About Concrete Column Calculation
This Concrete Column Calculator calculates rebar and dimensions for a square reinforced concrete column based on the design load, column height, concrete class, number of longitudinal bars, and concrete cover. The calculation selects the column cross-section, longitudinal bar diameter, and transverse reinforcement while checking section resistance, minimum and maximum longitudinal reinforcement, column slenderness, second-order effects, and reinforcement detailing limits.
The calculation method is based on EN 1992-1-1 "Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings". Concrete classes correspond to EN 206 "Concrete - Specification, performance, production and conformity". The design load should account for combinations of actions according to EN 1990 "Eurocode - Basis of structural design" and the relevant actions according to EN 1991 "Eurocode 1: Actions on structures".
Guidelines and recommendations
Design properties of materials
Design strength of concrete. For the selected concrete class, the characteristic cylinder strength fck is used, which is the first number in the class designation. For example, for C20/25, fck = 20 MPa. The design compressive strength is calculated using αcc = 0.85 and the partial safety factor γc = 1.50:
fcd = 0.85 · fck / 1.50
For example, for C20/25 concrete, fcd = 11.3 MPa. For high-strength concrete above C50/60, the parameters of the equivalent rectangular compression block are additionally adjusted.
Design strength of reinforcement. For longitudinal reinforcement, the characteristic yield strength is taken as fyk = 500 MPa with the partial factor γs = 1.15. The design strength of reinforcement is:
fyd = 500 / 1.15 = 434.8 MPa
The modulus of elasticity of reinforcing steel is taken as Es = 200000 MPa.
Selection of column cross-section and longitudinal reinforcement
Selection sequence. The calculator starts with a square section of 250 x 250 mm and increases the side dimension in 50 mm increments up to the maximum checked size of 1500 x 1500 mm. For each section, longitudinal bar diameters of 12, 14, 16, 18, 20, 22, 25, 28, 32, 36 and 40 mm are checked. The first option that satisfies all verification conditions is selected.
Area of longitudinal reinforcement. For the specified number of bars n and bar diameter d, the reinforcement area is calculated as:
As = n · π · d2 / 4
The calculated area is checked against the minimum and maximum reinforcement limits. The minimum required reinforcement area is taken as the greater of the following two values:
As,min = max(0.10 · NEd / fyd, 0.002 · Ac)
The maximum longitudinal reinforcement area is taken as:
As,max = 0.04 · Ac
Here, NEd is the design axial force in N, and Ac is the concrete cross-sectional area in mm2. If the load is entered in tonnes, the calculation uses the conversion 1 t = 9.81 kN.
Bar arrangement. With 4 bars, the bars are placed at the corners of the section. With 8 bars, one intermediate bar is added on each side. With 12 bars, two intermediate bars are placed on each side. In the calculation, concrete cover is measured from the concrete surface to the outer surface of the transverse reinforcement.
The clear distance between adjacent longitudinal bars must not be less than the greater of d and 25 mm. If a combination of bar diameter, concrete cover, and section size does not provide the required spacing, that combination is excluded from the selection.
Slenderness and second-order effects
Column slenderness. The effective length is taken equal to the entered column height L. For a square section, the radius of gyration is calculated as:
i = h / √12
The slenderness ratio is calculated as:
λ = L / i
where h is the side dimension of the square section in mm.
Limiting slenderness. To determine whether second-order effects must be considered, the EN 1992-1-1 relationship is used:
λlim = 20 · A · B · C / √n
The calculation uses fixed coefficients A = 0.70 and C = 0.70. The coefficient A corresponds to the adopted effective creep ratio φef = 2.143. The coefficient B depends on the amount of longitudinal reinforcement:
B = √(1 + 2 · ω)
ω = As · fyd / (Ac · fcd)
The relative axial force is calculated as:
n = NEd / (Ac · fcd)
If the actual slenderness λ is lower than the limiting value λlim, no additional second-order moment is introduced. If λ ≥ λlim, the calculator determines the additional eccentricity using the nominal curvature method.
Initial imperfections. The minimum eccentricity is taken as the greater of the following two values:
e0 = max(h / 30, 20 mm)
A geometric imperfection is also included:
ei = L / 400
Second-order effects. For a slender column, the additional curvature is determined taking into account the axial force level, reinforcement ratio, concrete class, and the adopted creep ratio. The basic curvature is calculated using the reinforcement yield strain fyd / Es and the effective depth of the reinforcement. The additional eccentricity is determined as:
e2 = kr · kφ · (1 / r0) · L2 / 10
The additional second-order moment is then:
M2 = NEd · e2
For section verification, the greater of the moment caused by the minimum eccentricity and the moment including geometric imperfection and second-order effects is used:
MEd = max(NEd · e0, NEd · ei + M2)
Section resistance check
Combined compression and bending. The selected section is checked not only for axial compression. For each combination of column size and reinforcement, the neutral axis position is determined so that the internal axial force from the concrete and reinforcing steel equals the specified design load.
