Section properties

The section builder: every geometric property of a cross-section, from a standard shape, a parametric shape, an outline you draw as points, or a section built up from parts of different materials. The tool has no design code and no LRFD / ASD choice; it reads "Calculated", and its values feed any member calculation.

Inputs of the section properties #

Shape picks one of four ways to describe the section.

Standard shape. Region, then family, then designation. The list holds only what the server's source setting allows, so a family whose only source is a publisher's or vendor's table may be absent until the owner decides on its use. If the server has no shape database, the list is empty and says so; enter the dimensions as a parametric shape. A calculation saved with a shape the server no longer offers reports Not feasible and says why; nothing is replaced silently.

Parametric shapes. Only the dimensions of the chosen shape are shown.

• I-shape: depth d, flange width bf and thickness tf, web thickness tw, root fillet radius, toe radius. Equal flanges off gives a different bottom flange. Sloped flanges on gives the flange slope (rise over run: 0.1667 is 1:6, AISC S; 0.14 is 14 %, IPN) and where tf is measured, as a fraction of the outstand from the tip (0.5 is mid-outstand). For a rolled W-shape the fillet radius is kdes − tf from the AISC Shapes Database.
• Channel: the same, on one side of the web.
• T-shape: the same, plus a stem toe radius and, when the flange is sloped, a taper of the stem faces.
• Angle: vertical leg h, horizontal leg b, thickness t (and a different thickness of the vertical leg if you need one), root radius, and toes with a radius or a 45 degree bevel.
• Hollow rectangle (RHS, HSS): width, height, wall thickness, outside corner radius (0 is sharp; the AISC Manual HSS tables use twice the design thickness, and the design thickness is 0.93 times the nominal for ERW HSS, AISC 360-22 B4.2), and the inside radius, by default the outside radius less the wall.
• Hollow circle (CHS, pipe): outside diameter D and wall t.
• Rectangle: b and h, with square corners, a corner radius or a corner bevel. Round bar: D.
• Lipped C, track, Z with lips, hat: depth, width, thickness and inside bend radius, all out to out; the lip (a Z's may be at another angle and its lower flange another width); the hat's outstanding flange.
• Rail: overall depth, head width and depth, web thickness, base width, base depth at the web and at the tips, and two radii. Straight flanks: a published rail profile with head arcs goes in as a custom outline.

Custom outline. A table of points in order around the outline: x, y, a corner radius r (a tangent arc at that point, at any angle) and a bulge (the side to the next point is an arc; bulge = tan(sweep / 4), the DXF convention; positive is counterclockwise; two points with a bulge of 1 each make a circle). A point with a radius cannot touch a curved side. The Loop column separates outlines: the lowest number is the outline, each other number a hole. Up to 200 points and 20 loops.

Built up from parts. A table of parts, each a plate, a parametric shape or a named database shape (W14X90, or EU-IPE:IPE 200 to name the family too). The columns d, b, tw, tf, r and lip hold whatever the kind uses: a plate is b wide and d high; an angle has its thickness in tw; an RHS its outside radius in r; a hat its flange in lip. Each part is mirrored about its own y axis if asked, rotated, then moved by dx and dy from its own origin: plate, I, tube and bar at the center; channel and C at the back of the web at mid-depth; angle at the heel; tee at the flange top; Z on the web; hat at the flange's centre line. Parts may touch, which welds them into one section, but may not overlap. Up to 30 parts. Each part has its own E, Fy and unit weight.

Built up from rectangles. The older table of solid rectangles and holes, each by width, height and center; holes lie inside one solid rectangle.

Material. The unit weight for the weight per length (steel 490 pcf, concrete 150 pcf). Poisson's ratio for the shear areas only.

Results and checks of the section properties #

The x axis is horizontal and the y axis vertical, both through the centroid; the centroid is measured from the left and bottom edges of the bounding box. The step-by-step text names the method of each property:

Both bases. The finite element J and Cw are the true values of the outline. AISC's Cw, ro and H, and the equations of AISC 360 that use them, rest on the thin-walled values: a W14X90 has Cw = 15,830 in.⁶ on the true outline and 15,940 in.⁶ thin-walled (the table says 16,000); a C10X20 has 44.2 in.⁶ and 56.7 in.⁶ (the table says 56.9). Use the basis your equation assumes. The J of an HSS is tabulated by Bredt's thin-walled formula (HSS8X4X1/2: 61.1 in.⁴), a little under the true J of the solid wall (61.9 in.⁴).

