Glass Iceberg

AMS ICEBERG, ICELAND Northern lights observatory

AR0133 - Technoledge Structural Design Final Report - 16 April 2021 Anurag Sonar 5201756 Sjoerd van Hedel 4546199 Marnix van den Assum 4594207

AMS Iceberg

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Index 1. Location 2. Design Concept 3. Component Size 4. Assembly Order 5. Safety Analysis 6. Design of connections 7. Sustainability 8. Structural Analysis 9. Renders

AMS Iceberg

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1.

Location

The site is located on the South-West part of Iceland called Gunnuhver which is famous for the northern lights and also for its hot water spring. The presence of thermal spring are taken advantage of in means of passive heating strategies, as discussed in chapter 7: Sustainability.

Geothermal Spring

Lighthouse

Figure 1: Map of Iceland

Site Location

Sea Edge

Figure 2: Lighthouse

AMS Iceberg

Figure 3: Thermal Spring

N

Figure 4: Location, Gunnuhver, Reykjanes, Iceland

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2.

Design Concept

Design inspiration and references

Our design is based on two references: An Iceberg and the Cleveland Clinic Lou Ruvo Center for Brain Health of Frank Gehry.

The Iceberg is refering to Iceland and its arctic environment. Frank Gehry is an insparation for using his organic surfaces in Architecture.

By combining these two an organic Iceberg has been created.

Figure 5: Icerberg. Source: https://thumbor.thedailymeal.com/NSizt8RyIIkqf1w4U1HnVlmuhh8=/870x565/https://www.theactivetimes.com/sites/default/files/uploads/0/0-shutterstock_57.jpg

AMS Iceberg

Figure 6: Cleveland Clinic Lou Ruvo Center for Brain Health of Frank Gehry. Source: https://artpil.com/wp-content/uploads/2019/03/Frank-Gehry-Lou-Ruvo-Center-for-Brain-Health.jpg

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Form Exploration & Evolution The form exploration & evolution in short: The original form exploration started with a dome and a portal structure. Together we decided to conitue with a portal structure with a panorama view towards the northern light, geysers and lighthouse. During this process the floor plan has been optimized and a portal frame made out of three parts was chosen. Due to the span of the portal structure and the size of the roof panels the width of the floor plan is reduced to max 16,5 meters. The outcome is an observatory with a double curved roof with straight components.

Figure 7: First sketch of the portal frames

AMS Iceberg

Figure 8: Panoramic form exploration

Figure 11: 3D view of the structure

Figure 9: Section showing the portal frames

Figure 12: Portal frames in 3 components

Figure 10: Floor plan based on circles to create panoramic view

Figure 13: Final floor plan

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Plan & Structural Grid

B

G

F0

H

1

I

I’

H’

G’

290

15800

19550

A

C

D

E

Overal a symmetrical grid is created within the boundaries of the size of the components.

F’

E’

D’

C’ B’

A’

15800

Apart from the size of the roof panels, symmetry is an important aspect. Due to fabrication costs not every elements can be identical. Therefore the top arch is divided by 18 to create a symmetrical shape and a distance of 2.9 meters between the portal frames.

The biggest span of the two arches is 16.5 meters in the middle of the floor plan. Because of the cantilever of 1.4 meters, a total of 17.9 meters is reached. This can be divided by 6, and results in roof 3 panels.

16500

The structural grid is based on the size of the roof panels and their size limit of 3.2 x 6 meter.

0 1200

0

1200

2 3

2400

N

1400

43250 49500

Figure 14: Structural Grid

AMS Iceberg

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Section of the structure Below, two sections of the building are shown.

In the section the relation with the human scale is visible.

As can be seen the floor is lowered. This is done to ephasize the panoramic view of the sky. Second is because of the size of the portal frames. Due to dimensions of the portal frames and the height of the roof, the lowest point would be at a height of 2 meters. The structure has to be lifted 1 meter or the floor 1 meter lowered.

6.00M 4.50M

3.00M

0.00M

A

B-B’

5.70M

4.50M

3.00M

B

0.00M

A-A’

B’

A’ Figure 15: Sections

AMS Iceberg

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3.

Component Size

As mentioned in the structural grid, the design is made regarding the components size limit of 3.2x6 meters.

Since all panels are within this size limit, they can be transported easily in 40ft container.

