Report (47) ESCHIligiER SCHNEIDERAVY
STRUCTURAL ENGINEERS
FS2V20°1675x1001_7SOFG9x3
Design calculations FS2V x 7 edge zone
for mounting of photo voltaic modules in freeland facilities
project: Cleanwater Rabbit Material
OR-97224 Durham
customer: Schletter Inc.
3761 E Farnum Place
Tucson,AZ 85706
owner: Solar City
design: Schneider Structural Engineers,Ron Schneider
1700 E Ft. Lowell Road,Suite 109
Tucson,AZ 85719
structural design: Schneider Structural Engineers, Ron Schneider
1700 E Ft. Lowell Road,Suite 109
Tucson,AZ 85719
the design calculation contains following pages
calculation: Pages 1-12
annex:
drawn up: 10/31/2012
10/31/2012 1
CHLETTER
SCHNEIDER®V®
STRUCTURAL ENGINEERS
1. Introduction
1.1 Project description
The following sections contain the determination of the forces and the structural design calculations of the
ground mounted photovoltaic system.
The location is:
OR-97224 Durham 45.408703(degree of lattitude)
1.2 construction
The solar panels are fixed to the inclined support structure using clamp fasteners.The purlins are clamped to the
girders,which are spaced using equal spans.
The modules have the following dimensions:
h= 65.9 in b= 39 in d= 1.22 in support frame work
modules per row x= 7
number of rows y= 2 8.0
maximum power a 255 Wp 7.0
total dimensions of a solar mounting unit
L= 23.44 ft support frame length 6.0
B= 10.34 ft projection of the PV body 5.0
H= 11.01 ft total panel height
h= 6.77 ft total body height N.0
module type SolarWorld 255 3.0
size of facility 0.01 MWp
number of support frames 3 2.0
1.0
number of support sections 3 x(ft]
number of fields 2 0.0
girder span a= 8.5 ft -10.0 -5.0 0.0 5.0
purlin cantilever Icant= 3.23 ft on both sides
tilt of modules with horizontal plain R= 20
minimum height above ground level hmin= 36 in
1.3 Technical codes
• ASCE7-05 Chapter 6:wind loads
• ASCE7-05 Chapter 7:snow loads
• ASCE7-05 Chapter 2: combinations of Load
• International Building Code, IBC,2009
• Aluminum Design Manual, Eighth Edition,2005
• Wind Design based on Ruscheweyh Consult Wind Tunnel Test Report#RC 1127/0510-e
10/31/2012 2
• TSHLTR SCHNEIDER ®y."
STRUCTURAL ENGINEERS
2 Load actions
s with:
g 13 ° inclination
I
7.-
g [psf] based on International Building Code, IBC,2009
according to manufacturers certificate
w [psf] ASCE7-05 Chapter 6:wind loads
=- - s [psf] ASCE7-05 Chapter 7:snow loads
W [psf]] ASCE7-05 Chapter 6:wind loads
nh 1V Y
w.
W
b=h-cos
2.1 permanent loads
g= 2.59 psf selfweight of solar modules according to manufacturers specifications.
2.2 snow loads zone of snow loads 25 lb/sq ft (Based on 45.5 psf ground snow load) (ASCE7-05 Eq.7-1, 7-2)
ss= 25.0 psf
Is= 0.8 Ce= 0.9 Ct= 1.2 Cs= 0.91 (ASCE7-05,Ch.7)
2.3 wind loads: wind zone: 95 mph terrain category C Iw= 0.87 (ASCE7-05,Table 6-1)
height above ground z< 6.8 ft
vref= 94.5 mph
gref= 23 psf
q(z)= 12.1 psf (peak velocity pressure) (RC 1127/0510-e)
wind forces: force coefficient: CN(+)= 1.05 [-] (RC 1127/0510-e)
CN(.)= -1.38 [-]
pressure coefficient: top Cp,net= 1.65 [-] loading
Cp,net= -2.40 [-] uplifting
central Cp,net= 1.65 [-] loading (RC 1127/0510-e)
Cp,net= -2.40 [-] uplifting
bottom Cp,net= 1.65 [-] loading
Cp,net= -2.40 [-] uplifting
(pressure= 1.00 on a length N10
peak load in sidewise edge zones Lam= 1.00 on a length N10
fpressure= 1.00 on a length h/10
peak load in top/bottom edges fsuction= 1.00 on a length h/10
ti
10/31/2012 3
ESEHLITTsEIR
SCHNEIDER A®�
STRUCTURAL ENGINEERS
2.4 load combinations
Load and resistance factors:
y9= 1.20 y9= 0.9 where acting favorable
yq= 1.60
Combination Factors: Wow= 0.50
Wo,s= 0.31
The following load combinations are considered at ultimate limit states design:
LK 1: yy•g+yq S+Wo,w•yq•w (Eq 16-3, IBC,2009)
LK 2: yg•g+Wo,s'Yq•s+Yq•w (Eq 16-4, IBC,2009)
LK 3: 0.9•g+yq•w for lifting wind actions (Eq 16-6, IBC,2009)
3 Design calculations
3.1 purlins
Aluminum purlins are used to transfer loads to the support structure.
These are designed as continuous beams with cantilevers. While producing and assembling these can be
considered as beams with internal hinges and be jointed with splices in the specified positions.
material EN AW-6105 T5 fn= 35.0 ksi 4= 0.85
4f0= 29.8 ksi
profile SO
A= 1.07 in 2
Sy= 0.86 in 3
S1= 0.47 in 3
ly= 1.10 in4
I,= 0.77 in4
g= 1.26 lb/ft
total length !tot= 23.44 ft R= 20 °
a= 8.49 ft sin p= 0.342
!cant= 3.23 ft CAS p= 0.94
The load effects resulting from wind and snow have to be positioned unfavorable for determination of the
forces.The calculation assumes a continuous beam with equal spans.
M1,total M1,partial M2,total M2,partial MB,total MB,partlal
0.070 0.096 0.000 0.000 -0.125 -0.1251 bending moment factors
Atotal Apartial Btotal Bpartial Qtotal Qpartial
0.375 0.438 1.250 1.250 0.625 0.625 force coefficients
permanent loads gs,,= 7.86 psf gs,y= 2.86 psf incl. Profil
snow loads ss,Z= 60.70 psf ss,y= 22.09 psf
wind load(pressure) Ws,+Z= 139.4 psf ws,+y= 54.68 psf
wind load(drag) Ws,_Z= -183.2 psf ws,_y= -79.54 psf
10/31/2012 4
• ESEHLETTER SCHNEIDER e.:
STRUCTURAL ENGINEERS
inner purlin
Mx6, M1 MB
A
A TB
LK 1 MI,y= 1.023 kft MI,Z= 0.262 kft
LK 2 M1,y= 0.864 kft M1,Z= 0.094 kft
LK 3 M1,y= -0.846 kft MI,Z= 0.013 kft
LK 1 MAY= 0.783 kft MA,Z= 0.202 kft
LK 2 MAY= 0.663 kft MA,Z= 0.075 kft
LK 3 MA,y= -0.626 kft MA,Z= 0.013 kft
LK 1 MB,y= -1.355 kft MB,Z= -0.350 kft
LK2 MB,y= -1.148 kft MB,Z= -0.131 kft
LK 3 MB,y= 1.084 kft MB,Z= -0.023 kft
LK 1 A= 1.039 kip Ah= 0.457 kip
LK 2 A= 0.879 kip Ah= 0.117 kip
LK 3 A= -0.839 kip Ah= 0.009 kip
LK 1 B= 1.596 kip Bh= 0.412 kip
LK 2 B= 1.351 kip Bh= 0.154 kip
LK 3 B= -1.276 kip Bh= 0.027 kip
stress evaluation of purlins
max My ax max MZ ax Eax rl[%J
LK 1 1.36 18.90 0.35 8.86 27.76 ksi 93.3 design equation
LK2 1.15 16.01 0.13 3.31 19.31 ksi 64.9 MMZ f
LK 3 1.08 15.11 0.02 0.59 15.70 ksi 52.8 Sy S=
purlin sections
!_ r!
ari
IV
inner purlin
partition of purlins 7195 mm
10/31/2012 5
• (Esc...ETTER
SCHNEIDER AV�
STRUCTURAL ENGINEERS
3.2 Design of girders
The load from the purlins is transferred to the rammed post using an inclined girder,which is connected to steel
post.
The loads on the girder result from the support reaction of the purlins. For the determination of forces
unfavorable load positions have to be used.
girder section extruded section Typ 4
material EN AW-6105 T5 f„= 35 ksi
(I)f„= 29.8 ksi
A= 1.69 in 2
Sy= 1.43 in 3
SZ= 1.04 in 3
ly= 2.85 in 4
IZ= 1.43 in 4
g= 2.00 lb/ft
Shapes of initial force variables with uniform concentrated load F="1"at purlin connections
bending moments(uniform load) spear forces uniform load)
-2.50
-2.00 1.0 -
c 1.50 0.5
E w
0.0
l3 �r .c
c-0.50 - w -0.5
• CD 0.00 -1.0
.0
0.50 X[ft] -1.5 x[ft]
0.0 2.0 4.0 6.0 8.0 10.0 0.0 2.0 4.0 6.0 8.0 10.0
total girder length IR= 9.1 ft
factor for moment in span fF= 0.01
factor for moment at support fs= -1.8 (left) fs= -2.09 (right)
factor for shear forces fv= 2.11
joint eccentricity of girder eZ= 0.79 in
For determination of the forces of the substructure,the wind forces have to be assumed to act in the quarter
points of the module surface.
Hence,there are two load postions of wind forces for each load combination.Subsequently,6 load combinations
have to be evaluated for determination of the governing loading.
10/31/2012 6
ESCHLETTER
SCHNEIDER e®C
STRUCTURAL ENGINEERS
internal forces at the support construction load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
minimum of axial force -0.38 -0.38 -0.14 -0.14 -1.30 -0.64 kip
maximum of axial force 3.61 3.69 2.03 2.20 0.06 0.06 kip
eccentricity moment Mhz 0.24 0.24 0.13 0.14 0.00 0.00 kft
max mid-span bending moment 0.25 0.26 0.15 0.16 -0.01 -0.01 kft
max. moment at support left -3.15 -3.16 -2.34 -2.33 1.54 1.54 kft
max. moment at support right -3.10 -3.10 -2.69 -2.68 2.67 2.67 kft
vertical reaction force(post) 3.36 3.36 2.84 2.84 -1.77 -1.77 kip
horizontal reaction force(post) 0.21 0.21 0.32 0.32 0.06 0.06 kip
mid-span stresses 4.25 4.34 2.42 2.62 -0.84 -0.45 ksi
stress moment at support left -28.53 -28.63 -20.76 -20.77 13.63 13.25 ksi
stress moment at support right -28.11 -28.11 -23.76 -23.76 22.35 22.35 ksi
max mid-span bending moment MF= max(A;B)•fF+Mez=0.01 • 1.60 + 0.24 = 0.26 kft
max. moment at support left Ms= max(A;B)•fs-MeZ= -1.8 • 1.6 - 0.00 = -2.92 kft
max. moment at support right Ms= max(A;B)•fs-MeZ= -2.1 • 1.6 - 0.00 = -3.34 kft
verification N+ 3 __ f„
Sy
maximum stresses max C5= 28.63 ksi utilization ratio 96 %
support system
post is connected at 77 %of planned girder length
strut is connected at 20 %of planned girder length
3.3 strut FS-System EN AW-6105 T5
Is= 63.2 in A= 1.03 int f„= 35.0 ksi
t= 0.16 in I= 0.672 in 4 ry= 0.81 in 4fn= 29.8 ksi
max N= 1.7 kip X= 78.2 6= 1.69 utilization ratio
min N= -3.2 kip w= 2.70 CTX= 8.51 = 29 %
The crossbar is connected to the ram post profile at 21.7 in above ground level.
55.013,
11S .
I N/
I o
I �
NJ I
OOO
IH__ HH'O „
'`
Reel
10/31/2012 7
• FSCHI:ET7" SCHNEIDER AV
Av
STRUCTURAL ENGINEERS
4 design of ram driven posts
The post is designed using a roll formed steel section,which is ram driven into the ground to a defined
depth.This item affords soil examinations and eventually loading tests to evaluate the transferable forces.
section properties
foundation bf= 5.55 in Nr 8
h= 6.26 in
t= 0.16 in
t=4mm
A= 2.72 in 2
Sy= 4.22 in 3
t=4mm ly= 13.34 in 4
60 g= 9.25 lb/ft
t
material properties S380
fy,s= 55.11 ksi
4= 0.9
N t=4mm fy,n= 50.00 ksi
ax= 36.94 ksi
utilization ratio rl= 74 %
1:b1
non bearing soil layer t= 0 in
estimated anchoring depth ts011= 96 in
initial forces at bottom fixed support load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
axial force at fixed support -5.75 -5.94 -3.65 -4.03 2.57 2.60 kip
shear force at fixed support 0.34 0.41 0.67 0.81 -1.05 -1.06 kip
end-restraint moment 12.23 12.23 7.12 6.27 -4.53 4.65 kft
stress analysis 36.85 36.94 21.57 19.29 13.81 14.18 ksi
max.tensile loads on support Nmax= 2.60 kip (1.47) belonging to V= 1.06 kip (0.66)
max. compression force at post Nm;n= -5.9 kip (-3.8) belonging to V= 0.81 kip (0.42)
max. bending moment at post Me= 12.2 kft (10.9)
(Values in parenthesis are service loads)
The restraint post support in the ground features a plastic reserve of 27 %
Me= 22 kft
10/31/2012 8
• FSCHLETTER
SCHNEIDER Aviv
STRUCTURAL ENGINEERS
5 Design of joints and connections
5.1 anchorage of modules on the purlins and connection of the purlins to the girder
• The connection of the purlins to the girder features clamps. Due to limited standards for reliable calculations,
the strength of the clamp fasteners has been evaluated by tests.
fastening of modules to purlins max FZ= 0.39 kip <Pbrg= 8.093 kip
clamping of purlins to girders max FZ= 1.28 kip <Pbrg= 34.17 kip
(strength of connections according to spec sheets from Schletter-Solarmontage GmbH)
5.2 connection between girder and post head
The most important feature of the construction is the design of the connection between the inclined girders
and the head piece of the ram driven posts.The following technical requirements have to be considered:
• transmission of forces in most unfavorable location Az=±1.6 in
• compensation of tolerances caused by ramming of the posts: A8=±2°
• tolerances in longitudinal and lateral direction Ax=±0.6 in
• rotation capacity of connection Acp=±15°
The load from the girder is transferred into the ram driven support by aluminum angles with slotted holes,
which allow for height adjustments.These are connected to flanges of the ram driven post using bolts,which
are subjected to shear and hole bearingforces.
J
The following internal forces have to be transmitted
max M= 1.11 kft x= 2.36 in
max V= 2.61 kip
max N= 4.74 kip
NF= -Nmin/4+Md/4= 2.60 kip
connection of frame section to the foundation
pair of bolts bolts M10 A2-70 f /
Vb°it= 6.74 kip 11= 39 %
bearing resistance steel { j
Vbrg= 9.32 kip r1= 28 %
bearing resistance aluminum
Vbrg= 5.40 kip 11= 48.2 %
connection girder bolts M12 A2-70
max V= 0.25•(max V2+max N2)°5= 1.353 kip Itt* reap.—
ultimate shear force
Vboit= 9.70 kip 11= 13.9 % " - €
V
y
10/31/2012 9
• ESSafror Mourtop Stearns V'
CHI.ETTER SCHNEIDER ..:
STRUCTURAL ENGINEERS
connection components for main beams
3 scaled load cases are analysed: Load 1:Vertical compression (2.2481 kip)
Load 2: Horizontal forces (2.2481 kip)
' Load 3:Vertical tensile forces (2.2481 kip)
. t
Olt._ t LF 2 -11,,,- ,.,_ ,.---,:
LF 3 irft.,4
Statical system with scaled load cases
Ill V'nYlr-.%-w..n,
(Meth
r
li+ resultant stress load 1
'}1F IT -,i.,i`1 i•'
T.vr.rt,:?c.rva
trix.VI.
4'01 tf) .t. il :307n1c,ti,a?
20,
11+�4`t1�t,� P��lI, e� • > ..
200 .1\ i ' ,,. ty i
{iAriltA .i, �- /� i I ra! tir
• t, <; '
EPI
QM Nin.
resultant stress load 2 resultant stress load 3
load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
longitudinal forces(vertical) -5.19 -23.78 -13.95 -15.30 8.92 9.15 f„= 35.0 ksi
shear forces(horizontal) 3.76 3.69 0.89 0.76 0.60 4.60 V,= 29.8 ksi
resultant stresses ksi 5.46 16.98 9.20 9.97 10.55 10.82 rl= 57 %
(utilization ratio)
calculation of the shear wedge
max 6„= 12.61 ksi
Ti= 42 % (utilization ratio)
resultant stresses in the shear wedge
All requiremnents are met due to utilization rates of all components smaller than 100%
10/31/2012 10
[ Ss• LETTER
SCHNEIDER®.:
STRUCTURAL ENGINEERS
. 5.3 top element post head
verification of bolt resistance head plate bolts M10 A2-70
Nallow= 6.56 kip lever arm of load transmission 2.36 in
Vallow= 4.98 kip
max M= 1.11 kft Nactual= 5.20 kip Nact.+ Vacs _ 0.644
max V= 2.61 kip Vactual= 0.65 kip Nall. Vall
max N= 4.74 kip
isometrical view head component
6r,..r.„
,c.T 1.,f`.1.- 1.124 kip Tr+V:.,r.Y:.-EPTR.,] 1.124 kip
t.,,r.9.
.124 kip :943a10,102.511 1.124 kip
_ fro
E
n'
G,
60,01
_ OM Mn
scaled load 2.25 kip vertical scaled load 2.25 kip horizontal
load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
longitudinal forces(vertical) -4.59 -4.74 -2.88 -3.17 1.93 2.29 fn= 35.0 ksi
shear forces(horizontal) -2.57 -2.61 -1.26 -1.34 0.56 -0.27 (l)fn= 29.8 ksi
resultant stresses ksi 1.12 0.92 -1.12 -1.52 8.05 7.49 h= 27 %
(utilization ratio)
5.4 bottom element post head
l ''
1}Fl
*11
oatM,u
resultant stresses ksi I 16.21 16.71 I 9.97 10.97 6.53 I 7.52 ri= 56 %
(utilization ratio)
10/31/2012 11
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STRUCTURAL ENGINEERS
5.6 Shape component post connection
For the connection of the strut to the post an extruded profile will be used,which is jointed with the webs of
the roll formed steel post by bolts.
The force flows through the neutral axis of the extruded part. Due to the adjustability eccentricities have to
be considered.
The inclined struts yields the following bolt forces:
max Z= 1.7 kip utilization ratio 30 peak borehole 2 bolts M 10 A2-70
min Z= -3.2 kip utilization ratio 11 shear failure 2 bolt M 10 A2-70 double shear plane
The analysis of the part is performed using principal stresses shown subsequently
max v„< 29.8 ksi
upper truss connection under uniform loads(.225 kip) utilization ratio 24 %
X0 m�.
o1.m 2010,0335 43 Tnoh Von Mees-Spa Tarp
D'
s
02 10 0Pa
. .101O,0050:53
5
9N1
vL
3,00: �. a �3, "•, ''�' k 1
��".��.� ��KOM,� Y rx� I r.!►�.r v2 .y I
+ ►.rib
3,0184,
2,004
1.905 Z 2,023
1.1
000611n. rA,
3 1.031 4
1 1 \
11.11
0,039139.
0.112 kip 0.112 kip 3.112 kip
vertical(y-direction) horizontal(z-direction) 0.112 kip
lower truss connection under uniform loads(.225 kip) utilization ratio 23.1 %
.,:Von„o, angle limitation 10.0 °
EnheiL
13.30 3010,10:29:32
Mon 1pn.y
Ern.M4
0110 ZOO,233504
3
2,409
O.SkN _
2,403 0.5 kN
1,818 " , �'
1,002 _3
1,300 li,•j:
1.21 F..-
�1.7
4836 ,
0.5 kN a51a 0.5 kN
0,095
0,017 ren.
principal stresses concernig centrical load transmission principal stresses(eccentrical load transmission)10°
bolt V110 A2-7( Vbo,t= 22.1 kip Vbrg= 19.2 kip utilization ratio 8 %
10/31/2012 12
• EINSCHL TER
SCHNEIDER ®��
STRUCTURAL ENGINEERS
FS2V20°1675x 1001_I 4S OF G 9x6
Design calculations FS2V x 14 edge zone
for mounting of photo voltaic modules in freeland facilities
project: Cleanwater Rabbit Material
OR-97224 Durham
customer: Schletter Inc.
3761 E Farnum Place
Tucson,AZ 85706
owner: Solar City
design: Schneider Structural Engineers, Ron Schneider
1700 E Ft. Lowell Road,Suite 109
Tucson,AZ 85719
structural design: Schneider Structural Engineers, Ron Schneider
1700 E Ft. Lowell Road, Suite 109
Tucson,AZ 85719
the design calculation contains following pages
calculation: Pages 1-12
annex:
drawn up: 10/31/2012
10/31/2012 1
ESCHLET7" R
SCHNEIDER ,�®�
STRUCTURAL ENGINEERS
1. Introduction
1.1 Project description
The following sections contain the determination of the forces and the structural design calculations of the
ground mounted photovoltaic system.
The location is:
OR-97224 Durham 45.408703(degree of!attitude)
1.2 construction
The solar panels are fixed to the inclined support structure using clamp fasteners. The purlins are clamped to the
girders,which are spaced using equal spans.
The modules have the following dimensions:
h= 65.9 in b= 39 in d= 1.22 in support frame work
modules per row x= 14
number of rows y= 2 8'0
maximum power a 255 Wp 7.0
total dimensions of a solar mounting unit
L= 46.96 ft support frame length 6.0
B= 10.34 ft projection of the PV body 5.0
H= 11.01 ft total panel height
h= 6.77 ft total body height N°
module type SolarWorld 255 3.0
size of facility 0.01 MWp
number of support frames 2 2.0
1.0
number of support sections 6 x[ft]
number of fields 5 0.0
girder span a= 8.2 ft -10.0 -5.0 0.0 5.0
purlin cantilever !cant= 3.10 ft on both sides
tilt of modules with horizontal plain R= 20 °
minimum height above ground level hmin= 36 in
1.3 Technical codes
• ASCE7-05 Chapter 6:wind loads
• ASCE7-05 Chapter 7: snow loads
• ASCE7-05 Chapter 2: combinations of Load
• International Building Code, IBC,2009
• Aluminum Design Manual, Eighth Edition,2005
• Wind Design based on Ruscheweyh Consult Wind Tunnel Test Report#RC 1127/0510-e
10/31/2012 2 I,
• CHLETTER
SCHNEIDER .®:
STRUCTURAL ENGINEERS
2 Load actions
. . s with:
g R ° inclination
g [psf] based on International Building Code, IBC,2009
I according to manufacturers certificate
w [psf] ASCE7-05 Chapter 6:wind loads
s [psf] ASCE7-05 Chapter 7:snow loads
W s ASCE7-05 Chapter 6:wind loads
w.
r.
b=h.cos'- ---------- .!
2.1 permanent loads
g= 2.59 psf selfweight of solar modules according to manufacturers specifications.
2.2 snow loads zone of snow loads 25 Iblsq ft (Based on 45.5 psf ground snow load) (ASCE7-05 Eq.7-1, 7-2)
ss= 25.0 psf
Is= 0.8 Ce= 0.9 Ct= 1.2 Cs= 0.91 (ASCE7-05, Ch.7)
2.3 wind loads: wind zone: 95 mph terrain category C Iw= 0.87 (ASCE7-05,Table 6-1)
height above ground z< 6.8 ft
vref= 94.5 mph
gref= 23 psf
q(z)= 12.1 psf (peak velocity pressure) (RC 1127/0510-e)
wind forces: force coefficient: CN(+)= 1.05 [-] (RC 1127/0510-e)
CNo= -1.38 [-]
pressure coefficient: top Cp,net= 1.65 [-] loading
Cp,net -2.40 [-] uplifting
central Cp,net= 1.65 [-] loading (RC 1127/0510-e)
Cp,net= -2.40 [-] uplifting
bottom Cp,net= 1.65 [-] loading
Cp,net= -2.40 [-] uplifting
fpressure= 1.00 on a length A/10
peak load in sidewise edge zones fsuction= 1.00 on a length A/10
fpressure= 1.00 on a length h/10
peak load in top/bottom edges faction= 1.00 on a length h/10
10/31/2012 3 I g
• rimSFHLETTER
SCHNEIDER AoAv
STRUCTURAL ENGINEERS
2.4 load combinations
Load and resistance factors:
yg= 1.20 yg= 0.9 where acting favorable
yq= 1.60
Combination Factors: Wo,w= 0.50
Wo,s= 0.31
The following load combinations are considered at ultimate limit states design:
LK 1: yg•g+Yq•s+Wo,W•Yq•w (Eq 16-3, IBC,2009)
LK 2: yg•g+Wo,s•yq•S+Yq•w (Eq 16-4, IBC,2009)
LK 3: 0.9•g+yq•w for lifting wind actions (Eq 16-6, IBC,2009)
3 Design calculations
3.1 purlins
Aluminum purlins are used to transfer loads to the support structure.
These are designed as continuous beams with cantilevers. While producing and assembling these can be
considered as beams with internal hinges and be jointed with splices in the specified positions.
material EN AW-6105 T5 f„= 35.0 ksi 4 = 0.85
cl)fn= 29.8 ksi
profile SO
A= 1.07 in 2
Sy= 0.86 in 3
SZ= 0.47 in 3
ly= 1.10 in4
IZ= 0.77 in 4
g= 1.26 lb/ft
total length hot= 46.96 ft R= 20 °
a= 8.15 ft sin g= 0.342
!cant= 3.10 ft cos 13= 0.94
The load effects resulting from wind and snow have to be positioned unfavorable for determination of the
forces.The calculation assumes a continuous beam with equal spans.
M1,total M1,partial M2,total M2,partial MB,total MB,partial
A 0.078 0.100 0.033 0.079 -0.105 -0.120 bending moment factors
Atotal Apartial Btotal Bpartial Qtotal Qpartial
0.395 0.447 1.132 1.218 0.605 0.620 force coefficients
permanent loads gs,Z= 7.86 psf gs,y= 2.86 psf incl. Profil
snow loads ss,Z= 60.70 psf ss,y= 22.09 psf
wind load(pressure) Ws,+z= 139.4 psf ws,+y= 54.68 psf
wind load(drag) Ws,-z= -183.2 psf ws,_y= -79.54 psf
10/31/2012 4
san.i� sr�e
• � CHLETTERSCHNEIDER .v:�`
STRUCTURAL ENGINEERS
inner purlin
Mx4 M1 MB
A TB
LK 1 M1 = 0.985 kft Mix= 0.253 kft
LK 2 M1,y= 0.832 kft 0.091 kft
LK3 M1,y= -0.809 kft Mu= 0.013 kft
LK 1 MA,y= 0.721 kft MA,Z= 0.186 kft
LK 2 MA,y= 0.611 kft MA,Z= 0.069 kft
LK 3 WY= -0.577 kft MA,Z= 0.012 kft
LK 1 MB,y= -1.189 kft MB,Z= -0.306 kft
LK 2 MB,y= -1.006 kft MB,Z= -0.112 kft
LK 3 MB,y= 0.966 kft M8,Z= -0.021 kft
LK 1 A= 1.009 kip Ah= 0.442 kip
LK 2 A= 0.854 kip Ah= 0.113 kip
LK 3 A= -0.813 kip Ah= 0.009 kip
LK 1 B= 1.486 kip Bh= 0.383 kip
LK 2 B= 1.257 kip Bh= 0.141 kip
LK 3 B= -1.198 kip Bh= 0.024 kip
stress evaluation of purlins
max My 6X max MZ 6X EcX TI I%]
LK 1 1.19 16.59 0.31 7.75 24.34 ksi 81.8 design equation
LK 2 1.01 14.03 0.11 2.84 16.87 ksi 56.7 M�+ MZ < f
LK 3 0.97 13.47 0.02 0.52 13.99 ksi 47.0 Sy SZ
purlin sections
rWEllr
r iJIr --_'
rs
inner purlin
10/31/2012 5
CHL TIER
Inc
SCHNEIDER ..:
STRUCTURAL ENGINEERS
3.2 Design of girders
The load from the purlins is transferred to the rammed post using an inclined girder,which is connected to steel
post.
The loads on the girder result from the support reaction of the purlins.For the determination of forces
unfavorable load positions have to be used.
girder section extruded section Typ 4
material EN AW-6105 T5 fn= 35 ksi
4f„= 29.8 ksi
A= 1.69 int
Sy= 1.43 in 3
SZ= 1.04 in 3
ly= 2.85 in 4
IZ= 1.43 in 4
g= 2.00 lb/ft
Shapes of initial force variables with uniform concentrated load F=1"at purlin connections
bending moments(uniform load) spgar forces uniform load)
-2.50
E.-2.00 - 1.0 .
c -1.50 ` 0.5
oIE - - 0.0m w -0.5-1.0
s 0.50 x[ft] -1.5 x[ft]
0.0 2.0 4.0 6.0 8.0 10.0 0.0 2.0 4.0 6.0 8.0 10.0
total girder length IR= 9.1 ft
factor for moment in span fF= 0.01
factor for moment at support fs= -1.8 (left) fs= -2.09 (right)
factor for shear forces fv= 2.11
joint eccentricity of girder eZ= 0.79 in
For determination of the forces of the substructure,the wind forces have to be assumed to act in the quarter
points of the module surface.
Hence,there are two load postions of wind forces for each load combination.Subsequently,6 load combinations
have to be evaluated for determination of the governing loading.
10/31/2012 6
• ESEHCETT-sER
SCHNEIDER ®.:
STRUCTURAL ENGINEERS
internal forces at the support construction load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
minimum of axial force -0.35 -0.35 -0.13 -0.13 -1.22 -0.61 kip
maximum of axial force 3.35 3.44 1.88 2.04 0.05 0.05 kip
eccentricity moment Mez 0.22 0.23 0.12 0.13 0.00 0.00 kft
max mid-span bending moment 0.23 0.24 0.14 0.15 -0.01 -0.01 kft
max. moment at support left -2.94 -2.94 -2.17 -2.16 1.49 1.49 kft
max. moment at support right -2.89 -2.88 -2.51 -2.50 2.51 2.51 kft
vertical reaction force(post) 3.13 3.13 2.65 2.65 -1.71 -1.71 kip
horizontal reaction force(post) 0.21 0.21 0.30 0.30 0.05 0.05 kip
mid-span stresses 3.95 4.04 2.25 2.43 -0.79 -0.43 ksi
stress moment at support left -26.56 -26.65 -19.31 -19.32 13.20 12.83 ksi
stress moment at support right -26.17 -26.17 -22.10 -22.11 20.99 20.99 ksi
max mid-span bending moment MF= max(A;B)•fF+Mez=0.01 • 1.49 + 0.23 = 0.24 kft
max. moment at support left Ms= max(A;B)•fs-Mez= -1.8 • 1.49 - 0.00 = -2.72 kft
max. moment at support right Ms= max(A;B)•fs-Mez= -2.1 • 1.49 - 0.00 = -3.11 kft
verification N +S _< f„
r
maximum stresses max a,= 26.65 ksi utilization ratio 90 %
support system
post is connected at 77 %of planned girder length
strut is connected at 20 %of planned girder length
3.3 strut FS-System EN AW-6105 T5
Is= 63.2 in A= 1.03 in 2 fn= 35.0 ksi
t= 0.16 in I= 0.672 in 4 ry= 0.81 in 4f„= 29.8 ksi
max N= 1.6 kip R= 78.2 a= 1.59 utilization ratio
min N= -3.0 kip (0= 2.70 aX= 7.92 TI= 27 %
The crossbar is connected to the ram post profile at 21.7 in above ground level.
55.0'_0 4
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10/31/2012 7
ESSHLETTER
SCHNEIDER Ave
STRUCTURAL ENGINEERS
4 design of ram driven posts
The post is designed using a roll formed steel section,which is ram driven into the ground to a defined
depth.This item affords soil examinations and eventually loading tests to evaluate the transferable forces.
section properties
foundation bf= 5.55 in Nr 8
h= 6.26 in
• t= 0.16 in
t=4mm
A= 2.72 in 2
Sy= 4.22 in 3
t=4mm ly= 13.34 in 4
60 g= 9.25 lb/ft
t
material properties S380
fy,s= 55.11 ksi
• 4= 0.9
N t=4mm fy,n= 50.00 ksi
• 6X= 34.35 ksi
utilization ratio rl= 69 %
1:bf
non bearing soil layer t= 0 in
estimated anchoring depth t5011= 96 in
initial forces at bottom fixed support load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
axial force at fixed support -5.35 -5.53 -3.38 -3.74 2.43 2.46 kip
shear force at fixed support 0.31 0.38 0.63 _ 0.76 -0.99 -1.00 kip
end-restraint moment 11.37 _ 11.38 6.59 5.80 -4.28 4.20 kft
stress analysis 34.27 34.35 19.98 17.84 13.06 12.85 ksi
max.tensile loads on support Nmax= 2.46 kip (1.4) belonging to V= 1.00 kip (0.62)
max.compression force at post Nmin= -5.5 kip (-3.53) belonging to V= 0.76 kip (0.39)
max. bending moment at post Me= 11.4 kft (10.12)
(Values in parenthesis are service loads)
The restraint post support in the ground features a plastic reserve of 27 %
Mp= 22 kft
10/31/2012 8 zo
Saw 1/1.1079 Systams
ff
SCHLETlER
SCHNEIDER ®V�
STRUCTURAL ENGINEERS
5 Design of joints and connections
5.1 anchorage of modules on the purlins and connection of the purlins to the girder
• The connection of the purlins to the girder features clamps. Due to limited standards for reliable calculations,
the strength of the clamp fasteners has been evaluated by tests.
fastening of modules to purlins max FZ= 0.39 kip <Pbrg= 8.093 kip
clamping of purlins to girders max FZ= 1.20 kip <Pbrg= 34.17 kip
(strength of connections according to spec sheets from Schletter-Solarmontage GmbH)
5.2 connection between girder and post head
The most important feature of the construction is the design of the connection between the inclined girders
and the head piece of the ram driven posts.The following technical requirements have to be considered:
• transmission of forces in most unfavorable location Az=±1.6 in
• compensation of tolerances caused by ramming of the posts: OR=±2°
• tolerances in longitudinal and lateral direction Ax=±0.6 in
• rotation capacity of connection pcp=± 15°
The load from the girder is transferred into the ram driven support by aluminum angles with slotted holes,
which allow for height adjustments.These are connected to flanges of the ram driven post using bolts,which
are subjected to shear and hole bearing forces.
The following internal forces have to be transmitted
max M= 1.03 kft x= 2.36 in
max V= 2.43 kip
max N= 4.41 kip
NF= -Nmin/4+Md/4= 2.42 kip f'
connection of frame section to the foundation
pair of bolts bolts M10 A2-70
Vbolt= 6.74 kip 11= 36 %
bearing resistance steel
Vbrg= 9.32 kip 11= 26 % sir
bearing resistance aluminum
Vbrg= 5.40 kip 11= 44.8 %
;
connection girder bolts M12 A2-70 , .z
max V= 0.25•(max V2+max N2)°'5= 1.258 kip `� `k. � .
%t
ultimate shear force
Vbolt= 9.70 kip 11= 13 % Au=;
10/31/2012 9 21
• CHLETI'R
SCHNEIDER wm®
STRUCTURAL ENGINEERS
connection components for main beams
3 scaled load cases are analysed: Load 1:Vertical compression (2.2481 kip)
Load 2: Horizontal forces (2.2481 kip)
• Load 3:Vertical tensile forces (2.2481 kip)
NAt -\a_
z
1:nt \I •• 4::.
AltLF 2 110 41,(-t_ ' t,,'
LF 3 r1P' `
�� ih
Statical system with scaled load cases ni °5 ,
t
[,_t.1.,
11V:NI3,W.115i
5,
N;
War
ystam
FISSHIL TER
SCHNEIDER A.V:
STRUCTURAL ENGINEERS
5.3 top element post head
verification of bolt resistance head plate bolts M10 A2-70
Naow= 6.56 kip lever arm of load transmission 2.36 in
Vauow= 4.98 kip
max M= 1.03 kft Nactual= 4.83 kip Nod Vact. = 0.557
max V= 2.43 kip Vactual= 0.61 kip Nall. Van
max N= 4.41 kip
isometrical view head component
[n.r:,T.,
C..2.I V41 1.124 kip Tw VAT-r..-:prrTry 1.124 kip
1.124 kip y`aro 'r'"" 1.124 kip
60.41
f+1:
C:1M1ri Id. ,•
9,V1 MT.
scaled load 2.25 kip vertical scaled load 2.25 kip horizontal
load combination 1 load combination 2 load combination 3
wind A wind B wind A wind B wind A wind B
longitudinal forces(vertical) -4.27 -4.41 -2.67 -2.95 1.82 2.16 f„- 35.0 ksi
shear forces(horizontal) -2.39 -2.43 -1.16 -1.24 0.53 -0.24 4f„= 29.8 ksi
resultant stresses ksi 1.03 0.85 -1.06 -1.43 7.63 7.00 h= 26 %
(utilization ratio)
5.4 bottom element post head
IK i sm,. Ty[Y.tFIr,'.u.vy
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ro
va
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r0,M
LOC Mr
resultant stresses ksi 15.08 15.55 9.24 10.18 6.17 7.09 rl= 52 %
(utilization ratio)
•
10/31/2012 11 2.�
• ESeHs'imitiisrli SCHNEIDER®v AM
STRUCTURAL ENGINEERS
5.6 Shape component post connection
For the connection of the strut to the post an extruded profile will be used,which is jointed with the webs of
the roll formed steel post by bolts.
The force flows through the neutral axis of the extruded part. Due to the adjustability eccentricities have to
be considered.
The inclined struts yields the following bolt forces:
max Z= 1.6 kip utilization ratio 28 peak borehole 2 bolts M 10 A2-70
min Z= -3.0 kip utilization ratio 11 shear failure 2 bolt M 10 A2-70 double shear plane
The analysis of the part is performed using principal stresses shown subsequently
max 6„< 29.8 ksi
upper truss connection under uniform loads(.225 kip) utilization ratio 23 %
T,p YOMNtr-Sprnro
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02.10. 10,0050:53
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vr. Y , i9 4,0� 1
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2.004 `u '.i 3,016 ♦t4A P ,. i); %
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1.005 t 2,023 4
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0,C05 Nn. 1'c,i5, 1,031 sr 1.
fii,i�iii1
0,039 Mn.
0.112 kip 0.112 kip 3.112 kip
• vertical(y-direction) horizontal(z-direction) 0.112 kip
lower truss connection under uniform loads(.225 kip) utilization ratio 21.8 %
•
T.,"Voe,5Pa,w angle limitation 10.0 °
33.90.X110,b:29:32
TYG:Van Was kurvp
01 10 2010,DEAa
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2,409 - _`.t—.-,'
0.5 kN -7,:;7"—'!--
-^ -_ 1.403 0.5 kN
1.119 _
1,837
0,
1,227 p Yt 11,
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0,535 _ 'r�p k's-
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ocla 0.5kN `1
0.5kN ..4'4.
0,995 IN,. „Lf.-
0,017 Nn
principal stresses concernig centrical load transmission principal stresses(eccentrical load transmission)10°
bolt V110 A2-7( VboIt= 22.1 kip Vbrs= 19.2 kip utilization ratio 8 %
10/31/2012 12
2,0