Deck Joist Span Calculator

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Deck Joist Span Calculator

Calculate the maximum allowable span for deck joists based on lumber species, size, spacing, and load conditions per IRC Table R507.6.

Lumber Species / Grade

Douglas Fir-Larch #1 & Better Douglas Fir-Larch #2 Hem-Fir #1 & Better Hem-Fir #2 Southern Pine #1 Southern Pine #2 Spruce-Pine-Fir #1 & Better Spruce-Pine-Fir #2 Redwood #1 Western Red Cedar #1

Joist Size

2×6 2×8 2×10 2×12

Joist Spacing (inches on center)

12" 16" 24"

Total Design Load (psf)

40 psf (10 DL + 30 LL — Residential) 50 psf (10 DL + 40 LL — Standard Deck) 60 psf (10 DL + 50 LL — Heavy Use)

Actual Joist Span (ft) — optional, for stress check

Calculate

function decCalc() { // ─── IRC Table R507.6 Maximum Joist Spans (feet-inches) ─────────────────── // Structure: spanTable[species][size][spacing_index] = span in decimal feet // spacing_index: 0=12", 1=16", 2=24" // Load basis: 40 psf total (10 DL + 30 LL). Adjustment applied for other loads. const spanTable = { douglas_fir_larch_1: { "2x6": [9.6, 8.8, 7.7], "2x8": [12.7, 11.7, 10.1], "2x10": [16.1, 14.9, 12.11], "2x12": [18.0, 16.6, 14.5] }, douglas_fir_larch_2: { "2x6": [9.4, 8.7, 7.6], "2x8": [12.5, 11.5, 10.0], "2x10": [15.10,14.7, 12.8], "2x12": [17.9, 16.4, 14.3] }, hem_fir_1: { "2x6": [9.1, 8.4, 7.4], "2x8": [12.0, 11.1, 9.8], "2x10": [15.3, 14.1, 12.3], "2x12": [17.5, 16.1, 14.0] }, hem_fir_2: { "2x6": [8.9, 8.2, 7.2], "2x8": [11.9, 10.11,9.6], "2x10": [15.1, 13.11,12.1], "2x12": [17.3, 15.11,13.10] }, southern_pine_1: { "2x6": [10.1, 9.3, 8.1], "2x8": [13.4, 12.3, 10.8], "2x10": [17.0, 15.8, 13.7], "2x12": [19.6, 18.0, 15.7] }, southern_pine_2: { "2x6": [9.11, 9.1, 7.11], "2x8": [13.1, 12.0, 10.5], "2x10": [16.8, 15.4, 13.4], "2x12": [19.1, 17.7, 15.3] }, spruce_pine_fir_1: { "2x6": [9.4, 8.7, 7.6], "2x8": [12.5, 11.5, 10.0], "2x10": [15.10,14.7, 12.8], "2x12": [17.9, 16.4, 14.3] }, spruce_pine_fir_2: { "2x6": [9.1, 8.4, 7.4], "2x8": [12.1, 11.2, 9.9], "2x10": [15.5, 14.3, 12.5], "2x12": [17.8, 16.3, 14.2] }, redwood_1: { "2x6": [8.7, 7.11, 6.11], "2x8": [11.4, 10.6, 9.1], "2x10": [14.6, 13.4, 11.7], "2x12": [16.8, 15.4, 13.4] }, western_cedar_1: { "2x6": [8.4, 7.8, 6.8], "2x8": [11.0, 10.2, 8.10], "2x10": [14.1, 13.0, 11.3], "2x12": [16.2, 14.11,13.0] } };

// Lumber section properties (actual dressed dimensions) const sectionProps = { "2x6": { b: 1.5, d: 5.5 }, "2x8": { b: 1.5, d: 7.25 }, "2x10": { b: 1.5, d: 9.25 }, "2x12": { b: 1.5, d: 11.25 } };

// Fb (psi) and E (psi) reference design values const lumberProps = { douglas_fir_larch_1: { Fb: 1000, E: 1700000 }, douglas_fir_larch_2: { Fb: 900, E: 1600000 }, hem_fir_1: { Fb: 975, E: 1600000 }, hem_fir_2: { Fb: 850, E: 1300000 }, southern_pine_1: { Fb: 1250, E: 1700000 }, southern_pine_2: { Fb: 1100, E: 1600000 }, spruce_pine_fir_1: { Fb: 875, E: 1500000 }, spruce_pine_fir_2: { Fb: 800, E: 1400000 }, redwood_1: { Fb: 825, E: 1100000 }, western_cedar_1: { Fb: 700, E: 1100000 } };

// Load adjustment factor (relative to 40 psf baseline) // Span ∝ (w_base / w_design)^(1/3) for bending-controlled members const loadAdjFactor = { 40: 1.0, 50: Math.pow(40/50, 1/3), 60: Math.pow(40/60, 1/3) };

const species = document.getElementById("dec-species").value; const size = document.getElementById("dec-size").value; const spacing = parseInt(document.getElementById("dec-spacing").value); const load = parseInt(document.getElementById("dec-load").value); const actualFt = parseFloat(document.getElementById("dec-actual").value);

const spacingIdx = { 12: 0, 16: 1, 24: 2 }[spacing];

