# Loading According to EN 1991-1-4 and Safety Against Overturning of Circular Cylinders

### Technical Article

This article describes the determination of force coefficients by using a wind load and the calculation of a stability factor due to overturning.

Tilt safety factor <1: There is a risk of the component tipping over.

Tilt safety factor = 1: Stiffness moment and stall moment are equal. The model is unstable and it cannot be excluded that it tilts.

Tilt safety factor> 1: The model is not at risk of tipping over.

#### Example

The circular cylinder in the example has a diameter of 2.5 m and a height of 6 m. The site is located in wind load zone 2 with terrain category 3.

Basic value of the basic velocity:

v _{b0} = 25.0 m/s

Direction factor:

c _{dir} = 1

Season coefficient:

c _{season} = 1

Density of air at 1,013 hPa air pressure and T = 10 ° C:

ρ = 1.25 kg/m³

Kinematic Toughness of Air:

ν = 15 ∙ 10 ^{-6}

Base velocity:

v _{b} = c _{dir} ∙ c _{season} ∙ v _{b0} = 25.0 m/s

Basic Velocity Pressure:

q _{b} = 1/2 ∙ ρ ∙ v _{b} ^{2} = 0.391 kN/m²

Peak velocity pressure:

q _{p} = 1.5 ∙ q _{b} = 0.586 kN/m²

Gust velocity:

$${\mathrm v}_\mathrm{ze}\;=\;\sqrt{\frac{2\;\cdot\;{\mathrm q}_\mathrm p}{\mathrm\rho}}\;=\;30,619\;\mathrm m/\mathrm s$$

Equivalent roughness:

k = 0.2 mm (galvanized steel)

Ratio of equivalent roughness and width:

k/b = 8 ∙ 10 ^{-5}

Reynolds Number:

$${\mathrm R}_\mathrm e\;=\;\frac{\mathrm b\;\cdot\;{\mathrm v}_\mathrm{ze}}{\mathrm v}\;=\;5,1\;\cdot\;10^6$$

Basic force coefficient of a cylinder with infinite slenderness:

$${\mathrm c}_{\mathrm f0}\;=\;1,2\;+\;\frac{0,18\;\cdot\;\log\;({\displaystyle\frac{10\;\cdot\;\mathrm k}{\mathrm b}})}{1\;+\;0,4\;\cdot\;\log\;({\displaystyle\frac{{\mathrm R}_\mathrm e}{10^6}})}\;=\;0,7666$$

Effective slenderness:

λ = l/b = 2.4

Reduction factor:

ψ _{λ} = 0.65

Structure coefficient:

c _{s} c _{d} = 1

Reference surface:

A _{ref} = l ∙ b = 15 m²

Force coefficient:

c _{f} = c _{f0} ∙ ψ _{λ} = 0.498

Wind power:

F _{w} = c _{s} c _{d} ∙ c _{f} ∙ q _{p} ∙ A _{ref} = 4.377 kN

Area load from wind:

F _{w} = F _{w}/A _{ref} = 0.29 kN/m²

**Stability factor due to tilting**

Height of circular cylinder:

h = 6 m

Distance of supports:

a = 1.35 m

Self-weight:

F _{G} = 18.495 kN

Tilting moment:

M _{K} = F _{w} ∙ h/2 = 13.13 kNm

Stiffness moment:

M _{S} = F _{G} ∙ a/2 = 12.48 kNm

Tipping safety factor:

η = M _{S}/M _{K} = 0.95

When calculating by means of RFEM, the position of the resultant results in an extension that lies behind the tilting edge of the circular cylinder. The model would therefore be unstable if the supports are not additionally secured against pulling out.

Figure 02 - Resultant Position

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