# Strength Design for Flexure

Article 9.44 summarizes the basic assumptions for strength design of flexural members.
The following formulas are derived from those assumptions.
The area As of tension reinforcement in a reinforced-concrete flexural member
can be expressed as the ratio

where b = beam width and d = effective beam depth  distance from the extreme compression surface to centroid of tension reinforcement. At nominal (ultimate) strength of a critical section, the stress in this steel will be equal to its yield strength Æ’y, psi, if the concrete does not first fail in compression. (See also Arts. 9.47 to 9.50 for additional reinforcement requirements.)

## Singly-Reinforced Rectangular Beams

For a rectangular beam, reinforced with only tension steel (Fig. 9.12), the total tension force in the steel at nominal (ultimate) strength is

resists AsÆ’s . Forces equal in magnitude to these but opposite in direction stress the tension reinforcement. The depth to the neutral axis c can be found from the maximum compressive strain of 0.003 in / in or by equating the compression and tension  forces on the section. (See also Art. 9.64.)

## T-Beams

When a T form is used to provide needed compression area for an isolated beam,  flange thickness should be at least one-half the web width, and flange width should not exceed 4 times the web width.

When a T is formed by a beam cast integrally with a slab, only a portion of the slab is effective. For a symmetrical T-beam, the effective flange width should not exceed one-fourth the beam span, nor should the width of the overhang exceed 8 times the slab thickness nor one-half the clear distance to the next beam. For a beam having a flange on one side only, the effective flange width should not exceed one-twelfth the span, 6 times the slab thickness, nor one-half the clear distance to the next beam.
The overhang of a T-beam should be designed to act as a cantilever. Spacing of the cantilever reinforcement should not exceed 18 in or 5 times the flange thickness.
In computing the moment capacity of a T-beam, it may be treated as a singlyreinforced beam with overhanging concrete flanges (Fig. 9.15). The compression force on the web (rectangular beam) is

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