5. Bar Stress Near Tension Face Equal to ε_y + 0.003

Figure 7 - Strains, Forces, and Moment Arms (ε_s = 0.00507 in./in.)

In ACI 318-19 provisions, this control point corresponds to the tension-controlled strain limit of ɛ_y + 0.003 (used to be 0.005 in ACI 318-14). It is the strain at the tensile limit of the transition zone for ϕ, used to define a tension-controlled section.

Additional resources concerning code provision changes in ACI 318-19 can be found in “ACI 318-19 Code Revisions Impact on StructurePoint Software” technical article.

The following show the general procedure to calculate the axial and moment capacities of the core wall section at this control point, all the calculated values are shown in the next Table.

5.1. c, a, and strains in the reinforcement

    ACI 318-19 (Table 21.2.2)

    ACI 318-19 (22.2.2.1)

Where c is the distance from the fiber of maximum compressive strain to the neutral axis.    ACI 318-19 (22.2.2.4.2)

    ACI 318-19 (22.2.2.4.1)

Where:

a = Depth of equivalent rectangular stress block

    ACI 318-19 (Table 22.2.2.4.3)

5.2. Forces in the concrete and steel

Since h₁ + h₂ = 104 in. > a = 60.79 in. > h₁ = 12 in., the area and centroid of the concrete equivalent block (see Figure 2 and 7) can be found as follows:

Where:

    ACI 318-19 (22.2.2.4.1)

If the reinforcement layer is located within the depth of the equivalent rectangular stress block (a), it is necessary to subtract 0.85f_c’ from f_s,i before computing F_s,i since the area of the reinforcement in this layer has been included in the area used to compute C_c.

The force developed in the reinforcement layer (F_s,i) is considered as compression force (C_s,i) if the effective depth of this steel layer (d_i) is less than c (the distance from the fiber of maximum compressive strain to the neutral axis), otherwise it is considered as tension force (T_s,i).

5.3. ϕP_n and ϕM_n

Using values from the next Table: