the face of the column or pedestal, or at the point of inflection in footings designed as continuous beams. General practice accepts the same formula as used in the design of beams and slabs (see Formula (14), Chapter IV), น = V/Zojd in which the Zo is the sum of the perimeters, in inches, of the cross-sections of all horizontal tension-rods at the section considered, within the effective width of the footing. Having found the bond-stresses at the critical sections, and made any necessary changes in the amount of kind of reinforcement, the rods must be checked for ANCHORAGE to make sure that the steel at any section can resist the working stresses without pulling loose from the concrete. For example, if deformed bars are used, and if f, is 16 000 lb per sq in, there must be an embedment of 40 diameters at the section where the full strength of the steel is needed; an embedment of 20 diameters where one half the full amount is required, and so on in the same ratio. In the case of PILE-FOOTINGS the bond-stresses are very likely to be relatively high near the edges of the footing-slabs, as the pile-reactions are treated as concentrated loads, or forces acting at the center lines of the piles and often cause higher unit bond-stresses in these sections of the footings than in sections adjacent to the column. Likewise in a STEPPED FOOTING the bond-stress should be investigated at the edge of each step where the depth of the section abruptly decreases. The Joint Committee, 1924, requires that the permissible bond-stress in footings, in which the reinforcement is placed in more than one direction, shall not exceed 75% of the values otherwise allowed. If this requirement is followed, the bond-stresses are almost invariably a critical element of the design and require that the ends of all bars be hooked when used in footings with two-way reinforcement. 9. Design-Procedure for Concrete Wall-Footings. The following are the steps taken in this type of design. (1) The PROJECTION OF THE FOOTING SLAB on each side of the wall is determined by dividing the weight, in pounds, per linear foot to be supported, including the weight of the wall and the estimated weight of the footing itself, by the unit soil-pressure, in pounds per square foot. Then w net soil-pressure in pounds per square foot design-load in pounds divided by footing-area in square feet. = = (2) The MAXIMUM BENDING MOMENT at the face of the wall is computed by Formula (1), (3) The DEPTH AS GOVERNED BY MOMENT is computed by the Formula, (4) The DEPTH AS GOVERNED BY DIAGONAL TENSION is computed by Formula (14), (5) The STEEL SECTION-AREA, per linear foot of footing, is computed by Concrete Wall-Footing. Details of the section and plan of this footing are shown in Fig. 11. v, limited to 60 lb per sq in (reinforcement anchored) u, limited to 150 lb per sq in (deformed bars anchored) Soil-load 4 000 lb per sq ft = It is required to design the footing for an 18-in concrete bearing-wall, supporting upon soil, a load, including its own weight, of 25 000 lb per lin ft. (1) PROJECTION OF FOOTING-SLAB. Estimating the weight of the footing at 1 000 lb per lin ft, the footing-width is making the projection, 1, 2.5 ft on each side of the wall. The DESIGN-Load is the net unit soil-pressure, exclusive of the weight of the footing, or (2) The MAXIMUM BENDING MOMENT at the face of the wall is computed by Formula (1), (3) The DEPTH AS GOVERNED BY MOMENT is computed by Formula (3), (4) The DEPTH AS GOVERNED BY SHEAR is investigated by Formula (14), Accept a depth of 11 + 3 = 14 in. Total weight per linear foot = (6.5 × 1.16 × 1) X 150 = 1 130 lb, which is sufficiently close to the assumed weight. (5) The STEEL SECTION-AREA is computed by Formula (17), Chapter II, As a trial, 5%-in square bars, 5 in on centers are selected. (6) The BOND-STRESS is computed by Formula (14), Chapter IV, u = V/Zojd = 2.5 X 3 850 = 166 lb per sq in in which 2.5 in the denominator is the perimeter of the cross-section of a %-in square bar, and 2.4 the number per linear foot, at the required spacing. As this stress is too high, the number of bars is recalculated on the basis of u = 150 lb per sq in, and by a derivative of the same formula, the number of For this spacing %-in square bars, 41⁄2 in on centers are used, a deformed type being selected and both ends hooked. The reinforcement is placed as shown in Fig. 11. 11. Design-Procedure for Independent Concrete Footings. The following are the usual steps in the procedure. (1) The AREA OF THE FOOTING-SLAB is determined by dividing the load used in the design of the column in the story immediately above the footing, plus any live or dead load in that story, plus the weight of the pedestal, if there is one, plus the estimated weight of the footing itself, by the unit soil-pressure, in pounds per square foot. Then, w = net soil-pressure in pounds per square foot = design-load divided by footing-area Note that if the footing-areas are to be PROPORTIONED FOR EQUAL SETTLEMENT, the procedure on page 210 should be followed in determining the area of the footing-slab. (2) The DEPTH AS GOVERNED BY PUNCHING SHEAR at the face of the column or pedestal is computed by Formulas (18), (19), and (21), For PILE-FOOTINGS the punching shear over exterior piles should be tested as described in Article 7 of this chapter. (3) The MAXIMUM BENDING MOMENT at the face of the column or pedestal is computed by Formulas (5), (6), and (7) or (8), M6w(a+1.33c1)c2 (for oblong footings) M6w(a+1.33c)c,2 (for oblong footings) 6w(a + 1.33c)c2 (for square footings, with square columns or round columns) 6w(a+1.2c)c2 For a round or octagonal column, a is the side of an equivalent square. (4) The DEPTH AS GOVERNED BY THE BENDING MOMENT at the face of the column or pedestal. The crushing strength of the concrete is checked by Formula (9), Chapter II, If the stress is excessive, the required depth is computed by making b the actual width of the section, and making corresponding changes in the values of j and k. Then by Formula (10) Chapter II, (5) The DEPTH AS GOVERNED BY DIAGONAL TENSION, at a distance out from the face of the column equal to the depth of the footing, or as described for pile footings in Article 6, is computed by Formula (1), Chapter IV, and Formula (15), this chapter, For square footings with round columns, make a equal to 0.886 times the diameter of the column. (6) The SECTION-AREA OF THE STEEL, in each direction, is computed by Formula (12), Chapter II, (7) The BOND-STRESSES AND ANCHORAGE are computed by Formulas (14) and (16), Chapter IV, u = V/Zojd 1 = (1/4)(f./u)i 12. Typical Design of an Independent Reinforced-Concrete Column Footing. Details of footings of this type are (2) The DEPTH AS GOVERNED BY PUNCHING SHEAR is computed by Formula (19), |