Structural Engineering Tools

Reinforced concrete slab serviceability to SIA 262

Checks a strip of reinforced concrete slab under uniform, partial and line loads in service, to SIA 262:2025: the moments of the load combinations, concrete compression and creep, bar stresses and crack control, crack width, long-term deflection with cracking, creep and shrinkage, finishes, comfort and natural frequency. 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 strip of reinforced concrete slab under uniform, partial and line loads in service, to SIA 262:2025: the moments of the load combinations, concrete compression and creep, bar stresses and crack control, crack width, long-term deflection with cracking, creep and shrinkage, finishes, comfort and natural frequency. Every step shows its formula and the clause it comes from.

What it checks

  • Load combinations: the self-weight g1 = γRC · h is added to the loads entered; for each combination, ΣF, RA, RB, MA = −ηA · M0,max, Mmax at xM and MB = −ηB · M0,max, per metre of width, then Mqp, Mfr and Mra at the critical sections.
  • Section per metre of width: as and a′s, d and d′sup, with fcm = fck + 8, clause 3.1.2.2.3, equation (6).
  • Cracking moments Mcr and M′cr (4.2.1.14), 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).
  • Bar stresses in the span and over the support against σs,adm = √(9 · Es · fctm · wnom / Øs) ≤ fyk, clause 4.4.2.3.4, equation (102), with wnom from Table 17: at first cracking (minimum reinforcement, 4.4.2.3.3) and under the quasi-permanent load.
  • No yielding: σs,ra ≤ fyd − 80 N/mm² under the characteristic combination (Table 17).
  • Crack width (optional) to EN 1992-1-1 §7.3.4, equations (7.8) to (7.11), against wmax.
  • Deflection: wc (4.4.3.2.4), the estimates wcφ = wc · (1 + φ), equation (103), and w104 = (1 − 20 · ρ′)/(10 · ρ^0.7) · (0.75 + 0.1 · φ) · (h/d)³ · wc, clause 4.4.3.2.5, equation (104), and a detailed calculation of the curvatures along the span to EN 1992-1-1 §7.4.3, equations (7.18) to (7.21).
  • Deflection limits (4.4.3.2.1): w∞ for appearance, Δw = w∞ − wg1,0 for finishes and partitions, and wq,fr under ψ1 · qk for comfort.
  • Natural frequency f1 ≥ fmin (4.4.4.2), from the Rayleigh quotient of the static deflection curve.

What you enter and what you get

You enter the static system (simply supported, fixed at one or both ends, or a span of a continuous member with the support moments ηA and ηB as fractions of M0, the largest moment of the same loads on a simple span), the span l and, for a panel spanning both ways, the share α of the load carried by this strip. Then h, the bottom bars Ø at s with cover c, the top bars Ø′ at s′ with cover c′, whether the top bars run through the span, the materials, the creep and shrinkage data and the faces exposed to drying. You enter up to five uniform loads, each on the whole span or on a part of it, and up to five line loads across the strip at x1, each with a permanent and a variable part (g2,1 and q1, G1 and Q1 for the first), then ψ1 and ψ2, the requirement level, the crack width option and the deflection limits as fractions of the span.

You get φ and εcs, the section stiffnesses, the support forces and moments of each load combination, the moments at the critical sections, every check with its utilisation and clause, and both deflection estimates. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

  • Moments come from an elastic, uncracked analysis; the redistribution caused by cracking is not followed.
  • ηA and ηB apply to every load combination: take them from an elastic analysis of the continuous member under a similar layout of the loads.
  • A line load is entered in kN per metre of width; a load on a small area is entered divided by the width over which it is spread.
  • A two-way panel is checked as a beam strip under α · p, with α from your plate analysis.
  • The bottom bars are assumed to run to the supports.
  • φ follows EN 1992-1-1 Annex B and εcs EN 1992-1-1 §3.1.4, or your own values. The notional size h0 = 2 · Ac/u counts only the faces exposed to drying.
  • Equation (104) is an upper bound (4.4.3.2.6). The detailed calculation is the detailed study of 4.4.3.2.3.
  • For finishes, the creep under g1 before they are placed is counted as occurring after, on the safe side.

