Steel column

A steel member in axial compression or tension with bending and shear, to AISC 360-22 Chapters D, E, F, G and H, with ASCE 7-22 load combinations and the approximate second-order analysis of Appendix 8. Families: W, S, M, HP, C, MC, WT, MT, ST, rectangular or square HSS, round HSS, pipe, single angles, double angles, two tees flange to flange, built-up I from plates (equal or different flanges) and a single plate or bar, with pin and eyebar ends.

Inputs of the steel column #

• Member: first what the member is: one rolled shape, HSS or pipe; a single angle; a double angle; two tees flange to flange; a built-up I from plates; or a plate or bar. Then the shape (AISC Shapes Database v16.0) or the plates, and the steel. W, S, M, HP, C, MC, L and tees take A992, A572 Gr. 50, A913 Gr. 65 or A36 (Manual Table 2-4; a tee takes its parent's grades); HSS take A500 Gr. C (Fy = 50 ksi), A500 Gr. B (46 ksi) or A1085 (50 ksi); pipe takes A53 Gr. B (35 ksi); plates take A572 Gr. 50 or A36 (Table 2-5). A steel that does not suit the section is reported as not feasible, so a built-up member needs its grade changed from the A992 default.
• Single angle: the design basis. E5(a) for an individual member or a web of a planar truss, E5(b) for a web of a box or space truss, with the connected leg (long or short), and your statement that requirements (1) to (3) of E5 are met: loaded at the ends through one leg, welded or at least two bolts, no transverse load between. The other two requirements are computed: Lc/r up to 200, and a long leg less than 1.7 times the short. If any of them fails the calculation does not go on: E5 sends the member to Chapter H. Chapter H is the third basis: the eccentricities ew and ez of the load about the principal axes, signs as in Example E.14B (positive ew compresses the toe of the long leg, positive ez the heel), and moments Mx and My of the loads, read as moments about w and z.
• Double angles and double tees: the number of intermediate connectors (a = L/(n + 1)), whether they are welded or pretensioned (Eq. E6-2) or bolted snug-tight (Eq. E6-1), and your statement that the end connection is welded or pretensioned, which E6.1 requires. For two tees, also the gap between the flanges. The separation of a double angle is in its name.
• Built-up I: the width and thickness of each flange, the web depth and thickness. Different flanges make it singly symmetric.
• Plate or bar: width and thickness, and the end: plain, pin-connected (pin, hole, distance a, edge distance) or eyebar (pin, hole, edge distance, head diameter, radius of transition).
• Lengths and bracing: the member length L and, for each buckling axis, the unbraced length and the effective length factor (Kx Lx, Ky Ly, and Kz Lz for torsional buckling of W-shapes). K is the engineer's input (Commentary Table C-A-7.1 or Appendix 7); with the direct analysis method K = 1.0 (Section C3). Lb is the unbraced length of the compression flange for lateral-torsional buckling.
• Loads: either service loads by load type (D, L, Lr, S, R, W, E), combined by ASCE 7-22 2.3.1 / 2.4.1 (W and E in both directions), or required strengths entered per case (factored for LRFD). Each row has the axial force P (compression positive, tension negative), the moments at the top and the bottom as moment-diagram ordinates (the same sign at both ends is single curvature), the mid-height moment of loads applied along the member (wL²/8, added to the end-moment line), and optionally the shears Vx and Vy (blank: taken from the moments as

  |Mtop − Mbot|/L + 4|Mmid|/L).

• Second-order effects: either the moments come from a second-order analysis, or the approximate method of Appendix 8 is applied: B1 = Cm/(1 − αPr/Pe1) ≥ 1 on the no-translation moments, with Cm from the end moments (Eq. A-8-4) or 1.0 when there is transverse loading, Pe1 = π²EI*/L² (K1 = 1.0) with EI* = 0.8τbEI for the direct analysis method or EI for the effective length method. B2 is entered from the story analysis and multiplies the axial force and moments of the W and E load types (taken as the lateral-translation effects Plt and Mlt).
• Flexure of a tee or double angle, and of a singly symmetric built-up I: whether the stem or web legs are in tension, in compression or reverse along the unbraced length under Mx (F9); which flange is in compression under Mx (F4, F5). They are your reading of the moment: with a reversal on a tee the lower of the two cases is used.
• Flexure: Cb by Eq. F1-1 from the moment diagram along the member (when Lb is the member length; for a shorter Lb, Cb = 1.0 unless entered), or entered. The H1.2 increase of Cb by √(1 + αPr/Pey) under axial tension can be switched off.
• Tension end connection: no holes and all elements connected (Ae = Ag), or the net area and the shear lag factor U (Table D3.1) entered. The net area is either entered or taken from up to 20 failure paths (B4.3b): holes on the path, Σ s²/4g of its diagonals, thickness, with one hole diameter. U is yours: the end connection decides it, and for open sections D3 lets it stop at the connected area over the gross area.

Auto-design (editor toolbar) varies the shape of the given family (W, S, M, HP, C, MC, tee, angle, double angle, rectangular HSS, round HSS or pipe), lightest first, optional depth limit; steel grade when unlocked. A double angle stays on its legs back to back and separation; a member from plates keeps its plates. Objectives: lightest (steel weight); smallest depth, 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 (parallel or tapered flanges, a compact web), rectangular, square and circular hollow sections, hot-finished or cold-formed, channels of either flange form, tees, and single angles (with Member set to Single angle). A hollow wall is the nominal thickness of the table, without the 0.93 factor AISC applies to ASTM A500; a slender web of a rectangular section reads NOT FEASIBLE. Double shapes, plates and cold-formed sections are not on this list: no matching section of AISC 360 is built for them here. 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 #

The flexure and interaction checks report the combination that governs each; the diagrams show the first-order moments along the member, bottom to top.

