1. Maximum Compression

Control Points (Moment Rotation about the Negative Y-Axis)

Begin the calculation for the moment capacity where the flange of the T-shaped cross-section is in compression and the column at the bottom of the stem is in tension.

1.1. Nominal axial compressive strength

From Tables 1 and 2:

Calculate total gross cross-sectional area:

Calculate the center of gravity (geometrical centroid):

ACI 318-19 (22.4.2.2)

Since the section is irregular (not symmetrical) about the y-axis, the moment capacity associated with the maximum axial compressive strength is not equal to zero. As commonly is the case in symmetrical reinforcing arrangements.

ACI 318-19 (22.2.2.4.1)

The area of the reinforcement has been included in the area (A_g) used to compute C_c. As a result, it is necessary to subtract 0.85f_c’ from f_s’ before computing C_si for each reinforcement layer (i):

Where i indicates the reinforcement layer number as shown in the following Table.

The concrete compression force is located at the centroid of the section making the location of the geometric centroid coincide with the plastic centroid (x̄ = x̄_p). Thus, the moment capacity is developed by the reinforcement only since the bars forces are not at the geometric centroid. The following Table shows the calculation of the moment capacity associated with the maximum axial compressive strength.

Table 3 - Concrete Shape Data
Layer	A_s/bar, in²	# of bars, in	d, in	C_s,kip	M_sc, kip-ft
1	0.79	12	2.5	-536.6	-7,052.2
2	0.79	12	11.5	-536.6	-6,649.8
3	0.31	2	20.0	-35.1	-410.0
4	0.31	2	32.0	-35.1	-375.0
5	0.31	2	44.0	-35.1	-340.9
6	0.31	2	56.0	-35.1	-304.8
7	0.31	2	68.0	-35.1	-269.7
8	0.31	2	80.0	-35.1	-234.6
9	0.31	2	92.0	-35.1	-199.5
10	0.31	2	104.0	-35.1	-164.4
11	0.31	2	116.0	-35.1	-129.3
12	0.31	2	128.0	-35.1	-94.2
13	0.31	2	140.0	-35.1	-59.1
14	0.31	2	152.0	-35.1	-24.0
15	0.31	2	164.0	-35.1	11.1
16	0.31	2	176.0	-35.1	46.2
17	0.31	2	188.0	-35.1	81.2
18	0.31	2	200.0	-35.1	116.3
19	0.31	2	212.0	-35.1	151.4
20	0.31	2	224.0	-35.1	186.5
21	0.31	2	236.0	-35.1	221.6
22	0.31	2	248.0	-35.1	256.7
23	0.31	2	260.0	-35.1	291.8
24	0.31	2	272.0	-35.1	326.9
25	0.31	2	284.0	-35.1	362.0
26	0.31	2	296.0	-35.1	397.1
27	0.31	2	308.0	-35.1	432.2
28	0.31	2	320.0	-35.1	467.3
29	0.31	2	332.0	-35.1	502.3
30	0.31	2	344.0	-35.1	537.4
31	0.31	2	356.0	-35.1	572.5
32	0.31	2	368.0	-35.1	607.6
33	0.79	3	376.5	-134.1	2,417.7
34	0.79	2	386.0	-89.4	1,682.6
35	0.79	3	395.5	-134.1	2,630.1
				M_o = ∑M_sc, kip-ft	-4,008

1.2. Factored axial compressive strength

ACI 318-19 (Table 21.2.2)

1.3. Maximum (allowable) factored axial compressive strength

ACI 318-19 (Table 22.4.2.1)