Design example of wind loading on ground photovoltaic system

1. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
WIND LOAD ON SURFACES (WALLS) EC-1-4
Assumptions:
Assume that structural factor cscd is equal to 1 (EN1991-1-4,cl.6.0).1.
Assume that lack of correlation of wind pressure between the windward and leeward side is2.
taken equal to 1 (EN1991-1-4,cl.7.2.2(3)).
Building data
Type of structure: PHOTOVOLTAIC SYSTEM
Total length of strucutre: d 5800mm:=
Width of structure: b 2690mm:=
Height of structure: h 3400mm:=
Spacing frame to frame: ss 2900mm:=
No of frames: No_frames 3:=
Basic values
110

2. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
Fundamental basic wind velocity
(CYS NA EN1991-1-4,fig.1):
vb.o 30m s
1-
:=
Season factor
(EN1991-1-4, NA 2.4/cl.4.2(2)):
cseason 1.0:=
Directional factor
(EN1991-1-4, NA 2.4/cl.4.2(2)):
cdir 1.0:=
Basic wind velocity
(EN1991-1-4,cl.4.2(2)):
vb cdir cseason vb.o 30 m s
1-
=:=
1.25kg m
3-
:=
Density of air:
Reference mean velocity pressure
(EN1991-1-4,cl.4.5(1)):
qb
vb
2
2
 562.5 N m
2-
=:=
Orography
Orography factor
(EN1991-1-4,cl.4.3.3(2):
co 1.0:=
Obstruction height
(EN1991-1-4,Annex A.5):
have 15m:=
Distance to the nearest adjacement
building
(EN1991-1-4,Annex A.5):
x 500m:=
Displacement height
(EN1991-1-4,Annex A.5):
hdis min 0.8 have 0.6h,( ) x 2 haveif
min 1.2 have 0.2 x- 0.6 h,( ) 2 have x< 6 have<if
0 x 6 haveif
0 m=:=
210

3. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
Terrain category
(EN1991-1-4,table 4.1):
Terrain_category "I":=
Roughness length,z0
(EN1991-1-4,table 4.1):
zo 0.003m Terrain_category "0"=if
0.01m Terrain_category "I"=if
0.05m Terrain_category "II"=if
0.3m Terrain_category "III"=if
1.0m Terrain_category "IV"=if
10 mm=:=
Roughness length,zmin
(EN1991-1-4,table 4.1): zmin 1m Terrain_category "0"=if
1m Terrain_category "I"=if
2m Terrain_category "II"=if
5m Terrain_category "III"=if
10m Terrain_category "IV"=if
1 10
3
 mm=:=
Peak wind velocity pressure
Reference height
(EN1991-4,figure 7.4)
ze h 3.4 m=:=
Maximum height
(EN1991-1-4,cl.4.3.2(1)):
zmax 200m:=
Factor, z0,II
(EN1991-4,table 4.1)
z0.II 50mm:=
310

4. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
Terrain factor
(EN1991-1-4,cl.4.3.2(1)):
kr 0.19
zo
z0.II






0.07
 0.17=:=
Roughness factor
(EN1991-1-4,cl.4.3.2(1)):
cr kr ln
zmin
zo






 0.782=:=
Mean wind velocity
(EN1991-1-4,cl.4.3.1(1)):
vm cr co vb 23.453 m s
1-
=:=
Turbulence factor
EN1991-1-4,cl.4.4(1)):
kI 1.0:=
Turbulence intensity
EN1991-1-4,cl.4.4(1)):
Iv
kI
co ln
zmin
zo







0.217=:=
Peak velocity pressure
EN1991-1-4,cl.4.5(1))::
qp 1 7 Iv+( ) 0.5  vm
2
 0.866 kN m
2-
=:=
Structural factor cscd
Assume structural factor is 1
(for buildings with a height less than 15m)
(EN1991-1-4,cl.6.2(1)):
cs.d 1:=
Wind pressure coefficients for canopy roof structure (EN1991-1-4,cl.7.3)
There is no blockage beneath the canopy, however the values of cp.net and cf have been taken
using the ϕ=0 for minimum values and ϕ=all for maximum values.
The overall force coefficient represent the resulting force. The net pressure coefficient represents
the maximum local pressure for all wind directions and have been used in the design of roofing
elements and fixing.
410

5. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
Table 1: cf values for monopitch canopies (EN1991-1-4,Table 7.6)
Wind pressures for modules 30deg
Wind suction φ=0 (max.) - Upward acting wind action
External pressure coefficient for zone A
(EN1991-1-4,Table 7.6):
cp.net.A.up.30 3.0-:=
Wind pressure for zone A
(EN1991-1-4,Eq.5.1)
we.A.up.30 qp cp.net.A.up.30 2.599- kN m
2-
=:=
510

6. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
External pressure coefficient for zone B
(EN1991-1-4,Table 7.6):
cp.net.B.up.30 3.8-:=
Wind pressure for zone B
(EN1991-1-4,Eq.5.1)
we.B.up.30 qp cp.net.B.up.30 3.292- kN m
2-
=:=
Wind suction φ=0 (max.) - Downward acting wind action
External pressure coefficient for zone A
(EN1991-1-4,Table 7.6):
cp.net.A.do.30 2.2:=
Wind pressure for zone A
(EN1991-1-4,Eq.5.1)
we.A.do.30 qp cp.net.A.do.30 1.906 kN m
2-
=:=
External pressure coefficient for zone B
(EN1991-1-4,Table 7.6):
cp.net.B.do.30 3.2:=
Wind pressure for zone B
(EN1991-1-4,Eq.5.1)
we.B.do.30 qp cp.net.B.do.30 2.772 kN m
2-
=:=
Figure 2: Location of the centre of force for monopitch canopies (EN1991-1-4,Figure 7.16)
Effective area between two
supports
Aref.mid b ss 7.801 m
2
=:=
Effective area of edges
supports
Aref.edg
Aref.mid
2
3.9 m
2
=:=
610

7. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
Wind loads for modules 30deg
Overall factor coefficient for
upward acting wind action
(EN1991-1-4,Table 7.6):
cf.up.30 1.8-:=
Overall factor coefficient for
upward acting wind action
(EN1991-1-4,Table 7.6):
cf.do.30 1.2:=
Downward acting wind force
at edge frame
(EN1991-1-4,Eq.5.3)
Fw.ed.do.30 cs.d cf.do.30 qp Aref.edg 4.055 kN=:=
Downward acting wind force
at middle frame
(EN1991-1-4,Eq.5.3)
Fw.mid.do.30 cs.d cf.do.30 qp Aref.mid 8.11 kN=:=
Upward acting wind force
at edge frame
(EN1991-1-4,Eq.5.3)
Fw.ed.up.30 cs.d cf.up.30 qp Aref.edg 6.082- kN=:=
Upward acting wind force
at middle frame
(EN1991-1-4,Eq.5.3)
Fw.mid.up.30 cs.d cf.up.30 qp Aref.mid 12.164- kN=:=
No. 4 Load cases for wind force on structure for inclination of 30deg (edge members)
b
4
0.672 m=
Fw.ed.do.30 4.055 kN= Fw.ed.do.30 4.055 kN= b
4
0.672 m=
Fw.ed.up.30 6.082- kN= Fw.ed.up.30 6.082- kN=
b
4
0.672 m=
b
4
0.672 m=
710

8. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
No. 4 Load cases for wind force on structure for inclination of 30deg (middle members)
b
4
0.672 m=
Fw.mid.do.30 8.11 kN= Fw.mid.do.30 8.11 kN= b
4
0.672 m=
Fw.mid.up.30 12.164- kN= Fw.mid.up.30 12.164- kN=
b
4
0.672 m=
b
4
0.672 m=
Frictional force on structure (EN1991-1-4,cl.7.5)
Frictional force should be considered to the roof canopy structures - see EN1991-1-4,cl.7.3.(7)
Surface type
(EN1991-1-4,Table 7.10):
Surface_type "Very rough":=
Frictional coefficient
(EN1991-1-4,Table 7.10):
cfr 0.01 Surface_type "Smooth"=if
0.02 Surface_type "Rough"=if
0.04 Surface_type "Very rough"=if
0.04=:=
Reference area: Afr 2 ss b 15.602 m
2
=:=
Frictional force per frame
(EN1991-1-4,Eq.5.7):
Ffr cfr qp
Afr
ss
 0.186 kN m
1-
=:=
810

9. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
910

10. WIND LOAD CALCULATION BASE ON EN1991-4PV SYSTEM REV.A
Calculated by:V.N.
Reviewed by: V.N.
1010