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.
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
- Standard: EN 1995-1-2:2004 — Eurocode 5: Design of Timber Structures — Part 1-2: Structural Fire Design.
- Charring rates (β₀) are taken from EN 1995-1-2 Table 3.1 for standard fire exposure (ISO 834).
- The simplified effective charring depth method (§3.4.3) is used, incorporating a 7 mm zero-strength layer to account for thermal degradation ahead of the char front.
- Corner rounding is implicitly handled by the zero-strength layer approach; for detailed analysis, the notional charring depth method (§3.4.2) with βn should be used.
- Bending resistance is calculated about the strong axis only. Lateral torsional buckling and shear checks are not included.
- Fire design partial factor γ_M,fi = 1.0 and k_mod,fi = 1.0 per EN 1995-1-2 §2.3 (accidental design situation).
- The calculator assumes uniform fire exposure on the specified number of sides and a rectangular cross-section.
- Protective cladding, intumescent coatings, and non-standard fire curves (parametric fire) are not considered.
- For columns or members with combined axial and bending loads, additional checks per EN 1995-1-2 §6.3 are required.
- Reference: Buchanan, A.H. & Abu, A.K. (2017). Structural Design for Fire Safety, 2nd ed. Wiley.