Engineering task and calculation objective
The EC1 module calculates wind loads to Eurocode 1, DIN EN 1991-1-4:2010-12, together with the German National Annex. From the wind zone, terrain category and structure height it determines the peak velocity pressure; combined with the aerodynamic force or pressure coefficients of the component in question and the structural factor, this yields the wind forces to be applied. The module can be used on its own, but it is optimized for use within module EN22 (stability-related verifications for vertical vessels).
In pressure equipment and plant engineering, wind loads have to be calculated for every component installed outdoors: columns, vertical vessels, stacks, pipe bridges and steel structures. Together with dead weight and, where applicable, seismic action, the wind load governs the stresses in skirts, support brackets and foundation anchorage, and it is frequently the decisive load case for slender, tall equipment. For Germany, the National Annex defines the wind zones with their basic wind velocities as well as the simplified and detailed velocity-pressure profiles.
Standard and calculation basis: Eurocode 1 / DIN EN 1991-1-4: 2010-12, Nationaler Anhang Deutschland
Calculation workflow
- Determine wind zone and basic wind velocity: The installation site defines the wind zone according to the wind-zone map of the National Annex and hence the basic wind velocity; from this, the basic velocity pressure is obtained using the air density.
- Determine terrain category and height profile: The surrounding terrain roughness (inland, mixed profile, coastal, or terrain categories I to IV) and the reference height of the component determine how the peak velocity pressure qp(z) varies with height — either using the simplified method of the National Annex or the detailed height profile.
- Determine aerodynamic coefficients: The force coefficient cf is determined for the component — for circular cylinders as a function of Reynolds number, surface roughness and slenderness (reduction via the solidity ratio and the effective slenderness), for other cross-sections from the tables of the standard. Attachments such as ladders, piping and platforms increase the reference area or are treated separately.
- Apply the structural factor: The structural factor cscd accounts for the gust correlation over the size of the structure and the dynamic amplification due to susceptibility to vibration; for compact, stiff structures it may be taken as 1.0, whereas for slender, vibration-prone equipment it has to be determined separately.
- Calculate and hand over wind forces: The wind force follows section by section from Fw = cscd · cf · qp(ze) · Aref. The resulting forces and moments for each height section are reported and can be transferred directly into the stability calculation of the equipment (e.g. module EN22). Where relevant, vortex-induced cross-wind vibration must be checked in addition.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Wind zone | WZ | – |
| Basic wind velocity | vb,0 | m/s |
| Reference wind velocity pressure | qb,0 | kN/m² |
| Differentiated wind zone | Wzdiv | – |
| Terrain category | Gkat | – |
| Corrected wind velocity pressure | qb | kN/m² |
| Increase factor | κH | - |
| Terrain height above sea level | HS | m |
| Force coefficient | cf | - |
| Structural factor not prone to vibration (acc. to EN 13445, 22.4) | cscd | - |
| Area subject to flow | A | m² |
| Start height | za | m |
| Height of bearing | zL | m |
| End height | ze | m |
| Height | h | m |
| Reference height a | hba | m |
| Reference height b | hbb | m |
| Reference height c | hbc | m |
| Area used for calculation | Abem | m² |
| Reference area a | Arefa | m² |
| Reference area b | Arefb | m² |
| Reference area c | Arefc | m² |
| Area to compensate | Acomp | m² |
| Force coefficient of area to compensate | cf,comp | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| qpza | qpz | kN/m² |
| qpzb | qpz | kN/m² |
| qpzc | qpz | kN/m² |
| Fwa | Fw | kN |
| Fwb | Fw | kN |
| Fwc | Fw | kN |
| Wind force | Fw | kN |
| la | l | m |
| lb | l | m |
| lc | l | m |
| Mwa | Mw | kN·m |
| Mwb | Mw | kN·m |
| Mwc | Mw | kN·m |
| Wind force moment | Mw | kN·m |
Calculation options
Wind zone
0 · 1 · 2 · 3 · 4 · Free Input
Differentiated wind zone
Midland · Coastal areas and Baltic Sea islands · Noth Sea islands
Terrain category
I open sea; Lakes with at least 5 km of open space downwind... · II Terrain with hedges, individual farmsteads, houses or trees... · III suburbs, industrial or commercial areas; forests · IV Urban areas where at least 15% of the area is built up with buildings... · II+III Midland · I+II coastal areas… · I Islands of the North Sea
Type
Column · Vertical piping · Horizontal piping · Platform · Ladder · Scaffolding
Worked example
For a free-standing column (outside diameter including insulation 1.2 m, height 10 m) located in wind zone 2, inland terrain, the resulting wind force is to be estimated using the simplified method of the German National Annex to DIN EN 1991-1-4 — a worked example of how to calculate wind loads to Eurocode 1. The force coefficient is taken as cf = 0.7 (rough cylinder in supercritical flow, including the slenderness reduction), the structural factor as cscd = 1.0.
