Footing Bearing Pressure (Eccentric)

Soil pressure under a rectangular spread footing carrying axial load plus moment — checks for uplift and reports peak/min pressure.

Inpute = M/P, kern = B/6 , full contact: q = P/A ± 6M/(L·B²) , partial (e>B/6): q_max = 2P/[3L(B/2 − e)]

Vertical load P (kN)or enter kip — converts to kNMoment M (kN·m)or enter kip·ft — converts to kN·mFooting length B (moment direction) (m)or enter ft — converts to mFooting width L (m)or enter ft — converts to mAllowable bearing q_a (kPa)or enter ksf — converts to kPa

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The engineering

A spread footing carrying both a vertical load and a moment develops a non-uniform soil pressure. Resolve the moment into an eccentricity e = M/P and compare it to the kern distance B/6. Inside the kern the whole base stays in compression and the pressure varies linearly from q_min to q_max; outside the kern the near edge lifts, contact reduces to a triangular block, and q_max climbs sharply.

The rule to memorize is the middle-third: keep the resultant within the kern (e ≤ B/6) and you avoid uplift entirely — good practice for footings on soil, which cannot take tension. Once e exceeds B/6 the linear formula no longer applies; use the triangular partial-bearing form, and watch q_max, which grows fast as the bearing area shrinks.

Compare q_max against your allowable bearing q_a (a service-level, factor-of-safety-included value). If utilization exceeds 1.0, enlarge the footing in the moment direction — a small increase in B pays off because the moment term scales with B².

Where this math comes from

Spread footing design grew out of the empirical bearing-value tables that municipal building codes carried from the late 1800s, but the rational treatment of eccentric loading — the middle-third rule — comes from masonry and gravity-dam analysis, where engineers had long insisted the resultant stay in the kern to keep joints in compression. The same logic transferred cleanly to soil, which likewise cannot resist tension across the footing base.

Joseph E. Bowles codified the practical procedure most working foundation engineers still use in his textbook Foundation Analysis and Design (first edition 1968), collecting the full-contact and partial-contact pressure formulas, the kern check, and worked footing examples into one reference. His treatment of the triangular partial-bearing case is the version reproduced on this card.

1885Municipal building codesPublish presumptive allowable bearing tables for footing design.
1943Karl TerzaghiBearing capacity theory puts soil pressure limits on a mechanistic footing.
1968Joseph E. BowlesFoundation Analysis and Design collects the eccentric-footing pressure formulas used here.
1996Joseph E. Bowles5th edition refines the partial-contact and biaxial eccentricity treatment.

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