Standards and code basis
Beam sizing in Canadian construction is governed by two standards used together:
- NBCC 2020, Division B Part 4 — establishes the structural loads (dead, live, snow) that beams must be designed for. Residential floor live load: 1.9 kPa. Dead load (framing, finishes): typically 0.5 kPa.
- CSA O86-19 (Engineering Design in Wood) — provides the species-specific design values (Fb for bending, E for modulus of elasticity) used in the sizing formulas. This is the governing Canadian standard for wood structural design.
Your inputs — what each field means
| Input | What it represents | Effect on sizing |
|---|---|---|
| Span (ft) | The clear distance between beam supports (posts or walls) | Moment and deflection both increase with the square of span. Doubling the span quadruples the required section modulus. |
| Tributary width (ft) | The width of floor (or roof) area the beam supports, measured from midpoint to midpoint on each side | Directly multiplies the load per linear foot. A 12 ft tributary width means the beam carries the weight of 12 ft of floor. |
| Dead load (psf) | The permanent weight of framing, sheathing, finishes, and mechanical systems | Typically 10 psf for residential floors (5 psf framing + 5 psf finishes). Used in the total UDL. |
| Live load (psf) | The variable load from people, furniture, and storage | NBCC 2020 minimum for residential floors: 40 psf (1.9 kPa). Deflection is checked against live load only (L/360 limit for floors). |
| Species / grade | The lumber species and grade, or engineered wood product | Determines Fb (bending strength, psi) and E (stiffness, psi). Higher grades and LVL are significantly stronger. |
| Use type | Floor beam or roof beam | Changes the deflection limit: L/360 for floors (stricter — prevents plaster cracking and perceptible bounce), L/240 for roofs. |
The calculation — step by step
Species design values used in this calculator (from CSA O86-19):
| Species / Product | Fb (psi) | E (psi) |
|---|---|---|
| SPF Select Structural | 1,710 | 1,380,000 |
| DF-L Select Structural | 2,395 | 1,600,000 |
| LVL 1.9E | 3,307 | 1,900,000 |
| Glulam 20f-EX | 2,958 | 1,800,000 |
- Calculate uniform distributed load (UDL):
w = (dead load + live load) × tributary width ÷ 12
Units: psf × ft ÷ 12 = lb/ft. Example: (10 + 40) psf × 10 ft ÷ 12 = 41.7 lb/ft. - Calculate maximum bending moment (simply supported):
M = w × L² ÷ 8
Units: ft-lbs. Maximum moment occurs at midspan for a uniformly loaded simply supported beam. - Calculate required section modulus:
S_req = (M × 12) ÷ Fb
The factor of 12 converts M from ft-lbs to in-lbs. S is in in³. - Find the smallest section with S ≥ S_req. The calculator scans the available section table (2×8 through 6×12) from smallest to largest and selects the first section where the tabulated S value meets or exceeds S_req.
- Check deflection for that section:
δ = (5 × w × L⁴) ÷ (384 × E × I)
Where L is converted to inches (L × 12), and I is the moment of inertia of the selected section (in⁴).δ_limit = L (inches) ÷ 360 (floor) or ÷ 240 (roof)
The beam passes deflection if δ ≤ δ_limit.
Reading your result
- Total load (lbs): The total weight the beam carries — UDL × span.
- Moment (ft-lbs): The maximum bending moment at midspan.
- Required S (in³): The minimum section modulus needed to keep bending stress within the Fb limit for your species.
- Recommended size: The smallest standard section that satisfies the bending check. You should verify it also passes deflection.
- Deflection (inches): Calculated mid-span deflection under full UDL.
- Deflection limit (inches): L/360 for floors or L/240 for roofs. If deflection exceeds this limit, select the next larger section and re-run.
- Deflection pass/fail: Whether the recommended section meets the deflection criterion.
Assumptions and limitations
- Assumes simply supported (single-span) beam. Continuous beams over multiple spans have lower midspan moments and can use smaller sections.
- Uses total UDL for deflection check. For strict code compliance, deflection should be checked under live load only. This calculator uses total load — a conservative approach.
- Does not apply load duration factors (Kd), system factors (KH), or treatment factors (Kт) from CSA O86. These factors can increase or decrease the design Fb by up to 25%. A licensed structural engineer accounts for all CSA O86 factors in a stamped design.
- Section dimensions are nominal (2×8 = 1.5″ × 7.25″ actual). The S and I values used reflect actual dimensions.
- Does not check shear stress, bearing stress at supports, or lateral-torsional buckling — all of which can govern for deep sections with long spans. Engineer review is required for permit applications.
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