Code Reference: EN 1993-1-1:2005 Sections 5-6

EN 1993-1-1 Sections 5 (Structural Analysis) and 6 (Ultimate Limit States) provide the framework for all steel structural systems. EN 1993-1-1 Clause 5.2 defines first-order and second-order analysis requirements. EN 1993-1-1 Clause 5.3 covers global and member imperfections.

Steel Framing Systems Overview

In European practice, the braced frame is the most common system for low-to-mid-rise steel buildings (up to 10 storeys). Portal frames dominate single-storey industrial buildings (warehouses, factories, hangars). Moment-resisting frames are used where architectural freedom from bracing is required. Concrete-core braced systems are the dominant solution for high-rise steel buildings in the UK (e.g., the City of London).

Global Imperfections (EN 1993-1-1 Clause 5.3)

EN 1993-1-1 requires consideration of both global (frame) and local (member) imperfections:

Initial sway imperfection:

[ \phi = \phi_0 \times \alpha_h \times \alpha_m ]

For a 5-storey building (h = 17.5 m) with 4 braced bays (m = 4): (\alpha_h = 2/\sqrt{17.5} = 0.478), but minimum is 2/3, so (\alpha_h = 0.667) (\alpha_m = \sqrt{0.5(1 + 1/4)} = \sqrt{0.625} = 0.791) (\phi = (1/200) \times 0.667 \times 0.791 = 1/379)

The initial sway imperfection (\phi) determines the equivalent horizontal forces that must be applied at each floor level for the structural analysis.

Second-Order Effects (EN 1993-1-1 Clause 5.2)

EN 1993-1-1 Clause 5.2.1 requires second-order effects to be considered when the frame's sensitivity to sway is significant. The sensitivity parameter (\alpha_{cr}) is:

[ \alpha*{cr} = \frac{F*{cr}}{V*{Ed}} = \frac{H*{Ed}}{V*{Ed}} \times \frac{h}{\delta*{H,Ed}} ]

Where (F*{cr}) is the elastic critical buckling load, (V*{Ed}) is the vertical load, (H*{Ed}) is the horizontal reaction, (h) is the storey height, and (\delta*{H,Ed}) is the first-order sway displacement.

For braced frames, the horizontal bracing system is designed for (\alpha*{cr} \geq 10) in most cases. For unbraced moment frames, (\alpha*{cr}) is typically 4-8, requiring second-order analysis.

Frame Classification — Braced vs Unbraced

EN 1993-1-1 Clause 5.2.1(4) classifies frames based on their sway sensitivity:

For sway frames, the effective buckling length of columns increases significantly: a column in a sway frame has (L*{cr} = 2.0 \times L) for pinned bases and (L*{cr} = 1.0-1.5 \times L) for fixed bases, depending on the beam-to-column stiffness ratio. Non-sway (braced) frames use (L_{cr} = 0.7-1.0 \times L).

Worked Example — Bracing System Design

Problem: Design a concentric X-bracing system for a 6-storey steel frame. Storey height 3.5 m, bay width 6.0 m. Wind load per storey: wk = 30 kN. Steel grade S355. Building is non-sway per EN 1993-1-1.

Step 1 — Wind load combination (EN 1990): Ultimate horizontal force per storey: (F*{Ed,storey} = 1.5 \times 30 = 45) kN Total base shear: (V*{Ed} = 6 \times 45 = 270) kN

Step 2 — Brace force (X-bracing, tension-only): Brace length: (Lb = \sqrt{3.5^2 + 6.0^2} = 6.95) m Angle to horizontal: (\theta = \arctan(3.5/6.0) = 30.3^\circ) Force per brace (2 braces per bay, assume tension-only design): (N{Ed,b} = 270 / (2 \times \cos 30.3^\circ) = 270 / (2 \times 0.864) = 156) kN

Step 3 — Section selection: Try CHS 114.3 (\times) 5.0 in S355: A = 1,720 mm², i = 38.7 mm Lcr = 6,950 mm (tension: no buckling, but slenderness check for handling) (\lambda1 = 93.9 \times \epsilon = 93.9 \times 0.814 = 76.4) (\bar{\lambda} = (6,950 / 38.7) / 76.4 = 179.6 / 76.4 = 2.35) For tension: (N{t,Rd} = A \times fy / \gamma{M0} = 1,720 \times 355 / 1.0 = 611) kN (> 156) kN — OK.

