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Mon Jun 13 2022
Eurocode 1
Wind load on signboards (force coefficient)
Description:
Calculation of wind load action effects on signboards with rectangular surface area. The total horizontal force,
horizontal eccentricity, and base overturning moment are calculated from the force coefficient corresponding to
the overall effect of the wind action on the structure
According to:
EN 1991-1-4:2005+A1:2010 Section 7.4.3
Supported National
Annexes:
Only countries that adopt CEN recommended values for section 7.4.3 of EN1991-1-4 are supported. The value of
the peak velocity pressure can be specified manually. Otherwise automatic calculation of peak velocity pressure is
supported, in addition to countries that adopt the CEN recommended values for NDPs, also for the following
National Annexes: Finland, Portugal. The National Annexes of Germamy, Norway, Spain, Sweden, Switzerland are
NOT supported (enter peak velocity pressure manually).
Input
=
II
vb =
20
m/s
Width of the signboard wind loaded area
b=
6
m
Height of the signboard wind loaded area
h=
1.86
m
Separation height of the signboard wind
loaded area from the ground
zg =
5.17
m
Terrain category
Basic wind velocity
Notation for wind load on signboards (see also EN1991-1-4 Figure 7.21)
Orography factor at reference height ze
Structural factor
c0(ze) =
1
cscd =
1
Nationally Defined Parameters
Air density
ρ=
1.25
kg/m3
Results
Effective wind pressure
Total wind horizontal force
Total wind overturning moment at base
Horizontal eccentricity of the resultant wind
force
weff = 0.921 kN/m2
Fw = 10.281 kN
Mw = 62.71 kNm
e = ±0.25b = ±1.50 m
Notes
1. The calculated effective wind pressure weff, total wind force FW, and total wind overturning moment MW
correspond to the total wind action effects and they are appropriate for global verifications of the element
according to the force coefficient method. For local verifications appropriate wind pressure on local
surfaces must be estimated according to the relevant external pressure coefficients, as specified in
EN1991-1-4 §5.2.
2. The calculated wind action effects are characteristic values (unfactored). Appropriate load factors should
be applied for the relevant design situation. For ULS verifications the partial load factor γQ = 1.50 is
applicable for variable actions.
Details
Input Data
Terrain category: = II
Basic wind velocity: vb = 20 m/s
Width of the signboard wind loaded area: b = 6 m
Height of the signboard wind loaded area: h = 1.86 m
Separation height of the signboard wind loaded area from the ground: zg = 5.17 m
Orography factor at reference height ze: c0(ze) = 1
Structural factor: cscd = 1
Nationally Defined Parameters
Air density: ρ = 1.25 kg/m3
Calculation of peak velocity pressure
Reference area and height
The reference height for the wind action ze is located at the center of the signboard, as specified in EN1991-1-4
§7.4.3(3). The reference area for the wind action Aref is the wind loaded area of the signboard, as specified in
EN1991-1-4 §7.4.3(3). Therefore:
ze = zg + h / 2 = 5.170 m + 1.860 m / 2 = 6.100 m
Aref = b ⋅ h = 6.000 m ⋅ 1.860 m = 11.16 m2
Basic wind velocity
The basic wind velocity vb is defined in EN1991-1-4 §4.2(2)P as a function of the wind direction and time of year at
10 m above ground of terrain category II. The value of vb includes the effects of the directional factor cdir and the
seasonal factor cseason and it is provided in the National Annex. In the following calculations the basic wind
velocity is considered as vb = 20.00 m/s.
Terrain roughness
The roughness length z0 and the minimum height zmin are specified in EN1991-1-4 Table 4.1 as a function of the
terrain category. For terrain category II the corresponding values are z0 = 0.050 m and zmin = 2.0 m.
The terrain factor kr depending on the roughness length z0 = 0.050 m is calculated in accordance with EN1991-14 equation (4.5):
kr = 0.19 ⋅ (z0 / z0,II)0.07 = 0.19 ⋅ (0.050 m / 0.050 m)0.07 = 0.1900
The roughness factor cr(ze) at the reference height ze accounts for the variability of the mean wind velocity at the
site. It is calculated in accordance with EN1991-1-4 equation 4.4. For the examined case ze ≥ zmin:
cr(ze) = kr ⋅ ln(max{ze, zmin} / z0) = 0.1900 ⋅ ln(max{6.100 m, 2.0 m} / 0.050 m) = 0.9128
Orography factor
Where orography (e.g. hills, cliffs etc.) is significant its effect in the wind velocities should be taken into account
using an orography factor c0(ze) different than 1.0, as specified in EN1994-1-1 §4.3.3. The recommended
procedure in EN1994-1-1 §4.3.3 for calculation of the orography factor c0(ze) is described in EN1994-1-1 §A.3.