// Parse table value (stored as feet.inches float, e.g. 12.7 = 12'-7") function parseSpan(val) { const ft = Math.floor(val); const inc = Math.round((val - ft) * 100); return ft + inc / 12; // convert to decimal feet }

const rawSpan = spanTable[species][size][spacingIdx]; const baseSpanFt = parseSpan(rawSpan); const adjFactor = loadAdjFactor[load]; const maxSpanFt = baseSpanFt * adjFactor;

const maxSpanIn = maxSpanFt * 12; const maxFt = Math.floor(maxSpanFt); const maxIn = Math.round((maxSpanFt - maxFt) * 12);

// ─── Engineering verification (bending & deflection) ────────────────────── const sp = sectionProps[size]; const lp = lumberProps[species]; const b = sp.b; const d = sp.d; const S = (b * d * d) / 6; // Section modulus (in³) const I = (b * d * d * d) / 12; // Moment of inertia (in⁴) const w = (load * spacing / 12); // Uniform load (lb/ft) const wIn = w / 12; // lb/in

// Size factor CF for bending (NDS Supplement Table 4A) const CF = { "2x6": 1.3, "2x8": 1.2, "2x10": 1.1, "2x12": 1.0 }[size]; const CD = 1.0; // Load duration factor (normal) const CM = 1.0; // Wet service (assume dry) const Fb_adj = lp.Fb * CD * CM * CF; // Adjusted Fb (psi)

// Max span from bending: M = wL²/8 ≤ Fb'·S // L_bend = sqrt(8 · Fb' · S / w_in) in inches const L_bend_in = Math.sqrt((8 * Fb_adj * S) / wIn); const L_bend_ft = L_bend_in / 12;

// Max span from deflection: Δ = 5wL⁴/(384EI) ≤ L/360 // L_defl = (384 · E · I / (5 · w_in · 360))^(1/3) const L_defl_in = Math.pow((384 * lp.E * I) / (5 * wIn * 360), 1/3); const L_defl_ft = L_defl_in / 12;

const engMaxFt = Math.min(L_bend_ft, L_defl_ft);

// ─── Actual span check ──────────────────────────────────────────────────── let actualCheck = ""; if (!isNaN(actualFt) && actualFt > 0) { const actualIn = actualFt * 12; const M_actual = (wIn * actualIn * actualIn) / 8; const fb_actual = M_actual / S; const defl_actual = (5 * wIn * Math.pow(actualIn, 4)) / (384 * lp.E * I); const defl_limit = actualIn / 360; const bendRatio = (fb_actual / Fb_adj * 100).toFixed(1); const deflRatio = (defl_actual / defl_limit * 100).toFixed(1); const pass = actualFt Actual Span Check: ${actualFt} ft

CheckValueLimitRatioStatus Bending Stress${fb_actual.toFixed(0)} psi${Fb_adj.toFixed(0)} psi${bendRatio}%${parseFloat(bendRatio) Deflection${defl_actual.toFixed(3)}"${defl_limit.toFixed(3)}" (L/360)${deflRatio}%${parseFloat(deflRatio)

${icon} ${pass ? "Span is ACCEPTABLE" : "Span EXCEEDS maximum — reduce span or upgrade lumber"}

`; }

const html = ` ### Results

IRC Table R507.6 Max Span${maxFt}'-${maxIn}" (${maxSpanFt.toFixed(2)} ft) Bending-Controlled Max Span${L_bend_ft.toFixed(2)} ft Deflection-Controlled Max Span (L/360)${L_defl_ft.toFixed(2)} ft Governing Criterion${L_bend_ft Adjusted Fb (F'b)${Fb_adj.toFixed(0)} psi Tributary Width per Joist${(spacing/12).toFixed(2)} ft Design Load per Joist${w.toFixed(1)} lb/ft Section Modulus S${S.toFixed(2)} in³ Moment of Inertia I${I.toFixed(2)} in⁴

${actualCheck}`;

document.getElementById("dec-result").innerHTML = html; }

#### Formulas Used

1. Bending-controlled maximum span:

M = wL²/8 ≤ F'b · S  →  Lbend = √(8 · F'b · S / w)

Where: w = uniform load per joist (lb/in), F'b = adjusted bending stress (psi), S = bd²/6 (in³)

2. Deflection-controlled maximum span (L/360 live load limit):

Δ = 5wL⁴ / (384EI) ≤ L/360  →  Ldefl = ∛(384 · E · I / (5 · w · 360))

Where: E = modulus of elasticity (psi), I = bd³/12 (in⁴)

3. Adjusted bending design value:

F'b = Fb · CD · CM · CF

CD = 1.0 (normal duration), CM = 1.0 (dry service), CF = size factor (1.0–1.3)

4. Load adjustment for non-40 psf loads:

Ladj = Ltable · (40 / wdesign)1/3

5. Tributary load per joist:

w = Total Load (psf) × Spacing (ft)

#### Assumptions & References

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