Worked example

A 240 mm slab, end span of a continuous slab with l = 6 m, Ø12 at 150 mm at the bottom and Ø14 at 150 mm over the support, fck = 30 N/mm², g2,1 = 2 kN/m² and q1 = 2 kN/m² on the whole span, a further q2 = 2 kN/m² from 3 m to 6 m, a permanent line load G1 = 4 kN/m at 2 m, increased requirements, wmax = 0.3 mm and fmin = 5 Hz. These are the module's own results for its worked example, computed when this page was built.

Inputs
InputValueRef.
Support conditions of the spanSpan of a continuous member
Moment at the left support, fraction of M0 ηA0
Moment at the right support, fraction of M0 ηB1
Span l6 m
Slab thickness h240 mm
Bottom bars: diameter Ø12 mm
Bottom bars: spacing s150 mm
Bottom bars: concrete cover c30 mm
Top bars over the supports: diameter Ø′14 mm
Top bars over the supports: spacing s′150 mm
Top bars: concrete cover c′30 mm
Do the top bars run through the span?No
Characteristic compressive strength fck30 N/mm²§ 3.1.2.2.2
Mean tensile strength fctm2.9 N/mm²§ 3.1.2.2.4
Modulus of elasticity Ecm32000 N/mm²§ 3.1.2.3.3
Unit weight of reinforced concrete γRC25 kN/m³
Characteristic yield strength fyk500 N/mm²
Modulus of elasticity Es205000 N/mm²
Resistance factor for steel γs1.15§ 2.4.2.6
Creep coefficient φComputed (EN 1992-1-1 Annex B)§ 3.1.2.6
Relative humidity of the environment RH50 %
Cement classN — normal hardening
Age of the concrete at loading t028 days
Age considered (service life) t50 years
Shrinkage strain εcsComputed (EN 1992-1-1 §3.1.4)§ 3.1.2.7
Age at the end of curing ts7 days
Faces of the slab exposed to dryingBoth faces
Number of uniform loads2
ExtentWhole span
Permanent part g2,12 kN/m²
Variable part q12 kN/m²
ExtentPart of the span
Starts at, from the left support a23 m
Ends at, from the left support b26 m
Permanent part g2,20 kN/m²
Variable part q22 kN/m²
Number of line loads1
Position, from the left support x12 m
Permanent part G14 kN/m
Variable part Q10 kN/m
Combination factor, frequent ψ10.5
Combination factor, quasi-permanent ψ20.3
Requirement levelIncreased§ 4.4.2.2.3
Tensile strength for the first crackMean tensile strength (4.4.1.3)§ 4.4.1.3
Exposure to chlorides, frost or sea water?No — X0 or XCEN 1992-1-1 §7.2(2)
Compute the crack width?Yes
Bond of the bars k1High-bond bars (0.8)EN 1992-1-1 §7.3.4(3)
Crack spacing factor for the cover k33.4EN 1992-1-1 §7.3.4(3)
Crack spacing factor for the bond length k40.425EN 1992-1-1 §7.3.4(3)
Limiting crack width (optional) wmax0.3 mm
Deflection used in the checksDetailed — curvatures along the span§ 4.4.3.2.3
Limit for appearance: l divided by l/wadm300§ 4.4.3.1.1
Check the deflection after the finishes are placed?Checked
Limit: l divided by l/wadm500§ 4.4.3.2.1
Check the deflection under the frequent variable load?Checked
Limit: l divided by l/wadm350§ 4.4.3.2.1
Check the natural frequency?Checked§ 4.4.4.1
