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    Geotechnical / Foundations

    Mat Foundation (Rigid Method)

    Bearing pressure and punching shear for a rigid mat: P/A ± M/S at the corners, then the ACI two-way shear check at the column. A full finite-element mat with soil springs is a different model; this is the closed-form check that decides whether the mat is the right size.

    MethodRigid matBearingPassPunchingPass
    Maximum bearing
    110.8 kPa
    Allowable 200 kPa
    Minimum bearing
    89.2 kPa
    Full contact
    Bearing utilisation
    55%
    Within allowable
    Punching utilisation
    32%
    φVc 3813 kN per column
    Pressure at the four corners
    P/A ± Mx/Sx ± My/Sy. The maximum governs the bearing check.
    Pressure at the four corners
    CornerPressure (kPa)
    +x, +y110.8
    +x, −y104.2
    −x, +y95.8
    −x, −y89.2

    A negative minimum means part of the mat is not in contact; the rigid method is then invalid.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Maximum bearing against total load
    The allowable line is the horizontal limit.
    Canonical equations
    The exact relationships implemented by this engine.

    q = P/A ± Mx/Sx ± My/Sy · Rigid-mat method, ACI 336.2R.

    Sx = Lx·Ly²/6, Sy = Ly·Lx²/6 · For a rectangular plan.

    φVc = 0.75·0.33·√f′c·b₀·d · ACI 318 §22.6.5.2, SI units.

    engineering methodology

    A clear path from inputs to results.

    Bearing pressure and punching shear for a rigid mat: P/A ± M/S at the corners, then the ACI two-way shear check at the column. A full finite-element mat with soil springs is a different model; this is the closed-form check that decides whether the mat is the right size.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Set mat length lx (m).
    2. Set mat width ly (m).
    3. Set thickness (mm).
    4. Set total vertical load (kn).
    5. Read the headline metrics, then check the table for the detail.

    The formula

    Reference: ACI 336.2R rigid-mat method; ACI 318 §22.6 punching shear.

    Worked example

    At the default inputs

    Inputs
    • Mat length Lx (m): 12; Mat width Ly (m): 10; Thickness (mm): 700; Total vertical load (kN): 12000; Moment about x (kN·m): 1500; Moment about y (kN·m): 800; Concrete f′c (MPa): 30; Allowable bearing (kPa): 200; Column size (mm): 500; Number of columns: 9
    Calculation path
    1. 1

      Average pressure → 100.0 Add the moments → 110.8 kPa Punching → 32%

    Result

    Maximum bearing: 110.8 kPa · Minimum bearing: 89.2 kPa · Bearing utilisation: 55%

    Interpreting the result

    The 12.0 × 10.0 m mat carries 1.200e+4 kN at 110.8 kPa maximum bearing (55% of allowable) and 32% of the punching capacity.

    Assumptions & limitations

    • Rigid mat with a linear pressure distribution.
    • No uplift; a negative minimum invalidates the method.
    • Punching is checked per column at d/2.

    Frequently asked questions

    Is this a finite-element mat?

    No. It is the rigid-mat closed form; a soil-spring FEM is a different model.

    Why does the minimum pressure matter?

    If it goes negative, part of the mat lifts off and P/A ± M/S no longer applies.

    Methodology last reviewed 2026-10-23. Results are informational and not financial or engineering advice — see our disclaimer.