Glulam Beam Design Worked Example: NDS 2018 24F-V4 with Lateral-Torsional Stability

Glued laminated timber (glulam) beams are engineered wood products fabricated by face-bonding individual lumber laminations under controlled factory conditions. Unlike sawn lumber — where strength is limited by the largest natural defect in the piece — glulam disperses strength-reducing characteristics across laminations, producing a member with both higher allowable design stresses and greater dimensional flexibility. A 24F-V4 glulam, the focus of this example, carries a reference bending design value of 2,400 psi (Fbx) with visually graded Western Species laminations symmetrically arranged (V4 layup: balanced, four outermost tension laminations are higher-grade).

This worked example walks through the complete NDS 2018 design check for a simply supported 6-3/4 × 24 inch 24F-V4 glulam beam spanning 30 feet under combined dead load (including self-weight) and snow load. You will compute adjusted design values using the NDS format conversion factors (CD, CM, Ct, CL, CV), verify flexure with lateral-torsional stability, check shear and bearing at supports, and confirm live-load and total-load deflection limits per IBC Table 1604.3.

PRELIMINARY — NOT FOR CONSTRUCTION. This example is for educational use. All results must be independently verified by a licensed Professional Engineer before use in any design.

Design parameters

Step 1: Reference design values — 24F-V4 glulam

Per NDS 2018 Table 5A (Structural Glued Laminated Timber — Softwood Species, Balanced Layup), the reference design values for a 24F-V4 glulam are:

24F-V4 is a balanced layup — the tension and compression zones at positive bending have equal reference design values because the outer tension and compression laminations are the same grade. For negative bending (bottom face in tension), Fbx⁻ is reduced to 1,450 psi because the outer tension lamination is the lower-grade core lamination, not the high-grade outer lamination.

Step 2: Section properties and loads

Section properties

b = 6.75 in, d = 24.0 in
A = b × d = 6.75 × 24.0 = 162.0 in²
Sx = b × d² / 6 = 6.75 × 576 / 6 = 648.0 in³
Ix = b × d³ / 12 = 6.75 × 13,824 / 12 = 7,776 in⁴

Self-weight

NDS 2018 Table 5A also lists the specific gravity for Western Species glulam. Using SG = 0.50 (assumed for Western Species, softwood):

Unit weight = 62.4 × SG / 12² = 62.4 × 0.50 × (1/12) = 62.4 × 0.50 = 31.2 pcf (typical dry density)
Self-weight = A × unit_weight / 144 = 162.0 × 31.2 / 144 = 35.1 plf

Refined: Most 24F-V4 glulam beams use Douglas Fir-Larch laminations with SG ≈ 0.50.
Mass density = SG_dry × 62.4 pcf = 0.50 × 62.4 = 31.2 pcf
Self-weight = 31.2 × (6.75 × 24.0 / 144) = 31.2 × 1.125 = 35.1 plf

Use 35.1 plf for self-weight, rounded to 35 plf.

Loads

Tributary width: 8 ft
Superimposed dead: w_D_sup = 15 psf × 8 ft = 120 plf
Self-weight: w_D_self = 35 plf
Total dead: w_D = 155 plf
Snow: w_S = 30 psf × 8 ft = 240 plf

Factored loads (ASCE 7-22 LRFD)

For roof snow, the controlling ASCE 7-22 LRFD combination is (D + S):

wu = 1.2 D + 1.6 S = 1.2 × 155 + 1.6 × 240 = 186 + 384 = 570 plf

For the strength load combinations that include snow, the NDS 2018 size factor CF, volume factor CV, and load duration factor CD apply.

Maximum bending moment and shear:

Mu = wu × L² / 8 = 570 × 30² / 8 = 570 × 900 / 8 = 64,125 lb-ft = 769.5 kip-in
Vu = wu × L / 2 = 570 × 30 / 2 = 8,550 lb = 8.55 kips

Step 3: Adjusted bending design value

Per NDS 2018 Section 5.3, the allowable bending stress F'b is computed by multiplying the reference value Fb by all applicable adjustment factors:

F'b = Fb × CD × CM × Ct × CL × CV × Cfu × Cc × Ci × Cr

For this 24F-V4 glulam beam under dry, normal-temperature conditions with full lateral support:

Load duration factor CD

Per NDS 2018 Table 2.3.2, snow load has a load duration of 1.15. The LRFD load combination (1.2D + 1.6S) is treated as a snow-dominant combination: CD = 1.15.

Wet service factor CM

Per NDS 2018 Table 5A footnote and Table 5B, glulam members in dry service conditions (MC ≤ 16%) take CM = 1.0 for bending. This beam is in a conditioned interior space: CM = 1.0.

Temperature factor Ct

Per NDS 2018 Section 5.3.2, Ct = 1.0 for temperatures ≤ 100°F (sustained). Interior roof beam: Ct = 1.0.

Beam stability factor CL

Per NDS 2018 Section 5.3.6, the beam stability factor accounts for lateral-torsional buckling when the compression edge is not continuously braced. For this beam:

The roof sheathing is nailed to the top flange at 6 in o.c., providing continuous lateral support. The unbraced length for the compression flange is:

Lu = 0 in (continuously braced by sheathing). But per NDS 2018 3.3.3, verify that the sheathing attachment satisfies the lateral support requirement: nailed wood structural panels at 6 in o.c. qualify as continuous lateral support per NDS 2018 Commentary C3.3.3.

With full lateral support, CL = 1.0.

Verification (even though CL = 1.0, compute for reference):

lu = 360 in (if unbraced — worst case for illustration)
le = 1.63 × lu + 3 × d = 1.63 × 360 + 3 × 24.0 = 586.8 + 72.0 = 658.8 in

RB = √(le × d / b²) = √(658.8 × 24.0 / 6.75²) = √(15,811 / 45.56) = √347.0 = 18.63

Since RB = 18.63 ≤ 50 → CL is computed per Eq. 3.3-6 (NDS 2018). But with full lateral support, per Section 3.3.3.1, CL = 1.0.

Volume factor CV

Per NDS 2018 Section 5.3.6, the volume factor for a glulam beam subjected to bending is:

CV = (21 / L)^(1/x) × (12 / d)^(1/x) × (5.125 / b)^(1/x) ≤ 1.0

For 24F-V4 (Western Species, four tension laminations), x = 10 per NDS Table 5.3.1:

CV = (21/30)^(0.10) × (12/24)^(0.10) × (5.125/6.75)^(0.10)
CV = 0.965 × 0.933 × 0.975 = 0.878

The volume factor accounts for the size effect in glulam — larger beams have a higher probability of containing a strength-reducing defect, so the allowable stress is reduced. CV = 0.878.

Curvature factor Cc

Per NDS 2018 Section 5.4.1, Cc applies only to curved members. Straight beam: Cc = 1.0.

Flat use factor Cfu

Per NDS 2018 Table 5B footnote, Cfu = 1.0 for members loaded about their strong axis (depth > width). Not applicable here since loading is about the strong axis naturally. Cfu = 1.0 for strong-axis bending per the note to Table 5B.

Adjusted bending stress

F'b = 2,400 × 1.15 × 1.0 × 1.0 × 1.0 × 0.878 × 1.0 × 1.0 × 1.0 × 1.0
F'b = 2,400 × 1.15 × 0.878 = 2,400 × 1.0097 = 2,423 psi

Wait — check Cfu. Actually per NDS 2018 Table 5B, for glulam loaded parallel to the wide face (standard orientation), the bending design value does not receive Cfu. Cfu = 1.0. And Cc = 1.0, Ci = 1.0, Cr = 1.0.

F'b = 2,400 × 1.15 × 1.0 × 1.0 × 1.0 × 0.878 = 2,400 × 1.0097 = 2,423 psi

Step 4: Flexural strength check

Per NDS 2018 Section 5.3.1, the LRFD factored bending resistance is:

φb = 0.85 (LRFD, NDS Table N3.1, glulam bending)
Mn = F'b × Sx = 2,423 × 648.0 = 1,570,104 lb-in = 1,570 kip-in
φb Mn = 0.85 × 1,570 = 1,334 kip-in

Check: Mu = 769.5 kip-in ≤ 1,334 kip-in → OK (utilization = 0.577)

Step 5: Shear strength check

Per NDS 2018 Section 5.3.2:

F'v = Fv × CD × CM × Ct × Ci
F'v = 265 × 1.15 × 1.0 × 1.0 × 1.0 = 305 psi

The adjusted shear resistance is based on the full cross-section area for rectangular beams. Per NDS 2018 Eq. 3.4-1:

φv = 0.75 (LRFD, NDS Table N3.1, glulam shear)
Vn = F'v × b × d / 1.5 = 305 × 6.75 × 24.0 / 1.5 = 305 × 108 = 32,940 lb
φv Vn = 0.75 × 32,940 = 24,705 lb = 24.7 kips

