Web-tapered member
A doubly symmetric welded I-section with a single linear web taper and equal prismatic flanges, the typical column or rafter of a metal building frame, in axial force, major-axis flexure and shear, by AISC Design Guide 25 (2nd Ed., 2021) on the AISC Specification. The required strengths are your entries from a second-order frame analysis.
Inputs of the tapered member #
- Member: the length, the clear web depth at the small and the large end, the web thickness, the flanges (both the same), the steel.
- Bracing and loads: the in-plane Kx over the whole length (1.0 with a direct analysis), the brace points measured from the small end (both flanges braced, as girts or purlins with flange braces do), and the required strengths per case: P (compression positive), the moments at the two ends (varying linearly) and the largest shear.
Auto-design varies the flange and web thicknesses, lightest first. Depths, flange width, length, bracing and required strengths are kept.
Checks performed #
| Check | Basis |
|---|---|
| In-plane elastic buckling, I at 0.5 L (Ismall/Ilarge)^0.0732 from the small end | DG25 Eqs. A-3, A-4 (Eq. 4-4) |
| Out-of-plane buckling per unbraced length, Iy at its middle | DG25 Eq. 5-4 |
| Compression at every section: Fe = γe fr, Fn, effective area of the slender web and flanges, Pn = Fn Ae | DG25 5.3.2; 360-22 E3, E7.1 (Table E7.1) |
| Tension yielding of the smallest section | 360-22 D2 |
| Compression flange yielding (Rpc, Rpg) and flange local buckling at every section | 360-22 F4, F5 |
| Lateral-torsional buckling per unbraced length by the stress ratios fr/FeLTB1, Cb and γeLTB1 | DG25 Eqs. 5-23 to 5-31 |
| Shear of the unstiffened web | 360-22 G2.1 |
| Axial force and flexure with the largest ratios in each unbraced length | 360-22 H1.1; DG25 5.5 |
The flexural checks are made at the ends and quarter points of each unbraced length (the sections where the ratios are largest for a linear taper and a linear moment); the lateral-torsional buckling equations of single curvature (Eqs. 5-25 to 5-27) apply when the moment keeps its sign within the length, the general ones (Eqs. 5-23, 5-24 with γeLTB = Cb γeLTB1) otherwise.
Limitations #
- Doubly symmetric sections with one linear taper only: singly symmetric, stepped or multiply tapered members are not covered (DG25 Appendix C).
- Torsional and constrained-axis torsional buckling are not computed: they do not govern when both flanges are braced at the same points.
- Unstiffened webs; tension field action and the inclined-flange term of the web shear (DG25 Eq. 5-54) are not used (conservative here).
- The frame analysis, its second-order effects and stiffness reductions (DG25 Ch. 4, 6) are yours.
- The inelastic lateral-torsional buckling equation is read with π √(Fyc/(γe fr)) and π √(Fyc/FL) from a text layer that drops the symbols; Example 5.2b's 2,520 kip-in. confirms the reading.
Verification examples #
Verification status: 17 values compared in 5 examples (5 published, 0 hand calculations from the cited equations): 17 within tolerance, 0 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.
AISC Design Guide 25 (2nd Ed.) Example A1 (equivalent moment of inertia and PeL), Example 5.2a (axial compression of a linearly tapered column braced at 90 in.) and Example 5.2b (flexure: Cb, γeLTB1, LTB and FLB strengths of the lower unbraced length).