# Determination of Wind Loads for Canopy Roof Structures According to EN 1991-1-4

### Technical Article

#### Determination of Coefficients

To determine the load, the force coefficients c_{f} and the entire pressure coefficients c_{p,net }according to Table 7.6 to 7.8 should be used. If there is an obstruction below or immediately next to the roof (for example stored goods), the degree of the obstruction has to be determined and interpolated in the tables between ϕ = 0 (unobstructed) and ϕ = 1 (totally obstructed).

To determine the resulting entire pressure coefficient, a classification of surfaces is performed similiar to that of closed buildings. This applies only to the design of the roof covering and its anchorage elements.

Figure 01 - Classification of Surfaces Total Pressure Coefficients

#### Position and Form of the Resulting Wind Power

To design the supporting structure, it is necessary to apply the resulting wind power in the distance of d/4 of the windward side. d is the dimension for the roof surface downwind. The graphic 7.17 displays six possible load arrangements depending on the sign of the force coefficient.

Figure 02 - Load Arrangement of Resulting Wind Force

Since the wind load is acting as surface load and not as nodal load on the roof covering, and its centroid position amounts to 1/4 of the roof length, it is necessary to find an appropriate load situation which considers this. Such an eccentric load arrangement leads to a highly loaded stability analysis of possible central supports. A possible load arrangement would be a surface load in the shape of a square parabola because its center of gravity is situated in 1/4 of the length.

#### Example Troughed Roof

Length = 15 m

Width = 12 m

Height of valley = 6 m

Roof inclination = -5 °

Wind load = 0.5 kN/m²

No obstruction → ϕ = 0

c_{f} = +0.3 maximum all ϕ

c_{f} = -0.5 minimum ϕ = 0

#### Resulting Wind Force

RFEM and RSTAB contain the load generators for enclosed buildings with rectangular ground plan. It can be selected if the load is applied only to the walls, the roof or the entire building.

Supporting structures for canopy roofs cannot be calculated automatically. However, the load generator with levels can be used after having determined the coefficients.

Wind pressure:

${\mathrm F}_{\mathrm w,\max}\;=\;{\mathrm c}_\mathrm f\;\cdot\;{\mathrm q}_\mathrm h(\mathrm{ze})\;\cdot\;{\mathrm A}_\mathrm{ref}\;=\;0.3\;\cdot\;0.5\;\cdot\;\frac{15\;\cdot\;12}{\cos\;5^\circ}\;=\;27.10\;\mathrm{kN}$

Wind suction:

${\mathrm F}_{\mathrm w,\min}\;=\;{\mathrm c}_\mathrm f\;\cdot\;{\mathrm q}_\mathrm h(\mathrm{ze})\;\cdot\;{\mathrm A}_\mathrm{ref}\;=\;-0.5\;\cdot\;0.5\;\cdot\;\frac{15\;\cdot\;12}{\cos\;5^\circ}\;=\;-45.17\;\mathrm{kN}$

Friction forces according to Section 7.5 are not considered in this example.

#### Largest Load Ordinates of the Parabolic Load

Attention is only paid to load positions 2 and 5. Load positions 3 and 6 are not necessary due to the symmetry.

$\begin{array}{l}\mathrm q(\mathrm{Pressure})\;=\;\frac{27.1}{\left({\displaystyle\frac{12}3}\right)}\;=\;6.775\;\mathrm{kN}/\mathrm m\;=\;0.45\;\mathrm{kN}/\mathrm m²\\\mathrm q(\mathrm{Suction})\;=\;\frac{-45.17}{\left({\displaystyle\frac{12}3}\right)}\;=\;-11.293\;\mathrm{kN}/\mathrm m\;=\;-0.75\;\mathrm{kN}/\mathrm m²\end{array}$

With these load ordinates and by using this quadratic equation, if necessary in Excel, the variable load values per x-location can be determined and exported to RFEM or RSTAB.

#### Keywords

en 1991-1-4 canopy roof wind load

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