Timber Beam Calculator — NDS Wood Beam Design Guide

Timber beam sizing per NDS 2018. Bending, shear, deflection, and bearing checks for sawn lumber, glulam, and engineered wood beams. Free calculator + span tables.

This page explains how to size timber beams by hand and how the Steel Calculator timber design tool automates NDS checks. The interactive calculator runs in your browser; this documentation is useful even without JavaScript.

Quick Timber Beam Span Table (Douglas Fir-Larch No. 2, 40 psf LL + 10 psf DL)

"OK" = demand/capacity < 0.85 under combined dead + live. Use the calculator for exact values.

NDS Timber Beam Design — Step by Step

Step 1 — Determine applied loads

w_dead = dead load (psf) x tributary width (ft) + beam self-weight
w_live = live load (psf) x tributary width (ft)
w_total = w_dead + w_live

Load duration factor CD depends on the shortest-duration load: CD = 1.00 for floor live (10-year), CD = 1.15 for roof snow (2-month), CD = 1.25 for construction loads (7-day), CD = 1.60 for wind/seismic (10-minute).

Step 2 — Compute maximum moment and shear

M_max = w_total x L^2 / 8    (simply-supported, uniform load)
V_max = w_total x L / 2      (at supports)

For concentrated loads at midspan: M_max = P x L / 4
For third-point loads: M_max = P x L / 3

Step 3 — Check bending stress

fb = M / S  (actual bending stress)
Fb' = Fb x CD x CM x Ct x CL x CF x Cfu x Ci x Cr  (allowable)

Check: fb <= Fb'

For Southern Pine No. 2 (2x10): Fb = 1,050 psi. With CD = 1.00 (floor), Cr = 1.15 (repetitive member): Fb' = 1,050 x 1.00 x 1.15 = 1,208 psi. S for 2x10 (1.5 x 9.25 in) = 1.5 x 9.25^2 / 6 = 21.4 in^3. Moment capacity: M_allow = Fb' x S = 1,208 x 21.4 = 25,850 lb-in = 2,154 lb-ft.

For a 14 ft span with 16 in OC spacing, w_total = 69.3 lb/ft: M = 69.3 x 14^2 / 8 = 1,698 lb-ft. fb = 1,698 x 12 / 21.4 = 952 psi < 1,208 psi. OK.

Step 4 — Check shear stress

fv = 3 x V / (2 x b x d)     (rectangular section)
Fv' = Fv x CD x CM x Ct x Ci

Check: fv <= Fv'

Shear rarely governs for timber beams at typical span-to-depth ratios (L/d > 15). It becomes critical for short, deep beams with heavy loads near supports.

Step 5 — Check deflection

delta_LL = 5 x w_live x L^4 / (384 x E x I)       (uniform load)
delta_total = 5 x w_total x L^4 / (384 x E x I)

LL deflection limit: L/360 (floors), L/240 (roofs without plaster)
Total deflection limit: L/240 (typical)

E does NOT get the CD adjustment — deflection is independent of load duration. For a 2x10 Southern Pine floor joist at 14 ft span, E = 1.6e6 psi, I = 98.9 in^4: delta_LL = 5 x (40 x 1.33/12) x (14 x 12)^4 / (384 x 1.6e6 x 98.9) = 0.23 in. L/360 = 168/360 = 0.47 in. OK.

Step 6 — Check bearing at supports

fc_perp = R / (b x L_bearing)
Fc_perp' = Fc_perp x CM x Ct x Ci x Cb

Check: fc_perp <= Fc_perp'

For Southern Pine No. 2: Fc_perp = 565 psi. With 1.5 in bearing on a 2x4 sill plate, L_bearing = 1.5 in, reaction R = 485 lb: fc_perp = 485 / (1.5 x 1.5) = 216 psi < 565 psi. OK.

Adjustment Factors That Affect Timber Beam Capacity

Load Duration Factor CD (NDS Table 2.3.2)

Wood is stronger under short-duration loads. CD applies to ALL design values except E and Fc_perp.

Wet Service Factor CM

Wood loses strength when moisture content exceeds 19%. CM depends on species and property:

Southern Pine and Douglas Fir retain full design values in wet service — a major reason they dominate structural framing.

Beam Stability Factor CL

CL accounts for lateral-torsional buckling. For a beam with a continuously braced compression edge (subfloor, sheathing, decking), CL = 1.0. For unbraced beams:

CL = (1 + FbE/Fb*) / 1.9 - sqrt[((1 + FbE/Fb*)/1.9)^2 - (FbE/Fb*)/0.95]

FbE = 1.20 x Emin' / (Rb)^2
Rb = sqrt(Le x d / b^2)
Le = effective unbraced length

For a 2x10 (d = 9.25 in, b = 1.5 in) with Le = 12 ft: Rb = sqrt(144 x 9.25 / 2.25) = 24.3. FbE = 1.20 x 580,000 / 24.3^2 = 1,178 psi. Fb* = Fb x CD = 1,050 x 1.0 = 1,050 psi. FbE/Fb* = 1.12. CL = (1 + 1.12)/1.9 - sqrt[((1+1.12)/1.9)^2 - 1.12/0.95] = 1.12 - 0.33 = 0.79. So unbraced, the allowable Fb drops from 1,050 to 830 psi — a 21% reduction.

