Angle Worked Example - Equal Angle to Eurocode 3

A complete Eurocode 3 capacity check for a representative equal angle - classification, cross-section resistance and compression buckling about the governing principal (v-v) axis. Angles are not checked for lateral-torsional buckling.

Angle sections are designed about their principal axes, not the geometric leg directions, and this worked example reflects that. After classifying the legs in compression, the cross-section resistances N_pl,Rd, M_c,y,Rd and M_c,z,Rd are derived. Angles are not susceptible to lateral-torsional buckling in the usual sense, so no M_b,Rd check is performed.

The governing check for most single angles is compression buckling about the weak principal v-v axis. Because angles are usually connected through one leg only, the load is eccentric, and EN 1993-1-1 Annex BB.1.2 applies effective-slenderness rules that reduce the buckling capacity accordingly - the example derives the effective slenderness λ̄_eff,v, the reduction factor χ_v and the resistance N_b,Rd. These are the values produced by the interactive angle capacity tool.

Representative section EA 80×80×8 in grade S275 is Class 3. Major-axis bending resistance M_c,y,Rd = 3.5 kNm, minor-axis M_c,z,Rd = 3.5 kNm, axial squash N_pl,Rd = 338 kN, and compression buckling N_b,Rd = 78 kN at 3 m.

Section properties

Mass: 9.6 kg/m
Area, A: 12.3 cm²
Iᵧ (major): 72.2 cm⁴
I_z (minor): 72.2 cm⁴
iᵧ: 2.43 cm
i_z: 2.43 cm

Cross-section resistances

Class: 3
Mc,y,Rd: 3.5 kNm
Mc,z,Rd: 3.5 kNm
Npl,Rd: 338.3 kN

Cross-section & member checks - full derivation

Material

Yield strength

f_y = 275\ \mathrm{N/mm^{2}}\quad (S275)

Material factor

\varepsilon = \sqrt{\dfrac{235}{f_y}} = 0.9244

Cross-section classification (§5.5.2, angle legs)

Leg slenderness

\dfrac{h}{t} = \dfrac{80}{8} = 10.00,\quad \dfrac{b+h}{2t} = 10.00 \Rightarrow \mathbf{Class\ 3}

Cross-section resistances (§6.2)

Axial squash, Npl,Rd (§6.2.4)

N_{pl,Rd} = \dfrac{A f_y}{\gamma_{M0}} = \dfrac{1230 \times 275}{1.0 \times 10^{3}} = \mathbf{338}\ \mathrm{kN}

Major-axis bending, Mc,y,Rd (§6.2.5)

M_{c,y,Rd} = \dfrac{W_{el,y} f_y}{\gamma_{M0}} = \mathbf{3.5}\ \mathrm{kNm}

Minor-axis bending, Mc,z,Rd (§6.2.5)

M_{c,z,Rd} = \dfrac{W_{el,z} f_y}{\gamma_{M0}} = \mathbf{3.5}\ \mathrm{kNm}

Lateral-torsional buckling

Not applicable

\text{Angles are not checked for LTB (EN 1993-1-1)}

Compression buckling, Nb,Rd (Annex BB.1.2) - Lcr = 3 m

Effective slenderness (principal v-v axis governs)

\bar\lambda_{eff,v} = 0.35 + 0.7\bar\lambda_v = 1.901

Reduction factor

\chi_v = 0.229\quad(\text{curve b},\ \alpha = 0.34)

Buckling resistance (governing)

N_{b,Rd} = \chi_v\,\dfrac{A f_y}{\gamma_{M1}} = \mathbf{77.5}\ \mathrm{kN}

Run EA 80×80×8 with your own loads in the tool →

See the design theory behind these checks, or browse the EA property table.

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