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Section verification · EN 1993-1-1 §6.2

Verification of welded steel rectangular hollow sections (RHS/SHS)

This tool calculates the section properties and the stresses of a welded rectangular hollow section (RHS/SHS) subjected to axial force N, shears Vz and Vy, bending moments My and Mz and torsional moment Mt, with resistance verification according to EN 1993-1-1 §6.2 (Eurocode 3). Torsional shear stresses are computed with Bredt theory, applicable to thin-walled closed sections.

Enter the width, height and thicknesses of the section and the design actions to obtain the full check with all intermediate steps. Export the report to PDF and Excel.

Section properties of the box section
The geometric properties (area A, moments of inertia Iy and Iz, elastic moduli Wel and plastic Wpl) are obtained as the difference between the outer and inner rectangles. The Bredt torsional moment of inertia is It = 4·Am² / Σ(s/t), where Am is the area enclosed by the mean line and s/t is the perimeter/thickness ratio of each wall.

Torsional shear stresses — Bredt theory
In thin-walled closed sections torsion generates a constant shear flow q = Mt/(2·Am), giving the shear stress τt = q/t in each wall, inversely proportional to the local thickness.

Section classification and EC3 verification
The section class (Class 1–4) is determined according to EN 1993-1-1 Table 5.2 from the b/t ratios of the web and flange. For Class 1 and 2 sections the resistance checks are carried out plastically according to §6.2.9; for Class 3 sections the elastic Von Mises criterion is used according to §6.2.1.

Code references: EN 1993-1-1:2005 §6.2.1, §6.2.7, §6.2.9, Tab. 5.2 · NTC 2018

Geometry
Actions & Stresses
EC3 Verification
Conventions
Spazio pubblicitario — 728×90
S Top flange
Open the section library
mm
mm
I Bottom flange
mm
mm
W Webs (2 vertical plates)
mm
mm
CALC mm
mm
hw = H − ts − ti  |  Box width = dw + 2·tw
NNotation
ATotal area
ȳCentroid from bottom
IxMoment of inertia x-axis
IyMoment of inertia y-axis
Wx,sSection modulus top
Wx,iSection modulus bottom
ix, iyRadius of gyration
ItTorsion const. (Bredt)
⊞Cross section
Top flange
Bottom flange
Webs
Centroid ȳ
—
∑Section properties
Format
Decimals 2

Export geometry and properties to Excel (.xlsx)

Spazio pubblicitario — 300×250
FDesign actions
kN
kN
kN
kN·m
kN·m
kN·m
σStresses normali — Navier
σ(y,z) = N/A − My·(y−ȳ)/Ix + Mz·z/Iy  [My>0 → tension inf.]
τStresses tangenziali
τVz = Vz·S(y)/(Ix·t) [Jourawsky vert.]  |  τVy = Vy·S(z)/(Iy·t) [Jourawsky oriz.]  |  τMt = Mt/(2·Am·t) [Bredt]
VMVon Mises — σVM = √(σ²+3τ²)
⬛Stress map
—
↓Export completo

Geometry + properties + actions + all stresses

⚙Steel & Partial factors
EN10025 MPa
EN10025 MPa
—
—
S355 (t≤40 mm): fy=355 MPa, fu=510 MPa  |  γM0=γM1=1.00 (NA-IT)
FDesign actions (Ed)
kN
kN
kN
kN·m
kN·m
kN·m

NEd > 0 = tension  |  My,Ed > 0 = tension inf.  |  Vy,Ed = shear in the horizontal plane

↯Section class

EN 1993-1-1 Tab.5.2  |  ε = √(235/fy)

—
✓Design resistances (Rd)
gross Rd Checks with unreduced resistances
η values computed on Rd gross: without reduction for torsion, high shear or axial force
§6.2.7 Torsion Mt (Bredt)
§6.2.6 Shear Vz (reduced for Mt)
§6.2.6 Shear Vy — horizontal (reduced for Mt)
§6.2.4 Axial force N (reduced for Mt and shear)
§6.2.5 Bending My, Mz — lorda e ridotta (V + Mt)
§6.2.1 / §6.2.9 Stress check / Interactions N + My + Mz
Cl.1-2: plastic interactions §6.2.9  |  Cl.3-4: elastic stress check §6.2.1
▣Checks summary

Export EC3 verification report to PDF (with section figure)

Spazio pubblicitario — 300×250
xyzReference system
y z G (ȳ) x
xLongitudinal axis (out of plane) — member direction
yVertical axis — positive upwards
zHorizontal axis — positive to the right
ȳCentroid measured from the bottom face
NAxial force N
N > 0 Tension (+) N < 0 Compression (−)
σN = N / A
N > 0Tension — arrows point away from the section on both sides
N < 0Compression — arrows converge towards the section
MyBending moment My (vertical plane)
My>0 −σ +σ n.n. tension bottom fibre · compression top fibre
σMy = −My · (y − ȳ) / Ix
My > 0Tension in the bottom fibres (y < ȳ), compression in the top ones
My < 0Tension in the top fibres (y > ȳ), compression in the bottom ones
MzBending moment Mz (horizontal plane)
Mz>0 n.n. −σ +σ z → tension on the right (z>0) · compr. on the left
σMz = +Mz · z / Iy
Mz > 0Tension in the fibres at z > 0 (right), compression at z < 0 (left)
Mz < 0Tension in the fibres at z < 0 (left)
VzVertical shear Vz
Vz>0 τmax τ(y) parab.
τVz = Vz · S(y) / (Ix · t(y))
Vz > 0Downward shear — shear stresses in the −y direction in the web
τParabolic in the web; maximum at the centroid (Jourawsky)
MtTorsional moment Mt (Bredt)
Am
τMt = Mt / (2 · Am · t)
Mt > 0Counter-clockwise torsion (viewed from +x) — shear flow circulating in the section
AmArea enclosed by the mean profile of the closed section (Bredt)
σStresses normali — segno
σ = N/A − My·(y−ȳ)/Ix + Mz·z/Iy
σ > 0Tension — the fibre is under axial tension
σ < 0Compression — the fibre is under axial compression

Nelle schede risultati: celle rosse = tension, celle blu = compression.

τStresses tangenziali — note

Shear stresses are reported as absolute value (τ ≥ 0). The sign of the flow depends on the shear and torsion direction, but only the magnitude matters for the Von Mises check.

τtot = |τVz| + |τMt|
τVzShear contribution — Jourawsky; maximum at the centroid in the web
τMtTorsion contribution — Bredt; constant per wall, varies with t
σVMVon Mises: √(σ² + 3τ²) — always positive, yield criterion
ΣFormula summary
σ = N/A − My·(y−ȳ)/Ix + Mz·z/Iy τVz = Vz·S(y) / (Ix·t) [Jourawsky] τMt = Mt / (2·Am·t) [Bredt] τtot = |τVz| + |τMt| σVM = √(σ² + 3·τtot²)

S(y) = momento statico della parte di sezione al di sopra della fibra y rispetto all'asse baricentrico.
Am = area enclosed by the mean profile of the closed section.