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Quick Design: EN 1992-1-1:2004 Column

Overview

This calculator is for the design of reinforced non-prestressed concrete columns as per EN 1992-1-1:2004, Eurocode 2: Design of concrete structures. 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

General

Design Basis

  • This tool has been created in alignment with the design principles set out in EN 1992-1-1:2004.
  • The design equations for circular columns are supplemented by the research paper “Shear design of circular concrete sections using the Eurocode 2 truss model” by Orr et al.

‘Best Practice’

Users have the option of toggling whether ‘best practice’ values should be applied throughout the calculation or not. These values comprise the following:

  • Single curvature bending – an additional term, M02 + M2, is added to the moment calculation for slender members if the column is bending in single curvature:
    MEd=max[M0e+M2;M02;M01+0.5M2;Mmin;M02+M2] M_{Ed} = \max \left[ M_{0e} + M_2 \;;\; M_{02} \;;\; M_{01} + 0.5\,M_2 \;;\; M_{min} \;;\; M_{02} + \,M_2 \right]
  • Slenderness limit, λlim – absolute maximum value of 50 or:
    15.4⋅Cn \frac{15.4 \cdot C}{\sqrt{n}}
  • Biaxial Bending Utilisation of circular columns is taken as the square root of equation 5.39:
    (MEdzMRdz)a+(MEdyMRdy)a≤1.0 \sqrt{\left(\frac{M_{Edz}}{M_{Rdz}}\right)^{a}+\left(\frac{M_{Edy}}{M_{Rdy}}\right)^{a}}\le 1.0
  • Shear web width bw of circular columns is calculated using the equivalent rectangle as discussed in section ‘Calculation of bw’’.
  • Biaxial Shear Utilisation is calculated as the resultant of the mono-axial shear utilisations in the ‘Y’ and ‘Z’ axes. EN1992-1-1:2004 does not provide specific guidance on how to consider a concrete section for biaxial shear, so this value is provided as a conservative safeguard:
    (VEdzVRdz)2+(VEdyVRdy)2 \sqrt{\left(\frac{V_{Edz}}{V_{Rdz}}\right)^{2}+\left(\frac{V_{Edy}}{V_{Rdy}}\right)^{2}}
  • Maximum spacing of longitudinal bars set to 175mm, which assumes that the face of the column could be in tension. If best practice is not selected then the default value is 400mm, which assumes the section is in compression.
  • Minimum number of longitudinal bars in a circular column = 6.
  • Minimum bar spacing:
Bar Diameter (mm) Minimum Spacing (mm)
12 40
16 45
20 50
25 55
32 70
> 32 90

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 η.fcd is reduced by 10% for circular sections as per 3.1.7(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 λ.X.

Column Design

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 ‘stocky’), 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.

The work flow for calculating second order moments based on the first order input is as follows:

Calculate Slenderness

5.8.3.2 (Eq. 5.14)
λ=l0i \lambda = \frac{l_0}{i}
5.8.3.1 (Eq. 5.13N)
λlim=20ABCn \lambda_{\text{lim}} = \frac{20ABC}{\sqrt{n}}

Calculate Moment

Imperfection Moment:5.2(7) (Eq. 5.2)
Mimp=ei⋅NEd M_{imp} = e_i \cdot N_{Ed}
ei=θi⋅l02 e_i = \frac{\theta_i \cdot l_0}{2}
Minimum Moment:6.1(4)
Mmin=e0⋅NEd M_{min} = e_0 \cdot N_{Ed}
e0=max[h30;20] e_0 = \max \left[ \frac{h}{30} \;;\; 20 \right]
Non-Slender Columns:
MEd=max[M02+Mimp;Mmin] M_{Ed} = \max \left[ M_{02} \;+\; M_{imp} \;;\; M_{min} \right]
Slender, Braced Columns:
MEd=max[M0e+M2;M02;M01+0.5M2;Mmin] M_{Ed} = \max \left[ M_{0e} + M_2 \;;\; M_{02} \;;\; M_{01} + 0.5\,M_2 \;;\; M_{min} \right]
Slender, Unbraced Columns:
MEd=max[M0e+M2;Mmin] M_{Ed} = \max \left[ M_{0e} + M_2 \;;\; M_{min} \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 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 Check

Check column for biaxial bending if:5.8.9 (Eq 5.38.a, 5.38.b)
λyλz≤2andλzλy≤2 \frac{\lambda_y}{\lambda_z} \leq 2 \quad \text{and} \quad \frac{\lambda_z}{\lambda_y} \leq 2
and \text{and}
(ey/heqez/beq)≤0,2or(ez/beqey/heq)≤0,2 \left( \frac{e_y / h_{eq}}{e_z / b_{eq}} \right) \leq 0{,}2 \quad \text{or} \quad \left( \frac{e_z / b_{eq}}{e_y / h_{eq}} \right) \leq 0{,}2
Biaxial utilisation is calculated as:5.8.9 (Eq 5.39)
(MEdzMRdz)a+(MEdyMRdy)a≤1,0 \left( \frac{M_{Edz}}{M_{Rdz}} \right)^a + \left( \frac{M_{Edy}}{M_{Rdy}} \right)^a \leq 1{,}0

Shear Capacity

The applied shear force is initially checked against the shear capacity of the concrete only. If the resistance exceeds the applied shear, then the capacity of the section is taken as that of the concrete, VRd = VRd,c.

If the applied shear is greater than the capacity of the concrete, then the resistance of the section is taken as the minimum of the shear reinforcement capacity and the crushing strength of the inclined concrete strut, VRd = min[ VRd,max; VRd,s ].

The values for VRd,c, VRd,max and VRd,s are calculated using the equations set out in En 1992-1-1:2004 for rectangular sections. The equations for circular columns are taken from “Shear design of circular concrete sections using the Eurocode 2 truss model”.

For both shapes, the upper and lower bound value for the concrete strut capacity, (VRd,max) are determined for cotθ = 1 and cotθ = 2.5 respectively. If the applied shear force VEd is greater than the upper bound value, then cotθ = 2.5 is used to define the strut angle. If the shear force is less than the lower bound, cotθ = 1 is used. When VEd is between these two values, the design angle of θ is iteratively increased until VRd,max > VEd. This angle is used in the rest of the calculation.

Calculation of bw

The section width for rectangular sections is taken as the perpendicular dimension to the direction of the applied shear force. For circular sections, when best practice is applied, an ‘equivalent rectangle’ is used to calculate the compression strut cross-section. The width of this rectangle ‘bw’ is taken as the smaller of the width of the circular section at the centroid of the compression chord and the width of the circular section at the centroid of tension reinforcement. If best practice is not applied, the shear web width is taken as the diameter of the circle.

Section Diagram

Approximation of z

This calculator uses 0.9d as an approximation for the internal lever arm of the section when calculating the shear reinforcement capacity. This is a suggested value in EN 1992-1-1:2004 for members without axial load, and as such may not be accurate.

Concrete Strut Strength

This calculator allows for a column to be designed with an axial tension force. When calculating the concrete strut capacity in clause 6.2.3(3) (Eq 6.9), the value of fcd needs to be modified to suit tension conditions in the concrete strut. To do this, the concrete strength is calculated according to 6.5.2(2), using strength reduction factors of 0.6.v’ (6.57N).

Shear Capacity Of Rectangular Columns

Concrete Shear Capacity, VRd,c :6.2.2 (Eq 6.2.a, 6.2.b)
VRd,c=[CRd,c⋅k(100⋅ρl⋅fck)1/3+k1⋅σcp]⋅bw⋅d V_{Rd,c} = \left[ C_{Rd,c} \cdot k \left( 100 \cdot \rho_l \cdot f_{ck} \right)^{1/3} + k_1 \cdot \sigma_{cp} \right] \cdot b_w \cdot d
VRd,c,min=(vmin+k1⋅σcp)⋅bw⋅d V_{Rd,c,min} = \left( v_{min} + k_1 \cdot \sigma_{cp} \right) \cdot b_w \cdot d
Inclined Concrete Strut Capacity, VRd,max :6.2.3(3) (Eq 6.9)
VRd,max=αcw⋅bw⋅z⋅ν1⋅fcd/(cotθ+tanθ) V_{Rd,max} = \alpha_{cw} \cdot b_w \cdot z \cdot \nu_1 \cdot f_{cd} \,/\, (\cot\theta + \tan\theta)
Shear Reinforcement Capacity, VRd,s :6.2.3(3) (Eq 6.8)
VRd,s=Asws⋅z⋅fywd⋅cotθ V_{Rd,s} = \frac{A_{sw}}{s} \cdot z \cdot f_{ywd} \cdot \cot\theta

Shear Capacity Of Circular Columns

Concrete Shear Capacity, VRd,c :(Eq 17), derived from 6.2.2(2) (Eq 6.4)
VRd,c=3πr24⋅(fctd)2+σcp⋅fctd V_{Rd,c} = \frac{3 \pi r^2}{4} \cdot \sqrt{ \left( f_{ctd} \right)^2 + \sigma_{cp} \cdot f_{ctd} }
Inclined Concrete Strut Capacity, VRd,max :6.2.3(3) (Eq 6.9)
VRd,max=αcw⋅bw⋅z⋅ν1⋅fcd/(cotθ+tanθ) V_{Rd,max} = \alpha_{cw} \cdot b_w \cdot z \cdot \nu_1 \cdot f_{cd} \,/\, (\cot\theta + \tan\theta)
Shear Reinforcement Capacity, VRd,s :(Eq 18) derived 6.2.3(3) (Eq 6.8)
VRd,s=λ1⋅λ2⋅Asws⋅z⋅fywd⋅cotθ V_{Rd,s} = λ_1 \cdot λ_2 \cdot \frac{A_{sw}}{s} \cdot z \cdot f_{ywd} \cdot \cot\theta
λ1=0.85;λ2=1.0 λ_1 = 0.85 \;;\; λ_2 = 1.0

Effects Of Creep

Users have several options for defining the effects of creep on the column they are designing.

If the column is non-slender, then default values may be used in the calculations. This will set the value of ‘A’ to 0.7 in Eq 5.13N for the slenderness limit.

There are no default values specified for the creep factor used to calculate curvature (Kφ) in EN 1992-1-1: 2004. If the column is determined to be slender, the user must input their own value or provide sufficient data to calculate the effective creep ratio φef.

Effective Creep Ratio5.8.4 (Eq 5.19)
φef=φ(∞,t0)⋅M0EqpM0Ed≡φ(∞,t0)⋅N0EqpN0Ed \varphi_{ef} = \varphi_{(\infty, t_0)} \cdot \frac{M_{0Eqp}}{M_{0Ed}} ≡ \varphi_{(\infty, t_0)} \cdot \frac{N_{0Eqp}}{N_{0Ed}}

Annex B of EN 1992-1-1:2004 is used to calculate φ(∞,t0). This calculator substitutes quasi-permanent moment for axial load, as this is deemed to be comparable and simpler to derive.

