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RC Slab Design: worked example
A reinforced concrete slab panel checked for flexure, shear, deflection, crack control and bar spacing.
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
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Inputs
| Slab type | One-way |
| Clear span lx | 5000 mm |
| Thickness h | 220 mm |
| Design strip width b | 1000 mm |
| Support condition | simply supported |
| Concrete | C30/37 |
| Reinforcing steel | B500S |
| Nominal cover cnom | 25 mm |
| Added dead load gk | 1.5 kN/m² |
| Live load qk | 3 kN/m² |
| Main bar (x) spacing | T12 @ 175 mm |
| Main bar (y) spacing | T10 @ 250 mm |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Flexure As (x) | 558 mm²/m | 646 mm²/m | 86.4% | PASS |
| As,min (x) | 285 mm²/m | 646 mm²/m | 44.1% | PASS |
| Secondary As (y) | 246 mm²/m | 314 mm²/m | 78.2% | PASS |
| Bar spacing (x) | ≤ 400 mm | 175 mm | 43.8% | PASS |
| Bar spacing (y) | ≤ 450 mm | 250 mm | 55.6% | PASS |
| Shear VRd,c | VEd = 34.9 kN/m | 102.5 kN/m | 34.0% | PASS |
| Deflection l/d (x) | ≤ 37.4 | 26.5 | 70.7% | PASS |
| Crack width wk | ≤ 0.4 mm | 0.210 mm | 52.5% | PASS |
Calculation steps
Flexural Design (11 steps)
EC2 §3.1.6(1)
Design concrete strength
fcd = 0.85·fck/γc
fcd = 0.85 × 30 / 1.5
fcd = 17.00 MPa
EC2 §3.2.7(2)
Design steel strength
fyd = fyk/γs
fyd = 500 / 1.15
fyd = 434.8 MPa
Effective depths
dx = h − cnom − φx/2; dy = h − cnom − φx − φy/2
dx = 189.0 mm, dy = 178.0 mm
EC2 Table
Design moment (span)
M⁺Ed = β × ned × lx²
M⁺Ed = 0.1250 × 13.95 × 5.000²
M⁺Ed = 43.59 kN·m/m
EC2 §6.1(4)
Flexural design (x-direction, span)
K = MEd/(b·d²·fck)
K = 43593750 / (1000 × 189.0² × 30)
K = 0.0407
EC2 §6.1(4)
Lever arm
z = d·min(0.5+√(0.25−K/1.134), 0.95)
z = 189.0 × min(0.5+√(0.25−0.0407/1.134), 0.95)
z = 179.5 mm
EC2 §6.1(4)
Required reinforcement (span)
As,req = MEd/(fyd·z)
As,req = 43593750 / (434.8 × 179.5)
As,req,x = 558 mm²/m
EC2 §9.3.1.1(1)
Minimum main reinforcement
As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d)
As,min = max(0.26×2.9/500×1000×189.0, 0.0013×1000×189.0)
As,min = 285 mm²/m
EC2 §9.3.1.1(2)
Secondary (transverse) reinforcement
As,sec ≥ 0.2·As,main
As,sec = 0.2 × 558
As,min,y = 246 mm²/m
EC2 §9.2.1.1(3)
Maximum reinforcement
As,max = 0.04·b·h
As,max = 0.04 × 1000 × 220
As,max = 8800 mm²/m
Provided reinforcement
As,prov = π·φ²/4 × (1000/s)
As,prov,x = 646 mm²/m, As,prov,y = 314 mm²/m
Shear Check (4 steps)
EC2 §6.2
Design shear force
VEd per support type
ned = 13.95 kN/m², lx = 5.000 m
VEd = 34.88 kN/m
EC2 §6.2.2(1)
Size effect factor
k = min(1 + √(200/d), 2.0)
k = min(1 + √(200/189.0), 2.0)
k = 2.000
EC2 §6.2.2(1)
Concrete shear resistance
VRd,c = max[CRd,c·k·(100ρl·fck)^⅓·b·d, vmin·b·d]
ρl = 0.00342, vmin = 0.542
VRd,c = 102.48 kN/m
EC2 §6.2.1(4)
