A raft is one thick slab under the whole building. It is modelled as a plate on springs (the Winkler model): the soil under each point pushes back in proportion to how far that point settles. Stiff parts of the raft spread the column loads; the springs give the soil pressure; the plate moments give the steel; each column is checked for punching. Every number below comes from the free STATIX raft foundation calculator with the inputs in step 1.
1. The problem
Input
Value
Design code
SANS 10100-1
Length Lx
14 m
Width Ly
10 m
Depth h
900 mm
Soil stiffness
Subgrade modulus k
k subgrade modulus
15000 kN/m³
Allowable bearing qa, SLS
150 kPa
Columns one per line: name, x, y (m from the lower-left corner), cx, cy (mm), G, Q [, W] (kN)
The raft is divided into a grid of plate elements. Every node rests on a spring of stiffness k (the modulus of subgrade reaction, kN/m³). The plate bends and the springs compress until the column loads and the soil pressure balance.
raft 14.0 × 10.0 m, h = 900 mm, d = 834 mm
k = 15,000 kN/m³, E_c = 24.65 GPa
plate stiffness D = 1,559,726 kNm
3. Soil pressure and settlement
The pressure under the raft is the spring stiffness times the settlement. The largest pressure (at service loads) must stay within the allowable bearing pressure. The difference in settlement across the raft shows how evenly it carries the load; the raft must also stay in contact with the soil everywhere.
[SANS 10160-5 / EN 1997-1 (allowable pressure, SLS)]
SLS G + Q: q = k w, k = 15000 kN/m3; the largest soil pressure under the raft = 90.5 kPa
90.5 ≤ 150.0 kPa OK
[practice (Winkler springs)]
largest 6 mm, smallest 4.2 mm, difference 1.9 mm (SLS); a Winkler model gives no settlement trough beyond the loads - compare with a settlement analysis
INFO
[practice (no tension in the soil)]
the whole raft stays in contact
PASS
4. Bending steel: bottom and top, both ways
A raft works like an upside-down flat slab. The soil pushes up between the columns, so mid-panel the raft bends with the top in tension; under each column the bottom is in tension. The plate moments, with the twisting moment added where it adds (Wood–Armer), are averaged over a strip and give the steel in four layers: bottom and top, along x and along y.
Bottom bars along x: A_s,req <= provided:
[SANS 10100-1 4.4.4, 4.11.4; Wood-Armer (practice)]
M = 496.6 kNm/m at (7.23, 5.45 m), ULS 1,2G + 1,6Q (STR) (Wood-Armer, averaged over 2h = 1800 mm across; the elastic peak 581.8 kNm/m; column footprints left out); d = 842 mm; K = 0.023; A_s,req 1586, minimum 1170 mm2/m; Y16 @ 125 = 1608 mm2/m
1,586 ≤ 1,608 mm²/m OK
Bottom bars along y: A_s,req <= provided:
[SANS 10100-1 4.4.4, 4.11.4; Wood-Armer (practice)]
M = 206.7 kNm/m at (6.55, 4.88 m), ULS 1,2G + 1,6Q (STR) (Wood-Armer, averaged over 2h = 1800 mm across; the elastic peak 291.4 kNm/m; column footprints left out); d = 826 mm; K = 0.010; A_s,req 673, minimum 1170 mm2/m; Y20 @ 250 = 1257 mm2/m
1,170 ≤ 1,257 mm²/m OK
Top bars along x: A_s,req <= provided:
[SANS 10100-1 4.4.4, 4.11.4; Wood-Armer (practice)]
M = 166.1 kNm/m at (2.98, 8.6 m), ULS 1,2G + 1,6Q (STR) (Wood-Armer, averaged over 2h = 1800 mm across; the elastic peak 168.1 kNm/m; column footprints left out); d = 842 mm; K = 0.008; A_s,req 530, minimum 1170 mm2/m; Y20 @ 250 = 1257 mm2/m
1,170 ≤ 1,257 mm²/m OK
Top bars along y: A_s,req <= provided:
[SANS 10100-1 4.4.4, 4.11.4; Wood-Armer (practice)]
M = 269.8 kNm/m at (13.8, 4.16 m), ULS 1,2G + 1,6Q (STR) (Wood-Armer, averaged over 2h = 1800 mm across; the elastic peak 279.2 kNm/m; column footprints left out); d = 826 mm; K = 0.013; A_s,req 878, minimum 1170 mm2/m; Y20 @ 250 = 1257 mm2/m
1,170 ≤ 1,257 mm²/m OK
5. Punching at each column
Each column can punch through the raft. The column load, less the soil pressure inside the perimeter, is checked on the column face and on a perimeter away from it. Corner and edge columns have shorter perimeters, so they are often critical.
Punching at column A1 (corner):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 920 kN, net soil pressure 71.3 kPa deducted; d = 834 mm, rho = 0.172 %. u0=800 mm: v0=1.713 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=4902 mm: v=0.189 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column B1 (edge):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 1440 kN, net soil pressure 84.5 kPa deducted; d = 834 mm, rho = 0.172 %. u0=1200 mm: v0=2.000 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=6204 mm: v=0.245 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column C1 (corner):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 920 kN, net soil pressure 71.3 kPa deducted; d = 834 mm, rho = 0.172 %. u0=800 mm: v0=1.713 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=4902 mm: v=0.189 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column A2 (corner):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 920 kN, net soil pressure 71.3 kPa deducted; d = 834 mm, rho = 0.172 %. u0=800 mm: v0=1.713 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=4902 mm: v=0.189 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column B2 (edge):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 1440 kN, net soil pressure 84.5 kPa deducted; d = 834 mm, rho = 0.172 %. u0=1200 mm: v0=2.000 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=6204 mm: v=0.245 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column C2 (corner):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 920 kN, net soil pressure 71.3 kPa deducted; d = 834 mm, rho = 0.172 %. u0=800 mm: v0=1.713 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=4902 mm: v=0.189 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
Punching at column B0 (interior):
[SANS 10100-1 4.4.5, 4.6.2]
ULS 1,2G + 1,6Q (STR): V_Ed = 2760 kN, net soil pressure 79.9 kPa deducted; d = 834 mm, rho = 0.172 %. u0=2000 mm: v0=1.889 MPa vs v_max=4.108 MPa -> OK; u1 (1.5d)=12008 mm: v=0.234 MPa vs v_c=0.263 MPa -> OK, no links needed
PASS
6. Durability
A raft is cast against the soil, so the cover must suit the exposure.
[SANS 10100-1 4.11.2.2, 4.11.2.4, 4.11.2.10; SANS 2001-CC1:2007 Table 3]
severe (in contact with soil) exposure, class 30 (f_cu 30): Table 3 45 mm; given 50 mm
45 ≤ 50 mm OK
k is a modelling choice, not a soil constant: try a lower and a higher value to see how much the moments change. The calc sheet repeats each step for every load combination.
Run this example yourselfOpen the free STATIX raft foundation calculator and press Load the example (14 × 10 m raft, 7 columns) under "How it is calculated". Change any value and every step updates, with a calc sheet. Open the raft foundation calculator
A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.
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