Detailed design procedure for solar panel mounting structure with dual axis tracking capability for Sub urban West Bengal(Wind load calculation have been done for this region only).

1. 1
Design of a solar dual axis tracker module mounting
structure capable of surviving wind load on rooftops
of sub urban West Bengal
Introduction
As global temperature increases and the increasing levels of fossil fuel emissions in the environment, the
energy sector is taking drastic steps to make a transition from the fossil fuels era to the sustainable energy
era.Many developing nations have taken a drastic steps to increase their electric energy generation from
renewable sources,like solar ,wind ,hydro , wave and tidal power. In many developing countries like
India and China, solar energy accounts for a large chunk of electricity generated from renewable sources.
One technology that can boost energy generation from solar energy is dual axis solar tracking systems
that can change the orientation of an array of solar panels so that they are aligned directly towards the sun
through out the day, hence ensuring the solar panels are better exposed to incident sun radiation.
Dual axis tracking systems typically consists of an optical sensor,micro controller and geared motor and
bearings and actuators. The idea of the dual axis solar tracking system is to increase electric power
generation from solar energy farms by keeping solar panels aligned towards the sun through the length of
the generation period. The dual axis solar tracking system can increase power generation by almost 40%
from a latitude tilted fixed solar panel array of same capacity. Array sizes for solar dual axis trackers tend
to be larger as the tracking system is costly. For this the structure supporting the array for a dual axis
tracker must be made so that it may support the weight of the array and wind loads. As a result structures
having tracking capability tend to be more robust, which means costs increase as well as the weight.
However it has been found that the expenses are heavily tilted in favor of using tracking systems. The
extra cost of purchasing tracking systems can be recovered within 4-5 years from the extra generation
resulting from running a tracking system.
Objective
The objective of this study is to determine the correct shape and dimension of structural members for a
solar dual axis tracker PV module mounting structure that can withstand high wind velocities ~ 160-
180kmph.
Analysis and assumptions
Load on a solar dual axis tracker can be divided into two types: Dead load and Wind load.
Dead load is that load which acts on the structure when there is no wind. Hence,it consists of weight of
solar panels and structural members. It acts vertically downward at all times.
Wind load is load on solar structure that acts when wind blows at high velocities and puts pressure on the
solar PV array as a result of that.

2. 2
In our analysis we have:
1. Only hollow tube sections have been chosen for use as structural member.
2. Solar module mounting structure has to support load for solar photo voltaic array with generating
capacity of 5kWp.
3. Generating capacity of each solar PV panel is 315Wp. Number of panels = 16.
4. Dimension of each solar panel = 2m * 1m.
5. Weight of solar panel = 26kg.
6. Estimated life of structure = 25 years.
7. Estimated height of building on which PV module will be installed = 20m (Class A).
8. The steel used for this structure has been assumed to be mild steel (Yst = 250MPa and E = 300GPa).
9. Factor of safety has been assumed to be 1.5.
10. The factor of safety for this application has been assumed to be 1.5 that is for mild steel
(Yst=250MPa) permissible design stress in longitudinal direction is 165MPa. However some tolerance is
provided, because such high winds are a rare occurrence which is around +15MPa. Therefore in some
places stresses as high as 175-180MPa have been deemed safe.
11. For designing base plate and anchor bolts, physical properties of concrete such as cube strength (σcu)
and binding strength (σb) have been taken as 2.1N/mm2
and 0.6N/mm2
.
Methodology
1. Wind force is calculated in the horizontal direction and weight of structure is calculated in the
vertically downward direction.
2. Moments of wind forces are calculated and checked whether stress generated is within
permissible limit considering bending about major axis .
3. Moments of forces due to weight of structural components and panels are calculated and stresses
developed are checked with permissible stress values considering bending about minor axis.
4. In all cases the design criteria or the maximum stresses in structural member is produced when
array is vertical.
Diagrams

3. 3
Figure 1
Figure 2

4. 4
Figure 3
Conditions under wind load:
Figure 4

5. 5
Figure 5
Direction of forces due to wind load and structural weight
(dead load)

6. 6
Figure 6
Calculations
Calculation of design wind speed:
Design wind speed Vd = k1.k2.k3.Vb,where k1 = risk coefficient for different classes of structure, k2=
terrain factor for difference in design height and terrain type and k3=topography factor.
Vb = basic wind speed which for eastern coastalregions of India = 50m/s.
K1 = 0.9 for estimated life of structure = 25 years.
K2 = 1.12 for terrain category 1 and building class A.
K3 = 1 considering upwind slope at site lesser than 3˚.
Vd = 50.4 m/s.
Calculation of design wind pressure:
Design wind pressure (pd) = 0.6Vz
2
= 0.6*(50.4)2
= 0.6*2540.16 = 1524.096n/m2
= 155.36 kg/m2
~150kg/m2.

