How to Analyze and Design a Structural Glued Laminated Timber Beam in ASD Using NDS 2024 and the NDS Supplement (Simple-Span Floor Beam Example with Table 5A Bending Stresses, Volume Factor, and Serviceability)

This note is stand-alone for flexure, shear, and deflection design checks for engineers reviewing a simple-span glued laminated timber (glulam) beam under ASD. It uses reference bending stresses and stiffness from the NDS Supplement Table 5A (bending members) for a selected stress class, applies adjustment factors in NDS 2024 Chapter 5, and compares demand to adjusted allowable stresses F′_b and F′_v. It does not replace a full design package (connections, bearing perpendicular to grain, notches, holes, ponding, vibration, fire, or load combinations beyond the single combination shown).

Companion overview: NDS Supplement Tables 1A–6B (what each table is for). Wood design modules: StructSuite wood beam design (when available in your build).

What governs in real design?

Continuous beams (hogging at interior supports) and F_bx⁻ are covered in the two-span continuous glulam example.

1. Problem statement and beam summary

A simple-span interior floor beam supports a uniform floor dead and live load over a rectangular tributary width. The beam is laterally braced along the compression edge (e.g., by continuous floor sheathing nailed per code) so beam stability factor C_L is taken as 1.0 after verifying lateral stability requirements in NDS 5.3.4 for the actual unbraced length and loading. This example uses one load combination (D + L) for strength; serviceability splits dead and live for deflection.

Schematic — simple-span glulam floor beam (elevation)

Uniform line load w (dead plus live) along the girder; span L between bearing centers. Joists and deck load the beam; compression at the top of the beam in positive bending is often laterally braced by structural sheathing (not shown).

  Uniform line load w (lb/ft), service D + L for strength
           ↓   ↓   ↓   ↓   ↓   ↓   ↓   ↓   ↓
        =======================================   ← glulam (b × d), strong-axis bending
        ○                                   ○
     bearing                            bearing
        ←──────────── L ────────────────→

Figure (schematic). Structural glued laminated timber simple-span beam elevation with uniformly distributed load; use with NDS Supplement Table 5A bending checks.

Sign convention for bending: Simple-span positive moment at midspan uses F_bx⁺ from Table 5A. If your beam has negative moment regions (continuous spans, cantilevers), check F_bx⁻ in those zones per the same adjustment path.

2. Section properties (gross section)

For a rectangular section b × d:

S = bd²/6     I = bd³/12

With b = 5.125 in. and d = 15.0 in.:

Moment of inertia (hand check): d³ = 15³ = 3,375 in.³; bd³ = 5.125 × 3,375 = 17,296.875 in.⁴; I = 17,296.875/12 ≈ 1,441.4 in.⁴ (gross section).

Rounding in this note: S and I are taken to one decimal in.³ / in.⁴ for the worked lines; bending stresses to the nearest 10 psi where rounding would change the story (otherwise whole psi); w in lb/in to two decimal places; deflection to two decimal places of an inch. Use full precision on contract calculations.

3. Reference design values (Supplement Table 5A)

For structural glued laminated timber used as a bending member, Supplement Table 5A lists F_bx⁺, F_bx⁻, F_vx, E, and E_min for each stress class. For 24F-1.8E (illustrative values consistent with the NDS Supplement):

Use the exact tabulated values from your project’s Supplement edition and layup; do not substitute Table 5B (compression members) for beam bending.

4. Load duration, moisture, temperature, and stability factors

Load duration factor C_D (NDS Table 4.3.1): For a combination controlled by floor live load with dead load also present, C_D is based on the shortest-duration load in the combination—here normal live duration—so C_D = 1.0.

Wet service factor C_M (NDS Chapter 5): Dry service, C_M = 1.0 for F_b, F_v, and E (confirm dry vs wet definitions per NDS for your use).

Temperature factor C_t (NDS Table 5.3.4): T ≤ 100 °F, C_t = 1.0.

Beam stability factor C_L (NDS 5.3.4 / 5.3.5): This example assumes continuous lateral restraint of the compression edge such that C_L = 1.0. If l_u or l_e is large relative to d, C_L must be calculated—do not assume 1.0 without checking. For glulam F_bx per Supplement Table 5A, C_V and C_L are not applied simultaneously as two separate multipliers—use the lesser of C_V and C_L in the F_bx adjustment path (verify wording in your NDS/Supplement edition). This does not apply to sawn lumber (C_F, not C_V).

Volume factor C_V (NDS 5.3.6, Equation 5.3-1): For structural glued laminated softwood bending members, C_V is not a function of stress class (24F-1.8E etc.); it depends on span L (ft), depth d (in.), width b (in.), and species group (exponent x). NDS Supplement Table 5A uses x = 10 for all species except Southern Pine (x = 20 for Southern Pine). This example is Douglas Fir-Larch → x = 10.

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

Shortcut (when all limits are met): If L ≤ 21 ft, d ≤ 12 in., and b ≤ 5.125 in., C_V = 1.0 without the product form. Here d = 15 in. > 12 in., so the full expression applies.

Numeric substitution (L = 16 ft, d = 15 in., b = 5.125 in., x = 10):

C_V = (21/16)^0.1 × (12/15)^0.1 × (5.125/5.125)^0.1 ≈ 1.028 × 0.978 × 1 ≈ **1.005**

The product exceeds 1.0 before the cap; C_V = min(1.005, 1.0) = 1.0.

Flat use factor C_fu: 1.0 (member is edge-loaded, not flatwise bending).

Stress interaction factor C_i and repetitive-member factor C_r: 1.0 for this single glulam beam (no repetitive-member increase unless criteria met).

5. Adjusted ASD stresses (demand vs capacity)

5.1 Flexure (midspan, positive moment)

Maximum moment for uniform load on a simple span:

M = wL²/8    (with w in lb/ft, L in ft → M in ft-lb)

M = 800 × 16² / 8 = 25,600 ft-lb = **307,200 lb-in.**

Bending stress:

f_b = M / S = 307,200 / 192.2 ≈ **1,600 psi**

Adjusted bending stress capacity (positive zone):

F′_b = F_bx⁺ × C_D × C_M × C_t × min(C_L, C_V) × C_fu × C_i × C_r

F′_b = 2,400 × 1.0 × 1.0 × 1.0 × min(1.0, 1.0) × 1.0 × 1.0 × 1.0 = **2,400 psi**

Flexure check: f_b ≈ 1,600 psi ≤ F′_b = 2,400 psi → OK for this trial section with C_V = 1.0 per Equation 5.3-1.

5.2 Shear (maximum at support, unreinforced rectangular section)

Maximum shear (simple span, UDL):

V = wL/2 = 800 × 16 / 2 = **6,400 lb**

Shear stress for a rectangular section (NDS 5.3.7 shear stress model as applicable):

f_v = 3V / (2bd) = 3 × 6,400 / (2 × 5.125 × 15) = **125 psi**

f_v = 1.5V / A with A = bd = 76.875 in.² → 1.5 × 6,400 / 76.875 = **125 psi**

Adjusted shear capacity:

F′_v = F_vx × C_D × C_M × C_t × C_i

F′_v = 265 × 1.0 × 1.0 × 1.0 × 1.0 = **265 psi**

Shear check: f_v = 125 psi ≤ F′_v = 265 psi → OK.

(If shear reinforcement or notch details apply, use the governing NDS provisions for those cases—this example is plain beam shear.)

6. Deflection (serviceability)

Adjusted modulus for deflection: Elastic deflection uses E′ in EI. Per NDS and the Supplement tables for glulam, E′ = E × C_M × C_t (for moisture and temperature effects on stiffness), unless your edition lists additional factors. This example matches Section 4 (dry service, T ≤ 100 °F):

E′ = E × C_M × C_t = (1.8 × 10⁶) × 1.0 × 1.0 = **1.80 × 10⁶ psi**

Use the reference E from Table 5A for this δ calculation. E_min from Table 5A is for stability / buckling-related uses (e.g. beam stability C_L, column design), not for ordinary service deflection of a prismatic beam unless your procedure explicitly requires it.

For uniform load, maximum deflection of a simple span (L_in = span in inches; exponent 4 is on L, not on the unit subscript):

δ = 5 w_in (L_in)⁴ / (384 E′ I)

where w_in = (lb/ft)/12. Use I from Section 2 (1,441.4 in.⁴), L_in = 192 in.

Live-load only (w_L = 500 lb/ft → w_in = 41.67 lb/in):

δ_L = 5(41.67)(192)⁴ / (384 × 1.80 × 10⁶ × 1,441.4) ≈ **0.28 in.**

IBC Table 1604.3 often uses L/360 for live load on floors supporting flexible elements; verify project criteria.

L/360 = 192/360 = **0.53 in.**

Live-load deflection: 0.28 in. ≤ 0.53 in. → OK for L/360.

Total load (w = 800 lb/ft → w_in = 66.67 lb/in):

δ_D+L = 5(66.67)(192)⁴ / (384 × 1.80 × 10⁶ × 1,441.4) ≈ **0.46 in.**

Compare to your specified total-load limit (e.g. L/240 where permitted). L/240 = 192/240 = 0.80 in. → OK for that limit.

Long-term deflection (creep): Elastic δ above uses E′ for immediate deflection. Sustained (dead and long-duration) loads cause creep in timber; total deflection over time can exceed the elastic value. Apply NDS, IBC, and project criteria for creep factors, reduced effective stiffness, or additional limits where required.

7. Governing checks (this example)

C_V and C_L are often governing in real designs—recalculate them for the actual l_u, bracing, and layup rather than using this example’s assumptions alone.

8. Relation to software and Table 5A / 5B

Structural analysis programs and StructSuite modules should apply the same NDS adjustment factors and use Table 5A for beam reference values and Table 5B only for columns or combined stress per Supplement scope. If negative moment exists, F_bx⁻ governs in those regions alongside stability (C_L).

9. References (NDS 2024 and NDS Supplement)

• NDS 2024 Chapter 4 — Load duration (C_D).
• NDS 2024 Chapter 5 — ASD adjustments for timber; Equation 5.3-1 (C_V); beam stability (C_L); shear.
• NDS Supplement Table 5A — Reference design values for glulam bending members (F_bx⁺, F_bx⁻, F_vx, E).
• IBC — Deflection limits (Table 1604.3); live load magnitude (Table 1607.1).

This technical note is educational. Confirm all reference stresses, C_V and C_L calculations, load magnitudes, deflection limits, and bearing / connection design with the governing NDS edition, Supplement, IBC, and the authority having jurisdiction.