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Design guide

Pad footing design to Eurocode 2: bearing, bending, punching shear and anchorage

A pad footing to EN 1992-1-1, worked step by step: ground pressure with eccentricity, bending at the face, beam shear, punching shear and anchorage.

Open the footing calculator

A newly cast concrete pad footing with column starter bars in an excavation
Reading time
5 minutes
Standard
EN 1992-1-1
Clauses
6.2.2, 6.4.4, 6.4.5, 9.8.2
Calculator
Footing
Updated
On this page 8 sections
  1. Step 1: Loads on the ground
  2. Step 2: Ground pressure
  3. Step 3: Bending at the face of the column
  4. Step 4: Beam shear
  5. Step 5: Punching shear
  6. Step 6: Anchorage of the bars
  7. The answer
  8. Points to remember

A pad footing spreads a column load over enough ground to keep the bearing pressure within what the soil can take, and must be strong enough itself to carry that pressure back to the column. EN 1992-1-1 covers the concrete design: bending at the face of the column, beam shear, punching shear (6.4) and the anchorage of the bars (9.8.2).

This guide works through the calculator's example: a 2400 × 2400 × 500 mm pad under a 400 × 400 mm column carrying = 900 kN and = 400 kN, with 500 mm of soil over it and a design bearing resistance of 400 kPa.

The answer, worked out below

Ground pressure
343.8 kPa
against σRd = 400 kPa
Moment at the column face
378.13 kNm
bars along L
Bars, each way
19H12 @ 125
As,prov = 2149 mm²
Punching
0.750 MPa
vEd at the governing perimeter

A footing is sized in two passes: its plan from the ground, its depth from the concrete.

Designing a pad footing to EN 1992-1-1
  1. Column load Gk and Qk, a trial base L × B × h
  2. Total load on the ground: column, base and soil over it
  3. Is σmax ≤ σRd, with the load in the middle third?

    Yes

    1. The plan size works

    No

    1. Make the base larger in plan
  4. Net pressure from the column load alone
  5. Bending at each face of the column, bars both ways
  6. Beam shear at d from the face
  7. Punching at the column face, and on perimeters within 2d
  8. Does every check pass?

    Yes

    1. The depth works

    No

    1. Make the base deeper
  9. Anchor the bars beyond the critical section (9.8.2)

Step 1: Loads on the ground

The ultimate load from the column comes from Expression 6.10. The weights of the base and of the soil over it are added for the bearing check, since the ground carries those too:

EN 1991-1-1 §5.2.1, Table A.1

Self-weight of the base

Reinforced normal-weight concrete, 25 kN/m³ (Table A.1).

= 72.00 kN
EN 1991-1-1 §5.2.1

Weight of the soil over the base

The backfill over the base, from your soil depth hs and unit weight γs.

= 50.40 kN
EN 1990 §6.4.3.2(3), Eq. (6.10)
EN 1990 §A1.3.1(4), Table A1.2(B)

Design load from the column (Expression 6.10)

This load alone causes the bending and shear in the base.

= 1815.0 kN
EN 1990 §6.4.3.2(3), Eq. (6.10)

Total design load on the ground

= 1980.2 kN

Step 2: Ground pressure

For a concentric load the pressure is uniform, . With a moment it varies linearly; with the eccentricity ,

which is valid only while the whole base stays in compression, (the load in the middle third). The calculator refuses a base where part would lift off.

Ground pressure under the base

σRd is your design bearing resistance from EN 1997, which this tool does not derive. The ULS loads of EN 1990 Table A1.2(B) are used, so check that they match your EN 1997 design approach.

= 343.8 kPa ✓ OK

The design bearing resistance is your input from a geotechnical design to EN 1997; the tool does not derive it. For an eccentric load, here the calculator's second example with a moment about one axis:

Eccentricity of the load on the ground

With r ≤ 1 the load lies in the middle third (the kern) and the whole base presses on the ground.

= 0.172 ✓ OK

Ground pressure under the base

σRd is your design bearing resistance from EN 1997, which this tool does not derive. The ULS loads of EN 1990 Table A1.2(B) are used, so check that they match your EN 1997 design approach.

= 327.8 kPa ✓ OK
soil cover 500NEd = 1395 kNMEd = 126.0 kNmσRd = 350 kPaσmin = 231.3 kPaσmax = 327.8 kPaL = 2800
Ground pressure. ULS ground pressure from the total load (column, base and soil); it must stay within the design bearing resistance σRd.

