| Span (m) | w_dead (kN/m) | w_live (kN/m) | P (kN) | Width b (mm) | Preset | Limit | Suggested size (mm) |
|---|---|---|---|---|---|---|---|
| 4.0 | 0.8 | 1.5 | 0 | 50 | Douglas Fir-Larch No.2 | L/360 | 50 × 200 (example) |
| 5.5 | 1.0 | 2.0 | 3.0 | 75 | Glulam GL24h | L/360 | 75 × 350 (example) |
- Maximum moment (simply supported): Mmax = wL²/8 + PL/4
- Adjusted allowable bending stress: Fb,allow = (Fb×Cd×Cm×Ct×Cf×Cr) / φ
- Section modulus (rectangular): S = bd²/6
- Second moment of area (rectangular): I = bd³/12
- Deflection: Δ = 5wL⁴/(384EI) + PL³/(48EI)
- Sizing: Solve for d from S and from I, then use the larger.
- Enter the span and your line loads (dead and live).
- Add a midspan point load if equipment or a concentrated load exists.
- Select a timber preset, or choose custom and enter Fb and E.
- Set adjustment factors only if you know your code values.
- Enable deflection sizing and choose a limit like L/360.
- Press Calculate to see the suggested beam size and checks.
- Download CSV or PDF to keep the results with your notes.
Load definition and realistic inputs
Start with the correct line load on the beam. Convert any area load (kN/m²) into a line load (kN/m) by multiplying by tributary width, then add permanent dead load components separately from live load. Include any concentrated midspan point load for posts, equipment, or localized storage.
Bending demand and required section modulus
The calculator assumes a simply supported beam and combines uniform and point loading to estimate maximum moment: Mmax = wL²/8 + PL/4. It then computes a required section modulus, Sreq, using an adjusted allowable bending stress. For a rectangular section, S = bd²/6, so depth is the fastest way to improve bending capacity.
Serviceability control through deflection limits
Strength alone may not control timber beams; deflection and vibration often drive sizing. The tool checks deflection with Δ = 5wL⁴/(384EI) + PL³/(48EI) against a limit like L/360. Use service loads here, commonly live load for floors, to keep finishes tight and occupants comfortable.
Material selection and adjustment factors
Species and grade affect both bending strength (Fb) and stiffness (E). Presets give typical values, while custom inputs support project data. Adjustment factors represent service conditions and permitted code modifiers. The safety modifier φ reduces the effective allowable stress, nudging the recommendation toward a conservative, buildable size.
Example sizing walkthrough and example data
Example case: L = 4.0 m, wdead = 0.8 kN/m, wlive = 1.5 kN/m, P = 0 kN, b = 50 mm, deflection limit L/360, factors at 1.0, and φ = 1.0. The calculator sizes depth for bending and deflection, then suggests the next practical depth that passes both checks.
- Inputs: 4.0, 0.8, 1.5, 0, 50, L/360
- Outputs: suggested b×d size, fb, Δ, PASS/FAIL
- Exports: CSV or PDF for documentation
1) Does this calculator replace a stamped design?
No. It provides a preliminary estimate for simply supported rectangular beams. Final design should include local code load combinations, bearing, lateral stability, connections, and any required professional review.
2) Which loads should I use for bending?
Bending is often checked using the controlling combination of dead and live line loads, plus any concentrated loads. Use the load-case selector to compare dead-only, live-only, or combined loading.
3) Which loads should I use for deflection?
Deflection is usually a serviceability check. Many designers use live load only for floors and total load for some roofs. Enter the service line load and service point load in the deflection inputs.
4) Why does depth change more than width?
Rectangular bending capacity increases with d² and stiffness increases with d³. That means small depth increases provide large improvements in both strength and deflection performance compared with width changes.
5) What does the safety modifier φ do?
φ increases conservatism by reducing the effective allowable bending stress used in sizing. A higher φ typically produces a larger suggested depth, which can help cover uncertainties in loading and assumptions.
6) How do I convert area load to line load?
Multiply the area load (kN/m²) by the beam tributary width (m). For example, 2.0 kN/m² over 1.8 m tributary width becomes 3.6 kN/m on the beam.
7) What assumptions are built into the formulas?
The beam is assumed simply supported with a constant rectangular section, uniform load along the span, and any point load applied at midspan. Different support conditions require different moments and deflection equations.