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ACI 318-19 Column P–M Interaction Diagram

Rectangular tied or spiral column, uniaxial bending, by strain compatibility (§22.2): ε_cu = 0.003, β₁, displaced concrete in the compression block, φ from the extreme tension strain with the ACI 318-19 limit ε_ty + 0.003 (Table 21.2.2), φP_n,max (Table 22.4.2.1), pure tension (§22.4.3). Checked point by point against StructurePoint's spColumn example.

Section & Materials

b (width) in

h (depth, bending direction) in

f′c psi

f_y psi

Cover to bar center in

Column type

Reinforcement

Bars, compression face

Size

Bars, tension face

Size

Side bars per side (between faces)

Size

Demand (factored)

P_u (compression +) kip

M_u kip-ft

Results

DCR (radial, constant e = M_u/P_u)—

A_st · ρ_g—

β₁ · ε_y—

φP_n,max Table 22.4.2.1—

Control Points (design values)

§22.2Strain compatibility, εcu = 0.003, equivalent block a = β1·c at 0.85f′c; compression bars inside the block are reduced by 0.85f′c

Table 21.2.2φ = 0.65 (tied) / 0.75 (spiral) for εt ≤ εty; 0.90 for εt ≥ εty + 0.003 (ACI 318-19; ACI 318-14 used 0.005); linear between

Table 22.4.2.1φPn,max = 0.80·φPo (tied), 0.85·φPo (spiral); Po = 0.85f′c(Ag − Ast) + fy·Ast

VerifyStructurePoint "Interaction Diagram – Tied RC Column Design Strength (ACI 318-19)", 2022 (also Wight, 8th ed., Ex. 11-1): 16×16 in, f′c 5000 psi, Gr 60, 4 #9 each face — all 8 control points reproduced (regression test).

ScopeUniaxial bending, rectangular section, moments about mid-depth (symmetric reinforcement). Slenderness (§6.6.4 moment magnification) and biaxial bending are NOT included.

Preliminary calculation tool. Final design requires the full text of ACI 318 and review by a licensed PE. This tool follows ACI 318-19, the edition referenced by the 2021 and 2024 IBC; ACI CODE-318-25 was published in January 2025 and is expected in the 2027 IBC (changes include development length equations and seismic provisions).