Thermal Action on Steel — Fire Design & Elevated Temperature

ISO 834 standard fire curve, section factor (Am/V or Hp/A), critical temperature method, steel strength reduction at elevated temperature, fire resistance ratings, and protection methods.

Steel behavior at elevated temperature

Steel does not burn, but it loses strength and stiffness rapidly above 300 degrees C. At 400 degrees C, steel retains approximately 100 percent of its room-temperature yield strength. At 550 degrees C, strength drops to approximately 60 percent. At 700 degrees C, only about 23 percent remains. This is why unprotected steel beams and columns fail within 15-20 minutes in a standard fire — the steel temperature reaches 550-700 degrees C long before the fire is controlled.

The design strategy for steel in fire is to either (a) protect the steel from heat so it stays below a critical temperature during the required fire resistance period, or (b) design the member to carry the fire-condition loads at reduced strength.

Steel strength reduction factors

Source: EN 1993-1-2 Table 3.1, AISC Appendix 4 Table A-4.2.1. Values are similar across all codes.

Section factor (Am/V or Hp/A)

The section factor determines how quickly a steel member heats up. It is the ratio of the heated surface area to the volume (mass) of steel. Higher section factors mean faster heating (thinner, lighter members heat faster).

• Am/V — Eurocode notation (m^-1). Am = heated perimeter, V = cross-section area.
• Hp/A — AISC notation (in^-1 or m^-1). Hp = heated perimeter, A = cross-section area.
• ks — AS 4100 notation: ksm = exposed surface area / mass per unit length.

For common cases:

• 4-sided exposure (column): Am/V = (2b + 2d - 2tw) / A, where b = flange width, d = depth, tw = web thickness.
• 3-sided exposure (beam with slab on top flange): Am/V = (b + 2d - tw) / A.

A W14x82 with 4-sided exposure: Am/V = (2 x 10.13 + 2 x 14.31 - 2 x 0.510) / 24.0 = 47.5 / 24.0 = 1.98 in^-1 = 78 m^-1. A W8x31 with 4-sided exposure: Am/V = (2 x 8.00 + 2 x 8.00 - 2 x 0.285) / 9.12 = 31.4 / 9.12 = 3.44 in^-1 = 135 m^-1. The lighter section heats 73 percent faster.

Critical temperature method

The simplest fire design approach determines the temperature at which the member fails under fire-condition loads. Fire loads are reduced from ambient design: the EN 1993-1-2 fire combination is approximately 0.6 to 0.7 times the ambient ULS loads.

The utilization factor in fire: mu_0 = E_fi,d / R_fi,d,0, where E_fi,d = fire-condition design effect, R_fi,d,0 = ambient design resistance.

The critical temperature theta_cr can be read from charts or calculated: theta_cr = 39.19 x ln(1 / (0.9674 x mu_0^3.833) - 1) + 482 (EN 1993-1-2 Eq. 4.22).

For mu_0 = 0.5: theta_cr = 39.19 x ln(1/(0.9674 x 0.5^3.833) - 1) + 482 = 39.19 x ln(1/0.0678 - 1) + 482 = 39.19 x ln(13.75) + 482 = 39.19 x 2.62 + 482 = 585 degrees C.

If the unprotected steel reaches 585 degrees C in 15 minutes but the required fire resistance is 60 minutes, fire protection must slow the heating rate so that 585 degrees C is not reached for at least 60 minutes.

Worked example — fire protection thickness

Member: W14x82 beam, 3-sided exposure (slab above), required fire rating R60 (60 minutes). Critical temperature = 585 degrees C. Section factor Hp/A = 1.55 in^-1 (3-sided) = 61 m^-1.

Using board protection (gypsum, thermal conductivity lambda_p = 0.20 W/mK, density = 800 kg/m^3):

The required protection thickness can be estimated from EN 1993-1-2 Annex D or manufacturer data. For Am/V = 61 m^-1 and theta_cr = 585 degrees C at 60 minutes, typical gypsum board thickness = 15 mm (single layer).

Using intumescent coating: for the same section factor and fire rating, typical dry film thickness = 1.2-1.5 mm. Intumescent coatings expand 20-50 times their thickness when exposed to heat, forming an insulating char layer.

Spray-applied cementitious fireproofing (vermiculite/cement, lambda_p = 0.12 W/mK): required thickness approximately 20-25 mm for R60 at this section factor.

Code comparison — fire design

All four codes use essentially the same steel property reduction factors and section factor approach. The main differences are in load combinations and how the required fire rating is determined by the building code.

Common pitfalls

• Assuming all steel members need the same protection thickness. Heavy columns (low Am/V) heat much slower than light beams (high Am/V). Specifying uniform protection thickness wastes material on heavy members and under-protects light members.
• Ignoring 3-sided vs 4-sided exposure. A beam protected by a concrete slab on its top flange has a significantly lower section factor than the same beam with 4-sided exposure. Using 4-sided values for beams with composite decks over-specifies protection.
• Not checking connection temperatures. Bolts and welds at connections can reach higher temperatures than the mid-span beam if the connection is at a thin web or exposed to fire from multiple sides. EN 1993-1-2 Clause 4.2.1 requires connection checks.
• Specifying intumescent coatings for concealed steelwork. Intumescent coatings must be inspected for correct dry film thickness. If the steel is concealed behind cladding during construction and later, inspection and maintenance are impractical. Board or spray protection is preferred for concealed members.

Run this calculation

• Section Properties Database
• Beam Calculator

Related references

• Fire Resistance Overview
• Steel Fire Protection
• Steel Material Properties
• Deflection Limits
• How to Verify Calculations
• steel beam capacity calculator
• column capacity calculator

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.