The circle's shear area. At a Poisson's ratio of 0.3 a solid circle has Asy = 0.851 A, the energy value 6(1+v)²/(7+14v+8v²) of the elastic solution. It is not Cowper's 0.886, a different definition; compare like with like.

Several materials. The elastic values are transformed by E, and the plastic values by Fy, to the first part's material. A is then the transformed area; A gross is shown as well, and the weight is each part's own. Parts that do not touch have J = the sum of the pieces and no shear center or Cw of their own, and the result says so.

A standard shape shows its family, standard, source and source kind, its source flag, and how the family compares with published tables, when that record is on hand. The numbers are calculated here, from the row's nominal dimensions, by the same engine as every other option.

The drawing (on screen, in the report and on the PDF / DXF drawing sheet) shows the true outline to scale, arcs as fine chords of at most 3 degrees, with the holes and the parts, the centroid, the shear center when it is apart from the centroid, the centroidal x and y axes, the principal axes 1 and 2 when Ixy is not zero, the overall dimensions with the centroid located from the left and bottom edges, and the callouts of the shape. Parts are numbered up to 8 where a leader can reach them; the input summary lists every part.

Limitations #

• Exact properties: none on the shape beyond what can be drawn: straight sides and circular arcs. An ellipse or a spline goes in as a series of arcs.
• Finite element properties: the mesh has a vertex limit, and the size of the elements has a floor of 1/5,000 of the section's diagonal. The density falls for thin walls, and the mesh check states the density used: full density up to a size-to-wall ratio of 120, half to 500, a quarter beyond, which kept the time to about 12 s in the worst outlines tried (a tube of 1,000 in. diameter and 0.01 in. wall). Walls too thin for the mesh (around one millionth of the size) are Not feasible, never an approximate number.
• Thin-walled values ignore fillets and tapers; Cw of a tee or an angle is its own small formula; a custom outline, a built-up section, a rail or a solid has none.
• Family constants are given for equal-flange I, channels, tees, equal-thickness angles, RHS and CHS. An unequal-flange I and cold-formed shapes give J and Cw thin-walled only.
• Toe radii larger than fit are reduced to the largest that fits, and the result says so.
• Gross section only. No effective (reduced) section for slender elements, no bolt holes unless you draw them, no residual stress.
• Plastic moduli assume the whole section yields, each material at its Fy.
• Database rows: where a table gives no toe radius, the row's radius is one constant per family, chosen against published values and stated with the source.
• Tables: 200 points, 20 loops, 30 parts, 30 rectangles, and at most 4,000 chords after the curves are divided.
• Older calculations: every older input still loads and calculates, on this engine. J is now the true J: it no longer ignores fillets or sums rectangles, so saved J values change. Closed-cell built-up sections now give the torsion stiffness of a closed cell.

Verification examples #

Verification status: 138 values compared in 33 examples (21 published, 12 hand calculations from the cited equations): 129 within tolerance, 9 recorded deviations. Code basis: the provisions it uses were read in the target edition.

Closed-form hand calculations and the AISC Shapes Database v16.0 (tests/test_verify_section_properties.py). Tolerance 1 %.

Published section properties of the AISC Shapes Database v16.0, each shape built from its tabulated dimensions. The J of a rolled shape now comes from the true outline; the HSS rows compare the thin-walled value, AISC's basis:

\* Documented deviation AISC-L-TOES: the database does not list an angle's toe radius; with the assumed r / 2 the minor principal Iz is 1.5 % high, and Zx is 3.54 against 3.50 in³ (1.0 %). The former deviations for J of rolled shapes and the weak axis of channels are retired: the true outline now matches both tables. The same three shapes are also run through the standard-shape option on a test copy of their database rows.