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Foundation Design: worked example
An isolated pad footing checked for bearing pressure, bending, punching shear and one-way shear.
EN 1992-1-1:2004 — Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings · SI units · Calculator v1.0
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Inputs
| Foundation type | Isolated |
| Concrete | C25/30 |
| Reinforcing steel | B500 (fyk 500) |
| Cover | 75 mm |
| Allowable bearing pressure | 200 kPa |
| Surcharge | 0 kPa |
| Footing B × L | 2.6 × 2.6 m |
| Thickness h | 550 mm |
| Column cx × cy | 400 × 400 mm |
| Axial load ND / NL | 800 / 400 kN |
| Moment MD / ML | 0 / 0 kN·m |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Soil bearing | 190.7 kPa | 200.0 kPa | 95.4% | PASS |
| Flexure ∥ L | 2027 mm² | 2212 mm² | 91.6% | PASS |
| Flexure ∥ B | 2099 mm² | 2212 mm² | 94.9% | PASS |
| One-way shear (∥ B) | 419.4 kN | 441.2 kN | 95.0% | PASS |
| Punching shear | 0.628 MPa | 0.749 MPa | 83.9% | PASS |
| Development | 592 mm | 1025 mm | 57.7% | PASS |
Calculation steps
Bearing & sizing (service) (5 steps)
Service load on soil (self-weight + surcharge included)
P = N_D + N_L + W_f + q_s·A
P = 800 + 400 + 89.2 + 0.0
P = 1289.2 kN
Eccentricity along L
e = M/P
e = 0.0/1289.2
e = 0 mm ≤ L/6 = 433 mm
Peak service pressure
q = P/A · (1 ± 6e/L)
A = 6.76 m²
q_max = 190.7 kPa, q_min = 190.7 kPa
EN 1997 / geotech
Allowable pressure comparison
q_max ≤ q_allow (from the geotechnical report)
190.7 vs 200.0
Ratio = 0.954 → OK
Suggested minimum area (concentric)
A_req = P/q_allow
A_req = 1289.2/200.0
A_req = 6.45 m² (provided 6.76 m²)
Factored net pressure (strength) (2 steps)
EN 1990
Factored column load (net — footing weight causes no footing shear/moment)
Pu = 1.35·N_D + 1.5·N_L; Mu = 1.35·M_D + 1.5·M_L
Pu = 1.35×800 + 1.5×400
Pu = 1680.0 kN, Mu = 0.0 kN·m
Net factored pressure distribution along L
q_u = Pu/A · (1 ± 6e_u/L)
e_u = 0 mm
q_u = 248.5 … 248.5 kPa (avg 248.5)
Flexure (critical sections at column faces) (6 steps)
EC2 9.8
Cantilever moments at the column faces
M = ∫q_u·x dA over the cantilever
cant_L = 1100 mm (q from 248.5 kPa edge), cant_B = 1100 mm (avg q)
Mu,L = 390.9 kN·m; Mu,B = 390.9 kN·m
EC2 6.1
Bending along L: section design
K = MEd/(b·d²·fck); z = d·[0.5+√(0.25−K/1.134)] ≤ 0.95d
K = 390.9×10⁶/(2600×467²×25) = 0.0276
z = 444 mm
EC2 6.1
Bending along L: required steel
As = MEd/(fyd·z), fyd = fyk/1.15
As = 390.9×10⁶/(435×444)
As,req = 2027 mm²
EC2 6.1
Bending along B: section design
K = MEd/(b·d²·fck); z = d·[0.5+√(0.25−K/1.134)] ≤ 0.95d
K = 390.9×10⁶/(2600×451²×25) = 0.0296
z = 428 mm
EC2 6.1
Bending along B: required steel
As = MEd/(fyd·z), fyd = fyk/1.15
As = 390.9×10⁶/(435×428)
As,req = 2099 mm²
EC2 9.2.1.1 / 9.3.1.1
Minimum reinforcement
As,min = max(0.26·fctm/fyk, 0.0013)·b·d
along L: 1619 mm²; along B: 1564 mm²
Provide: 11φ16 @ 236 mm ∥L; 11φ16 @ 236 mm ∥B