In the following calculations the orography factor is considered as c0(ze) = 1.000.
Mean wind velocity
The mean wind velocity vm(ze) at reference height ze depends on the terrain roughness, terrain orography and
the basic wind velocity vb. It is determined using EN1991-1-4 equation (4.3):
vm(ze) = cr(ze) ⋅ c0(ze) ⋅ vb = 0.9128 ⋅ 1.000 ⋅ 20.00 m/s = 18.26 m/s
Wind turbulence
The turbulence intensity Iv(ze) at reference height ze is defined as the standard deviation of the turbulence
divided by the mean wind velocity. It is calculated in accordance with EN1991-1-4 equation 4.7. For the examined
case ze ≥ zmin.
Iv(ze) = kI / [ c0(ze) ⋅ ln(max{ze, zmin} / z0) ] = 1.000 / [ 1.000 ⋅ ln(max{6.100 m, 2.0 m} / 0.050 m) ] = 0.2082
Basic velocity pressure
The basic velocity pressure qb is the pressure corresponding to the wind momentum determined at the basic
wind velocity vb. The basic velocity pressure is calculated according to the fundamental relation specified in
EN1991-14 §4.5(1):
qb = (1/2) ⋅ ρ ⋅ vb2 = (1/2) ⋅ 1.25 kg/m3 ⋅ (20.00 m/s)2 = 0.250 kN/m2
where ρ is the density of the air in accordance with EN1991-1-4 §4.5(1). In this calculation the following value is
considered: ρ = 1.25 kg/m3.
Peak velocity pressure
The peak velocity pressure qp(ze) at reference height ze includes mean and short-term velocity fluctuations. It is
determined according to EN1991-1-4 equation 4.8:
qp(ze) = (1 + 7⋅Iv(ze)) ⋅ (1/2) ⋅ ρ ⋅ vm(ze)2 = (1 + 7⋅0.2082) ⋅ (1/2) ⋅ 1.25 kg/m3 ⋅ (18.26 m/s)2
⇒ qp(ze) = 0.512 kN/m2
Calculation of wind forces on the structure
Structural factor
The structural factor cscd is determined in accordance with EN1991-1-4 Section 6. A value of cscd = 1.0 is generally
conservative for small structures not-susceptible to wind turbulence effects. In the following calculations the
structural factor is considered as cscd = 1.000.
Force coefficient
The force coefficient cf is given in EN1991-1-4 Sections 7 and 8 depending on the type of structure or structural
element. According to EN1991-1-4 §7.4.3, for signboards with zg ≥ h / 4 or b / h ≤ 1, the force coefficient is cf =
1.800.
Total wind force
The wind force on the structure Fw for the overall wind effect is estimated according to the force coefficient
method as specified in EN1991-1-4 §5.3.
Fw = cscd ⋅ cf ⋅ qp(ze) ⋅ Aref = 1.000 ⋅ 1.800 ⋅ 0.512 kN/m2 ⋅ 11.16 m2 = 10.281 kN
The total wind force Fw takes into account the overall wind effect. The corresponding effective wind pressure
weff on the reference wind area Aref is equal to:
weff = Fw / Aref = 10.281 kN / 11.16 m2 = 0.921 kN/m2
This effective pressure weff = 0.921 kN/m2 is appropriate for global verifications of the structure according to the
force coefficient method. It is not appropriate for local verifications of structural elements. For the latter case
appropriate wind pressure on local surfaces must be estimated according to the relevant pressure coefficients,
as specified in EN1991-1-4 §5.2.
Overturning moment
According to EN1991-1-4 §7.4.3 the resultant force normal to the signboard should be taken to act at the height
of the center of the signboard. The total overturning moment Mw acting at the base of the structure is equal to:
Mw = Fw ⋅ (zg + h / 2) = 10.281 kN ⋅ (5.170 m + 1.860 m / 2) = 62.71 kNm
The overturning moment corresponds to the wind action total effect, i.e. it is the total overturning moment for
all the base supports.
Horizontal eccentricity
According to EN1991-1-4 §7.4.3 the resultant force normal to the signboard should be taken to act with a
horizontal eccentricity e = ±0.25b, where b is the width of the signboard wind loaded area. The total torsional
moment Tw acting at the base of the structure is equal to:
Tw = ±0.25 ⋅ b ⋅ Fw = ±0.25 ⋅ 6.000 m ⋅ 10.281 kN = 15.42 kNm
The torsional moment corresponds to the wind action total effect, i.e. it is the total torsional moment for all the
base supports.
Additional notes
The calculated wind action effects are characteristic values (unfactored). Appropriate load factors should
be applied for the relevant design situation. For ULS verifications the partial load factor γQ = 1.50 is
applicable for variable actions according to EN1990.
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