Nonprestressed beams should be designed for flexure as explained in Arts. 9.44 to 9.46. If beam capacity is inadequate with tension reinforcement only and the capacity must be increased without increasing beam size, additional capacity may be provided by addition of compression bars and more tension-bar area to match the compression forces developable in the compression bars (Fig. 9.14). (Shear, torsion, development, crack control, and deflection requirements must also be met to complete the design. See Arts. 9.47 to 9.51 and 9.65 to 9.67.) Deflection need not be calculated for ACI 318 Building Code purposes if the total depth h of the beam, including top and bottom concrete cover, is at least the fraction of the span L given in Table 9.15.
A number of interdependent complex requirements (Art. 9.49) regulate the permissible cutoff points of bars within a span, based on various formulas and rules for development (bond). An additional set of requirements applies if the bars are cut off in a tensile area. These requirements can be satisfied for cases of uniform gravity load and nearly equal spans for the top bars by extending at least 50% of the top reinforcement to a point in the span 0.30Ln beyond the face of the support, and the remainder to a point 0.20Ln, where Ln = clear span. For the bottom bars, all requirements are satisfied by extending at least 40% of the total reinforcement into the supports 6 in past the face, and cutting off the remainder at a distance 0.125Ln from the supports. Note that this arrangement does not cut off bottom bars in a tensile zone. Figure 9.34 shows a typical reinforcement layout for a continuous beam, singly-reinforced.
The structural detailing of reinforcement in beams is also affected by ACI 318 Building Code requirements for structural integrity. Beams are categorized as either perimeter beams or nonperimeter beams. (A spandrel beam would be a perimeter beam.) In perimeter beams, at least one-sixth of the tension-reinforcement area required for negative moment (As /6) at the face of supports, and one-quarter of the tension-reinforcement area required for positive moment (As /4) at midspan have to be made continuous around the perimeter of the structure. Closed stirrups are also required in perimeter beams. It is not necessary to place closed stirrups within the joints. It is permissible to provide continuity of the top and bottom bars by splicing the top bars at midspan and the bottom bars at or near the supports.
Splicing the bars with Class A tension lap splices (Art. 9.49.7) is acceptable. (See Fig. 9.35a.)
For nonperimeter beams, the designer has two choices to satisfy the structural integrity requirements: (1) provide closed stirrups or (2) make at least one-quarter of the tension-reinforcement area required for positive moment (As /4) at midspan continuous. Splicing the prescribed number of bottom bars over the supports with Class A tension lap splices is acceptable. At discontinuous ends, the bottom bars must be anchored with standard hooks. (see Fig. 9.35b.)
The limit in the ACI 318 Building Code on tension-reinforcement ratio that it not exceed 0.75 times the ratio for balanced conditions applies to beams (Art. 9.46). Balanced conditions in a beam reinforced only for tension exist when the tension steel reaches its yield strength Æ’y simultaneously with the maximum compressive strain in the concrete at the same section becoming 0.003 in / in. Balanced conditions occur similarly for rectangular beams, and for T-beams with negative moment, that are provided with compression steel, or doubly-reinforced. Such sections are under balanced conditions when the tension steel, with area As, yields just as the outer concrete surface crushes, and the total tensile-force capacity AsÆ’y equals the total compressive-force capacity of the concrete plus compression steel, with area A. Note that the capacity of the compression steel cannot always be taken as s AÆ’ , because the straight-line strain distribution from the fixed points of the outer s y concrete surface and centroid of the tension steel may limit the compression-steel stress to less than yield strength (Fig. 9.14).
For design of doubly-reinforced beams, the force AsÆ’y in the tension steel is limited to three-fourths the compression force in the concrete plus the compression in the compression steel at balanced conditions. For a beam meeting these conditions in which the compression steel has not yielded, the design moment strength is best determined by trial and error:
1. Assume the location of the neutral axis.
2. Determine the strain in the compression steel.
3. See if the total compressive force on the concrete and compression steel equals AsÆ’y (Fig. 9.36).