Fire Resistance

This is an optional check, enabled via the Fire Resistance Check option, per EN 1992-1-2, Annex C. The method uses the column geometry, reinforcement and fire design actions to determine the required minimum column dimension and reinforcement axis distance, and is performed independently about each column axis using the corresponding slenderness and eccentricity. Annex C does not define which side of a rectangular section is the column width, so b is conservatively taken as the minimum column dimension for both axes.

Note
  • Annex C Tables C.1 to C.9 are only tabulated for columns exposed on more than one side; there is no one-side exposure variant in the tabulated method, so this option is not offered for this check.

Fire Check Inputs

The following parameters are determined for the axis being checked:

  • Fire resistance rating
  • Column slenderness, λ
  • Fire load level, n
  • Fire load eccentricity, e
  • Mechanical reinforcement ratio, ω
  • Column width, b (minimum column dimension)
  • Reinforcement axis distance, a

The fire load level is calculated as:

5.3.3(2) (Eq. 5.8a)
n=NEd,fi0.7(Acfcd+Asfyd) n = \frac{N_{Ed,fi}}{0.7(A_c f_{cd} + A_s f_{yd})}

where fcd and fyd are the ordinary (ambient) design strengths of concrete and steel.

The fire load eccentricity is calculated from the first order fire design actions about the axis being checked, converted to millimetres:

5.3.3(2) (Eq. 5.8b)
e=MEd,fiNEd,fi e = \frac{M_{Ed,fi}}{N_{Ed,fi}}

The calculated eccentricity is used directly to select and interpolate between the Annex C tables (see “Selection of Annex C Tables” below). It is not reduced; eccentricities above the highest tabulated value are outside the scope of Annex C (see “Fire Check Criteria”).

The mechanical reinforcement ratio is calculated as:

5.3.3(2)
ω=AsfydAcfcd \omega = \frac{A_s f_{yd}}{A_c f_{cd}}

The reinforcement axis distance is taken as the distance from the exposed concrete surface to the centre of the longitudinal reinforcement.

The column slenderness used for the fire check is taken as the ambient (normal temperature) slenderness for the axis being checked. Annex C notes that its notations, including slenderness, are as defined in Clause 5.3.3. Per B.3.1(5), the effective length in fire l0,fi may be taken as l0 as a safe simplification, so a separate fire-specific effective length is not calculated here.

Fire Check Criteria

This module only performs fire checks using the tabulated method in EN 1992-1-2 Annex C. For concrete columns outside this scope, use the separate Fire Resistance Design module.

Annex C(1) applies to columns in braced structures with a width up to 600 mm and slenderness up to λ = 80 under standard fire exposure. The tabulated method is not used, and the fire check is reported as failed, when:

  • The column is not braced about both axes.
  • Fire axial load NEd,fi ≤ 0.
  • Slenderness λ > 80.
  • Fire load level n > 0.7.
  • Mechanical reinforcement ratio ω < 0.1 or ω > 1.0.
  • Fire eccentricity e > ehigh = min(0.5b, 200 mm), the highest tabulated eccentricity (Tables C.3, C.6 and C.9).
Note
  • Values below the lowest tabulated slenderness, load level or eccentricity are conservatively taken as the lowest available table value. This is not conservative for the mechanical reinforcement ratio (a lower ω requires larger dimensions), so ω < 0.1 is outside the scope of the tables.
  • Columns wider than 600 mm are not rejected: they exceed every tabulated minimum width, so the check is governed by the axis distance. Cells marked (1) in Annex C require a width greater than 600 mm and a particular assessment for buckling, so they are always reported as failed.

Selection of Annex C Tables

The required fire dimensions are obtained from Tables C.1 to C.9. The appropriate tables depend on the mechanical reinforcement ratio and fire eccentricity. The eccentricity limits used to select the surrounding tables depend on the column width:

Annex C, Tables C.1, C.4, C.7
elow=max(0.025b,10) e_{low} = \max(0.025b,\ 10)
Annex C, Tables C.2, C.5, C.8
emoderate=min(0.25b,100) e_{moderate} = \min(0.25b,\ 100)
Annex C, Tables C.3, C.6, C.9
ehigh=min(0.5b,200) e_{high} = \min(0.5b,\ 200)

Mechanical reinforcement ratio is considered using the tabulated values:

Annex C, Tables C.1 to C.9
ω=0.1,0.5,1.0 \omega = 0.1,\ 0.5,\ 1.0

The eccentricity and mechanical reinforcement ratio therefore identify four surrounding tables from C.1 to C.9 for interpolation.

Annex C Reference Tables

Tables C.1 to C.9 below (click a table title to expand) are transcribed from EN 1992-1-2 Annex C and give the minimum column width bmin (mm) and reinforcement axis distance a (mm) required for a given standard fire resistance R (min), slenderness λ and fire load level n, for columns exposed on more than one side. Tables C.1 to C.3 apply to mechanical reinforcement ratio ω = 0.1, Tables C.4 to C.6 to ω = 0.5, and Tables C.7 to C.9 to ω = 1.0; within each group of three, the tables correspond to low, moderate and high first order moment (i.e. increasing fire load eccentricity), as described in “Selection of Annex C Tables” above. Where a cell offers two alternative bmin/a combinations, either combination is an acceptable requirement.

