About

Structural integrity during a fire event determines the evacuation window and the safety of emergency responders. This calculator estimates the time to failure for structural elements (steel beams, columns, and reinforced concrete slabs) when exposed to standard fire curves (ISO 834 or ASTM E119). Accurate calculation of the Fire Resistance Rating (FRR) is critical for compliance with building codes, particularly for high-rise or public occupancy structures where failure leads to catastrophic collapse.

Engineers must account for the degradation of mechanical properties at elevated temperatures. As temperature rises, the Yield Strength f_y of steel and the Compressive Strength f_c of concrete decrease non-linearly. This tool utilizes empirical data for material specific heat, thermal conductivity, and section factors to predict the critical time t_crit at which the load-bearing capacity drops below the applied load.

Formulas

The temperature increase of a steel section Δθ_a,t during a time interval Δt is calculated as:

A_m ⋅ h_netV ⋅ c_a ⋅ ρ_a ⋅ Δt

Where A_m/V is the section factor, c_a is specific heat, and h_net is the net heat flux. Failure occurs when steel temperature θ_a exceeds the critical temperature θ_crit:

θ_crit = 39.19 ⋅ ln10.9674 ⋅ μ₀ − 1 + 482

Where μ₀ is the degree of utilization (load ratio).

Reference Data

Material	Temp (°C)	Strength Retention factor (k_y,θ)	Elastic Modulus factor (k_E,θ)	Thermal Expansion
Carbon Steel	20	1.00	1.00	0
Carbon Steel	400	1.00	0.70	5.2 × 10^-3
Carbon Steel	600	0.47	0.31	8.6 × 10^-3
Carbon Steel	800	0.11	0.09	1.2 × 10^-2
Concrete (Normal)	200	0.95	0.85	Varies
Concrete (Normal)	600	0.45	0.35	Varies
Timber (Glulam)	300	Charring starts	N/A	N/A
Stainless Steel	600	0.62	0.55	9.8 × 10^-3

Frequently Asked Questions

The Section Factor represents the ratio of the heated surface area to the volume of the member. A higher Am/V ratio means the steel heats up faster because there is more surface area absorbing heat relative to the mass available to store it. Heavy, thick columns have low Am/V and inherent fire resistance.

Intumescent coatings expand when exposed to heat, forming an insulating char layer. In calculations, this introduces a variable thermal resistance term. The effective thermal conductivity of the coating is much lower than steel, delaying the time it takes for the core steel temperature to reach critical failure levels.

While both use a logarithmic time-temperature curve, the coefficients differ slightly. ISO 834 (Eurocode) typically rises slightly faster in the initial phase compared to ASTM E119. However, for most standard ratings (60-120 mins), the engineering outcomes are comparable, though specific certification requirements dictate which curve must be used.

High moisture content creates internal steam pressure when heated rapidly. If this pressure exceeds the concrete's tensile strength, explosive spalling occurs, exposing the reinforcement bars to direct fire. Calculations often assume a simplified reduction in effective cross-section to account for this.