Course · lesson 2 of 7

Pad footings: moments, biaxial loads and uplift

RC Design 1 lesson 7 designed a pad under a concentric load. Real columns also bring moments and horizontal forces, and light frames bring uplift. This lesson follows the pressure under the base as the load moves off-centre, checks overturning and sliding, and uses the STATIX pad footing calculator for every number.

1. Learning outcomes

After this lesson you can:

turn N, M and H into an eccentric load on the base, with the pad and soil weight included;
find the pressure under a pad with one or two moments, and recognise loss of contact;
use the middle-third rule and the kern to size a pad;
check overturning and sliding, and know where uplift is designed;
read the pressure plot and the combination table of the STATIX pad footing calculator.

2. Before you start

RC Design 1, lesson 7 (a concentric pad: bearing, bending, shear, punching) and lesson 1 of this course.
The free pad footing calculator.
A pocket calculator and about 50 minutes.

3. Eccentric load

A moment is an off-centre load. A column load N with a moment M is the same as N acting a distance e = M/N from the centre. The footing's own weight and the soil on it are part of N: they pull e back towards the centre.

Horizontal load and the lever. A horizontal force at the top of the stub adds H times the depth to the underside of the base to the moment. The calculator does this for you, and adds the weight of the pad, the stub and the soil over the pad to N.

4. Pressure under the base

Three regimes. While e stays inside the middle third (e ≤ B/6) the whole base presses on the soil, with a trapezoidal pressure. At e = B/6 the pressure just reaches zero at the heel. Beyond it the heel lifts off and the pressure under the rest becomes a steeper triangle.

The elastic pressure formula. With the whole base in contact the pressure varies linearly: the average N/A, plus and minus the bending terms. With two moments the largest and smallest values are at opposite corners.

When the heel lifts. Beyond the middle third only part of the base bears, over a length 3(B/2 − e), and the peak pressure rises fast. The STATIX pad footing calculator reports “uplift — heel lifts” and fails the bearing check for any service combination that loses contact: it keeps every SLS combination inside the middle third.

full contact (e ≤ B/6): q = N/A (1 ± 6e/B) heel lifts (e > B/6): q_max = 2N / (3L (B/2 − e)), contact length 3 (B/2 − e) biaxial, full contact: q = N/A (1 ± 6e_x/B ± 6e_y/L), while 6e_x/B + 6e_y/L ≤ 1

5. Biaxial moments

Biaxial moments. A corner column or a column with moments both ways tilts the pressure in two directions. The largest pressure is at one corner and the smallest at the opposite one; both must stay within the allowable pressure and above zero.

The middle third in plan. For a load off-centre in both directions the safe zone is a diamond, the kern: the base stays fully in contact while 6e_x/B + 6e_y/L ≤ 1. Its points are at B/6 and L/6 from the centre.

6. Overturning, sliding and uplift

Overturning and sliding. About the toe the weight restores and the moment overturns; their ratio is B/(2e), with a biaxial version. Sliding is resisted by base friction μ N. The calculator checks both on the service combinations against safety factors you set (1.5 by default). On SANS with wind it also checks them on the EQU row 0.9 G + 1.6 W (SANS 10160-1) against 1.0, with the pad and soil weight × 0.9; the row closest to its limit governs. Passive earth on the buried face can be added.

Uplift. On light frames the 0.9 G + 1.6 W combination can put the column in tension. The holding-down bolts and the stub carry it into the pad, and the pad's own weight (with the soil on it) must hold it down. In STATIX the ULS rows drive the pad's bending and the holding-down bolt design; the stability checks run on the service combinations with the safety factors and, on SANS, on the EQU row 0.9 G + 1.6 W with SF 1.0 (no bearing check on that row).

Which combination checks what in the STATIX pad footing calculator. Bearing and contact use the service combinations; stability uses them too and, on SANS with wind, the EQU row 0.9 G + 1.6 W (SF 1.0); the reinforced concrete and the bolts use the ultimate ones; the optional GEO bearing (lesson 1) uses the ultimate ones with the factored soil.

7. In STATIX

In STATIX: give the loads per source with their moments and horizontal forces, the pad and stub, and the required safety factors. The calculator draws the pressure under the base and lists every combination with its pressure, contact and safety factors.