Calculator Input
Formula Used
This calculator evaluates a prismatic rectangular section under static loading. It computes support reactions, then builds shear and bending moment distributions along the member length. Stress and deflection follow from classical beam relations.
For partial UDL cases, the calculator uses the active loaded segment at each position to build piecewise shear and moment values. Safety factor equals allowable stress divided by calculated bending stress.
How to Use This Calculator
- Select a support condition: simply supported or cantilever.
- Choose the load type: point load, full UDL, or partial UDL.
- Enter beam length and load magnitude using the shown units.
- For point loads, enter the load position from the left or fixed end.
- For partial UDL, enter the start and end positions of the loaded zone.
- Enter rectangular section width, section height, elastic modulus, and allowable stress.
- Click Analyze Static Load to show reactions, maximums, stress, deflection, and the Plotly graph.
- Use the export buttons to save a summary and the full position-based dataset.
Example Data Table
| Scenario | Support | Load Input | Section | Example Insight |
|---|---|---|---|---|
| Case A | Simply Supported | Point load: 18 kN at 2.5 m on a 6 m span | 120 mm × 240 mm, E = 200 GPa | Good for checking reaction split and local moment peak. |
| Case B | Simply Supported | UDL: 8 kN/m over the full 5 m span | 150 mm × 300 mm, E = 210 GPa | Useful for symmetrical moment and deflection behavior. |
| Case C | Cantilever | Partial UDL: 6 kN/m from 1 m to 3.5 m | 100 mm × 220 mm, E = 190 GPa | Highlights fixed-end moment growth from eccentric loading. |
Frequently Asked Questions
1. What does this calculator analyze?
It analyzes static beam loading for simply supported and cantilever members. It returns reactions, maximum shear, maximum bending moment, bending stress, deflection, and a quick safety comparison using your allowable stress input.
2. Which load types are included?
You can evaluate a single point load, a full-span uniformly distributed load, or a partial uniformly distributed load. Those cover many common educational, laboratory, and preliminary structural physics problems.
3. Why do I need section width and height?
Width and height define the rectangular section properties. The calculator uses them to compute second moment of area and section modulus, which directly control bending stress and elastic deflection.
4. Are the deflection values exact?
They are numerical estimates based on classical elastic beam theory. For linear material behavior and a constant rectangular section, the results are usually very useful for screening and comparison work.
5. What units should I enter?
Use meters for length, kN for point load, kN/m for distributed load, millimeters for section size, GPa for elastic modulus, and MPa for allowable stress. Outputs follow matching engineering units.
6. What does safety factor mean here?
Safety factor equals allowable stress divided by calculated bending stress. A value above one means the chosen allowable limit exceeds the computed stress for the entered loading case.
7. Can I use it for final design approval?
It is best for study, verification, and early-stage sizing. Final design decisions should also include code checks, material limits, serviceability rules, connections, buckling, and professional review where needed.
8. What do the exports contain?
The CSV and PDF exports include the main results and the full position-by-position dataset. That makes it easier to archive runs, share findings, or reuse the distributions in reports.