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Date: 29-01-2022
Eurocode 1
Wind load on circular cylinders (force coefficient)
Description:
Calculation of wind load action effects on circular cylinder elements. The total horizontal wind force is calculated from
the force coefficient corresponding to the overall effect of the wind action on the cylindrical structure or cylindrical
isolated element
According to:
EN 1991-1-4:2005+A1:2010 Section 7.9.2
Applicable for:
Cylindrical structures, isolated cylindrical elements
Supported National
Annexes:
Only countries that adopt CEN recommended values for sections 7.9.2 and 7.13 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
Terrain category = II
Illustration of Terrain categories reproduced from EN1991-1-4 Annex A
Basic wind velocity vb = 30.2 m/s
Diameter of the cylindrical element b= 1.9 m
Length of the cylindrical element l= 2 m
Maximum height above ground of the z= 5.5 m
cylindrical element
Surface type = smooth concrete
Orography factor at reference height ze c0(ze) = 1
Structural factor cscd = 1
Nationally Defined Parameters
Air density ρ= 1.25 kg/m3
Results
Effective wind pressure weff = 0.535 kN/m2
Total wind horizontal force Fw = 2.034 kN
Notes
1. The calculated effective wind pressure weff and total wind force FW correspond to the total wind action effects
and they are appropriate for global verifications of the structure according to the force coefficient method. For
local verifications, such as verification of the cylinder's shell, appropriate wind pressure on local surfaces must
be estimated according to the relevant external pressure coefficients, as specified in EN1991-1-4 §7.9.1.
2. For cylinders near a plane surface with a distance ratio zg/b < 1.5 special advice is necessary. See EN1991-1-4
§7.9.2(6) for more details.
3. For a set of cylinders arranged in a row with normalized center-to-center distance zg/b < 30 the wind force of
each cylinder in the arrangement is larger than the force of the cylinder considered as isolated. See EN1991-1-4
§7.9.3 for more details.
4. 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 = 30.2 m/s
Diameter of the cylindrical element: b = 1.9 m
Length of the cylindrical element: l = 2 m
Maximum height above ground of the cylindrical element: z = 5.5 m
Surface type: = smooth concrete
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 equal to the maximum height above ground of the section being
considered, as specified in EN1991-1-4 §7.9.2(5). The reference area for the wind action Aref is the projected area of
the cylinder, as specified in EN1991-1-4 §7.9.2(4). Therefore:
ze = z = 5.500 m
Aref = b ⋅ l = 1.900 m ⋅ 2.000 m = 3.80 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. It is calculated as:
vb = cdir⋅cseason⋅vb,0
where vb,0 is the fundamental value of the basic wind velocity which is defined in EN1991-1-4 §4.2(1)P as the
characteristic 10 minutes mean wind velocity at 10 m above ground level for terrain category II. The value of vb,0 is
provided in the National Annex based on the climatic conditions of the region where the structure is located. The
influence of altitude on the basic wind velocity vb may also be specified in the National Annex.
The directional factor cdir and the seasonal factor cseason are defined in EN1991-1-4 §4.2(2)P and they take into
account the effects of wind direction and time of the year. Their values are generally equal to cdir = 1.0 and cseason =
1.0. The National Annex may specify values of cdir and cseason different than 1.0.
In the following calculations the basic wind velocity is considered as vb = 30.20 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 EN1991-1-4
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
of the structure due to the height above ground level and the ground roughness of the terrain upwind of the structure.
It is calculated in accordance with EN1991-1-4 equation 4.4.
For the case where ze ≥ zmin:
cr(ze) = kr ⋅ ln(ze / z0) = 0.1900 ⋅ ln(5.500 m / 0.050 m) = 0.8931
Orography factor
Where orography (e.g. hills, cliffs etc.) increases wind velocities by more than 5% the effects should be taken into
account using an orography factor c0(ze) different than 1.0, as specified in EN1994-1-1 §4.3.3. In general the effects of
orography may be neglected when the average slope of the upwind terrain is less than 3° up to a distance of 10 times
the height of the isolated orographic feature. 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 = 0.8931 ⋅ 1.000 ⋅ 30.20 m/s = 26.97 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 case where ze ≥ zmin:
Iv(ze) = kI / [ c0(ze) ⋅ ln(ze / z0) ] = 1.000 / [ 1.000 ⋅ ln(5.500 m / 0.050 m) ] = 0.2127
where the turbulence factor is considered as kI = 1.000 in accordance with EN1991-1-4 §4.4(1).
