Steel Section Properties

European (EN 10365), American (AISC), and Indian (IS 808) standard section databases, plus custom section calculator.

Custom Section Calculator

User Defined

Select a section type, enter dimensions, and get full mechanical properties.

I-Section

Box / RHS

CHS / Pipe

Solid Rect.

Solid Circle

T-Section

Channel

L-Section

Double-L

Height h [mm]

Flange Width b [mm]

Flange thick. tf [mm]

Web thick. tw [mm]

Height h [mm]

Width b [mm]

Wall thickness t [mm]

Outer Dia. D [mm]

Wall thick. t [mm]

Height h [mm]

Width b [mm]

Diameter D [mm]

Total Height h [mm]

Flange Width b [mm]

Flange thick. tf [mm]

Web thick. tw [mm]

Height h [mm]

Flange Width b [mm]

Flange thick. tf [mm]

Web thick. tw [mm]

Height h [mm]

Width b [mm]

Thickness t [mm]

Height h [mm]

Width b [mm]

Thickness t [mm]

Gap g [mm]

Section Properties

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Results update automatically.

Note: Results are for ideal (sharp-cornered) sections. Fillet radii, weld sizes, and manufacturing tolerances are not considered.

📒 Section Properties — Geometry, Formulas & Diagrams

I / H Section IPE · HEA · HEB · HEM · W · S · ISMB · ISLB

Doubly symmetric open section. Strong axis (y-y) is horizontal — the flanges carry most of the bending moment. Weak axis (z-z) is vertical. The web resists shear. Widely used for beams and columns.

Dimensions

h_w = h − 2·t_f (clear web height)

Property	Formula (simplified, no root radius)	Unit
A	2·b·t_f + h_w·t_w	mm²
I_y	(b·h³ − (b−t_w)·h_w³) / 12 ← strong axis	mm⁴
I_z	(2·t_f·b³ + h_w·t_w³) / 12 ← weak axis	mm⁴
W_el,y	I_y / (h/2)	mm³
W_el,z	I_z / (b/2)	mm³
W_pl,y	t_w·h_w²/4 + b·t_f·(h_w+t_f)	mm³
W_pl,z	b²·t_f/2 + t_w²·h_w/4	mm³
i_y	√(I_y / A)	mm
i_z	√(I_z / A)	mm
I_T	(2·b·t_f³ + h_w·t_w³) / 3 (St. Venant, open)	mm⁴

Tabulated values include root-radius fillet correction (reduces A by ~1–3%). Warping constant I_w requires numerical integration.

Channel Section UPN · UPE · C · MC · ISMC · ISSC

Singly symmetric open section. Centroid displaced from web toward flanges (e_z). Shear center lies outside the section on the open side. Pure bending about the strong y-y axis avoids torsion; about the weak z-z axis, torsion is induced unless load passes through the shear center.

Centroid from back of web (e_z)

e_z = (b²·t_f + h_w·t_w²/2) / A

Centroid is closer to the web than the flange tip mid-point.

Property	Formula	Unit
h_w	h − 2·t_f	mm
A	2·b·t_f + h_w·t_w	mm²
I_y	(b·h³ − (b−t_w)·h_w³) / 12 ← strong axis	mm⁴
I_z	Parallel axis theorem about e_z: = 2(t_f·b³/12 + b·t_f·(b/2−e_z)²) + h_w·t_w³/12 + h_w·t_w·(t_w/2−e_z)² ← weak axis	mm⁴
W_el,y	I_y / (h/2)	mm³
W_el,z,max	I_z / (b − e_z) (flange tip)	mm³
W_el,z,min	I_z / e_z (back of web)	mm³
i_y	√(I_y/A)	mm
i_z	√(I_z/A)	mm

Shear Center (S)

e_S = 3·t_f·b² / (h·t_w + 6·t_f·b) from back of web (approx., uniform thickness)

Load must pass through the shear center to avoid torsion. For UPN/C sections, shear center lies outside the section on the open side.

Equal Angle L (EU) · L (AISC) · ISA Equal

Doubly symmetric about the 45° diagonal (principal axes u-u and v-v). The conventional legs axis (y-y, z-z) are NOT the principal axes — they are at 45° to them. The minimum radius of gyration i_v governs buckling in compression members.

Centroid (equal legs, from outer corner)

ȳ = z̄ = (a²·t − t²·(a−t)/2) / A ≈ (2·a−t) / 4 (approx.)

Property	Formula	Unit
A	t·(2a − t)	mm²
I_y = I_z	t·(a³ − (a−t)²·t/2 − (2a−t)·ȳ²) (about centroidal leg axes)	mm⁴
I_u	I_y + I_yz (max principal — u-u axis at +45°)	mm⁴
I_v	I_y − I_yz (min principal — v-v axis at −45°)	mm⁴
I_yz	−t·(a−t)·(ȳ − t/2)·(z̄ − t/2) (product of inertia)	mm⁴
i_u	√(I_u/A)	mm
i_v	√(I_v/A) ← governs buckling	mm
I_T	t³·(2a−t) / 3 (St. Venant, thin-walled open)	mm⁴

For equal legs: I_yz = −(I_u−I_v)/2. Principal axes u-u and v-v are at 45° to the legs. The minimum second moment of area I_v is approximately half of I_u.