Table C.1 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.1, Low First Order Moment (e = 0.025b, with e ≥ 10 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 150* 25* 150* 25*
40 150* 25* 150* 25* 150* 25* 150* 25*
50 150* 25* 150* 25* 150* 25* 200* 25*
60 150* 25* 150* 25* 200* 25* 250* 25*
70 150* 25* 150* 25* 250* 25* 300* 25*
80 150* 25* 200* 25* 250
300*
30
25*
350* 25*
60 30 150* 25* 150* 25* 200* 25* 200
250*
30
25*
40 150* 25* 150* 25* 200* 25* 250* 25*
50 150* 25* 200* 25* 250* 25* 300 25
60 150* 25* 200
250*
40
25*
250
300*
40
25*
350
400*
30
25*
70 200* 25* 250
300*
30
25*
300
350*
40
25*
450
550*
35
25*
80 200
250*
30
25*
250
300*
40
25*
400
450*
30
25*
550
600
60
35
90 30 150* 25* 200* 25* 200
250*
50
25*
250
300*
30
25*
40 150
200*
35
25*
200
250*
30
25*
250* 25* 300 25
50 200* 25* 250* 25* 300* 25* 350
400*
50
25*
60 200
250*
35
25*
250
300*
40
25*
350
400*
35
25*
450
550*
50
25*
70 250* 25* 300
350*
35
25*
400
550*
45
25*
600 40
80 250
300*
30
25*
350
400*
35
25*
550
600*
40
25*
(1)
120 30 200* 25* 250* 25* 250* 25* 300
350
45
25
40 250* 25* 250* 25* 300* 25* 400* 25*
50 250* 25* 300* 25* 350
400*
50
25*
450
500*
50
25*
60 250* 25* 350* 25* 450
500*
40
25*
550 50
70 250
300*
50
25*
400* 25* 500
550*
60
25*
(1)
80 300* 25* 450
500*
40
25*
600 45 (1)
180 30 250* 25* 250* 25* 350* 25* 400
450*
50
25*
40 250* 25* 300
350*
30
25*
400* 25* 450
500*
50
25*
50 250
300*
50
25*
350
400*
50
25*
450
500*
40
25*
550
600
60
35
60 300
350*
40
25*
450* 25* 550
600
40
25
(1)
70 350
400*
30
25*
500* 25* 600 80 (1)
80 400
450*
30
25*
550
600*
45
25*
(1) (1)
240 30 250* 25* 350* 25* 450* 25* 500
550*
40
25*
40 300* 25* 400* 25* 500* 25* 600* 25*
50 350* 25* 450* 25* 550
600*
50
25*
(1)
60 400* 25* 500
550*
60
25*
600 80 (1)
70 450* 25* 600* 25* (1) (1)
80 500* 25* 600 80 (1) (1)
Table C.2 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.1, Moderate First Order Moment (e = 0.25b, with e ≤ 100 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 200
250*
30
25*
300
350*
30
25*
40 150* 25* 150
200*
30
25*
300* 25* 500
550*
40
25*
50 150 25 200
250*
40
25*
350
500*
40
25*
550* 25*
60 150* 25* 300* 25* 550* 25* 600 30
70 200* 25* 350
500*
40
25*
550
600*
30
25*
(1)
80 250* 25* 550* 25* (1) (1)
60 30 150
200*
30
25*
200
300*
40
25*
300
500*
40
25*
500* 25*
40 200
250*
30
25*
300
350*
35
25*
450
550*
50
25*
550
600*
40
25*
50 200
300*
40
25*
350
550*
45
25*
550
600
30
30
600 55
60 250
400*
35
25*
450
550*
50
25*
600 35 (1)
70 300
500*
40
25*
550
600*
30
25*
600 80 (1)
80 400
550*
40
25*
600 30 (1) (1)
90 30 200
250*
40
25*
300
400*
40
25*
500
550*
50
25*
550
600*
40
25*
40 250
350*
40
25*
350
550*
50
25*
550
600*
35
25*
600 50
50 300
500*
40
25*
500
550*
60
25*
600 40 (1)
60 300
550*
50
25*
550
600*
45
25*
(1) (1)
70 400
550*
50
25*
600 45 (1) (1)
80 500
600*
60
25*
(1) (1) (1)
120 30 250
350*
50
25*
400
550*
50
25*
550* 25* 550
600
60
45
40 300
500*
50
25*
500
550*
50
25*
550
600
50
25
(1)
50 400
550*
50
25*
550
600*
50
25*
600 60 (1)
60 500
550*
50
25*
550
600
55
50
(1) (1)
70 500
600*
60
25*
600 60 (1) (1)
80 550
600*
50
25*
(1) (1) (1)
180 30 400
500*
50
25*
500
550*
60
25*
550
600
60
30
(1)
40 500
550*
50
25*
550
600*
50
25*
600 80 (1)
50 550* 25* 600 60 (1) (1)
60 550
600*
50
25*
600 80 (1) (1)
70 600 55 (1) (1) (1)
80 600 70 (1) (1) (1)
240 30 500
550*
60
25*
550
600*
40
25*
600 75 (1)
40 550* 25* 600 60 (1) (1)
50 550
600*
60
25*
600 80 (1) (1)
60 600 60 (1) (1) (1)
70 600 80 (1) (1) (1)
80 (1) (1) (1) (1)
Table C.3 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.1, High First Order Moment (e = 0.5b, with e ≤ 200 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 400
550*
40
25*
550* 25* (1)
40 200* 25* 550* 25* 550
600
35
30
(1)
50 250
300*
30
25*
550
600*
30
25*
(1) (1)
60 300
550*
40
25*
600 50 (1) (1)
70 400
550*
40
25*
(1) (1) (1)
80 550 25 (1) (1) (1)
60 30 300
500*
35
25*
500
550*
50
25*
550
600
50
40
(1)
40 350
550*
40
25*
550
600
40
30
(1) (1)
50 450
550*
50
25*
550
600
50
40
(1) (1)
60 550 30 600 80 (1) (1)
70 550 35 (1) (1) (1)
80 550 40 (1) (1) (1)
90 30 350
550*
50
25*
550
600
45
40
600 80 (1)
40 500
600
60
30
550
600
60
50
(1) (1)
50 550 40 600 80 (1) (1)
60 550
600
50
45
