Flitch-plate beam
A flitch-plate beam: two sawn lumber plies with one steel plate between them, or three plies with two plates, bolted through. The wood and its bolts are designed to NDS 2024, the plates to AISC 360-22, with ASCE 7-22 load combinations in ASD or LRFD. The parts share the load in proportion to their stiffness; the bolts that carry the plate's share from the wood (and the reaction share at the supports) are designed too.
Inputs of the flitch-plate beam #
- Wood plies: the layup (one plate between two plies, two plates between three plies), species and grade, ply size (dimension lumber 2" to 4" thick; every ply the same), or Other with reference values you enter (including the size factor) and the specific gravity G used for the bolt bearing strength (NDS Table 12.3.3A). The self-weight uses the wood density entered and 490 pcf for the steel.
- Steel plates: thickness and depth (equal to or less than the wood depth), position (flush top, centred, flush bottom), steel (ASTM A36, A572 Gr. 50 or Fy and Fu entered; E = 29,000 ksi) and the lateral bracing of the plate for AISC F11.2: at the bolts (Lb = the bolt spacing in a row, the conservative choice) or continuously by the plies in contact on both faces (DeStefano 2007: the wood braces the plate against lateral buckling). The choice is yours.
- Length, supports and bearing: any number of pins or fixed ends, the bearing length, and what bears at the supports: the wood plies only (the usual detail: bolts at the ends carry the plate's reaction into the wood), wood and plate together (the plate must be flush with the bottom), or the plate only (the bolts carry the wood's reaction into the plate).
- Loads: line loads in plf and point loads in lb by load type, and where they bear: on the wood (joists on top or hung from the plies: the plate's share passes through the bolts), on the plate, or on both together (a flush top shared by stiffness: only the self-weights pass through the bolts).
- Bolts: diameter, one row or two staggered rows, the spacing s in each row (two rows are staggered at s/2), the distance from the top of the wood to the top row and between the rows, the end distance, the number of bolts and their pitch at each support, the number of bolts that carry each point load (usual practice: bolts at each concentrated load; your choice), and whether special detailing for cross-grain shrinkage is provided (it waives the 5 in. limit between outer rows of NDS 12.5.1.3).
- Lateral stability: the unbraced length lu of the compression edge and the load case for le (NDS Table 3.3.3). CL is computed with the total wood width (the plies are bolted through the plates and act together).
- Service conditions and factors: wet service, temperature, incising, the repetitive member factor (not usual for a flitch beam; NDS 4.3.9 is your judgment), the shear reduction near the supports (3.4.3.1) and the bearing deformation limit.
- Deflection and long-term load: span / n for live and total load, creep of the wood in the total deflection (NDS 3.5.2 applied to the wood part: Itr,LT = Iw / Kcr + n Is), the sustained part of the live load, unseasoned lumber (Kcr = 2.0), and whether the steel and the bolts are designed for the long-term share: under sustained load the wood creeps and sheds load to the steel; the long-term part (D plus the sustained part of L) is then shared with the wood E divided by Kcr. Off by default; your judgment.
- Load duration (code options): CD per load type (ASD) and the live load type for λ (LRFD), as for the sawn lumber beam.