Lowest admissible natural frequency fmin5 Hz§ 4.4.4.2
Calculation: Self-weight
StepValueRef.
Self-weightγRC·hg1 = 6.00 kN/m²
Calculation: Load combinations and their moments
Step1Quasi-permanentg + ψ2·q2Frequentg + ψ1·q3Characteristicg + qRef.
Total load on the span ΣF kN per mg1 + the loads of the combination57.461.070.0
Force at the left support RA kN per m21.622.625.2
Force at the right support RB kN per m35.838.444.8
Moment at the left support MA kNm per m−ηA·M0,max0.00.00.0
Largest moment in the span Mmax kNm per m25.927.330.6
Its position, from the left support xM m2.042.072.12
Moment at the right support MB kNm per m−ηB·M0,max-44.1-46.8-53.5
Calculation: Section
StepValueRef.
Slab thicknessper metre of width, b = 1000 mmh = 240 mm
Bottom barsπ·Ø²/4·1000/s — Ø12 @ 150 mmas = 754 mm²/m
Effective depth of the bottom barsh − c − Ø/2d = 204 mm
Top bars over the supportsØ14 @ 150 mma′s = 1,026 mm²/m
Effective depth of the top bars (from the bottom face)h − c′ − Ø′/2d′sup = 203 mm
Calculation: Materials
StepValueRef.
Mean compressive strengthfck + 8fcm = 38.0 N/mm²§ 3.1.2.2.3 (6)
Design yield strength of the barsfyk/γsfyd = 434.8 N/mm²§ 2.4.2.5 (4)
Short-term modular ratioEs/Ecmαe = 6.41
Calculation: Creep
StepValueRef.
Notional size2·Ac/u, u = 2,000 mm per metreh0 = 240 mmEN 1992-1-1 Annex B (B.6)
Humidity factor[1 + (1 − RH/100)/(0.1·∛h0)·α1]·α2φRH = 1.731EN 1992-1-1 Annex B (B.3)
Strength factor16.8/√fcmβ(fcm) = 2.725EN 1992-1-1 Annex B (B.4)
Age at loading adjusted for the cementt0·(9/(2 + t0^1.2) + 1)^α ≥ 0.5, α = 0t0,adj = 28.0 daysEN 1992-1-1 Annex B (B.9)
Age factor1/(0.1 + t0^0.2)β(t0) = 0.488EN 1992-1-1 Annex B (B.5)
Notional creep coefficientφRH·β(fcm)·β(t0)φ0 = 2.304EN 1992-1-1 Annex B (B.2)
Humidity–size coefficient1.5·[1 + (0.012·RH)^18]·h0 + 250·α3 ≤ 1500·α3βH = 600 daysEN 1992-1-1 Annex B (B.8)
Development with time[(t − t0)/(βH + t − t0)]^0.3, t = 18,250 daysβc(t, t0) = 0.990EN 1992-1-1 Annex B (B.7)
Creep coefficientφ0·βc(t, t0)valid for compressive stresses up to 0.45·fck at loadingφ(t, t0) = 2.28EN 1992-1-1 Annex B (B.1)
Calculation: Shrinkage
StepValueRef.
Humidity factor1.55·[1 − (RH/100)³]βRH = 1.356EN 1992-1-1 Annex B (B.12)
Basic drying shrinkage0.85·[(220 + 110·αds1)·exp(−αds2·fcm/10)]·10⁻⁶·βRHεcd,0 = 0.482 ‰EN 1992-1-1 Annex B (B.11)
Size coefficientfrom h0, linear between the values of Table 3.3kh = 0.810EN 1992-1-1 §3.1.4(6)
Development of drying(t − ts)/[(t − ts) + 0.04·√h0³]βds(t, ts) = 0.992EN 1992-1-1 §3.1.4 (3.10)
Drying shrinkageβds·kh·εcd,0εcd = 0.387 ‰EN 1992-1-1 §3.1.4 (3.9)
Final autogenous shrinkage2.5·(fck − 10)·10⁻⁶εca,∞ = 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 + εcaεcs = 0.437 ‰EN 1992-1-1 §3.1.4 (3.8)
Calculation: Cracking of the sections
StepValueRef.
Size factor1/(1 + 0.5·t), t = h/3 in mkt = 0.962§ 4.4.1.3 (100)