Step 4 — Deflection check (serviceability): Wind load per storey at SLS: wk = 30 kN Approximate apex deflection from brace elongation: (\delta_h = \delta_b / \cos \theta) Brace axial elongation: (\delta_b = (30 \times 10^3 \times 6,950) / (1,720 \times 210,000) = 0.58) mm per brace Storey drift: (\delta_h = 0.58 / 0.864 = 0.67) mm Total building drift (6 storeys): ~4.0 mm Limit H/500 = 21,000/500 = 42 mm — OK.

Design Resources

• EN 1993 Steel Grades
• European Steel Properties
• EN 1993 Bolt Capacity
• IPE/HEA/HEB Beam Sizes
• EN 1993 Column Buckling
• All European References

Frequently Asked Questions

What framing systems are recognized by EN 1993? EN 1993-1-1 covers braced frames (with concentric or eccentric bracing), unbraced moment-resisting frames, portal frames, and framed tube systems. The Eurocode provides guidance for both elastic and plastic global analysis across all system types. For seismic design, EN 1998-1 supplements these with ductility classification (DCL, DCM, DCH) and specific q-factors for each system type: moment-resisting frames (q = 4-6.5), concentrically braced frames (q = 2.5-4.8), and eccentrically braced frames (q = 5-6.5).

How does EN 1993 handle frame imperfections? EN 1993-1-1 Clause 5.3 requires consideration of both global (frame sway) and local (member bow) imperfections. The global initial sway imperfection (\phi = \phi_0 \times \alpha_h \times \alpha_m) with basic value (\phi_0 = 1/200). Member bow imperfections depend on the buckling curve and are typically L/200 to L/300 for hot-rolled sections. Imperfections are introduced in the analysis model as equivalent geometric imperfections (not as loads). For second-order analysis, the imperfections must be applied in the most unfavourable direction and combined with the load effects.

What is the difference between a sway frame and a non-sway frame per EN 1993-1-1? A non-sway (braced) frame has (\alpha*{cr} \geq 10), meaning second-order PA effects are less than 10% of first-order effects. A sway (unbraced) frame has (\alpha*{cr} < 10) and requires explicit second-order analysis. The classification dramatically affects column design: non-sway columns use effective lengths Lcr (\leq 1.0 \times L) (typically 0.7-1.0L), while sway columns use Lcr up to 2.0-3.0 (\times) L depending on end fixity. The (\alpha*{cr}) parameter is calculated as (\alpha*{cr} = H*{Ed} \times h / (V*{Ed} \times \delta_{H,Ed})) using the first-order sway displacement under horizontal loads.

When should plastic global analysis be used instead of elastic analysis? Plastic global analysis per EN 1993-1-1 Clause 5.4 is appropriate for braced frames and portal frames where ductility demands are predictable. It requires Class 1 sections in all plastic hinge locations and adequate rotation capacity. Elastic global analysis is used for moment frames in moderate-to-high seismicity regions, frames with significant second-order effects, and frames where section classification is Class 3 or 4. Plastic analysis is most efficient for portal frame design (the dominant European application), where it typically reduces the rafter and column sizes by 15-25% compared with elastic design.

What are the drift limits for steel frames in European practice? EN 1993-1-1 recommends inter-storey drift h/300 and total drift H/500 under serviceability wind loads. For seismic drift, EN 1998-1 Clause 4.4.3.2 limits inter-storey drift: 1.0% of storey height for buildings with brittle non-structural elements, 1.5% for buildings with ductile non-structural elements. For wind-excited tall buildings (H > 50 m), occupant comfort criteria based on peak acceleration (typically 0.05-0.10 m/s² for 5-year return wind) may govern the required frame stiffness. The UK NA specifies drift limits based on cladding type: h/300 for flexible cladding, h/500 for brittle cladding.

Reference only. Verify all values against the current edition of EN 1993-1-1:2005 Sections 5-6 and the applicable National Annex. This information does not constitute professional engineering advice.