Pad footings and punching

Every column ends on a foundation. This lesson sizes a pad footing for the soil, designs its bottom steel, checks shear and punching to SANS 10100-1, and then looks at punching in flat slabs.

1. Learning outcomes

After this lesson you can:

size a pad footing for the allowable bearing pressure, with the right loads;
find the net design pressure and the bending moment at the column face;
design the bottom steel and check one-way shear;
check punching at the perimeter and at the column face;
check punching in a flat slab and set out shear links.

2. Before you start

Lesson 1 (bending), lesson 3 (v_c) and lesson 5 (the column above).
The free pad footing and punching shear calculators. A second worked pad example is on Pad footing design to SANS 10100.
A pocket calculator and about 60 minutes.

3. What a pad footing does

A pad footing spreads one column's load over enough soil to carry it. The column pushes down on a small area; the soil pushes back up over the whole base.

4. Bearing: sizing the base

Bearing pressure under service loads (G + Q), including the base, the column stub and the soil on top. A moment tips the pressure into a trapezoid: q = N/(BL) × (1 ± 6e/B). The largest pressure must not pass the allowable bearing pressure, and the base must not lift off anywhere (STATIX).

STATIX checks bearing with the service combination G + Q, and adds the weight of the base, the column stub and the soil above the base. A horizontal force H adds a moment H(h + X) at the underside, where X is the stub height.

5. Designing the base

Two different pressures. Bearing is checked with service loads and everything the soil carries. Bending, shear and punching use only the factored column load spread over the base (the net pressure), because the weight of the base and the soil on it is carried straight down and does not bend it.

ultimate column load: the larger of 1.2G + 1.6Q and 1.35G + 1.0Q net design pressure: q_u = N_u / (B L) (with a moment: × (1 + 6e_x/B + 6e_y/L))

How a footing bends. Turn it upside down and it is two cantilevers loaded by the soil pressure, fixed at the column. The bottom is in tension, and cracks would start at the column face, which is where the bending is checked (SANS 10100-1, 4.10).

Where to check a footing (plan). 1: bending at the column face. 2: one-way shear across the whole width; for SANS, STATIX checks it 1.5d from the face (4.10.3.3.2). 3: punching on a perimeter 1.5d out from the column, plus the column face itself for the maximum shear stress.

bending at the face: M = q_u l²/2 per metre, with l = (B − c)/2; A_s as in lesson 1 minimum steel: 0.13% of b h one-way shear: v = V/(B d) at 1.5d from the face ≤ v_c (no links in a footing)

With a moment the pressure varies, and STATIX takes the bending from that linear pressure (4.10.2.1). In a rectangular base the steel across the short way is partly banded under the column (4.10.3.2).

6. Punching

Punching shear. Around a concentrated load the concrete can fail on a cone, sloping out at about 30 to 45 degrees. It happens suddenly. Slabs on columns and footings under columns are both checked for it.

The punching perimeter for a square column c × c: a square 1.5d out from each face, so each side is c + 3d and u = 4c + 12d (STATIX keeps the corners square). The shear stress is v = V/(u d), where V is the load outside the perimeter.

perimeter at 1.5d: u = 4c + 12d (square column c) V = q_u × (area outside the perimeter); v = β V / (u d) ≤ v_c column face: v₀ = β V / (4c × d) ≤ 0.75√f_cu and 4.75 MPa

β allows for moment transfer; under a footing with no moment it is 1.0 (SANS, STATIX). v_c is the lesson 3 formula with the average steel of the two directions.

7. Punching in flat slabs

Moment transfer. A column at the edge or corner of a slab also passes moment into it, which loads one side of the perimeter harder. The shear is increased by a factor β; the STATIX punching calculator uses 1.15 for interior, 1.4 for edge and 1.25 for corner columns unless you give the moment.

Punching in a flat slab with shear links. Check perimeters from 1.5d outwards in steps of 0.75d until v is below v_c. Where links are needed, place at least two rings: the first 0.5d from the face, the next no more than 0.75d further, and links no more than 1.5d apart around a ring (STATIX).

v ≤ 1.6v_c: ΣA_sv = (v − v_c) u d / (0.87 f_yv) v ≤ 2v_c: ΣA_sv = 5 (0.7v − v_c) u d / (0.87 f_yv) at least 0.4 u d / (0.87 f_yv); above 2v_c the slab is too thin

8. Detailing footings

Bottom cover in footings. Cast the base on a thin blinding layer and stand the bars on chairs, so the cover is real. Concrete cast straight against soil needs much more cover (lesson 8).

Where to go next. STATIX has calculators for the other common foundations: the strip footing, the raft (a plate on springs) and the pile cap (strut and tie).