Steel beam
A rolled W-shape beam in major-axis bending and shear, to AISC 360-22 Chapters F and G, with ASCE 7-22 load combinations. One model covers simple spans, cantilevers, overhangs, propped and fixed beams and continuous beams.
Inputs of the steel beam #
- Member: the W-shape (AISC Shapes Database v16.0), the steel (A992, A572 Gr. 50, A913 Gr. 65, A36) and whether the self-weight is added to the dead load.
- Length and supports: the beam length and any number of supports, each a pin (roller) or a fixed end, at any position. Two pins at the ends make a simple span; a fixed end alone makes a cantilever; supports inside the ends make overhangs; three or more make a continuous beam.
- Loads: line loads (uniform, partial or linearly varying; From = To = 0 loads the whole length; leave w at To blank for a uniform load) and point loads, each with its load type (D, L, Lr, S, R, W, E). See Loads and combinations.
- Lateral bracing: the compression flange is braced continuously, at the supports only, at a spacing, or at given points. Cb is computed by Eq. F1-1 from each combination's moment diagram, or entered. An unbraced cantilever segment uses Cb = 1.0. Brace points are taken to brace both flanges.
- Deflection limits: span / n for live load and total load; IBC 2021 Table 1604.3 floor values (360 and 240) are prefilled and 0 turns a check off. For a cantilever the span is twice the overhang (Table 1604.3 note h).
Auto-design (editor toolbar) varies the W-shape (lightest first, optional depth limits); steel grade when unlocked. Objectives: lightest (steel weight); shallowest, then lightest. Kept unless you select them: steel. Every other input is kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Flexure, each unbraced segment and combination | F2 yielding and lateral-torsional buckling (Eqs. F2-1 to F2-6); F3 flange local buckling for noncompact or slender flanges (Eqs. F3-1, F3-2) |
| Shear | G2.1: φv = 1.00 and Cv1 = 1.0 when h/tw ≤ 2.24√(E/Fy), else φv = 0.90 with Cv1 by Eqs. G2-3 / G2-4 (kv = 5.34) |
| Live load deflection | Each of L, Lr, S and R alone (service), against span / n |
| Total load deflection | The ASD gravity combinations (service), against span / n |
The reactions at each support (largest and smallest over the combinations) are listed with the key results. The diagrams show the shear and moment of the combination that governs flexure and the deflection of the governing service combination.
Limitations #
- Doubly symmetric rolled W-shapes with compact webs (F2, F3). A shape whose web is not compact (F4, F5) is reported as not feasible.
- Major-axis bending only; no axial load, torsion, web openings, concentrated-force checks (J10) or bearing.
- Lateral-torsional buckling uses the unbraced segments between brace points; bracing strength and stiffness (Appendix 6) are the engineer's responsibility.
Verification examples #
AISC Design Examples v16.0, in LRFD and ASD:
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| F.1-1A | W18×50, 35 ft, continuously braced | φMn = 379 kip-ft, Mn/Ω = 252 kip-ft | 378.8, 252.0 |
| F.1-2B | Braced at the third points | Cb = 1.01, φMn = 304 kip-ft | 1.014, 306.5 |
| F.1-3B | Braced at midspan | Cb = 1.30, φMn = 288 kip-ft | 1.299, 287.6 |
| F.3B | W21×48, noncompact flanges | φMn = 398 kip-ft, Mn/Ω = 265 kip-ft | 397.9, 264.7 |
| G.1B | W24×62 shear | φVn = 306 kips, Vn/Ω = 204 kips | 305.7, 203.8 |
AISC Steel Construction Manual, 16th Ed., Table 3-2 (p. 3-25), each shape continuously braced and as a 2Lr span braced at midspan with Cb = 1.0 (Lb = Lr), LRFD and ASD:
| Shape | φbMpx | φbMrx | Lp / Lr (ft) | φvVnx | ILX Calcs |
|---|---|---|---|---|---|
| W21×55 | 473 | 289 | 6.11 / 17.4 | 234 | 472.5, 287.8, 6.11 / 17.38, 234.0 |
| W18×40 | 294 | 180 | 4.49 / 13.1 | 169 | 294.0, 179.6, 4.49 / 13.10, 169.2 |
| W16×40 | 274 | 170 | 5.55 / 15.9 | 146 | 273.8, 169.5, 5.55 / 15.89, 146.4 |
| W14×43 | 261 | 164 | 6.68 / 20.0 | 125 | 261.0, 164.5, 6.68 / 20.03, 125.4 |
| W12×65 (noncompact flange) | 356 | 231 | — / 35.1 | 142 | 356.2, 231.0, — / 35.15, 141.6 |
Moments in kip-ft, shears in kips; the ASD values (Mpx/Ωb, Mrx/Ωb, Vnx/Ωv) agree in the same way. For W12×65 the Manual lists Lp′ (where lateral-torsional buckling reaches the flange local buckling strength, Manual Eq. 3-2), not the Eq. F2-5 value ILX reports, so Lp is not compared.
The F.1-2B value is 0.8 % above the Example because the Example rounds Cb to 1.01 before using it.