Size of the panels Heat strengthened

Annealed

Cold bended Glass Heat Strengthened 3 x 8 mm Laminated Interlayer: PVB

Annealed Glass 3 x 8 mm Laminated Interlayer: Sentriglas plus (SGP)

Figure 16: Sections

6000

5700

2900 2900

2900

2900 6000 6000

5910

2080

Figure 17: Explode View Panels

AMS Iceberg

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3

3 2 19 portal frames are shown in figure 19, since

1

Portal Frames

11

3

30003 14

18

1400

1400

3

5

6

3

7

3

3

4

3

11

13

3

8

3

3

12

4100

5700

10

3

3

8 3

9

33

30003 14

3

17

15

Heat tempered 5 x 10 mm Laminated Sacrificial layer (only 1 & 3) Interlayer: Sentriglas plus (SGP)

3

3

18

12

3

1400

3

15

19

3

3

16

3

2080

2

4100

1

3

6000

3

2

2080

The portal frames are divided in 3 components: the left (1) and right (3) component are at maximum 33x6 meters. The middle one (2) 6 is between 8 and 10 meters and has to be 7 laminated. Because of these three components the portal frames are able to be transported.

10

3

4

6000

half of it is symmetrical. 10 differente Portal frames remain. The portal frames are made out of heat-strengthened glass.

5700

Splice lamination

19

3

16

1

3

2

4 3

3

36

35

7 3

3 38

3 9

3 10

2500 3 3 11 12

3 13

3 14

3 15

3 16

3 17

3 18

Heat strengthened

3 19

3

Figure 18: Portal Frame dimension

2080

6000

2080

Size of the portal frames

AMS Iceberg 4 3

35

36

7 3

38

3 9

3 10

2500 3 3 11 12

3 13

3 14

Figure 19: Portal Frames

3 15

3 16

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Limits of the components On the previous pages, the size limitations of the components has already been discussed.

However, there is another limit to the components.

Since the roof panels are cold bended, research had to be done on the bending of the panels.

Figure 20: Cold bending according to Sedak

When cold bending the panels, torsion and bending occurs in the panels. As a group we contacted Chris Noteboom and he told us that the radius of bending should be 1500 times the tickness. Since we are using 3x8mm glass we calculated with a thickness of 24mm.

In the assembly the panels will be placed on three out of the four supports. In this cold bending case the fourth support is pushed upwards or downwards, this creates torsion.

As can be seen in figure 24, the diagonal represents the torsion of a bended cantilever.

The limit of the cold bending is when the diagonal arch has a smaller radius than 24 meter.

In figure 23 can be seen how the minimum lenght of a diagonal should be for a given deflection.

Figure 22: Dimensions and bending of the panel

Figure 23: Minimum length for cold bending 431mm

Figure 21: 3D model showing the radius of the roof

In figure 22 can be seen how this is tested in the model. Also in the appendix the required forces for bending the glass are calculated.

Figure 24: Arched diagonal by torsion in the plane

AMS Iceberg

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Computational Design The grasshopper file was one of our tools to do research in the limitations of our design. The sizes of the panels and the cold bending research was done by the grasshopper model.

Figure 25: Grasshopper Script

AMS Iceberg

Figure 26: Rhino File

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4.

Assembly Order

In general the design of AMS IceBerg has been influenced by the limitations of (regular) transport and means of fabrication. This has resulted in using float glass panes of 3m wide and 6m long to make the panels for the facades of the building. For the portal frames it means being cut into three pieces, at the exact point where the bending moment is zero. At this point different elements of the portal frame are connected using a hinge connection.

As for the order of assembly, the general design has not been influenced but the way the connections have been designed has. The main difference is that when more than two elements come together in a connection, the connections are staggered instead of ortho linear. By making use of this principle, panels can be added one after another more easily.

IKEA Style Order of assembly

How to connect the elements

Place first two portal frames

Pin connection Page 20

Place vertical panels

Side panel connection Page 19

Install Cantilevers

Install cold bent panels

Connection Page 20 Cantilever

Figure 27: Detail connection facade panels

On the right, the order of assembly and the way the connections should be made are shown. The left column shows the overall strategy on how to assemble everything while maintaining a stable structure throughout. The right side shows how the elements are connected to each other.

Install side panels (same method as other vertical panels?)

