Checks a rectangular or circular reinforced concrete tension member in service, to SIA 262:2025: the cracking force reduced by restrained shrinkage, crack control by the bar stresses, the crack width and the elongation with tension stiffening. 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 fyd = fyk/γs, clause 2.4.2.5, equation (4).
- Shrinkage restrained by the bars: σc,cs = εcs · Ecm · αe · ρn / (1 + αe · ρn · (1 + χ · φ)), with ρn = As/Ac,n, and the bar compression σs,cs = −σc,cs/ρn.
- Cracking force: fct,eff = kt · fctm, clause 4.4.1.3, equations (99) and (100); Ncr,0 = fct,eff · Ai at loading and Ncr,∞ = (fct,eff − σc,cs) · Ai in the long term, which tells whether the tie is cracked.
- Admissible bar stress: σs,adm = √(9 · Es · fctm · wnom / Øs) ≤ fyk, clause 4.4.2.3.4, equation (102), with wnom from Table 17.
- Check 1, minimum reinforcement (4.4.2.3.3): the bars take the whole cracking force, σs,r = Ncr/As ≤ σs,adm (Table 17).
- Check 2: σs,qp = Nqp/As ≤ σs,adm (Table 17).
- Check 3, no yielding: σs,ra = Nra/As ≤ fyd − 80 N/mm² (Table 17).
- Check 4, crack width (optional) under Nqp, to EN 1992-1-1 §7.3.4, equations (7.8) to (7.11), with k2 = 1.0 and a tension band of depth hc,ef = min(2.5 · a ; t/2) along every face (EN 1992-1-1 §7.3.2(3)), against wmax.
- Elongation under Nqp: εm = ζ · εII + (1 − ζ) · εI, with ζ = 1 − β · (Ncr,∞/Nqp)², β = 0.5, EN 1992-1-1 §7.4.3, equations (7.18) and (7.19), less the shortening from restrained shrinkage in the uncracked parts; then Δl = εtot · l.
What you enter and what you get
You enter the shape (rectangle or circle), h, b and the optional length l, the bars along each face, Ø, c and Øw, and the materials. For creep and shrinkage: RH, the cement class, t0, t, ts and the ageing coefficient χ, or your own φ, εcs and χ. You enter NG and NQ as characteristic values, tension positive, with ψ1 and ψ2. Then the requirement level, the tensile strength for the first crack and the crack width data.
You get the cracking forces at loading and in the long term, the state of the tie, every check with its utilisation and clause, the crack width and the elongation. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- φ follows EN 1992-1-1 Annex B and εcs EN 1992-1-1 §3.1.4, or your own values. fck is used for creep and shrinkage only.
- χ = √t0/(1 + √t0) by default, for the concrete stress that shrinkage builds up gradually.
- Use the upper fractile of the tensile strength (4.4.1.4) when the crack comes from a restrained deformation and a strong concrete is unfavourable.
- The crack width is computed under the quasi-permanent force, if it cracks the tie.
- The elongation is skipped if l is left blank.
Worked example
A 300 × 300 mm tie 8 m long with 8Ø16, fck = 30 N/mm², 70 % relative humidity, NG = 250 kN and NQ = 150 kN, increased requirements and wmax = 0.3 mm. These are the module's own results for its worked example, computed when this page was built.
Inputs| Input | Value | Ref. |
|---|
| Shape of the tie | Rectangle | |
|---|
| Depth h | 300 mm | |
|---|
| Width b | 300 mm | |
|---|
| Length of the tie (optional) l | 8 m | |
|---|
| Bars along each face of width b (corners included) nb | 3 | |
|---|
| Bars along each face of depth h (corners included) nh | 3 | |
|---|
| Bar diameter Ø | 16 mm | |
|---|
| Concrete cover to the links c | 30 mm | |
|---|
| Link 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 | 70 % | |
|---|
| 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 | |
|---|
| Ageing coefficient χ | Computed, χ = √t₀/(1 + √t₀) | |
|---|
| Tension force, permanent part NG | 250 kN | |
|---|
| Tension force, variable part NQ | 150 kN | |
|---|
| Combination factor, frequent ψ1 | 0.5 | |
|---|
| Combination factor, quasi-permanent ψ2 | 0.3 | |
|---|
| Requirement level | Increased | § 4.4.2.2.3 |
|---|
| Tensile strength for the first crack | Mean tensile strength (4.4.1.3) | § 4.4.1.3 |
|---|
| Compute the crack width? | Yes | |
|---|
| Bond of the bars k1 | High-bond bars (0.8) | EN 1992-1-1 §7.3.4(3) |
|---|
| Crack spacing factor for the cover k3 | 3.4 | EN 1992-1-1 §7.3.4(3) |
|---|
| Crack spacing factor for the bond length k4 | 0.425 | EN 1992-1-1 §7.3.4(3) |
|---|
| Limiting crack width (optional) wmax | 0.3 mm | |
|---|
Calculation: Section| Step | Value | Ref. |
|---|
| Gross concrete areab·h | Ac = 90,000 mm² | |
|---|
| Bars8Ø16 | As = 1,608 mm² | |
|---|
| Reinforcement ratioAs/Ac | ρ = 1.79 % | |
|---|
| Distance of the bar axis to the facec + Øw + Ø/2 | a = 46 mm | |
|---|
Calculation: Materials| 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 = 98,696 mm² | |
|---|
Calculation: Creep| Step | Value | Ref. |
|---|
| Notional size2·Ac/u, u = 1,200 mm (perimeter) | h0 = 150 mm | EN 1992-1-1 Annex B (B.6) |
|---|
| Humidity factor[1 + (1 − RH/100)/(0.1·∛h0)·α1]·α2 | φRH = 1.508 | 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 = 2.007 | EN 1992-1-1 Annex B (B.2) |
|---|
| Humidity–size coefficient1.5·[1 + (0.012·RH)^18]·h0 + 250·α3 ≤ 1500·α3 | βH = 475 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) = 0.992 | 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) = 1.99 | EN 1992-1-1 Annex B (B.1) |
|---|
Calculation: Shrinkage| Step | Value | Ref. |
|---|
| Humidity factor1.55·[1 − (RH/100)³] | βRH = 1.018 | EN 1992-1-1 Annex B (B.12) |
|---|
| Basic drying shrinkage0.85·[(220 + 110·αds1)·exp(−αds2·fcm/10)]·10⁻⁶·βRH | εcd,0 = 0.362 ‰ | EN 1992-1-1 Annex B (B.11) |
|---|
| Size coefficientfrom h0, linear between the values of Table 3.3 | kh = 0.925 | EN 1992-1-1 §3.1.4(6) |
|---|
| Development of drying(t − ts)/[(t − ts) + 0.04·√h0³] | βds(t, ts) = 0.996 | EN 1992-1-1 §3.1.4 (3.10) |
|---|
| Drying shrinkageβds·kh·εcd,0 | εcd = 0.334 ‰ | 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 = 0.384 ‰ | EN 1992-1-1 §3.1.4 (3.8) |
|---|
Calculation: Shrinkage restrained by the bars| Step | Value | Ref. |
|---|
| Ageing coefficient√t0/(1 + √t0) | χ = 0.841 | |
|---|
| Concrete tension from restrained shrinkageεcs·Ecm·αe·ρn/(1 + αe·ρn·(1 + χ·φ)), ρn = As/Ac,n | σc,cs = 1.09 N/mm² | |
|---|
| Bar compression from restrained shrinkage−σc,cs/ρn | σs,cs = -59.9 N/mm² | |
|---|
Calculation: Combinations| Step | Value | Ref. |
|---|
| Quasi-permanentNG + ψ2·NQ | Nqp = 295 kN | |
|---|
| FrequentNG + ψ1·NQ | Nfr = 325 kN | |
|---|
| CharacteristicNG + NQ | Nra = 400 kN | |
|---|
Calculation: Cracking force| Step | Value | Ref. |
|---|
| Size factor1/(1 + 0.5·t), t = smallest dimension in m | kt = 0.870 | § 4.4.1.3 (100) |
|---|
