Angle Section Properties Quick Reference — Equal & Unequal Leg L-Shapes

Quick-reference tables for AISC angle section properties. Covers equal leg angles (L designation with both legs identical) and unequal leg angles (different leg lengths). Properties include cross-sectional area (A), moment of inertia about major and minor axes (Ix, Iy, Iz), elastic section modulus (Sx, Sy), radius of gyration (rx, ry, rz), plastic section modulus (Zx, Zy), weight per foot, and the critical rz value for single-angle column design. All values from the AISC Steel Construction Manual, 16th Edition.

Angles are the most common structural shape after W-shapes. They appear in virtually every steel connection and are the primary truss member shape for spans under 80 feet. Understanding angle properties — particularly the minor axis rz — is essential for single angle compression design per AISC 360 Section E5.

Understanding Angle Properties

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

Equal Leg Angles — Section Properties

Equal leg angles have both legs the same length. Properties are symmetric about the 45-degree axis between the legs. The x-x and y-y axes are parallel to the legs; the z-z axis is the minor principal axis.

Unequal Leg Angles — Section Properties

Unequal leg angles have different leg lengths. Properties about the x-x axis (parallel to the longer leg) and y-y axis (parallel to the shorter leg) differ. The minor principal z-z axis angle is critical for single-angle buckling.

Source: AISC Steel Construction Manual, 16th Edition, Tables 1-7 and 1-8. All values in US customary units.

Single Angle Compression Design — The rz Factor

The most important property for single angle design is rz, the radius of gyration about the minor principal axis. Per AISC 360 Section E5:

• Equal leg angles connected through one leg: Use effective KL/r = 72 + 0.75 * (L/rx) for the slenderness check. This accounts for the eccentricity of applying the load through one leg rather than through the centroid.
• Unequal leg angles connected through the long leg: Use effective KL/r = 72 + 0.80 * (L/rx). The factor is higher (0.80 vs 0.75) because the eccentricity is larger.
• Unequal leg angles connected through the short leg: Use effective KL/r = 72 + 1.0 * (L/rx). The eccentricity is largest when the angle is connected through the shorter leg, hence the highest factor.

Example: L4x4x1/2, 6 ft long, connected through one leg. L/rx = 72/1.22 = 59.0. KL/r effective = 72 + 0.75 _ 59.0 = 116.3. Fe = pi^2 _ E / (KL/r)^2 = pi^2 _ 29000 / 116.3^2 = 21.2 ksi. Fcr = 0.877 _ Fe = 18.6 ksi (elastic buckling, since KL/r > 113). phi*Pn = 0.90 * 3.75 _ 18.6 = 62.8 kips.

Angle Weight by Size — Quick Reference

For material takeoffs and estimating, the weight per foot (Wt) column above gives the dead weight. Quick weight ranges for equal leg angles:

Frequently Asked Questions

What is the difference between rz and ry for angles? rz is the radius of gyration about the minor principal axis — it is always smaller than ry. The minor principal axis is rotated at an angle between the legs (at 45 degrees for equal leg angles). For a single angle in compression, buckling will occur about the z-z axis because it has the lowest I and r. For L6x6x1/2: rx = 1.87 in, ry = 1.87 in, rz = 1.18 in. The rz value is what controls the single angle compression capacity.

Can angles be used as beams? Yes, but with limitations. Single angles used as beams are subject to lateral-torsional buckling about the geometric axis, and the flexural capacity depends on whether the outstanding leg tip is in tension or compression. AISC 360 Section F10 provides specific provisions for single angle flexure. For typical lintel applications (angle supporting brick veneer), a limit of L/600 deflection is commonly specified. Continuous lateral bracing from the supported masonry provides torsional restraint.

What steel grades are angles available in? Standard angles are ASTM A36 (Fy = 36 ksi, Fu = 58 ksi). Higher-strength angles are available in ASTM A572 Gr 50 (Fy = 50 ksi). For high-strength applications, ASTM A588 (weathering steel, Fy = 50 ksi) angles are available. Always confirm the grade on the mill certification, as many service centers stock only A36.

How do I select an angle for a truss web member? For truss web members (axially loaded, pinned ends): Calculate required area A_req = Pu / (phi * Fcr). Estimate KL/r for the minor axis (rz controls). Select an angle with rz meeting the target slenderness. Check the effective slenderness per AISC E5 accounting for end connection eccentricity. For long members, rz is more important than A — a thicker angle at a smaller leg size may give higher capacity than a larger leg with thin walls.

Try it now: Calculate angle capacity with our free steel design tools

Related Pages

• Angle Steel Sizes — Complete angle size database
• Steel Angle Weight Calculator — Calculate angle weight and cost
• Bolt Bearing and Tear-Out Design — Angle connection design
• Truss Member Design — Using angles as truss web and chord members
• Section Properties Lookup

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from this information.

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