Cold bend Page 18 Connection

Repeat

Figure 28: Assembly order

AMS Iceberg

Figure 29: Location connections

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5.

Safety Analysis

Matrix of risk analysis

This chapter will discuss the various risk scenarios that need to be considered and relevant measures taken to make the structure safe for the users.

Being located in Iceland, the structure will be prone to wind and snow loads. Hail storms and snow accumulation is common throughout the year. Apart from these natural factors the glass structure should also resist human activities such as vandalism, car accidents and maintenance. These situations can be assessed and taken into account in the design. We can assume that: Risk(RD) = probability consequence

(*

exposure)

* Figure 30: Risk analysis table by ABT

Risk Analysis Table by ABT. RD value should be less than 70. RD = WS x BS x ES < 70

The higher the probability the lower the consequences should be and vice versa. The RD value for these scenarios are based on the table provided (fig_5.1).

RD = WS x BS x ES < 70 (Thumb rule) For values above 70, we provide some design suggestions and measures to avoid/reduce the impact of these risks. We provide measures for three main structural elements, 1. Facade Panel 2. Roof Panel 3. Portal Frame

Risk Scenario

Façade Panel

Roof Panels

Portal Frame

RD Value

WS

BS

ES

RD Value

WS

BS

ES

RD Value

WS

BS

ES

Snow Accumulation

18

6

1

3

108

6

3

6(3+3)

36

6

2

3

Terrorist Attack

20

1

0.5

40

20

1

0.5

40

20

1

0.5

40

Fire

20

1

0.5

40

20

1

0.5

40

20

1

0.5

40

Explosion

20

1

0.5

40

20

1

0.5

40

20

1

0.5

40

Tsunami

20

1

0.5

40

20

1

0.5

40

20

1

0.5

40

Earthquake

11

0.5

0.5

40

18

0.5

0.5

6

129

0.5

6.5

40

Hail Storm

9

6

0.5

3

42

6

1

7

0

0

0

0

Vandalism

18

6

1

3

9

3

1

3

54

3

6

3

No Maintenance

6

6

1

1

42

6

1

7

18

6

1

3

Vehicle Impact

54

3

6

3

0

0

0

0

21

3

1

7

Figure 31: Risk Analysis for AMS Iceberg

Examples of calculation and illustration of possible risk scenarios from previous assignments

AMS Iceberg

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Consequence & Safety Measures: Facade Panel Facade Panels are most prone to structural damage due to vandalism and vehicle impacts. The possible structural damage due to snow accumulation is significantly less as the portal frames and the roof panels take compressive forces.

In our design, the facade panels are annealed glass with SGP inter-layer. This is mainly to optimize the material and provide safety during such events. Since the structure is located in the outskirts, the probability of vandalism is less. However, if the structure is placed in an urban context we suggest to use heat strengthened or tempered glass due to more exposure to vandalism.

Façade Panel

Risk Scenario RD Value

Consequences

Measures

Snow Accumulation

18

Possibility of buckling in the glass panels.

SGP to be used as an interlayer for the glass panel to reduce the buckling. Design overhang to reduce snow accumulation near the façade. Raising structure above ground.

Terrorist Attack

20

Cracking or complete failure of glass panel

Laminated tempered glass with SGP interlayer,

Fire

20

Partial failure at certain junctions

Periodic Fire rated tempered glass

Explosion

40

Complete failure of structure

Tempered glass with lamination and sacrificial layer to reduce glass hitting humans.

Tsunami

40

Breaking of glass due to high pressure winds/water or debris hitting the surface

Raising the structure to reduce direct impact

Earthquake

11

Complete Failure of the façade panel

Proper connection with the portal can help reduce or delay the impact

Hail Storm

9

Cracking in glass panel

Design overhang to reduce hail stone hitting the façade.

Vandalism

18

Cracking or complete failure of glass panel

Laminated tempered glass with SGP interlayer, Additional coating till 2.1m from ground to increase the structural stability.

No Maintenance

6

Surface or edge damage. Change in lamination or interlayer color. Can cause transparency issues over a period of time.

Regular Maintenance. Avoid outdoor connections

Vehicle Impact

54

Complete Failure of the façade panel

SGP to be used as an interlayer for the glass panel to reduce the buckling.Fully tempered glass with lamination. Surround the structure with boulders. Raise strucre above ground to reduce impact.