Drawings #

The drawing sheet (PDF / DXF, Drawing sheet button) shows the column elevation with the axial loads by type (or the governing required strength) on the top, the member length, the ends as braced points and a callout with the effective-length factors and unbraced lengths used in the design, the first-order moment diagrams about each axis for the governing combination drawn along the column from the base to the top, and the section of the family with its dimensions: S, M, HP as the W-shape, and outlines without the fillets for channels, tees, angles, double angles, two tees, built-up I and plates. Intermediate connectors are counted in the calculation, not drawn. End fixity, brace locations between the ends, the base plate and splices are not part of the calculation and are not drawn; the sheet notes say so.

Limitations #

• A W-shape whose web is not compact for flexure (F4 / F5) is reported as not feasible; an S, M or HP-shape only when it carries Mx. A channel that is not compact (flange or web) carrying Mx is reported as not feasible: F2 covers compact channels only. The rolled channels at Fy up to 50 ksi do not reach it.
• These combinations read NOT FEASIBLE with a message, never a number: moment My on a double angle (F9 covers the plane of symmetry); any moment or shear on two tees flange to flange (Chapter F has no section for this cruciform); a moment on a single angle under E5 (change to Chapter H); shear on a single angle.
• Double channels, and members built up with lacing or perforated plates, are not covered. E6.2(b) to (e) (end welds, fastener spacing along the plates, cover plates, lacing) are detailing for you to check; only E6.2(a) is computed.
• Bracing offset from the shear center (E4(d) to (f)) is not covered. Under E5 the flexural-torsional check takes the lengths Kx Lx (about w), Ky Ly (about z) and Kz Lz as entered; the modified slenderness replaces the effective lengths for flexural buckling.
• Built-up sections ignore the fillet welds in their section values, as the Design Examples do, and a member from plates has no section choice in auto-design. D6.2(f) keeps the edge distance above 2/3 of the body width; a head is not otherwise checked.
• H1.3 (separate in-plane and out-of-plane checks) and H2 are not offered; H1.1 is used, which is always permitted. Torsion (H3) is not checked.
• The approximate second-order method takes Mr = B1 Mnt + B2 Mlt with the member's largest first-order moments (conservative). B2 is not computed (it is a story quantity, entered). In the direct entry mode all moments are treated as Mnt.
• The moment diagram between the ends is the end-moment line plus a parabola for the transverse load (Cb and the largest moment are taken from it); other load patterns can be entered as required strengths with Cb.
• Concentrated forces (J10), bearing, splices and connections are not checked.
• A500 Gr. B round HSS are taken with Fy = 46 ksi (ASTM A500-21); the Manual Table 2-4 text on disk was not legible for this row, so this value is still to be confirmed against the printed table.

Verification examples #

Verification status: 217 values compared in 71 examples (71 published, 0 hand calculations from the cited equations): 216 within tolerance, 1 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, LRFD and ASD (all within 1 %):

AISC Steel Construction Manual, 16th Ed., column tables (φcPn / Pn/Ωc in kips, pinned, Lc on both axes):

E.1C reads Fn from Manual Table 4-14 and H.3 / H.4 take Cb = 1.14 from Manual Table 3-1 (ILX computes 1.136 by Eq. F1-1). For F.8 the Manual table value is compared: ILX computes Se with the compression flange reduced and the neutral axis shifted, as F7.2(c) states; Example F.8B removes the ineffective width from both flanges, which is conservative (45.4 kip-ft). Flexure and shear examples written for beams are run as a member with the same moment or shear entered and no axial force.

The other families, against AISC Design Examples v16.0, LRFD and ASD (all within 1 % unless said so):

Example E.14A rounds Lc/r up to 127 before finding the buckling stress; unrounded it is 126.6, so ILX reads 52.8 kips, 1.05 % above the printed value. This is recorded as a deviation. Example E.12 rounds ho to 11.3 in. and carries a rounded centroid; ILX keeps ho = 11.25 in. and is 0.6 % lower. Example D.9's plate is run with the pitch and gages of its figure.

Manual Table 4-11 (concentrically loaded single angles, Fy = 50 ksi, run on the Chapter H basis): L12×12×1 1/4, L12×12×1, L6×6×9/16 and L6×6×5/16, at 1 to 20 ft, all within 1 %. On a slender leg the flexural-torsional stress is taken with the effective area: this is what reproduces the Table, and it is the lower reading of E7's sentence on single angles. Read the other way, as the stress of E3 alone with the effective area and that of E4 on the gross area, the L6×6×5/16 would be up to 19 % higher at short lengths.

Checked by hand only, from the cited equations, because no published example is on disk: channels (E4-3, E7), S, M and HP (as rolled I-shapes), E5 through the short leg and E5(b), E6-1, E4-4 on unequal angles, net area by paths on a shape, beam-column cases of tees, double angles, channels and built-up I (through flexure checked in the steel beam's verification). F4, F5, F9, F10 and G3 are verified with the steel beam against Design Examples F.10, F.11, F.14 and G.3, G.8; E.14B runs F10 here.

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 L 100x100x10; 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, and C, WT and L within 3 %, where the database has a US row).