Wind load is one of the significant actions on roofs. While other loads such as the self-weight of materials, imposed loads, service loads, and snow loads are pointed downwards, wind load on roofs tends to pull the roof upwards. As a result, when wind load is acting on roofs, there is a possibility of the reversal of internal forces in the members of the roofs trusses or rafters from tensile to compressive or vice versa. This is why the application of wind load on roofs is so important.

The method for the application of wind load on roofs is given in EN 1991-1-4:2005 (Eurocode 1 Part 4). The effect of wind on any structure (i.e. the response of the structure), depends on the size, shape, and dynamic properties of the structure. Wind action is represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind. It is important to note that the wind actions calculated using EN 1991-1-4 are characteristic values and are determined from the basic values of wind velocity or velocity pressure. Unless otherwise specified, wind actions are classified as variable fixed actions.

**Procedure for the calculation of Wind Load on Roofs**

(1) Determine the peak velocity pressure q_{p} by calculating/obtaining the following values;

- basic wind velocity V
_{b} - reference height Z
_{e} - terrain category
- characteristic peak velocity pressure q
_{p} - turbulence intensity I
_{v} - mean wind velocity V
_{m} - orography coefficient c
_{o}(z) - roughness coefficient c
_{r}(z)

(2) Calculate the wind pressures using the pressure coefficients;

- external pressure coefficient c
_{pe} - internal pressure coefficient C
_{pi} - net pressure coefficient c
_{p,net} - external wind pressure: w
_{e}= q_{p}c_{pe} - internal wind pressure: W
_{i }= q_{p}C_{p}

(3) Calculate the wind force

- determine the structural factor: C
_{s}C_{d} - wind force F
_{w }calculated from force coefficients - wind force F
_{w}calculated from pressure coefficients

A pioneering wind tunnel experiment (Stanton, 1908) showed that when the roof slope is greater than 70 degrees from horizontal on the windward side, the roof surface can be treated as a vertical surface, with the external pressure coefficient c_{pe} equal to +0.5 (positive). The positive normal wind pressure reduces as the roof slope lowers. The pressure drops to zero when the roof slope approaches 30 degrees. A negative normal pressure (suction) acts upwardly normal to the slope when the roof slope falls below 30°.

As the slope declines, the suction pressure increases until it reaches its maximum value when the slope is zero (i.e. a flat roof). If the roof slope is 45 degrees, for example, c_{pe} = (45/100 – 0.2) = +0.25. If the roof slope is 30°, c_{pe} = (30/60 – 0.5) = 0.0. If the roof slope is 10° c_{pe} = (10/30 – 1.0) = -0.67 (upwards suction). If the roof slope is 0°, c_{pe} = (0/30 – 1) = 1.0 (upwards suction).

Based on the same experiment results, c_{pe} = -1.0 (upwards suction) for all roof slopes on the leeward roof slope. Thus, c_{pe} = 1.0 (upwards suction) for the windward part of a flat roof and c_{pe} = -0.5 (upwards suction) for the leeward side.

A building is subjected to internal pressures due to apertures in the walls, in addition to external wind pressures. Therefore, we have to also consider the internal pressure coefficients c_{pi}. The result of wind blowing into a building through an opening facing the opposite direction as the wind blowing onto the building is the formation of internal pressure within the structure.

**Positive internal pressure**: When wind blows into an open-sided building or into a workshop through a large open door, the internal pressure seeks to force the roof and side coverings outwards, resulting in positive internal pressure.

**Negative internal pressure (suction)**: This is formed within a building when the wind blows in the opposite direction, tending to pull the roof and side coverings inwards.

The coefficient of internal suction c_{pi} = ±0.2 in normal permeability shops (covered with corrugated sheets), and ±0.5 in buildings with extensive apertures (in the case of industrial buildings). Internal suction, or pressure away from the interior surfaces, is shown by a negative number, whereas internal pressure is indicated by a positive value.

