REVIEWED BLD2022-0998+LOCKED Structural_Calculations+7.28.2022_10.41.20_AM+3018235buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
Project:
Lastverteilung
pz [kN/m2]
0.37
0.28
0.19
0.10
0.01
-0.07
-0.16
-0.25
-0.34
-0.43
-0.52
-0.61
Max: 0.37
Min : -0.61
Supportloads and Anchoring
0609 - DomeGuru - Hype
Client: Domeguru sp. Z o.o.
ul. Madalinskiego 5
70-101 Szczecin Poland
Analysis: buro fur leichtbau - Tritthardt + Richter
Westendstr. 3 78315 Radolfzell - Germany
www.bfl-tr.com
REV-1 15/04/2020 1 /9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
1. Preface
1.1 Construction
Subject of analysis is a geodesic dome structure made of transparent polycarbonat tiles.
By means of a simplified FEM model the support reactions due to windloads are calculated.
Deadload is evaluated precisely G = 106,5 [kg]
1.2 Computermodel
The system geometry of the geodesic dome was provided by Client
As only support reactions are calculated the computer model is simplified.
1.3 Software
DLUBAL RFEM 8.Oxy
Structural engineering software for analysis and design
1.4 Codes
DIN EN 13782
refer to: www.dlubal.de
Temporary Structures - Tents - Safety
REV-1 15/04/2020 2/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
2.
Geometry
Dome
Topview
Sideview
REV-1 15/04/2020 3/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
I Material
3.1 Polycarbonat Tiles
MAKROLIFE- TECHNICAL SPECIFICATIONS
Property Value
Physical properties
Unit
Standard
Density
1,2
g/cm3
ISO 1183
Refractive index (20 'C)
1,586
ISO 489
Moisture absorption 24 hours, 23 'C. 50% RH
0,15
%
ISO 62
Mechanical properties
Tensile strength at yield (at break)
60 (70)
N/mm'
ISO 527
Elongation at yield (at break)
6 (110)
%
ISO 527
Elastic modulus
-2300
N/mm'
ISO 527
Flexural modulus
-2300
N/mm'
ISO 178
Charpy unnotched impact strength -40 'C
NB
W/m'
ISO 179/1eU
Charpy notched impact strength -30 °C
11
kJ/m'
ISO 179/1eA
Izod notched impact strength -23 'C
65
W/m'
ISO 18011A
Izod notched impact strength -30 'C
10
kJ/m'
ISO 18011A
Thermal properties
Linear coefficient of thermal expansion (20-70 'C)
65x10-1
K^
ISO 11359-2
Heat deflection temperature. HDT A (1,80 N/mm')
132
°C
IS0 75
Heat deflection temperature. HDT B (0,45 N/mm')
142
°C
ISO 75
Vicat temperature VST/B 120
149
°C
ISO 306
Vicat temperature VST/B 50
148
°C
ISO 306
Thermal conductivity
0,20
W/m.K
DIN 8302
Electrical properties
Volume resistivity, dry
-10'-
0 . m
IEC 60093
Surface resistivity. dry
10'6
Q
IEC 60093
Dielectnc strength. dry
30
Wlmri
IEC 60243
Dielectric constant dry 50 Hz
3
IEC 60250
Dielectric constant dry 1 MHz
2,9
IEC 60250
Dissipation factor (tan b), dry 50 Hz
0.001
IEC 60250
Dissipation factor (tan 6). dry 1 MHz
0,01
IEC 60250
3.2
3.3
Door frame
[mm] [mm]
Aluminium Profile 30 x 30 x
Nuts and Bolts
refer to manufacturers specifications
[mm]
2
EN-AW 6060 T66
REV-1 15/04/2020 4/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
4. Loads
4.1 Deadload
according to DIN - EN 13782 : 2015 Temporary Structures - Tents - Safety
For this structure precise evaluation of deadload is possible
Primary structure steel - Polycarbonat tiles, nuts + bolts
4.2 Windloads
gk = 106,5 [kg]
This structure is allowed to be erected at places with v_ref < 28 m/s (acc. EN 1991-1-4)
If the structure should be used at places with higher wind velocity than v_ref = 28 m/s additional
investigations according to local situation have to be executed.
4.2.1 Velocity pressure
Velocity pressure according to TAB. 1 Page 13
Tabelle 1 — Boengeschwindigkeitsdruck qn(-,,)
Bezugshohe
Boengeschwindigkeitsdruck
-e
qp(-e)
m
kN/m2
=e < 5
0,50
5<-e_<10
0,60
10 < =e < 15
0,66
15<-e<_20
0,71
20 < -e <_ 25
0,76
Velocitypressure 5m < h < 10m q,w1 = 0,50 [KN/mZ]
(Velocity pressure equals 3 sec gust velocity of 28,3 m/s or 101,8 km/h)
4.2.2 Pressure coefficients
Aerodynamic pressure coefficients for closed structure according to DIN - EN 1991-1-4 "External
pressure coefficients cp,10 for vaulted roofs and domes"
The local loads on the dome surface are evaluated by linear interpolation of given values.
Additional inner pressure is not considered as the structure can be closed without any addtional
members (door shut).
REV-1 15/04/2020 5/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
4.2.2 External pressure coefficients cp,10 for vaulted roofs and domes
' B if
n c * �.
h
+ CDe.10• {: d ►I
K
K
K
- Cpe,10
Geometry of building with cupola or dome
Height of circumferential vertical wall (middle axis)
Diametre of dome
Rise of dome
Relation of heigth of wall and diametre
Relation rise of dome and diametre
b=d
c,j., = constant
along each plane
C(h/d=0)
i
C(h/d>_0,5)
B(h/d=0)
B(h/d-0,5)
r/ a=u,50
(EN 1991-1-4 + NA)
h
= 0,5
[m]
d
3,50
[m]
f
= 1,75
[m]
h/d
= 0,14
f/d
= 0,50
[Interval) f/d]
[linear equation y = a
* x + m]
...x=f/d
A (h/d = 0)
10,05 - 0,5]
f(x):
y =
1,50
* x
+
0,05
A (h/d = 0,25)
[0,05 - 0,5]
f(x):
y =
4,89
* x
+
-1,64
A (h/d > 1,0)
[0,05-0,1]
[0,1-0,33]
[0,33-0,5]
f(x):
f(x):
f(x):
y =
y =
y =
-5,00
1,04
13,75
* x
* x
* x
+
+
+
-1,15
-1,75
-6,08
B (h/d = 0)
[0,05-0,5]
f(x):
y =
-2,11
* x
+
-0,14
B (h/d > 0,5)
[0,05-0,1]
[0,1-0,25]
[0,25-0,5]
f(x):
f(x):
f(x):
y =
y =
y =
-6,00
-2,67
-0,40
* x
* x
* x
+
+
+
-0,20
-0,53
-1,10
C (h/d = 0)
[0,05 - 0,5]
f(x):
y =
0,00
(const.)
C (h/d > 0,5)
[0,05 - 0,5]
f(x):
y =
-0,50
(const.)
linear interpolation for h/d values
Value at A: for h/d =
0,14
Value at B: for h/d =
0,14
Value at C: for h/d =
0,14
REV-1
15/04/2020
Cpe,10 = 0,80 [ / ]
Cpe,10 = -1,23 [ / ]
Cpe,10 = -0,14 [ / ]
buro fur leichtbau Tritthardt + Richter
lightweight design Tel.: + 49 (0)7732 - 94089 00
4.2.3 Windloads on domestructure
�
B ` B
+ `C b=d
A'
cFa„ = konstant
entlang jeder Ebene
Value of windload at point A = 0,40 [KN/mz]
B = -0,61 [KN/mz]
c = -0,07 [KN/mz]
LF2: Wind X
Belastung [kN
Lastverteilung
pz [kN/m2]
0.37
0.28
0.19
0.10
0.01
-0.07
-0.16
-0.25
-0.34
-0.43
-0.52
-0.61
Max: 0.37
Min : -0.61
Example windload input in software
Wx, k (Resultant)
P-z
Fx
Fy
Fz
[KN]
[KN]
[KN]
2,13
0,00
1 -2,84
E hor E vert.
.07
Fz/A-0up
-0,30 [KN/mz / Groundarea]
REV-1 15/04/2020 7/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
4.3 Ballast
For necessary global equilibrium and stabilisation of structure against uplift and sliding the
total selfweight is augmented by ballast.
Global Equilibrium E 1/y µ N> E y H
Friction coefficient µ, r >= 0,6
Safety factor for check of global equilibrium y, f = 1,2
Characteristic Actions due to wind on the structure
Wx
Fx
Fy
Fz
lRes-hl
[KN]
[KN]
[KN]
E
2,13
E[KN]
2,13
Destabilizing Action
Res E H = sgrt(E Px 2 +E Py2) . y,f
Fx,act
= use [KN]
Dome self -weight 107
+ Ballast 660 = 767
[kg] E Pz
= r 7,67 [KN]
Stabilizing Resistance
(E Pz" y,f + E Pz) • µ
Fx,react
= use [KN]
Check of Sliding
Erµ N > 17 H
Dest.+Stab — 0
o,00 1<= 0 OK
With additional ballast of 660 kg the total self -weight of the structure is high enough to prove
global equilibrium according to EN - EN 13782 Temporary Structures - Tents
4.3.1 Flexible hose with sand
i
Rho, Sand
1400
[kg/m3]
Torus:
Diameter D
326
[cm] (ring)
Diameter d
24,5
[cm] (nose)
Volume:
2II2 *
R * rz
V =
0,48
[m3]
Weight
V*rho
G =
675
[kg]
REV-1 15/04/2020 8/9
buro fur leichtbau
lightweight design
Tritthardt + Richter
Tel.: + 49 (0)7732 - 94089 00
4.4 Anchoring
LK1: MaRgebende Lastkombination
Lagemeaktionen[kN]
Loadcombination 1.0 deadload + 1.2 wind X
o.za Ii o.za I+ o,,, I o.oa l
o zz I i
ons I +
oil I i
- I+ z
o, al e �x oo ,
1 Ilrr��I I d02�toos
o.oa l o.io l o.is l o.zz°�sl ozA psl To.-
io.o,
Max P-Z: 0.28, Min P-Z: -0.07 kN
Node Anchoring forces [kN]
N r.
51
52
53
54
55
56
81
85
93
151
152
153
154
155
175
179
187
' 202
207
221
232
E Loads
PX
P,
PZ
0,16
0,04
0,23
0,24
0,11
0,24
0,29
0,18
0,27
0,27
-0,10
0,28
0,06
0,01
0,13
0,01
0,00
0,03
0,00
-0,02
-0,07
-0,01
-0,02
-0,06
-0,01
0,00
-0,04
0,16
-0,21
0,10
0,24
-0,20
0,16
0,28
-0,14
0,22
0,07
-0,12
0,04
0,04
0,02
0,03
0,08
0,12
0,13
0,16
0,20
0,11
0,26
0,22
0,18
0,02
0,01
-0,01
0,06
0,00
0,02
0,07
0,00
0,15
0,12
-0,08
0,21
2,56
0,00
2,35
LK1: MaiSgebende Lastkombination
Lage-aktionen[kN]
0 z4
�is
azs
s s
o.is
rssi
0.00
04
a o.oi
0.07 .oi
nos 0o
0.24 o°
az�.zz o
Max P-X: 0.29, Min P-X: -0.01 kN
min.:
max.:
I Res-h l I RES 1
sgrt(Px2+Py2) sgrt(Px2+Py2+PZ2)
0,16
0,28
0,26
0,36
0,34
0,44
0,29
0,40
0,06
0,14
0,01
0,03
0,02
0,07
0,02
0,06
0,01
0,04
0,26
0,28
0,31
0,35
0,31
0,38
0,14
0,14
0,04
0,05
0,14
0,19
0,26
0,28
0,34
0,39
0,02
0,02
0,06
0,06
0,07
0,17
0,14
0,25
0,01
0,02
0,34
0,44
max. design anchoring force relevant due to random wind direction F,d = 0,44 [KN]
choice of anchor -type with load capacity according to max. anchoring force
e.g. Deck Screws M6 x 50 DIN 571 A2 (suitable timber -ground assumed...)
REV-1 15/04/2020 9/9