Step 3: Bending at the face of the column

The base bends upward like an inverted cantilever beyond each face of the column.

Cantilever beyond the column face, along L

= 1000 mm
EN 1992-1-1 §9.8.2.1(1)

Bending moment at the column face (bars along L)

From the net upward pressure of the column load only: the weights of the base and the soil over it rest on their own share of the ground pressure. Pressures in kPa.

= 378.13 kNm
MEd,x = 378.13 kNmσface = 315.1 kPaσedge = 315.1 kPaax = 1000d = 454
Bending at the column face, bars along L. The net upward pressure from the column load alone bends the base beyond the face; MEd is taken at the face over the full width.

The steel is then designed as for a beam, over the full width of the base, with the second layer of bars at a slightly smaller effective depth:

EN 1992-1-1 §4.4.1.1(2)P, Eq. (4.1)

Effective depth, bars along L

The bottom layer.

= 454.0 mm
EN 1992-1-1 §6.1(2)P

Required tension reinforcement

= 1960.73 mm²
EN 1992-1-1 §9.2.1.1(1), Eq. (9.1N)
EN 1992-1-1 §9.3.1.1(1)

Minimum tension reinforcement

b = 2400 mm, the full width the bars are spread over.

= 1641 mm²
EN 1992-1-1 §9.3.1.1(3)
EN 1992-1-1 §8.2(2)

Bars along L

19H12 @ 125 mm across 2400 mm: the lightest that passes; smax = 250 mm.

= 2149 mm² ✓ OK
The bottom reinforcement mat of a pad footing on spacer blocks in its excavation, a column starter cage standing in the middle
On site: the two layers of bottom bars sit on spacer blocks over the blinding, which keeps their cover, and the column's starter bars stand up from the middle of the mat.

Step 4: Beam shear

Beam shear is checked on a section at from the face of the column across the full width, against (Expression 6.2.a). The shear is the net pressure on the area beyond that section:

EN 1992-1-1 §6.2.1(8)
EN 1992-1-1 §6.2.2(1)

Shear at d from the column face, along L

The net upward pressure (column load only) beyond d from the face, over the full width. Pressures in kPa.

= 412.9 kN
EN 1992-1-1 §6.2.2(1), Eq. (6.2.a)
EN 1992-1-1 §6.2.2(1), Eq. (6.2.b)

Shear resistance without shear reinforcement

vmin governs (Expression 6.2.b). σcp = 0 (no axial force); N in N, lengths in mm.

= 448.25 kN
EN 1992-1-1 §6.2.1(3)

Shear check

No shear reinforcement is needed.

✓ OK

Step 5: Punching shear

Punching is the column pushing a cone of concrete out of the base. EN 1992-1-1 checks it in two places:

At the column face, the shear stress on the perimeter of the column must not exceed the crushing limit (6.4.5(3)):

EN 1992-1-1 §6.4.2(1), Eq. (6.32)
EN 1992-1-1 §6.4.4(1)

Mean effective depth and steel ratio for punching

The bars are spread evenly over the base, so each ratio over the full width equals the ratio over the column width plus 3d each side (6.47).

= 0.00200
EN 1992-1-1 §6.4.5(3), Eq. (6.53)

Perimeter of the column

= 1600 mm
EN 1992-1-1 §6.4.5(3), Eq. (6.53)

Punching stress at the column face

The full column load at the face, without the soil-pressure deduction (conservative). d is the mean of the two layers.

= 2.532 MPa ✓ OK

On control perimeters at a distance from the face, with rounded corners. For a slab the basic control perimeter is at ; in a footing, the ground pressure inside the perimeter relieves the shear, so clause 6.4.4(2) asks for perimeters within to be checked, with:

The resistance rises as the perimeter comes closer to the column ( grows), but so does the stress; the calculator tries perimeters from to and reports the one that governs:

EN 1992-1-1 §6.4.4(1), Eq. (6.47)

Punching resistance at 2d (no shear reinforcement)

ρl = √(ρlx ρly) from the bars of both layers, at most 0.02.

= 0.413 MPa
EN 1992-1-1 §6.4.4(2), Eq. (6.48)
EN 1992-1-1 §6.4.4(2), Eq. (6.50)
EN 1992-1-1 §6.4.4(2), Eq. (6.49)

Punching at the governing perimeter (a = 407 mm)

Perimeters from 0.1d to 2d were checked; this one has the least margin. The soil pressure inside it (σnet in kPa) is deducted (6.4.3(8), 6.48).

