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Quick Design: AS 3600:2018 Column

Overview

This calculator is for the design of reinforced non-prestressed concrete columns as per AS 3600:2018. 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 ligatures 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 20mm for calculations.

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 ‘N’ 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.

Notes
  • Moments are taken about the plastic centroid of the section.
  • The concrete block strength α2.fc is reduced by 5% for circular sections as per 10.6.2.5 NOTE 3.
  • 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 γ.ku.d0.

Column Design

Axial Capacity

The ultimate compression strength of a column is defined as it’s squash load (Nuo). This is calculated assuming the section’s reinforcement has reached it’s full yield stress (fsy) in compression and the concrete is under a uniform compressive stress of α1f’c (10.6.2.2). The tensile capacity of the section is calculated as the strength of the reinforcement and ignores any contribution from the concrete.

Design Moments

The moments used to design a concrete column depend on the slenderness of the column in the considered axis. If the column is not slender (or ‘short’), then the column only needs to be checked for first order moments. The column must be designed for second order moments for each axis about which it is slender.

Users have the option to directly provide second-order moments to be used in the calculation. This option is only available if the column is slender.

Column Moments

M1*=max[Mmin;min[Mtop;Mbottom]] M^*_1 = \max \left[ M_{min} \;;\; \min \left[ M_{top} \;;\; M_{bottom} \right] \right]
M2*=max[Mmin;max[Mtop;Mbottom]] M^*_2 = \max \left[ M_{min} \;;\; \max \left[ M_{top} \;;\; M_{bottom} \right] \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.
  • Mmin is calculated as N* x 0.05D (10.1.2).

Calculate Slenderness

A column is deemed to not be slender if it is within the limits outlined below. A column’s slenderness ratio (Le / r) should not exceed 120. Note that radius of gyration is calculated as (I / A)0.5.

Braced:10.3.1(1)
Ler≤max[25;αc(38−f′c15)(1+M1*M2*)] \frac{L_e}{r} ≤ \max \left[ 25 \;;\; α_c \left(38 – \frac{f’_c}{15} \right) \left(1 + \frac{M^*_1}{M^*_2}\right) \right]
αc=2.25−2.5N*ϕNuofor N*ϕNuo≥0.15;or \alpha_c = \sqrt{\,2.25 – 2.5 \dfrac{N^*}{\phi N_{uo}}\,} \qquad \text{for } \dfrac{N^*}{\phi N_{uo}} \geq 0.15;\ \text{or}
αc=13.5N*ϕNuofor N*ϕNuo<0.15 \alpha_c = \sqrt{\,\dfrac{1}{3.5 \dfrac{N^*}{\phi N_{uo}}}\,} \qquad \text{for } \dfrac{N^*}{\phi N_{uo}} < 0.15
Unbraced:10.3.1(2)
Ler≤22 \frac{L_e}{r} ≤ 22

Moment Magnification

If a column is found to be slender, then the design moment is calculated as the first order moment multiplied by a magnification factor (δ). For braced columns, this factor is equal to the braced moment magnifier (δb). For unbraced columns it is the larger of the braced moment magnifier and the sway moment magnifier (δs). This tool does not offer a calculation for δs, so the user must calculate it separately as outlined in 10.4.3(b).

Braced Moment Magnification Factor, δb10.4.2
δb=km(1−N*Nc)≥1 \delta_b = \dfrac{k_m}{\left(1 – \dfrac{N^*}{N_c}\right)} \;\geq\; 1
km=(0.6−0.4M1*M2*)≥0.4 k_m = \left(0.6 – 0.4 \dfrac{M_1^*}{M_2^*}\right) \;\geq\; 0.4
Buckling Load, Nc10.4.4
Nc=(π2Le2)[182do(ϕMc)1+βd]where Mc is the balance moment, Mub when ku=0.545 N_c = \left(\dfrac{\pi^2}{L_e^2}\right) \left[ \dfrac{182 d_o \, (\phi M_c)}{1 + \beta_d} \right] \qquad \text{where } M_c \text{ is the balance moment, } M_{ub} \text{ when } k_u = 0.545
βd=GG+Q \beta_d = \dfrac{G}{G + Q}

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 parallel to the x-axis, which intersects this coordinate (N = design axial load). The moment capacity is taken at the point where this line intersects the interaction line.