Figure 32: Safety measures for Facade Panels

AMS Iceberg

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Consequence & Safety Measures: Roof Panel Facade Panels are most prone to structural damage due to snow accumulation and hail storms. The possible structural damage due to vandalism is significantly less as they are placed above possible human interaction.

In our design, the glass roof panels used are heat strengthened. Our calculations show that these panels can resist the point load of 1350 N which means that they do not fail during maintenance work. To avoid snow accumulation the slope of the roof is designed to allow natural sliding.

Roof Panels

Risk Scenario RD Value

Consequences

Measures

Snow Accumulation

108

Snow load can cause bendng in the roof panel leading to structural damage.

The slope of the roof should be able to reduce snow accumulation.

The roof panels should be laminated, so as to minimise fatality.

Terrorist Attack

20

Cracking of roof panel or failure

Tempered glass with lamination and sacrificial layer

Fire

20

Partial failure at certain junctions

Periodic Fire rated tempered glass

Explosion

40

Complete failure of structure

Tempered glass with lamination and sacrificial layer to reduce glass hitting humans.

Tsunami

40

Complete failure of structure

Raise the structure above the ground level to reduce direct impact

Earthquake

18

Cracking of roof panel or failure

Additional lateral support

Hail Storm

42

Cracking of roof panel

Tempered glass with lamination and sacrificial layer. Change roof angle to reduce direct impact.

Vandalism

9

Cracking of roof panel

The roof panels should be laminated, so as to minimise fatality.

No Maintenance

42

Surface or edge damage. Change in lamination or interlayer color. Can cause transparency issues over a period of time.

Regular Maintenance. Connections to be designed properly to reduce dust accumulation

Vehicle Impact

0

Figure 33: Safety measures for Roof Panels

AMS Iceberg

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Consequence & Safety Measures: Portal Frame Portal frames are most prone to structural damage due to vandalism and events like earthquake.

In our design, the glass portal frame used are heat strengthened. As these frames are responsible for carrying most of the compressive loads it is important to protect it with possible vandalism.

We propose to add a sacrificial layer to the fins to avoid structural damages.

Portal Frame

Risk Scenario RD Value

Consequences

Measures

Snow Accumulation

36

Portal frame may undergo deformation (due to buckling) or cracking at junctions of maximum bending and snow accumulation.

The portal frames can be connected with additional lateral support. The overlap in between glass layers can be increased to reduce the possibility of structural failure at maximum bending.

Terrorist Attack

20

Cracking of Portal frame. Possible failure between targeted portal frame span

Tempered glass with lamination and sacrificial layer

Fire

20

Partial failure at certain junctions

Periodic Fire rated tempered glass

Explosion

40

Complete failure of structure

Tempered glass with lamination and sacrificial layer to reduce glass hitting humans.

Tsunami

40

Breaking of glass due to high pressure water or debris hitting the surface

Raise the structure above the ground level to reduce direct impact

Earthquake

129

The portal frame is the most affected and can undergo complete failure.

Additional lateral support. Connection with ground is crucial to reduce or delay the impact.

Hail Storm

0

Vandalism

54

Cracking of Portal frame. Possible failure between targeted portal frame span

Laminated tempered glass with SGP interlayer, The overlap in between glass should be increased. Additional coating till 2.1m from ground to increase the structural stability.

No Maintenance

18

Surface or edge damage. Change in lamination or interlayer color. Can cause transparency issues over a period of time.

Regular Maintenance. Avoid outdoor connections

Vehicle Impact

21

Portal frame may undergo complete failure or cracking due to vehicle impact

Fully tempered glass with lamination. Surround the structure with boulders. Raise strucre above ground to reduce impact.

Figure 34: Safety measures for Portal Frames

AMS Iceberg

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6.

Design of Connections

Overview of connections

1

3

2 5

7 8 4 6 9 10 Figure 35: Side Elevation: Portal frame

There are 5 important junctions that are identified to explore further. The connections are made out of steel and are kept as minimal as possible.

