Wind Load on a Pole or Mast under DBN V.1.2-2: W0, Height Coefficient Ch, Example

The formula and its parts

The ultimate design wind load under clause 9.4 of DBN V.1.2-2:2006 is Wm = γfm · W0 · C. The coefficient C is built under clause 9.7: C = Caer · Ch · Calt · Crel · Cdir · Cd.

• γfm, the reliability factor for the ultimate value (Table 9.1): 1.00 for a 50-year return period, 0.87 for 25 years, 1.14 for 100 years; for mass construction the period is taken equal to the service life;
• W0, the characteristic wind pressure at 10 m height that is exceeded on average once in 50 years: from the map (Fig. 9.1) or from Annex E for cities. Regions 1–5 on the map are 400, 450, 500, 550 and 600 Pa; Annex E gives 370 Pa for Kyiv;
• Caer, the aerodynamic coefficient for the section shape (Annex I);
• Ch, the coefficient for height and terrain type;
• Calt, the coefficient for altitude above sea level: equal to 1 up to 500 m, and above that taken from the formula in the current edition of the standard;
• Crel, the relief coefficient: 1 unless the pole stands on a slope or hill;
• Cdir, the direction coefficient: usually 1;
• Cd, the dynamic coefficient that accounts for wind gusts.

The overall calculation sequence, of which this is the first step, is shown in Calculation of a Wind Turbine Pole. W0 values for regional centres are collected in Wind Zones of Ukraine.

Terrain type

The standard distinguishes four terrain types, and the type is set separately for each wind direction:

• I: open sea and lake surfaces, flat plains without obstacles for at least 3 km;
• II: countryside with fences, small structures, houses and trees;
• III: suburban and industrial zones, large forests;
• IV: urban areas where at least 15 % of the surface is covered by buildings with an average height above 15 m.

A structure is considered to stand in a terrain of a given type if that terrain extends in the direction in question for 30Z when the height Z is below 60 m, and for 2 km for greater heights. On the border of two types, or when in doubt, the type that gives the larger Ch is taken.

Height coefficient Ch: which table to use

The standard has two tables. Table 9.01 applies to structures whose longest natural period does not exceed 0.25 s, and Table 9.02 to all others. For a wind turbine pole with a heavy head the period is usually longer, so Table 9.02 is needed, and it gives higher values: at 10 m height and type II the coefficient is 1.50 against 0.90 in Table 9.01.

The period T = 1/f1 comes from the natural frequency calculation. Intermediate values of Ch are found by linear interpolation.

Coefficient Ch from Table 9.02 of DBN V.1.2-2:2006, for structures with a natural period above 0.25 s.

Dynamic coefficient Cd

For structures with a period up to 0.25 s, Cd = 1. For others it is taken from graphs 9.5–9.10, and for steel stacks and column-type apparatus without lining from Fig. 9.8, on the left curve. If Cd comes out above 1.2, the standard requires a special dynamic calculation of the gust component (clause 9.13).

There is a second condition. For tall structures with h/d above 7 (h is the height, d the minimum section size at 2/3 of the height) an additional check for vortex excitation is needed (clause 9.17). For a 20 m pole with a diameter of 0.8 m at 2/3 of the height, h/d is 25, so the check is needed.

Aerodynamic coefficient

Caer for round and multi-sided poles comes from Annex I. The annex does not cover every number of sides, and when the value is missing, clause 9.8 allows the coefficient to be taken from reference and experimental data or from wind-tunnel tests. In practice a value with a margin is taken for a pole with more sides.

Example of a pressure calculation

Conditional data: W0 = 500 Pa (region 3), terrain type II, height Z = 20 m, a sway period above 0.25 s (so Table 9.02), γfm = 1.00, Calt = Crel = Cdir = 1, Caer = 1.0, Cd = 1.0. The coefficient Ch for Z = 20 m and type II is 1.85.

Then Wm = 1.00 · 500 · 1.85 · 1.0 · 1.0 = 925 Pa. At a height of 10 m (Ch = 1.50) the pressure would be 750 Pa, so the load rises with height. The force per metre of height is obtained by multiplying the pressure by the pole diameter at that level.

Ice and wind loads combined

Section 10 requires them to be considered for antenna mast structures and similar structures. The load is the weight of ice plus the normal wind pressure on the iced elements; the standard sets ultimate design values for each part.

The ice wall thickness b depends on the ice region (the map in Fig. 10.1 or Annex Zh) and is given for a 10 mm wire at 10 m height. For other heights it is multiplied by the coefficient k: 0.8 at 5 m, 1.0 at 10 m, 1.2 at 20 m, 1.4 at 30 m. For elements up to 70 mm in diameter, the coefficient μ1 for the diameter is added, and the density of ice is 0.9 g/cm³. For example, Annex E gives b = 19 mm for Kyiv and a wind pressure with ice of WB = 160 Pa.

In the Carpathians and Crimea, and on summits and passes, ice data are taken from special observations.

What to send for a calculation

• the town or the coordinates of the site;
• the terrain type in each wind direction;
• the altitude of the site and any slopes or hills nearby;
• the ice region, if known;
• the section shape and size of the pole and the height of the structure, and for sway, its natural frequency.

With these data the designer calculates the wind load. If you need a pole or a mast, the usual order applies: KM and KMD drawings and steel structure fabrication.

Standards and validity

• DBN V.1.2-2:2006 “Loads and actions. Design standards”: section 9 (wind loads), section 10 (ice and wind loads), annexes E, Zh and I.
• DBN V.1.2-14:2018: consequence classes of the structure, on which the importance factor depends.

The map and table numbers here are for reference: a real project takes the values from the current edition of the standard together with its amendments, and the validity of the document is checked beforehand.