Calculator Inputs
Example Data Table
| Example | Support | Load case | Span | Section | E | Primary load | Approx. max deflection |
|---|---|---|---|---|---|---|---|
| 1 | Simply supported | Midspan point load | 4.0 m | 50 × 200 mm | 11,000 MPa | 2.0 kN | 7.27 mm |
| 2 | Simply supported | Uniform load | 3.6 m | 63 × 225 mm | 11,000 MPa | 2.5 kN/m | 8.31 mm |
| 3 | Cantilever | Free-end point load | 2.0 m | 75 × 225 mm | 11,500 MPa | 1.2 kN | 3.91 mm |
Formula Used
Rectangular section stiffness: I = b × h³ / 12
Section modulus: Z = b × h² / 6
Elastic beam relation: EIy'' = M(x)
Common maximum deflection equations used in this tool:
- Simply supported beam with midspan point load:
δmax = P L³ / 48EI - Simply supported beam with full-span uniform load:
δmax = 5 w L⁴ / 384EI - Cantilever with free-end point load:
δmax = P L³ / 3EI - Cantilever with full-span uniform load:
δmax = w L⁴ / 8EI
For point loads placed away from midspan or away from the free end, the calculator applies the corresponding piecewise elastic-curve equations and samples the full member length to find the maximum deflection location.
How to Use This Calculator
- Select the support condition: simply supported or cantilever.
- Choose the load case that matches your timber member.
- Enter the span length in metres.
- Enter the timber section width and depth in millimetres.
- Select a timber grade preset or enter a custom modulus of elasticity.
- Leave the custom I field blank for rectangular sections, or enter a known value.
- Enter the load magnitude in kN or kN/m.
- If using an offset point load, enter the load position.
- Choose the serviceability limit ratio such as L/240 or L/360.
- Optionally include self-weight using density and section size.
- Submit the form to see deflection, reactions, moment, stress, and the graph.
- Use the CSV and PDF buttons to export your results.
Frequently Asked Questions
1) What does this calculator check?
It estimates elastic deflection for common timber beam cases, then compares the maximum value against a selected serviceability limit such as L/240, L/360, or L/480.
2) How is the second moment of area calculated?
For a rectangular timber section, the calculator uses I = b × h³ / 12. You can override that value if you already know the section property.
3) Which modulus of elasticity should I use?
Use the design value that matches your timber grade, standard, moisture condition, and project assumptions. If you already have a verified value, choose the custom E option.
4) Can I include self-weight?
Yes. The checkbox adds member self-weight as a full-span uniform load using the section size and entered density value.
5) Why do point load and uniform load results differ?
They produce different bending moment distributions. Because deflection follows the elastic curve created by those moments, the same total load can give different maximum deflections.
6) What deflection limit is commonly used?
It depends on the member use, finish sensitivity, code, and project criteria. Floors, roofs, and members supporting brittle finishes often use different serviceability limits.
7) Is this enough for structural design?
No. It is a fast calculation aid. Final design should also check bending, shear, bearing, vibration, stability, connections, duration effects, and applicable code requirements.
8) When should I use a custom I value?
Use it when the section is not rectangular, when you are using a built-up member, or when manufacturer data provides a verified section property.