Load-Bearing Wall Beam Span Calculator
ANA›Life Services Authority›National Calculator Authority›Load-Bearing Wall Beam Span Calculator
.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
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 Uniform Load (w) — lb/ft
Total load per linear foot of beam (dead + live load)
Allowable Bending Stress (Fb) — psi
Allowable fiber stress in bending (e.g. 1500 psi for Douglas Fir #2, 25000 psi for A36 steel)
Beam Width (b) — inches
Actual (dressed) width of beam cross-section
Beam Depth (d) — inches
Actual (dressed) depth of beam cross-section
Modulus of Elasticity (E) — psi
E for wood ≈ 1,200,000–1,900,000 psi; E for steel = 29,000,000 psi
Deflection Limit (L / ?)
Denominator of L/n deflection limit (e.g. 360 for live load, 240 for total load)
Calculate Maximum Span
function loaCalc() { const resultDiv = document.getElementById('loa-result'); resultDiv.style.display = 'block';
// --- Gather inputs --- const w = parseFloat(document.getElementById('loa-load').value); const Fb = parseFloat(document.getElementById('loa-fb').value); const b = parseFloat(document.getElementById('loa-width').value); const d = parseFloat(document.getElementById('loa-depth').value); const E = parseFloat(document.getElementById('loa-E').value); const denom = parseFloat(document.getElementById('loa-deflimit').value);
// --- Validation --- const errors = []; if (isNaN(w) || w 0) { resultDiv.innerHTML = 'Please fix the following:' + errors.map(e => '').join('') + ''; return; }
// --------------------------------------------------------------- // SECTION PROPERTIES // S = section modulus = b * d² / 6 (in³) // I = moment of inertia = b * d³ / 12 (in⁴) // --------------------------------------------------------------- const S = (b * d * d) / 6.0; // in³ const I = (b * d * d * d) / 12.0; // in⁴
// Convert uniform load from lb/ft → lb/in const w_in = w / 12.0; // lb/in
// --------------------------------------------------------------- // CRITERION 1 — Bending Stress // For a simply supported beam with uniform load: // M_max = w * L² / 8 // σ = M / S ≤ Fb // → Fb = (w_in * L²) / (8 * S) // → L² = (8 * S * Fb) / w_in // → L_bending = sqrt((8 * S * Fb) / w_in) [inches] // --------------------------------------------------------------- const L_bending_in = Math.sqrt((8.0 * S * Fb) / w_in); const L_bending_ft = L_bending_in / 12.0;
// --------------------------------------------------------------- // CRITERION 2 — Deflection // For a simply supported beam with uniform load: // δ_max = (5 * w_in * L⁴) / (384 * E * I) // Limit: δ_max ≤ L / denom // → (5 * w_in * L⁴) / (384 * E * I) = L / denom // → L³ = (384 * E * I) / (5 * w_in * denom) // → L_deflection = cbrt((384 * E * I) / (5 * w_in * denom)) [inches] // --------------------------------------------------------------- const L_deflection_in = Math.cbrt((384.0 * E * I) / (5.0 * w_in * denom)); const L_deflection_ft = L_deflection_in / 12.0;
// --------------------------------------------------------------- // GOVERNING SPAN — lesser of the two criteria // --------------------------------------------------------------- const L_max_in = Math.min(L_bending_in, L_deflection_in); const L_max_ft = L_max_in / 12.0; const governs = (L_bending_in v.toLocaleString('en-US', {minimumFractionDigits: dec, maximumFractionDigits: dec});
resultDiv.innerHTML = ` ### Results
ParameterValue Section Modulus (S)${fmt(S, 3)} in³ Moment of Inertia (I)${fmt(I, 3)} in⁴ Max Span — Bending${fmt(L_bending_ft)} ft (${fmt(L_bending_in)} in) Max Span — Deflection (L/${denom})${fmt(L_deflection_ft)} ft (${fmt(L_deflection_in)} in) ✅ Governing Max Span${fmt(L_max_ft)} ft (${fmt(L_max_in)} in) — ${governs} Controls Actual Bending Stress at Max Span${fmt(stress_act)} psi (Allowable: ${fmt(Fb)} psi) Actual Deflection at Max Span${fmt(defl_act, 4)} in (L/${fmt(defl_ratio, 0)})
⚠️ This result assumes a simply supported beam with a uniformly distributed load. Always verify with a licensed structural engineer before construction.
`; }
#### 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″).
- 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.
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