(1) (1) (1)
70 550
600
60
50
(1) (1) (1)
80 600 70 (1) (1) (1)
120 30 550
600
40
30
550 50 (1) (1)
40 550
600
50
45
600 70 (1) (1)
50 550
600
55
50
(1) (1) (1)
60 550
600
60
50
(1) (1) (1)
70 600 70 (1) (1) (1)
80 (1) (1) (1) (1)
180 30 550 50 600 80 (1) (1)
40 550 60 (1) (1) (1)
50 600 70 (1) (1) (1)
60 (1) (1) (1) (1)
70 (1) (1) (1) (1)
80 (1) (1) (1) (1)
240 30 600 70 (1) (1) (1)
40 (1) (1) (1) (1)
50 (1) (1) (1) (1)
60 (1) (1) (1) (1)
70 (1) (1) (1) (1)
80 (1) (1) (1) (1)
Table C.4 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.5, Low First Order Moment (e = 0.025b, with e ≥ 10 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 150* 25* 150* 25*
40 150* 25* 150* 25* 150* 25* 150* 25*
50 150* 25* 150* 25* 150* 25* 200* 25*
60 150* 25* 150* 25* 150* 25* 200
250*
30
25*
70 150* 25* 150* 25* 200* 25* 250* 25*
80 150* 25* 150* 25* 200
250*
30
25*
300* 25*
60 30 150* 25* 150* 25* 150
200*
30
25*
200
250*
35
25*
40 150* 25* 150* 25* 200* 25* 250
300*
30
25*
50 150* 25* 150
200*
35
25*
200
250*
40
25*
250
350*
40
25*
60 150* 25* 200
250*
30
25*
250
300*
30
25*
300
450
40
25
70 150* 25* 200
250*
35
25*
250
350*
40
25*
350
600
45
25
80 150
200*
35
25*
250
300*
30
25*
300
500*
40
25*
450
600
50
35
90 30 150* 25* 150
200*
40
25*
200
250*
40
25*
250
300*
40
25*
40 150* 25* 200
250*
35
25*
250
300*
30
25*
300
400*
40
25*
50 150
200*
40
25*
200
250*
45
25*
250
350*
45
25*
350
550*
45
25*
60 200* 25* 250
300*
35
25*
300
400*
45
25*
400
600
50
35
70 200
250*
35
25*
250
350*
45
25*
350
600*
45
25*
550
600
50
45
80 200
250*
45
25*
250
400*
50
25*
400
600
50
35
600 60
120 30 150
200*
35
25*
200
250*
40
25*
250
300*
45
25*
350
500*
45
25*
40 200* 25* 250* 25* 300
350*
45
25*
400
550*
50
25*
50 200
250*
40
25*
250
300*
45
25*
350
450*
45
25*
450
600*
50
25*
60 200
250*
50
25*
300
350*
45
25*
400
550*
50
25*
500
600
60
35
70 250
300*
35
25*
350
450*
45
25*
500
600
50
40
600 45
80 250
300*
45
25*
400
550
50
25
500
600
60
45
600 60
180 30 200
250*
45
25*
250
300*
35
25*
350
400*
45
25*
450
500*
45
25*
40 250* 25* 300
350*
45
25*
450* 25* 500
600
55
50
50 250
300*
35
25*
350
400*
45
25*
500
550
40
25
600 65
60 300
350*
40
25*
450* 25* 500
600
60
55
600 80
70 350* 25* 500
550*
40
25*
600 65 (1)
80 400
450*
30
25*
500
600
55
45
600 80 (1)
240 30 250* 25* 350* 25* 450
500*
45
25*
550
600
65
50
40 250
300*
40
25*
400
450*
45
25*
500
550*
60
25*
600 75
50 350
400*
30
25*
450
500*
50
25*
550
600
70
55
(1)
60 400
450*
35
25*
500
600*
50
25*
600 75 (1)
70 450
500*
30
25*
550
600
75
50
(1) (1)
80 500
550*
40
25*
600 70 (1) (1)
Table C.5 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.5, Moderate First Order Moment (e = 0.25b, with e ≤ 100 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 150* 25* 200
250*
30
25*
40 150* 25* 150* 25* 150* 25* 300
350*
45
25*
50 150* 25* 150* 25* 200
250*
30
25*
350
450*
40
25*
60 150* 25* 150* 25* 250
300*
30
25*
500
550*
30
25*
70 150* 25* 150
200*
35
25*
350
400
30
25
550
600
35
30
80 150* 25* 200
250*
30
25*
400
500
40
25
600 50
60 30 150* 25* 150
200*
35
25*
250
350*
35
25*
350
550
40
25
40 150* 25* 200
300*
30
25*
300
500*
35
25*
450
600
50
30
50 150
200*
30
25*
200
350*
40
25*
300
550*
45
25*
500
600
50
35
60 150
200*
35
25*
250
500*
40
25*
400
600
45
30
600 45
70 200
300*
30
25*
300
500*
40
25*
500
600
40
35
600 80
80 200
300*
35
25*
350
600*
40
25*
550
600
55
40
(1)
90 30 150
200*
35
25*
200
300*
45
25*
300
550*
45
25*
500
600
50
40
40 200
250*
35
25*
250
500*
45
25*
350
600*
50
25*
550
600
50
45
50 200
300*
40
25*
300
550*
45
25*
500
600
50
35
600 55
60 200
400
50
25
350
600*
50
25*
550
600
50
45
(1)
70 300
500*
35
25*
400
600
50
35
600 50 (1)
80 300
600*
40
25*
500
600
55
40
600 80 (1)
120 30 200
300*
45
25*
300
550*
45
25*
450
600*
50
25*
500
600
60
50
40 200
350*
50
25*
350
550*
50
25*
500
600
50
40
600 55
50 250
450*
45
25*
450
600*
50
25*
500
550
55
45
600 80
60 300
500*
50
25*
500
600
45
40
550
600
60
60
(1)
70 350
550*
50
25*
500
550
50
45
600 75 (1)
80 400
600*
50
25*
500
550
55
50
(1) (1)
180 30 300
450*
45
25*
450
600*
50
25*
500
600
60
50
600 75
40 350
500*
50
25*
500
600*
50
25*
600 60 (1)
50 450
500*
50
25*
500
600
60
50
600 70 (1)
60 500
600*
50
25*
550
600
60
55
(1) (1)
