Reinforced concrete column serviceability to SIA 262
Checks a rectangular or circular reinforced concrete column under compression and bending in service, to SIA 262:2025: concrete stress and creep, the long-term transfer of the load to the bars by creep and shrinkage, the axial shortening, and crack control where the moment opens the section. Every step shows its formula and the clause it comes from.
Basic SIA 262:2025
Part of the Basic plan
This module is included in the Basic plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a rectangular or circular reinforced concrete column under compression and bending in service, to SIA 262:2025: concrete stress and creep, the long-term transfer of the load to the bars by creep and shrinkage, the axial shortening, and crack control where the moment opens the section. Every step shows its formula and the clause it comes from.
What it checks
- Section and materials: Ac, As, ρ, the idealised area Ai = Ac + (αe − 1) · As, and fcm = fck + 8, clause 3.1.2.2.3, equation (6).
- Combinations: quasi-permanent, frequent and characteristic values of N and M from the permanent and variable parts.
- State of the section: the largest stress under the characteristic combination, uncracked, σc,max = N/Ai ± M/Wi, with fct,eff = kt · fctm, clause 4.4.1.3, equations (99) and (100).
- Concrete compression, check 1: σc,qp ≤ 0.6 · fcm (3.1.2.6.3), the range of the creep model.
- Transfer of the sustained force to the bars: the change of the concrete stress by creep and shrinkage, Δσc = −(σc0 · φ − εcs · Ecm) · αe · ρn / (1 + αe · ρn · (1 + χ · φ)), with the age-adjusted modulus Ec,adj = Ecm/(1 + χ · φ); then σc,∞, σs,∞ and the share of Nqp carried by the concrete, at loading and in the long term.
- Bars stay elastic, check 2 (optional): σs,∞,max ≤ fyk, the most compressed bar including the bending part under Mqp. This is a plausibility criterion of the module, not a clause.
- Axial shortening: ε0 = Nqp/(Ecm · Ai) and ε∞ = σs,∞/Es, then Δl0 and Δl∞ over the height l.
- Crack control to Table 17, with wnom = 0.5 mm (increased) or 0.2 mm (high), only where the moment opens the section.
What you enter and what you get
You enter the shape (rectangle or circle), h in the plane of the moment and b, the optional height l, the bars along each face, Ø, c and Øw, and the materials. For creep and shrinkage: RH, the cement class, t0, t and ts, or your own φ and εcs. You enter NG, NQ, MG and MQ as characteristic values, compression positive, with ψ1 and ψ2. Then the requirement level and the ageing coefficient χ, computed as √t0/(1 + √t0) or entered.
You get φ and εcs, the stresses at loading and in the long term, the shortenings, and each check with its utilisation. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- The moment is entered at the section checked, with the eccentricities and second-order effects of your own analysis under service loads.
- φ follows EN 1992-1-1 Annex B and εcs EN 1992-1-1 §3.1.4. The creep coefficient is valid for compressive stresses up to 0.45 · fck at loading.
- If the section stays compressed under every combination, no crack reinforcement is needed (4.4.2.3.5) and the Table 17 checks are not made.
- Once the bars yield, the concrete takes all further creep.
- For exposure classes XD, XF and XS, a limit of k1 · fck under the characteristic combination can be added, to EN 1992-1-1 §7.2(2). SIA 262 has no such limit.