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 following fundamental relation, as specified in
EN1991-14 §4.5(1):
qb = (1/2) ⋅ ρ ⋅ vb2 = (1/2) ⋅ 1.25 kg/m3 ⋅ (30.20 m/s)2 = 0.570 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⋅0.2127) ⋅ (1/2) ⋅ 1.25 kg/m3 ⋅ (26.97 m/s)2
⇒ qp(ze) = 1.132 kN/m2
where the density of the air is considered as ρ = 1.25 kg/m3 in accordance with EN1991-1-4 §4.5(1).
The calculated value of qp(ze) corresponds to an exposure factor ce(ze):
ce(ze) = qp(ze) / qb = 1.132 kN/m2 / 0.570 kN/m2 = 1.9854
Therefore the peak velocity pressure is calculated as qp(ze) = 1.132 kN/m2.
Wind velocity corresponding to peak velocity pressure
The peak wind velocity v(ze) at reference height ze is the wind velocity corresponding to the peak velocity pressure
qp(ze). It is calculated according to the following fundamental relation, as specified in EN1991-14 §4.5(1):
v(ze) = [2 ⋅ qp(ze) / ρ ]0.5 = [2 ⋅ 1.132 kN/m2 / 1.25 kg/m3 ]0.5 = 42.55 m/s
where ρ = 1.25 kg/m3 is the density of the air as mentioned above.
Calculation of wind forces on the structure
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
Structural factor
The structural factor cscd takes into account the structure size effects from the non-simultaneous occurrence of peak
wind pressures on the surface and the dynamic effects of structural vibrations due to turbulence. 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 such as buildings with height less than 15 m or chimneys with
circular cross-sections whose height is less than 60 m and 6.5 times the diameter.
In the following calculations the structural factor is considered as cscd = 1.000.
Reynolds number
Reynolds number characterizes the air flow around the object. For air flow around cylindrical objects Reynolds number
is calculated according to EN1991-1-4 §7.9.1(1):
Re = b ⋅ v(ze) / ν = 1.900 m ⋅ 42.55 m/s / 15.0 ×10-6 m2/s = 5.3901 ×106
where the kinematic viscosity of the air is considered as ν = 15.0 ×10-6 m2/s in accordance with EN1991-1-4 §7.9.1(1).
Effective slenderness
The effective slenderness λ depends on the aspect ratio and the position of the structure and it is given in EN1991-1-4
§7.13(2).
For circular cylinders with length l ≤ 15 m the effective slenderness λ is equal to:
λ15 = min(l / b, 70) = min(2.000 m / 1.900 m, 70) = 1.053
Therefore λ = λ15 = 1.053
End effect factor
The end effect factor ψλ takes into account the reduced resistance of the structure due to the wind flow around the end
(end-effect). The value of ψλ is calculated in accordance with EN1991-1-4 §7.13 . For solid structures (i.e. solidity ratio
φ = 1.000) the value of the end effect factor ψλ is determined from EN1991-1-4 Figure 7.36 as a function of the
slenderness λ.
The estimated value for the end effect factor is ψλ = 0.602
Equivalent surface roughness
The equivalent surface roughness k depends on the surface type and it is given in EN1991-1-4 §7.9.2(2). According to
EN1991-1-4 Table 7.13 for surface type "smooth concrete" the corresponding equivalent surface roughness is k =
0.2000 mm.
Force coefficient without free-end flow
For circular cylinders the force coefficient without free-end flow cf,0 depends on the Reynolds number Re and the
normalized equivalent surface roughness k/b. The force coefficient without free-end flow cf,0 is specified in EN1991-1-
4 §7.9.2. The value cf,0 is determined according to EN1991-1-4 Figure 7.28 for the values of Re = 5.3901 ×106, k =
0.2000 mm, b = 1.900 m, k/b = 0.000105.
The estimated value for the force coefficient without free-end flow is cf,0 = 0.785
Force coefficient
The force coefficient cf for finite cylinders is given in EN1991-1-4 §7.9.2(1) as:
cf = cf,0 ⋅ ψλ
where cf,0 is the force coefficient without free-end flow, and ψλ the end effect factor, as calculated above. Therefore:
cf = cf,0 ⋅ ψλ = 0.785 ⋅ 0.602 = 0.473
Total wind force
The total wind force on the structure Fw is estimated as:.
Fw = cscd ⋅ cf ⋅ qp(ze) ⋅ Aref = 1.000 ⋅ 0.473 ⋅ 1.132 kN/m2 ⋅ 3.80 m2 = 2.034 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 = 2.034 kN / 3.80 m2 = 0.535 kN/m2
Additional notes
The effective pressure weff = 0.535 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, such as the shell of
the cylinder. For the latter case appropriate wind pressure on local surfaces must be estimated according to the
relevant external pressure coefficients, as specified in EN1991-1-4 §7.9.1.
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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