Check: Vu = 8.55 kips ≤ 24.7 kips → OK (utilization = 0.346)

Note: The shear check is at a distance d from the support face per NDS 2018 Section 3.4.3.1 when the reaction is compressive (bearing at the bottom face). At x = d = 24 in from the support centerline:

Vu_at_d = Vu - wu × d / 12 = 8.55 - 570 × 2.0 / 1,000 = 8.55 - 1.14 = 7.41 kips ≤ 24.7 kips → still OK

Step 6: Bearing at supports

Per NDS 2018 Section 5.3.7, the allowable compression perpendicular to grain is:

F'c⟂ = Fc⟂x × CM × Ct × Ci × Cb
F'c⟂ = 650 × 1.0 × 1.0 × 1.0 × Cb

The bearing area factor Cb accounts for the additional bearing capacity provided by the unloaded wood beyond the bearing plate. Per NDS 2018 Section 3.10.4:

Bearing length lb = 6.0 in (steel bearing plate at each support)
Cb = (lb + 0.375) / lb = (6.0 + 0.375) / 6.0 = 1.0625 ≤ 1.75 per NDS Commentary

But Cb for glulam is computed per NDS 5.3.7 differently. For end bearings less than 6 in from the member end and lb ≤ 6 in:

Cb = 1.0 for lb < 6 in per NDS Table 3.10.4 footnote
With lb = 6.0 in: Cb = 1.0 per the standard (lb must be ≥ 6 in for the factor to apply)

For a 6-inch bearing plate at the beam end:

F'c⟂ = 650 × 1.0 × 1.0 × 1.0 × 1.0 = 650 psi

φc⟂ = 0.90 (LRFD, NDS Table N3.1)
Ab = b × lb = 6.75 × 6.0 = 40.5 in²
Rn = F'c⟂ × Ab = 650 × 40.5 = 26,325 lb = 26.3 kips
φc⟂ Rn = 0.90 × 26.3 = 23.7 kips

Check: Ru = Vu = 8.55 kips ≤ 23.7 kips → OK (utilization = 0.361)

Step 7: Deflection — serviceability

Per IBC 2024 Table 1604.3, allowable deflections for roof beams supporting non-plaster ceilings:

• Live load (snow): L/240
• Total load: L/180

Snow load deflection

Service snow load: w_S = 240 plf = 20.0 lb/in
Service moment: M_S = w_S × L² / 8 = 20.0 × 360² / 8 = 20.0 × 129,600 / 8 = 324,000 lb-in

Use the reference modulus E' = Ex × CM × Ct × Ci = 1.8 × 10⁶ × 1.0 × 1.0 × 1.0 = 1.80 × 10⁶ psi
(No CD applied for deflection — deflection uses service-level loads)

Δ_S = 5 × w_S × L⁴ / (384 × E' × Ix)
Δ_S = 5 × 20.0 × 360⁴ / (384 × 1.80 × 10⁶ × 7,776)
Δ_S = 5 × 20.0 × 1.6796 × 10¹⁰ / (384 × 1.80 × 10⁶ × 7,776)
Δ_S = 1.6796 × 10¹¹ / (5.378 × 10¹²) = 0.0312 × 10⁻¹ = 0.312 in

Wait — more carefully:

Ix = 7,776 in⁴
E' Ix = 1.80 × 10⁶ × 7,776 = 1.3997 × 10¹⁰ lb-in²

Δ_S = 5 × 20.0 × (360)⁴ / (384 × 1.3997 × 10¹⁰)
(360)⁴ = 1.6796 × 10¹⁰
Numerator = 5 × 20.0 × 1.6796 × 10¹⁰ = 1.6796 × 10¹²
Denominator = 384 × 1.3997 × 10¹⁰ = 5.3748 × 10¹²
Δ_S = 1.6796 × 10¹² / 5.3748 × 10¹² = 0.312 in

Snow deflection limit: L/240 = 360/240 = 1.50 in

Check: 0.312 in ≤ 1.50 in → OK (utilization = 0.208)

Total load deflection

Service total load: w_total = w_D + w_S = 155 + 240 = 395 plf = 32.92 lb/in
Δ_total = Δ_S × (32.92 / 20.0) = 0.312 × 1.646 = 0.514 in

Total deflection limit: L/180 = 360/180 = 2.00 in

Check: 0.514 in ≤ 2.00 in → OK (utilization = 0.257)

Step 8: Camber recommendation

Per AITC 117 (Standard Specifications for Structural Glued Laminated Timber), manufacturing camber is recommended to offset dead load deflection. The dead load deflection:

Δ_D = Δ_S × (155/240) = 0.312 × 0.646 ≈ 0.202 in

Recommended camber = 1.5 × Δ_D = 1.5 × 0.202 ≈ 0.31 in, specify 3/8 in upward camber at mid-span. This ensures the beam appears flat under dead load and any creep deflection.

Results summary

Key takeaways

• The volume factor CV is critical for glulam. For a 30-ft beam, CV = 0.878 reduces the allowable bending stress by 12%. For longer spans (60+ ft), CV typically drops below 0.80, making the volume reduction the controlling factor in glulam beam design rather than flexural demand.

• 24F-V4 balanced layup simplifies sign-independent design. With Fbx = 2,400 psi for both positive and negative bending in the strong axis, the same adjusted design value can be used throughout. For unbalanced layups (24F-V2, 24F-V3), negative bending capacity is substantially lower (often 1,000–1,400 psi) and must be checked at cantilevers, overhangs, and continuous spans.

• Shear and bearing rarely control glulam beam design. With Fvx = 265 psi and a d/b ratio of 24/6.75 = 3.56, flexure governs for all but very short, heavily loaded beams. Bearing at supports is also rarely critical for glulam because the LRFD φ-factor for compression perpendicular to grain is high (0.90) and the bearing plate can always be lengthened.

• Lateral-torsional stability at erection is a construction safety concern. While the completed assembly has full lateral support from sheathing, the bare beam during erection requires temporary bracing. At 30 ft span, the unbraced length of the compression edge during hoisting may trigger LTB. The erector must provide intermediate lateral support at intervals not exceeding 10 ft.

• Deflection and vibration typically govern glulam spans. With flexural utilization of only 0.577, deflection and vibration performance — not strength — control whether a 6-3/4 × 24 beam is adequate at this span. Vibration analysis per the AITC Technical Note 18 may indicate a need for a deeper or wider section for occupant comfort.

FAQ

What is the difference between 24F-V4 and 24F-V8 glulam?

Per NDS 2018 Table 5A, both have Fbx = 2,400 psi, but V8 has twice as many high-grade tension laminations (8 vs 4 in the bottom tension zone). V8 provides higher tension strength (Ftx = 1,600 psi vs 1,100 psi for V4), making V8 appropriate for members with high tensile demand such as bottom chords of trusses and heavily loaded beams with tension at the bottom face. For pure bending applications where compression governs (this example), V4 and V8 perform identically.

When should I use glulam instead of sawn lumber?

Use glulam when: (1) the required beam depth exceeds typical sawn timber availability (over 12 in deep), (2) the span exceeds 20 ft where sawn lumber depth-to-span ratios become inefficient, (3) curved or arched members are needed (glulam can be manufactured to any radius over about 15 ft), (4) higher allowable design stresses are required (2,400 psi vs ~900–1,200 psi for typical No.2 sawn), or (5) architectural appearance matters — glulam beams can be specified with architectural-grade appearance faces.

How is the camber calculated for glulam beams?

Per AITC 117-2010, the recommended manufacturing camber equals 1.5 times the dead load deflection for roof beams to account for long-term creep. For floor beams supporting storage or partitions, use 2.0 × dead load deflection. The camber is built into the beam during the gluing process and is identified on the beam tag. Always clearly note on the shop drawings whether the camber dimension is relative to the top-of-beam or bottom-of-beam reference line to avoid incorrect bearing seat elevations.

What fire resistance does a 6-3/4 × 24 glulam beam provide?

Per NDS 2018 Chapter 16 (ASD/LRFD for Fire Design) and IBC Section 722.1, exposed glulam beams char at approximately 1.5 inches per hour (Western Species, softwood). A 6-3/4-inch-wide beam provides approximately 4.5 hours of one-sided char exposure before char depth reaches the center. For a standard 1-hour fire resistance rating, the effective char depth is 1.8 in (1.5 in char + 0.3 in heated zone), leaving an effective section of 6.75 - 2 × 1.8 = 3.15 in width and 24.0 - 2 × 1.8 = 20.4 in depth. The reduced section must still carry the fire-level loads (typically 1.0 D + 1.0 L). Refer to AWC TR-10 for detailed fire calculation procedures.