Worked example
A 400 × 400 mm column 3.2 m high with 8Ø20, fck = 30 N/mm², NG = 1,600 kN, NQ = 600 kN, MG = 20 kNm and MQ = 15 kNm, at 50 % relative humidity. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Shape of the column | Rectangle | |
| Depth in the plane of the moment h | 400 mm | |
| Width b | 400 mm | |
| Height of the column (optional) l | 3.2 m | |
| Bars along each face of width b (corners included) nb | 3 | |
| Bars along each side face (corners included) nh | 3 | |
| Bar diameter Ø | 20 mm | |
| Concrete cover to the ties c | 30 mm | |
| Tie diameter Øw | 8 mm | |
| Characteristic compressive strength fck | 30 N/mm² | § 3.1.2.2.2 |
| Mean tensile strength fctm | 2.9 N/mm² | § 3.1.2.2.4 |
| Modulus of elasticity Ecm | 32000 N/mm² | § 3.1.2.3.3 |
| Characteristic yield strength fyk | 500 N/mm² | |
| Modulus of elasticity Es | 205000 N/mm² | |
| Resistance factor for steel γs | 1.15 | § 2.4.2.6 |
| Creep coefficient φ | Computed (EN 1992-1-1 Annex B) | § 3.1.2.6 |
| Relative humidity of the environment RH | 50 % | |
| Cement class | N — normal hardening | |
| Age of the concrete at loading t0 | 28 days | |
| Age considered (service life) t | 50 years | |
| Shrinkage strain εcs | Computed (EN 1992-1-1 §3.1.4) | § 3.1.2.7 |
| Age at the end of curing ts | 7 days | |
| Compression force, permanent part NG | 1600 kN | |
| Compression force, variable part NQ | 600 kN | |
| Bending moment, permanent part MG | 20 kNm | |
| Bending moment, variable part MQ | 15 kNm | |
| Combination factor, frequent ψ1 | 0.5 | |
| Combination factor, quasi-permanent ψ2 | 0.3 | |
| Requirement level | Normal | § 4.4.2.2.3 |
| Tensile strength for the first crack | Mean tensile strength (4.4.1.3) | § 4.4.1.3 |
| Exposure to chlorides, frost or sea water? | No — X0 or XC | EN 1992-1-1 §7.2(2) |
| Ageing coefficient χ | Computed, χ = √t₀/(1 + √t₀) | |
| Check that the bars stay elastic in the long term? | Yes |
| Step | Value | Ref. |
|---|---|---|
| Gross concrete areab·h | Ac = 160,000 mm² | |
| Bars8Ø20 | As = 2,513 mm² | |
| Reinforcement ratioAs/Ac | ρ = 1.57 % | |
| Concrete area net of the barsAc − As | Ac,n = 157,487 mm² | |
| Distance of the bar axis to the facec + Øw + Ø/2 | a = 48 mm |
| Step | Value | Ref. |
|---|---|---|
| Mean compressive strengthfck + 8 | fcm = 38.0 N/mm² | § 3.1.2.2.3 (6) |
| Design yield strength of the barsfyk/γs | fyd = 434.8 N/mm² | § 2.4.2.5 (4) |
| Modular ratioEs/Ecm | αe = 6.41 | |
| Idealised areaAc + (αe − 1)·As | Ai = 173,587 mm² |
| Step | Value | Ref. |
|---|---|---|
| Notional size2·Ac/u, u = 1,600 mm (perimeter) | h0 = 200 mm | EN 1992-1-1 Annex B (B.6) |
| Humidity factor[1 + (1 − RH/100)/(0.1·∛h0)·α1]·α2 | φRH = 1.778 | EN 1992-1-1 Annex B (B.3) |
| Strength factor16.8/√fcm | β(fcm) = 2.725 | EN 1992-1-1 Annex B (B.4) |
| Age at loading adjusted for the cementt0·(9/(2 + t0^1.2) + 1)^α ≥ 0.5, α = 0 | t0,adj = 28.0 days | EN 1992-1-1 Annex B (B.9) |
| Age factor1/(0.1 + t0^0.2) | β(t0) = 0.488 | EN 1992-1-1 Annex B (B.5) |
| Notional creep coefficientφRH·β(fcm)·β(t0) | φ0 = 2.366 | EN 1992-1-1 Annex B (B.2) |
| Humidity–size coefficient1.5·[1 + (0.012·RH)^18]·h0 + 250·α3 ≤ 1500·α3 | βH = 540 days | EN 1992-1-1 Annex B (B.8) |
| Development with time[(t − t0)/(βH + t − t0)]^0.3, t = 18,250 days | βc(t, t0) = 0.991 | EN 1992-1-1 Annex B (B.7) |
| Creep coefficientφ0·βc(t, t0)valid for compressive stresses up to 0.45·fck at loading | φ(t, t0) = 2.35 | EN 1992-1-1 Annex B (B.1) |
| Step | Value | Ref. |
|---|---|---|
| Humidity factor1.55·[1 − (RH/100)³] | βRH = 1.356 | EN 1992-1-1 Annex B (B.12) |