70 500
600
55
35
600 65 (1) (1)
80 500
600
60
55
600 75 (1) (1)
240 30 450
500*
45
25*
550
600
55
25
600 70 (1)
40 450
550*
50
25*
600 50 600 80 (1)
50 500
600*
55
25*
600 65 (1) (1)
60 550
600
55
40
600 75 (1) (1)
70 600 60 (1) (1) (1)
80 600 70 (1) (1) (1)
Table C.6 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 0.5, High First Order Moment (e = 0.5b, with e ≤ 200 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 250
300*
35
25*
500
550*
40
25*
40 150* 25* 150
200*
30
25*
300
450*
35
25*
550 30
50 150* 25* 200
250*
30
25*
400
500*
40
25*
550
600
50
40
60 150* 25* 200
300*
35
25*
450
550*
50
25*
(1)
70 150* 25* 250
400*
40
25*
500
600
40
30
(1)
80 150* 25* 300
500*
40
25*
550
600
50
40
(1)
60 30 150
200*
30
25*
200
450*
40
25*
450
550
50
30
550
600
50
40
40 150
250*
35
25*
250
500*
40
25*
500
550
40
35
600 60
50 200
300*
35
25*
300
550*
45
25*
500
550
55
40
(1)
60 200
500*
40
25*
400
600
40
30
550
600
50
45
(1)
70 200
550*
40
25*
500
550
40
35
600 60 (1)
80 250
600*
40
25*
500
600
45
35
(1) (1)
90 30 250
450*
40
25*
300
500*
50
25*
500
600
55
40
600 80
40 200
500*
50
25*
350
550
50
35
550
600
60
50
(1)
50 250
550*
45
25*
500
550
45
40
600 60 (1)
60 250
550
50
30
500
550
50
45
600 80 (1)
70 300
550
50
35
550
600
50
45
(1) (1)
80 350
600
50
35
550
600
60
50
(1) (1)
120 30 250
550*
50
25*
500
550
50
40
550 50 (1)
40 300
600*
50
25*
500
550
55
45
550
600
60
55
(1)
50 400
550
50
35
500
600
60
45
600 80 (1)
60 450
600
50
40
550 50 (1) (1)
70 500
550
50
45
550
600
60
55
(1) (1)
80 550
600
50
45
600 70 (1) (1)
180 30 500
550
45
30
550 55 600 75 (1)
40 500
600
50
40
550 60 (1) (1)
50 500
550
60
50
600 70 (1) (1)
60 550 55 600 75 (1) (1)
70 550 60 (1) (1) (1)
80 600 60 (1) (1) (1)
240 30 550
600
50
45
600 70 (1) (1)
40 550
600
60
55
600 75 (1) (1)
50 600 65 (1) (1) (1)
60 600 70 (1) (1) (1)
70 600 75 (1) (1) (1)
80 600 80 (1) (1) (1)
Table C.7 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 1.0, Low First Order Moment (e = 0.025b, with e ≥ 10 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 150* 25* 150* 25*
40 150* 25* 150* 25* 150* 25* 150* 25*
50 150* 25* 150* 25* 150* 25* 150
200*
30
25*
60 150* 25* 150* 25* 150* 25* 200
250*
30
25*
70 150* 25* 150* 25* 150
200*
30
25*
250* 25*
80 150* 25* 150* 25* 200
250*
30
25*
250
300*
30
25*
60 30 150* 25* 150* 25* 150* 25* 200
300*
40
25*
40 150* 25* 150* 25* 200
250*
30
25*
250
350*
35
25*
50 150* 25* 150
200*
30
25*
200
250*
40
25*
250
350*
40
25*
60 150* 25* 150
250*
40
25*
250
300*
35
25*
300
600*
40
25*
70 150* 25* 200
250*
35
25*
250
400*
40
25*
350
450
40
35
80 150
200*
30
25*
200
300*
40
25*
300
550*
40
25*
350
450
45
40
90 30 150* 25* 200* 25* 200
250*
40
25*
250
600*
45
25*
40 150* 25* 200
250*
35
25*
250
350*
35
25*
300
600
45
30
50 150
200*
35
25*
200
250*
40
25*
250
400*
45
25*
350
600
45
35
60 150
250*
40
25*
250
300*
55
25*
300
550*
45
25*
400
600
50
40
70 200
250*
35
25*
300
350*
35
25*
350
600
45
35
550
600
50
45
80 200
250*
40
25*
300
500
40
25
350
600
50
40
550
600
65
55
120 30 150
200*
40
25*
200
250*
45
25*
250
400*
40
25*
400
600*
40
25*
40 200
250*
30
25*
250* 25* 300
400*
45
25*
400
600
50
30
50 200
250*
40
25*
250
300*
35
25*
350
550*
40
25*
550
600
45
40
60 200
250*
45
25*
250
400*
45
25*
400
600*
50
25*
550
600
60
50
70 250* 25* 350
450*
35
25*
550
600
40
35
600 70
80 250
300*
35
25*
350
550*
40
25*
550
600
50
45
(1)
180 30 200
250*
50
25*
300* 25* 350
450*
45
25*
500
600
50
45
40 250* 25* 300
350*
45
25*
450
550*
45
25*
550
600
60
55
50 250
300*
30
25*
350
450*
40
25*
450
600
50
40
600 70
60 250
350*
40
25*
350
500*
50
25*
550
600
55
50
600 80
70 300
400*
45
25*
450
600
45
35
550
600
70
65
(1)
80 350
450*
40
25*
550
600
50
40
600 75 (1)
240 30 250* 25* 350
400*
40
25*
500
600*
40
25*
550
600
70
60
40 250
350*
40
25*
400
450*
50
25*
500
600
60
40
600 75
50 350
400*
30
25*
450
550*
45
25*
550
600
55
50
(1)
60 350
450*
45
25*
500
600
50
35
600 70 (1)
70 400
500*
50
25*
500
600
60
45
(1) (1)
80 450
550*
45
25*
550
600
60
50
(1) (1)
Table C.8 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 1.0, Moderate First Order Moment (e = 0.25b, with e ≤ 100 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 150* 25* 200
300
30
25
