Load-Bearing Wall Beam Span Calculator
Calculate the maximum allowable span for a load-bearing wall beam using bending stress and deflection criteria per standard structural engineering principles.
Total load per linear foot of beam (dead + live load)
Allowable fiber stress in bending (e.g. 1500 psi for Douglas Fir #2, 25000 psi for A36 steel)
Actual (dressed) width of beam cross-section
Actual (dressed) depth of beam cross-section
E for wood ≈ 1,200,000–1,900,000 psi; E for steel = 29,000,000 psi
Denominator of L/n deflection limit (e.g. 360 for live load, 240 for total load)
Formulas Used
Section Properties:
- Section Modulus:
S = b·d² / 6(in³) - Moment of Inertia:
I = b·d³ / 12(in⁴)
Criterion 1 — Bending Stress (simply supported, uniform load):
- Maximum moment:
M = w·L² / 8 - Bending stress:
σ = M / S ≤ Fb - Solving for span:
L_bending = √(8·S·Fb / w)
Criterion 2 — Deflection (simply supported, uniform load):
- Max deflection:
δ = 5·w·L⁴ / (384·E·I) - Deflection limit:
δ ≤ L / n - Solving for span:
L_deflection = ∛(384·E·I / (5·w·n))
Governing Span: L_max = min(L_bending, L_deflection)
Note: w is converted from lb/ft to lb/in (÷12) before applying inch-based formulas.
Assumptions & References
- Beam is modeled as simply supported at both ends with a uniformly distributed load.
- Beam cross-section is rectangular (solid sawn lumber or equivalent).
- Input dimensions should be actual (dressed) dimensions, not nominal (e.g., a 2×10 is actually 1.5″ × 9.25″).
- Allowable bending stress (Fb) should already include applicable adjustment factors (Cd, CM, CF, etc.) per NDS.
- Typical Fb values: Douglas Fir-Larch #2 ≈ 900–1,500 psi; LVL ≈ 2,600 psi; A36 Steel ≈ 23,760 psi (0.66·Fy).
- Typical E values: Softwood lumber ≈ 1,200,000–1,900,000 psi; LVL ≈ 1,900,000–2,000,000 psi; Steel = 29,000,000 psi.
- Deflection limits per IBC/ASCE 7: L/360 for live load only; L/240 for total load (floors); L/180 for roofs.
- Lateral bracing of the compression flange/edge is assumed adequate (no lateral-torsional buckling check).
- Shear capacity is not checked here — verify separately, especially for short, heavily loaded spans.
- References: AISC Steel Construction Manual; NDS (National Design Specification for Wood Construction); IBC 2021; ASCE 7-22.
- ⚠️ This tool is for preliminary estimation only. All structural designs must be reviewed and stamped by a licensed structural engineer.