Eurocode Design Guide · Part 7 of 9

Steel Member Design — EN 1993-1-1 (Eurocode 3)

Cross-section classification, flexural resistance, lateral-torsional buckling, shear, column buckling curves, beam-column interaction (Method 2), connection design (EC3-1-8), and seismic steel provisions per EC8 §6.

Pre-Sizing Rules of Thumb
Cross-Section Classification
Beam Flexure
Lateral-Torsional Buckling (LTB)
Shear Design
Column Design — Axial Compression
Combined Loading — Beam-Columns
Connections Overview (EC3-1-8)
Seismic Steel Design (EC8 §6)

1. Pre-Sizing Rules of Thumb

Beam (simply supported): h ≈ L/20 | SI: h(mm) ≈ L(m)×50 | US: h(in) ≈ L(ft)/1.5
Beam (continuous): h ≈ L/25 (use L of longest span)
Column (axial dominated): A ≈ N_Ed/(0.40·f_y) preliminary
Long spans >9 m: Deflection often governs — check L/300 before ULS design
Plate girder: h/L ≈ 1/12–1/15; flange width ≈ h/3–h/5

2. Cross-Section Classification (EC3 §5.5)

Classification determines which resistance model applies. The section class equals the worst class of any individual element (flange or web). ε = √(235/f_y) normalises limits to S235.

Class 1

Full plastic rotation capacity. Use W_pl. Allows plastic hinge redistribution.

Class 2

Full plastic moment, limited rotation. Use W_pl. No redistribution.

Class 3

Elastic moment only. Use W_el. Local buckling before full plasticity.

Class 4

Local buckling before elastic limit. Use effective section W_eff.

Element	Stress state	Class 1	Class 2	Class 3
Outstand flange (c/t_f)	Compression	≤ 9ε	≤ 10ε	≤ 14ε
Internal web (c/t_w)	Pure bending	≤ 72ε	≤ 83ε	≤ 124ε
Internal web (c/t_w)	Pure compression	≤ 33ε	≤ 38ε	≤ 42ε

For S355: ε = √(235/355) = 0.814. Class 1 outstand flange limit = 9×0.814 = 7.33. Most standard IPE and HEA sections are Class 1 for S355 under bending.

3. Beam Flexure (EC3 §6.2.5)

EC3 — Design moment resistance

Class 1/2 M_c,Rd = W_pl·f_y / γ_M0 kN·m (plastic)

Class 3 M_c,Rd = W_el,min·f_y / γ_M0 kN·m (elastic)

Class 4 M_c,Rd = W_eff,min·f_y / γ_M0 kN·m (effective)

γ_M0 = 1.0 (EN recommended)

EC3 vs AISC 360: EC3 M_c,Rd = W_pl·f_y/γ_M0 (γ_M0=1.0) and AISC φM_n = 0.9·Z_x·F_y. The 10% difference (γ_M0=1.0 vs φ=0.9) is offset by European load factors being slightly higher. For a typical gravity case (1.35G+1.5Q vs 1.2D+1.6L), the overall reliability targets are equivalent.

4. Lateral-Torsional Buckling (EC3 §6.3.2)

EC3 — LTB design buckling resistance

M_b,Rd = χ_LT·W_pl,y·f_y / γ_M1 kN·m

χ_LT = 1 / (Φ_LT + √(Φ_LT² − λ̄_LT²)) ≤ 1.0

Φ_LT = 0.5·[1 + α_LT·(λ̄_LT−0.2) + λ̄_LT²]

λ̄_LT = √(W_pl,y·f_y / M_cr)

M_cr = C₁·(π²EI_z/L²)·√(I_w/I_z + L²GI_t/π²EI_z) kN·m

γ_M1 = 1.0 (EN recommended)

LTB Imperfection Factors α_LT

Buckling Curve	α_LT	Application (rolled I-sections)
a	0.21	h/b > 2, general method
b	0.34	h/b ≤ 2, general method
c	0.49	Welded I, h/b > 2
d	0.76	Welded I, h/b ≤ 2

Modified Method (EC3 §6.3.2.3)

EC3 — LTB correction factor f (for rolled sections)

f = 1 − 0.5·(1−k_c)·[1 − 2·(λ̄_LT−0.8)²] ≤ 1.0

χ_LT,mod = χ_LT / f ≤ 1.0

k_c = moment distribution correction (0.4–1.0 per Table 6.6); uniform moment: k_c=1.0
The modified method generally gives less conservative results for non-uniform moment.

Try it yourself → LTB Check Calculator

5. Shear Design (EC3 §6.2.6)

EC3 — Plastic shear resistance

V_pl,Rd = A_v·(f_y/√3) / γ_M0 kN

A_v (rolled I) = A − 2b·t_f + (t_w+2r)·t_f ≥ η·h_w·t_w mm²

η = 1.2 for S235–S460 (EN recommended)

Shear-Moment Interaction

When V_Ed > 0.5·V_pl,Rd, reduce the plastic moment resistance:

EC3 §6.2.8 — Reduced moment due to shear

M_y,V,Rd = [W_pl,y − ρ·A_w²/(4t_w)]·f_y/γ_M0 kN·m

ρ = (2·V_Ed/V_pl,Rd − 1)²

6. Column Design — Axial Compression (EC3 §6.3.1)

EC3 — Flexural buckling resistance

N_b,Rd = χ·A·f_y / γ_M1 kN

χ = 1 / (Φ + √(Φ²−λ̄²)) ≤ 1.0

Φ = 0.5·[1 + α·(λ̄−0.2) + λ̄²]

λ̄ = √(A·f_y/N_cr)

N_cr = π²·E·I / (KL)² kN (Euler)

Buckling Curves (EC3 Table 6.2)

Curve	α	Application
a₀	0.13	Hot-finished CHS (S355 and above)
a	0.21	Rolled I, h/b >1.2, t_f ≤40mm, y-y axis
b	0.34	Rolled I, h/b >1.2, t_f ≤40mm, z-z axis
c	0.49	Welded box, t_f ≤40mm; RHS hot-finished
d	0.76	Welded I, t_f >40mm, z-z axis

EC3 vs AISC 360 column curves: AISC uses two equations (elastic: F_e governs above 4.71√E/F_y; inelastic below). EC3 uses a single χ formula with curve-specific α. For S355 rolled I-sections about the strong axis (curve a), results are broadly similar to AISC for λ̄ = 0.5–1.5.

