European Wind Load — EN 1991-1-4 Wind Actions on Steel Structures

Complete reference for wind action determination on structural steel buildings per EN 1991-1-4 (Eurocode 1: Actions on structures — Part 1-4: Wind actions). Fundamental basic wind velocity vb,0 mapping, terrain roughness categories 0 through IV, peak velocity pressure qp(z) calculation, structural factor cscd for steel frames, external and internal pressure coefficients cpe and cpi, and a fully worked wind load example for a 4-storey steel office frame.

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EN 1991-1-4 Wind Loading Framework

EN 1991-1-4 provides the methodology for determining wind actions for the structural design of buildings and civil engineering works. The wind action is represented as a set of pressures or forces acting on the external and internal surfaces of the structure. The peak velocity pressure qp(z) at height z forms the basis of all wind pressure calculations.

The fundamental relationship (EN 1991-1-4, Cl. 4.5, Eq. 4.8):

qp(z) = [1 + 7 × Iv(z)] × 0.5 × ρ × vm²(z)

Where:

• qp(z) = peak velocity pressure at height z (N/m²)
• Iv(z) = turbulence intensity at height z
• ρ = air density (recommended value 1.25 kg/m³, UK NA = 1.226 kg/m³)
• vm(z) = mean wind velocity at height z (m/s)

Step 1 — Fundamental Basic Wind Velocity vb,0

The fundamental basic wind velocity vb,0 is the 10-minute mean wind velocity at 10 m height in open country terrain (Category II) with an annual probability of exceedance of 0.02 (50-year return period).

EN 1991-1-4 National Annex defines vb,0 values. Representative UK values (BS EN 1991-1-4 UK NA):

The basic velocity pressure qb,0 is derived: qb,0 = 0.5 × ρ × vb,0²

Basic Wind Velocity vb

The basic wind velocity vb is the fundamental velocity adjusted for direction and season:

vb = cdir × cseason × vb,0

For permanent building design, both factors are taken as 1.0 unless a refined directional analysis is undertaken.

Step 2 — Mean Wind Velocity vm(z)

vm(z) = cr(z) × co(z) × vb

Terrain Roughness Factor cr(z)

This factor accounts for the variability of mean wind velocity with height and terrain roughness:

cr(z) = kr × ln(z/z0)  for z ≥ zmin
cr(z) = cr(zmin)       for z < zmin

Where kr = 0.19 × (z0 / z0,II)^0.07 and z0,II = 0.05 m (reference roughness for Category II).

Terrain Categories (EN 1991-1-4 Table 4.1)

Orography Factor co(z)

co(z) = 1.0 unless the site is on a hill, ridge, cliff, or escarpment where wind speed-up occurs (EN 1991-1-4 Annex A.3). For exposed hilltop sites, co(z) can reach 1.3-1.6, significantly increasing wind pressures.

Step 3 — Turbulence Intensity Iv(z)

Iv(z) = kI / [co(z) × ln(z/z0)]  for z ≥ zmin

Where kI = 1.0 (turbulence factor, recommended value).

For terrain Category II at z = 10 m: Iv(10) = 1.0 / [1.0 × ln(10/0.05)] = 1.0 / 5.298 = 0.189 → 19% turbulence intensity.

Step 4 — Peak Velocity Pressure qp(z) — Worked Table

Using vb,0 = 23.5 m/s, ρ = 1.226 kg/m³, Terrain Category II:

For a 4-storey office (overall height ~16 m), the peak velocity pressure at roof level (z = 16 m) is approximately 0.83 kN/m².

Step 5 — Structural Factor cscd

For buildings with height less than 15 m, cscd = 1.0 (EN 1991-1-4 Cl. 6.2(1)). For taller buildings:

cscd = [1 + 2 × kp × Iv(zs) × √(B² + R²)] / [1 + 7 × Iv(zs)]

Where:

• B² = background turbulence factor (lack of correlation of pressures)
• R² = resonant response factor
• kp = peak factor (typically 3.0-3.5 for structural response)
• zs = reference height for structural factor (≈ 0.6 × h for vertical structures)

For typical multi-storey steel frames (up to 40 m height), cscd ranges from 0.95 to 1.05. Conservatively, use cscd = 1.0 for frames under 30 m unless dynamic analysis is required (EN 1991-1-4 Cl. 6.2(2) — Figure 6.1 criteria).