Effective tensile strengthkt·fctmfor the cracking moments and the deflectionfct,eff = 2.79 N/mm²§ 4.4.1.3 (99)
Cracking moment, span section (sagging)fct,eff·II/(h − yI), uncracked section with αeMcr = 27.8 kNm§ 4.2.1.14
Cracking moment, support section (hogging)fct,eff·II/yI, tension at the top faceM′cr = 28.4 kNm§ 4.2.1.14
Calculation: Stiffness of the sections
StepValueRef.
Effective long-term modulusEcm/(1 + φ)φ of the creep part above; increased later if the concrete stress exceeds 0.4·fcmEc,eff = 9,751 N/mm²EN 1992-1-1 §7.4.3 (7.20)
Long-term modular ratioEs/Ec,effαe,∞ = 21.02
Gross concrete section, spanb·h³/12Ic = 1,152 10⁶ mm⁴
Uncracked section, long term, spanconcrete + αe,∞·barsII = 1,252 10⁶ mm⁴
Cracked section, long term, spancompressed concrete + αe,∞·barsneutral axis xII = 66 mm from the topIII = 398 10⁶ mm⁴
Uncracked section, long term, supportI′I = 1,399 10⁶ mm⁴
Cracked section, long term, supportcompression at the bottom; xII = 69 mm from the bottomI′II = 513 10⁶ mm⁴
Calculation: Bending moments at the critical sections
StepValueRef.
Span (x = 2.13 m)cracked: |Mra| > Mcr = 27.8 kNmMqp ; Mfr ; Mra = 25.9 ; 27.2 ; 30.6 kNm
Right supportcracked: |Mra| > Mcr = 28.4 kNmMqp ; Mfr ; Mra = -44.1 ; -46.8 ; -53.5 kNm
Calculation: Check 1 — concrete compression under the quasi-permanent load
StepValueRef.
Largest compression at loading (right support)cracked section, Ecm|σc,qp| = 10.14 N/mm²
Stress–strength ratio|σc|/fcm = 0.267
Concrete compression within the range of the creep model|σc,qp|/(0.6·fcm)η = 0.445 · Pass44 % of the capacity used§ 3.1.2.6.3
Calculation: Admissible bar stress
StepValueRef.
Nominal crack widthincreased requirementswnom = 0.5 mmTable 17
Admissible bar stress, span√(9·Es·fctm·wnom/Øs) ≤ fyk, Øs = 12 mmσs,adm = 472 N/mm²§ 4.4.2.3.4 (102)
Admissible bar stress, right support√(9·Es·fctm·wnom/Øs) ≤ fyk, Øs = 14 mmσs,adm = 437 N/mm²§ 4.4.2.3.4 (102)
Calculation: Check 2 — bar stress when the section cracks, span
StepValueRef.
Cracking moment for the first crackwith fct,eff = kt·fctmMcr = 27.8 kNm§ 4.4.1.3
Bar stress just after crackingcracked section under Mcr, Ecmσs,r = 193 N/mm²
Bar stress at first cracking (minimum reinforcement)σs,r/σs,admη = 0.409 · Pass41 % of the capacity usedTable 17
Calculation: Check 3 — bar stress when the section cracks, right support
StepValueRef.
Cracking moment for the first crackwith fct,eff = kt·fctmMcr = 28.4 kNm§ 4.4.1.3
Bar stress just after crackingcracked section under Mcr, Ecmσs,r = 148 N/mm²
Bar stress at first cracking (minimum reinforcement)σs,r/σs,admη = 0.338 · Pass34 % of the capacity usedTable 17
Calculation: Check 4 — bar stress under the quasi-permanent load, span
StepValueRef.
Bar stress under the quasi-permanent loadcracked section, Ec,effcompression in the concrete -4.31 N/mm² (long term)σs,qp = 189 N/mm²
