Steel beam

A beam of any section AISC 360-22 Chapters F and G cover, in bending and shear about one axis, with ASCE 7-22 load combinations: rolled I-shapes (W, S, M, HP), channels (C, MC), rectangular and round HSS, pipe, tees (WT, MT, ST), single and double angles, rectangular bars, and welded built-up I-shapes and plate girders with transverse stiffeners. One model covers simple spans, cantilevers, overhangs, propped and fixed beams and continuous beams. Biaxial bending stays in the steel column.

Inputs of the steel beam #

• Section type: the family. The Shape list shows that family's AISC shapes (AISC Shapes Database v16.0). A built-up I takes its plates: web depth h between the flanges and thickness tw, width and thickness of each flange (the two flanges may differ). A bar takes its depth and thickness.
• Steel: the grade must suit the shape, as the AISC Manual lists them (Tables 2-4 and 2-5): rolled shapes A992, A572 Gr. 50, A913 Gr. 65, A36; HSS A500 Gr. C or B, A1085; pipe A53 Gr. B; plates and bars A36 (up to 8 in.), A572 Gr. 50 (up to 4 in.). A steel that does not suit reads NOT FEASIBLE with the choices. A992 is still the default, so a new built-up I or HSS starts by asking you to choose.
• Bending axis: x or y, and for a single angle also w (major principal) or z (minor principal). The load acts perpendicular to the axis chosen.
• Stem or web legs (tees, double angles): pointing down or up. Toe of the leg (single angles): pointing up or down; for the w-axis this is the long leg's toe, for the z-axis both toes. Positive moment puts the top of the section in compression, and a section whose strength depends on the sign is checked at each sign, as F1 asks in reverse curvature.
• Lateral-torsional restraint (single angles): none between the braces, or at the point of maximum moment only (F10.2). This is your judgment. Continuous restraint is the bracing choice "continuous".
• Include self-weight: added to the dead load. A built-up I counts its flanges and web, not its stiffeners.
• 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. Tees and double angles do not use Cb (F9.2).
• Web and stiffeners (built-up I): no transverse stiffeners, a spacing (with one at each end of the beam) or given positions. A panel counts as stiffened only with a stiffener on both sides, so include the beam ends if they have one; a panel that is not, or with a/h above 3, uses kv = 5.34. a is the spacing, center to center. Stiffener width and thickness, pairs or one side. Tension field action in interior panels is your choice (G2.2 is permitted, not required) and is off by default.
• 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 shape of the given family, lightest first (W-shapes as before, optional depth limits; an HSS stays rectangular or round; a double angle keeps its leg arrangement and gap); steel grade when unlocked, among those that suit the family. For a built-up I it varies the web and flange thickness over standard plates, keeping the depth h and the plate widths as you entered them, the bottom flange following the top flange's change; it does not search the depth. A bar is not sized. Objectives: lightest (steel weight); shallowest, then lightest. Kept unless you select them: steel. Every other input is kept; see Auto-design.

Shapes from other markets (extra choices). The Shape list can change from the AISC Shapes Database to the section database: region, family and designation, as the section builder picks them. In: rolled I-shapes with parallel or tapered flanges (HE, IPE, IPN, UB, UC, H, ISMB and similar) with a compact web; channels (UPE, UPN, PFC and similar) under the channel section type; single angles under the angle section type; tees under the tee section type. Double angles, hollow sections and cold-formed sections are not offered on this type, and a saved one reads NOT FEASIBLE. US shapes stay on the AISC list, with their data and results unchanged.

The design code stays AISC 360. Fy and Fu are your inputs, with no assumed grade and no default: a shape from another market is checked to AISC 360 with your material, not to its own national code, and the sheet says so. Whether that material suits AISC 360 (Section A3.1) is your judgment. Properties are the database's, calculated from nominal dimensions; Cw, ro and H are thin-walled and J by finite elements on the true outline, the basis AISC 360's equations assume. The designation shows as the market prints it, in US and metric. Without a shape database on the server the choice does not appear. Auto-design stays on the AISC shapes unless you chose another family; then it searches that family only, lightest first, with your Fy and Fu.

