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Quick Design: ACI 318-25 Column

Overview

This calculator is for the design of reinforced non-prestressed concrete columns as per ACI CODE-318-25. The following calculations are performed:

  • Column slenderness is determined in each direction depending on user inputs.
  • Design bending moments are calculated based on slenderness.
  • Moment capacities are derived from interaction diagrams, which are drawn based on the section properties of the column.
  • Shear capacities of the section are determined using the inclined strut truss model.
  • Detailing checks are performed on the section.

Assumptions

  • When calculating shear, the angle of the shear reinforcement is assumed to be perpendicular to the longitudinal reinforcement and the longitudinal reinforcement is parallel with all faces of the concrete.
  • Aggregate size is assumed to be 0.75in (20mm) for calculations.
  • λ = 1 as normal density concrete is assumed (19.2.4).
  • No transverse load is assumed to act between the column supports.
  • bw is taken as the diameter when calculating shear capacity for circular sections as per 22.5.2.1(c).

Section Analysis

Interaction Diagrams

The bending capacity of the concrete column is derived from interaction diagrams drawn for each axis. The interaction line is plotted by calculating values of M and P at varying depths of the neutral axis. This is done by determining the strains in the concrete and reinforcement bars for a given depth of the neutral axis. These strains can be converted into forces, which can then be used to calculate the maximum axial load and bending moment that the column can resist for that neutral axis depth. The reduction factor for each point on the interaction line is calculated as per Table 21.2.1(a), with a minimum value provided by Table 21.2.2.

Notes
  • Moments are taken about the plastic centroid of the section.
  • The resultant concrete force is assumed to act at the centroid of the rectangular stress block.
    • For rectangular sections, this is taken as half the height of the block.
    • For circular sections, this is calculated by finding the centroid of the segment in compression, where the height of the segment is equal to β1.c.

Column Design

Axial Capacity

The greatest compression strength of a column is defined as it’s factored axial resistance with zero eccentricity (P0). This is calculated assuming the section’s reinforcement has reached it’s full yield stress (fy) in compression and the concrete is under a uniform compressive stress of 0.85f’c (22.2.2.4.1). The maximum nominal axial compressive strength of the column (Pn,max) comprises a reduced value of P0, where the reduction relates to the confinement of the column’s core as per Table 22.4.2.1. The reduction factor (ϕcc) is taken as 0.65 for compression-controlled sections.
The tensile capacity of the section is calculated as the strength of the reinforcement at yield and ignores any contribution from the concrete.

Core Confinement

The confinement of the column core, as referenced in section 10.10.4, is calculated by comparing the volume ratio of the confining spiral reinforcement, ρs, to the limiting ratio as per clause 25.7.3.3. Note that only spiral reinforcement is considered to confine the column’s core and the maximum confinement pitch is 3in (75mm) as per clause 25.7.3.1(b).

Equation 25.7.3.3
ρs≥0.45(AgAch−1)f′cfyt \rho _s \geq 0.45 \left(\frac{A_g}{A_{ch}} – 1 \right) \frac{f’_c}{f_{yt}}
Equation 25.7.3.3
ρactual=VspiralVcore≥ρs \rho _{actual} = \frac{V_{spiral}}{V_{core}} \geq \rho _s

Design Moments

Sway and Non-Sway

The calculation of column end moments will depend on whether it acts as a sway or non-sway element, which can be determined as per clause 6.2.5.1. For non-sway columns, the end moments can be calculated directly using first-order linear analysis and then converted to the design end moments M1 and M2.

If the column is acting as a sway element, the design end moments, M1 and M2, can then be derived using clause 6.6.4.6.1. The calculation of magnified moments to this clause is beyond the scope of this calculator, however users may specify the directions in which the column acts as a sway element and provide magnified moments directly.

Following the calculation of M1 and M2 moments, the column can be checked for slenderness and designed for Mc, regardless of its sway status (10.16.4).

