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Static calculation of the
7th Circle Installation
Table of Content1. Task and approach2. The models
1. Geometry2. Boundary conditions3. Material data4. Mesh
3. The load cases1. Gravity2. Gravity and Constant wind pressure in different directions
4. Results5. Conclusion 6. Our suggestions
Task and approach• Investigation of the structure of the recent
geometry, which is designed from bronze plane shell with steel pillars and braces.
• A static calculation was made as an approach of the structure, and will be introduced with a 3D FE model.
• The simulations were done with a given geometry, sections and wall thickness.
• The constant wind load is assumed and substituted with a 600 N/m2 pressure.
The Model1. The geometry• Steel structure:
Sections: SHS 40x40x2.5: base pilars L60x60x5: first horizontal braces (at 2000 mm) L50x50x4: the rest of the horizontal braces diagonal braces side braces
• The bronze shells were modeled without the motives cut out.The wall thickness of the shell: 20 mm
• For a better overview, the calculation was done without the steel structure as well. In those models the wall thickness of the shell is 40 mm.
Total height: 12650 mmMass of the steel structure: 8713.2 kgMass of the bronze shell (20mm thickness): 222276.8 kgTotal mass: 230990 kgMass of the bronze shell (40 mm thickness): 444550 t
The Model1. The geometry
Inner column
The Model2. Boundary conditions• Fixed supports at the base pilars ground level• Global Gravity: 9.81 m/s2
3. Material data
4. Mesh• Number of elements: 9057• Number of nodes: 7025
• Number of shell elements: 7488
Steel Bronze
Density [kg/m3] 7850 8800
Elastic Modulus[MPa] 210000 110000
Poisson Ratio 0.3 0.3
Load Cases1. Gravity2. Gravity + Constant Wind Dir1 perpendicular to Face 13. Gravity + Constant Wind Dir2 perpendicular to Face 2 and 34. Gravity + Constant Wind Dir3: perpendicular to Face 1, 2, 3
inner and Face 75. Gravity + Constant Wind Dir4: perpendicular to Face1 inner
and Face7(See figures on the next page.)
• The constant wind load is assumed and substituted with a 600 N/m2 pressure.
Load Cases2nd load casePerpendiculat to Face 1
3rd load casePerpendiculat to Face 2 and 3
4th load casePerpendicular to Face 1, 2, 3 inner and Face 7
5th load case
Results: 1. GravityDisplacement [mm]
Total displacement: 41.45 mmDeformation scale: 20x
X Y Z
min -0.348 -0.015 -1.694
max 2.97 9.86 0.026
X Y Z
min -1.011 -0.047 -6.328
max 15.039 41.148 0.1
Original modelWall thickness of the shell: 20 mm
Model without steel structureWall thickness of the shell: 40 mm
Total displacement: 10.283 mmDeformation scale: 20x
Results: 1. Gravity
• Equivalent stress max: 78.996 MPa• Deformation scale: 20x
Results: 2. Gravity + Constant Wind Dir1Displacement [mm]
X Y Z
min -0.144 -2.098 -1.241
max 2.207 6.851 0.1805
Total displacement: 7.303 mmDeformation scale: 20 x
Original modelWall thickness of the shell: 20 mm
Model without steel structureWall thickness of the shell: 40 mm
X Y Z
min -0.5308 -1.76 -1.67
max 3.61 9.19 0.13
Total displacement: 10.023 mmDeformation scale: 20 x
Results: 2. Gravity + Constant Wind Dir1
• Equivalent stress max: 63.474 MPa• Deformation scale: 20x
Results: 3. Gravity + Constant Wind Dir2Displacement [mm]
X Y Z
min -0.376 -0.051 -4.083
max 8.01 23.603 0.052
Total displacement: 24.814 mmDeformation scale: 20 x
Original modelWall thickness of the shell: 20 mm
X Y Z
min -0.81 -0.072 -9.69
max 23.141 61.589 0.15
Model without steel structureWall thickness of the shell: 40 mm
Total displacement: 62.064 mmDeformation scale: 20 x
Results: 3. Gravity + Constant Wind Dir2• Equivalent stress max: 207.662 MPa• Deformation scale: 20x
Results: 4. Gravity + Constant Wind Dir3Displacement [mm]
X Y Z
min -2.091 -4.689 -0.745
max 0.16 4.59 0.972
Total displacement: 5.17 mmDeformation scale: 50 x
Original modelWall thickness of the shell: 20 mm
Results: 4. Gravity + Constant Wind Dir3Displacement [mm]
X Y Z
min -0.938 -0.058 -7.355
max 17.47 54.627 0.11
Total displacement: 55.031 mmDeformation scale: 50 x
Model without steel structureWall thickness of the shell: 40 mm
Results: 4. Gravity + Constant Wind Dir3• Equivalent stress max: 173.595 MPa• Deformation scale: 50x
Results: 5. Gravity + Constant Wind Dir4Displacement [mm]
X Y Z
min -0.599 -0.016 -2.266
max 3.702 13.785 0.0651
Total displacement: 14.581 mmDeformation scale: 20 x
Original modelWall thickness of the shell: 20 mm
X Y Z
min -1.12 -0.078 -10.809
max 25.875 75.078 0.18
Model without steel structureWall thickness of the shell: 40 mm
Total displacement: 75.63 mmDeformation scale: 20 x
Results: 5. Gravity + Constant Wind Dir4
• Equivalent stress max: 128.541 MPa• Deformation scale: 50x
Conclusion• The Gravity causes a total deformation of over 40 mm if the steel
structure is not included, even with the wall thickness of 40 mm.• The steel structure can be seen behind the bronze shell if the
motives are cut out.• The wind pressure in the calculation is a rough approach, the
loads coming from the weather (e.g. wind blows, heat), should be examineed more detaled.
• The mode shapes and the vibration should be taken into consideration.
Our suggestions• A composite material could substitute the bronze shell.• Advantages of the use of composite material:
• The composite material has lower density than the bronze, therefore the weight of the shell would be significantly less.
• The visible steel structure would not be necessary to use in the monument.• The surface can be treated, so the visual effect would be similar as the
original idea.• Useing metal blowing technology causes a special visual effect: the color
seems to be different from the different angle of view.• The wall thickness of the composite shell can be changeable (thicker at
ground level), therefore the monument would be stiffer.• The manufacturing tool can be formed as the motives are already cut out
while produceing the shell parts.• The composite material is weather resistant.
For a more punctual offer, we would need a fully dimensioned 3D model.
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