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Timber Beam Design Calculator

Design timber beams per NDS 2018 and Eurocode 5 standards. Check bending, shear, deflection, and bearing for sawn lumber.

Structural Analysis Structural engineers, timber designers, architects Commercial Intent: MEDIUM

Engineering Formulas

Adjusted Bending Stress

Fb' = Fb × CD × CM × Ct × CF × Cr × Ci
Where: CD = load duration, CM = moisture, Ct = temp, CF = size, Cr = repetitive

F_b': Adjusted bending design value (MPa)

F_b: Reference bending design value (MPa)

C_D: Load duration factor

C_M: Wet service factor

C_t: Temperature factor

C_F: Size factor

C_r: Repetitive member factor (1.15)

Required Section Modulus

Sreq = Mmax / Fb'
Sact = b × d² / 6
Check: Sact ≥ Sreq

S_req: Required section modulus (mm³)

S_act: Actual section modulus (mm³)

M_max: Maximum bending moment (kNm)

b: Beam width (mm)

d: Beam depth (mm)

Shear Check

fv = 1.5 × V / (b × d)
fv ≤ Fv'

f_v: Actual shear stress (MPa)

V: Maximum shear force (kN)

F_v': Adjusted shear design value (MPa)

Deflection Check

Δ = 5wL⁴/(384EI) (simple)
Δ = wL⁴/(8EI) (cantilever)
Δ ≤ L/240 or L/360

Δ: Maximum deflection (mm)

E: Modulus of elasticity (MPa)

I: Moment of inertia (mm⁴)

L: Span (mm)

Bearing Check

fc⊥ = R / (b × lb)
fc⊥ ≤ Fc⊥'

f_c⊥: Actual bearing stress (MPa)

R: Reaction force (kN)

l_b: Bearing length (mm)

F_c⊥': Adjusted compression perpendicular (MPa)

Worked Example

Douglas Fir No.2 Floor Beam

span: 4width: 50depth: 200appliedLoad: 5species: douglas-firgrade: no2moisture: dryloadDuration: standardrepetitiveMember: falsetempRange: le-38bearingLength: 100cantilever: false

Mmax

M = 5 × 4² / 8 = 10 kNm

Vmax

V = 5 × 4 / 2 = 10 kN

Sreq

S_req = 10 × 10⁶ / 8.27 = 1,209,188 mm³

Sact

S_act = 50 × 200² / 6 = 333,333 mm³ — FAILS

Result: 50×200 Douglas Fir No.2 fails bending. Recommend larger section (min depth ~290 mm).

Engineering Notes

Always provide lateral bracing at supports and intermediate points.

For beams deeper than 300 mm, consider lateral-torsional buckling.

Notching at supports reduces shear capacity significantly.

Glulam and LVL have higher design values than sawn lumber.

Deflection often governs for longer spans — increase depth if deflection fails.

Assumptions

• Sawn lumber (not glulam or LVL)

• Beam is laterally braced

• Load is uniformly distributed

• Simple span or cantilever conditions

• No notching at supports

Common Mistakes

✕ Not applying size factor for deep beams

✕ Using ultimate loads instead of service loads for deflection

✕ Forgetting lateral bracing requirements

✕ Not checking bearing stress at supports

✕ Using green (wet) strength for dry conditions

Frequently Asked Questions

What is the NDS?

The National Design Specification (NDS) for Wood Construction is the US standard for timber design, published by the American Wood Council.

What are the different load duration factors?

C_D accounts for the duration of load: 1.0 for permanent (10+ yr), 1.15 for 10-yr (snow), 1.25 for 2-mo (construction), 1.6 for wind/earthquake.

When do I use repetitive member factor?

Use C_r = 1.15 when beams are spaced ≤ 600mm apart with at least 3 members. This accounts for load sharing between adjacent members.

What is the size factor?

The size factor C_F accounts for the fact that larger timber members have lower strength per unit area due to more defects in larger pieces.

What is a typical deflection limit?

L/240 for total load (roofs), L/360 for live load (floors), L/480 for brittle finishes. Our calculator uses L/240 by default.

References & Standards

NDS 2018Eurocode 5 (EN 1995-1-1)IS 883

NDS 2018

National Design Specification for Wood Construction

Eurocode 5 (EN 1995-1-1)

Design of Timber Structures

IS 883

Design of Structural Timber in Building

AWC Wood Handbook

Wood as an Engineering Material

Related Calculators

Bending Moment Calculator

Calculate bending moments for beam design.

Moment of Inertia Calculator

Calculate section properties.

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