3. Flexural Reinforcement Requirements

The required flexural reinforcement is traditionally calculated at three critical sections: at the stem base, the toe and heel at the face of the stem.

Calculate the required reinforcement to resist the moment at the stem base:

Use #8 bars with 2.0 in. concrete cover per ACI 318-14 (Table 20.6.1.3.1). The distance from extreme compression fiber to the centroid of longitudinal tension reinforcement, d, is calculated below:

To determine the area of steel, assumptions have to be made whether the section is tension or compression controlled, and regarding the distance between the resultant compression and tension forces along the beam section (jd). In this example, tension-controlled section will be assumed so the reduction factor ϕ is equal to 0.9, and jd will be taken equal to 0.95d. The assumptions will be verified once the area of steel is finalized.

The required reinforcement at initial trial is calculated as follows:

Recalculate ‘a’ for the actual As = 0.79 in.2:

Therefore, the assumption that section is tension-controlled is valid.

The minimum reinforcement shall not be less than

ACI 318-14 (9.6.1.2(a))

And not less than

ACI 318-14 (9.6.1.2(b))

Maximum spacing allowed:

Check the requirement for distribution of flexural reinforcement to control flexural cracking:

ACI 318-14 (Table 24.3.2)

ACI 318-14 (24.3.2.1)

Provide #8 bars at 9 in. centers.

Note that the stem bending moment decreases rapidly with increasing distance from the bottom. For this reason, only part of the main reinforcement is needed at higher elevations and alternate bars can be discontinued where no longer needed. More information about cutting bars in the stem are provided in the reference. All the values in the following table are calculated based on the procedure outlined above for the stem.

Table 2 - Reinforcing Design Summary

Critical Section

Stem Base

Toe

Heel

Design Moment, Mu (ft-kips)

45.7

24.3

29.9

Effective depth, d (in.)

13.5

14.5

14.5

As,req (in.2)

0.78

0.38

0.47

As,min (in.2)

0.54

0.58

0.58

Reinforcement

#8 @ 9 in.

#7 @ 12 in.

#7 @ 12 in.