Structural Char Depth Assessment Calculator

ANA›Life Services Authority›National Calculator Authority›Structural Char Depth Assessment Calculator

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Structural Char Depth Assessment Calculator

Estimates the char depth in exposed timber structural members during fire exposure using the parametric charring rate method per Eurocode 5 (EN 1995-1-2). Determines residual cross-section dimensions and assesses structural adequacy.

Timber Species / Grade

Softwood (C16–C24) — β₀ = 0.65 mm/min Glued Laminated Timber (GL24–GL32) — β₀ = 0.65 mm/min Hardwood (D30–D70, ρ ≥ 450 kg/m³) — β₀ = 0.50 mm/min LVL (Laminated Veneer Lumber) — β₀ = 0.70 mm/min Custom charring rate

Custom One-Dimensional Charring Rate β₀ (mm/min)

Fire Exposure Duration t (minutes)

Original Member Width b (mm)

Original Member Depth h (mm)

Number of Exposed Sides

1 side (e.g. floor beam, one face exposed) 3 sides (e.g. beam exposed on bottom and two sides) 4 sides (e.g. column, all sides exposed)

Corner Rounding / Zero-Strength Layer k₀ Factor

Standard (k₀ = 1.0, t ≥ 20 min) Early stage (k₀ = 0.5, t < 20 min, linear interpolation)

Applied Bending Moment M_Ed (kNm) (optional — for capacity check)

Characteristic Bending Strength f_m,k (N/mm²)

Modification Factor for Fire k_mod,fi

Typically 1.0 for fire design per EN 1995-1-2 §2.3

Partial Factor for Fire γ_M,fi

Typically 1.0 for fire design per EN 1995-1-2 §2.3

Calculate Char Depth

function scda_updateCharRate() { var sel = document.getElementById('scda_timber_species'); var customGroup = document.getElementById('scda_custom_rate_group'); customGroup.style.display = (sel.value === 'custom') ? 'block' : 'none'; }

function scda_getCharRate() { var sel = document.getElementById('scda_timber_species'); if (sel.value === 'custom') { return parseFloat(document.getElementById('scda_custom_rate').value); } return parseFloat(sel.value); }

function scda_calc() { var resultDiv = document.getElementById('scda_result'); resultDiv.style.display = 'block'; resultDiv.className = 'calc-result';

// --- Retrieve inputs --- var beta0 = scda_getCharRate(); var t = parseFloat(document.getElementById('scda_fire_duration').value); var b = parseFloat(document.getElementById('scda_beam_width').value); var h = parseFloat(document.getElementById('scda_beam_depth').value); var sides = parseInt(document.getElementById('scda_exposed_sides').value); var k0 = parseFloat(document.getElementById('scda_k0').value); var M_Ed = parseFloat(document.getElementById('scda_applied_moment').value); var fm_k = parseFloat(document.getElementById('scda_bending_strength').value); var kmod_fi = parseFloat(document.getElementById('scda_kmod_fi').value); var gamma_m_fi = parseFloat(document.getElementById('scda_gamma_m_fi').value);

// --- Validation --- var errors = []; if (isNaN(beta0) || beta0 2.0) errors.push("Charring rate β₀ must be between 0.1 and 2.0 mm/min."); if (isNaN(t) || t 240) errors.push("Fire duration must be between 1 and 240 minutes."); if (isNaN(b) || b 2000) errors.push("Member width must be between 50 and 2000 mm."); if (isNaN(h) || h 2000) errors.push("Member depth must be between 50 and 2000 mm."); if (isNaN(M_Ed) || M_Ed 0 N/mm²."); if (isNaN(kmod_fi) || kmod_fi 0."); if (isNaN(gamma_m_fi) || gamma_m_fi 0.");

if (errors.length > 0) { resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = 'Input Errors:' + errors.map(function(e){ return ''; }).join('') + ''; return; }

// --------------------------------------------------------------- // STEP 1: Notional charring depth (one-dimensional) d_char,0 // d_char,0 = β₀ × t [EN 1995-1-2 Eq. 3.1] // --------------------------------------------------------------- var d_char0 = beta0 * t; // mm

// --------------------------------------------------------------- // STEP 2: Design charring depth d_char,n (includes corner rounding // and zero-strength layer via βn = 1.5 × β₀ for softwood/glulam, // or equivalently d_char,n = d_char,0 + k0 × d0) // // Per EN 1995-1-2 §3.4.2: // d_char,n = βn × t // where βn accounts for corner rounding (r = d_char,n) and // zero-strength layer d0 = 7 mm. // // Simplified approach (§3.4.3): // d_eff = d_char,0 + k0 × d0 // with d0 = 7 mm (zero-strength layer) // --------------------------------------------------------------- var d0 = 7.0; // mm — zero-strength layer (EN 1995-1-2 §3.4.3) var d_eff = d_char0 + k0 * d0; // effective charring depth (mm)

