All worked examples
Worked example · Pro tool
RC Column Design: worked example
A reinforced concrete column checked for axial load with biaxial bending, slenderness and second-order effects.
EN 1992-1-1:2004 — Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings · SI units · Calculator v1.1
These are the real results of the RC Column Design for the inputs below, read-only. Open the calculator with these values already loaded to change them.
Open with these inputs7-day free trial, no card. Sign in
Inputs
| Section type | Rectangular |
| Width b | 400 mm |
| Height h | 400 mm |
| Clear height l0 | 3.5 m |
| Effective-length factor k | From end-condition selection |
| Concrete | C30/37 |
| Reinforcing steel | B500S |
| Nominal cover cnom | 25 mm |
| Axial load NEd | 1500 kN |
| End moments My,top / My,bot | 120 / 80 kN·m |
| Out-of-plane moment Mz | 60 kN·m |
| Links | 200 mm spacing |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Slenderness λ | ≤ 26.2 | 15.2 | 57.9% | PASS |
| Min eccentricity | 30.00 kN·m | 120.00 kN·m | 0.0% | PASS |
| N-M Interaction | ≤ 1.0 | 0.49 | 48.9% | PASS |
| As,min | 345 mm² | 2513 mm² | 13.7% | PASS |
| As,max | ≤ 6400 mm² | 2513 mm² | 39.3% | PASS |
| Link spacing | ≤ 400 mm | 200 mm | 50.0% | PASS |
Calculation steps
Minimum Eccentricity (2 steps)
EC2 §6.1(4)
Minimum eccentricity
e0 = max(h/30, 20mm)
e0 = max(13.3, 20)
e0 = 20.0 mm → MEd,min = 30.00 kN·m
EC2 §6.1(4)
Design moment
MEd = max(|MEd|, MEd,min)
max(120.00, 30.00)
MEd = 120.00 kN·m
Slenderness Check (4 steps)
EC2 §5.8.3.2
Radius of gyration
i = √(Ic/Ac) = √(b·h³/12 / (b·h))
Ic = 2133333333 mm⁴, Ac = 160000 mm²
i = 115.5 mm
EC2 §5.8.3.2
Slenderness ratio
λ = leff / i
λ = 1750 / 115.5
λ = 15.2
EC2 §5.8.3.1
Limiting slenderness parameters
A = 1/(1+0.2φef), B = √(1+2ω), C = 1.7 − rm
A = 0.70, ω = 0.402, B = 1.34, rm = 0.67, C = 1.03, n = 0.551
λlim = 20×0.70×1.34×1.03/√0.551 = 26.2
EC2 §5.8.3.1
Slenderness classification
λ ≤ λlim → Short column; λ > λlim → Slender column
15.2 ≤ 26.2
✓ SHORT COLUMN — no second order effects
Interaction Diagram (3 steps)
EC2 §6.1
Section properties
Ac = b×h, As = Σ(area of each bar)
Ac = 160000 mm², As = Σ over 8 bars
As = 2513 mm²
EC2 §3.1.7, §6.1(5)
Maximum axial capacity (pure compression, uniform strain εc2 = 0.002)
N0 = fcd·(Ac − As) + As·min(fyd, Es·εc2)
N0 = 17.00×(160000 − 2513) + 2513×min(434.8, 400)
N0 = 3682.6 kN
EC2 §6.1
N-M interaction check
Design point must lie within interaction curve
(NEd, MEd) = (1500.0, 120.00) kN, kN·m
Utilization = 48.9% — ✓ PASS
Reinforcement Limits (3 steps)
EC2 §9.5.2(2)
Minimum reinforcement
As,min = max(0.1·NEd/fyd, 0.002·Ac)
max(0.1×1500000/434.8, 0.002×160000)
As,min = 345 mm²
EC2 §9.5.2(3)
Maximum reinforcement
As,max = 0.04·Ac (outside laps)
As,max = 0.04 × 160000
As,max = 6400 mm²
EC2 §9.5.2
Check
As,min ≤ As ≤ As,max
345 ≤ 2513 ≤ 6400
ρ = 1.57% — ✓ PASS
Link Design (3 steps)
EC2 §9.5.3(1)
Minimum link diameter
φlink,min = max(6mm, φbar/4)
max(6, 20/4)
φlink,min = 6 mm — ✓
EC2 §9.5.3(3)
Maximum link spacing
scl,max = min(20φbar, b, h, 400mm)
min(400, 400, 400, 400)
scl,max = 400 mm — ✓
EC2 §9.5.3(4)
Critical zone
lc = max(h, b, l0/6, 450mm)
max(400, 400, 583, 450)
lc = 583 mm — spacing in zone = 0.6×400 = 240 mm
Design basis and assumptions
- National Annex: none applied as a whole — the EN recommended values are used, except where noted below. There is no National Annex selector; check the values against the annex for your project.
- αcc = 0.85 in fcd = αcc·fck/γc (the UK National Annex value; EN 1992-1-1 §3.1.6(1) recommends 1.0).
- The N–M interaction check uses the same diagram as Column Interaction: pure compression N0 = fcd·(Ac − As) + As·min(fyd, Es·εc2), εc2 = 0.002 (EN 1992-1-1 §3.1.7, §6.1(5)).
- γc = 1.5 and γs = 1.15 (EN 1992-1-1 Table 2.1N, persistent and transient), editable.
- Slenderness uses the nominal-curvature method with a user-set effective creep ratio and effective-length factor — accuracy depends on choosing the right end-restraint case (or a genuinely first-principles Custom value).
- Biaxial bending is checked as a separate tab against the full 3D interaction surface — the primary ULS tab checks uniaxial bending about one axis only.
- Applied axial force, unless you use the optional NGk/NQk breakdown (which applies only the code’s standard gravity combination), is an input from your own load takedown.
- Bar layout is Outer/Inner ring based — code rules on intermediate bars along a long face are your responsibility to apply via the Inner ring, not automatically enforced.
- Link/tie spacing shown doesn’t add to the axial/moment capacity — it’s what makes the longitudinal bars’ capacity achievable in reality, not itself a strength-check output.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.