Beam Input Form
Example Data Table
The sample values below show a common simply supported beam check with one point load and one full span uniform load.
| Input | Example Value | Unit |
|---|---|---|
| Span length | 6 | m |
| Point load | 20 | kN |
| Point load position | 2.5 | m |
| Uniform load | 5 | kN/m |
| Elastic modulus | 200 | GPa |
| Second moment of area | 8500 | cm4 |
| Extreme fibre distance | 150 | mm |
| Deflection limit | 360 | L/360 |
Formula Used
Support Reactions
For a simply supported beam with one point load and a full span uniform load:
RA = P(L - a) / L + wL / 2
RB = Pa / L + wL / 2
Shear Force
V(x) = RA - wx - P when x is at or after the point load. Before the point load, remove P from the expression.
Bending Moment
M(x) = RAx - wx² / 2 - P(x - a) when x is at or after the point load. Before the point load, remove the final point load term.
Bending Stress
σ = Mc / I
The calculator converts units internally and reports stress in MPa.
Deflection Method
The deflection estimate uses elastic curvature:
y'' = M / EI
The program integrates curvature numerically and applies simple support boundary conditions at both ends.
How to Use This Calculator
- Enter the clear beam span in metres.
- Enter the point load and its location from the left support.
- Enter the full span uniform load.
- Use a load factor of 1 for service load checks.
- Enter elastic modulus, second moment of area, and extreme fibre distance.
- Add allowable stress and deflection limit values.
- Enter a check position to review local shear and moment.
- Press the calculate button to display results above the form.
- Use CSV for spreadsheets or PDF for a simple saved report.
Simply Supported Beam Calculation Guide
Overview
A simply supported beam has one pinned support and one roller support. It is common in floors, lintels, bridges, platforms, and temporary works. The support arrangement lets the beam rotate, while the reactions carry vertical load. This calculator helps estimate those reactions and the main bending checks.
Load Setup
Start with a clear span. Then enter a point load and its distance from the left support. You may also add a full length uniform load. The tool combines both cases by superposition. That means each load effect is found separately, then added together. This approach is useful for early design checks and study work.
Reading Results
The reaction values show how much load each support must resist. Shear values help locate sudden force changes. Bending moment values show where the beam is most stressed. Deflection estimates show expected movement under service loading. Stress and deflection ratios compare the result with chosen limits.
Assumptions
The calculator uses elastic beam theory. It assumes small deflection, straight members, simple supports, and constant stiffness. It also assumes the uniform load covers the full span. Real projects may include partial loads, moving loads, torsion, lateral buckling, holes, connection flexibility, and vibration. Those cases need deeper analysis.
Input Consistency
Use consistent inputs. The span and load position use metres. The point load uses kilonewtons. The uniform load uses kilonewtons per metre. Elastic modulus uses gigapascals. Second moment of area uses centimetres to the fourth power. Extreme fibre distance uses millimetres.
Design Checks
The load factor field lets you study factored loading. Keep it at one for service checks. Increase it when comparing stronger design combinations. The deflection limit is entered as a span ratio, such as L over 360. A lower ratio allows more movement. A higher ratio creates a stricter check.
Check Point Review
The check point field is helpful during review. Enter any location along the span. The output reports local shear and bending moment there. This is useful near loads, supports, bearing plates, openings, or service attachments. It also helps verify hand sketches before detailed design work begins safely.
Export Options
The result table is designed for quick notes. Use the CSV export for spreadsheets. Use the PDF export for records. Always confirm final beam size with local codes, material rules, safety factors, and a qualified engineer.
FAQs
1. What is a simply supported beam?
It is a beam supported at both ends, usually by a pin and roller. The supports resist vertical load while allowing rotation, which creates a common and simple structural model.
2. Can this calculator handle both point and uniform loads?
Yes. It combines one point load and one full span uniform load using superposition. Enter zero for either load when it does not apply.
3. What does reaction RA mean?
RA is the vertical reaction at the left support. It shows how much load the left support must carry under the entered loading conditions.
4. What does maximum bending moment show?
It shows the highest internal bending demand in the beam. This value is important for bending stress checks and section selection.
5. Why is deflection important?
Deflection shows how much the beam may move under load. Excessive deflection can damage finishes, affect serviceability, or make a structure feel unsafe.
6. What is the load factor field for?
The load factor multiplies point and uniform loads. Use one for normal service checks. Use a higher value when studying factored design combinations.
7. Does this replace a structural engineer?
No. It is a planning and learning tool. Final designs should follow local codes and should be checked by a qualified professional.
8. Why do I need section properties?
Elastic modulus, moment of inertia, and fibre distance are needed for stiffness and stress checks. They describe how the selected beam section behaves.