Square Hollow Section (SHS) SHS (EN) · HSS Square (AISC)

Doubly symmetric closed section. Highly efficient in torsion (closed path → Bredt's formula). Equal I_y = I_z. Used for columns and members under combined bending and torsion.

Key dimensions

a_i = a − 2t (inner side length) A_m = (a−t)² (mid-line enclosed area, Bredt)

Property	Formula	Unit
A	a² − a_i² = 4t·(a−t)	mm²
I_y = I_z	(a⁴ − a_i⁴) / 12	mm⁴
W_el	I / (a/2)	mm³
W_pl	(a³ − a_i³) / 6	mm³
i	√(I/A)	mm
I_T	4·A_m² / (4(a−t)/t) = t·(a−t)³ (Bredt, closed)	mm⁴
W_T	I_T / (a/2) (torsion section modulus)	mm³

Comparison: Closed vs Open section torsion

For open section (same area): I_T,open = 4t³·a / 3
For closed SHS: I_T,closed = t·(a−t)³
Ratio ≈ (a/t)² / 4 — closed section is far stiffer in torsion.

For SHS 100×5: I_T,closed/I_T,open ≈ (100/5)²/4 = 100× stiffer.

Rectangular Hollow Section (RHS) RHS (EN) · HSS Rect. (AISC)

Doubly symmetric closed section with different strong (h) and weak (b) axis properties. Excellent for beams under biaxial bending or combined bending and torsion. Bredt's formula gives the torsional constant.

Key dimensions

h_i = h − 2t (inner height) b_i = b − 2t (inner width)
A_m = (h−t)·(b−t) (mid-line enclosed area, Bredt's formula)

Property	Formula	Unit
A	b·h − b_i·h_i	mm²
I_y	(b·h³ − b_i·h_i³) / 12 ← strong axis	mm⁴
I_z	(h·b³ − h_i·b_i³) / 12 ← weak axis	mm⁴
W_el,y	I_y / (h/2)	mm³
W_el,z	I_z / (b/2)	mm³
W_pl,y	(b·h² − b_i·h_i²) / 4	mm³
W_pl,z	(h·b² − h_i·b_i²) / 4	mm³
i_y	√(I_y/A)	mm
i_z	√(I_z/A)	mm
I_T	2·t·(h−t)²·(b−t)² / (h+b−2t) (Bredt, closed)	mm⁴

Circular Hollow Section (CHS) CHS (EN) · HSS Round (AISC)

Doubly (fully) symmetric closed section. Equal bending stiffness in all directions: I_y = I_z. Most efficient shape for pure torsion. The torsional constant I_T = I_p (polar moment of area), exact (not approximate).

Key dimensions

D_i = D − 2t (inner diameter)

Property	Formula	Unit
A	π·(D² − D_i²)/4 = π·t·(D−t)	mm²
I_y = I_z	π·(D⁴ − D_i⁴) / 64 ← equal both axes	mm⁴
W_el	I / (D/2) = π·(D⁴−D_i⁴) / (32·D)	mm³
W_pl	(D³ − D_i³) / 6	mm³
i	√(I/A) = √(D²+D_i²) / 4	mm
I_p	π·(D⁴ − D_i⁴) / 32 = 2·I (polar moment)	mm⁴
I_T	I_p = 2·I (exact — closed circular section)	mm⁴
W_T	I_T / (D/2) = π·(D⁴−D_i⁴) / (16·D)	mm³

Why I_T = I_p for CHS (exact, not approximate)

For circular cross-sections, the shear stress distribution under torsion is exactly linear — plane sections remain plane and warping is zero. Bredt's formula and the exact torsion formula coincide. This is unique to circular sections; all other closed sections require numerical corrections.

How Section Properties Drive Design

The properties tabulated in this database appear directly in the AISC 360-22, EC3, and IS 800 code equations. Understanding which property does what prevents confusion when selecting sections.

