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Steel Beam Section Properties Calculator

Calculate section properties for steel beams including area, moment of inertia, section modulus, and radius of gyration. Supports I-beams, channels, hollow sections, and custom shapes.

Steel Structures Structural engineers, steel detailers Commercial Intent: VERY HIGH

Engineering Formulas

I-Beam Section Properties

Ix = (bf × h³ - (bf - tw) × d³) / 12
Zx = Ix / (h/2)
rx = √(Ix / A)

b_f: Flange width

h: Section height

t_w: Web thickness

d: Web depth = h - 2t_f

I_x: Moment of inertia about x-x

Z_x: Elastic section modulus

r_x: Radius of gyration

Rectangular Section

Ix = b × d³ / 12
Zx = b × d² / 6
rx = d / √12

b: Width

d: Depth

Worked Example

UB 406×178×60 I-Beam

shape: ibeambf: 178tf: 14h: 406tw: 8

Web Depth

d = 406 - 2 × 14 = 378 mm

Area

A = 2 × 178 × 14 + 378 × 8 = 4,984 + 3,024 = 8,008 mm²

(178 × 406³ - 170 × 378³) / 12 = 228.3 × 10⁶ mm⁴

228.3 × 10⁶ / 203 = 1,124 × 10³ mm³

Result: A = 8,008 mm², Ix = 228 × 10⁶ mm⁴, Zx = 1,124 × 10³ mm³

Engineering Notes

For composite beams, use the equivalent steel section method for transformed section properties.

Section properties in design software (Tekla, SAP2000) may differ from manual calculations due to fillet radii.

For lateral-torsional buckling, use Iy and torsional constant (J) in addition to Ix.

Standard UK sections (UB, UC) have dimensions in the format: Depth × Width × Weight per metre.

Assumptions

• Material is homogeneous and isotropic

• Section is prismatic (constant cross-section)

• Elastic behavior (small strains)

• Shear deformation is neglected

Common Mistakes

✕ Confusing Ix and Zx — remember Zx = Ix / c (not c/2 for non-symmetric sections)

✕ Using mm⁴ units for Ix in formulas that expect cm⁴ or m⁴

✕ Not accounting for web-to-flange fillet radius

✕ Forgetting to check both strong axis (x-x) and weak axis (y-y)

✕ Using gross section properties for sections with large holes

Frequently Asked Questions

What is the difference between Ix and Zx?

Ix (moment of inertia) is the second moment of area, measuring resistance to bending. Zx (section modulus) is Ix divided by the extreme fiber distance, used for stress calculations: σ = M/Z.

What is radius of gyration?

The radius of gyration (r) is the square root of I/A. It represents the distribution of area about an axis and is used in slenderness calculations for column buckling.

How do I select a steel beam size?

Calculate the required section modulus from Z = M/σ_allowable. Then select a beam where Zx ≥ required Z. For deflection control, check Ix ≥ 5wL⁴/(384EI_allowable).

What is a universal beam (UB)?

A Universal Beam (UB) is a standard I-section with parallel flanges. Common sizes: 254×102, 305×165, 406×178, 533×210, 610×229, 914×305 (depth × flange width in mm).

Why is the I-beam shape so efficient?

The I-beam concentrates material in the flanges (far from the neutral axis) where bending stress is highest, maximizing Ix and Zx for the amount of steel used.

What is a CHS section used for?

Circular Hollow Sections (CHS) are used for columns, bracing, trusses, and piles. They have equal strength in all directions, good torsional resistance, and aesthetic appeal.

How do I check if a section is compact?

A section is compact if its flange and web can reach yield stress before local buckling occurs. Check flange: b/t ≤ 9ε and web: d/t ≤ 80ε (for grade S275, ε = 0.92).

What steel grade should I use?

Common grades: S235 (general), S275 (common), S355 (high-strength). S355 is most common for structural steelwork in Europe. Higher grades reduce weight but increase cost.