Biaxial Bending Check10.6.4
(Mx*ϕMux)an+(My*ϕMuy)an≤1.0 \left( \dfrac{M_x^*}{\phi M_{ux}} \right)^{a_n} \;+\; \left( \dfrac{M_y^*}{\phi M_{uy}} \right)^{a_n} \;\leq\; 1.0
αn=0.7+1.7N*ϕNuo,with 1≤αn≤2 \alpha_n = 0.7 + 1.7 \dfrac{N^*}{\phi N_{uo}}, \quad \text{with } 1 \leq \alpha_n \leq 2

Shear Capacity

The total shear capacity of the column is calculated as the capacity of the concrete combined with the capacity of the shear reinforcement. This value is limited to the crushing strength of the shear web.

10.4.2
Vu=min[Vuc+Vus;Vu.max] V_u = \min \left[ V_{uc} + V_{us} \;;\; V_{u.max} \right]
Shear Strength Limited By Web Crushing8.2.3.3
Vu.max=0.55[0.9f′cbvdv(cotθv+cotαv1+cot2θv)] V_{u.\max} = 0.55 \left[ \, 0.9 f’_c \, b_v \, d_v \left( \dfrac{ \cot \theta_v + \cot \alpha_v }{ 1 + \cot^2 \theta_v } \right) \right]
8.2.1.9
dv=max[0.72D;0.9d] d_v = \max \left[ 0.72D \;;\; 0.9d \right]
8.2.4.2(1)
θv=(29+7000εx) \theta_v = \left( 29 + 7000 \, \varepsilon_x \right)
Mid-Height Strain, εx8.2.4.2.2
εx=|M*dv|+|V*|+0.5N*2(EsAst)≤3.0×10−3 \varepsilon_x = \dfrac{ \left|\dfrac{M^*}{d_v}\right| + \left|V^*\right|+ 0.5N^* }{ 2\left(E_s A_{st}\right) } \;\leq\; 3.0 \times 10^{-3}
Note
  • Mid-height strain calculation excludes the contribution of steel on the mid-height line.

If εx is found to be negative (in compression), then the value should be further modified using the equation below:

εx=−2.0×10−3≤|M*dv|+|V*|+0.5N*2(EsAst+EcAct)≤0 \varepsilon_x = -2.0 \times 10^{-3} \;\leq\; \dfrac{ \left|\dfrac{M^*}{d_v}\right| + \left|V^*\right|+ 0.5N^* }{ 2\left(E_s A_{st} + E_c A_{ct}\right) } \;\leq\; 0
Concrete Contribution To Shear Strength, Vuc8.2.4.1
Vuc=kvbvdvf′c V_{uc} = k_vb_vd_v\sqrt{f’_c}
Calculation of kv
8.2.4.2(2)
when Asvs<Asv.mins,kv=[0.41+1500εx][13001000+kdgdv] \text{when } \dfrac{A_{sv}}{s} \lt \dfrac{A_{sv.min}}{s},\quad k_v =\left[ \dfrac{0.4}{1 + 1500 \, \varepsilon_x} \right] \left[ \dfrac{1300}{1000 + k_{dg} d_v} \right]
8.2.4.2(5)
when Asvs≥Asv.mins,kv=[0.41+1500εx] \text{when } \dfrac{A_{sv}}{s} \geq \dfrac{A_{sv.min}}{s},\quad k_v =\left[ \dfrac{0.4}{1 + 1500 \, \varepsilon_x} \right]
Shear Reinforcement Contribution To Shear Strength kv8.2.5.2
Vus=(Asvfsy.fdvs)cot(θv) V_{us} = \left( \dfrac{A_{sv} \, f_{sy.f} \, d_v}{s} \right) \cot(\theta_v)

Biaxial Shear Capacity

This calculator includes a value for ‘Biaxial Shear’, which is calculated as the resultant of the mono-axial shear utilisations in the ‘Y’ and ‘Z’ axes. AS3600 does not provide specific guidance on how to consider a concrete section for biaxial shear, so this value is provided as a conservative safeguard.

Change Log

  1. Initial deployment 05/09/2025.
  2. Added Bending Moment Diagrams April 2026.
  3. Fixed render error in Bending Moment Diagrams July 2026.
  4. Removed logic to subtract Ec.ε from reinforcement force
    when calculating interaction diagram. Subtracting concrete stress block
    value when within stress block instead July 2026.

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Updated November 2, 2026

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