What is the difference between Ix, Zx and Sx?

Ix is the second moment of area and governs stiffness: it appears in every deflection formula, and doubling it halves the deflection. The other two are section moduli, and the letters for them are reversed between codes, so check which one you are reading. AS 4100, NZS 3404 and Japanese practice call the ELASTIC modulus Z and the PLASTIC modulus S; AISC in the United States uses exactly the opposite, S for elastic and Z for plastic; Eurocode avoids the clash entirely with W_el and W_pl, and IS 800 with Z_e and Z_p. Whatever it is called, the elastic modulus equals I divided by the distance to the extreme fiber and governs bending stress while the section stays elastic, since stress is M over it. The plastic modulus governs capacity once the whole section has yielded, which is what limit-state codes design to. The plastic value is always the larger of the two; their ratio is the shape factor, about 1.15 for an I-section and 1.5 for a solid rectangle. StructureCalcs prints whichever letters your selected design code uses, and a placed library section uses the letters of the catalog it came from.

Why is the radius of gyration important?

Because it governs buckling. It equals the square root of I divided by A, and a compression member’s slenderness is its effective length divided by r. Capacity falls away as slenderness rises, so the smaller of rx and ry is the one that matters — a column will buckle about whichever axis is weakest, not the one you drew first.

Which steel section standards does StructureCalcs include?

Six: AS/NZS (Australian), AISC (American), EN 10365 (European), BS 4 (British), JIS (Japanese) and IS 808 (Indian), covering more than 2,600 sections in total. Designations repeat across standards — a C 250 is a different shape in Australia, America and India — so the standard is part of the name. The properties served name the edition they came from, and the API exposes it, so any number can be traced back to a source.

Why do calculated section properties differ from the published table?

Because a drawn shape has square corners and a rolled one does not, and the difference runs in both directions. An open section — an I, a channel, an angle — has a root radius where the web meets each flange, which is extra material the square-cornered drawing leaves out, so computed values come out slightly below published ones. A hollow section has rounded outside corners instead, which is material the drawing includes and the real tube does not, so computed values come out slightly above. Either way it is a percent or two, and it is why the section library stores published properties rather than recomputing them.

When should I draw a section instead of picking one from the library?

Whenever the shape is not in a catalog. Plate girders, cover-plated beams, composite steel-and-concrete decks, crane rails, castellated members and any section with a hole cut in it all fall outside the standard tables. The Section Calculator computes area, centroid, Ix, Iy, Ixy, the principal axes and angle, radii of gyration and both elastic and plastic section moduli from the geometry you draw, and those values feed straight back into a beam, truss or frame analysis.

Understanding steel sections: shapes, properties, and how to choose

Every shape on this page is drawn to real dimensions and its properties computed by the same engine that runs the Section Calculator. The calculators carry a library of 2,600+ published sections across six standards; this page is about what those numbers mean.

Why the shape is the whole point

Bending stiffness comes from I, the second moment of area, and I grows with the square of how far material sits from the neutral axis. Move steel outward and it works disproportionately harder. Every rolled shape in use is an answer to that one observation.

Figure 1.A universal beam drawn to 310UB40.4 nominal dimensions (304 × 165, flanges 10.2 mm, web 6.1 mm). The marked point is the centroid — the axis bending is measured about. Area 5×10³ mm², Ix 84.3×10⁶ mm⁴, Iy 7.6×10⁶ mm⁴.

Look at the two I values. The same steel is 11 times stiffer about the strong axis than the weak one, purely because of where it sits. That ratio is the reason an I-beam is an I-beam — and the reason a beam laid on its side is a mistake you only make once.

The four families, drawn

I-sections (UB, UC, W, IPE, HEA/HEB, ISMB) put nearly all the material in two flanges as far apart as rolling allows, with just enough web to carry shear and hold them there. Universal beams are deep and narrow, for bending. Universal columns are roughly square, so their weak axis is not far behind their strong one — which is what a column, buckling in whichever direction it likes, actually needs.

Figure 2.A 250 PFC channel. Note where the centroid sits: pushed toward the web, not at the middle of the flanges. Ix 44.4×10⁶ mm⁴ against Iy 3.6×10⁶ mm⁴.

