at a cross-section of each strip A WL at the edge of column capital or over it, shall be taken as 30 (24) The positive bending moment taken at a cross-section of each strip A, WL midway between column centers shall be taken as 80 (25) The positive bending moment taken at a cross-section of each strip B, taken in the middle of the panel shall be taken as WL (26) The negative bending moment taken at a cross-section of each strip B on the center line of the columns shall be taken as WL Bending Moment Coefficients, Wall Panels. (27) Where wall panels with standard drops and capitals are carried by columns and girders built in walls, as in skeleton construction, the same coefficients shall be used as for an interior panel, except as follows: The positive bending moments on strips A and B midway between wall and first line of columns shall be increased twenty-five (25%) per cent. (28) Where wall panels are carried on new brick walls, these shall be laid in Portland cement mortar and shall be stiffened with pilasters as follows: If a sixteen-inch wall is used, it shall have a four-inch pilaster. If a twelve-inch wall is used, it shall have an eight-inch pilaster. The length of pilasters shall be not less than the diameter of the column, nor less than one-eighth (%) of the distance between pilasters. The pilasters shall be located opposite the columns as nearly as practicable, and shall be corbeled out four inches at the top, starting at the level of the base of the column capital. Not less than eight (8") inches bearing shall be provided for the slab, the full length of wall. The coefficients of bending moments required for these panels shall be the same as those for the interior panels except as provided herewith: The positive bending moments on strips A and B midway between the wall and first line of columns shall be increased fifty (50%) per cent. (29) Where wall panels are supported on old brick walls, there shall be columns with standard drops and capitals built against the wall which shall be tied to the same in an approved manner, and at least an eight-inch bearing provided for the slab, the full length. Where this is impracticable, there shall be built a beam on the underside of slab adjacent to the wall between columns, strong enough to carry twenty-five per cent (25%) of the panel load. The coefficients of bending moments for the two cases of slab support herein described shall be the same as those specified in Sec. 27 and Sec. 28 for skeleton and wall bearing condition respectively. (30) Nothing specified above shall be construed as applying to a case of slabs merely resting on walls or ledges, without any condition of restraint. These shall be figured as in ordinary beam and girder construction specified in the Ordinances. Bending Moment Coefficients, Wall and Interior Columns. (31) Wall columns in skeleton construction shall be designed to resist a WL bending moment of at floors and at roof. The amount of steel required 30 WL for this moment shall be independent of that required to carry the direct load. It shall be placed as near the surfaces of the column as practicable on the tension sides, and the rods shall be continuous in crossing from one side to another. The length of rods below the base of the capital and above the floor line shall be sufficient to develop their strength through bond, but not less than forty (40) diameters, nor less than one-third (%) the clear height between the floor line and the base of the column capital. (32) The interior columns must be analyzed for the worst condition of unbalanced loading. It is the intention of this ruling to cover ordinary cases of eccentric loads on the columns by the requirement of Sec. 5. Where the minimum size of column therein specified is found insufficient, however, the effect of the resulting bending moment shall be properly divided between the adjoining slab and the columns above and below according to best principles of mechanics and the columns enlarged sufficiently to carry the load safely. Bending Moment Coefficients, Panels without Drops, or Capitals, or Both. (33) In square panels where no column capital or no depressions are used, the sum total of positive and negative bending moments shall be equal to that computed by the following formula: where = B.M. numerical sum of positive and negative bending moments, regardless of algebraic signs. W = total live and dead load on the whole panel. L k = = length of side of a square panel, c. to c. of columns. ratio of the radius of the column or column capital to panel length, L. This total bending moment shall be divided between the positive and the negative moments in the same proportion as in the typical square panels for two-way or four-way systems specified above for interior and wall panels respectively. Point of Inflection. (34) For the purpose of making the calculations of the bending moment at the sections away from the column capital, the point of inflection shall be considered as being one-quarter (4) the distance center to center of columns, both cross-wise and diagonally, from the center of the column. Tensile Stress in Steel and Compressive Stress in Concrete. (35) The tensile stress in steel and the compressive stress in the concrete to resist the bending moment shall be calculated on the basis of the reinforcement and slab in the width included in a given strip, and according to the assumptions and requirements given in sections 532 to 535 inclusive of the building ordinance. The steel shall be considered as being concentrated at the center of gravity of all the bands of steel in a given strip. (36) For the four-way system of reinforcement the amount of steel to resist the negative bending moment over the support in each strip A shall be taken as the sum of the areas of steel in one cross band and one diagonal band. The amount of steel to resist the positive bending moment of each strip B shall be considered as the area of the steel in a diagonal band. The amount of steel to resist the positive bending moment in each strip A shall be considered as the area of the steel in a cross-band, and the amount of steel to resist the negative moment in each strip B shall be the steel included in the width of strip B. (37) For the two-way system of reinforcement the amount of steel to resist the bending moment in any strip shall be considered as the area of steel included in the width of the strip. (38) In both systems of reinforcement the compressive stress in the concrete in any strip shall be calculated by taking the area of steel considered for each strip, and applying it in a beam formula based on the principles of section 535 of the building ordinance. (39) Where drop panels are used, the width of beam assumed to resist the compressive stresses over the column capital shall be the width of the drop. (40) The width of beam where no drop panels are used, shall be the width of steel bands. Where this is found insufficient, the area shall be increased by introducing compression steel in the bottom of slab. |