BEAM SPAN (BUILT-UP)
About this calculator
This beam span calculator estimates the maximum simple-span length of a built-up dimensional-lumber beam (one to three plies of 2x6, 2x8, 2x10, or 2x12) based on its bending capacity and an L/360 live-load deflection limit. The calculation assumes #2 Spruce-Pine-Fir (Fb = 875 psi, E = 1,400,000 psi) with a size factor Cf, repetitive-member factor not applied (single-beam case), normal load duration. Enter the lumber size, the number of plies nailed or bolted into a built-up beam, the tributary width the beam is carrying, and the floor live and dead loads. Output is the maximum span where the beam stays within both bending strength and deflection limits. ESTIMATE ONLY — built-up beams should be sized by an engineer or a code-stamped span table for any actual structure.
How to use this calculator
Pick the dimensional lumber size and the number of plies in your built-up beam — 1 is a single beam, 2 is the typical built-up header (two 2x10s nailed together with ½-inch plywood spacer), 3 is a heavy header for wide openings or interior loads. Enter the tributary width — half the joist span on each side of the beam, or the full joist span if the beam sits at the end of the floor system.
Set the floor live load (40 psf for general living areas per IRC, 30 psf for sleeping rooms only) and dead load (10 psf for typical wood-framed floors, 15–20 psf for tile or stone finishes). The result is the maximum simple-span length where #2 SPF lumber stays within both bending strength and L/360 deflection limits.
Worked example
A built-up beam of two 2x10s carrying a 12-ft tributary width with 40 psf live + 10 psf dead:
Total uniform load: (40 + 10) × 12 = 600 plf. Bending limit (Sx = 21.39 in³, Cf = 1.1, N = 2): √((8 × 875 × 1.1 × 42.78) ÷ (12 × 600)) ≈ 6.77 ft. Deflection L/360 limit (E = 1.4M, I = 198): about 11 ft.
Bending governs at 6.77 ft → max span ≈ 6.5 ft for this load.
Stepping up to three 2x10s on the same load: bending limit jumps to about 8.3 ft. Stepping up to 2-2x12s (Sx = 31.64, I = 178): bending ~ 8.2 ft, deflection ~ 12 ft → max span ~ 8 ft.
For a 10-ft span carrying 600 plf, you'd need either 3-2x12s or an LVL beam — built-up dimensional lumber tops out fast at heavy loads.
Common mistakes & waste factors
Forgetting tributary width is half the room. For a beam down the middle of a 24-ft room, tributary = 12 ft (6 ft of joists on each side). For a beam at the end wall, tributary = full joist span.
Treating built-up beams like solid beams. A 2-2x10 isn't equivalent to a single 4x10 — it's slightly weaker because the plies don't share load perfectly. The Cf and section modulus N×Sx multiplier handles this, but ignore the ply count and you'll undersize.
Skipping the ½-inch plywood spacer between plies. Built-up beams need a structural plywood spacer between members for proper load sharing — gluing and nailing alone isn't enough for engineered performance.
Sizing for #1 grade when buying #2. Lumberyards usually stock #2 SPF or DFL — the calculator's Fb = 875 psi is for #2. #1 grade has higher Fb (about 1,000 psi) but costs 30% more and is rarely stocked.
Rules of thumb
#2 SPF: Fb = 875 psi, E = 1.4M psi. Cf: 2x6 = 1.3, 2x8 = 1.2, 2x10 = 1.1, 2x12 = 1.0.
L/360 deflection: maximum allowable bend = span ÷ 360 (about 0.4 inch per 12 ft). Live-load only.
Tributary width = half joist span each side, or full joist span if beam is at end.
Built-up beam ply count rough rule: each added ply adds ~25–30% capacity (not a clean multiplier).
Above ~10 ft span carrying 500+ plf, switch to LVL or PSL — built-up SPF becomes too deep or too many plies to be practical.