4. Bar Stress Near Tension Face Equal to f_y, (f_s = f_y)

Figure 7 - Strains, Forces, and Moment Arms (f_s = f_y)

This strain distribution is called the balanced failure case and the compression-controlled strain limit. It marks the change from compression failures originating by crushing of the compression surface of the section, to tension failures initiated by yield of longitudinal reinforcement. It also marks the start of the transition zone for ϕ for columns in which ϕ increases from 0.75 for spiral columns (or 0.65 for tied columns) up to 0.90.

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 8 - Cracked Column Section Properties (f_s = f_y)

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: