Sawn lumber beam
A sawn lumber beam, joist or header in bending, shear and bearing, to NDS 2024 Chapters 2 to 4 with ASCE 7-22 load combinations, in ASD or LRFD. One model covers simple spans, cantilevers, overhangs and continuous beams. Every combination is checked with its own load duration factor CD (ASD) or time effect factor λ (LRFD), so a dead load alone (CD = 0.9) can govern.
Inputs of the sawn lumber beam #
- Member: species (Douglas Fir-Larch, Hem-Fir, Spruce-Pine-Fir, Southern Pine) and grade (Select Structural to Stud), nominal size (2x4 to 4x16 dimension lumber, 6x6 to 12x16 timbers) and the number of plies acting as one member. Other takes reference values you enter (including the size factor). The self-weight uses the density entered (35 pcf is the basis of the Supplement section tables).
- Length and supports: any number of pins or fixed ends (as for the steel beam) and the bearing length lb at the supports. The bearing area factor Cb applies to bearings more than 3 in from the member end (NDS 3.10.4).
- Loads: line loads in plf and point loads in lb, each with its load type (D, L, Lr, S, R, W, E). Live load patterning on continuous beams is not automatic: enter the partial loads that govern.
- Lateral stability: the unbraced length lu of the compression edge (0 = braced continuously, CL = 1.0) and the load case of NDS Table 3.3.3 for the effective length le. The general values are permitted for any single span or cantilever.
- Service conditions and factors: wet service (CM), temperature (Ct), incising (Ci), repetitive member (Cr = 1.15 for three or more members at 24 in or less joined by sheathing), flat use (Cfu), the shear reduction near the supports (3.4.3.1, for a member bearing on one face and loaded on the other) and the bearing deformation limit (0.04 in tabulated, or 0.02 in with 0.73 Fc⊥, NDS 4.2.6).
- Deflection limits: span / n for live and total load (IBC Table 1604.3 values prefilled, 0 turns a check off). The total deflection includes creep when checked: ΔT = Kcr ΔLT + ΔST (NDS 3.5.2) with the long-term load D plus the sustained part of L that you enter (0 is usual for occupancy live load; storage is long-term). Kcr = 1.5 for seasoned lumber in dry service, 2.0 for unseasoned lumber or wet service.
- Load duration (code options): CD per load type for ASD (NDS Table 2.3.2: live 1.0, roof live 1.25, snow 1.15, wind and earthquake 1.6; rain is not listed in the table, 1.15 is prefilled and the choice is yours) and the live load type for λ in LRFD (occupancy 0.8, storage 0.7, impact 1.25).
Auto-design (editor toolbar) varies the nominal size and number of plies; species and grade when unlocked. Objectives: least wood (section area); shallowest, then least wood; lowest cost index (lumber). Kept unless you select them: grade, species. Every other input is kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Bending stress, positive and negative moment, every combination | fb = M/S ≤ Fb' = Fb (CD or KF φ λ) CM Ct CL CF Cfu Ci Cr (Table 4.3.1); CL by Eq. 3.3-6 with RB = √(le d / b²) |
| Shear stress | fv = 3V/(2bd) ≤ Fv', with the loads within d of the support faces neglected (uniform) or reduced by x/d (point) when chosen |
| Bearing at the supports | fc⊥ = R/(b lb) ≤ Fc⊥' = Fc⊥ CM Ct Ci Cb (no CD in ASD; KF φ without λ in LRFD, Table 4.3.1) |
| Beam slenderness | RB = √(le d / b²) ≤ 50 (3.3.3.7) when the compression edge is unbraced |
| Live load deflection | Each of L, Lr, S and R alone, against span / n; cantilevers use twice the overhang |
| Total load deflection | The ASD gravity combinations with creep (NDS 3.5.2) |
An upward reaction is reported as an advisory (provide an uplift connection). The steps show every factor with its basis.
Drawings #
The drawing sheet (PDF / DXF, Drawing sheet button) shows the beam elevation with the supports, the loads by type in plf and lb and the spans, the section at the actual dressed size (each ply drawn, the member mark with species and grade), and the shear, moment and deflection diagrams of the governing combinations at the elevation's scale. Ply fastening, bearing hardware, connections and brace locations are not part of the calculation and are not drawn; the sheet notes say so.