Step 6 — External Pressure Coefficients cpe

Vertical Walls (EN 1991-1-4 Table 7.1)

For a rectangular building, the external pressure depends on the zone and the ratio h/d (height to depth in the wind direction):

cpe on Zone D is positive (pressure). All other zones are negative (suction). The value depends on the h/d ratio; use h/d ≤ 0.25 for low-rise and h/d ≥ 1.0 for tall slender buildings.

Flat Roof (EN 1991-1-4 Table 7.2)

Flat roof suction at corners (Zone F) can be severe — this is the governing case for roof cladding fixings and purlin uplift design.

Step 7 — Internal Pressure Coefficient cpi

EN 1991-1-4 Cl. 7.2.9: The internal pressure depends on the distribution and size of openings in the building envelope:

For a typical office building (closed, glazed facade), use cpi = +0.2 (internal pressure, adding to external suction) and cpi = -0.3 (internal suction, adding to external pressure). Check both cases.

Worked Example — 4-Storey Steel Office Frame

Building details:

• Plan: 30 m (L, wind direction) × 20 m (B, cross-wind)
• Height: h = 16 m (4 floors at 4 m)
• Location: Manchester (vb,0 = 23.5 m/s)
• Terrain: Category III (suburban/urban fringe)
• cscd = 1.0 (building < 30 m, steel frame)

Step 1 — Peak Velocity Pressure

vb = cdir × cseason × vb,0 = 1.0 × 1.0 × 23.5 = 23.5 m/s

For Category III: z0 = 0.3 m, zmin = 5 m, kr = 0.19 × (0.3/0.05)^0.07 = 0.19 × (6)^0.07 = 0.215

At z = 16 m (roof height): cr(16) = 0.215 × ln(16/0.3) = 0.215 × 3.977 = 0.855 vm(16) = 0.855 × 1.0 × 23.5 = 20.09 m/s Iv(16) = 1.0 / ln(16/0.3) = 1.0 / 3.977 = 0.251

qp(16) = [1 + 7 × 0.251] × 0.5 × 1.226 × (20.09)² = (1 + 1.757) × 0.613 × 403.6 = 2.757 × 247.4 = 682 N/m² = 0.68 kN/m²

Step 2 — External Pressure on Walls

h/d = 16/30 = 0.533 (linear interpolation required in Table 7.1)

Net pressure across building (D - E) = 0.50 - (-0.25) = 0.75 kN/m² × 20 m width = 15.0 kN/m (UDL on frame).

Step 3 — Include Internal Pressure (Critical Case)

Internal pressure, cpi = +0.2:

• Windward: 0.68 × (0.73 - 0.2) = 0.68 × 0.53 = 0.36 kN/m²
• Leeward: 0.68 × (-0.37 - 0.2) = 0.68 × (-0.57) = -0.39 kN/m²
• Net = 0.36 - (-0.39) = 0.75 kN/m² → 15.0 kN/m

Internal suction, cpi = -0.3:

• Windward: 0.68 × (0.73 + 0.3) = 0.68 × 1.03 = 0.70 kN/m²
• Leeward: 0.68 × (-0.37 + 0.3) = 0.68 × (-0.07) = -0.05 kN/m²
• Net = 0.70 - (-0.05) = 0.75 kN/m² (coincidental — not always the case)

Step 4 — Frame Wind Loads per Storey

Using the uniform net pressure of 0.75 kN/m² across the 20 m building width, distributed by tributary height to each floor diaphragm:

Wind force per floor = 0.75 kN/m² × 20 m × tributary height. This loading is applied as a point load at each floor diaphragm to the lateral load-resisting system (braced bay or moment frame).

Step 5 — Design Implications

• Base shear: VEd = 210 kN (to be resisted by vertical bracing or frame action)
• Base overturning moment: MEd = 1,920 kNm
• The wind load is combined per EN 1990 6.4.3.2 with γQ = 1.5 (ULS wind-leading) → Design base shear = 315 kN, design moment = 2,880 kNm
• Verify that the steel bracing members resist this load at EN 1993-1-1 cross-section and buckling checks

Wind Loading on Free-Standing Steel Structures

For lattice towers, sign gantries, and similar free-standing steel structures, EN 1991-1-4 Cl. 7.6 to 7.11 provides specific force coefficients:

For a steel lattice tower with solidity ratio φ = 0.2 (light bracing), Cf ≈ 2.0. The wind force is Fw = cscd × Cf × qp(ze) × Aref, where Aref = projected area of all members in one face.

