Steel fire resistance
A W-shape beam or column in a fire: its strength at the steel temperature by the simple methods of AISC 360-22 Appendix 4.2.4d (with the critical temperatures of 4.2.4e for reference), and the thickness of its fire protection for a rating by the calculation methods of Appendix 4.3.2, which are the equations of IBC 2021 722.5.
Inputs of the fire design #
- Member: the shape (W, S, M, HP), its steel (Appendix 4.2.3b covers Fy up to 65 ksi), beam or column.
- Strength at temperature: the steel temperature T in °F or °C, your value from a heat transfer analysis of the design-basis fire (4.2.2), taken uniform over the section. The nominal loads D, L, S and the forces AT from the fire (restrained thermal expansion, your entry), combined by Eq. A-4-1 with 1.2D or 0.9D (your choice where the dead load counteracts). The design is LRFD with the ambient resistance factors, as Appendix 4.1.2 requires; the LRFD / ASD switch does not apply. Lb and Cb for flexure (Lb = 0 when the compression flange is braced continuously); K and L about each axis for a column, and whether the column is a gravity column between cooler columns (Eq. A-4-10, your statement: a fire on one floor only).
- Protection: the rating R (from the building code), the thickness provided, and the member's W/D, computed from the shape or entered (IBC Tables 722.5.1(1), (4)). Sprayed beam: the W/D and thickness of the beam in the listed assembly, and whether the rating is restrained. Sprayed column: the listed assembly's constants C1, C2 (for R in hours or minutes, as the listing prints them) and the W/D range of its tests. Gypsum board column: the total Type X board thickness.
Auto-design varies the protection thickness, thinnest first: sprayed material by 1/16 in. from 3/8 in., gypsum board by 1/2 or 5/8 in. layers. The member, the temperature, the loads, the rating and the listed assembly are kept.
Checks performed #
| Check | Basis |
|---|---|
| Retention factors kE, kp, ky, interpolated | Appendix 4.2.3b, Table A-4.2.1 |
| Load combination (0.9 or 1.2)D + AT + 0.5L + 0.2S | Eq. A-4-1 |
| Compression of a nonslender column, Fn(T) = 0.42^√(Fy(T)/Fe(T)) Fy(T) | 4.2.4d(b), Eqs. A-4-9, A-4-10 |
| Flexure of a compact W, lateral-torsional buckling at temperature | 4.2.4d(e), Eqs. A-4-13 to A-4-19 |
| Shear yielding | 4.2.4d(g), Chapter G |
| Axial force and flexure | 4.2.4d(h), Chapter H1.1 |
| Critical temperatures (notes) | 4.2.4e, Eqs. A-4-22, A-4-23 |
| Sprayed beam: substitution thickness, W/D ≥ 0.37, h ≥ 3/8 in., R ≥ 1 h, compact if restrained | 4.3.2c, Eq. A-4-32 (IBC Eq. 7-17) |
| Sprayed column: thickness from the listed constants, within their W/D range | 4.3.2a(b), Eq. A-4-26 (IBC Eq. 7-13) |
| Gypsum board column: rating of the board, W/D taken as 3.65 above it, at most 4 hours | 4.3.2a(a), Eqs. A-4-24, A-4-25 (IBC Eq. 7-12) |
At or below 400 °F the ambient strengths are used (4.2.4d). The heated perimeters are those of IBC Figures 722.5.1(1) and 722.5.2: column contour 4bf + 2d − 2tw, box 2(bf + d); beam contour 3bf + 2d − 2tw. Note that the IBC numbers the substitution's beams the other way round from AISC: here "listed" and "this beam" are named.
Limitations #
- The steel temperature is your entry: no heat transfer (lumped mass) analysis is made.
- Slender sections (compression) and noncompact sections (flexure) are out of the simple method's scope and stop as not feasible.
- Composite beams (4.2.4d(f)), filled and encased columns, HSS (their A/P correlations), intumescent or mastic coatings and the connections are not covered.
- The reading of Eq. A-4-10 (n in both terms) is from the text layer of the specification (to confirm against the code text).
- The protection's attachment, density and installation follow the listed assembly.
Verification examples #
Verification status: 15 values compared in 10 examples (5 published, 5 hand calculations from the cited equations): 15 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
AISC Design Guide 19 (2003) Examples VI-2 (gypsum board), VI-3 (sprayed column), VII-1 and VII-2 (beam substitution): the rating equations are unchanged in 360-22 Appendix 4.3.2 and IBC 2021 722.5. No published example of the 360-22 simple methods at elevated temperature is in the free library: the strength values are hand calculations of Eqs. A-4-9 to A-4-19 with Table A-4.2.1.