AMS Iceberg

Figure 36: Key connections and components

01. Cantilever glass beam 02. Glass roof panel 03. Stainless steel connection 04. Aluminium profile 05. Stainless steel pin in glass 06. Glass portal frame 07. Glass facade panel 08. Facade to portal connection 09. Embedded steel channel 10. Nylon bearing blocks

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Connections: Roof panels

1 8 R

R

R 4

Figure 37: Roof connection forces overview

2 1

6

3

2

5 3 5 7

7

4 6

Figure 38: Roof panel connection detail_Cross section

Figure 39: SS Plate embedded in Portal frame

Figure 40: Roof panel connection detail_Exploded isometric

1. Rubber gasket 2.Gap for expansion 3. SS Pin 4. Aluminium profile 2mm thk 5. SS Plate embedded in glass portal frame 6. Aluminium plate welded to roof 7.

Portal frame 8. Roof glass panel

AMS Iceberg

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Connections: Facade - Portal Frame

1

Figure 41: Embedded plates specifications

2 1 3 4 2 2

5

3

4 5 Figure 42: Facade Panel to portal frame_Plan

Figure 43: Facade Panel to portal frame_Isometric

Figure 44: Glass Panel to Portal frame detail_Exploded isometric

1. Glass Portal frame 2. T-Shaped SS plate (embedded in portal) 3. Glass facade panel 4. SS one side bolt 5. Rectangular SS Plate (embedded in gass facade)

AMS Iceberg

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Connections: Portal - Cantilever

Figure 45: Portal frame to Portal_3D & Plan

Figure 47: Cantilever to Portal frame detail_Isometric View

5 1 2

1 4

3 2 3 5

4 6 7

Figure 46: Portal frame to Portal_Exploded Isometric

1. Portal frame part 1 54mm thk 2. Portal frame part 2 54mm thk 3. Titanium/SS Embedded plate 10mm thk 4. SS Pin 70mm dia 5. Embedded roof connection

AMS Iceberg

Figure 48: Cantilever to Portal frame detail_Exploded Isometric View

1. Roof plate connection 2. Cantilever glass beam 3. Titanium/ SS plate with hole 4. SS Pin 5. Glass Portal frame 6. Glass facade panel 7. Facade connection

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Connections: Facade - Floor

1

1

2 2 3 4

3 5

6

4

5

6 Figure 49: Facade Panel to Base_Cross Section

1. Facade Panel 26mm thk 2. Structural Silicon 3. Hilti Mortar 4. SS Profile embedded in floor 5. Nylon Bearing layer 12mm 6. Floor finish (Openable for maintenance & replacement)

AMS Iceberg

Figure 50: Facade panel to flooring_Exploded isometric

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7. Sustainability

Passive Heating and Circularity

The presence of thermal springs on the site provides us an opportunity to utilise the energy for passive heating of the structure.

The conections and structure is designed keeping the reuseability aspect as a whole. The important feature of our design is that 80% of the structural components can be reused. The whole structure can be easily dismantled and reused almost as a whole in another location.

We intend to chanelize the hot water from the thermal spring in our structure and then circulate it through pipes layed under the flooring.

The portal frames allow for modularity in design.

The structure can be also split into 2 seperate structures based on change in function. The facade panels connection with the base is the most critical connection and thus removing these panels would be a bit hectic job.

The floor surface is kept in contact with these pipes carrying hot water and emit heat inside the structure. We also provide a small outlet which can be helpful for taking out the heat during summers.

Heat loss due to air gaps

80% REUSABLE Concrete/ Natural stone flooring with good thermal conductivity

Inlet from thermal spring

Hot water storage

Natural air inlet through earth duct for natural ventilation

EASILY DISMANTLED MODULAR DESIGN EASILY TRANSPORTED SIMPLE CONNECTIONS

Figure 51: Passive heating strategy_radiant floor heating

AMS Iceberg

Figure 52: Circularity of structural components

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8.

Structural Verification

Structural Concept

Main concept: The load carrying structure is made out of glass portal frames, oriented over the short side of the building. The portal frames carry the loads of facade and roofpanels that ensure the lateral stability of the structure.

Portal frames

Stiff skin

Figure 53: Structural concept 2900

0 290

2900

2900

2900

Stable structure 2900

2900

290

0

0

900

290

290

0

290

0

2 900

900

290

0

2

290

0

2 900

0

1200

1200 0

15800

15800

290

0

16500

2

N

1400

AMS Iceberg

2400

2400

Figure 54: Structural plan

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

2400

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Lateral Stability Lateral stability:

Alternative loadpaths:

Forces that act on the long sides of the building are being transfered by roof panels, portal frames and facade panels on the short sides of the building. Forces that act on the short sides of the building are being transfered by facade panels on the long side.