Channels (PFC, C, MC, UPE) are an I-section with one flange half removed. They fit flat against a wall or another member, which is why they turn up as edge beams, purlins and stair stringers. The asymmetry has a consequence worth respecting: load a channel through its centroid and it twists, because the shear center is outside the section entirely. Either restrain it or load it through the shear center.

Figure 3.A 150×150×6 square hollow section. Ix and Iy are equal at 12.0×10⁶ mm⁴ — a closed shape with nothing to distinguish the two directions.

Hollow sections (SHS, RHS, CHS) are closed, so they are enormously stiffer in torsion than any open shape — an open section resists twist only by warping, a closed one by a shear flow around the tube. They also have equal or near-equal I about both axes, which makes them excellent columns and braces, and they look clean enough to leave exposed. The cost is connections: you cannot bolt to the inside of a tube.

Figure 4.A 150×90×10 unequal angle with its PRINCIPAL axes drawn. They are rotated 20.1° from the legs — so bending about the drawn horizontal is not bending about a principal axis, and the section deflects sideways as well as down.

Angles (EA, UA, L) are the cheapest useful shape: bracing, lintels, and the members of light trusses. An unequal angle is the standard demonstration that the axes you drew are not necessarily the axes the section bends about. Its minimum I — 0.9×10⁶ mm⁴ here, about the weaker principal axis rather than about either leg — is what governs buckling, and reading Iy off a table instead is a genuine trap.

What each property is for

A — area (mm²). Axial capacity and self-weight. Steel is 7,850 kg/m³, so a section weighs 7.85 kg/m per cm² of area. The UB above works out at 40.0 kg/m.
Ix, Iy — second moment of area (mm⁴). Bending stiffness, and the I in every deflection formula. Deflection is inversely proportional to it: double I and you halve the deflection.
S — elastic section modulus (mm³), = I / c. Bending strength while the section stays elastic. Stress is M divided by it, so it is what a moment gets compared against. The UB above has S = 554×10³ mm³.
Z — plastic section modulus (mm³). Capacity once the whole section has yielded, which is what limit-state codes design to. It is always larger than the elastic modulus; their ratio is the shape factor — about 1.15 for an I-section, 1.5 for a solid rectangle. Here Z/S = 1.11. ⚠ Australian (AS 4100) and Japanese tables reverse these two letters, so check which table you are reading.
r — radius of gyration (mm), = √(I/A). Buckling. Slenderness is Le/r, and a compression member’s capacity falls away with it — so the smaller of rx = 129 mm and ry = 39 mm is the one that matters.
Imax, Imin and θp — the principal values. For any symmetric shape these coincide with Ix and Iy. For an angle, a Z-section or anything built up asymmetrically, they do not — and the principal ones are the real ones.

Six standards, and why the edition matters

The calculators carry six national libraries: AS/NZS (UB, UC, PFC, EA, UA, SHS/RHS/CHS), AISC (W, HP, C, MC, L, HSS, Pipe), EN 10365 (IPE, HEA/HEB/HEM, UPN), BS 4, JIS (H, I, channel, angle) and IS 808 (ISMB, ISMC, ISA). Pick a standard in the calculator and the section list, E and the properties come with it.

Two practical warnings. First, designations repeat across standards — a “C 250” is not the same shape in Australia, America and India, so the standard is part of the name. Second, editions differ: sections get added, withdrawn, and occasionally re-rolled to different dimensions. The properties served by this site name the edition they came from, and the API exposes it, so a number can be traced to a source rather than trusted on faith.

Why drawn properties and published properties differ

The shapes on this page are built from rectangles with square corners; real sections are not square at the corners, and the difference goes in both directions.

An open rolled section — I-section, channel, angle — has a root radius where the web meets each flange. That is material the square-cornered drawing leaves out, so the drawn A and I come out slightly below the published values.
A hollow section has rounded outside corners instead. That is material the drawing puts in and the real tube does not have, so the drawn values come out slightly above the published ones.

Either way the gap is a percent or two, and either way it is correct behavior rather than an error: the picture and the number describe the shape that was drawn.