| Effective tensile strengthkt·fctm | fct,eff = 2.52 N/mm² | § 4.4.1.3 (99) |
|---|
| Cracking force at loadingfct,eff·Ai | Ncr,0 = 249 kN | § 4.4.1.3 |
|---|
| Cracking force in the long term(fct,eff − σc,cs)·Airestrained shrinkage uses up part of the tensile strength | Ncr,∞ = 141 kN | |
|---|
| State of the tie | cracked (Nra > Ncr,∞) | |
|---|
Calculation: Admissible bar stress| Step | Value | Ref. |
|---|
| Nominal crack width | wnom = 0.5 mm | Table 17 |
|---|
| Admissible bar stress√(9·Es·fctm·wnom/Øs) ≤ fyk | σs,adm = 409 N/mm² | § 4.4.2.3.4 (102) |
|---|
Calculation: Check 1 — bar stress when the tie cracks (minimum reinforcement)| Step | Value | Ref. |
|---|
| Cracking force for the first crackkt·fctm·Ai | Ncr = 249 kN | § 4.4.1.3 |
|---|
| Bar stress at the crackNcr/As | σs,r = 155 N/mm² | |
|---|
| Bar stress at first crackingσs,r/σs,adm | η = 0.378 · Pass38 % of the capacity used | Table 17 |
|---|
Calculation: Check 2 — bar stress under the quasi-permanent force| Step | Value | Ref. |
|---|
| Bar stress under NqpNqp/As (at a crack) | σs,qp = 183 N/mm² | |
|---|
| Bar stress under the quasi-permanent forceσs,qp/σs,adm | η = 0.449 · Pass45 % of the capacity used | Table 17 |
|---|
Calculation: Check 3 — no yielding of the bars| Step | Value | Ref. |
|---|
| Bar stress under NraNra/As | σs,ra = 249 N/mm² | |
|---|
| Bar stress against fyd − 80 N/mm²σs,ra/(fyd − 80) | η = 0.701 · Pass70 % of the capacity used | Table 17 |
|---|
Calculation: Check 4 — crack width under N_qp (EN 1992-1-1 §7.3.4)| Step | Value | Ref. |
|---|
| Depth of the effective tension band along each facemin(2.5·a ; t/2) | hc,ef = 115 mm | EN 1992-1-1 §7.3.2(3) |
|---|
| Effective tension areaband of depth hc,ef along every face | Ac,eff = 85,100 mm² | |
|---|
| Effective reinforcement ratioAs/Ac,eff | ρp,eff = 1.89 % | EN 1992-1-1 §7.3.4 (7.10) |
|---|
| Maximum crack spacingk3·c + k1·k2·k4·φ/ρp,eff, k2 = 1.0 | sr,max = 417 mm | EN 1992-1-1 §7.3.4 (7.11) |
|---|
| Mean strain difference, steel to concrete[σs − kt·fct,eff/ρp,eff·(1 + αe·ρp,eff)]/Es ≥ 0.6·σs/Es, kt = 0.4σs = 183 N/mm² | εsm − εcm = 0.603 ‰ | EN 1992-1-1 §7.3.4 (7.9) |
|---|
| Crack widthsr,max·(εsm − εcm) | wk = 0.251 mm | EN 1992-1-1 §7.3.4 (7.8) |
|---|
| Crack width against the limitwk/wmax | η = 0.838 · Pass84 % of the capacity used | EN 1992-1-1 §7.3.1 |
|---|
Calculation: Elongation under the quasi-permanent force| Step | Value | Ref. |
|---|
| Strain, uncracked (long term)Nqp/(Ec,eff·Ai,eff) | εI = 0.231 ‰ | |
|---|
| Strain at a crack (bare bars)Nqp/(Es·As) | εII = 0.895 ‰ | |
|---|
| Distribution coefficient1 − β·(Ncr,∞/Nqp)², β = 0.5; 0 if uncracked | ζ = 0.885 | EN 1992-1-1 §7.4.3 (7.19) |
|---|
| Mean strain from the forceζ·εII + (1 − ζ)·εI | εm = 0.819 ‰ | EN 1992-1-1 §7.4.3 (7.18) |
|---|
| Shortening from restrained shrinkage (uncracked parts)σs,cs/Es | (1 − ζ)·εs,cs = -0.034 ‰ | |
|---|
| Mean strain of the tie | εtot = 0.785 ‰ | |
|---|
| Elongation of the tieεtot·l | Δl = 6.28 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 does shrinkage lower the cracking force?
The bars restrain the shrinkage of the concrete, which leaves a tensile stress σc,cs in it and uses up part of its tensile strength. In the worked example the cracking force falls from 249 kN at loading to 141 kN in the long term.
Why is the elongation smaller than that of the bare bars?
Between the cracks the concrete still carries tension. ζ weighs the cracked strain εII against the uncracked strain εI.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
Norm: SIA 262:2025 · Page updated: 29 October 2026