**Worked Example**

Calculate the wind action on the walls and roof of a building with the data given below. Consider when the wind is coming perpendicular (0°) to the length of the building, and normal to it (90°).

**Building data**

Type of roof; Duopitch

Length of building; L = **30000** mm

Width of building; W = **15000** mm

Height to eaves; H = **6000** mm

Pitch of roof; α_{0} = **15.0**°

Total height; h = **8010** mm

Tekla Tedds will be used for executing the wind load analysis on the building. The key to the pressure coefficients for a building with a duopitch roof is given below (Figure 7.8 EN 1991-1-1:2005). Note that * e = B or 2h* whichever is smaller, where

**is the crosswind dimension.**

*b*Location of building; **Onitsha, Anambra State,** **Nigeria**

Wind speed velocity; v_{b,map} = **40.0** m/s

Distance to shore; L_{shore} = **50.00** km

Altitude above sea level; A_{alt} = **50.0**m

Altitude factor;c_{alt} = A_{alt}/1m × (0.001 + 1) = **1.050**

Fundamental basic wind velocity; v_{b,0} = v_{b,map} × c_{alt} = **42.0** m/s

Direction factor; c_{dir} = **1.00**

Season factor; c_{season} = **1.00**

Shape parameter K; K = **0.2**

Exponent n; n = **0.5**

Air density; ρ = **1.226** kg/m^{3}

Probability factor; c_{prob} = [(1 – K × ln(-ln(1-p)))/(1 – K × ln(-ln(0.98)))]^{n} = **1.00**

Basic wind velocity (Exp. 4.1); v_{b} = c_{dir} × c_{season} × v_{b,0} × c_{prob} = **42.0** m/s

Reference mean velocity pressure; q_{b} = 0.5 × ρ × v_{b}^{2} = **1.081** kN/m^{2}

**Orography**

Orography factor not significant; c_{o} = 1.0

Terrain category; Country

Displacement height (sheltering effect excluded); h_{dis} = 0 mm

The velocity pressure for the windward face of the building with a 0 degree wind is to be considered as 1 part as the height h is less than b (cl.7.2.2). The velocity pressure for the windward face of the building with a 90 degree wind is to be considered as 1 part as the height h is less than b (cl.7.2.2)

**Peak velocity pressure – windward wall – Wind 0 deg and roof**

Reference height (at which *q* is sought); z = **6000** mm

Displacement height (sheltering effects excluded); h_{dis} = **0** mm

Exposure factor (Figure NA.7); c_{e} = **2.05**

Peak velocity pressure; q_{p} = c_{e} × q_{b} = **2.22** kN/m^{2}

**Structural factor**

Structural damping; δ_{s} = **0.100**

Height of element; h_{part} = **6000** mm

Size factor (Table NA.3); c_{s} = **0.884**

Dynamic factor (Figure NA.9); c_{d} = **1.003**

Structural factor; c_{sCd} = c_{s} × c_{d} = **0.887**

**Peak velocity pressure – windward wall – Wind 90 deg and roof**

Reference height (at which *q* is sought); z = **8010** mm

Displacement height (sheltering effects excluded); h_{dis} = **0** mm

Exposure factor (Figure NA.7); c_{e} = **2.23**

Peak velocity pressure; q_{p} = c_{e} × q_{b} = **2.41** kN/m^{2}

**Structural factor**

Structural damping; δ_{s} = **0.100**

Height of element; h_{part} = **8010** mm

Size factor (Table NA.3); c_{s} = **0.911**

Dynamic factor (Figure NA.9); c_{d} = **1.016**

Structural factor; c_{sCd} = c_{s} × c_{d} = **0.925**

**Structural factor – roof 0 deg**

Structural damping; δ_{s} = **0.100**

Height of element; h_{part} = **8010** mm

Size factor (Table NA.3); c_{s} = **0.888**

Dynamic factor (Figure NA.9); c_{d} = **1.003**

Structural factor; c_{sCd} = c_{s} × c_{d} = **0.891**

**Peak velocity pressure for internal pressure**

Peak velocity pressure – internal (as roof pressure); q_{p,i} = **2.41** kN/m^{2}