40 150* 25* 150* 25* 150* 25* 250
450*
30
25*
50 150* 25* 150* 25* 200* 25* 300
500*
35
25*
60 150* 25* 150* 25* 200
250*
30
25*
400
550*
40
25*
70 150* 25* 150* 25* 250
300*
35
25*
500
600
35
30
80 150* 25* 150
250*
30
25*
300
500*
35
25*
500
600
60
35
60 30 150* 25* 150
200*
30
25*
200
400*
40
25*
300
600
50
30
40 150* 25* 150
250*
40
25*
250
500*
40
25*
400
600
50
35
50 150* 25* 200
400*
35
25*
300
600*
40
25*
500
600
45
40
60 150
200*
30
25*
200
450*
40
25*
400
600
40
30
550
600
40
40
70 150
200*
35
25*
240
550*
40
25*
450
500
45
35
600 60
80 200
250
30
25
300
550
40
25
500
600
50
40
600 80
90 30 200* 25* 200
300*
40
25*
250
550*
40
25*
500
600
50
45
40 200
250*
30
25*
200
400*
50
25*
300
600
50
35
500
600
60
50
50 200
300*
35
25*
250
550*
50
25*
400
600
50
40
600 55
60 200
400
40
25
300
600*
45
25*
500
600
50
45
600 70
70 200
450*
45
25*
300
600
50
35
550
600
55
50
(1)
80 200
500*
50
25*
400
600
50
35
600 55 (1)
120 30 200
250
40
25
250
400*
50
25*
450
600
45
30
600 60
40 200
300*
45
25*
300
500*
40
25*
500
600
50
35
(1)
50 250
400*
40
25*
400
550*
40
25*
550
600
50
45
(1)
60 250
450*
50
25*
400
500
50
35
600 55 (1)
70 300
500*
40
25*
500
600
45
35
(1) (1)
80 300
550*
50
25*
500
600
60
40
(1) (1)
180 30 300
400*
35
25*
450
550*
50
25*
500
600
60
45
(1)
40 300
450*
40
25*
500
600
40
30
550
600
65
60
(1)
50 400
500*
40
25*
500
600
45
35
600 75 (1)
60 400
550*
45
25*
500
600
55
45
(1) (1)
70 400
600
50
30
500
600
65
50
(1) (1)
80 500
600
45
35
600 70 (1) (1)
240 30 400
500*
45
25*
500
600
40
30
600 60 (1)
40 450
550*
45
25*
500
600
55
40
600 80 (1)
50 450
600*
50
25*
500
600
65
45
(1) (1)
60 500
600
45
35
550
600
70
55
(1) (1)
70 500
600
50
40
600 75 (1) (1)
80 500
600
60
45
(1) (1) (1)
Table C.9 – Minimum Dimensions and Axis Distances for Rectangular and Circular Columns; Mechanical Reinforcement Ratio ω = 1.0, High First Order Moment (e = 0.5b, with e ≤ 200 mm)
Standard
fire
resistance
λ Column width bmin / axis distance a, mm
n = 0.15 n = 0.3 n = 0.5 n = 0.7
bmin a bmin a bmin a bmin a
30 30 150* 25* 150* 25* 200
300*
30
25*
500
550
30
25
40 150* 25* 150* 25* 250
450*
30
25*
500
600
40
30
50 150* 25* 150
200*
30
25*
300
500*
35
25*
550 35
60 150* 25* 200
250*
30
25*
350
500*
40
25*
550 50
70 150* 25* 200
300*
30
25*
450
550*
50
25*
(1)
80 150* 25* 250
350*
30
25*
500
600
35
30
(1)
60 30 150* 25* 200
450*
35
25*
350
600
40
30
550
600
45
40
40 150
200*
30
25*
200
500*
40
25*
450
500
50
35
600 60
50 150
250*
35
25*
250
550*
40
25*
500
600
40
35
600 80
60 200
350*
30
25*
300
600*
40
25*
500
600
50
40
(1)
70 250
450*
30
25*
350
600
40
30
550
600
50
45
(1)
80 250
500*
55
25*
450
500
40
35
600 70 (1)
90 30 200
300*
35
25*
250
550*
50
25*
500
600
50
40
600 70
40 200
450*
40
25*
300
600
50
30
500
600
55
45
(1)
50 200
500*
45
25*
350
600
50
35
550 50 (1)
60 200
550*
50
25*
450
600
50
40
600 60 (1)
70 250
600
45
30
500
600
50
45
600 80 (1)
80 250
500
50
35
500
600
55
45
(1) (1)
120 30 200
450*
50
25*
450
600*
45
25*
550
600
55
50
(1)
40 250
500*
50
25*
500
600
40
30
600 65 (1)
50 300
550*
40
25*
500
600
50
35
(1) (1)
60 350
550*
45
25*
500
600
60
40
(1) (1)
70 450
600
40
30
550
600
60
50
(1) (1)
80 450
600
45
30
600 65 (1) (1)
180 30 350
550*
45
25*
500
600
45
40
600 80 (1)
40 450
600
45
30
500
600
60
45
(1) (1)
50 450
600
50
35
500
600
70
55
(1) (1)
60 500
600
45
40
550
600
70
65
(1) (1)
70 500
600
50
40
600 75 (1) (1)
80 500
600
55
45
(1) (1) (1)
240 30 500
600
40
35
550
600
55
50
(1) (1)
40 500
600
50
40
550
600
65
55
(1) (1)
50 500
600
55
45
600 70 (1) (1)
60 500
600
60
45
(1) (1) (1)
70 500
600
70
50
(1) (1) (1)
80 550
600
60
55
(1) (1) (1)
Notes
  • * Normally, the cover required by EN 1992-1-1 for durability and bond will control the value of a instead of the tabulated value.
    1. Requires a width greater than 600 mm. Particular assessment for buckling is required; the calculator reports the fire check as failed if an interpolation passes through one of these entries (see “Special Buckling Assessment” below).
    2. Values are tabulated at λ = 30, 40, 50, 60, 70, 80 and n = 0.15, 0.3, 0.5, 0.7; the calculator linearly interpolates between tabulated values as described in “Interpolation of Table Requirements” below.