7. 7
Design of structure member type 1
Dead load moment on square hollow section
Weight of each solar panel = 26 kg
Area of each solar panel = 1 * 2 m2
= 2m2
Weight of solar panel per unit area = 13kg/m2
Considering one square hollow section to support 4 half solar panels,
We calculate the U.D.L. of the solar panels = 13 kg/m2
* 0.5 m = 6.5 kg/m
As shown in the figure the square hollow section is subjected to dead weight consisting of panel load and
its own self weight.
Self weight of square hollow section will be varying with the dimensions of square hollow section we
choose.
2. For SHS 32.0 *32.0 * 2.6, self weight = 2.26kg/m and Zx = Zy = 2.51cm3
.
Design against dead load:
Total dead load U.D.L acting on member = (6.5+2.26)kg/m = 8.76kg/m.
Figure 7
Maximum value of bending moment acting on member about minor axis = (8.76 * 1 *0.5) kg-m = 4.38
kg-m = 43 N-m.
Maximum stress induced in the member = 17.11 N/mm2
.

8. 8
Figure 8
Design against wind load:
Wind pressure acting on array = 150kg/m2
.
Figure 9
Considering wind force to be uniformly distributed over whole length of a member, U.D.L. for wind load
acting on structure member 1 = 150 kg/m2
*0.5m = 75 kg/m.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
-60
-40
-20
20
40
60
x
y
B.M.D. of structure member 1 about horizontal axis due to dead load

9. 9
Figure 10
Maximum value of bending moment acting on member = 367.875 N-m.
Maximum value of stress induced in member about major axis = (367.875/2.51) N/mm2
= 146.56 N/mm2
.
Figure 11
As both the stresses are within the 165N/mm2
permissible limit we may safely use SHS 32.0 *32.0 * 2.6
as a type 1 structural member as shown in the figure.
Design of structure member type 2
For the next section, let us see the diagram. It clearly shows that the structural members at the edges will
have higher forces acting on it than the members along the center.
We find that concentrated loads act on the member due to loading of SHS members that it supports.
For this member we selected rectangular hollow section, and try to find a section with the correct Zx value
for supporting wind load and Zy value for supporting dead load.
f(x)=(-75*(x^2)/2)*9.81
f(x)=((-75*(x^2)/2)+(168.75*(x-1)))*9.81
f(x)=((-75*(x^2)/2)+(168.75*(x-1))+(131.25*(x-3)))*9.81
f(x)=((-75*(x^2)/2)+(168.75*(x-1))+(131.25*(x-3))+(131.25*(x-5)))*9.81
f(x)=((-75*(x^2)/2)+(168.75*(x-1))+(131.25*(x-3))+(131.25*(x-5))+(168.75*(x-7)))*9.81
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
-300
-200
-100
100
200
300
400
x
y
B.M.D. of structure member 1 about vertical axis due to wind load

10. 10
1. For rectangular hollow section 122.0 * 61.0 *3.6, w = 9.67 kg/m ,Ixx = 232.66 cm4
, Zx =
38.13cm3
.
Design against dead load:
As the array is vertical and the dead load forces are acting vertically along the same line, there are no
moments caused by dead load forces.
The reactions will be different for 2 members that are at outer location from 2 members that are at inner
locations.
Figure 12

11. 11
Figure 13
Figure 5 shows the forces and reactions for structure member 2 at outer location and Figure 6 shows the
same for structure member 2 at inner location.
Design against wind load
As the forces are higher for member at outer location, we shall carry the analysis for that single member
only.

