| Case | b0 × h0 (mm) | Exposure | β (mm/min) | k0 (mm) | η0 | t (min) | d_eff (mm) | b_r × h_r (mm) | Indicative status |
|---|---|---|---|---|---|---|---|---|---|
| Beam A | 140 × 300 | Three faces | 0.65 | 7 | 0.55 | 45 | 36.3 | 67.4 × 263.7 | Often passes at moderate utilization |
| Column B | 200 × 200 | Four faces | 0.65 | 7 | 0.60 | 60 | 46.0 | 108.0 × 108.0 | May fail for higher axial demand |
| Beam C | 90 × 240 | One face | 0.50 | 7 | 0.70 | 30 | 22.0 | 90.0 × 218.0 | Often sensitive to utilization choice |
- Charring depth:
d_char = β · t - Effective char depth:
d_eff = d_char + k0 + a0 - Residual dimensions: depend on exposed faces (e.g., for three faces:
b_r = b0 − 2·d_eff,h_r = h0 − d_eff) - Capacity proxy: axial uses
A = b·h; bending usesZ = b·h² / 6 - Utilization at time t:
η_t = η0 · (Prop0 / Propt)
- Choose Check at a fire duration for a known rating time.
- Select Exposure faces to match the actual fire exposure.
- Enter b0 and h0 in millimetres, then set η0.
- Pick a timber preset or supply a custom β.
- Adjust k0 and a0 only when justified.
- Press Calculate to view results above the form.
- Use Download CSV or Download PDF for documentation.
1) Fire resistance in timber members
Timber commonly performs predictably in fire because the outer layer chars and insulates the core. The calculator models this by reducing the cross-section over time and then comparing the remaining geometric capacity proxy to the original section. This supports early-stage checks and reporting.
2) Charring rate and timber selection
Charring rate β is the primary driver of section loss. Typical values used here are 0.65 mm/min for many softwood or glued laminated members and 0.50 mm/min for some hardwoods. Select code-approved rates for your project, then verify that the chosen exposure pattern reflects the real fire scenario.
3) Zero-strength layer and allowances
In addition to char depth, designers often account for a weakened zone behind the char line. This is represented by the zero-strength layer k0. The additional allowance a0 can capture detailing tolerance, rounding, or conservative assumptions. Together, they increase the effective depth deff = β·t + k0 + a0 and reduce residual dimensions.
4) Exposure patterns and residual dimensions
The number of faces exposed matters. A beam exposed on three faces (bottom and both sides) reduces width by 2·deff and depth by 1·deff. For example, with β=0.65 mm/min, k0=7 mm, a0=0, and t=45 min, deff=36.3 mm. A 140×300 mm beam then becomes approximately 67.4×263.7 mm.
5) Utilization, capacity proxy, and rating output
The tool uses either area A (axial) or section modulus Z (bending) as a capacity proxy. If your ambient utilization is η0, the fire-time utilization is estimated as ηt = η0·(Prop0/Propt). When ηt reaches 1.0, the member is treated as failing. The rating label is shown in 15-minute classes for quick communication.
1) Is this a code-compliant fire design?
No. It is an estimating tool that models section loss and a simple utilization relationship. Use it for screening and documentation, then complete design checks to the governing standard with qualified review.
2) What should I enter for ambient utilization η0?
Use the ratio of design demand to ambient design capacity for the same action (bending or axial). If unknown, run a conservative range such as 0.50 to 0.80 and compare outcomes.
3) Which exposure pattern is most common for beams?
Three faces is common for beams supporting floors, where the top face is protected by decking or slab. If all faces can be exposed, select four faces for a more severe scenario.
4) Why include k0 and a0?
k0 represents a weakened zone behind the char line, while a0 adds allowance for conservatism or detailing tolerances. Increasing either value reduces the residual section and shortens the estimated rating.
5) Why does bending often degrade faster than axial?
Bending capacity proxy Z depends on depth squared. When depth reduces, Z can drop rapidly, increasing utilization. Axial proxy A reduces linearly with dimensions, so it may degrade more gradually for some cases.
6) What happens if b_r or h_r becomes zero?
The remaining section is treated as lost, and the utilization becomes effectively infinite. In practice, you should treat this as failure and consider protection, larger sections, or reduced exposure.
7) Can I use this for protected timber or encapsulated members?
You can approximate by reducing exposure severity or adjusting effective time, but protection behaviour is system-specific. For protected assemblies, use test data or standard methods that explicitly model protection and delamination.