**Pressures and forces**

Net pressure; p = c_{sCd} × q_{p} × c_{pe} – q_{p,i} × c_{pi}

Net force; F_{w} = p_{w} × A_{ref}

**Roof load case 1 – Wind 0, c _{pi} 0.20, -c_{pe}**

Zone | Ext pressure coefficientc _{pe} | Peak velocity pressureq _{p}, (kN/m^{2}) | Net pressurep (kN/m ^{2}) | AreaA _{ref} (m^{2}) | Net forceF _{w} (kN) |

F (-ve) | -1.10 | 2.41 | -2.84 | 13.28 | -37.78 |

G (-ve) | -0.80 | 2.41 | -2.20 | 36.47 | -80.23 |

H (-ve) | -0.40 | 2.41 | -1.34 | 183.18 | -245.64 |

I (-ve) | -0.50 | 2.41 | -1.56 | 183.18 | -284.97 |

J (-ve) | -1.30 | 2.41 | -3.27 | 49.75 | -162.87 |

Total vertical net force; F_{w,v} = **-783.83** kN

Total horizontal net force; F_{w,h} = **21.79** kN

**Walls load case 1 – Wind 0, c _{pi} 0.20, -c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

A | -1.20 | 2.41 | -3.05 | 20.60 | -62.77 |

B | -0.80 | 2.41 | -2.19 | 84.47 | -185.17 |

D | 0.74 | 2.22 | 0.97 | 180.00 | 174.37 |

E | -0.38 | 2.22 | -1.22 | 180.00 | -219.73 |

**Overall loading**

Equivalent leeward net force for overall section; F_{l} = F_{w,wE} = **-219.7** kN

Net windward force for overall section; F_{w} = F_{w,wD} = **174.4** kN

Lack of correlation (cl.7.2.2(3) – Note); f_{corr} = **0.85**; as h/W is 0.534

Overall loading overall section; F_{w,D} = f_{corr} × (F_{w} – F_{l} + F_{w,h}) = **353.5** kN

**Roof load case 2 – Wind 0, c _{pi} -0.3, +c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

F (+ve) | 0.20 | 2.41 | 1.15 | 13.28 | 15.31 |

G (+ve) | 0.20 | 2.41 | 1.15 | 36.47 | 42.03 |

H (+ve) | 0.20 | 2.41 | 1.15 | 183.18 | 211.11 |

I (+ve) | -0.50 | 2.41 | -0.35 | 183.18 | -64.23 |

J (+ve) | -1.30 | 2.41 | -2.07 | 49.75 | -102.91 |

Total vertical net force; F_{w,v} = **97.86** kN

Total horizontal net force; F_{w,h} = **112.74** kN

**Walls load case 2 – Wind 0, c _{pi} -0.3, +c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

A | -1.20 | 2.41 | -1.84 | 20.60 | -37.94 |

B | -0.80 | 2.41 | -0.99 | 84.47 | -83.38 |

D | 0.74 | 2.22 | 2.17 | 180.00 | 391.28 |

E | -0.38 | 2.22 | -0.02 | 180.00 | -2.83 |

**Overall loading**

Equivalent leeward net force for overall section; F_{l} = F_{w,wE} = **-2.8** kN

Net windward force for overall section; F_{w} = F_{w,wD} = **391.3** kN

Lack of correlation (cl.7.2.2(3) – Note); f_{corr} = **0.85**; as h/W is 0.534

Overall loading overall section; F_{w,D} = f_{corr} × (F_{w} – F_{l} + F_{w,h}) = **430.8** kN

