Timber Beam Design Calculator

Inputs

Example Data Table

Formula Used

This calculator models a simply supported rectangular timber beam with:

• Uniform line load w (from area loads × spacing, plus self-weight if enabled)
• Optional midspan point load P

Section properties (rectangular)

• Area: A = b · h
• Second moment: I = b · h³ / 12
• Section modulus: S = b · h² / 6

Strength checks

• Max moment (uniform): M = w · L² / 8
• Max moment (midspan point): M = P · L / 4
• Bending stress: σ = M / S
• Max shear (uniform): V = w · L / 2
• Max shear (point): V = P / 2
• Rectangular shear stress: τ_max = 1.5 · V / A

Deflection check (midspan)

• Uniform load: δ = 5 · w · L⁴ / (384 · E · I)
• Midspan point load: δ = P · L³ / (48 · E · I)
• Allowable deflection: δ_allow = L / (limit)

How to Use This Calculator

1. Select units (Metric or Imperial) and choose a load input mode.
2. Enter span, spacing, and beam width/depth for the trial section.
3. Add dead and live loads, and an optional midspan point load.
4. Enter allowable bending/shear values and modulus of elasticity.
5. Pick a deflection limit (or enter a custom denominator).
6. Press Calculate to view results above the form.
7. Use the CSV/PDF buttons to save a report of the latest run.

Professional Article

Design intent and scope

Timber beams are often governed by a balance between strength and serviceability. This tool evaluates a simply supported rectangular member under uniform loading and an optional midspan point load, giving demand‑to‑capacity ratios for bending, shear, and deflection.

Key inputs and typical ranges

Span, spacing, section width, and section depth drive performance. For residential floors, spans around 3–6 m and spacing near 400–600 mm are common. Typical total surface loads may fall near 2–4 kN/m², while allowable bending values may range 8–18 MPa depending on grade factors.

Converting surface loads to line load

When loads are entered as surface values, the calculator multiplies (dead + live) by spacing to create a line load w in kN/m. For example, 1.0 kN/m² dead plus 2.0 kN/m² live at 0.40 m spacing becomes 1.2 kN/m before self‑weight. Self‑weight is estimated from density, gravity, and cross‑section area.

Section properties used by the calculator

Section capacity depends on basic geometric properties. The calculator uses area A = b·h, section modulus S = b·h²/6, and second moment I = b·h³/12. These govern stresses and deflection response and allow comparison between trial sizes.

Strength checks for bending and shear

Maximum moment combines uniform and point‑load effects, using M = wL²/8 and M = PL/4. Bending stress is computed as σ = M/S and compared to the allowable Fb. Maximum shear uses V = wL/2 plus V = P/2, with rectangular shear τmax = 1.5V/A checked against Fv.

Serviceability and deflection limits

Deflection is calculated at midspan using δ = 5wL⁴/(384EI) for uniform load and δ = PL³/(48EI) for a midspan point load. The allowable limit is L/240, L/360, L/480, or a custom denominator. Many floor systems target L/360, while brittle finishes may warrant L/480.

Interpreting results and sizing guidance

Results show PASS/FAIL and utilization ratios. If bending governs, increase depth first because S grows with h². If deflection governs, depth is even more effective because I grows with h³. The guidance values for required S and I help estimate a suitable depth while keeping width.

Good practice notes for timber projects

Use this output for preliminary sizing and coordination. Confirm bearing length, lateral stability, moisture effects, connection details, and code factors for duration of load and member configuration. Always review designs with the governing standard and local project requirements.

FAQs

1. Does the calculator include timber self‑weight automatically?

Yes, when enabled it estimates self‑weight from density, gravity, and cross‑section area, then adds it to the applied line load. Disable it if your dead load already includes member weight.

2. What beam support condition is assumed?

The equations assume a simply supported beam with maximum moment at midspan and maximum shear at supports. Cantilevers, continuous spans, and fixed ends need different factors and should be checked separately.

3. How are area loads converted to a line load?

The tool multiplies the combined surface load by the tributary spacing. For example, 3.0 kN/m² at 0.40 m spacing becomes 1.2 kN/m before adding self‑weight.

4. Why can deflection control even when stresses pass?

Deflection depends strongly on stiffness EI and span length. A beam may have adequate strength yet feel bouncy or crack finishes. Increasing depth is usually the most effective way to reduce deflection.

5. What do the utilization ratios mean?

Each ratio is demand divided by allowable capacity. Values at or below 1.00 indicate the check passes. The governing ratio highlights whether bending, shear, or deflection is driving the design.

6. Can I model a point load that is not at midspan?

This version treats the point load as acting at midspan for a conservative, simple check. Off‑center loads change moment and deflection shapes, so verify with appropriate beam formulas or software.

7. What should I verify outside this calculator?

Confirm bearing length, lateral restraint, notch and hole limits, connection design, load duration and moisture adjustments, fire requirements, and the governing standard for your region before finalizing member sizes.