Steel Cladding and Secondary Member Wind Design

Purlins and Side Rails

Wind suction (uplift) typically governs the design of roof purlins and wall side rails. The critical load combination for a roof purlin is:

0.9 × Dead (self-weight + cladding) + 1.5 × Wind uplift

Where wind uplift pressure is based on qp(z) × cpe (most negative zone) — cpi. For a flat roof corner zone (F): cpe,10 = -1.8, with cpi = +0.2 → net cpeff = -2.0. If qp = 0.82 kN/m² (z = 15 m), net uplift = 1.64 kN/m², which easily exceeds the dead load of a typical steel roof system (0.50-0.75 kN/m²), resulting in net uplift on purlins.

Wind Pressure Quick-Reference Table

Frequently Asked Questions

What is the difference between vb,0 and vb in EN 1991-1-4?

vb,0 is the fundamental basic wind velocity — the 10-minute mean wind velocity at 10 m height in open flat terrain (Category II) for a 50-year return period, as given by the National Annex wind map. vb = cdir × cseason × vb,0 is the basic wind velocity adjusted for local wind direction effects and seasonal probability. For permanent building design, cdir = cseason = 1.0 is conservative, so vb = vb,0 in most cases. For temporary works with a defined direction (e.g., exposed to prevailing south-westerly in the UK), cdir may be relaxed, reducing the design wind action.

When can I use cscd = 1.0 for a steel building?

EN 1991-1-4 Cl. 6.2(1) permits cscd = 1.0 for buildings of height less than 15 m. For taller buildings, cl. 6.2(2) and Figure 6.1 provide criteria: if the building height is less than the value given by Figure 6.1 (which depends on the fundamental frequency range and terrain), cscd = 1.0. For a typical steel moment frame up to 40 m height with a natural frequency above 1 Hz, cscd ≈ 0.97-1.03 and can be conservatively taken as 1.0. For slender steel structures (h/B > 5), dynamic analysis is required and cscd must be calculated explicitly.

How do I account for wind loading on open steel structures like pipe racks?

For open steel structures such as pipe racks and cable trays, EN 1991-1-4 Cl. 7.11 applies for lattice structures. The key parameter is the solidity ratio φ = A/Ac (projected solid area divided by enclosed area). For φ < 0.1, use Cf ≈ 1.6 × φ + 1.3. For 0.1 ≤ φ ≤ 0.7, Cf varies between 1.4 and 2.4 depending on cross-section shape. The reference area Aref is the projected area of all members in one face. Wind load on the pipes/cables themselves should be added using Cl. 7.6 (circular cylinders) with Cf ≈ 0.7 for rough industrial pipes.

What internal pressure coefficient should I use for an industrial steel building with roller shutter doors?

If the roller shutter doors represent a dominant opening (area ≥ 2 × the total opening area on all other faces), and if the door is on the windward face and can be assumed open under storm conditions, use cpi = +0.9 × cpe(D). If the door is on the windward face and the building has no other significant openings, this creates extreme internal pressure that can govern purlin uplift and wall frame design. Many designers specify that roller shutters must be closed in high wind — in this case, treat as a closed building with cpi = ±0.2 or -0.3. The specification on the drawings is critical for the design assumption.

How does the UK National Annex modify EN 1991-1-4 wind provisions?

The UK NA makes several modifications: (1) provides a detailed vb,0 map with contours at 1 m/s intervals across the country (Figure NA.1); (2) specifies ρ = 1.226 kg/m³; (3) modifies terrain categories slightly — Category 0 is subdivided into 0 (sea, vb,0 × 1.06) and 0* (coastal strip within 1 km of sea); (4) provides a simplified method for buildings less than 20 m tall (BS EN 1991-1-4 UK NA Annex A) using a single effective qp. (5) For town terrain (Category IV), displacement height hdis = 0.8 × have of adjacent buildings is subtracted from z. Always refer to the current UK NA for site-specific design.

Related Pages

• EN 1990 Load Combinations →
• EN 1993 Steel Design Overview →
• European Snow Load per EN 1991-1-3 →
• EN 1998 Seismic Design →
• Wind Load Calculator Tool →
• ASCE 7 Wind Load (USA) →
• AS/NZS 1170.2 Wind Load (Australia) →

Educational reference only. Wind velocities and pressure coefficients must be verified against the current National Annex for the building jurisdiction. All wind load calculations must be independently verified by a qualified structural engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION without professional structural engineering review.