Model Inputs
Loads
Partial linear distributed loads
| x1 (ft) | x2 (ft) | q1 (kip/ft) | q2 (kip/ft) |
|---|
Concentrated loads
| x (ft) | P (kip) |
|---|
Results
Beam on an elastic (Winkler) foundation
This free, browser-based tool analyzes a straight beam resting on a continuous Winkler elastic foundation — a bed of independent springs whose reaction is proportional to the local deflection. Using the finite element method, it computes the deflection, slope, shear, bending moment and subgrade reaction (soil pressure) along the whole beam, and it can model a realistic compression-only (no-tension) foundation that releases wherever the beam lifts off. Everything runs in your browser — no download, no license, and no data leaves your computer.
Analysis methods and assumptions
Finite element formulation
The beam is discretized into two-node Hermitian cubic beam elements, each node carrying a vertical displacement and a rotation. Each element contributes a consistent Euler–Bernoulli beam-bending stiffness matrix (from EI) and a consistent Winkler foundation stiffness matrix (from the spring constant k), so the soil support is smeared continuously along the element rather than lumped at nodes. Distributed loads are turned into equivalent consistent nodal forces with four-point Gauss integration, and point loads are distributed to the nodes through the element shape functions. The global system is assembled, the end boundary conditions applied, and the equations solved directly by Gaussian elimination with partial pivoting. Moment and shear are recovered from the second and third derivatives of the displacement field and the subgrade reaction is p = −k·w.
Compression-only foundation
By default the springs act in both directions (linear). With the compression-only option the analysis becomes nonlinear: it iterates, deactivating the foundation on any element where the beam moves upward (which would imply a physically impossible tensile reaction) and re-solving, until no further elements lift off. The lifted length, iteration count and convergence status are reported. Standard Winkler assumptions apply: the soil springs are independent (no shear coupling between them), the beam is prismatic with constant EI, and displacements are small.
Frequently asked questions
What does this beam on elastic foundation calculator do?
It analyzes a straight beam resting on a continuous elastic (Winkler) foundation and returns the deflection, slope, shear, bending moment and subgrade reaction (soil pressure) along the full length of the beam. You define the span, flexural stiffness EI, the foundation spring constant, the end supports, and any distributed or concentrated loads, and the tool plots and tabulates the full response.
What is a Winkler elastic foundation?
The Winkler model represents the supporting soil as a bed of independent, closely spaced linear springs. The reaction at any point is proportional to the deflection at that point: p = k times w, where k is the foundation spring constant (the modulus of subgrade reaction times the beam width). The springs do not interact with one another, which makes the model simple and widely used for footings, mat strips and rail or pipe support.
What solution method does it use?
It uses the finite element method. The beam is divided into two-node Hermitian cubic beam elements, each with a consistent beam-bending stiffness matrix and a consistent Winkler foundation stiffness matrix. Distributed loads are converted to consistent nodal forces using four-point Gauss integration, point loads are placed with the element shape functions, and the assembled system is solved directly by Gaussian elimination with partial pivoting.
What is the compression-only (no-tension) option?
Real soil can push up on a beam but cannot pull it down, so where the beam lifts off there should be no reaction. When the compression-only subgrade box is checked the tool runs an iterative analysis: it deactivates the foundation springs on any element where the beam displaces upward and re-solves until no further elements lift off, so the reaction is never tensile. It reports how much of the beam has lifted off and how many iterations were used.
What boundary conditions and loads are supported?
Each end can be fixed, pinned, guided (rotation prevented, vertical translation free) or free with no support, so the beam can be supported by the foundation alone or by a combination of end supports and the elastic bed. Loads include any number of partial linearly varying distributed loads (defined by start and end position and start and end intensity) and any number of concentrated point loads, with downward positive.
Which units does it use and can I export the results?
You can switch between US customary and SI units at any time and all inputs and results convert automatically; internally the engine works in US units. The full sampled response (position, load, deflection, moment, shear and subgrade reaction) can be exported to a CSV file for use in Excel or other software.
Is it free to use?
Yes. It runs entirely in your browser, with no download, no license and no data leaving your computer. For continuous beams with multiple spans and supports, the companion GoBeam spreadsheet offers a full Excel-based analysis.