Property	Symbol	Used in	Why it matters
Gross area	A (cm²)	Axial: φP_n=φF_cr·A	More area → more compression capacity
Plastic section modulus	W_pl,y / Z_x (cm³)	Flexure: M_p=F_y·Z_x	Governs compact beams (no LTB)
Elastic section modulus	W_el,y / S_x (cm³)	LTB: M_r=0.7F_y·S_x; stress: σ=M/S	Governs non-compact or LTB-reduced moment
Second moment of area	I_y (cm⁴)	Deflection: δ=5wL⁴/384EI; stiffness EI	Stiff beams deflect less under service loads
Radius of gyration	i_y, i_z (cm)	Buckling: KL/r_min governs column F_cr	Higher r → lower slenderness → more capacity
Torsional constant	I_T / J (cm⁴)	LTB: L_r formula; torsional stiffness	Higher J → longer L_r → less LTB sensitivity
Warping constant	I_w / C_w (cm⁶)	LTB: r_ts, L_r; EC3 χ_LT factor	Larger C_w → better warping resistance → higher LTB capacity

Shape Factor — Plastic vs Elastic Efficiency

The shape factor f = W_pl/W_el (or Z_x/S_x) measures how much additional moment capacity a compact section can develop beyond first-yield. For I-sections f ≈ 1.12–1.18. For solid rectangles f = 1.5. For CHS f ≈ 1.27. A higher shape factor means more reserve capacity in the plastic range — but only compact sections can reach it.

Example: IPE 300 (f'c irrelevant — steel only)

W_pl,y = 628 cm³ · W_el,y = 557 cm³
Shape factor = 628/557 = 1.128 → compact IPE 300 develops 12.8% more moment than a purely elastic analysis predicts

Section Selection Strategy

Beam (bending governs): Maximise Z_x/weight (W_pl/G). Wide-flange I-shapes (W, IPE, HEA) are most efficient. The deeper the section, the larger Z_x per kg.
Column (compression governs): Maximise r_min/area. Square HSS and wide-flange (H/W) sections with equal flange and web dimensions give similar r_x and r_y — avoiding one axis governing by a wide margin.
Column with bending (beam-column): Need both good Z_x and r_y. Heavy W-shapes (W14, HEB) with wide flanges balance both.
Truss chord (compression): HSS SHS/RHS or double angles — closed sections prevent torsional buckling; double angles allow bolted connections to gusset plates.
Truss diagonal (tension): Single or double angles, flat plates, or round bars (no buckling concern). Net section fracture and connection geometry govern.

Quick Compactness Check (AISC Table B4.1b, F_y = 345 MPa)

Element	Compact limit λ_p	Non-compact limit λ_r
I-section flange b_f/(2t_f)	9.15	24.1
I-section web h/t_w	90.6	137
SHS/RHS b/t	35.2	39.7
CHS D/t	50.6	141

If both flange and web are compact, the section can reach M_p=F_y·Z_x. If one or both are non-compact, the moment capacity is reduced per §F4/F5. Most standard hot-rolled W-shapes and IPE/HEA/HEB sections with F_y ≤ 355 MPa are compact.

Structural Steel Profile Matrix & Section Property Tables

This section provides structural steel cross-sectional tables for immediate geometric and mechanical parameter lookup across three major global standards. The interactive database allows engineers to filter and compare profile dimensions — cross-sectional area (A), second moment of area (I), elastic section modulus (W_el), plastic section modulus (W_pl), radius of gyration (i), and torsional constants — across European, American, and Indian section catalogs.

European EN 10365 Table: Standard hot-rolled profiles — IPE (parallel flange I-beams), HEA, HEB, HEM (wide flange H-sections), UPN/UPE (channels), SHS, RHS, CHS (hollow sections), and equal angles (L). Properties include I_y, I_z, W_el,y, W_pl,y, i_y, and torsional constant I_T. Material grades S235, S275, S355, and S460 per EN 10025.
AISC Table: Standard American W-shapes, S-shapes, HP bearing piles, C/MC channels, L angles, and HSS (round, square, rectangular) sections. Provides A, I_x, I_y, S_x, S_y, Z_x, Z_y, and r_x, r_y per ASTM material grades A36 (F_y = 250 MPa), A500, and A992 (F_y = 345 MPa).
IS 808:1989 Table: ISMB (medium weight I-beams), ISLB (light I-beams), ISWB (wide flange beams), ISHB (column sections), and ISMC (channels). Section dimensions and properties for structural steel design checks per IS 800:2007 under axial, flexural, and lateral torsional buckling (LTB) criteria using Fe 250 and Fe 345 material grades per IS 2062.

Steel Section Properties

Custom Section Calculator

Section Properties

📒 Section Properties — Geometry, Formulas & Diagrams

I / H Section IPE · HEA · HEB · HEM · W · S · ISMB · ISLB

Channel Section UPN · UPE · C · MC · ISMC · ISSC

Equal Angle L (EU) · L (AISC) · ISA Equal

Square Hollow Section (SHS) SHS (EN) · HSS Square (AISC)

Rectangular Hollow Section (RHS) RHS (EN) · HSS Rect. (AISC)

Circular Hollow Section (CHS) CHS (EN) · HSS Round (AISC)

How Section Properties Drive Design

Shape Factor — Plastic vs Elastic Efficiency

Section Selection Strategy

Quick Compactness Check (AISC Table B4.1b, Fy = 345 MPa)

Structural Steel Profile Matrix & Section Property Tables

Related Calculators & Guides

Quick Compactness Check (AISC Table B4.1b, F_y = 345 MPa)