M1=min[MtopMbottom] M_1 = \min \left[ M_{top} \;\; M_{bottom} \right]
M2=max[M2,minmax[MtopMbottom]] M_2 = \max \left[ M_{2,min} \;\; \max \left[ M_{top} \;\; M_{bottom} \right] \right]
M1=M1ns+δsM1s M_1 = M_{1ns} \;+\; \delta _{s}M_{1s}
M2=max[M2,minM2ns+δsM2s] M_2 = \max \left[ M_{2,min} \;\; M_{2ns} \;+\; \delta _{s}M_{2s}\right]
Notes
  • M1 / M2 is taken as negative when the column is bent in single curvature. In this calculator, this is when the moments have the same sign.
  • When M2,min is greater than M2, the column is assumed to bent in single curvature.
  • M2,min is calculated as Pfe, where e is 0.6 + 0.03h (15 + 0.03h for metric).

Calculate Slenderness

A column is deemed to not be slender if it is within the limits outlined below. A column’s slenderness ratio is calculated as klu / r, where radius of gyration is calculated as (I / A)0.5.

Equation 6.2.5.1b & c
klur≤min[4034+12(M1/M2)] \frac{kl_u}{r} \leq \min \left[ 40 \;\; 34 + 12(M_1/M_2) \right]
Equation 6.2.5.1a
klur≤22 \frac{kl_u}{r} \leq 22

Magnified Moment For Curvature, Mc

If a column is found to be slender, then the design moment needs to be factored to account for curvature. Note that in equations 6.6.4.4.4a to c, βdns is the ratio of the sustained load, which must be provided by the user in this calculation. The second moment of area, I, is calculated as per Table 6.6.3.1.1(b) in equation 6.6.4.4.4c.

Equation 6.6.4.5.1
Mc=δM2 M_c = \delta M_2
Equation 6.6.4.5.2
δ=Cm1−Pu0.75Pc≥1.0 \delta = \frac{C_m}{1 – \frac{P_u}{0.75P_c}} \geq 1.0
6.6.4.5.3
Cm=0.6−0.4M1M2 C_m = 0.6 – 0.4\frac{M_1}{M_2}
Equation 6.6.4.4.2
Pc=π2(EI)eff(klu)2 P_c = \frac{\pi ^2(EI)_{eff}}{(kl_u)^2}
6.6.4.4.4 a-c
(EI)eff=max[0.4EcIg1+βdns0.2EcIg+EsIse1+βdnsEcI1+βdns] (EI)_{eff} = \max \left[ \frac{0.4E_cI_g}{1 + \beta_{dns}} \;\; \frac{0.2E_cI_g + E_sI_{se}}{1 + \beta_{dns}} \;\; \frac{E_cI}{1 + \beta_{dns}} \right]

Bending Capacity

The bending moment capacity is calculated in each axis by plotting the coordinates of the design forces (axial load and bending moment) on the interaction diagrams. A line is drawn through the origin, which intersects the design coordinate. The moment capacity (ϕMn,axis) and axial capacity (ϕPn,axis) are taken at the point where this line intersects the interaction line. The Bresler equation below considers the axial capacity of each axis (ϕPnz and ϕPny) with the maximum axial capacity of the section (ϕP0) to conclude a resistance for the column (ϕPr). This value is compared to the factored applied axial load (Pu) to determine a biaxial utilization. Note that the Bresler equation in not applicable to columns where the axial utilization is less than 10%.

1ϕPr=1ϕPnz+1ϕPny−1ϕP0 \frac{1}{ϕP_r} = \frac{1}{ϕP_{nz}} + \frac{1}{ϕP_{ny}} – \frac{1}{ϕP_{0}}

Shear Capacity

The total shear capacity of the column (Vn) is calculated as the capacity of the concrete (Vc) combined with the capacity of the shear reinforcement (Vs).

Equation 22.5.1.1
Vn=Vc+Vs V_n = V_{c} + V_{s}

Shear Design Parameters

The following general parameters and limits apply to the calculation of shear capacity.

  • d is taken as 0.8h for rectangular columns.
  • d is taken as 0.8 times the diameter for circular sections.
  • bw is taken as the diameter for solid circular sections (22.5.2.1).

As per 22.5.3.1, the value of √f’c used to calculate Vc, Vci, and Vcw for one-way shear shall not exceed 100psi (8.3MPa).