One-way (beam) shear (4 steps)
EC2 6.2.2
Critical sections at d from each column face
V = resultant of q_u outside the section
x_L = 633 mm, x_B = 649 mm from edges
Vu,L = 409.0 kN; Vu,B = 419.4 kN
Concrete shear resistance ∥ L
VRd,c = max(0.12·k·(100ρ·fck)^⅓, vmin)·b·d
k = 1.654, ρl = 0.182%, vRd,c = 0.372 MPa
VRd,c = 452.2 kN → ratio 0.905
Concrete shear resistance ∥ B
same provision, d of the upper layer
k = 1.666, ρl = 0.189%, vRd,c = 0.376 MPa
VRd,c = 441.2 kN → ratio 0.950
EC2 6.2.2(6)
Note
Loads within 2d of the face may be reduced by a_v/2d — enhancement conservatively ignored here
Conservative
Two-way (punching) shear (4 steps)
EC2 6.4.4(2)
Foundation punching: perimeters within 2d, resistance enhanced by 2d/a, load reduced by soil reaction inside
vEd = β·VEd,red/(u·d) ≤ vRd,c·2d/a
checked a = 2d and a = d; β = 1.00
governing a = 1.0d
At a = 2d
u = 7368 mm, VEd,red = 617.3 kN
u = 7368 mm at a = 2.00d, β = 1.00, vRd,c·2d/a = 0.374 MPa
vEd = 0.183 vs 0.374 MPa → 48.8%
At a = d
u = 4484 mm, VEd,red = 1293.2 kN
u = 4484 mm at a = 1.00d, β = 1.00, vRd,c·2d/a = 0.749 MPa
vEd = 0.628 vs 0.749 MPa → 83.9%
EC2 6.4.5(3)
Maximum shear at the column perimeter
vEd,0 = β·VEd/(u0·d) ≤ vRd,max
u0 = 1600 mm, ν = 0.540, vRd,max = 4.50 MPa
vEd,0 = 2.288 MPa → 50.8% OK
Development / anchorage (1 steps)
EC2 8.4.3 / 8.4.4
Straight development of bottom bars beyond the column face
lbd = (φ/4)·(σsd/fbd) ≥ max(0.3·lb,rqd, 10φ, 100)
available = cantilever − end cover = 1100 − 75
required 592 mm vs available 1025 mm → OK (straight)
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.
- Flexure uses the αcc = 0.85 lever-arm form, z = d·[0.5 + √(0.25 − K/1.134)] ≤ 0.95d.
- Punching shear at the column face uses vRd,max = 0.5·ν·fcd with fcd = fck/1.5 (αcc = 1.0).
- γc = 1.5 and γs = 1.15 (fixed); actions γG = 1.35, γQ = 1.5.
- Bearing pressure and capacity checks assume rigid-footing behavior with a linear soil-pressure distribution — not a full soil-structure-interaction (FEM) analysis.
- Allowable bearing pressure and pile capacities must come from an actual geotechnical investigation for the site — this tool never assumes or estimates them.
- Mat/raft foundations use a simplified rigid-strip moment estimate (Mu ≈ qu·l²/10 per metre width), explicitly flagged PRELIMINARY in the results — not a substitute for a proper plate/FEM analysis of the actual mat.
- Strength checks use the gravity load combination only (1.35G + 1.5Q per EC2, 1.2D + 1.6L per ACI) — ACI’s 1.4D combination can govern when live load is below 12.5% of dead, and lateral load combinations aren’t covered.
- One-way and punching (two-way) shear are checked at the code-specified critical sections (d and d/2 from the column/pile face).
- Verify all provisions against the governing code edition and applicable National Annex before use.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.