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Quick Design: NZS 3101:2006 Column

Overview

This calculator is for the design of reinforced, non-prestressed concrete columns as per NZS 3101:2006. 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.

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 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 β1c.

Column Design

Axial Capacity

The ultimate compression strength of a column is defined as 0.85.φ.Nn,max. This is calculated as per equation 10-10. 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.

Column Moments

M1=min[Mtop;Mbottom] M_1 = \min \left[ M_{top} \;;\; M_{bottom} \right]
M2=max[M2,min;max[Mtop;Mbottom]] M_2 = \max \left[ M_{2,min} \;;\; \max \left[ M_{top} \;;\; M_{bottom} \right] \right]
Notes
  • M1 / M2 is taken as positive when the column is bent in single curvature. In this calculator, this is when the moments have the same sign.
  • M2,min is calculated as N* x (15 + 0.03h) (Eq. 10-9).

Calculate Slenderness

A column is deemed to not be slender if it is within the limits outlined below. Note that radius of gyration is calculated as (I / A)0.5.

10.3.2.3.4 (Eq. 10-2)
kLur≤34−12M1M2≤40 \frac{kL_u}{r} ≤ 34 – 12\frac{M_1}{M_2} ≤ 40

Moment Magnification

If a column is found to be slender, then the design moment is calculated as the first order moment, M2, multiplied by a magnification factor (δ).

10.3.2.3.5 (Eq. 10-4)
δ=Cm1−N*0.75Nc≥1.0 δ = \frac{C_m}{1 – \frac{N^*}{0.75N_c}} ≥ 1.0
10.3.2.3.5 (Eq. 10-5)
Nc=π2EIkLu2 N_c = \frac{π^2EI}{kL_u^2}
10.3.2.3.5 (Eq. 10-6)
EI=0.2EcIg+EsIse1+βd EI = \frac{0.2E_cI_g + E_sI_{se}}{1 + β_d}
10.3.2.3.5 (Eq. 10-8)
Cm=0.6+0.4M1M2≥0.4 C_m = 0.6+0.4\frac{M_1}{M_2} ≥ 0.4

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 (N = design axial load). The moment capacity is taken at the point where this line intersects the interaction line.

Note
  • No equation for biaxial bending is included in NZS 3101:2006. This calculator only considers the uniaxial capacity and utilisation column.

Shear Capacity

The total shear capacity of the column is calculated as the capacity of the concrete, Vc, combined with the capacity of the shear reinforcement, Vs:

10.3.10.3.1 (Eq. 10-11)
φVn=Vc+Vs≥V* φV_n = V_c + V_s ≥ V^*

Concrete Shear Capacity

10.3.10.3.1 (Eq. 10-11)
Vc=kaknvbAcv V_c = k_ak_nv_bA_{cv}
10.3.10.3.1 (Eq. 10-12)
vb=(0.07+10pw)f′c v_b = (0.07 + 10p_w)\sqrt{f’_c}
10.3.10.3.1 (Eq. 10-13)
0.08f′c<vb<0.2f′c 0.08 \sqrt{f’_c} < v_b < 0.2 \sqrt{f’_c}
10.3.10.3.1 (Eq. 10-14)
kn=1+3N*Agfc′ k_n = 1 + \frac{3N^*}{A_gf_c’}
10.3.10.3.1 (Eq. 10-14)
3N*Agfc′≤0.3 \frac{3N^*}{A_gf_c’} ≤ 0.3

For members subject to axial tension, kn is given by:

10.3.10.3.1 (Eq. 10-15)
kn=1+12N*Agfc′≥0 k_n = 1 + \frac{12N^*}{A_gf_c’} ≥ 0

Steel Shear Capacity

For rectangular sections:

10.3.10.3.2 (Eq. 10-17)
Vs=Avfytds V_s = \frac{A_vf_{yt}d}{s}

For circular sections:

10.3.10.3.2 (Eq. 10-18)
Vs=πAhfytd′′2s V_s = \frac{πA_hf_{yt}d^{\prime\prime}}{2s}

Confinement and Anti-Buckling

This calculator checks that adequate confinement is provided to the core of the column and that the ties are sufficiently large to prevent buckling of the longitudinal reinforcement.

Concrete Confinement

10.3.10.6.1 (Eq. 10-22)
AgAc≤1.5 \frac{A_g}{A_c} ≤ 1.5
10.3.10.6.1 (Eq. 10-22)
ptm≤0.4 p_tm ≤ 0.4

For rectangular sections:

10.3.10.6.1 (Eq. 10-22)
Ash=(1−ptm)shh′′3.3AgAcf′cfytN*φf′cAg−0.0065shh′′ A_{sh} = \frac{(1 – p_tm)s_hh^{\prime\prime}}{3.3}\frac{A_g}{A_c}\frac{f’_c}{f_{yt}}\frac{N^*}{φf’_cA_g} – 0.0065s_hh^{\prime\prime}

For circular sections:

10.3.10.5.1 (Eq. 10-20)
ps=(1−ptm)2.4AgAcf′cfytN*φf′cAg−0.0084 p_s = \frac{(1 – p_tm)}{2.4}\frac{A_g}{A_c}\frac{f’_c}{f_{yt}}\frac{N^*}{φf’_cA_g} – 0.0084

Lateral Restraint of Longitudinal Bars Against Premature Buckling

For rectangular sections:

10.3.10.6.1 (Eq. 10-23)
Ate=ΣAbfy135fytshdb A_{te} = \frac{ΣA_bf_y}{135f_{yt}}\frac{s_h}{d_b}

For circular sections:

10.3.10.5.1 (Eq. 10-21)
ps=Ast155d′′fyfyt1db p_s = \frac{A_{st}}{155d^{\prime\prime}}\frac{f_y}{f_{yt}}\frac{1}{d_b}

Fire Resistance

This is an optional check, enabled via the Fire Resistance Check option, per Clause 4.6.2 and Table 4.7 of NZS 3101:2006.

4.6.2 (Eq. 4-1)
ηfi=Nf*Nu η_{fi} = \frac{N^*_f}{N_u}

Table 4.7 – Fire resistance criteria for structural adequacy for columns

Fire resistance rating
(minutes) 		Minimum dimensions
(mm)
Column exposed on more than one side Column exposed on
one side
ηfi = 0.2 ηfi = 0.5 ηfi = 0.7 ηfi = 0.7
30 b
a 		200
25 		200
25 		200
30 		155
25
60 b
a 		200
25 		200
35 		250
45 		155
25
90 b
a 		200
30 		300
45 		350
50 		155
25
120 b
a 		250
40 		350
45 		350
55 		175
35
180 b
a 		350
45 		350
60 		450
70 		230
55
240 b
a 		350
60 		450
75 		500
70 		295
70

Change Log

16th September 2026 – Fire Resistance Check
  • NEW: Fire resistance check per Clause 4.6.2 and Table 4.7, covering fire load level, minimum column width, axis distance, and reinforcement detailing requirements.
10th July 2026 – Interaction Diagram & Reporting Update
  • NEW: Added bending moment diagrams.
  • Updated: Removed logic to subtract Ec.ε from reinforcement force when calculating the interaction diagram. The concrete stress block value is now subtracted directly when within the stress block instead.
15th January 2026 – Initial Deployment
  • NEW: Initial deployment of the NZS 3101:2006 Concrete Column Design calculator.

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Updated November 2, 2026

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