Try it yourself → Steel Column Calculator

7. Combined Loading — Beam-Columns (EC3 §6.3.3)

Method 2 (Annex B) provides interaction equations that are simpler to apply manually. Two equations must both be satisfied:

EC3 Annex B Method 2 — Interaction equations

Eq. 1 N_Ed/(χ_y·N_Rk/γ_M1) + k_yy·M_y,Ed/(χ_LT·M_y,Rk/γ_M1) + k_yz·M_z,Ed/(M_z,Rk/γ_M1) ≤ 1.0

Eq. 2 N_Ed/(χ_z·N_Rk/γ_M1) + k_zy·M_y,Ed/(χ_LT·M_y,Rk/γ_M1) + k_zz·M_z,Ed/(M_z,Rk/γ_M1) ≤ 1.0

k_yy, k_yz, k_zy, k_zz = interaction factors from Annex B Table B.1/B.2 (depend on λ̄, C_my, C_mz, n_pl)
χ_y, χ_z = flexural buckling reduction factors for each axis
χ_LT = LTB reduction factor (1.0 if torsional restraint adequate)

Try it yourself → Combined (Beam-Column) Calculator

8. Connections Overview (EC3-1-8)

Bolt Grades and Strengths

Grade	f_ub (MPa)	f_yb (MPa)	Common Use
4.6	400	240	Secondary connections, light duty
8.8	800	640	Primary connections — most common
10.9	1000	900	High-strength; HRC/HSFG connections

EC3-1-8 — Bolt capacity in shear and bearing

F_v,Rd = α_v·f_ub·A / γ_M2 kN (shear per bolt)

F_b,Rd = k₁·α_b·f_u·d·t / γ_M2 kN (bearing)

α_v = 0.6 (shear plane in shank); 0.5 (shear plane in thread)
α_b = min(e₁/3d₀, f_ub/f_u, 1.0)
k₁ = min(2.8·e₂/d₀−1.7, 2.5) for edge; 2.5 for inner
γ_M2 = 1.25

EC3-1-8 — Fillet weld capacity

F_w,Rd = f_vw,d·a_w·l_eff kN

f_vw,d = f_u / (√3·β_w·γ_M2)

β_w = 0.80 (S235), 0.85 (S275), 0.90 (S355), 1.00 (S420/S460)
a_w = weld throat; l_eff = effective weld length

9. Seismic Steel Design (EC8 §6)

Ductility Classes

DCL (q ≤ 1.5): Standard EC3 design, no special detailing. Low-seismicity only.
DCM (1.5 < q ≤ 4): Moderate ductility. Class 1 or 2 cross-sections in dissipative zones.
DCH (q > 4): High ductility. Class 1 in dissipative zones, strict connection requirements.

Material overstrength: γ_ov = 1.25 for S235/S275/S355 (used in capacity design calculations).

Moment-Resisting Frame (MRF) — DCH (EC8 §6.6)

Beams: Class 1 required; θ_p,Cd ≥ 35 mrad chord rotation capacity in plastic hinges
Strong column / weak beam: ΣM_Rc/ΣM_Rb ≥ 1.3 at every beam-column joint
Connections: M_j,Rd ≥ 1.1·γ_ov·M_pl,Rd of connected beam
Panel zone: V_wp,Rd ≥ V_wp,Ed from capacity design

Concentrically Braced Frame (CBF) — EC8 §6.7

EC8 §6.7.4 — Brace overstrength uniformity

Ω_i = N_pl,Rd,i / N_Ed,i (overstrength of each brace)

Requirement Ω_max / Ω_min ≤ 1.25 (uniformity across storeys)

Column N_Ed = N_Ed,G + 1.1·γ_ov·Ω_min·N_Ed,E kN (capacity design)

Steel Flexural Design → Steel Column →

← Previous 6. RC Design (EC2) Next → 8. Serviceability Checks

Educational use only. Design expressions use EN 1993-1-1:2005 and EN 1998-1:2004 recommended values. National Annexes may modify γ_M0, γ_M1, buckling curve assignments, and seismic detailing requirements. Always verify against the current EN text and applicable NA.

Steel Member Design — EN 1993-1-1 (Eurocode 3)

Contents

1. Pre-Sizing Rules of Thumb

2. Cross-Section Classification (EC3 §5.5)

3. Beam Flexure (EC3 §6.2.5)

4. Lateral-Torsional Buckling (EC3 §6.3.2)

LTB Imperfection Factors αLT

Modified Method (EC3 §6.3.2.3)

5. Shear Design (EC3 §6.2.6)

Shear-Moment Interaction

6. Column Design — Axial Compression (EC3 §6.3.1)

Buckling Curves (EC3 Table 6.2)

7. Combined Loading — Beam-Columns (EC3 §6.3.3)

8. Connections Overview (EC3-1-8)

Bolt Grades and Strengths

9. Seismic Steel Design (EC8 §6)

Ductility Classes

Moment-Resisting Frame (MRF) — DCH (EC8 §6.6)

Concentrically Braced Frame (CBF) — EC8 §6.7

Related Tools & Guides

LTB Imperfection Factors α_LT