For concrete up to C50/60, the rectangular compression block uses the depth factor λc = 0.80, the stress factor η = 1.00, and the ultimate concrete strain εcu = 3.5‰. For concrete classes above C50/60, the following relationships are used:
λc = 0.80 - (fck - 50) / 400
η = 1 - (fck - 50) / 200
εcu = [2.6 + 35 · ((90 - fck) / 100)4]‰
Reinforcement stresses. Bar strains are determined from a linear strain distribution over the section depth. Steel stress is calculated using Es and is limited to the design strength ±fyd. The resistance moment MRd is determined from the forces in the concrete compression block and all reinforcing bars.
The section is considered adequate when its design resistance satisfies:
MRd ≥ MEd
If this condition is not satisfied, the calculator first checks the next longitudinal bar diameter and then moves to the next square section size.
Transverse reinforcement
Tie diameter. The minimum diameter of transverse reinforcement is taken as the greater of 6 mm and one quarter of the longitudinal bar diameter:
dsw ≥ max(6 mm, d / 4)
The calculated value is rounded up to one of the available diameters: 6, 8, 10, 12, 14 or 16 mm.
Tie spacing. The maximum spacing in the middle region is calculated as:
smax = min(20 · d, h, 400 mm)
The resulting value is rounded down in 25 mm increments. A reduced spacing is used in the end regions:
send = 0.60 · smax
The length of each end region is taken equal to the column side dimension h, but not more than half of the column height.
Additional transverse links. For arrangements with 8 and 12 longitudinal bars, the spacing between intermediate bars is checked. If the calculated clear interval exceeds 150 mm, internal transverse links are added. With 8 longitudinal bars, 2 additional links are used at each tie level. With 12 bars, 4 links are used.
Concrete volume and material mass
Column volume. The geometric volume is calculated from the square section dimension and the column height:
V = h2 · L
For the displayed result, dimensions are converted from millimetres to metres, so the volume is shown in m3.
Reinforcement mass. The mass of longitudinal bars and transverse reinforcement is calculated from their cross-sectional area and total length. A steel density of 7850 kg/m3 is used. When calculating the length of one closed tie, an additional total allowance of 20 · dsw is included for tie closure.
Concrete mass. A concrete density of 2450 kg/m3 is used. Before calculating the concrete mass, the volume occupied by the calculated reinforcement is deducted from the geometric column volume so that the steel volume is not counted as both concrete and steel. The total column mass is calculated as the sum of the concrete mass, longitudinal reinforcement mass, and transverse reinforcement mass.
FAQs
Why can the column cross-section increase when the column height increases?
As the height increases, the slenderness of the reinforced concrete column also increases. Once the calculated slenderness limit is exceeded, the calculator includes an additional second-order bending moment, which increases the required section resistance. Therefore, a taller column under the same axial load may require a larger cross-section or a larger longitudinal rebar diameter.
Why does a higher concrete class not always reduce the column dimensions?
Concrete strength is only one of the conditions used to calculate rebar and dimensions. The final size also depends on slenderness, minimum and maximum reinforcement ratios, bar arrangement, concrete cover, and the ability of the section to resist combined axial compression and bending. Above a certain level, increasing the concrete class may therefore no longer change the selected column section.
Why does changing the concrete cover affect the calculation result?
Increasing the concrete cover moves the longitudinal bars closer to the centre of the section. This reduces the lever arm of the reinforcement and can reduce the resistance to bending moment. It also reduces the available space for the bars, so some combinations of bar diameter and section size may be rejected.
Why are additional transverse links needed with 8 or 12 longitudinal bars?
The outer closed tie directly restrains mainly the bars located near the corners of the section. When the spacing between longitudinal bars becomes large, intermediate bars require additional transverse restraint. The calculator therefore adds internal links automatically when the clear interval exceeds 150 mm.
How does the Concrete Column Calculator select the final cross-section and rebar diameter?
The calculation starts with a 250 x 250 mm section and the smallest available longitudinal bar diameter. Each option is checked in sequence for reinforcement area, bar spacing, slenderness, second-order effects, and resistance under combined compression and bending. The first option that satisfies all checks is selected as the result.