Timber Frame Design Calculator
Beam sizing from span, load, and wood species using NDS bending and deflection checks.
About this calculator
This calculator runs the two classic checks a timber beam must pass: bending stress and deflection. Uniform Load On Beam (lb/ft) is Total Load (dead + live) times Tributary Width, then Max Bending Moment follows the standard simply-supported beam formula M = wL^2/8. Actual Bending Stress (fb) is that moment divided by the beam's Provided Section Modulus (S = b x d^2/6), so it depends only on span, load, tributary width, and the chosen beam width and depth -- Wood Species never enters this particular formula, because fb is a demand number, not a capacity number. Species only shows up on the capacity side: Required Section Modulus is M x 12 / Fb, where Fb is the species' allowable bending stress, taken from the American Wood Council's NDS Supplement Table 4D for No.
1 grade sawn timber (1000 psi for Douglas Fir-Larch up to 1100 psi for Southern Pine, as low as 575 psi for Eastern White Pine), and Bending Demand/Capacity Ratio compares the two. Because Beam Depth appears squared in the section modulus, small increases in depth cut bending stress sharply -- far more efficient than adding width. Deflection follows a separate track: Max Deflection scales with the beam's stiffness (E, also species-dependent) and moment of inertia (I = b x d^3/12, cubed in depth), checked against the L/240 serviceability limit, which itself depends only on span. A beam can pass bending and still fail deflection, or vice versa -- both checks are reported independently so you can see which one governs.
Inputs
Results
Actual bending stress (fb)
864 psi
Figures current as of 2018. Source: American Wood Council, National Design Specification (NDS) for Wood Construction, 2018 Edition, Supplement Table 4D (Reference Design Values for Visually Graded Timbers, Sizes 5x5 and Larger)
How to Use This Calculator
- Enter Beam span, Total load (dead + live), and Tributary width.
- Set Beam width (b), Beam depth (d), and Wood species.
- Review the Actual bending stress (fb) (psi) result.
- Use Bending demand/capacity ratio and Bending check pass to inform your decision.
How the result changes with Beam depth (d)
| Beam depth (d) | Actual bending stress (fb) |
|---|---|
| 5 | 3,456 psi |
| 7.5 | 1,536 psi |
| 15 | 384 psi |
| 25 | 138 psi |
What each input means
- Beam span
- Clear span of the beam between supports.
- Total load (dead + live)
- Combined dead load + live load on the floor or roof (e.g., 40 live + 10 dead = 50 psf).
- Tributary width
- Half the bay spacing on each side of the beam. For a 16 ft bay, tributary width is 8 ft.
- Beam width (b)
- Actual width of the timber beam cross-section.
- Beam depth (d)
- Actual depth of the timber beam cross-section.
- Wood species
- 0 = Douglas Fir-Larch, 1 = Southern Pine, 2 = Eastern White Pine, 3 = Red Oak, 4 = Western Red Cedar.
What each result means
- Actual bending stress (fb)
- Computed bending stress at midspan: fb = M/S.
- Bending demand/capacity ratio
- S_required / S_provided. Must be ≤ 1.0 to pass.
- Bending check pass
- 1 = pass (ratio ≤ 1.0), 0 = fail.
- Required section modulus
- Minimum section modulus needed: S = M×12 / Fb.
- Provided section modulus
- Section modulus of chosen beam: S = b×d²/6.
- Max deflection
- Maximum midspan deflection under uniform load.
- Deflection limit (L/240)
- Allowable deflection per L/240 serviceability limit.
- Deflection demand/capacity
- Actual / allowable deflection. Must be ≤ 1.0 to pass.
- Deflection check pass
- 1 = pass, 0 = fail.
- Uniform load on beam
- Load per linear foot: total_psf × tributary_width.
- Max bending moment
- M = wL²/8 for simply-supported beam.
- Moment of inertia (I)
- I = b×d³/12 for rectangular section.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersBeam span = 12, Total load (dead + live) = 50, Tributary width = 8, Beam width (b) = 6 = 6 input(s) provided
- Calculate Actual bending stressActual bending stress = (M_lbft * 12) / S_provided864 = 864
- Calculate Bending demand/capacity ratioBending demand/capacity ratio = S_required / S_provided0.864 = 0.864
- Calculate Bending check passBending check pass1 = 1
Figures and sources
- NDS-2018 reference design values (Fb, E) for visually graded sawn timber, No. 1 grade, by species (2018) — American Wood Council, National Design Specification (NDS) for Wood Construction, 2018 Edition, Supplement Table 4D (Reference Design Values for Visually Graded Timbers, Sizes 5x5 and Larger)
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Does changing the wood species affect the actual bending stress?
No. Actual Bending Stress (fb) is purely a function of the applied moment divided by the beam's own cross-section (fb = M x 12 / S_provided) -- it is a demand number that depends on span, load, tributary width, beam width, and beam depth, never on the species' allowable stress value. Species only changes what stress the beam is ALLOWED to carry (Fb), which shows up in Required Section Modulus and the Bending Demand/Capacity Ratio, not in the stress itself.
Why does increasing beam depth help so much more than increasing beam width?
Section modulus is S = b x d^2/6, so depth is squared while width is linear -- doubling Beam Depth (d) quarters the bending stress contribution from that term, while doubling Beam Width (b) only halves it. The same squaring effect is even stronger for deflection, where moment of inertia uses d^3, which is why timber framers reach for a deeper beam before a wider one when a span is under-sized.
Can a beam pass the bending check but fail the deflection check, or the reverse?
Yes, and this calculator reports them as two independent pass/fail results precisely because that happens often. A short, heavily loaded beam tends to be strength-governed (bending fails first), while a long, lightly loaded beam is often stiffness-governed (deflection fails first, well before the wood would actually break). Always check both Bending Check Pass and Deflection Check Pass before finalizing a size.
What does the Required Section Modulus number actually depend on?
Required Section Modulus (S_required = M x 12 / Fb) depends only on the applied moment (from span, load, and tributary width) and the species' allowable bending stress (Fb, taken from the American Wood Council's NDS-2018 reference design values for No. 1 grade sawn timber) -- it does not depend on the beam width or depth you actually entered at all. It tells you the minimum section modulus ANY beam of that species would need; Provided Section Modulus is what your chosen dimensions actually deliver, and the ratio of the two is the Bending Demand/Capacity Ratio.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Timber Grade Selection Calculator
Compare 9 species/grade combinations for a beam application with bending and deflection checks.
Structural EngineeringWood Beam Design Calculator
Check bending adequacy of wood beams per NDS ASD: compare actual bending stress against adjusted allowable stress.
Timber FramingPost and Beam Layout Calculator
Post spacing, post count, beam quantities, and post load capacity for rectangular post-and-beam structures.
Timber FramingTimber Connector Design Calculator
Bolt count, spacing, and capacity for timber connections using NDS lateral design values.
Structural EngineeringSteel Beam Selection Calculator
Determine required section modulus, moment of inertia, and approximate beam weight for steel beam design with uniform and point loads.
More in Construction & Building Trades.