1. Portal frame fails: lateral forces are transfered by the connecting roofpanels to the next portal frame which transfer the forces to the ground 2. Roof panel fails: Lateral forces travel around the broken panels and are transfered by the facade connecting facade panel 3. Facade panel fails: Forces are drawn off by connecting roof panels.

1

2

Figure 55: Lateral stability

3 AMS Iceberg

Figure 56: Alternative loadpaths

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Portal frames Evolution of the portal frame: The portal frames are designed to have the lowest bending moment as possible and to follow the moment line so they have the most efficient shape possible. In order to transport the portal frames they are cut into three pieces that fit into a standard 40 foot shipping container. The cut has been made at the exact spots where the bending moment is zero so a hinge connection can be used.

Snow

Figure 57: Process of the portal frame

Snow

Schematic for calculations: The image on the right is a schematic of the portal frame with the cantilever part. The elements that are calculated in this paragraph are appointed. For each of these elements calculations are made to theoretically test if they meet the constructural requirements. The elements are tested on the maximum pressure, tension, deflection and whether they would buckle in a real life situation. Calculations and eplenatory schematics are found on the next pages.

Roof panel Beam

Facade panel

Pin in a plate

Fin

Wind

Silicone attachment

‘Gallow’

Figure 58: Portal frame diagram

AMS Iceberg

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Calculations Assumptions for calculations

What do we calculate?

General inputs

For the structural verification of this design, the biggest elements are tested. This means that the portal frame in the middle and the a neighbouring roof and facade panel are tested with hand calculations.

The picture on the previous page shows an overall schematic of what we are calculating.

First of all, we want the structure to hold when it’s build.

This means calculating the primary construction (the portal frames) for taking the self load, the wind loads, the load of snow falling on the roof and the load of a person or machine being on the roof for maintainence or repairs. The secondary structure, the roof and facade panels, are calculated for carrying their own weight plus wind, snow and point loads.

Young’s modulus Eglass Shear modulus Gglass Max deformation σmax, annealed σ max, heat strengthened ρ glass

Elements are calculated in the order top to bottom to make sure that all elements will hold the load of the weight they are carrying so the order is: Roof panel, Beam (middle part of the portal frame), ‘Gallow’, Pin, fin, facade panel, Silicone.

= 69 GPa = 26 GPA = L/250 = 25 MPa = 45 MPa = 2500 kg/m3

Roof panel (heat strengthened)

Inputs: Length = 5533 mm The outcome of the calculations tell whether the stresses Width = 2900 mm and deformations are within the limits and whether com- Thickness = 24 mm Figure 59: Location of calculated elements ponents will buckle. The panels are calculated for taking q load = 5.3kN/m It is assumed that the portal frame is orthagonal uniform and point loads seperately along with corner panel Max deflection = 12.84 mm and that it is made out of straight, rectengular glass buckling. For the other elements uniform loads are used for A point load = 100 x 100 mm beams and fins. The beams and fins are made out of deformations and stresses, point loads for buckling.

F point load = 1350 N five panes with a thickness of 10 mm each. Sentryglas with a thickness of 0.89 mm is used as an adhesive to make a uniform element.

Roof and facade panels are made out of three panes with a thickness of 8 mm. 0.76 mm PVB is used for laminating the roofpanels because of its visco-elastic properties, what makes cold bending possible.

0.89 mm Sentryglas is used for the facade panels and titanium and steel are used in the connections.

Further assumptions made for the calculations can be found in the following schemes and tables.

AMS Iceberg

Results uniform load: σmax Deflection

= 4.7 MPa = 4.5 mm

Results Point load load: σmax

= 6.29 MPa

Results Corner panel buckling: σmax = 3.16 MPa

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Calculations Beam (heat strengthened)

ωB

Inputs: Length = 10000 mm Height = 1000 mm Thickness = 50 mm q load = 5.3 kN/m Max deflection = 40 mm Results Beam in bending: σmax Deflection

B B

C C

= 8.02 MPa = 2.4 mm

D

D

ωD

A

Results Buckling check: P’ = 2151.1 kN W’ = 359.2 kN/m

ω

C

Figure 61: Deformation diagram

Beam with two cantilvers (heat strengthened) F = 28.925kN q = 5.785kN/m

B

C

D

2.9kN/m q = 5.785kN/m

5700mm

A 1400mm

3000mm

Results Right cantilever: σmax Deflection ωD

= 12.83 MPa = 1.1 mm

Results Left cantilever: σmax Deflection ωB

= 16.12 MPa = 1.1 mm

Results Fin: σmax Deflection ωC

= 3.53 MPa = 5.5 mm

Overall results: The maximum deflection in the middle of the portal frame as a whole is the deflection at point D plus the deflection in the middle of the beam. This deflection is: 12.6 + 2.4 = 15 mm. This is well within range.

