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Two-Node Spring Stiffness Matrix Calculator — result sheet
Build the local 2×2 stiffness matrix for a linear spring element and calculate nodal forces, extension, and strain energy.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: K = [[k, −k], [−k, k]]; F = K·u; spring extension = u₁−u₂; strain energy = ½k(u₁−u₂)², with displacements converted to metres.
A two-node axial spring relates the relative displacement of its endpoints to equal-and-opposite nodal forces. The matrix is singular before a support or boundary condition is applied because a rigid translation does not stretch the spring. This page builds the element matrix and reports its internal response; it does not solve a complete finite-element structure.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Spring stiffness — N/m; minimum 1.0E-6; maximum 1000000000000
- Node 1 displacement — mm; minimum -1000000; maximum 1000000
- Node 2 displacement — mm; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Spring stiffness | 12000 |
| Node 1 displacement | 2 |
| Node 2 displacement | -1 |
K = [[12000, −12000], [−12000, 12000]] N/m; extension = 3 mm; nodal forces are +36 N and −36 N; stored energy is 0.054 J.
Assumptions and limits
- The spring is linear, axial, and small-displacement with constant stiffness k.
- Node displacements are entered in millimetres and converted to metres for force and energy calculations.
- Positive force follows the local matrix convention F₁=k(u₁−u₂) and F₂=k(u₂−u₁).
- The local element matrix is not a globally assembled structure and no support condition is guessed.
- Damping, nonlinearity, buckling, plasticity, three-dimensional orientation, and dynamic mass effects are excluded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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