Calculator Inputs
This page models a 1D axial bar mesh with linear two-node elements. Keep units consistent across force, length, area, and modulus.
Example Data Table
These sample values match the default inputs already loaded in the calculator.
| Item | Value 1 | Value 2 | Value 3 |
|---|---|---|---|
| Element Lengths | 1.20 m | 0.80 m | 1.00 m |
| Areas | 0.0030 m² | 0.0025 m² | 0.0020 m² |
| Elastic Moduli | 2.10e11 Pa | 2.10e11 Pa | 2.10e11 Pa |
| Nodal Loads | Node 2: 0 N | Node 3: 5000 N | Node 4: 10000 N |
| Support Model | Node 1 fixed, rightmost node free | ||
Formula Used
This calculator uses the linear finite element method for a one-dimensional axial bar system. Each element has two nodes and one axial displacement degree of freedom per node.
Element stiffness matrix:
k_e = (A_e E_e / L_e) [ [ 1, -1 ], [ -1, 1 ] ]
Global equilibrium:
K u = F
Element strain:
epsilon_e = (u_j - u_i) / L_e
Element stress:
sigma_e = E_e * epsilon_e
Element axial force:
N_e = A_e * sigma_e
Total strain energy:
U = 1/2 * sum( (A_e E_e / L_e) * (u_j - u_i)^2 )
The present model assumes linear elasticity, small deformation, and axially loaded bar elements. Use consistent units for all entries.
How to Use This Calculator
- Select one, two, or three active bar elements.
- Enter element lengths, cross-sectional areas, and elastic moduli.
- Enter nodal point loads at the active nodes.
- Choose whether the rightmost active node is restrained.
- Keep all units consistent before solving.
- Click the solve button to assemble the global stiffness matrix.
- Review displacements, reactions, stresses, axial forces, and the displacement graph.
- Use the CSV and PDF buttons to export results.
Frequently Asked Questions
1. What does this calculator solve?
It solves a one-dimensional axial bar finite element problem. The tool assembles the global stiffness matrix, applies nodal loads and support conditions, then computes nodal displacements, support reactions, strains, stresses, and axial forces.
2. How many elements can I use here?
This version supports up to three linear bar elements connected in series. That keeps the page simple, readable, and fast while still showing full finite element assembly and response calculations.
3. Why do my units matter so much?
The solver does not convert units automatically. If length, area, modulus, and force use inconsistent scales, your displacements and stresses will be misleading. Use one consistent system from start to finish.
4. What changes when I fix the right node?
Restraining the rightmost active node changes the free degrees of freedom and the reduced stiffness matrix. That usually lowers displacement and can change internal force sharing between elements.
5. What is AE/L in the output table?
AE/L is the scalar stiffness coefficient for each bar element. Larger area, larger modulus, or shorter length increases axial stiffness and makes that element resist deformation more strongly.
6. Can different elements use different materials?
Yes. Each element accepts its own elastic modulus and area. That lets you model stepped members, mixed materials, or stiffness transitions along the bar chain.
7. Is this suitable for beam bending or 2D meshes?
No. This page is limited to axial bar elements in one dimension. Beam bending, frame behavior, plate analysis, and two-dimensional meshes require different element formulations and extra degrees of freedom.
8. What does the Plotly graph show?
The graph plots nodal displacement against position along the assembled bar. It helps you see how deformation changes from node to node and where the largest movement occurs.