Section verification · EN 1993-1-1 §6.2

Verification of welded steel I-sections

This tool calculates the section properties and the stresses of a welded I-section (equivalent to IPE, HEA, HEB) subjected to axial force N, shears V_z and V_y, bending moments M_y and M_z and torsional moment M_t, with resistance verification according to EN 1993-1-1 §6.2 (Eurocode 3). Normal stresses are computed with the Navier formula, shear stresses with the Jourawsky formula, and torsional stresses with De Saint-Venant theory.

Enter the section dimensions (height, flange width, web and flange thicknesses) and the design actions to obtain the full check with all intermediate steps, including the section class and the N+M+V interaction checks to EC3. The tool exports the report to PDF and Excel.

Section properties of the built-up section
The geometric properties (area A, moments of inertia I_y and I_z, elastic section moduli W_el and plastic W_pl, torsional moment of inertia I_t) are obtained by combining the three rectangular elements of the section: top flange, web and bottom flange. The De Saint-Venant torsional moment of inertia is I_t = Σ(b·t³/3), an expression valid for thin-walled open sections under uniform torsion.

Normal stresses — Navier formula
Normal stresses are the superposition of the contributions of axial force N (σ = N/A), bending moment M_y (σ = M_y·z/I_y) and bending moment M_z (σ = M_z·y/I_z). The maximum normal stress occurs at the flange tips, at the points furthest from the neutral axis.

Shear stresses — Jourawsky and De Saint-Venant
The shear stresses from shear V_z are computed with the Jourawsky formula τ = V_z·S/(I_y·t), where S is the first moment of the area above the fibre considered and t the local thickness. The distribution is parabolic in the web with a step change at the web–flange junctions. Uniform torsional shear stresses follow De Saint-Venant theory: τ_t = M_t·t/I_t, proportional to the local wall thickness and maximum in the thickest wall.

Section class and EC3 checks §6.2
The section classification (Class 1–4) defines the rotational behaviour and the resistance criterion to adopt (plastic or elastic). The resistance checks to EN 1993-1-1 §6.2 cover the interactions between axial force, bending moment and shear; where shear is high (V_Ed > 0,5·V_pl,Rd) the moment resistance is reduced according to §6.2.8.

Code references: EN 1993-1-1:2005 §5.5, §6.2 · NTC 2018 · Circolare 7/2019

S Top flange

Width b_s mm

Thickness t_fs mm

I Bottom flange

Width b_i mm

Thickness t_fi mm

W Web (1 vertical plate)

Overall height H mm

Thickness t_w mm

Web height h_w CALC mm

h_w = H − t_fs − t_fi

NNotation

ATotal area

ȳCentroid from bottom

I_xMoment of inertia x-axis

I_yMoment of inertia y-axis

W_x,sSection modulus top

W_x,iSection modulus bottom

i_x, i_yRadius of gyration

I_tTorsion const. (St. Venant)

I_wWarping constant

⊞Cross section

Top flange

Bottom flange

Web

Centroid ȳ

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∑Section properties

Format

Decimals 2

Export geometry and properties to Excel (.xlsx)

FDesign actions

Axial force NkN

Vertical shear V_zkN

Horizontal shear V_ykN

Moment M_y (vert. plane)kN·m

Moment M_z (horiz. plane)kN·m

Torsional moment M_tkN·m

σNormal stresses — Navier

σ(y,z) = N/A − M_y·(y−ȳ)/I_x + M_z·z/I_y [M_y>0 → tension at bottom]

τShear stresses

τ_Vz = V_z·S(y)/(I_x·t) [Jourawsky vert.] | τ_Vy = V_y·S(z)/(I_y·t) [Jourawsky oriz.] | τ_Mt = G·t·φ'·k [St.Venant — approximate value]

VMVon Mises — σ_VM = √(σ²+3τ²)

⬛Stress map

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↓Export completo

Geometry + properties + actions + all stresses

MATMaterial & factors

f_y — yield stressMPa

f_u — ultimate strengthMPa

γ_M0—

γ_M1—

F_EdDesign actions (E_d)

N_EdkN

V_z,EdkN

V_y,EdkN

M_y,EdkN·m

M_z,EdkN·m

M_t,EdkN·m

⌒Web-to-flange root

Root type

Value mm

No deduction on c/t — fully welded section

CLSection classification EN 1993-1-1 §5.5

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R_dDesign resistances (gross)

Open-section torsion: τ_t,Ed = M_t·t / I_t (St. Venant)

ηChecks summary (without reductions)

TTorsion §6.2.7 (St. Venant — open section)

VShear §6.2.6

NAxial force §6.2.4

MBending §6.2.5

N+MInteractions §6.2.9

Export EC3 verification report to PDF (with figures)

M_yBending moment M_y (vertical plane)

σ = −M_y·(y−ȳ)/I_x

M_y > 0Tensions the bottom fibres (tension at bottom, compression at top)

M_y < 0Tensions the top fibres (tension at top, compression at bottom)

V_zVertical shear V_z — Jourawsky

τ_Vz = V_z · S(y) / (I_x · t(y))

V_z > 0Downward shear — max τ at web centroid

τParabolic in the web; step change at the web/flange junction

M_tTorsion M_t — St. Venant (open section)

τ_t,max = M_t · t_max / I_t

M_t > 0Counter-clockwise torsion (viewed from +x) — τ varies linearly across the thickness

I_tSt. Venant torsion constant = Σ(b·t³/3) for thin-walled elements

I_wWarping constant — important for sections with flanges

σNormal stresses — sign

σ = N/A − M_y·(y−ȳ)/I_x + M_z·z/I_y

σ > 0Tension — the fibre is under axial tension

σ < 0Compression — the fibre is under axial compression

In the results panels: red cells = tension, blue cells = compression.

τShear stresses — notes

Shear stresses are reported as absolute value (τ ≥ 0). Only the magnitude matters for the Von Mises check.

τ_tot = |τ_Vz| + |τ_Vy| + |τ_Mt|

τ_VzVertical shear — Jourawsky; maximum at web centroid

τ_VyHorizontal shear — Jourawsky on the flanges; maximum at mid-width

τ_MtSt. Venant torsion — linear across the thickness; max = M_t·t/I_t

σ_VMVon Mises: √(σ² + 3τ²) — always positive, yield criterion

ΣFormula summary

σ = N/A − M_y·(y−ȳ)/I_x + M_z·z/I_y τ_Vz = V_z·S(y) / (I_x·t) [Jourawsky] τ_Vy = V_y·S(z) / (I_y·t) [Jourawsky] τ_Mt = M_t·t / I_t [St. Venant — prop. to distance from mid-plane] I_t = Σ b_i·t_i³/3 [thin-walled open section] I_w = (t_fs·b_s³·t_fi·b_i³·h²) / (12·(t_fs·b_s³+t_fi·b_i³)) [sym. approx.] σ_VM = √(σ² + 3·τ_tot²)

S(y) = first moment of the section area above fibre y about the centroidal axis.
For a symmetric section ȳ = H/2; for asymmetric sections the centroid is found by composition.