= 0.750 MPa ✓ OK

Drawn out over the perimeters, the two effects pull against each other. Here is the calculator's own punching check run at each distance for this base:

Punching across the perimeters within 2d

The pad of the worked example: NEd = 1815 kN on a 400 × 400 column, d = 448 mm. Close to the column the stress is high but so is the resistance, which grows as 2d/a; farther out, the ground pressure inside the perimeter takes load off VEd. The worst ratio lies in between.

  • vEd, design stress
  • vRd,c·2d/a, resistance
0.0 0.5 1.0 1.5 2.0 Shear stress (MPa) 300 400 500 600 700 800 Distance of the perimeter from the column face a (mm) vEd, design stress vRd,c·2d/a, resistance Governs at a = 407 mm 0.0 0.5 1.0 1.5 2.0 Shear stress (MPa) 400 600 800 Distance of the perimeter from the column face a (mm) Governs at a = 407 mm
Show the numbers
Distance of the perimeter from the column face a (mm)vEd, design stress (MPa)vRd,c·2d/a, resistance (MPa)
2241.1891.652
2691.0571.376
3140.9431.179
3580.8451.034
4030.7570.918
4480.6780.826
4930.6060.751
5380.5410.688
5820.4820.636
6270.4270.590
6720.3750.551
7170.3270.516
7620.2820.486
8060.2400.459
8510.1990.435
8960.1600.413
L = 2400B = 2400u0 = 1600 mm, the column faceGoverning perimeter: a = 407 mm, u = 4154 mmBasic control perimeter: 2d = 896 mm
Punching perimeters. Perimeters run at a from the column face with rounded corners; the green one governs. A perimeter is cut off where it meets the edge of the base.

If punching fails, the answer is a deeper base: shear reinforcement in footings is possible but rarely economic, and the calculator does not design it.

Step 6: Anchorage of the bars

The bars must be anchored beyond the critical section of Figure 9.13. The calculator takes the simplified section at from the edge and works out the force there from the pressure on the part of the base outside it:

with and from the pressure resultant to a line times the column width inside its face. Straight bars must then have a length at least equal to for the stress :

EN 1992-1-1 §9.8.2.2(5)
EN 1992-1-1 §9.8.2.2(1), Figure 9.13

Section for the anchorage of the bars along L

For straight bars without end anchorage the section nearest the edge is the most critical; x = h/2 is the simplification allowed.

= 250 mm
EN 1992-1-1 §9.8.2.2(2)

Ground pressure within x of the edge

The net upward pressure (column load only) over the strip of base between the edge and x. Pressures in kPa, lengths in m.

= 189.1 kN
EN 1992-1-1 §9.8.2.2(2), Eq. (9.13)
EN 1992-1-1 §9.8.2.2(3)

Tensile force to anchor at x

ze runs from R (at x/2 from the edge), to the column load taken 0.15c inside the face; zi = 0.9d is the simplification allowed.

= 432.6 kN
EN 1992-1-1 §9.8.2.2(4)
EN 1992-1-1 §9.8.2.2(1), Figure 9.13

Straight length available beyond x

Straight bars are anchored within x of the edge.

= 210 mm ✓ OK
x = 250column load, 0.15c inside the facezi = 409Fs = 432.6 kNR = 189.1 kNze = 935lb = 210lbd = 199 needed
Anchorage of the bars along L. After Figure 9.13: the pressure R within x of the edge, its lever arm ze to the column load 0.15c inside the face, and zi = 0.9d give the bar force Fs to anchor beyond x.

This is why the calculator often chooses small bars at a close spacing in a footing: the anchorage length grows with the bar diameter, while the room beyond is fixed by the depth.

The answer

The 500 mm base passes every check with two layers of 19H12 @ 125: 2149 mm² each way, against 1960.73 mm² needed along L. The ground pressure is 343.8 kPa against the 400 kPa allowed, and the anchorage of the bars is the check closest to its limit.

19H12 @ 125 (B1)19H12 @ 125 (B2)h = 500L = 2400cx = 400cnom = 40 mm to the bottom bars, cast on blinding.
Section A–A. Drawn to scale; dimensions in mm.

Points to remember

  • Use the net pressure (column load only) for bending and shear, and the total (with base and soil) for bearing.
  • Keep the load in the middle third; otherwise make the base larger.
  • Cover on blinding is at least 40 mm, and 75 mm when cast directly against the ground (4.4.1.3(4)).
  • Check punching on perimeters within , not only at , because the ground pressure inside the perimeter reduces the shear.

Open the footing calculator and try a thinner base to see punching govern.