Foundry roof beam

The problem: sizing the roof beam for the covered double-burner/coal-forge setup — a 10×10 ft shed roof, treated wood posts 10 ft apart, single beam spanning the gap. Will a 2×8 hold, or does it need to be a 2×10 (or doubled up)?

Concepts pulled in, in this order: force vectors and equilibrium (needed to find what the beam's supports are actually reacting against), free-body diagrams (applied to the beam itself, not an abstract shape), shear and moment (where the beam bends hardest under load), and bending stress — σ = Mc/I, via section modulus — the actual capacity check against real lumber.

Loads

• Dead load (metal roofing + framing): ~7 psf
• Design ground snow load: 20 psf — the real code value for Charleston, WV (city building documents), not a personal-memory estimate. Codes target a rare statistical event (~2%/year chance), not the worst a person has seen in 35 years — that gap is the whole reason to check the code number instead of eyeballing it.
• Total: 27 psf
• Tributary width to the front beam: 5 ft (half the 10 ft roof depth — the other half loads the rear wall/ledger)

Calculation

• Line load: w = 27 psf × 5 ft = 135 lb/ft
• Max moment (simple beam, span L = 10 ft): M = wL²/8 = 135 × 10² ÷ 8 = 1,688 lb-ft
• Required section modulus for a 2×10: S ≥ M/Fᵇ = (1,688 × 12 in/ft) ÷ 800 psi ≈ 25.3 in³ (Fᵇ = 800 psi, the published reference value for a #2 Southern Pine 2×10: Southern Forest Products Association, Southern Pine Use Guide, Table 1, 2013, normal load duration, dry service). Fᵇ is not one number for all lumber: for #2 Southern Pine it falls as the board gets wider, 1,000 psi for a 2×6, 925 for a 2×8, 800 for a 2×10, 750 for a 2×12.

Answer

A single 2×10 (S ≈ 21.4 in³) does not clear it: it needs 25.3 in³, so it is overstressed by about 18%. A single 2×8 (S ≈ 13.1 in³) is far short. Options that pass: a single 2×12 (S ≈ 31.6 in³, needs 27.0 at its 750 psi), a doubled 2×8 (S ≈ 26.3 in³, needs 21.9 at 925 psi), or a doubled 2×10 (S ≈ 42.8 in³, needs 25.3). This uses the table value with no adjustment factors; the NDS also adjusts for load duration, repetitive members and wet service, which would be a job for the engineer on a real build. All of these assume the beam is braced against rolling sideways; Breyer Chapter 1 shows how much that detail matters.

Open items for a later pass

Wind load, post buckling/compression check, and confirming the actual roof assembly weight once materials are picked. (Wind uplift and post buckling get their own chapters — Ch. 2 and Ch. 3 in the full guide, not yet built into a site page.)