Pad footing bearing pressure calculator

What it computes

The inputs are the column load N, the moment M in the direction of the footing length, the footing width B, length L and thickness t, the depth of the base below the ground, a soil from a drop-down (each with an allowable bearing pressure) and a checkbox to include the weight of the footing and of the soil above it. The sheet reports the total load P, the eccentricity, the average, largest and smallest pressures and the utilisation of the allowable pressure, and prints whether the base stays in full contact.

The formulas

• Total vertical load P = N + weight of the footing (24 kN/m^3 concrete) + weight of the soil above it (18 kN/m^3).
• Eccentricity e = M / P. The load stays in the middle third of the footing while e is no more than L / 6.
• Average pressure P / (B L). While e is within L / 6, the largest and smallest pressures are q = P / (B L) x (1 plus or minus 6 e / L).
• Beyond L / 6 the base is in partial contact and the largest pressure is q_max = 2 P / (3 B (L/2 - e)), with zero at the other edge.
• Utilisation = q_max / allowable bearing pressure.

Worked example

Defaults: N = 600 kN, M = 60 kN·m, a 2 m by 2.4 m footing 0.5 m thick, base 1 m below ground, medium dense sand (allowable pressure 200 kPa), weights included. Engine results:

The eccentricity of 0.0856 m is well inside the limit of 0.4 m, so the whole base is in contact with the soil. The largest pressure is 177.25 kPa, which uses 0.886 of the allowable pressure, so the sheet prints OK.

When the moment grows

With the moment raised to 250 kN·m the eccentricity becomes 0.357 m, close to the middle-third limit of 0.4 m. The largest pressure rises to 276.21 kPa while the smallest falls to 15.79 kPa, and the utilisation of 1.38 fails the check. The sheet says to enlarge the footing. A larger moment, or a smaller footing, takes the load outside the middle third and the formula switches to partial contact, with the other edge at zero.

What this is, and is not

The sheet source

# Pad footing: bearing pressure check

A template with inputs. Choose **Input** in the results bar to fill in the form. A rectangular
pad footing $B \times L$ carries a vertical column load $N$ and a moment $M$ about the axis
parallel to $B$. The total vertical load $P$ adds the weight of the footing and of the soil above
it, the eccentricity is $e = M/P$ and, while $e \le L/6$ (no uplift), the largest bearing pressure is
$q_{max} = \frac{P}{B L}\left(1 + \frac{6e}{L}\right)$. Beyond that the pressure acts on part of the
base only, $q_{max} = \frac{2P}{3B(L/2 - e)}$. It is compared with an allowable bearing pressure.

## Inputs
N:    ? 600 kN | vertical column load
M:    ? 60 kN*m | column moment, in the direction of L
B:    ? 2 m | footing width
L:    ? 2.4 m | footing length, in the direction of the moment
t:    ? 0.5 m | footing thickness
D_f:  ? 1 m | depth of the base below the ground
q_a:  ? [Soft clay = 80 kPa, Firm clay = 150 kPa, *Medium dense sand = 200 kPa, Dense gravel = 300 kPa] | soil, allowable bearing pressure
wts:  ? on | include the weight of the footing and of the soil above it

## Constants
gamma_c: 24 kN/m^3 | unit weight of concrete
gamma_s: 18 kN/m^3 | unit weight of the soil above the footing

## Vertical load
W_f: wts * gamma_c * B * L * t -> kN | weight of the footing
W_s: wts * gamma_s * B * L * (D_f - t) -> kN | weight of the soil above the footing
P:   N + W_f + W_s -> kN | total vertical load on the soil

## Bearing pressure
e:   M / P -> m | eccentricity of the load
e_lim: L / 6 | the load stays inside the middle third while e is below this
q_avg: P / (B * L) -> kPa | average pressure

if e <= e_lim:
    q_max: q_avg * (1 + 6 * e / L) -> kPa | largest pressure
    q_min: q_avg * (1 - 6 * e / L) -> kPa | smallest pressure
    The whole base stays in contact with the soil.
else:
    q_max: 2 * P / (3 * B * (L / 2 - e)) -> kPa | largest pressure, partial contact
    q_min: 0 kPa | smallest pressure
    Part of the base lifts off the soil.

util: q_max / q_a | utilisation of the allowable bearing pressure
if util <= 1: "OK: the largest pressure is within the allowable bearing pressure." else: "Fails: the largest pressure exceeds the allowable bearing pressure. Enlarge the footing."

How to use it

1. Open the template. Choose Open this template on this page. The sheet opens in a new tab of CivilKit Calcs, with the inputs set to the values used on this page.
2. Switch to Input mode. In the results bar choose Input. The input lines become boxes, lists, buttons and ticks.
3. Enter your values. Change the inputs to your own. Use your own loads, footing size and allowable pressure; to use a value that is not in the soil list, edit the list in the sheet. Every change recalculates the whole page.
4. Read and export the result. Read the results and the OK or not OK lines under them. Use Report, then Print PDF, Word or Excel, to keep the calculation with its workings.