5. Bar Strain Near Tension Face Equal to εy + 0.003

10 Bar Stress Near Tension Face Equal to ey+0.003

Figure 6 - Strains, Forces, and Moment Arms (εs = 0.00507 in./in.)

In ACI 318-19 provisions, this control point corresponds to the tension-controlled strain limit of ɛy + 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 irregular 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 a = 125 in. > h1 = 14 in., the area and centroid of the concrete equivalent block (see the previous Figure) can be found as follows:




    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 0.85fc from fs,i before computing Fs,i since the area of the reinforcement in this layer has been included in the area used to compute Cc.


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

5.3. ϕPn and ϕMn






Table 7 - Axial and Moment Capacity for the Fifth Control Point

Layer

As/bar, in2

# of bars, in

d, in

εs, in./in.

fs,i, kip

Cs,i,kip

Ts,i, kip

Mn,i, kip-ft

1

0.79

12

2.5

-0.00295

60.0

-536.6

0.0

-7,052.2

2

0.79

12

11.5

-0.00277

60.0

-536.6

0.0

-6,649.8

3

0.31

2

20.0

-0.00259

60.0

-35.1

0.0

-410.0

4

0.31

2

32.0

-0.00235

60.0

-35.1

0.0

-375.0

5

0.31

2

44.0

-0.0021

60.0

-35.1

0.0

-339.9

6

0.31

2

56.0

-0.00186

53.9

-31.3

0.0

-271.7

7

0.31

2

68.0

-0.00161

46.8

-26.9

0.0

-206.6

8

0.31

2

80.0

-0.00137

39.7

-22.5

0.0

-150.3

9

0.31

2

92.0

-0.00112

32.6

-18.1

0.0

-102.8

10

0.31

2

104.0

-0.00088

25.5

-13.7

0.0

-64.1

11

0.31

2

116.0

-0.00063

18.4

-9.3

0.0

-34.2

12

0.31

2

128.0

-0.00039

11.3

-7.0

0.0

-18.8

13

0.31

2

140.0

-0.00014

4.2

-2.6

0.0

-4.4

14

0.31

2

152.0

0.0001

2.9

0.0

1.8

1.2

15

0.31

2

164.0

0.00035

10.0

0.0

6.2

-2.0

16

0.31

2

176.0

0.00059

17.1

0.0

10.6

-14.0

17

0.31

2

188.0

0.00084

24.2

0.0

15.0

-34.8

18

0.31

2

200.0

0.00108

31.3

0.0

19.4

-64.4

19

0.31

2

212.0

0.00133

38.4

0.0

23.8

-102.8

20

0.31

2

224.0

0.00157

45.5

0.0

28.2

-150.0

21

0.31

2

236.0

0.00181

52.6

0.0

32.6

-206.1

22

0.31

2

248.0

0.00206

59.7

0.0

37.0

-270.9

23

0.31

2

260.0

0.0023

60.0

0.0

37.2

-309.3

24

0.31

2

272.0

0.00255

60.0

0.0

37.2

-346.5

25

0.31

2

284.0

0.00279

60.0

0.0

37.2

-383.7

26

0.31

2

296.0

0.00304

60.0

0.0

37.2

-420.9

27

0.31

2

308.0

0.00328

60.0

0.0

37.2

-458.1

28

0.31

2

320.0

0.00353

60.0

0.0

37.2

-495.3

29

0.31

2

332.0

0.00377

60.0

0.0

37.2

-532.5

30

0.31

2

344.0

0.00402

60.0

0.0

37.2

-569.7

31

0.31

2

356.0

0.00426

60.0

0.0

37.2

-606.9

32

0.31

2

368.0

0.00451

60.0

0.0

37.2

-644.1

33

0.79

3

376.5

0.00468

60.0

0.0

142.2

-2,562.9

34

0.79

2

386.0

0.00488

60.0

0.0

94.8

-1,783.7

35

0.79

3

395.5

0.00507

60.0

0.0

142.2

-2,788.1

Concrete

---

p =

35.02

---

---

-11,947

0.0

-125,029






Pn, kip

-12,331

Mn, kip-ft

-153,455