Bar stress under the quasi-permanent loadσs,qp/σs,admη = 0.400 · Pass40 % of the capacity usedTable 17
Calculation: Check 5 — bar stress under the quasi-permanent load, right support
StepValueRef.
Bar stress under the quasi-permanent loadcracked section, Ec,effcompression in the concrete -5.94 N/mm² (long term)σs,qp = 242 N/mm²
Bar stress under the quasi-permanent loadσs,qp/σs,admη = 0.553 · Pass55 % of the capacity usedTable 17
Calculation: Check 6 — no yielding of the bars, span
StepValueRef.
Bar stress under the characteristic combinationcracked section, Ecmσs,ra = 213 N/mm²
Bar stress against fyd − 80 N/mm²σs,ra/(fyd − 80)η = 0.599 · Pass60 % of the capacity usedTable 17
Calculation: Check 7 — no yielding of the bars, right support
StepValueRef.
Bar stress under the characteristic combinationcracked section, Ecmσs,ra = 278 N/mm²
Bar stress against fyd − 80 N/mm²σs,ra/(fyd − 80)η = 0.784 · Pass78 % of the capacity usedTable 17
Calculation: Check 8 — crack width, span (EN 1992-1-1 §7.3.4)
StepValueRef.
Depth of the effective tension areamin(2.5·(h − d) ; (h − x)/3 ; h/2)hc,ef = 58 mmEN 1992-1-1 §7.3.2(3)
Effective tension areab·hc,efAc,eff = 57,961 mm²
Effective reinforcement ratioAs/Ac,effρp,eff = 1.30 %EN 1992-1-1 §7.3.4 (7.10)
Maximum crack spacingk3·c + k1·k2·k4·φ/ρp,eff, k2 = 0.5 (bending), c = 30 mm, φ = 12 mmsr,max = 259 mmEN 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 = 0.4 (long term)σs = σs,qp = 189 N/mm²; the lower limit governsεsm − εcm = 0.553 ‰EN 1992-1-1 §7.3.4 (7.9)
Crack widthsr,max·(εsm − εcm)wk = 0.143 mmEN 1992-1-1 §7.3.4 (7.8)
Crack width against the limitwk/wmaxη = 0.477 · Pass48 % of the capacity usedEN 1992-1-1 §7.3.1
Calculation: Check 9 — crack width, right support (EN 1992-1-1 §7.3.4)
StepValueRef.
Depth of the effective tension areamin(2.5·(h − d) ; (h − x)/3 ; h/2)hc,ef = 57 mmEN 1992-1-1 §7.3.2(3)
Effective tension areab·hc,efAc,eff = 56,961 mm²
Effective reinforcement ratioAs/Ac,effρp,eff = 1.80 %EN 1992-1-1 §7.3.4 (7.10)
Maximum crack spacingk3·c + k1·k2·k4·φ/ρp,eff, k2 = 0.5 (bending), c = 30 mm, φ = 14 mmsr,max = 234 mmEN 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 = 0.4 (long term)σs = σs,qp = 242 N/mm²εsm − εcm = 0.843 ‰EN 1992-1-1 §7.3.4 (7.9)
Crack widthsr,max·(εsm − εcm)wk = 0.197 mmEN 1992-1-1 §7.3.4 (7.8)
Crack width against the limitwk/wmaxη = 0.657 · Pass66 % of the capacity usedEN 1992-1-1 §7.3.1
Calculation: Elastic deflection
StepValueRef.
Elastic deflection, gross concrete section∬ Mqp/(Ecm·Ic) dx dx, with the support conditionsquasi-permanent load, uncracked, short termwc = 1.88 mm§ 4.4.3.2.4
Calculation: SIA estimate
StepValueRef.
Creep coefficient usedfrom the section partφ = 2.28
Uncracked, with creepwc·(1 + φ)valid: the quasi-permanent moment stays below Mcrwcφ = 6.17 mm§ 4.4.3.2.4 (103)
