Beam load span.

How the math works

For a simply-supported beam with a uniform load:

Maximum moment:    M = w × L² / 8
Maximum deflection: δ = 5 × w × L⁴ / (384 × E × I)
Bending stress:     fb = M / S

   where:
     w = uniform load (lb/ft converted to lb/in)
     L = span (in)
     E = modulus of elasticity (psi)
     I = moment of inertia of section (in⁴)
     S = section modulus (in³)

The beam passes the bending check if fb ≤ Fb (allowable bending stress, from material properties). It passes the deflection check if δ ≤ L/360 for floor live load (industry standard) — or L/240 for less critical applications.

Section properties used

Wood: nominal sizes interpreted as actual dimensions (2×8 → 1.5″ × 7.25″). I and S calculated from rectangular geometry. Allowable Fb and E are typical Visually Graded #2 lumber values per the NDS Supplement (these vary by grade — Select Structural is higher, #3 is lower).

Steel: W-shape I and S values from AISC Steel Construction Manual (15th edition). Allowable bending stress Fb = 0.66 × Fy ≈ 24 ksi for A992 steel (Fy = 50 ksi) under ASD design (simplification).

What this calculator does NOT check

• Shear strength — Important for short, heavily-loaded beams. Wood shear is often the controlling factor for short spans.
• Bearing — The beam must rest on a wide enough support to avoid crushing the wood or yielding the steel at the bearing point.
• Lateral-torsional buckling — Slender steel beams can buckle sideways. AISC has specific provisions for unbraced length.
• Load combinations and factors — Real design uses dead load, live load, snow, wind, seismic, etc. with code-specified factors (LRFD or ASD).
• Long-term creep (wood) — Wood deflects more over time under sustained load. NDS applies a creep factor.
• Connection design — Where beams meet columns, hangers, or other beams. Connection failure is more common than beam failure.
• Moisture and temperature factors — Wet service, fire-treated, or high-temp environments reduce wood capacity.

When this is useful

• Sanity-checking a beam already specified by a structural engineer.
• Estimating ranges to discuss with a structural engineer ("can I span 12 feet with a 2x10?").
• Learning beam mechanics in school or self-study.
• Designing non-structural elements that won't injure anyone if they fail (e.g., a shelving system).

When this is NOT enough

• Any building permit-required structure.
• Anything supporting people, vehicles, or significant property.
• Anything with continuous occupancy or public use.
• Anything in a seismic, wind, or snow region with significant loads.
• Anything you wouldn't be financially or legally comfortable being responsible for if it failed.

Sources

• Wood design values (Fb, E): National Design Specification (NDS) for Wood Construction, AWC Supplement, Table 4A (Visually Graded Dimensional Lumber).
• Steel W-shape properties: AISC Steel Construction Manual, 15th edition, Part 1 (W-shapes).
• Beam formulas: Any structural mechanics textbook (Gere & Timoshenko, Mechanics of Materials).
• Deflection limits: IBC §1604.3 — L/360 for floors with live load, L/240 for other.
• Loads: ASCE 7-22 — Minimum Design Loads and Associated Criteria for Buildings and Other Structures.

Educational use only. This calculator is for learning and conversation, not design. Have a licensed structural engineer specify and stamp drawings for any beam that supports people, property, or anything you care about.

See also