Rolled profiles IPE / HE · EN 10365 · EN 1993-1-1 §6.2

Section check of commercial steel profiles IPE and HE (HEA, HEB, HEM)

Select a hot-rolled commercial profile from the EN 10365 sagomario — series IPE, HEA, HEB or HEM — and the tool loads its tabulated section properties (area A, second moments of area I_y and I_z, elastic and plastic section moduli W_el and W_pl, torsion constant I_t, warping constant I_w). It then computes the stresses under axial force N, shears V_z and V_y, bending moments M_y and M_z and torsional moment M_t, with resistance verification to EN 1993-1-1 §6.2 (Eurocode 3). Normal stresses use the Navier formula, shear stresses the Jourawsky formula and torsional stresses De Saint-Venant theory.

Because the properties come from the tabulated sagomario, the resistances account for the actual rolled geometry (root fillets). Pick a profile, enter the design actions and 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.

Tabulated section properties (EN 10365)
The properties (area A, moments of inertia I_y and I_z, elastic section moduli W_el and plastic W_pl, torsion constant I_t and warping constant I_w) are read directly from the standard sagomario for the selected profile. Unlike a built-up section computed from three rectangles, these values include the contribution of the root fillets of the rolled shape, so they match handbook tables and the resistances used in design.

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

EN Commercial profile — EN 10365

Series

Profile

Nominal mass —

Hot-rolled I / H sections to EN 10365. Tolerances EN 10034. Properties from the standard sagomario.

DIMGeometry — EN 10365

Height hmm

Width bmm

Web t_wmm

Flange t_fmm

Root radius rmm

Web depth h_w = h − 2t_fCALCmm

Symmetric I / H section: b_s = b_i = b, t_fs = t_fi = t_f.

NNotation (EC3 axes)

ACross-section area

I_y2nd moment — strong axis

I_z2nd moment — weak axis

W_el,yElastic modulus y

W_pl,yPlastic modulus y

W_el,zElastic modulus z

W_pl,zPlastic modulus z

i_y, i_zRadii of gyration

I_tTorsion constant

I_wWarping constant

⊞Cross section

Top flange

Bottom flange

Web

Centroid ȳ

—

∑Section properties

Format

Decimals 2

Export geometry and properties to Excel (.xlsx)

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 fillet deduction on c/t

CLSection classification EN 1993-1-1 §5.5

—

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.