Beam Input Form
Example Data Table
| Example | Span | E | I | Point Load | UDL | Limit |
|---|---|---|---|---|---|---|
| Steel floor beam | 6 m | 200 GPa | 8,500 cm⁴ | 20 kN at 3 m | 5 kN/m full span | L/360 |
| Light roof beam | 4 m | 200 GPa | 3,200 cm⁴ | 8 kN at 2 m | 1.5 kN/m full span | L/240 |
| Timber joist check | 3.6 m | 11 GPa | 1,150 cm⁴ | 2 kN at 1.8 m | 0.8 kN/m full span | L/360 |
Formula Used
This calculator uses static equilibrium for reactions. It then uses beam curvature to estimate slope and vertical deflection along the span.
Support reactions:
RA + RB = total load
RB × L = Σ(P × a) + Σ(w × loaded length × load centroid)
Bending moment at distance x:
M(x) = RA × x - point load effects - distributed load effects
Curvature relation:
E × I × d²y/dx² = M(x)
The program integrates curvature numerically. It adjusts the curve so deflection is zero at both supports.
Common checks:
Stress = M × c / I
Allowable deflection = L / selected ratio
Center point load deflection = P × L³ / (48 × E × I)
Full span uniform load deflection = 5 × w × L⁴ / (384 × E × I)
How to Use This Calculator
- Enter the beam span in meters.
- Select a material preset, or enter a custom elastic modulus.
- Enter the section moment of inertia in cm⁴.
- Add point loads, distributed loads, and optional self weight.
- Set the deflection limit, allowable stress, and load factor.
- Press the calculate button to view reactions, stress, slope, and deflection.
- Use the CSV or PDF button to save the result.
Simply Supported Beam Deflection Guide
About Simply Supported Beam Deflection
A simply supported beam rests on two supports. One support acts like a pin. The other acts like a roller. This setup lets the beam bend under load while the ends remain free to rotate. Deflection is the vertical movement caused by bending. It is important because a beam can be strong yet still feel unsafe or look damaged if it bends too much.
Why Deflection Checks Matter
Small deflection helps floors feel firm. It also protects finishes, ceilings, tiles, and service lines. Engineers often compare calculated deflection with limits such as span divided by 360. This calculator helps you review that serviceability limit. It also estimates bending stress, support reactions, slope, and the required moment of inertia. These values help during early sizing and comparison work.
Load Options Included
The tool supports common beam loading cases. You can enter up to two point loads. You can place each point load at any distance from the left support. You can also add a distributed load over all or part of the span. A separate self weight field lets you include beam weight as a uniform load. A load factor field allows quick service or conservative checks.
How Results Are Interpreted
The maximum deflection is shown in millimeters. Its location is shown in meters from the left support. The reaction values show how much force each support carries. The bending moment is used to estimate extreme fiber stress. The slope result shows beam rotation in milliradians. The status note compares deflection and stress with your chosen limits.
Design Use
Use this page for learning, estimating, and preliminary design. Always confirm final designs with local codes and a qualified professional. Real beams may include connections, lateral restraint, composite action, shear deformation, holes, cracks, and construction tolerances. These details can change the answer. Still, a clear deflection estimate is a strong first step for comparing spans, materials, and section sizes.
Good input quality matters. Measure the clear span carefully. Use the correct elastic modulus. Enter the section moment of inertia from a reliable table. Check units before submitting. A small unit mistake can create a very large error in calculated movement.
FAQs
What is beam deflection?
Beam deflection is the vertical movement of a beam under load. It depends on span, loading, material stiffness, and section stiffness.
What units should I use?
Use meters for span, GPa for elastic modulus, cm⁴ for inertia, kN for point loads, and kN/m for distributed loads.
What does L/360 mean?
L/360 means allowable deflection equals the span divided by 360. A 6 m beam has an L/360 limit of 16.67 mm.
Can I add more than one load?
Yes. This calculator supports two point loads, one partial distributed load, and self weight over the full span.
Why does moment of inertia matter?
Moment of inertia measures bending stiffness from section shape. A larger value usually lowers deflection and bending stress.
Is this suitable for final design?
Use it for estimates and learning. Final structural design should follow local codes and be reviewed by a qualified professional.
What is extreme fiber distance?
It is the distance from the neutral axis to the outermost fiber. It is used to estimate bending stress.
Why use a load factor?
A load factor increases entered loads for conservative checks. Use 1.00 for direct service load deflection estimates.