Wind load calculator (Eurocode and ASCE 7)

Introduction

Wind pressure rises with the square of the wind speed, and the wind gets stronger with height and over open ground. Building codes turn a mapped basic wind speed into a pressure at the height of interest, allowing for the terrain and gusts. In open country in Europe with a 27 m/s basic wind, the peak pressure 10 m above the ground is about 1.07 kPa; in a US suburb at 115 mph it is about 20 psf at 30 ft.

This calculator gives that pressure by the Eurocode EN 1991-1-4 (peak velocity pressure q_p) or the US standard ASCE 7-16 (velocity pressure q_z), with the exposure factors used. With a force or pressure coefficient and an area, it also gives the wind force. It is for engineers and builders checking signs, walls, roofs, canopies, fences and small structures.

Formulas

Eurocode EN 1991-1-4, terrain roughness z₀ and the basic wind speed v_b:

k_r = 0.19 (z₀ / 0.05)^0.07,   c_r = k_r ln(z / z₀)
v_m = c_r v_b,   I_v = 1 / ln(z / z₀)
q_p = (1 + 7 I_v) × ½ ρ v_m²,   ρ = 1.25 kg/m³

ASCE 7-16, exposure B, C or D:

K_z = 2.01 (z / z_g)^(2/α)       (z at least 15 ft)
q_z = 0.00256 K_z K_zt K_d K_e V²    psf, V in mph

Force on an area:

F = q × C × A

• Terrain categories 0 to IV: z₀ = 0.003, 0.01, 0.05, 0.3, 1.0 m
• Exposure B, C, D: α = 7.0, 9.5, 11.5 and z_g = 1 200, 900, 700 ft
• K_zt — topography (1 on flat ground); K_d — directionality (0.85 for buildings)

Assumptions and limitations

• The basic wind speed comes from the national annex map or the ASCE 7 wind map for the risk category. Eurocode speeds are 10-minute means; ASCE speeds are 3-second gusts, so the numbers are not comparable.
• Flat terrain is assumed. Hills, ridges and escarpments speed the wind up; enter K_zt for ASCE, or an orography factor through a higher v_b for the Eurocode.
• The force uses one coefficient for the whole area. Real design applies different external and internal pressure coefficients to each zone of the walls and roof; corners and edges see much higher suction.
• ASCE 7-22 revised some exposure constants and maps. Use the edition your building code adopts.

Worked example

A building in open country with low vegetation (terrain category II) has a basic wind speed of 27 m/s. What is the peak velocity pressure 10 m above the ground?

1. Roughness factor: k_r = 0.19 × (0.05 / 0.05)^0.07 = 0.19, so c_r = 0.19 × ln(10 / 0.05) = 1.007.
2. Mean wind speed: v_m = 1.007 × 27 = 27.2 m/s.
3. Turbulence intensity: I_v = 1 / ln(200) = 0.189.
4. Peak pressure: q_p = (1 + 7 × 0.189) × ½ × 1.25 × 27.2² = 1.07 kPa.

The exposure factor, q_p divided by the basic pressure ½ ρ v_b², is 2.35, as read from Figure 4.2 of the Eurocode.

FAQ

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