Section verification · EN 1993-1-1 §6.2

Verification of steel circular hollow sections (CHS)

This tool calculates the section properties and verifies the resistance of a circular hollow section (CHS) subjected to axial force N, shear V, bending moment M and torsional moment M_t, according to EN 1993-1-1 §6.2. The axial symmetry of the section gives I_y = I_z e W_el,y = W_el,z, with uniform flexural stiffness in every plane.

Enter the outer diameter, thickness and design actions to obtain the full check with all intermediate steps. Export the report to PDF e Excel.

Geometric properties of the CHS section
For a tubular section with outer diameter D and thickness t, the inner diameter is d = D−2t. The area is A = π(D²−d²)/4, the moment of inertia I = π(D⁴−d⁴)/64, the elastic section modulus W_el = 2I/D e quello plastico W_pl = (D³−d³)/6. The torsional moment of inertia I_t = 2I (closed axially symmetric section).

Shear stresses — Jourawsky
The shear stress distribution follows the Jourawsky formula τ = V·S/(I·t), with the maximum stress on the neutral axis. The plastic shear resistance is V_pl,Rd = A_v·(f_y/√3)/γ_M0 with A_v = 2A/π according to §6.2.6(3).

Shear stresses from torsion — Bredt
In circular hollow sections torsion generates a constant shear flow along the perimeter. The shear stress is τ_t = M_t·D/(2·I_t), uniform across the whole wall. The plastic torsional resistance is T_pl,Rd = W_T,pl·(f_y/√3)/γ_M0, dove W_T,pl = 2·A_m·t is the plastic torsional modulus with A_m = π·d_m²/4 the area enclosed by the mean line. Shear and torsional stresses add algebraically at the most stressed point.

Section classification and EC3 verification
The class of a CHS depends on the D/t ratio according to EN 1993-1-1 Table 5.2. Class 1 or 2 CHS can develop the full plastic resistance; Class 3 sections are limited to the elastic resistance. The N+M+V interaction checks follow §6.2.9 and §6.2.10.

Code references: EN 1993-1-1:2005 §6.2, §6.2.6(3)

CHS Circular hollow section (CHS)

Outer diameter D mm

Thickness t mm

Inner diameter d CALC mm

D/t CALC —

d = D − 2t | Thin-walled if D/t > 10 (CHS Class ≤ 3: D/t ≤ 90ε²)

NNotation

ASection area

IMoment of inertia

W_elElastic modulus

W_plPlastic modulus

iRadius of gyration

I_tTorsion const. (=2I)

W_tTorsion modulus

A_vShear area

○Cross section

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∑Section properties

Format

Decimals 2

Export geometry and properties to Excel (.xlsx)

FDesign actions

Axial force NkN

Shear V (resultant)kN

Moment MkN·m

Torsional moment M_tkN·m

For a CHS: axial symmetry → V = V_y or V_z, M = bending moment

σNormal stresses — Navier

σ = N/A ± M·(D/2)/I [M>0 → tension in extreme fibre]

τShear stresses

τ_V = V·S/(I·t) [Jourawsky max at centroid] | τ_Mt = M_t·(D/2)/I_t [outer surface]

VMVon Mises — σ_VM = √(σ²+3τ²)

○Stress map

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↓Full export

Geometry + properties + actions + all stresses

⚙Steel & Partial factors

Steel grade (EN 10025)

Thickness t: — mm | Thickness class: —

f_y — yieldMPa

f_u — ultimateMPa

γ_M0—

γ_M1—

S355: f_y=355 MPa, f_u=510 MPa (t≤16 mm) | γ_M0=γ_M1=1.00 (recommended — editable)

FDesign actions (E_d)

N_EdkN

V_EdkN

M_EdkN·m

M_t,EdkN·m

↯Section class

EN 1993-1-1 Tab.5.2 | ε = √(235/f_y) | Class 1 limit: D/t ≤ 50ε²

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✓Design resistances (R_d)

gross R_d Checks with unreduced resistances

η values on gross R_d: without reduction for torsion or high shear

§6.2.7 Torsion M_t

§6.2.6 Shear V_Ed

§6.2.4 Axial force N

§6.2.5 Bending M_Ed

§6.2.9 Interactions N + M + V + M_t

▣Checks summary

Export EC3 verification report to PDF

xyzReference system

xLongitudinal axis (out of plane)

y, zPrincipal axes — axial symmetry → I_y=I_z=I

GCentroid = geometric centre

σNormal stresses

σ = N/A ± M·(D/2) / I

σ > 0Tension

σ < 0Compression

For a CHS the σ distribution is linear across the diameter; the extreme fibre is at ±D/2.

τShear stresses

τ_V = V·S(r) / (I·t) [Jourawsky] τ_Mt = M_t·(D/2) / I_t [max at outer surface] I_t = 2·I (solid circular section → adapted for hollow)

τ_max,VAt the centroid: S_max = (D³−d³)/12 for a hollow section

VMVon Mises

σ_VM = √(σ² + 3·τ²)

The two critical fibres for a CHS are: the extreme bending fibre (max |σ|, max τ_Mt) and the centroid point (max τ_V).

EC3CHS section class — EN 1993-1-1 Table 5.2

ε = √(235/f_y)

Cl. 1D/t ≤ 50ε²

Cl. 250ε² < D/t ≤ 70ε²

Cl. 370ε² < D/t ≤ 90ε²

Cl. 4D/t > 90ε² → slender section (separate check)