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Steel Section Properties

AISC W-Shapes · A, Ix, Sx, Zx, Iy, ry

When to use: Look up cross-sectional properties for common AISC W-shapes when sizing beams and columns. Select a shape to read its area A, moment of inertia Ix, section moduli Sx / Zx, weak-axis Iy, and radius of gyration ry. The plastic modulus Zx drives flexural strength for compact members (LRFD φMn = 0.9·Fy·Zx).

Shape Selection
Key Relations
Sx = Ix / (d/2) (elastic modulus)
Zx = plastic section modulus
ry = √(Iy / A) (weak axis)
φMn = 0.9·Fy·Zx (compact)
Mn = Fy·Zx (plastic moment)
W12x26
Plastic Section Modulus Zx
37.2
in³
Results
Area A7.65 in²
Depth d12.2 in
Moment of Inertia Ix204 in⁴
Elastic Modulus Sx33.4 in³
Plastic Modulus Zx37.2 in³
Moment of Inertia Iy17.3 in⁴
Radius of Gyration ry1.51 in
Weight26 lb/ft
φMn (compact, Fy=50)139.5 kip·ft
Derived Note

Bending capacity (compact, Fy=50): φMn = 0.9·Fy·Zx/12 = 139.5 kip·ft

References
AISC Steel Construction Manual v15
AISC Shapes Database v15.0
ASTM A992 — Fy=50 ksi typical

Steel Section Properties — AISC W-Shapes

Look up cross-sectional properties for AISC W-shape steel sections including area A, depth d, moment of inertia Ix, elastic section modulus Sx, plastic section modulus Zx, weak-axis inertia Iy, and radius of gyration ry. Instantly compute the LRFD flexural design strength phiMn for compact sections with Fy = 50 ksi.

Engineering Concepts

The moment of inertia Ix determines a beam's resistance to bending deflection (δ = ML²/EI). The elastic section modulus Sx = Ix/(d/2) gives the first fiber to yield under bending stress (Fy = M/Sx). The plastic section modulus Zx accounts for full yielding across the section — for compact shapes the plastic moment Mp = Fy·Zx, giving approximately 10–15% more strength than the elastic limit.

Key Formulas

Elastic section modulus: Sx = Ix/(d/2). Plastic section modulus: Zx from AISC Shapes Database. Radius of gyration: ry = √(Iy/A). LRFD bending capacity (compact, Fy=50 ksi): φMn = 0.90·Fy·Zx / 12 kip·ft. Shape factor: Zx/Sx ≈ 1.10–1.15 for wide-flange sections. Deflection: δ_max = 5wL⁴/(384EI) for uniform load.

When to Use

Use to quickly retrieve AISC-tabulated properties when hand-checking beam capacity, column buckling, or deflection without access to the full Steel Construction Manual. Select the shape closest to your preliminary design and verify bending, shear, and deflection. For lateral-torsional buckling (LTB), also check Lb against Lp and Lr from AISC Chapter F.

Frequently asked questions

What is the difference between Sx and Zx?

Sx (elastic section modulus) = Ix/(d/2) assumes the extreme fiber first yields at Fy. Zx (plastic section modulus) assumes the entire cross-section yields at Fy, creating a full plastic hinge. Zx > Sx by the shape factor (≈1.12 for W-shapes), so Zx gives the true ultimate moment capacity for compact sections.

What does "compact" mean in AISC?

A compact section is one where local buckling of the flange or web does not occur before the plastic moment Mp is reached. Compactness is defined by flange width-to-thickness λf ≤ λpf and web slenderness λw ≤ λpw limits from AISC Table B4.1b. Most standard W-shapes with Fy = 50 ksi are compact.

Why is Iy important for columns?

Wide-flange columns typically have a much smaller weak-axis Iy than strong-axis Ix. Since a column buckles about its weakest axis, KL/ry often governs the AISC Chapter E buckling check. Always check both axes when the unbraced lengths differ.

How is the radius of gyration ry used?

ry = √(Iy/A) is the key parameter for column buckling: the slenderness ratio KL/ry determines whether buckling is inelastic or elastic per AISC E3. For beams, ry also appears in the LTB limiting unbraced length Lp = 1.76·ry·√(E/Fy) (AISC F2).

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