Tension reinforcement ratioAs/(b·d)span sectionρ = 0.370 %
Compression reinforcement ratioA′s/(b·d)ρ′ = 0.000 %
Largely cracked, with creep(1 − 20·ρ′)/(10·ρ^0.7)·(0.75 + 0.1·φ)·(h/d)³·wcw104 = 15.10 mm§ 4.4.3.2.5 (104)
Calculation: Detailed calculation
StepValueRef.
Effective modulusEcm/(1 + φ)Ec,eff = 9,751 N/mm²EN 1992-1-1 §7.4.3 (7.20)
Shrinkage strainfrom the section partεcs = 0.437 ‰
Distribution coefficient at the point of largest deflection1 − β·(Mcr/M)², β = 0.5 (sustained load); 0 where M ≤ Mcrζ = 0.000EN 1992-1-1 §7.4.3 (7.19)
Deflection if uncracked everywherecurvatures M/(Ec,eff·II) + shrinkagewI,∞ = 7.37 mm
Deflection if fully crackedcurvatures M/(Ec,eff·III) + shrinkagewII,∞ = 26.57 mm
Part due to shrinkageεcs·αe·S/I, weighted by ζwcs = 1.58 mmEN 1992-1-1 §7.4.3 (7.21)
Long-term deflection, quasi-permanent loadκ = ζ·κII + (1 − ζ)·κI, integrated twicew∞ = 7.19 mmEN 1992-1-1 §7.4.3 (7.18)
Instantaneous deflection under the self-weightEcm, cracking with β = 1wg1,0 = 1.12 mm
Calculation: Check 1 — appearance: long-term deflection
StepValueRef.
Admissible deflectionl/300wadm = 20.0 mm
Long-term deflection for appearancew∞/wadmη = 0.360 · Pass36 % of the capacity used§ 4.4.3.2.1
Calculation: Check 2 — damage to finishes: deflection after they are placed
StepValueRef.
Deflection after the finishes are placedw∞ − wg1,0Δw = 6.07 mm
Deflection after the finishes are placedΔw/wadmη = 0.506 · Pass51 % of the capacity used§ 4.4.3.2.1
Calculation: Check 3 — comfort: deflection under the frequent variable load
StepValueRef.
Short-term deflection from ψ1·qkw(g + ψ1·qk) − w(g), Ecm, β = 1wq,fr = 0.23 mmEN 1992-1-1 §7.4.3
Deflection under the frequent variable loadwq,fr/wadmη = 0.013 · Pass1 % of the capacity used§ 4.4.3.2.1
Calculation: Check 4 — natural frequency
StepValueRef.
Mass on the spanquasi-permanent loads/gdistributed as the loads arem = 5,851 kg per m
Short-term deflection under that massEcm, cracking with β = 1wqp,0 = 1.79 mm
First natural frequency(1/2π)·√(g·Σm·w/Σm·w²), Rayleigh quotient of the static deflection curvef1 = 13.26 Hz
Natural frequency above the limitfmin/f1η = 0.377 · Pass38 % of the capacity used§ 4.4.4.2

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 is equation (103) valid in the worked example?

The quasi-permanent moment in the span, 25.9 kNm, stays below Mcr = 27.8 kNm. The distribution coefficient ζ at the point of largest deflection is then 0, and equation (104) gives an upper bound only.

Which deflection is used in the checks?

You choose. The detailed calculation follows the curvatures along the span. The SIA estimate takes equation (103) when the span stays uncracked, otherwise equation (104). Both are always shown.

Which plan includes this module?

The Basic plan, with its calculation note.

Related

Norm: SIA 262:2025 · Page updated: 5 November 2026