(which in two-way reinforced concrete footings is to be resisted by one set of bars) may be taken to be at a vertical section passing through the face of the pier. In calculating this moment, all the upward load on the rectangle lying between a face of the pier and the edge of the footing is considered to act at a center of pressure located at a point halfway out from the pier, and half of the upward load on the two corner squares is considered to act at a center of pressure located at a point six-tenths of the width of the projection from the given section.
"With two-way reinforcement evenly spaced over the footing, it seems that the tensile stress is approximately the same in bars lying within a space somewhat greater than the width of the pier and that there is also considerable stress in the bars which lie near the edges of the footing. For intermediate bars, stresses intermediate in amount will be developed. For footings having two-way reinforcement spaced uniformly over the footing, the method proposed, for deter mining the maximum tensile stress in the reinforcing bars, is to use in the calculation of resisting moment at a section at the face of the pier the area of all the bars which lie within a width of footing equal to the width of pier plus twice the thickness of footing, plus half the remaining distance on each side to the edge of the footing. This method gives results in keeping with the results of t-ests. When the spacing through the middle of the width of the footing is closer, or even when the bars are concentrated in the middle portion, the same method may be applied without serious error. Enough reinforcement should be placed in the outer portion to prevent the concentration of tension cracks in the concrete and to provide for other distribution stresses.
"The method for calculating maximum bond stress in column footings having two-way reinforcement evenly spaced, or spaced as noted in the preceding paragraph, is to use the ordinary bond-stress formula, and to consider the circumference of all the bars which were used in the calculation of tensile stress, and to take for the external shear that amount of upward pressure or load which was used in the calculation of the bending moment at the given section." Example.—A column 2 feet square is to carry a load of 300,000 pounds on soil that may safely carry 3000 pounds per square foot. It is required to design a square footing with two-way reinforcement, using concrete of 2000 pounds compressive strength and unit stress of 10,000 upon the steel.
The required area of foot ing is 300000/3000 =100 square feet. A base 10 feet square will be used.
Using Talbot's rule, the moment of the load upon DCEF (Fig. 107) is 2X4X3000X2X12=576000 in.-lb.; that of the loads DFB and ACE is 4 X4 X3000 X 2.4X12= 1382-100 in.-lb.
Total, 31=576000+1382400=1958400 in.-lb.
The effective width of section is 2+2.1 X2+ 1.9=5.0 feet. The depth required for moment. is (Formula (9) Chapter DTI) Nineteen !-inch bars in the width of 8 feet gives an area of 5.8 in.' and a spacing of about 5 inches. lour additional bars or 23 in all should be used in the full svidth of 10 feet.
The maximum shear is equal to the load upon the area A BDC, This is rather high for plain bars, but deformed bars may be used.
According to Talbot's rules, the shear for diagonal tension may be computed on a section distant the depth of footing from the base of the pier, which will give a shear The volume of concrete in the above footing may be decreased by widening the base of the pier or placing a block of concrete under it as shown in Fig. 10S. If a step 6 inches wide be used, making the block 3 feet square, the depth of footing required is found to be 16 inches. Reinforcement for diagonal tension would be required for this depth but by increasing it to 17 inches, the shear may be so reduced as to snake this unnecessary. This change would decrease the volume of concrete required by about 30 per cent and increase the weight of steel by 20 to 25 per cent.
Four-way Reinforeentent.—When a four-way reinforcement is used, each set of bars is supposed to carry an equal share of the mo ment. As the length of the diagonal bars are not the same as those parallel to the sides of the footing, this supposition is only approxi mately correct, but in the absence of more definite information con cerning the distribution of stress it may be used in design.
If a four-way reinforcement be used in the example already given, as shown in Fig. 109, the depth required for shear at the base of the pier will be as before, 25 inches. The moment of the upward thrust upon the area ABCD about the section CD is, as before, 1,958,400 in.-lb. If the width of section be supposed to carry all of the compression due to this moment, the depth of section required will be The depth to the steel n•ill be made 2S inches at the base of the pier and slope to ti inches at the edges of the slab, thus giving greater depth than necessary it all intermediate points.