UNDERSTAND IT. WORK IT OUT.

Learn: Rectangular footing contact pressure

A moment makes footing contact pressure larger at one edge and smaller at the opposite edge. The linear full-contact model starts with average pressure and adds or subtracts an eccentricity-related variation.

Beginner-friendlyFree · No accountTwo worked examples + separate practice
01

What the formula is saying

Average pressure is N/A. The relative variation is 6e/B, so qmax and qmin are the average multiplied by 1 plus or minus that variation. Here e is the nonnegative magnitude of the eccentricity in the checked direction.

qmax,min = (N/A)(1 ± 6e/B)

Read the symbols in plain language

N
Vertical load

Vertical load. Spread the compressive resultant uniformly over the footing area as the reference pressure.

kN

Kilonewtons measure force; 1 kN = 1000 N.

A
Footing area

Footing area. Spread the compressive resultant uniformly over the footing area as the reference pressure.

m²

Square metres measure area; square the length conversion factor.

e
Eccentricity

Eccentricity. This factor must not exceed one in the stated no-tension full-contact model.

m

Metres measure length; 1 m = 1000 mm.

B
Dimension in bending direction

Dimension in bending direction. This factor must not exceed one in the stated no-tension full-contact model.

m

Metres measure length; 1 m = 1000 mm.

qmax
Result to find

Maximum compressive edge pressure.

kPa
qmin
Result to find

Minimum compressive edge pressure; full contact requires it to be nonnegative.

kPa

Sort out the units first

N is kN, A is m² and e and B are m. Both output pressures are kPa. B is the dimension in the direction of the pressure variation, not necessarily the smaller plan dimension.

Assumptions before calculating

Assume a rigid rectangular footing, one-axis eccentricity, compressive load and linear full contact. Require 0 ≤ e ≤ B/6; A and B must describe the same footing geometry.

02

Let’s solve one together

Read the given values, follow each operation, then check what the result means.

Use the following study data and find the requested result. Follow the calculation before trying the second case.

N · Vertical load
1000 kN
A · Footing area
6 m²
e · Eccentricity
0.1 m
B · Dimension in bending direction
2 m

  1. Find average contact pressure

    Spread the compressive resultant uniformly over the footing area as the reference pressure.

    (1000) ÷ (6) ≈ 166.6666667 kPa

  2. Find the relative pressure variation

    This factor must not exceed one in the stated no-tension full-contact model.

    6 × (0.1) ÷ (2) = 0.3

  3. Find the lower edge pressure

    Subtract the variation and verify that the resulting contact pressure is nonnegative.

    (166.6666667) × (1-(0.3)) ≈ 116.6666667 kPa

  4. Find the higher edge pressure

    Add the variation and report both edge pressures, not just the larger one.

    (166.6666667) × (1 + (0.3)) ≈ 216.6666667 kPa
Answer · qmax216.6666667 kPaqmin116.6666667 kPa

Does this worked answer make sense?

The average of qmax and qmin must equal N/A. At e = 0 the two pressures match; at e = B/6 the minimum is zero, marking the edge of the full-contact range.

A second worked example — different values

A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.

N · Vertical load
900 kN
A · Footing area
6 m²
e · Eccentricity
0.2 m
B · Dimension in bending direction
2.4 m

  1. Find average contact pressure

    Spread the compressive resultant uniformly over the footing area as the reference pressure.

    (900) ÷ (6) = 150 kPa

  2. Find the relative pressure variation

    This factor must not exceed one in the stated no-tension full-contact model.

    6 × (0.2) ÷ (2.4) = 0.5

  3. Find the lower edge pressure

    Subtract the variation and verify that the resulting contact pressure is nonnegative.

    (150) × (1-(0.5)) = 75 kPa

  4. Find the higher edge pressure

    Add the variation and report both edge pressures, not just the larger one.

    (150) × (1 + (0.5)) = 225 kPa
Answer · qmax225 kPaqmin75 kPa
03

Now try your own values

Change a value or its unit. The same method will show your calculation, step by step.

Vertical load. Spread the compressive resultant uniformly over the footing area as the reference pressure.

Footing area. Spread the compressive resultant uniformly over the footing area as the reference pressure.

Eccentricity. This factor must not exceed one in the stated no-tension full-contact model.

Dimension in bending direction. This factor must not exceed one in the stated no-tension full-contact model.

English, Arabic and Persian digits are supported. The steps convert inputs to the formula’s base units.

Results update only when you calculate. The lesson example above stays unchanged.

04

Your turn — check your understanding

Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.

N · Vertical load
1200 kN
A · Footing area
8 m²
e · Eccentricity
0.15 m
B · Dimension in bending direction
2.5 m

Find: Learn: Rectangular footing contact pressure

For repeating decimals, use at least four significant figures. Accepted rounding tolerance: 0.05% of the expected value; zero uses an absolute tolerance of 10⁻¹². Both answers must be correct together.

A hint, not the answer

Average pressure is N/A. The relative variation is 6e/B, so qmax and qmin are the average multiplied by 1 plus or minus that variation. Here e is the nonnegative magnitude of the eccentricity in the checked direction.

N is kN, A is m² and e and B are m. Both output pressures are kPa. B is the dimension in the direction of the pressure variation, not necessarily the smaller plan dimension.

Show the full practice solution

Compare the steps with your work; revealing a solution does not mark the lesson complete.

  1. Find average contact pressure

    Spread the compressive resultant uniformly over the footing area as the reference pressure.

    (1200) ÷ (8) = 150 kPa

  2. Find the relative pressure variation

    This factor must not exceed one in the stated no-tension full-contact model.

    6 × (0.15) ÷ (2.5) = 0.36

  3. Find the lower edge pressure

    Subtract the variation and verify that the resulting contact pressure is nonnegative.

    (150) × (1-(0.36)) = 96 kPa

  4. Find the higher edge pressure

    Add the variation and report both edge pressures, not just the larger one.

    (150) × (1 + (0.36)) = 204 kPa
Answer · qmax204 kPaqmin96 kPa

Avoid the common trap

Do not use signed negative e here: enter its magnitude and identify the compressed edge from the load sketch. Do not accept a negative qmin by simply ignoring it or compare only qmax without checking contact.

When this method applies — and when it does not

For e > B/6 this full-contact model predicts tension that soil cannot sustain; use a justified partial-contact or design method instead. Biaxial loading, flexible footings, soil nonlinearity and bearing/settlement acceptance are outside this lesson.

For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.

One idea understood. Keep going.

This optional checkmark is saved only in this browser. It is your own progress note, not a certificate.

Sources & further reading

References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.

Reading focus: Rectangular footing contact pressure. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.

Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.

Build on this lesson

Soil basics

Learn: Classical bearing capacity — basic form

A simple shallow-foundation bearing model separates resistance into cohesion, surcharge and soil-weight contributions. This lesson evaluates that three-term expression using supplied bearing-capacity factors.

Steps + calculator + practice
Soil basics

Learn: Footing load eccentricity

A vertical force and a moment can be represented by an equivalent force acting away from the footing centre. Eccentricity is the signed distance needed for that force to reproduce the supplied moment.

Steps + calculator + practice
Soil basics

Learn: Immediate elastic settlement

A loaded foundation compresses the supporting ground even when bearing failure is not reached. This elastic estimate combines contact pressure, foundation width, soil stiffness, Poisson’s ratio and an influence factor.

Steps + calculator + practice
Open standalone tool in a new tab

Menu