12. 12
Figure 14
Since the member is in cantilever, the maximum stress will occur at the center and will be the sum of
moments of all forces to one side of and about that point.
Moment acting at the center of the member = [{(168.75*2)+(337.5*1)}*9.81] = 6621.75 N-m.
Figure 15
Stress developed at the center of the member = M/zx =6621.75/38.13 = 173.66N/mm2
.
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
-6500
-6000
-5500
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
x
y
B.M.D. of structure member 2 at outer most location due to wind load

13. 13
Deflection of member at free end = (Ml2
/2EI) = (6621.75*(200)2
)/(2*300000*232.61) = 1.89cm.
For the inner members the free body diagram and bending moment diagram are shown below.
Figure 16
Figure 17
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
-5500
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
x
y
B.M.D. of structure member 2 at inner location due to wind load

14. 14
As can be seen from figure 17 the maximum bending moment acting on structure member 2 at inner
location is smaller compared to that at the outer location.
Hence,RHS 122.0 * 61.0 *3.6, may be safely used as structural member type 2.
Design of structural member type 3
For CHS 273.0*250.0*6.0, w= 39.51 kg/m, I=4487.08 cm4
, Z=328.72 cm3
.
Design against dead load
Figure 18
Maximum moment acting on structure member 3 due to dead load = [{(196.36*3) +
(161.32*1)}+(39.51*3*1.5)]*9.81 = 9101.18 N-m.
Figure 19
f(x)=((-39.41*(x^2)/2)+(-196.36*x))*9.81
f(x)=((-39.41*(x^2)/2)+(-196.36*x)+(-161.32*(x-2))
f(x)=((-39.41*(x^2)/2)+(-196.36*x)+(-161.32*(x-2))
f(x)=((-39.41*(x^2)/2)+(-196.36*x)+(-161.32*(x-2))
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
-10000
-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
1000
x
y
B.M.D. of structure member 3 due to dead load

15. 15
Maximum stress induced due to dead load = (9101.18/328.72) N/mm2
= 27.69 N/mm2
.
Design against wind load
Figure 20
Maximum moment due to wind load = [{(1350*3)+(1050*1)}*9.81] = 50031 N-m.
Figure 21
Maximum stress induced sue to wind load = (50031/328.72) N/mm2
= 152.20 N/mm2
.
Deflection of member at free end = Ml2
/2EI = (50031*3002
)/(2*300000*4487.08)cm = 1.12 cm.
f(x)=(-1350*x)*9.81
f(x)=((-1350*x)+(-1050*(x-2)))*9.81
f(x)=((-1350*x)+(-1050*(x-2))+(480
f(x)=((-1350*x)+(-1050*(x-2))+(480
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-50000
-45000
-40000
-35000
-30000
-25000
-20000
-15000
-10000
-5000
x
y
B.M.D. of structure member 3 due to wind load

16. 16
As the sum of the induced stress values (152.20+27.69 = 179.89 N/mm2
) is within the upper tolerance
limit for design stress i.e. 180N/mm2
, CHS 219.1*200*4.8 can be safely used as structure member 3.
Design of structure member 4:
For CHS 323.9*300.0*10.0, A = 98.65 cm2
, w = 77.44 kg/m, I = 12163.24 cm4
and Z = 751.05 cm3
.
Figure 22
Design against dead load
Total dead load acting vertically downward = 951.72 kg.
Self weight of member = 77.44kg/m. Length of member = 2.25 m.
Load carried by member at lowest point = {972.175 + (77.44*2.25)} = 1146.42 kg = 11246.33 N =
11.25 kN.
Compressive stress induced at this point = F/A = (11246.33)/(9865) = 1.14 N/mm2
Design against wind load
Vertical reaction force supplied by member to support structure from side wind = 4800 kg.
Moment of this force about lowest foundation = {(4800*9.81)*2.25} N-m = 105948 N-m.
Stress in member = (105948)/(751.05) = 141.07 N/mm2
.

17. 17
Deflection of member at top most end = (105948*2252
)/(2*300000*12163.24) = 0.74 cm.
Slenderness ratio of structure member 4 = λ = l/r = 2.25/(0.3239/2) = 13.89. The permissible value of
stress in axial compression is 150N/mm2
for λ = 10 and 148N/mm2
for λ = 20.
As sum of stress developed due to action of dead load and wind load (141.07 + 1.14 = 142.21 N/mm2
) is
within limit of 150 N/mm2
for we can safely use CHS 323.9*300.0*10.0 as structure member 4.
Design of structure member 5:
The maximum downward force on structure acts when the array is tilted at 45˚. In such a case,a
component of wind force acting vertically downward gets added to the dead load.
Total axial load = {(4800*0.707*9.81*0.707)+11246.33} = 34783.22 N.
Axial load = 34783.22 N, D = 323.9 mm, t = 10.0 mm, σcu = 2.1 N/mm2
.
Figure 23
Area required = (34783.22/(0.6*σcu) = 27605.73 mm2
.
(𝑡 + 2𝑐)(𝐷 − 𝑡)𝜋 = 27605.73
From the above equation, c= 9 mm.
Thickness of plate = tp = c*[(3*w)/σyt]1/2
= 9*[(3*1.26/165)]1/2
= 1.36 mm.

18. 18
Hence a base plate of dimensions 380.0*380.0*5.0 will be suitable for this application. However to
reduce stresses in anchor bolts we chase higher dimension preferably, 800.0mm*800.0mm*5.0mm.
Design of structure member 6:
The holding down system we have 4 anchor bolts that are placed diagonally at the corners of the square
base plate.
The maximum stress falls on the anchor bolts when the array is vertical.
For M27 bolts, db = 27mm, rb = 13.5mm and required diameter of hole = 29mm.
According to IS:800 guidelines, required distance of center of hole from closest edge = 51mm.
Figure 24

19. 19
Figure 25
The moment acting on the base (M) = 105.948 kN-m and normal force (N) = 11.25 kN.
The force from the compression area of the foundation (or base plate) acting upward is denoted by C and
the force from the anchor rod is denoted by T.
Distances,a = 0.349mm and b = 0.2405.
𝑀 = 𝑇 ∗ 𝑎 + 𝐶 ∗ 𝑏
𝑁 = 𝐶 − 𝑇
Substituting and rearranging,
𝐶 = 𝑁 + 𝑇
𝑇 = {𝑀 − (𝑁 ∗ 𝑏)}/(𝑎 + 𝑏)
Plugging values for known terms,
T = 175.14 kN.
Pull out force experienced by each anchor bolt = T/2 = 175.14/2 kN = 87.57 kN.
Cross sectional area required, to support this load @ design stress value of 165MPa = (87.57*103
)/165 =
530.73 mm2
.
C/s area = (π/4)d2
= 530.73 mm2
. Therefore, d = 25.99mm.

20. 20
There we select M27 bolts which has diameter of 27mm.
To provide sufficient area for binding between concrete and steel, we use a 250mm*250mm*5mm plate
welded to the anchor bolt that goes into the concrete.
Total area required for binding = 87.57*103
/σb = 87570/0.6 = 145950 mm2
.
Area of plate in contact with concrete = 2*{(250*250)-πrb
2
} mm2
~ 123855mm2
.
Required surface area of bolt in cement = (145950-123855) mm2
= 22095 mm2
.
Length of bolt required = l = 22095/(2πrb) = 260.5 mm ~ 26 cm.
Results
For the three structural member types shown in the figures 1 and 2, the following SHS and RHS have
been found to be suitable:
1. For structure member 1, SHS 32.0 * 32.0 * 2.6 will be suitable.
2. For structure member 2, RHS 127.0 * 50.0 * 4.6 will be suitable.
3. For structure member 3, CHS 219.1*200.0*4.8 will be suitable.
4. For structure member 4, CHS 323.9*300.0*10.0 will be suitable.
5. Base plate of dimension, 800.0mm800.0mm*10.0mm will be suitable.
6. Anchor bolts of M27 with 26 cm below foundation along with 250.0mm*250.0mm plate , will be
suitable.
Suggestions for improvement
1. Stiffeners can be used to strengthen the base of the post welded to the base plate.
Terminology
UDL = Uniformly Distributed Load.
Zx = Elastic section modulus about major axis.
Zy = Elastic section modulus about minor axis.
Vb = Basic wind speed in m/s.
Vd = Design wind speed in m/s.
Pd = Design wind pressure N/m2
.

21. 21
SHS = Square Hollow Section
RHS = Rectangular Hollow Section
CHS = Circular Hollow Section
Acknowledgment
I wouldlike tothankMr. Durjati Prosad Chattopadhayayfor givingme anoppotunitytoworkonthis
project.Also,Iwouldlike tothankMr. KrishnenduRoyChoudhuryforguidingme throughthe project.
References
1. Steel Designer Manual - Buick Davison and Graham W. Owens.
2. IS-875, IS-4923, IS-808.