2. Bar Stress Near Tension Face Equal to Zero, (ε_s = f_s = 0)

Figure 4 - Strain Diagram, Forces, and Moment Arms (ε_t = f_s = 0)

Strain ε_s is zero in the extreme layer of tension steel. This case is considered when calculating an interaction diagram because it marks the change from compression lap splices being allowed on all longitudinal bars, to the more severe requirement of tensile lap splices.     ACI 318-19 (10.7.5.2.1 and 2)

The following shows 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.

2.1. c, a, and strains in the reinforcement

c = d₁₆ = 218 in.

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)

    ACI 318-19 (Table 21.2.2)

    ACI 318-19 (22.2.2.1)

2.2. Forces in the concrete and steel

Since h₁ + h₂ + h₃ + h₄ = 208 in. > a = 163.5 in. > h₁ + h₂ + h₃ = 116 in., the area and centroid of the concrete equivalent block (see Figure 2 and 4) 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).

2.3. ϕP_n and ϕM_n

Using values from the next Table: