6. Pure Bending

13 Pure Bending

Figure 11 - Strains, Forces, and Moment Arms (Pure Moment)

This corresponds to the case where the nominal axial load capacity, Pn, is equal to zero. Iterative procedure is used to determine the nominal moment capacity as follows:

Try c = 6.256 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 (Table 21.2.2)

    ACI 318-19 (22.2.2.4.1)

    ACI 318-19 (22.2.2.1)

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:






14 Section

Figure 12 - Cracked Column Section Properties (Pure Moment)



The area of the reinforcement in this layer is not included in the area (ab) used to compute Cc. As a result, it is NOT necessary to subtract 0.85fc’ from fs5 before computing Fs5:

(Tension)



The area of the reinforcement in this layer is not included in the area (ab) used to compute Cc. As a result, it is NOT necessary to subtract 0.85fc’ from fs4 before computing Fs4:

(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:

Table 6 - Strains and internal force resultants (fs = fy)

Layer

d, in

ε, in./in.

fs, psi

Fs, kip

Cc, kip

Moment arm (r), in.

Moment, kip-ft

Concrete

---

0.00300

---

---

261.38

7.05

153.51

1

2.64

0.00174

50356

58.55*

---

7.37

35.94

2

4.79

0.00070

20357

40.91*

---

5.21

17.75

3

10.00

-0.00180

-52066

-132.25

---

0.00

0.00

4

15.21

-0.00429

-60000

-152.40

---

-5.21

66.14

5

17.37

-0.00533

-60000

-76.20

---

-7.37

46.77

Axial Force and Bending Moment

Pn, kip

0.00

Mn, kip-ft

320.11

ϕPn, kip

0.00

ϕMn, kip-ft

288.09

* The area of the reinforcement in this layer has been included in the area (ab) used to compute Cc. As a result, 0.85fc’ is subtracted from fs in the computation of Fs.


Where:


(+) = Compression

(-) = Tension




Since, the assumption that c = 3.25 in. is correct.


(+) = Counter Clockwise

(-) = Clockwise