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.
What the formula is saying
A moment equals force times perpendicular distance, M = N e. Rearranging gives e = M/N; the sign indicates which side of the reference the resultant acts on.
Read the symbols in plain language
- M
- Moment
Moment. Use the moment and compressive resultant from the same transferred load system.
kN·mUse kN·m as the base unit shown here. Use M in kN·m and compressive N in kN, giving e in m. The force and moment must be taken at the same footing reference level.
- N
- Vertical load
Vertical load. Divide the signed moment by positive compressive force to recover a signed distance.
kNKilonewtons measure force; 1 kN = 1000 N.
- e
- Result to find
Footing load eccentricity. Divide the signed moment by positive compressive force to recover a signed distance.
m
Sort out the units first
Use M in kN·m and compressive N in kN, giving e in m. The force and moment must be taken at the same footing reference level.
Assumptions before calculating
A positive compressive vertical resultant exists and the moment is about the relevant footing centroidal axis. The lesson uses signed M and N > 0.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find e and explain the result in the stated output unit.
- M · Moment
- 100 kN·m
- N · Vertical load
- 1000 kN
Identify the moment at the footing reference
Use the moment and compressive resultant from the same transferred load system.
(100) = 100 kN·mFind the equivalent force offset
Divide the signed moment by positive compressive force to recover a signed distance.
(100) ÷ (1000) = 0.1 m
Does this worked answer make sense?
Zero moment gives zero eccentricity. Doubling N with M fixed halves e; doubling M doubles it.
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.
- M · Moment
- -120 kN·m
- N · Vertical load
- 800 kN
Identify the moment at the footing reference
Use the moment and compressive resultant from the same transferred load system.
(-120) = -120 kN·mFind the equivalent force offset
Divide the signed moment by positive compressive force to recover a signed distance.
(-120) ÷ (800) = -0.15 m
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
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.
- M · Moment
- 150 kN·m
- N · Vertical load
- 1200 kN
Find: Learn: Footing load eccentricity
A hint, not the answer
A moment equals force times perpendicular distance, M = N e. Rearranging gives e = M/N; the sign indicates which side of the reference the resultant acts on.
Use M in kN·m and compressive N in kN, giving e in m. The force and moment must be taken at the same footing reference level.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the moment at the footing reference
Use the moment and compressive resultant from the same transferred load system.
(150) = 150 kN·mFind the equivalent force offset
Divide the signed moment by positive compressive force to recover a signed distance.
(150) ÷ (1200) = 0.125 m
Avoid the common trap
Do not divide force by moment. Do not mix moments from one level with forces from another without transfer, or remove the moment sign before understanding the resultant location.
When this method applies — and when it does not
Eccentricity alone does not determine the contact area or bearing pressure. Full contact, uplift, effective-width design, biaxial moments, settlement and stability need further checks. Near-zero N makes this representation highly sensitive.
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.
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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: Footing load eccentricity. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
- University of the West of England — GeotechniCAL: soil mechanics and foundations
- University of the West of England — GeotechniCAL: bearing capacity
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.