// --------------------------------------------------------------- // STEP 3: Residual cross-section dimensions // Exposed sides determine which dimensions are reduced. // sides=1: only depth reduced (bottom face) // sides=3: width reduced both sides, depth reduced one side (bottom) // sides=4: width and depth reduced on all sides // --------------------------------------------------------------- var b_res, h_res;

if (sides === 1) { b_res = b; h_res = h - d_eff; } else if (sides === 3) { b_res = b - 2 * d_eff; h_res = h - d_eff; } else { // 4 sides b_res = b - 2 * d_eff; h_res = h - 2 * d_eff; }

var warnings = []; if (b_res 1.0)"; statusClass = 'calc-fail'; warnings.push("Increase member dimensions, use a higher-density timber species, or reduce fire exposure duration."); }

var warnHtml = ''; if (warnings.length > 0) { warnHtml = '⚠ Warnings:' + warnings.map(function(w){ return ''; }).join('') + ''; }

resultDiv.className = 'calc-result ' + statusClass; resultDiv.innerHTML = '### Results ' + warnHtml + '' + 'ParameterValueUnit' + 'One-dimensional charring rate β₀' + beta0.toFixed(2) + 'mm/min' + 'Fire exposure duration t' + t.toFixed(0) + 'min' + 'Notional char depth d_char,0 = β₀ × t' + d_char0.toFixed(1) + 'mm' + 'Zero-strength layer d₀ (k₀ = ' + k0.toFixed(1) + ')' + (k0 * d0).toFixed(1) + 'mm' + 'Effective char depth d_eff = d_char,0 + k₀·d₀' + d_eff.toFixed(1) + 'mm' + 'Residual Cross-Section (' + sides + ' sides exposed)' + 'Original section b × h' + b.toFixed(0) + ' × ' + h.toFixed(0) + 'mm' + 'Residual section b_res × h_res' + b_res.toFixed(1) + ' × ' + h_res.toFixed(1) + 'mm' + 'Residual cross-sectional area A_res' + (A_res / 1e6).toFixed(4) + 'm²' + 'Residual section modulus W_res' + (W_res / 1e6).toFixed(2) + 'cm³' + 'Residual second moment of area I_res' + (I_res / 1e4).toFixed(0) + 'cm⁴' + 'Charred area percentage' + char_pct.toFixed(1) + '%' + 'Remaining section percentage' + remain_pct.toFixed(1) + '%' + 'Fire Design Bending Check' + 'Fire design bending strength f_m,d,fi = k_mod,fi × f_m,k / γ_M,fi' + fm_d_fi.toFixed(2) + 'N/mm²' + 'Fire design bending resistance M_Rd,fi' + M_Rd_fi.toFixed(2) + 'kNm' + 'Applied bending moment M_Ed' + M_Ed.toFixed(2) + 'kNm' + 'Utilisation ratio η = M_Ed / M_Rd,fi' + eta.toFixed(3) + '—' + 'Est. time to full char (conservative)' + t_full.toFixed(0) + 'min' + '' + '' + status + ''; }

#### Formulae Used

1. Notional (one-dimensional) char depth — EN 1995-1-2 Eq. 3.1:

d_char,0 = β₀ × t

where β₀ = one-dimensional charring rate (mm/min), t = fire duration (min).

2. Effective char depth (simplified method) — EN 1995-1-2 §3.4.3:

d_eff = d_char,0 + k₀ × d₀

where d₀ = 7 mm (zero-strength layer), k₀ = 1.0 for t ≥ 20 min (linearly interpolated for t < 20 min).

3. Residual section dimensions:

b_res = b − 2·d_eff (sides exposed laterally); h_res = h − n·d_eff (n = 1 or 2 depending on exposure)

4. Residual section modulus:

W_res = b_res × h_res² / 6

5. Fire design bending strength — EN 1995-1-2 §2.3:

f_m,d,fi = k_mod,fi × f_m,k / γ_M,fi

6. Fire design bending resistance:

M_Rd,fi = f_m,d,fi × W_res

7. Utilisation ratio:

η = M_Ed / M_Rd,fi ≤ 1.0

#### Assumptions & References

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