Glulam vs Sawn Lumber — When to Upgrade

Glulam beams are manufactured by gluing graded laminations under controlled conditions. The laminations are finger-jointed to create long lengths, and the layup can be unbalanced (higher-strength laminations in the tension zone) for cost efficiency.

Common Timber Beam Sizing Rules of Thumb

Floor joists (40 psf LL, 16 in OC)

Roof beams (30 psf LL, 24 in OC)

CD = 1.15 (snow load) increases allowable stress by 15% vs floor applications.

Worked Example — Timber Floor Beam

Problem: Select a timber beam for a residential floor. Span = 18 ft, spacing = 8 ft, DL = 15 psf, LL = 40 psf. Use Douglas Fir-Larch No. 2.

Loads

Tributary width = 8 ft
w_dead = 15 x 8 = 120 lb/ft + beam weight (assume 12 lb/ft) = 132 lb/ft
w_live = 40 x 8 = 320 lb/ft
w_total = 452 lb/ft

CD = 1.00 (floor live load governs)

Try 4x12 Douglas Fir No. 2

Section: 3.5 x 11.25 in (actual)
A = 39.38 in^2, S = 73.8 in^3, I = 415 in^4
Weight = 39.38/144 x 35 = 9.6 lb/ft (close to assumed 12)

Design values: Fb = 900 psi, Fv = 180 psi, E = 1.6e6 psi, Fc_perp = 625 psi

Bending check

M = 452 x 18^2 / 8 = 18,306 lb-ft = 219,672 lb-in
fb = 219,672 / 73.8 = 2,977 psi

Fb' = 900 x 1.00 x 1.0 (assume CL=1.0, braced by subfloor)
Fb' = 900 psi

fb = 2,977 >> 900 FAIL!

4x12 is far inadequate. The 8 ft tributary is heavy for timber.

Try 6x14 Douglas Fir No. 1

Section: 5.5 x 13.25 in
S = 5.5 x 13.25^2 / 6 = 161 in^3, I = 1,067 in^4
Fb = 1,100 psi (No. 1 grade)

fb = 219,672 / 161 = 1,364 psi
Fb' = 1,100 psi

fb = 1,364 > 1,100 FAIL (still 24% overstress)

Try 5.125x13.5 Glulam 24F-1.8E

S = 5.125 x 13.5^2 / 6 = 155.6 in^3
Fb = 2,400 psi, E = 1,800,000 psi

fb = 219,672 / 155.6 = 1,412 psi
Fb' = 2,400 x 1.00 x 0.80 (CV for depth ≈ 13.5 in) = 1,920 psi

fb = 1,412 < 1,920 OK. D/C = 0.74 ✓

Deflection: delta_LL = 5 x (320/12) x (18x12)^4 / (384 x 1.8e6 x (5.125 x 13.5^3/12))
I = 5.125 x 13.5^3 / 12 = 1,050 in^4
delta_LL = 5 x 26.67 x 429,981,696 / (384 x 1.8e6 x 1,050) = 0.32 in
L/360 = 216/360 = 0.60 in → 0.32 < 0.60 OK

Use 5.125 x 13.5 glulam 24F-1.8E.

This example shows why glulam is preferred for longer spans with wide tributaries: the sawn lumber options fail at 18 ft with 8 ft spacing, while glulam works with margin.

Engineered Wood Products for Beams

LVL (Laminated Veneer Lumber)

LVL is made from thin rotary-peeled veneers glued with the grain running parallel. Typical LVL bending stress: Fb = 2,600-3,000 psi, E = 1.8-2.0e6 psi. Common depths: 7.25 to 24 inches in 1/4-inch increments. LVL is heavier than glulam (42-45 pcf vs 35-38 pcf) but slightly stronger in bending.

PSL (Parallel Strand Lumber)

PSL uses long strands (up to 8 ft) of veneer bonded with waterproof adhesive under heat and pressure. Fb = 2,900 psi, E = 2.0e6 psi. PSL is used for heavily loaded beams and columns where high bearing stress perpendicular to grain governs (Fc_perp = 750 psi vs 565 psi for Southern Pine No. 2).

I-Joists

I-joists combine LVL or sawn lumber flanges with OSB webs. They are depth-efficient (9.5 to 24 inches deep) and very light (3-8 lb/ft). I-joist bending capacity depends on the flange size and grade, typically 2,000-5,000 lb-ft. They are limited to floor and roof joist applications — not suitable as girders or header beams.

Related Pages

• Wood timber calculator
• Beam capacity calculator
• Beam deflection calculator
• Beam span tables
• Load combinations calculator
• How to verify calculator results
• Disclaimer

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. All real-world structural design depends on project-specific factors. You are responsible for verifying inputs, validating results, and obtaining professional sign-off where required.