Calculator Input Panel
Use consistent units throughout. Example: meters, square meters, Pascals, and Newtons.
Example Data Table
These sample cases show how varying inputs affect displacement and stress behavior.
| Case | Total Length | Area | Young's Modulus | Elements | End Load | Distributed Load | Support |
|---|---|---|---|---|---|---|---|
| Steel Bar A | 2.0 | 0.005 | 200000000000 | 4 | 15000 | 0 | Fixed-Free |
| Steel Bar B | 3.0 | 0.004 | 210000000000 | 6 | 20000 | 800 | Fixed-Free |
| Aluminum Bar | 1.5 | 0.006 | 70000000000 | 5 | 12000 | 350 | Fixed-Fixed |
| Composite Study | 4.0 | 0.0035 | 95000000000 | 8 | 18000 | 500 | Fixed-Free |
Formula Used
Element stiffness matrix:
ke = (EA / Le) × [[1, -1], [-1, 1]]
Uniform axial load vector:
fe = qLe/2 × [1, 1]
Assembly equation:
K d = F
Element strain:
ε = (uj - ui) / Le
Element stress:
σ = E × ε
Internal axial force:
N = σ × A
This calculator applies the direct stiffness method for a one dimensional axial bar. It divides the member into equal linear elements, assembles the global stiffness matrix, applies support conditions, solves nodal displacements, and then back-calculates reactions, strains, stresses, and internal forces.
How to Use This Calculator
- Enter a model label for your own reference.
- Input total length, area, and Young's modulus.
- Choose how many equal finite elements to create.
- Enter the end point load and optional distributed load.
- Select the support condition for the bar model.
- Choose how many decimals you want displayed.
- Press Compute FEM Results to solve the model.
- Review summary cards, tables, and charts.
- Use CSV or PDF buttons to export the analysis.
Frequently Asked Questions
1. What type of problem does this calculator solve?
It solves one dimensional axial bar problems using equal linear finite elements. It is useful for estimating displacement, axial stress, reactions, and internal force under end and distributed loading.
2. Which units should I use?
Use consistent units only. For example, meters with square meters, Pascals, and Newtons. If units are mixed incorrectly, the numerical results will still solve but the physical meaning becomes wrong.
3. Why does increasing the number of elements matter?
More elements can better represent the structure and load distribution. For this simple axial bar, even a few elements often work well, but refined meshes help when you want smoother internal response detail.
4. What support conditions are available here?
This version supports fixed-free and fixed-fixed conditions. Fixed-free allows end movement at the last node. Fixed-fixed restrains both ends and redistributes reactions through the assembled system.
5. What is the difference between stress and internal force?
Stress is force divided by area. Internal force is the axial force carried by the element. The calculator first computes stress from strain and modulus, then multiplies stress by area.
6. Can I use negative loads?
Yes. Negative values simply reverse the loading direction. That can produce negative displacements, negative stresses, or opposite reactions depending on the support condition and material stiffness.
7. Why is the stiffness matrix shown?
It helps learners verify the assembled FEM system. Seeing the matrix and load vector makes the method transparent and useful for education, debugging, and comparing hand calculations.
8. Is this suitable for beams, plates, or nonlinear studies?
No. This page is for a one dimensional axial bar only. Beam bending, plate analysis, geometric nonlinearity, and material nonlinearity require different element formulations and more advanced solution logic.