In the world of advanced design software, one of the crucial aspects to consider when constructing tall buildings is their structural integrity in the face of powerful wind forces. The European standard EN 1991-1-4, commonly known as EC1 Wind, provides a comprehensive framework for calculating wind actions on structures. This calculation example focuses specifically on the design of a wall for a high-rise building, where wind loads play a pivotal role.

EC1 Wind EN 1991-1-4 calculation example for a wall of a high building

vb,0 = 26 m/s (user imposed in the wind family property list)

r = kg/m^{3} (recommended value in EC1).

h = 48 m

For X+ wind b = 20.4 m, d = 33.0 m, and for Y+ wind direction b = 33.0 m and d = 20.4 m.

For terrain category IV** z0** = 1.0 m,** zmin** = 10.0 m and** z0II** = 0.05 m.

**The results of the automatic calculation and creation of the loads:**

Calculation of CsCd for z = 0.6 h for X+ wind direction.

aerodynamic admittance functions Rh and Rb

In the h > 2b case, we consider:

The size of the remaining vertical zone between the b zones hdiff = h – (2b).

If the rest of the division of hdiff by b is 0 then hstrip = b and the number of strips nointerm= hdiff/ b. Else the number of strips nointerm = (the integer of hdiff/ b) + 1 and the i < nointerm -1 intermediate strips have hstrip (i < nointerm) = b, the last intermediate hstrip ( i = nointerm) being equal to the rest of the division of hdiff by b.

h = 48 m

**For X+ wind: direction**

b = 20.4 m, d = 33.0 m => h > 2b =>

hdiff = 7,2 m and the rest of the division of hdiff by b = 7,2 m => the number of intermediate strips nointerm = (integer of 7.2 m/ 20.4 m) + 1 = 0 + 1 = 1 the only intermediate strip is also the last one hstrip ( i = nointerm) = rest of 7.2 m/ 20.4 m = 7.2 m

=> We have to calculate qpz for 3 heights b, b + hstrip ( i = nointerm) and h (which is b + hstrip ( i = nointerm) + b ).

The area of each wall is bigger than 10 m^{2} so the cpe10 values are extracted from Table 7.1.

h / d = 48.0 m / 33.0 m = 1.4545454545454548 so we’ll linear interpolate the cpe10 values between the h/d =1 and h/d=5 lines resulting:

**cpe10**

- [A] -1.2
- [B] -0.8
- [C] -0.5
- [D] 0.8
- [E] -0.523

Both values of Cpi values, +0.2 and -0.3 (the default option in the cpe cpi dialog).

**NOTE:** *Advance Design considers that the internal pressure is the same in the entire building => zi = h => q _{p} (z_{i}) = q_{p} (h).*

CsCd is considered the same for the entire building per wind direction. The value for X+ is calculated above.

**For the A zones:**

- w A cpe10 & cpi1 (ze=b) = c
_{s}c_{d}∙ q_{p}(b) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -989.834 N/m2 (in WX+S load cases) - w A cpe10 & cpi1 (ze=b+bstrip) = c
_{s}c_{d}∙ q_{p}(b+hstrip) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -1095.867 N/m2 (in WX+S load cases) - w A cpe10 & cpi1 (ze=h) = c
_{s}c_{d}∙ q_{p}(h) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -1302.439 N/m2 (in WX+S load cases) - w A cpe10 & cpi1 (ze=b) = c
_{s}c_{d}∙ q_{p}(b) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -501.663 N/m2 (in WX+D load cases) - w A cpe10 & cpi1 (ze=b+bstrip) = c
_{s}c_{d}∙ q_{p}(b+hstrip) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -607.697N/m2 (in WX+D load cases) - w A cpe10 & cpi1 (ze=h) = c
_{s}c_{d}∙ q_{p}(h) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -814.268 N/m2 (in WX+D load cases)

Like all above the position and the geometry of the loads based on the zones provided by Figure 7.4 on the roof are calculated automatically. All the loads and the load cases are automatically generated.

e = MIN(b,2h) = 20.4 m

The highlighted loads are the ones the "w A cpe10 & cpi1" ones in the X+ S case.

**For Y+ wind direction:**

b = 33.0 m and d = 20.4 m => b < h ≤ 2b => We must calculate qpz for 2 heights b, and h

h / d = 48.0 m / 20.4 m = 2.3529411764705888 so we’ll linear interpolate the cpe10 values between the h/d =1 and h/d=5 lines resulting:

**cpe10**

- [A] -1.2
- [B] -0.8
- [C] -0.5
- [D] 0.8
- [E] -0.5676

Both values of Cpi values, +0.2 and -0.3 (the default option in the Cpe cpi dialog).

**NOTE:** *Advance Design considers that the internal pressure is the same in the entire building => zi = h => q _{p} (z_{i}) = q_{p} (h).*

For the A zones:

- w A cpe10 & cpi1 (ze=b) = c
_{s}c_{d}∙ q_{p}(b) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -1107.679 N/m2 (in WX+S load cases) - w A cpe10 & cpi1 (ze=h) = c
_{s}c_{d}∙ q_{p}(h) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -1241.515 N/m2 (in WX+S load cases) - w A cpe10 & cpi1 (ze=b) = c
_{s}c_{d}∙ q_{p}(b) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -619.508 N/m2 (in WX+D load cases) - w A cpe10 & cpi1 (ze=h) = c
_{s}c_{d}∙ q_{p}(h) ∙ -1.2 - q_{p}(h) ∙ 0.2 = -753.345 N/m2 (in WX+D load cases)

Like all above the position and the geometry of the loads based on the zones provided by Figure 7.4 on the roof are calculated automatically. All the loads and the load cases are automatically generated.

e = MIN(b,2h) = 33.0 m

The highlighted loads are the one the "w A cpe10 & cpi1" ones in the X+ S case:

All the cases and loads: