Section Properties of HSS, Channel and Angle: Where to Find Them

For HSS, C-channel and steel angle used in Canada, the authoritative source of section properties is the CISC Handbook of Steel Construction, which tabulates area, moment of inertia (I), section modulus (S and Z), radius of gyration (r) and torsional properties for each size. Producer catalogues and the free AISC Shapes Database are useful cross-checks, but they have to match the material actually specified. The modulus of elasticity, about 200 000 MPa, is the same for every structural steel grade.

This post is about finding and reading those numbers correctly for the three shapes that cause the most confusion. It doesn't replace a design check by an engineer, and it doesn't list design values for every size.

Where section properties come from

There are three common sources, and they aren't interchangeable:

For W-beams the sources agree closely, because the same rolled sections are sold in both countries. For HSS they can differ by several percent for the same nominal tube, which we explain below. If you're checking a beam, our companion post on W-beam section properties and moment of inertia covers wide-flange shapes.

The properties you'll see in the tables

Every shape table lists more or less the same set. What each one is for:

• Area (A). Cross-sectional area of steel, in mm². Sets tension capacity and the squash load of a column, and gives the mass per metre.
• Moment of inertia (Ix, Iy). Stiffness in bending, in mm⁴ (usually printed as x 10⁶ mm⁴). Used in deflection calculations.
• Elastic section modulus (Sx, Sy). I divided by the distance to the extreme fibre, in mm³ (x 10³). Relates bending moment to stress at first yield.
• Plastic section modulus (Zx, Zy). Used for the bending resistance of sections that can reach full plastic capacity.
• Radius of gyration (rx, ry, and rz for angles). Square root of I divided by A. Used in column and strut buckling. The smaller r is, the more slender the member.
• Torsional constants (J, and Cw for open shapes). Resistance to twisting. They matter for lateral-torsional buckling and for members loaded off-centre.
• Centroid and shear centre locations. Needed for channels and angles because they aren't symmetric about both axes.

Young's modulus doesn't appear per section because it doesn't change. All structural steel has a modulus of elasticity of about 200 000 MPa, whether it's 300W, 350W or A500 tube. A higher grade adds strength, not stiffness. If a member deflects too much, the fix is a bigger or deeper section, not a stronger grade.

HSS: wall thickness changes everything

HSS (hollow structural section) properties are listed by outside size and wall thickness, for example HSS 102x102x6.4. Two things trip people up.

Design wall thickness. Canadian tables for HSS made to CSA G40.21 use the nominal wall. US AISC tables for tube made to ASTM A500 use a reduced design wall, because that standard historically allowed walls thinner than nominal. For HSS 102x102x6.4, the CISC area is 2,320 mm², while the AISC metric area is 2,170 mm². Every other property shifts with it. Our post on HSS steel grades explains why, and why the engineer must use the table that matches the material ordered.

Rounded corners. Cold-formed HSS has rounded corners, so you can't get exact properties by treating the tube as two nested rectangles. Try it for HSS 102x102x6.4 using the real dimensions (101.6 mm outside, 6.35 mm wall):

• Sharp-corner area: 101.6² minus 88.9² is about 2,420 mm², against 2,320 mm² in the CISC table.
• Sharp-corner moment of inertia: (101.6⁴ minus 88.9⁴) / 12 is about 3.7 x 10⁶ mm⁴, which is higher than the published value for the same reason.

A hand calculation is fine for a sense of scale, but it overstates the section. Use table values for design.

Square HSS has the same properties about both axes, which is why it makes a good column. Rectangular HSS is stiffer about its long dimension; for a beam, the long side goes vertical. Round HSS is equal in every direction and has the best torsional resistance for its weight. See what is HSS steel for where each type is used.

C-channel: one-sided and off-centre

A C-channel has a web and two flanges, all on one side. That gives it some quirks:

• Strong and weak axes are very different. About its strong axis (web vertical) a channel behaves much like a light beam. About its weak axis it's flexible, and the properties on the two sides of the web aren't the same.
• The centroid is off the web. Tables give its distance from the back of the web (often shown as x with a bar over it). You need it for any calculation about the weak axis.
• The shear centre is outside the section. It sits behind the web, on the side away from the flanges. A load applied through the web, rather than through the shear centre, tends to twist the channel. That's why channels used as beams are usually braced, used in pairs back to back, or loaded through a connection that controls the twist.

For dimensions and mass, see C-channel sizes in Canada. For capacities, see C-channel load capacity.

Steel angle: the inclined z axis

Angles are the shape where people most often read the wrong number.

An equal-leg angle has the same properties about its x and y axes, which run parallel to the legs. But those aren't its weakest directions. An angle's principal axes are inclined. For an equal-leg angle the weak principal axis, usually labelled z, runs at 45 degrees. The radius of gyration about that axis, rz, is the smallest of all, and for a single angle used as a strut it usually governs buckling.

What to check in an angle table:

• x and y properties (Ix, Sx, rx and the same for y), for bending about axes parallel to the legs.
• rz, the minimum radius of gyration, for struts and bracing.
• Centroid location (x and y distances from the backs of the legs), because loads applied through one leg are eccentric.
• Unequal angles have different x and y values, and the table orientation (long leg vertical or horizontal) matters.

Angle lintels, shelf angles and bracing are often designed with these eccentricities in mind. Our worked steel angle lintel design example shows the properties in use, and steel angle load capacity covers the limits of a single angle.

Reading tables without mistakes

Most errors with section properties come from a short list:

• Units. Tables often print I in units of 10⁶ mm⁴ and S in 10³ mm³. Drop the multiplier and the answer is off by a factor of a thousand or a million.
• Wrong axis. Using Ix for a member that bends about its weak axis, or rx for an angle strut that will buckle about z.
• Wrong material basis. Taking AISC A500 properties for a CSA G40.21 tube, or the reverse.
• Mixed imperial and metric. HSS 4x4x1/4 and HSS 102x102x6.4 are the same tube, but properties in in⁴ and mm⁴ can't be mixed in one calculation.
• Nominal names as dimensions. The 102 in an HSS name is a rounded 4 in (101.6 mm). Use the table dimensions, not the name. Our HSS size chart shows how the names are rounded.

A section property tells you about the steel alone. Connections, bracing, load eccentricity and bearing decide whether that steel can actually be used at its capacity, which is why structural members are checked by a designer or engineer.

Getting HSS, channel and angle fabricated

Once the engineer has picked the sections, the drawings tell a fabricator what to make: the shape and size, the grade and standard, the lengths, the holes and the plates. We cut, drill and weld HSS posts and frames, channels and angles to shop drawings in our CWB certified shop, prime or galvanize them to suit the job, and deliver across the GTA and Ontario.

Send your drawings for a quote, or browse the steel products we supply and fabricate.