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 use: a label for the report; the Wizard cards prefill each use. Floor overhang and roof overhang: a support at 3/4 of the length, the bottom edge with its own unbraced length (the overhang's length). Header: a simple span, no repetitive member factor; the jack, king and trimmer studs are in the stud wall. Ridge beam: a simple span with the rafter loads per foot, an uplift row (negative W), the bottom edge free over the span, the shear reduction off (rafters hung from the side do not load the opposite face, NDS 3.4.3.1). Hip and valley: a simple span of the plan length with a triangular load from 0 at the low end to the peak; the peak for jack rafters of equal slope on both sides of a 45 degree plan line is w = q Lh / 2, q the load per horizontal square foot and Lh the plan length of the hip. That triangle is the usual idealization, not a code rule: it is your judgment, as is whether the top end is really supported (a hip carried only by other hips and a ridge board is not). The axial force of the sloped member and deflection normal to the slope are not included. Every card starts from typical loads: replace them.
• 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). A negative value acts upward; a line load with a value at To is trapezoidal or triangular.
• Partial loading: on by default. On a member with more than one span or an overhang, L, Lr and S also act on part of the spans (ASCE 7-22 4.3.3 and 7.5; an overhang counts as a span, S keeps half its value on the other spans, the dead load stays everywhere). Up to three spans take every subset; more take alternate spans, adjacent pairs, single spans and all but an end span. The combination names say which: "D + L [live on span 1]". ASCE 7-22 7.5.1 lets you turn snow partial loading off for rafters across the ridge of a gable of slope 1/2 to 7 on 12, by the option.
• Bottom edge under negative moment: sheathing on top does not brace the bottom edge. Choose its own unbraced length where nothing holds it (an overhang, an interior support, wind uplift on an exposed ridge beam).
• 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).

• Ply fastening (more than one ply): off by default, which leaves it as your design and gives the same results as before. On, the fasteners between plies are checked for a load from one side or both, single shear at each interface, the worst combination with its load duration or time effect factor. Common nails from each face (up to 3 plies) or through bolts (up to 4). The share of the load from the side, the length that takes a side point load and the service condition are inputs.

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 #

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 reference values of NDS 2024 Supplement Tables 4A, 4B (Southern Pine Select Structural, No. 1, No. 2 and No. 3 / Stud; the dense and non-dense grades are entered as reference values) and 4D, the Table 4A / 4B / 4D size factors, flat use factors and wet service factors were read against the NDS 2024 Supplement (Chapter 4, 2024-07) on 2026-11-08: every built-in value agrees (none changed from the 2018 Supplement). Flat use of timbers is not offered (Table 4D gives Cfu on Fb and E for beams and stringers). 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.
• Ply fastening is calculated for side loads on nails and through bolts. Screws and proprietary fasteners are not, and fasteners are not placed along the member by the local shear.
• Notched ends: see Wood bearing and notches. Lateral bracing design, vibration and fire design are the engineer's.

Verification examples #

Verification status: 55 values compared in 8 examples (4 published, 4 hand calculations from the cited equations): 50 within tolerance, 5 recorded deviations. Code basis: the provisions it uses were read in the target edition.

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):

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.