Model axial bar systems with stiffness, stress, and nodal loads. Export clean reports. Track displacement, reaction, strain energy, and force results.
| Element | Length (m) | Area (m²) | Elasticity (Pa) | Distributed Load (N/m) |
|---|---|---|---|---|
| 1 | 2.000 | 0.003000 | 200,000,000,000 | 0 |
| 2 | 1.500 | 0.002500 | 200,000,000,000 | 0 |
| 3 | 2.500 | 0.002000 | 210,000,000,000 | 0 |
Sample boundary condition: Node 1 fixed, Node 4 loaded by 25,000 N. This set produces displacement, stress, reaction, and stiffness outputs.
For a 1D axial bar element, local stiffness is:
k = AE / L
The local element stiffness matrix is:
[ke] = (AE/L) × [[1, -1], [-1, 1]]
The distributed axial load contribution is:
{fe} = qL/2 × [1, 1]
After assembly, the global system is:
[K]{U} = {F}
Then, strain, stress, axial force, and strain energy are:
ε = (u₂ - u₁) / L
σ = Eε
N = σA
Energy = 0.5 × (AE/L) × (u₂ - u₁)²
This calculator performs one-dimensional axial bar finite element analysis. It is designed for physics, mechanics, structural basics, and engineering education where users need fast stiffness-based solutions.
It assembles a global stiffness matrix from multiple bar elements, applies equivalent nodal loads, enforces restraints, solves unknown nodal displacements, and reports reactions, strains, stresses, axial forces, and strain energy.
Finite element analysis breaks a long member into smaller elements. This makes complex load paths easier to analyze. It also helps users understand how local element behavior contributes to overall structural response.
The page includes downloadable CSV and PDF outputs. These options are useful for documentation, reports, coursework, and quick comparisons between multiple trial cases.
It analyzes one-dimensional axial bar systems. Each element carries axial stiffness and axial load only. It does not solve beam bending, torsion, plate, or solid continuum problems.
The stiffness matrix links nodal forces to nodal displacements. It describes how strongly the whole element assembly resists deformation under the applied loading and support conditions.
Without a restraint, the model can translate freely. That makes the reduced stiffness matrix singular, so the solver cannot determine unique displacements or reactions.
Nodal force acts directly at a node. Distributed load acts along an element length. The calculator converts distributed load into equivalent nodal contributions during assembly.
First, displacement difference gives axial strain. Then stress is found using Hooke’s law, σ = Eε. Axial force is the stress multiplied by cross-sectional area.
Yes. Every element can have its own elasticity, area, length, and distributed load. That allows stepped bars and mixed-material axial systems.
Strain energy measures elastic energy stored in deformation. It helps assess internal response and confirms consistency with external work in linear static problems.
No. This page is for axial bar analysis only. Advanced frames, beams, shells, and solids need additional degrees of freedom and more complex element formulations.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.