Footing Pressure and Eccentricity Calculations

Footing contact pressure is influenced by both vertical load and moment. This page presents a transparent calculation for a rectangular footing under uniaxial eccentricity, then identifies when the simple full-contact equation no longer applies.

Engineering review status: Draft calculation guidance for review by a qualified geotechnical or structural engineer. It is not a site-specific foundation design.

Inputs and units

Symbol	Description	Typical unit
\(V\)	Resultant vertical load at the footing base	kN
\(M\)	Moment about the footing centroid	kN·m
\(B\)	Footing dimension in the direction of eccentricity	m
\(L\)	Footing dimension perpendicular to \(B\)	m
\(e\)	Load eccentricity	m
\(q_{avg}\)	Average contact pressure	kPa
\(q_{max}, q_{min}\)	Maximum and minimum edge pressures	kPa

Use one consistent sign convention for moment and eccentricity. The equations below report the pressure increase at one edge and the corresponding decrease at the opposite edge.

Step 1: Calculate eccentricity

The eccentricity of the vertical load resultant is:

$$ e = \frac{M}{V} $$

The equation requires \(V>0\). If load combinations can produce uplift or a very small vertical resultant, the calculation needs separate engineering treatment.

Step 2: Calculate average contact pressure

For a rectangular footing with gross plan area \(A=BL\):

$$ q_{avg} = \frac{V}{BL} $$

When \(V\) is in kN and \(B\) and \(L\) are in metres, the result is in kN/m², which is equivalent to kPa.

Step 3: Calculate edge pressures for full contact

For uniaxial eccentricity about the axis parallel to \(L\), a linear pressure distribution gives:

$$ q_{max,min} = \frac{V}{BL}\left(1 \pm \frac{6e}{B}\right) $$

This form assumes the footing remains in full contact with the supporting material. It is not valid once the calculated minimum pressure is negative because soil is normally not assumed to carry tension.

Worked example

Consider the following illustrative inputs:

• \(V=900\ \text{kN}\)
• \(M=90\ \text{kN·m}\)
• \(B=2.0\ \text{m}\)
• \(L=3.0\ \text{m}\)

First, calculate eccentricity:

$$ e=\frac{90}{900}=0.10\ \text{m} $$

Then calculate average pressure:

$$ q_{avg}=\frac{900}{2.0\times3.0}=150\ \text{kPa} $$

The edge pressures are:

$$ q_{max}=150\left(1+\frac{6\times0.10}{2.0}\right)=195\ \text{kPa} $$ $$ q_{min}=150\left(1-\frac{6\times0.10}{2.0}\right)=105\ \text{kPa} $$

For this load case, both calculated edge pressures are compressive, so the full-contact pressure distribution remains applicable within the stated assumptions.

Effective-area framework

Some foundation design methods represent eccentric loading using reduced effective dimensions:

$$ B' = B-2|e_B| $$ $$ L' = L-2|e_L| $$

The effective area and corresponding average effective pressure are:

$$ A'=B'L' $$ $$ q_{eff}=\frac{V}{A'} $$

This is a separate design framework. Do not combine it automatically with the linear edge-pressure equation. The selected bearing-capacity method, load convention, eccentricity directions and applicable project standard must be defined by the designer.

Important limitations

• The equations address contact pressure only. They do not establish allowable bearing pressure or settlement performance.
• Confirm whether loads are serviceability, ultimate, characteristic, factored, gross or net before comparing pressures with design resistance.
• If \(q_{min}<0\), the full-contact equation is no longer valid. A compression-only contact analysis or another approved method is required.
• Biaxial eccentricity, inclined loads, base inclination, groundwater, layered ground, uplift and cyclic loading require additional assessment.
• No universal eccentricity limit, factor of safety or acceptance threshold is applied on this page.

Related calculations

• Shallow Foundation Bearing Capacity Calculation
• Immediate Settlement of Shallow Foundations
• Retaining Wall Stability Calculations

References for engineering review

• FHWA, Shallow Foundations, Geotechnical Engineering Circular No. 6
• FHWA, Soils and Foundations Reference Manual, Volume II

Review checklist

Please confirm the load sign convention, definition of \(B\) and \(L\), full-contact validity check, treatment of biaxial eccentricity, and whether the effective-area method should be implemented for the intended Australian workflows.