**Roof load case 3 – Wind 90, c _{pi} 0.20, -c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

F (-ve) | -1.60 | 2.41 | -4.05 | 11.65 | -47.17 |

G (-ve) | -1.50 | 2.41 | -3.83 | 11.65 | -44.58 |

H (-ve) | -0.60 | 2.41 | -1.82 | 93.17 | -169.59 |

I (-ve) | -0.40 | 2.41 | -1.37 | 349.41 | -480.12 |

Total vertical net force; F_{w,v} = **-716.21** kN

Total horizontal net force; F_{w,h} = **0.00** kN

**Walls load case 3 – Wind 90, c _{pi} 0.20, -c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

A | -1.20 | 2.22 | -2.94 | 18.00 | -52.99 |

B | -0.80 | 2.22 | -2.12 | 72.00 | -152.86 |

C | -0.50 | 2.22 | -1.51 | 90.00 | -135.69 |

D | 0.70 | 2.41 | 1.08 | 105.07 | 113.92 |

E | -0.30 | 2.41 | -1.16 | 105.07 | -122.01 |

**Overall loading**

Equiv leeward net force for overall section; F_{l} = F_{w,wE} = **-122.0** kN

Net windward force for overall section; F_{w} = F_{w,wD} = **113.9** kN

Lack of correlation (cl.7.2.2(3) – Note); f_{corr} = **0.85**; as h/L is 0.267

Overall loading overall section; F_{w,D} = f_{corr} × (F_{w} – F_{l} + F_{w,h}) = **200.5** kN

**Roof load case 4 – Wind 90, c _{pi} -0.3, +c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

F (+ve) | 0.20 | 2.41 | 1.17 | 11.65 | 13.62 |

G (+ve) | 0.20 | 2.41 | 1.17 | 11.65 | 13.62 |

H (+ve) | 0.20 | 2.41 | 1.17 | 93.17 | 108.93 |

I (+ve) | 0.20 | 2.41 | 1.17 | 349.41 | 408.48 |

Total vertical net force; F_{w,v} = **526.08** kN

Total horizontal net force; F_{w,h} = **0.00** kN

**Walls load case 4 – Wind 90, c _{pi} -0.3, +c_{pe}**

Zone | Ext pressure coefficient c _{pe} | Peak velocity pressure q _{p}, (kN/m^{2}) | Net pressure p (kN/m ^{2}) | Area A _{ref} (m^{2}) | Net force F _{w} (kN) |

A | -1.20 | 2.22 | -1.74 | 18.00 | -31.30 |

B | -0.80 | 2.22 | -0.92 | 72.00 | -66.10 |

C | -0.50 | 2.22 | -0.30 | 90.00 | -27.24 |

D | 0.70 | 2.41 | 2.29 | 105.07 | 240.54 |

E | -0.30 | 2.41 | 0.04 | 105.07 | 4.60 |

**Overall loading**

Equiv leeward net force for overall section; F_{l} = F_{w,wE} = **4.6** kN

Net windward force for overall section; F_{w} = F_{w,wD} = **240.5** kN

Lack of correlation (cl.7.2.2(3) – Note); f_{corr} = **0.85**; as h/L is 0.267

Overall loading overall section; F_{w,D} = f_{corr} × (F_{w} – F_{l} + F_{w,h}) = **200.5** kN

**References**

(1) BS EN 1991-1-4: 2005, Actions on structures. General actions. Wind actions

(2) Stanton, T. E., 1908. Experiments on wind pressure. Minutes of the Proceedings of the Institution of Civil Engineers, 171, 175–200.

Sir, do you ever compare the feature of auto lateral wind load on software to the hand calculation? Is the result match?

Hi Jansen, which software do you have in mind? Anyway, it depends on the assumptions made during hand calculation, and the data fed into the software. Otherwise the results should be pretty close.

Sir.

I sincerely appreciate the work you have done so far. My question is, During design is it right to apply wind in both direction (0 degree and 90 degree) at the same time, or it should be applied in direction at a time.

Usually done one direction at a time.