Checks performed #

Live load deflection takes each of L, Lr, S and R alone (service), and total load deflection the ASD gravity combinations (service), both against span / n, with the moment of inertia of the axis chosen. A single angle bent about a geometric axis without continuous restraint uses the moment of inertia divided by 1.82, as Commentary F10 says for its total deflection.

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 #

• Bending about one axis. Biaxial bending stays in the steel column; so does the H2 stress ratio of a single angle with moments about both principal axes (Example F.11C's last step).
• No axial load, torsion, web openings, concentrated-force checks (J10), bearing or holes in the tension flange (F13.1). A channel loaded in the plane of its web is eccentric to the shear center: torsion is not checked here (see the steel beam with torsion).
• Reads NOT FEASIBLE, with the reason: a rolled I-shape or channel with a web or a channel flange that is not compact (F4 and F5 are built for built-up I only; none of the AISC shapes offered reaches this at the grades offered); a rectangular HSS with a slender web (F7.3(c)); a round section with D/t of 0.45 E/Fy or more; a built-up I outside F13.2; an unequal-leg angle on a geometric axis without continuous restraint; a double angle about its y-axis; a tee about its y-axis with Iy above Ix and without continuous bracing (F12 would need a buckling stress by analysis).
• Built-up I: welded, one grade, no cover plates, no hybrid girders. Flange-to-web welds, stiffener welds and their cutoffs (G2.4(b), (c)) and bearing stiffeners at reactions (J10.8) are not part of this calculation.
• End panels stay on G2.1. G2.3 permits a tension field in an end panel too; it is not built. Design Examples G.8A and G.8B do the same. In an end panel the value is on the safe side.
• Solid round bars are not offered: Chapter G has no section for their shear.
• Shear of a single angle bent about a principal axis divides between the legs; the program takes the short leg alone, as a conservative reading of G3. No published example.
• Lateral-torsional buckling uses the unbraced segments between brace points; bracing strength and stiffness (Appendix 6) are the engineer's responsibility.

Verification examples #

Verification status: 168 values compared in 37 examples (37 published, 0 hand calculations from the cited equations): 164 within tolerance, 4 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 Examples v16.0, in LRFD and ASD:

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:

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.

Two published values are recorded as deviations, each with its reason on the Verification page. F.8B: the Example takes a simpler, conservative section (the ineffective width off both flanges), the program follows F7.2(c) (off the compression flange, the neutral axis moving): 46.3 against 45.4 kip-ft; the effective width agrees. F.11B: the Example reuses a leg local buckling strength with the 0.80 of an unrestrained angle and says that is conservative; the program applies 0.80 only without restraint, so lateral-torsional buckling governs: 4.97 against 3.98 kip-ft, and the lateral-torsional buckling value agrees (5.53).

By hand only, from the equations, because no published example applies: S, M and HP shapes (F2, F3, G2.1); tee stems and double angle web legs in compression, and lateral-torsional buckling of tees and double angles (F9); unequal-leg angles on the principal axes (F10-4 with βw, F10.3 for each toe); bending about the y-axis of a tee (F12); singly symmetric built-up I (F4, tension flange yielding, Case 16) and doubly symmetric with a slender web (F5); transverse stiffeners (G2.4); the section values of a built-up I against closed forms. Example F.13 (a round bar) is out of scope.

Shapes from other markets: no published example applies AISC 360 to a non-US shape, so nothing here is checked against one. Hand calculations from the plain dimensions of HEB 300, SHS 200x200x10, CHS 273x10 and UPE 200; and the database path run on US shapes against the AISC path (W14X90, W21X50, W8X31, W30X90 within 1.5 %; HSS8X8X1/2, HSS12X6X1/4, HSS6.625X0.280 within 3 %; C15X33.9, MC12X35, WT8X25, MT6X5, L4X4X1/4, L6X4X1/2 within 3 %, 6 % where lateral-torsional buckling is involved, because J differs).