Auto-design (editor toolbar) varies the ply size, one or two plates, the plate thickness and the bolt diameter; for each candidate it derives the plate depth (full depth less 1/4 in., or the same fraction of the wood depth as given), the bolt rows within the plate and the edge distances, and the bolt spacing and bolt counts that carry the transfer scaled from the input as given. Species and grade are kept unless unlocked; span, supports and loads are never changed. Objectives: lightest (wood + steel weight); lowest cost index. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Load sharing | n = Es / E'w (E of the wood with CM, Ct, Ci; not Emin); each part bends about its own centroid with the same curvature: αs = Es Is / (E'w Iw + Es Is), αw = 1 − αs (DeStefano 2007; FPL Wood Handbook, transformed sections) |
| Wood bending, every combination | fb = αw M / Sw ≤ Fb' = Fb (CD or KF φ λ) CM Ct CL CF Ci Cr (NDS 3.3, Table 4.3.1) |
| Wood shear | fv = 3 Vw / (2 b d) ≤ Fv' with Vw = αw V, or the whole V where only the wood bears (the reaction passes through the plies next to the support) |
| Wood bearing at the supports | fc⊥ = R / (Σb lb) ≤ Fc⊥' (NDS 3.10.2, Cb), with αw R where wood and plate bear together |
| Plate flexure | AISC F11: Mn = Mp = Fy Z ≤ 1.5 Fy Sx (F11-1); lateral-torsional buckling by F11-3 / F11-4 with Lb = the bolt spacing and Cb = 1.0, or none when braced by the plies; φ = 0.90, Ω = 1.67; demand αs M (with the long-term share when chosen) |
| Plate shear | AISC G4 (doubly symmetric member): Vn = 0.6 Fy Aw Cv2, Aw = d t, Cv2 of G2.2 with kv = 5; φ = 0.90, Ω = 1.67; demand αs V, or V where only the plate bears |
| Plate bearing at the supports | AISC J7 (1.8 Fy Apb, φ = 0.75, Ω = 2.00) and local yielding of the plate edge (J10.2 with k = 0: Fy t lb, φ = 1.00, Ω = 1.50) where the plate bears |
| Bolt value | NDS 12.3 double shear, wood plies as side members and the steel plate as the main member (Fe = 1.5 Fu, Appendix I.2), wood loaded perpendicular to grain (Fe⊥, θ = 90°, Kθ = 1.25); two plates: NDS 12.3.8.2 (five members, Z = Zmin × 2). Z' = Z (CD ≤ 1.6, or KF 3.32, φz 0.65, λ ≤ 1.0) CM Ct Cg CΔ |
| Bolts: load transfer | q = αs w(on wood) − αw w(on plate) per unit length, each combination; force per bolt q s / rows ≤ Z'; the required spacing is reported |
| Bolts at the point loads | αs P / (bolts at the load) + q p ≤ Z' |
| Bolts at the supports | the plate's reaction share αs R (wood bears) or the wood's αw R (plate bears) over the support bolts ≤ Z' |
| Wood shear at the support bolts | where the plies hang on the bolts (plate bears): NDS 3.4.4, Vr' = (2/3) Fv' b de (de/d)² within 5d of the end |
| Bolt geometry | NDS Table 12.5.1A end distance (2D minimum, 4D full: CΔ), Table 12.5.1C edges (loaded 4D, unloaded 1.5D; the edge the bolts push the plies toward is loaded), Table 12.5.1D spacing between rows (the rows run across the beam), 12.5.1.3 5 in. between outer rows across the grain; AISC J3.5 / Table J3.4 edge and end distance in the plate, J3.4 spacing 2 2/3 d |
| Deflection | live (each live type alone) and total (ASD gravity combinations) with E'w Itr; creep: Δ = ΔST + (Itr / Itr,LT) ΔLT |
| Beam slenderness | RB ≤ 50 (NDS 3.3.3.7) when the compression edge is unbraced |
Drawings #
The sheet shows the beam elevation (supports, loads by type, spans, the plate edges hidden), the section (plies, plates, bolts with heads and nuts, widths and depths), the bolt pattern at the beam end (end distance, the support bolts and the first transfer bolts in their rows, spacings and edge distances), and the shear, moment and deflection diagrams. Washers, hole sizes, hangers and the supports themselves are not part of the calculation.
Limitations #
- Each part bends about its own centroid (curvature compatibility through the bolts); no horizontal shear connection between wood and steel is relied on, so a plate flush with the top or bottom adds no composite (parallel axis) stiffness. This is the usual practice (DeStefano 2007) and is conservative for stiffness.
- The plates run the full length; a plate only where the moment needs it is not covered.