Shear check (no shear links typical for slabs)
VEd ≤ VRd,c
34.88 ≤ 102.48
✓ No shear reinforcement needed
Spacing Check (3 steps)
EC2 §9.3.1.1(3)
Maximum main bar spacing
smax = min(3h, 400mm)
smax = min(3×220, 400)
smax,main = 400 mm
EC2 §9.3.1.1(4)
Maximum secondary bar spacing
smax = min(3.5h, 450mm)
smax = min(3.5×220, 450)
smax,sec = 450 mm
Spacing check
sx = 175 mm ✓, sy = 250 mm ✓
Deflection Check (5 steps)
EC2 §7.4.2(2)
Reference reinforcement ratio
ρ₀ = 10⁻³√fck
ρ₀ = 10⁻³ × √30
ρ₀ = 0.00548, ρ = 0.00342
EC2 Table 7.4N
Structural system factor
K per support type
Support: simply supported
K = 1
EC2 Eq. 7.16a
Basic l/d ratio (ρ ≤ ρ₀)
l/d = K·[11 + 1.5·√fck·ρ₀/ρ + 3.2·√fck·(ρ₀/ρ−1)^1.5]
ρ=0.00342, ρ₀=0.00548
l/d basic = 32.3
EC2 §7.4.2(2)
Steel provision modification
mod = min(As,prov/As,req, 1.5)
mod = min(646/558, 1.5)
mod = 1.16
EC2 §7.4.2
Final span/depth check
l/d actual ≤ l/d allowable
l/d allow = 37.4, l/d actual = 26.5 ✓
Crack Control (6 steps)
EC2 §7.3.2(3)
Cracked elastic neutral axis
x from b·x²/2 = αe·As·(d−x)
αe = Es/Ecm = 6.06, As = 646 mm²/m, d = 189.0 mm
x = 34.8 mm
EC2 §7.3.2(3)
Effective tension area
hc,eff = min(2.5(h−d), (h−x)/3, h/2)
hc,eff = min(77.5, 61.7, 110.0)
hc,eff = 61.7 mm, ρp,eff = 0.0105
EC2 §7.3.4(2)
Steel stress under service load
σs ≈ Ms/(As·0.87d)
σs = 26562500 / (646 × 164.4)
σs = 250.0 MPa
EC2 Eq. 7.11
Maximum crack spacing
sr,max = 3.4·c + 0.425·k₁·k₂·φ/ρp,eff
sr,max = 3.4×25 + 0.425×0.8×0.5×12/0.0105
sr,max = 279.9 mm
EC2 Eq. 7.9
Mean strain difference
(εsm−εcm) = max([σs − kt·fct,eff·(1+αe·ρp,eff)/ρp,eff]/Es, 0.6σs/Es)
kt=0.6, αe=6.06
(εsm−εcm) = 0.7499 × 10⁻³
EC2 Eq. 7.8
Calculated crack width
wk = sr,max · (εsm − εcm)
wk = 279.9 × 0.000750
wk = 0.210 mm ✓ (limit: 0.4 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).
- Rectangular-block lever arm z = d·[0.5 + √(0.25 − K/1.134)] ≤ 0.95d, the αcc = 0.85 form.
- γc = 1.5 and γs = 1.15 (EN 1992-1-1 Table 2.1N, persistent and transient), editable.
- One-way slabs are designed per metre-width strip like a wide shallow beam; two-way slabs use the coefficient method (edge conditions + span ratio), valid up to roughly ly/lx ≈ 2 — beyond that, most codes’ coefficient tables (and this tool) treat it as effectively one-way.
- lx must be entered as the shorter span for the two-way coefficient method to apply correctly — entering spans the wrong way round changes which moment coefficients apply, not just the drawing.
- Self-weight, if not overridden, assumes 25 kN/m³ × thickness — override it for a lightweight mix or to fold finishes/screed into self-weight differently.
- Top (hogging) reinforcement is only computed at edges explicitly marked Continuous.
- Cover, if not manually overridden, is calculated automatically from exposure/structural class.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.