Coatings and fire protection
I-section heated perimeter, area and section factor Hp/A
- where
- heated perimeter (mm)
- section depth (mm)
- sides exposed (4 or 3)
- protection type (0 profile, 1 box)
- flange width (mm)
- root radius (mm)
- web thickness (mm)
- cross-sectional area (mm²)
- flange thickness (mm)
- section factor (m⁻¹); the 1000 converts from mm⁻¹
- mass per metre (kg/m)
Explain this equation
Calculates the section factor of a rolled I or H section from its dimensions, used to pick fire protection thickness from a product’s assessment tables. With four sides and profile protection, the heated perimeter is also the paint area per metre run.
h, b, t_w, t_f and r are depth, flange width, web and flange thickness and root radius. s is the number of sides exposed: 4 all round, 3 with a slab on the top flange. X is 0 for profile protection that follows the steel and 1 for box protection such as boards. H_p is the perimeter heated in a fire and A the steel area. m is the mass per metre at 7850 kg/m³.
A section heats faster the more surface it has compared with its bulk, so the section factor is perimeter divided by area. The root radius term trims the corners where the web meets the flange. A box only sees the outside rectangle. The 1000 converts per mm to per metre.
Sense check: a 533 × 210 × 82 UB exposed on four sides has a section factor of about 176 m⁻¹; boxed under a slab it drops to about 121 m⁻¹.
Watch out: use the exposure that matches the real detail and the protection type of the product you are using.
Section factor Hp/A of a rolled I or H section from its dimensions, for choosing fire protection thickness from a product’s BS EN 13381 assessment, and the profile perimeter for paint area per metre.
Enter your values to see the result.
Good to know
Hp is the perimeter exposed to fire and A the steel area, so Hp/A (m⁻¹) measures how fast the section heats: high values heat quickly and need more protection. Profile protection (intumescent paint, sprays) follows the section outline including the root radii; box protection (boards) uses 2h + 2b, or 2h + b with a slab on top. The profile perimeter with s = 4 and X = 0 is also the paint area in m² per metre run (divide mm by 1000). The area formula is the Blue Book one for rolled sections, so results agree with tabulated values to within rounding.
Common mistake
Using the four-sided value for a beam under a concrete slab, or a box value for an intumescent coating, which gives the wrong thickness from the manufacturer’s tables.
Limits
Rolled I and H sections with parallel flanges. Hollow sections, tapered flanges and partially encased sections need the methods in the Yellow Book and BS EN 1993-1-2.
Sources
- SteelConstruction.info: Calculating section factors (Am = 2h + 4b + 2πr − 8r − 2tw four-sided; box 2h + 2b; three-sided profile 2h + 3b + 2πr − 8r − 2tw; three-sided box 2h + b; 533 × 210 UB 82: 176, 140, 156, 121 m⁻¹)
- ASFP Yellow Book: Fire protection for structural steel in buildings, 5th ed. (section factor Hp/A; products assessed to BS EN 13381-8 for reactive coatings)
- SCI / Steel for Life Blue Book: section dimensions and properties (533 × 210 × 82 UKB: h 528.3, b 208.8, tw 9.6, tf 13.2, r 12.7 mm, A 105 cm²)
- British Steel universal beams datasheet (UKB 203 × 133 × 25: h 203.2, b 133.2, tw 5.7, tf 7.8, r 7.6 mm; A 32.0 cm²; 25.1 kg/m)
- BS EN 1993-1-1 Eurocode 3: Design of steel structures – General rules (3.2.6: α = 12 × 10⁻⁶ per K, density 7850 kg/m³)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Always work to the engineer’s drawings and bending schedules, BS 8666, BS EN 1992, BS EN 1090-2, BS 5531/the BCSA National Structural Steelwork Specification and manufacturers’ data. Lifting must be planned under LOLER by a competent person.