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    Geotechnical / Piles

    Lateral Pile Analysis

    A laterally loaded pile solved as a beam on an elastic foundation. For a long pile the closed form is exact: the head deflection is 2Hβ/k and the maximum bending moment is H/β, four diameters or so below the surface.

    Head deflection8.1 mmMax bending moment546 kN·mCharacteristic length2.73 m
    Head deflection
    8.1 mm
    β 0.366 1/m
    Max bending moment
    546 kN·m
    At about 1/β depth
    Characteristic length
    2.73 m
    1/β
    Moment depth
    2.73 m
    Where the moment peaks
    Load response
    Constant subgrade modulus. Layered soil and p-y curves need a numerical solution.
    Load response
    Load (kN)Head deflection (mm)Max moment (kN·m)
    502.0137
    1004.1273
    2008.1546
    40016.31092
    80032.62184
    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Head deflection against load
    Linear in the load: the soil is modelled as elastic, so there is no yield.
    Head deflection against load0.0007.2914.5921.8829.1736.475050100100200200400400800800Lateral Pile Analysis
    Canonical equations
    The exact relationships implemented by this engine.

    EI·y″″ + k·y = 0 · Beam on an elastic foundation.

    β = (k/4EI)^(1/4) · k = kh·d.

    y₀ = 2Hβ/k · Hetényi, long pile.

    M = H/β · At about 1/β depth.

    engineering methodology

    A clear path from inputs to results.

    A laterally loaded pile solved as a beam on an elastic foundation. For a long pile the closed form is exact: the head deflection is 2Hβ/k and the maximum bending moment is H/β, four diameters or so below the surface.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Set pile diameter (mm).
    2. Set bending stiffness ei (mn·m²).
    3. Set subgrade reaction kh (mn/m³).
    4. Set lateral load at head (kn).
    5. Read the headline metrics, then check the table for the detail.

    The formula

    EI⋅y″″+k⋅y=0EI·y″″ + k·y = 0

    Reference: Hetényi beam on an elastic foundation; long-pile closed form.

    Worked example

    At the default inputs

    Inputs
    • Pile diameter (mm): 600; Bending stiffness EI (MN·m²): 250; Subgrade reaction kh (MN/m³): 30; Lateral load at head (kN): 200
    Calculation path
    1. 1

      Head deflection: 8.1 mm · Max bending moment: 546 kN·m · Characteristic length: 2.73 m · Moment depth: 2.73 m

    Result

    Head deflection: 8.1 mm · Max bending moment: 546 kN·m · Characteristic length: 2.73 m

    Interpreting the result

    A 200 kN lateral load moves the head 8.1 mm and peaks the moment at 546 kN·m, 2.73 m down.

    Assumptions & limitations

    • Constant subgrade modulus.
    • Elastic soil — no yield, no p-y curve.

    Frequently asked questions

    Why is the maximum moment below the surface?

    The soil reaction builds over the first metre or so, so the moment peaks at about 1/β and then decays.

    What if the pile is short?

    The closed form assumes a long pile; a short rigid pile rotates instead and needs the short-pile solution.

    Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.