It is also why the section library stores published properties rather than recomputing them from nominal dimensions: the published value is what the mill certifies and what code checks refer to. Use the library when you are picking a catalog section. Use the Section Calculator when the shape is not in a catalog — a plate girder, a cover-plated beam, a composite deck, a crane rail, a section with a hole cut in it.

Choosing a section, in order

Get the actions first. Run the beam, truss or frame and read the peak moment, shear and axial force.
Size for strength. Required Z ≈ M / (φ fy) for an elastic check, or S for a plastic one. That gives a starting depth.
Check deflection. Long spans are almost always governed by it. If the section fails here you need more I — a deeper section, not a heavier one of the same depth.
Check the weak axis and the restraint. An unrestrained beam can buckle laterally well below its in-plane capacity, and restraint spacing often decides the section.
Then weigh the practicalities. Availability, connection detail, fire-protection area, corrosion exposure, and whether anyone will see it.

Iterate in the calculator: change the section, watch the deflection, stop at the lightest one that passes. Because the library carries self-weight, switching sections updates the loading too — which matters more on long spans than people expect.

Where to go next

Section Calculator — draw any shape and get A, I, Z, S, r and the principal axes.
Cover-plated beam and welded box girder — built-up sections, worked through.
Composite deck — the transformed-area method, when concrete and steel act together.
Unequal angle — principal axes derived rather than asserted.
How to analyze a beam — where the moment you are sizing for comes from.

Frequently asked questions

What is the difference between Ix, Zx and Sx?: Ix is the second moment of area and governs stiffness: it appears in every deflection formula, and doubling it halves the deflection. The other two are section moduli, and the letters for them are reversed between codes, so check which one you are reading. AS 4100, NZS 3404 and Japanese practice call the ELASTIC modulus Z and the PLASTIC modulus S; AISC in the United States uses exactly the opposite, S for elastic and Z for plastic; Eurocode avoids the clash entirely with W_el and W_pl, and IS 800 with Z_e and Z_p. Whatever it is called, the elastic modulus equals I divided by the distance to the extreme fiber and governs bending stress while the section stays elastic, since stress is M over it. The plastic modulus governs capacity once the whole section has yielded, which is what limit-state codes design to. The plastic value is always the larger of the two; their ratio is the shape factor, about 1.15 for an I-section and 1.5 for a solid rectangle. StructureCalcs prints whichever letters your selected design code uses, and a placed library section uses the letters of the catalog it came from.
Why is the radius of gyration important?: Because it governs buckling. It equals the square root of I divided by A, and a compression member’s slenderness is its effective length divided by r. Capacity falls away as slenderness rises, so the smaller of rx and ry is the one that matters — a column will buckle about whichever axis is weakest, not the one you drew first.
Which steel section standards does StructureCalcs include?: Six: AS/NZS (Australian), AISC (American), EN 10365 (European), BS 4 (British), JIS (Japanese) and IS 808 (Indian), covering more than 2,600 sections in total. Designations repeat across standards — a C 250 is a different shape in Australia, America and India — so the standard is part of the name. The properties served name the edition they came from, and the API exposes it, so any number can be traced back to a source.
Why do calculated section properties differ from the published table?: Because a drawn shape has square corners and a rolled one does not, and the difference runs in both directions. An open section — an I, a channel, an angle — has a root radius where the web meets each flange, which is extra material the square-cornered drawing leaves out, so computed values come out slightly below published ones. A hollow section has rounded outside corners instead, which is material the drawing includes and the real tube does not, so computed values come out slightly above. Either way it is a percent or two, and it is why the section library stores published properties rather than recomputing them.
When should I draw a section instead of picking one from the library?: Whenever the shape is not in a catalog. Plate girders, cover-plated beams, composite steel-and-concrete decks, crane rails, castellated members and any section with a hole cut in it all fall outside the standard tables. The Section Calculator computes area, centroid, Ix, Iy, Ixy, the principal axes and angle, radii of gyration and both elastic and plastic section moduli from the geometry you draw, and those values feed straight back into a beam, truss or frame analysis.