Interpolation of Table Requirements

The fire requirements are determined using linear interpolation through four parameters. Annex C(2) permits linear interpolation between the different column tables (ω and e); the calculator also interpolates within each table for slenderness and fire load level.

For each selected Annex C table:

  1. The surrounding slenderness values are identified from λ = 30, 40, 50, 60, 70 and 80.
  2. The surrounding fire load levels are identified from n = 0.15, 0.3, 0.5 and 0.7.
  3. The requirements are first interpolated for fire load level.
  4. The resulting values are then interpolated for slenderness.

This produces a set of requirements from each of the four surrounding Annex C tables.

The results are then:

  1. Interpolated between the lower and upper eccentricity tables.
  2. Interpolated between the lower and upper mechanical reinforcement ratios.

The final result gives the required minimum column dimension, bmin, and reinforcement axis distance, a.

Notes
  • Where the table provides more than one acceptable combination, each combination is retained as an alternative requirement.
  • When any of slenderness, load level, mechanical reinforcement ratio or eccentricity falls outside or between the tabulated values used above, the report adds a note under the fire resistance criteria stating which values are not tabulated and are linearly interpolated between the adjacent Annex C tabulated values, or which values fall outside the tabulated range and use the nearest tabulated value directly.

Special Buckling Assessment

Some Annex C table entries are identified by the special condition “(1)”. If an interpolation passes through one of these entries, the normal tabulated result is not used. The fire check is reported as failed and a special buckling assessment is required.

Change Log

October 2026 – Fire Resistance Checks
  • NEW: Added column fire resistance checks to EN 1992-1-2 Annex C, checked about each axis.
  • Fixed: Longitudinal bar maximum spacing check for circular columns reporting a NaN allowable spacing and always failing. The limit now matches rectangular columns (175 mm with best practice, 300 mm without).

June 2026 – Interaction Diagram & Bending Moment Diagrams
  • 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.

November 2025 – Additional Moment & Shear Table Fixes
  • Updated: Moved additional moment calculation term M2 + M02 for single curvature behind best practice.
  • Fixed: Shear table values not updating in report.

October 2025 – Calculation & Report Improvements
  • Updated: Creep factor calculation to remove 0 default.
  • Updated: Strain calculation in compression bars to calculate and subtract equivalent concrete strain to ensure the force is not double counted.
  • Updated: Moved shear web width calculation for circular columns behind best practice toggle.
  • NEW: Added logic to calculate the ‘resultant’ biaxial utilisation for circular columns, behind best practice toggle.
  • Updated: Report styling to full width and generally refactored report layout.
  • Updated: Split detailing check for maximum spacing into max spacing general and max distance to restrained bar.
  • NEW: Added biaxial shear check to best practice.
  • NEW: Added M02 + M2 term for max moment in columns with single curvature.

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Updated November 2, 2026

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