- Dimension lumber plies only (2" to 4" thick); timbers, glulam and SCL plies are not covered (LVL plies can be entered as reference values but the SCL volume factor is not applied).
- NDS does not tabulate bolts with a steel centre plate and wood side members (Tables 12F / 12G cover wood main members); the module uses the yield limit equations of Table 12.3.1A. The reference design values are those of NDS 2024 Supplement Tables 4A, 4B and 4D, read on 2026-11-08 (as the sawn lumber beam).
- Friction between the plates and the plies is neglected (DeStefano 2007). Bolt bearing on the plate (AISC J3.11) is not checked separately: the NDS yield modes include the bearing of the plate (mode Im, Fe = 1.5 Fu).
- The plate edge local yielding check is J10.2 applied to a plate without flanges (k = 0): a module decision.
Verification examples #
Verification status: 43 values compared in 9 examples (5 published, 4 hand calculations from the cited equations): 41 within tolerance, 2 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.
backend/tests/test_verify_flitch_beam.py: the published values of DeStefano, "Flitch Plate Beams Design Guide", STRUCTURE magazine, June 2007 (Table 1, p. 56, DF-L No. 2 plies, A36 plates, E = 1,600,000 psi; the design example, p. 57), and hand calculations in closed form.
| Example | What it checks | Published / hand value | ILX Calcs |
|---|---|---|---|
| DESTEFANO-T1-2x10 | (2)-2x10 + PL 1/2 x 9 | n = 18.1, Itr = 748 in⁴, Str = 161.7 in³, M = 13,340 lb-ft, 74 %, V = 3,330 lb | 18.12, 748.4, 161.8, 13,350, 73.6 %, 3,330 |
| DESTEFANO-T1-3x2x10 | (3)-2x10 + (2) PL 1/2 x 9, Cr | Itr = 1,397, Str = 302.1, M = 28,649, 79 %, V = 4,995 | 1,398, 302.2, 28,680, 78.8 %, 4,995 |
| DESTEFANO-T1-2x12 | (2)-2x12 + PL 1/2 x 11 | Itr = 1,361, Str = 241.9, M = 18,142, 74 %, V = 4,050 | 1,361, 242.0, 18,150, 73.9 %, 4,050 |
| DESTEFANO-T1-2x8 | (2)-2x8 + PL 3/8 x 7 | Itr = 289, Str = 79.7, M = 7,173, 67 %, V = 2,610 | 289.5, 79.9, 7,189, 67.1 %, 2,610 |
| DESTEFANO-EX | 12 ft, 700 plf, 1/2 in. bolts | plate load 518 plf, plate reaction 3,108 lb, Z (mode Is) = 945 lb, spacing 21.9 in., 3.29 end bolts | 514.9 plf, 3,090 lb, 947 lb; 20.3 in. and 3.54 bolts (deviation: mode IIIs, 872 lb, governs) |
| HAND-1 | Plate F11 (Lb = 24 in.) and G4 | Mn = 298.0 kip-in (F11-3), Mp = 364.5 kip-in, Vn = 97.2 kips | same |
| HAND-1B | Plate braced by the plies | φMp = 328.1 kip-in | same |
| HAND-2 | Bolt with two plates (12.3.8.2) | Z = 2 × 473.6 = 947.3 lb; LRFD Z' = Z × 3.32 × 0.65 × 0.8 | same |
| HAND-3 | Deflection with creep, long-term share | ΔL = 0.195 in, ΔT = 0.280 in, αs = 0.736, αs,LT = 0.807 | same |
Deviation DESTEFANO-2007-BOLT: the example's bolt value is yield mode Is only; with a steel centre plate mode IIIs gives 872 lb and governs, so the module's spacing is 8 % closer (conservative). The free worked examples found cover section properties and the bolt rational method; Breyer, Design of Wood Structures (flitch beam example) is not free (research/DOCUMENTS_NEEDED.md).