| Basic drying shrinkage0.85·[(220 + 110·αds1)·exp(−αds2·fcm/10)]·10⁻⁶·βRH | εcd,0 = 0.482 ‰ | EN 1992-1-1 Annex B (B.11) |
| Size coefficientfrom h0, linear between the values of Table 3.3 | kh = 0.850 | EN 1992-1-1 §3.1.4(6) |
| Development of drying(t − ts)/[(t − ts) + 0.04·√h0³] | βds(t, ts) = 0.994 | EN 1992-1-1 §3.1.4 (3.10) |
| Drying shrinkageβds·kh·εcd,0 | εcd = 0.407 ‰ | EN 1992-1-1 §3.1.4 (3.9) |
| Final autogenous shrinkage2.5·(fck − 10)·10⁻⁶ | εca,∞ = 0.050 ‰ | EN 1992-1-1 §3.1.4 (3.12) |
| Autogenous shrinkage[1 − exp(−0.2·√t)]·εca,∞ | εca = 0.050 ‰ | EN 1992-1-1 §3.1.4 (3.11) |
| Total shrinkage strainεcd + εca | εcs = 0.457 ‰ | EN 1992-1-1 §3.1.4 (3.8) |
| Step | Value | Ref. |
|---|---|---|
| Quasi-permanentG + ψ2·Q | Nqp ; Mqp = 1,780 ; 24.5 kN ; kNm | |
| FrequentG + ψ1·Q | Nfr ; Mfr = 1,900 ; 27.5 kN ; kNm | |
| CharacteristicG + Q | Nra ; Mra = 2,200 ; 35.0 kN ; kNm |
| Step | Value | Ref. |
|---|---|---|
| Size factor1/(1 + 0.5·t), t = smallest dimension in m | kt = 0.833 | § 4.4.1.3 (100) |
| Effective tensile strengthkt·fctm | fct,eff = 2.42 N/mm² | § 4.4.1.3 (99) |
| Largest stress, characteristic combination, uncrackedN/Ai ± M/Wi (tension positive)the whole section stays compressed | σc,max = -9.72 N/mm² |
| Step | Value | Ref. |
|---|---|---|
| Largest compression at loadinguncracked section, Ecm | |σc,qp| = 12.32 N/mm² | |
| Stress–strength ratio | |σc|/fcm = 0.324 | |
| Concrete compression within the range of the creep model|σc,qp|/(0.6·fcm) | η = 0.540 · Pass54 % of the capacity used | § 3.1.2.6.3 |
| Step | Value | Ref. |
|---|---|---|
| Creep coefficient usedfrom the section part | φ = 2.35 | |
| Ageing coefficient√t0/(1 + √t0) | χ = 0.841 | |
| Age-adjusted effective modulusEcm/(1 + χ·φ) | Ec,adj = 10,764 N/mm² | |
| Concrete stress at loading (centric part)−Nqp/Ai | σc0 = -10.25 N/mm² | |
| Bar stress at loadingαe·σc0 | σs0 = -65.7 N/mm² | |
| Change of the concrete stress by creep and shrinkage−(σc0·φ − εcs·Ecm)·αe·ρn/(1 + αe·ρn·(1 + χ·φ)), ρn = As/Ac,npositive: the concrete is relieved | Δσc = 3.03 N/mm² | |
| Long-term concrete stressσc0 + Δσc | σc,∞ = -7.22 N/mm² | |
| Long-term bar stressσs0 − Δσc·Ac,n/As | σs,∞ = -255.8 N/mm² | |
| Share of Nqp carried by the concreteat loading → long term | Fc/Nqp = 91 % → 64 % |
| Step | Value | Ref. |
|---|---|---|
| Most compressed bar, long term|σs,∞| + bending part under Mqp (Ec,eff) | |σs,∞,max| = 282 N/mm² | |
| Bars below yield under the sustained load|σs,∞,max|/fyk | η = 0.564 · Pass56 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Instantaneous strainNqp/(Ecm·Ai) | ε0 = 0.320 ‰ | |
| Long-term strain|σs,∞|/Es (the bars and the concrete shorten together) | ε∞ = 1.248 ‰ | |
| Instantaneous shorteningε0·l | Δl0 = 1.03 mm | |
| Long-term shorteningε∞·lof which 2.97 mm after loading (creep and shrinkage) | Δl∞ = 3.99 mm |
How this module is verified
Verified clause by clause against SIA 262:2025 and against independent calculations used on real projects, before release.
Questions
Why do the bars carry more load with time?
Creep and shrinkage shorten the concrete, and the bars shorten with it. In the worked example the concrete share of Nqp falls from 91 % at loading to 64 % in the long term.
Why compare the shortenings of neighbouring members?
Differences of shortening between neighbouring columns, or between columns and cores, load the slabs and the partitions they carry.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Reinforced concrete column of any section
- Concrete tie serviceability
- Concrete columns: all modules
- SIA 262: modules and clauses
Norm: SIA 262:2025 · Page updated: 29 October 2026