Wind 1: from wind speed to peak pressure

Wind is the load that moves most with the site. This lesson follows SANS 10160-3 from the basic wind speed, through air density, terrain and height, to the peak velocity pressure q_p that every wind pressure is built on, with the STATIX wind load calculator.

1. Learning outcomes

After this lesson you can:

find the basic wind speed for a site and explain what it represents;
turn a speed into a pressure, with the air density for the site's altitude;
choose the terrain category and find the roughness factor c_r(z) at the reference height;
know when topography matters and what STATIX assumes;
work out q_p by hand and check it in the STATIX wind load calculator.

2. Before you start

Lesson 1: wind as a variable action.
Your copy of SANS 10160-3 (clause 7, Tables 1, 2 and 4, Annex A), the free wind load calculator and the wind load Learn page.
A pocket calculator with powers, and about 45 minutes.

3. Wind on a building

Wind on a building. The wind is slowed by the ground, so it blows harder higher up and harder over open country than over a town. Where it meets the building it pushes on the windward face and sucks on the sides, the roof and the back. This lesson finds the pressure the wind brings; lesson 5 spreads it over the building.

4. The basic wind speed and the air

The basic wind speed v_b. SANS 10160-3 maps South Africa into zones and lists towns in Annex A, with v_b of 32, 36 or 40 m/s. It is a 3-second gust at 10 m over open country, so no gust factor is added later. The lowest zone is not the usual one: look your site up.

Speed becomes pressure. Moving air of density ρ at speed v carries a pressure ½ ρ v² (clause 7.4). Because of the square, a small error in the wind speed is a large error in the load.

Air is thinner on the Highveld. Table 4 gives ρ by site altitude, and STATIX interpolates it from the altitude you enter. Using the sea-level value inland is safe but over-states the wind pressure by up to about a quarter.

5. Terrain and height

Terrain categories (SANS 10160-3 Table 2). The rougher the ground upwind, the more the wind near the ground is slowed: A is open sea or flat bare land, D a city centre with tall buildings. Choose by what the wind crosses on its way to the site, for each direction if it matters.

The wind profile. The roughness factor c_r(z) grows with height and is smaller over rough terrain. Below the height z_c of each category it stays constant (7.3.2.3): the code allows no further reduction near the ground.

SANS 10160-3 Table 1 and equation (5). Each terrain category has a gradient height z_g, a reference height z₀, the floor height z_c and the exponent α. STATIX uses exactly these values on the SANS route.

Topography. On the top of a hill or an escarpment the wind speeds up; the orography factor c_o allows for it (7.3.3). The STATIX wind calculator has no topography input and takes c_o = 1.0, so on such a site the pressure must be increased by hand.

The reference height. For ordinary buildings SANS 10160-3 takes the whole building's height h, to the top of the roof, as the reference height for the walls and the roof. The STATIX calculator lets you type the eaves height and adds the roof rise, or the top directly.

6. The peak velocity pressure

The chain to the peak velocity pressure q_p(z) (equations (3) to (6)): the basic speed, scaled to the height and terrain, turned into pressure. Every wall and roof pressure in lesson 5 is q_p times a coefficient.

q_b = ½ ρ v_b² (7.4, ρ from Table 4) c_r(z) = 1.36 ((z − z₀)/(z_g − z₀))^α, z not below z_c (eq. (5), Table 1) v_p(z) = c_r(z) c_o(z) v_b; q_p(z) = ½ ρ v_p² (eq. (3), (6))

7. In STATIX

The STATIX wind load calculator: choose SANS 10160-3, the basic wind speed, the terrain category and the site altitude, then the building's size. It shows q_p at the reference height and draws the pressure profile up the building.