Branch Weight & Load Estimator
ANA›Life Services Authority›National Calculator Authority›Branch Weight & Load Estimator
.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; } }
Branch Weight & Load Estimator
Estimates the weight of a tree branch and the bending moment (load) it exerts at its base attachment point, using a tapered cylinder model and wood density.
Branch Length (ft)
Diameter at Base (inches)
Diameter at Tip (inches)
Branch Angle from Vertical (degrees)
Wood Density
Light softwood (e.g. Pine) — 25 lb/ft³ Medium softwood (e.g. Fir) — 30 lb/ft³ Light hardwood (e.g. Maple) — 35 lb/ft³ Medium hardwood (e.g. Oak) — 45 lb/ft³ Dense hardwood (e.g. Hickory) — 55 lb/ft³ Custom...
Custom Wood Density (lb/ft³)
Snow/Ice Load (lb/ft²) (optional, 0 if none)
Calculate
document.getElementById('bra-density').addEventListener('change', function() { var cg = document.getElementById('bra-custom-density-group'); cg.style.display = (this.value === 'custom') ? 'block' : 'none'; });
function braCalc() { var resultDiv = document.getElementById('bra-result'); resultDiv.innerHTML = '';
var L = parseFloat(document.getElementById('bra-length').value); var db = parseFloat(document.getElementById('bra-diam-base').value); var dt = parseFloat(document.getElementById('bra-diam-tip').value); var angle = parseFloat(document.getElementById('bra-angle').value); var snow = parseFloat(document.getElementById('bra-snow').value) || 0;
var densitySelect = document.getElementById('bra-density').value; var density; if (densitySelect === 'custom') { density = parseFloat(document.getElementById('bra-custom-density').value); if (isNaN(density) || density Please enter a valid custom wood density.'; return; } } else { density = parseFloat(densitySelect); }
// Validation var errors = []; if (isNaN(L) || L = db) errors.push('Tip diameter must be less than base diameter.'); if (isNaN(angle) || angle 90) errors.push('Branch angle must be between 0° and 90°.'); if (isNaN(snow) || snow 0) { resultDiv.innerHTML = '' + errors.join('') + ''; return; }
// Convert inches to feet for diameters var rb = (db / 2) / 12; // base radius in ft var rt = (dt / 2) / 12; // tip radius in ft
// Volume of truncated cone (frustum): V = (πL/3) * (rb² + rbrt + rt²) var V = (Math.PI * L / 3) * (rbrb + rbrt + rt*rt);
// Branch weight (wood only) var W_wood = V * density; // lb
// Projected surface area for snow load (approximate as trapezoid of diameters along length) // Surface area projection = L * (db + dt) / 2 / 12 (in ft²) var projArea = L * (db + dt) / 2 / 12; // ft² var W_snow = snow * projArea; // lb
var W_total = W_wood + W_snow;
// Center of mass of frustum from base: // x_cm = (L/4) * (rb² + 2rbrt + 3rt²) / (rb² + rbrt + rt²) var denom = rbrb + rbrt + rtrt; var x_cm = (L / 4) * (rbrb + 2rbrt + 3rtrt) / denom;
// Horizontal component of weight creates bending moment // Bending moment at base = W_total * x_cm * sin(angle) var angleRad = angle * Math.PI / 180; var M = W_total * x_cm * Math.sin(angleRad); // ft·lb
// Shear force at base (perpendicular to branch axis) var shear = W_total * Math.sin(angleRad); // lb
// Axial compression at base (along branch axis) var axial = W_total * Math.cos(angleRad); // lb
// Section modulus at base: S = π * rb³ / 4 (for solid circle, ft³) var S = Math.PI * Math.pow(rb, 3) / 4; // ft³ // Bending stress at base var bendingStress = (S > 0) ? (M / S) * 144 : 0; // convert ft·lb/ft³ → lb/in² (psi): ×144
resultDiv.innerHTML = '### Results ' + '' + 'ParameterValue' + 'Branch Volume (frustum)' + V.toFixed(4) + ' ft³' + 'Wood Weight' + W_wood.toFixed(2) + ' lb' + 'Snow / Ice Weight' + W_snow.toFixed(2) + ' lb' + 'Total Branch Weight' + W_total.toFixed(2) + ' lb' + 'Center of Mass from Base' + x_cm.toFixed(3) + ' ft' + 'Bending Moment at Base' + M.toFixed(2) + ' ft·lb' + 'Shear Force at Base' + shear.toFixed(2) + ' lb' + 'Axial Compression at Base' + axial.toFixed(2) + ' lb' + 'Bending Stress at Base' + bendingStress.toFixed(1) + ' psi' + '' + 'Note: Results assume a solid wood frustum (tapered cylinder). Hollow, decayed, or multi-forked branches will differ.
'; }
#### Formulas Used
Volume (Frustum / Truncated Cone): V = (π · L / 3) · (rb² + rb·rt + rt²)
Branch Weight: Wwood = V · ρ (ρ = wood density in lb/ft³)
Snow/Ice Weight: Wsnow = qsnow · L · (db + dt) / 2 (projected surface area)
Center of Mass of Frustum from Base: xcm = (L/4) · (rb² + 2rbrt + 3rt²) / (rb² + rbrt + rt²)
Bending Moment at Base: M = Wtotal · xcm · sin(θ) (θ = angle from vertical)
Bending Stress at Base (solid circular section): σ = M / S where S = π·rb³ / 4
#### Assumptions & References
- Branch modeled as a solid truncated cone (frustum) — no hollow core or decay.
- Wood density values are for green (freshly cut) wood; dry wood is ~15–20% lighter.
- Snow load is applied to the projected horizontal surface area (trapezoidal approximation).
- Bending moment assumes the branch weight acts at its center of mass with a horizontal moment arm = xcm · sin(θ).
- Bending stress uses the elastic flexure formula (σ = M/S) for a solid circular cross-section at the base.
- Wood density references: USDA Forest Products Laboratory, Wood Handbook (2021), Table 5-3.
- For professional tree risk assessment, consult a Certified Arborist (ISA) or structural engineer.
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