Given values
| Wind zone | 2 (inland), v_b,0 = 25.0 m/s |
| Height h | 10 m |
| Diameter (including insulation) | 1.2 m |
| Force coefficient c_f (assumed) | 0.7 |
| Structural factor c_s c_d | 1.0 |
| Air density ρ | 1.25 kg/m³ |
Solution
Basic velocity pressure
qb = ρ/2 · vb² = 0.5 · 1.25 · 25.0² = 390.6 Pa ≈ 0.39 kN/m²
Peak velocity pressure (simplified method)
According to the simplified method of the German National Annex, for wind zone 2, inland terrain and structure heights up to 10 m: qp = 0.65 kN/m². The gust contribution and the height profile are included in this value on a lump-sum basis.
Resulting wind force
Reference area: Aref = d · h = 1.2 · 10 = 12 m²
Fw = cscd · cf · qp · Aref = 1.0 · 0.7 · 0.65 · 12 = 5.46 kN
For the stability verification the force is applied section by section over the height; with a uniform distribution, the resultant here acts at mid-height and produces a bending moment at the base of 5.46 · 5 = 27.3 kN·m.
Result
| Basic velocity pressure q_b | ≈ 0.39 kN/m² |
| Peak velocity pressure q_p | 0.65 kN/m² |
| Wind force F_w | ≈ 5.46 kN |
| Base moment (uniform load distribution) | ≈ 27.3 kN·m |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
What is the difference between the basic velocity pressure and the peak velocity pressure?
The basic velocity pressure qb is derived from the 10-minute mean wind velocity at 10 m height over open terrain (50-year return period). The peak velocity pressure qp(z) additionally includes the turbulence contribution of short gusts and the dependence on height and terrain roughness — it is the quantity that governs load determination and lies well above qb. In the simplified method of the German National Annex, qp is tabulated directly as a function of wind zone and building height.
Why does the force coefficient of a cylinder depend on the Reynolds number?
For circular cylinders, the flow separation point shifts with the Reynolds number: in the supercritical regime, where large process equipment practically always operates, the drag coefficient is significantly smaller than in the subcritical model-scale regime. In addition, surface roughness (insulation cladding, attachments) increases the coefficient, while finite slenderness reduces it through the end-effect reduction factor for flow around the free ends. A blanket coefficient applied without these influences can significantly over- or underestimate the load.
When am I allowed to set the structural factor cscd = 1.0?
The standard permits cscd = 1.0 for, among others, buildings less than 15 m high and for structures not susceptible to vibration. Slender columns and stacks with a low fundamental natural frequency, however, can respond with gust-induced amplification; in that case cscd has to be calculated using the procedure in the annex, and vortex-induced cross-wind vibration (Kármán vortices) must be investigated in addition. As a rough guide: height-to-diameter ratios h/d above about 6 to 7 and natural frequencies below 1 Hz call for special attention.
Which wind load applies to equipment standing inside a steel structure or on a pipe bridge?
Shielding may only be applied if it can be verified in accordance with the standard; in practice, free-standing equipment is usually calculated without shielding. Conversely, neighbouring structures can locally accelerate the oncoming flow (funnelling effect) or cause interference vortex excitation. Attachments on the equipment itself — ladders, platforms, tracing lines, insulation — must be included with their reference areas, since they can increase the total load considerably.