Additionally, as per 22.5.5.1.2, the value of Nu/6Ag used in the Vc equations shall not be taken greater than 0.05f’c.

The coefficients C1 to C4 used throughout the shear calculations depend on the unit system used, as given below.

Unit System C1 C2 C3 C4
Imperial 2 8 5 1
Metric 0.17 0.66 0.42 0.083

Concrete Shear Capacity

The concrete shear contribution (Vc) is calculated as per Table 22.5.5.1, depending on whether the provided shear reinforcement (Av) meets the minimum requirement (Av,min).

Table 22.5.5.1 (a) & (b)
Vc=max[C1λf′c+Nu6AgC2λ(ρw)1/3f′c+Nu6Ag]bwd V_c = \max \left[ C_1\lambda\sqrt{f’_c} + \frac{N_u}{6A_g} \;\; C_2\lambda(\rho_w)^{1/3}\sqrt{f’_c} + \frac{N_u}{6A_g} \right] b_wd
Table 22.5.5.1 (c)
Vc=(C2λsλ(ρw)1/3f′c+Nu6Ag)bwd V_c = \left(C_2\lambda_s\lambda(\rho_w)^{1/3}\sqrt{f’_c} + \frac{N_u}{6A_g}\right)b_wd

The value of Vc calculated above is subject to upper and lower limits as per 22.5.5.1.1. The lower limit does not apply where the column is subjected to net axial tension, or where 18.6.5.2 or 18.7.6.2.1 apply.

22.5.5.1.1
C4λf′cbwd≤Vc≤C3λf′cbwd C_4\lambda\sqrt{f’_c}\,b_wd \;\leq\; V_c \;\leq\; C_3\lambda\sqrt{f’_c}\,b_wd

The size effect modification factor, λs, used in Table 22.5.5.1(c), is calculated as per 22.5.5.1.3.

22.5.5.1.3
λs=21+d250≤1 \lambda_s = \sqrt{\frac{2}{1 + \dfrac{d}{250}}} \leq 1
22.5.5.1.3
λs=21+d10≤1 \lambda_s = \frac{2}{1 + \dfrac{d}{10}} \leq 1

Cross-sectional dimensions must also be selected to satisfy 22.5.1.2, which limits the maximum shear demand that can be carried regardless of the amount of shear reinforcement provided.

22.5.1.2
Vu≤ϕ(Vc+C2f′cbwd) V_u \leq ϕ\left(V_c + C_2\sqrt{f’_c}\,b_wd\right)

Steel Shear Capacity

The contribution of the shear reinforcement (Vs) is calculated as per 22.5.8.5.3.

22.5.8.5.3
Vs=Avfytds V_s = \frac{A_vf_{yt}d}{s}

Biaxial Shear Capacity

Shear is checked independently in each orthogonal axis of the column. As per 22.5.1.10, the interaction between the shear demand-to-capacity ratios in each axis can be neglected if either (a) or (b) is satisfied.

22.5.1.10a & b
Vu,xϕVn,x≤0.5 \frac{V_{u,x}}{ϕV_{n,x}} \leq 0.5
22.5.1.10a & b
Vu,yϕVn,y≤0.5 \frac{V_{u,y}}{ϕV_{n,y}} \leq 0.5

Where neither (a) nor (b) is satisfied, the column shall instead be checked against the biaxial shear interaction equation given in 22.5.1.11.

22.5.1.11
Vu,xϕVn,x+Vu,yϕVn,y≤1.5 \frac{V_{u,x}}{ϕV_{n,x}} + \frac{V_{u,y}}{ϕV_{n,y}} \leq 1.5

Change Log

  1. Initial deployment October 2026.
  2. October 2026:
    • Reduced the minimum concrete strength (f’c) for metric from 20 MPa to 17 MPa.
    • Added rounding to the values displayed on the bending moment diagrams.
    • Fixed undefined values and an incorrect cross-section check failure (22.5.1.2) in the concrete shear capacity report for columns in axial tension.
    • Fixed bending moment diagrams not displaying for columns in axial tension.

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Updated November 2, 2026

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