Limitations #
- Every NDS provision of the module was checked against the NDS 2024 text (2024 Edition with Commentary; the steps cite section, table and page): Tables 2.3.2 (CD), 2.3.3 (Ct), 2.3.5 (KF), 2.3.6 (φ), 3.3.3 (le, including the rows for four to seven loads new in 2024), 4.3.1, 4.3.8 (Ci), N3 (λ); Eqs. 3.3-5, 3.3-6, 3.4-2, 3.5-1, 3.10-2, 4.2-1 and 4.3-1 (timber size factor); 3.3.3.7 (RB ≤ 50), 3.4.3.1, 3.5.2 (Kcr), 4.1.4 (wet service above 19 %) and 4.3.9 (Cr). Corrected against the text: Fc⊥ takes no λ in LRFD (Table 4.3.1; the module had applied λ, which understated the LRFD bearing capacity by the factor λ), and the RB ≤ 50 limit is now checked.
- The NDS 2024 Supplement (design value tables) is not on disk: the reference values of Tables 4A, 4B (Southern Pine No. 2 only; other Southern Pine grades are entered as reference values) and 4D, the Table 4A / 4B size factors, flat use factors and wet service factors are those of the 2018 Supplement and stay marked [verify] (listed in
research/DOCUMENTS_NEEDED.md). The NDS 2024 Appendix E sample solutions confirm SPF No. 2 Ft = 450 psi and Fv = 135 psi, Hem-Fir No. 2 Ft = 525 psi and Fv = 150 psi, Southern Pine No. 2 2x4 Ft = 675 psi and Fv = 175 psi, and the Ft size factor 1.5 of 4 in wide lumber. - Not feasible: Stud grade wider than 6 in (use No. 3), timbers used flat, incised timbers, built-up timbers.
- Notched ends: see Wood bearing and notches. Fastening of plies, lateral bracing design, vibration and fire design are the engineer's.
Verification examples #
NDS 2024 has no worked beam example (its only sample solutions, Appendix E, are connection net-section and tear-out checks; the adjusted Ft and Fv they publish are verified through the column module). The module is verified against Breyer, Design of Wood Structures, Examples 6-18 / 6-19 (published values as tabulated in the free calcs.com validation page) and by hand calculations in closed form of the NDS 2024 equations (each derived step by step in backend/tests/test_verify_wood_beam.py):
| Example | What it checks | Published / hand value | ILX Calcs |
|---|---|---|---|
| BREYER-6-18 | 2x6 DF-L No. 1 rafter, 13.5 ft, D 14 + Lr 20 psf, braced; ASD | Fb' = 1870 psi, M = Fb' S = 1178 lb-ft, Fv' = 225 psi, V = 1237.5 lb, Fc⊥' = 625 psi | 1869 psi, 1178 lb-ft, 225 psi, 1237.5 lb, 625 psi |
| BREYER-6-18 | Same rafter, LRFD (Ex. 6-19) | Fb' = 2.58 ksi, M' = 1625 lb-ft, Fv' = 311 psi, V' = 1710 lb, Fc⊥' = 938 psi | 2582 psi, 1627 lb-ft, 311 psi, 1710 lb, 939 psi |
| HAND-1 | 2x10 DF-L No. 2 joist, 14 ft, D 20 + L 55 plf, ASD | fb = 1030.8 psi, Fb' = 1138.5 psi, fv at d = 49.5 psi, Δ_L = 0.300 in, Δ_T = 0.464 in | same (within 0.1 %) |
| HAND-1 | LRFD | Fb' = 1966.4 psi, Fv' = 311.0 psi, Fc⊥' = 939.4 psi (no λ) | same |
| HAND-2 | 4x10 DF-L No. 2, lu = 12 ft (beam stability) | RB = 14.08, CL = 0.979, Fb' = 1057 psi | same |
Only the capacities of the Breyer rafter are compared (the free reproduction does not give the rafter spacing). The open item is a comparison with the AWC Structural Wood Design Examples (beam stability, notched and point-loaded sawn beams), which are not free.