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

Figure 9 - 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.

For Concrete:

    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)

(Compression)    ACI 318-19 (22.2.2.4.1)

Where:

Figure 10 - Cracked Column Section Properties (ε_s = 0.00507 in./in.)

For Reinforcement:

The area of the reinforcement in this layer is not included in the area (ab) used to compute C_c. As a result, it is NOT necessary to subtract 0.85f_c’ from f_s5 before computing F_s5:

(Tension)

The area of the reinforcement in this layer is not included in the area (ab) used to compute C_c. As a result, it is NOT necessary to subtract 0.85f_c’ from f_s4 before computing F_s4:

(Tension)

The same procedure shown above can be repeated to calculate the forces in the remaining reinforcement layers, results are summarized in the following table:

Where: