Single story building design
Single storey shell structure This section explores the possibility of self-support shell structure covering an area of 40 by 40 metres. The shell is made of 250mm reinforced concrete Progress 1 - Free form generation
Progress 2 - Live physics simulation
5.45 m
Progress 3 - Finite element analysis
Max.Disp: 11.2 cm Mass weight: 1142 ton
11.7 m
0.5 cm
Sweep NURBS curves to create a free form surface to get orthogonal grids on the plan view.
Evaluate the height variation of the shell and analyse the water flow on the shell surface.
Select one point from each circle and project them to the zero level height.
Fix the perimeter and anchor point in red. Simulate soap film generation process in Kangaroo to create mean zero curvature mesh. (Livesoap component applied)
5.0 cm
Gravity and 2kN/m load are applied on the 250mm thick reinforced concrete shell. Anchor points are marked in grey circles. 2
Generation 1 Max. Disp 15.4cm | Mass: 1141ton
Max. Disp 5.3cm | Mass: 1145ton
Max. Disp 11.6cm | Mass: 1142ton
Max. Disp 4.7cm | Mass: 1150ton
Max. Disp 9.8cm | Mass: 1140ton
Max. Disp 4.8cm | Mass: 1150ton
Max. Disp 9.7cm | Mass: 1140ton
Max. Disp 4.6cm | Mass: 1146ton
Max. Disp 9.6cm | Mass: 1140ton
Max. Disp 4.4cm | Mass: 1150ton
Max. Disp 8.6cm | Mass: 1140ton
Max. Disp 4.3cm | Mass: 1149ton
Generation 4
Genetic algorithm optimisation This section explores the possibility of a self-support shell structure covering an area of 40 by 40 metres. The shell is made of 250mm reinforced concrete
Mutation
Generation 7
Generation 11
Rhino/Grasshopper Interface
FEA Interface
Variable: position of anchor points
Load: gravity + 2 kN/m2 live load Output: Max. disp and mass weight
Generation 20
Converge
Input
Goal
Generation 30
Selected
Generation 35 Max. Disp 8.6cm | Mass: 1140ton
Max. Disp 5.1cm | Mass: 1143ton
Max. Disp 4.6cm | Mass: 1145ton
Max. Disp 4.5cm | Mass: 1147ton
Max. Disp 4.3cm | Mass: 1148ton
Max. Disp 4.3cm | Mass: 1149ton
GA interface Objective: minimise Max.disp and mass weight
0.5 cm
5.0 cm
Structure material reduction Based on the selected iteration from GA optimisation, shell structure material utilisation is used to remove the extra material to make the shell more efficient and light-weighted, which will have little impact on the structure performance.
Material Utilisation
0.5%
Material utilisation of selected iteration
20%
0.5%
FEA
20%
Manually put draw circles to remove extra materials
0.5%
Remove the materials in the blue zone. There is little impact on material utilisation.
20%
0.5 cm
Max. Disp: from 4.6 cm to 4.7 cm Mass weight: from 1145 ton to 1066 ton
5 cm
Cross section thickness optimisation This is the last step to reduce shell cross-section profile thickness, which differs from 2cm to 30cm. The shell is made of reinforced concrete and the maximum allowed material utilisation is limited to 50%.
Overall perspective
0.5 cm
5 cm
Max.Disp: from 4.7 cm to 4.8 cm Mass weight: from 1066 ton to 64.2 kg Load and anchor are same as the preliminary stage.
2 cm
30 cm
The shell thickness mapping on the plan view.
Conclusion In the shell optimisation, it begins from a free form shell structure with Max. Displacement at 11.2 cm and mass weight at 1142 ton. However, through the GA optimisation (change anchors’ position), manual material reduction (puncture holes) and cross-section thickness optimisation, the Max. Displacement of the shell structure has been reduced to 4.8 cm, with only 64.2 kg of reinforced concrete covering an area of 40m by 40m. The thinnest part of the shell is only 20mm thick, but it is still able to support the live load at 2kN/m2.
Edge view comparing the thickness of top edge and column edge
Multi stories building design From solid wall to girded tube wall The test aims to replace the solid thick concrete wall with a steel tube which makes the load-bearing structure more efficient and light-weighted.
For facade walls: Max. Displacement: 0.34 cm Material Weight: 1400 ton Concrete slab: Density: 2500 kg/m3 Thickness: 150 mm Gravity: 9.8 N/kg Slab weight is evenly distributed on the facade
First principal stress lines on the facade with source points
Second principal stress lines on the facade with source points
Draw the first line to intersect with the 1st PSL and intent to paralel to the 2nd PSL
Duplicate and evenly rotate the line to intersect with centre line
Catenary lines from anchor to intersection points
Mirror the catenary lines
Horizontal reinforcement as the second layer
Slab weight distributed at intersection points between facade and slab
Steel tube generation procedure - form finding
For grid tube: Max. Displacement: 3.00 cm Material Weight: 139,447 kg (10% of the solid concrete wall) RHS: Width: 100 mm Height: 200 mm Flange and Web: 5 mm
Design interation and optimisation
Variables for optimisation Two variable inputs are used for the facade optimisation: 1. Angle of the first catenary line 2. Steel tube density Rotation angle from 20 - 60 degree.
Rhino/Grasshopper Interface
FEA Interface
Variable: bottom line rotation angle tube density
Angle = 25 degree
Angle = 37 degree
Angle = 49 degree
Angle = 60 degree
Load: gravity + 3200 kN live load per floor Output: Max. disp and mass weight Steel tube density from 1 to 10 (density is defined by subdivision times of the surplus angle)
Input
Goal
GA interface Objective: minimise Max.disp and mass weight
Density = 2
Density = 3
Density = 5
Density = 10
Evolution and optimisation Two optimisation goals are set: max. displacement and material weight. In the evolution, it attempts to reach the lowest value for both max. displacement and material weight. Nine iterations in the GA mutation stage are compared to each other and case No.3 is selected.
1
2
3
FEA of Case no. 3 The building envelope is 40 x 40 x 42m The facade truss is made of 200 x 100mm RHS steel beam For steel spatial frame, both top and bottom beams are 250 x 150 RHS steel, and middle web is 100 x 70mm steel.
14.929cm, 611.29ton 4
12.465cm, 616.47ton 5
10.281cm, 643.90ton
7
Selected 10.517cm, 639.13ton 6
9.588cm, 684.89ton
8
9.508cm, 692.96ton
9
0.5 cm Max. Displacement: 10.517 cm Material weight: from 639.125 ton (Inc. spatial frames) 9.092cm,713.19ton
8.975cm, 746.23ton
8.794cm, 793.51ton
10 cm
Beam profile optimisation Further optimisation for facade beam element profiles is applied. The profile height varies from 5 to 50 cm, and the width is set as twothirds of the height.
0.5 cm
5.0 cm
Max. Displacement: from 10.517 to 11.128 cm Material weight: from 639.125 ton to 671.645 ton (Inc. spatial frames)
Conclusion Steel truss tube is more efficient and lightweight than the solid reinforced concrete wall. Beam profile optimisation in this case increases the overall mass weight because the thickness of the bottom beam increases 2.5 times to achieve a better visual effect. The max.displacement point is located on the slab centre, which is a design flaw in this experiment.