This part of the portal frame has been calculated as a whole because ωC influences the deformation in point Pin in a hole (heat strengthened and D (kwispeleffect in Dutch). It is split up in the vertical steel) part (A-C), the cantilever on the left (B-C) and the cantiInputs: lever on the right (C-D).

Inputs: Height C-D Height B-C Height A-C Thickness left & right q load ωC,max relative to A ωB,max relative to C ωD,max relative to C

= 1000 mm = 150 mm = 1000 mm = 50 mm = 5.48kN/m = 22.8 mm = 5.6 mm = 12 mm

Pd = 28,9 kN Height = 1000 mm Thickness = 50 mm Kt = 3.5 mm d, hole = 170 mm d, pin = 70 mm Results Stress around hole: σmax

= 18.1 MPa

Figure 60: Structural diagram

Results Pin in plate:

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Calculations σmax σmax

= 44.1 MPa = 43.4 MPa

Fin (heat strengthened)

Results Fin under axial load: σmax = 25.5 MPa Ncr = 44.6 kN

Facade panel (annealed) Inputs: Length = 5700 mm Width = 2900 mm Thickness = 24 mm q load = 1 kN/m2 Max deflection = 11.6 mm A point load = 100 x 100 mm Results Uniform load:

Deflection

= 8.9 MPa = 8.3 mm

Results Point load load:

σmax

Results Corner panel buckling:

AMS Iceberg

= 2.45 MPa

Silicone Inputs:

Inputs: Length = 5700 mm Height = 1000 mm Thickness = 50 mm P = 27.4 kN n = 0.7 [-] (clamped in at bottom, hinge at top)

σmax

σmax

= 5.7 MPa

σmax

= 0.14 MPa

q = 1 kPa Center to center distance = 2900 mm

F = 2.9 N/mm Lmin = 20.7 mm Conclusion calculations The calculations show that allmost all chosen dimensions of the elements are big enough, only the fin should be 10 mm thicker. For the most parts it could be said that the dimensions are quite big, looking at the highest stresses and deformations. The next part of this paragraph gives estimations of optimised dimensions, as well as the sizes for the rest of the structure.

Optimisations Optimising dimensions is very important in order to minimise the use of materials and spare costs. The way the elements have been optimised is by trail and error in the calculations.

Roof panel: The limiting factor for optimising the roof panels is the deflection. The optimum thickness that we found for the roof panels is around 18mm. The optimum would be three panels with a thickness of 6 mm each since 3 panels is more safe

than 2.

Portal frame fins and beam: For the elements of the portalframe the thickness stays 50 mm to prevent buckling. The optimum height of the fins would be 750 mm and 700 mm for the beam.

Portal frame cantilever: The optimum thickness of the cantilever is 24 mm and the optimum height is 155 mm Facade panel: The optimum thickness of the facade panels would be around 20 mm. This means 2 panes of 10 mm.

Dimensions of the rest of the structure The height of the portal frames will gradually go down as we go from the center to the sides. The height of the portal frames going from the center to the side will approximately be, : 700 mm, 695mm, 690mm, 670mm, 640mm, 615mm, 590mm, 560mm, 535mm, 510mm. Each of these portal frames (except for the middle one) will be made twice since the structure is symmetrical. The fact that the portal frames have different sizes is not that big of a problem since they all differ in span anyhow.

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9. Renders

Figure 62: Render of the Observatory

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10.

Reflection

As a group we loved to work on this project, we all learned a lot. However, there are a few points we would like to improve if there was more time: • Further research in connections • Research on foundation • FEA models • Calculations with the true shape instead of simplifications • Optimization of the portal frame

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Appendix

Calculations Cold Bending Properties: Youngs Mudulus [N/mm2] Denisty (kg/mm3) Parameters Case 1 Height plate (3x8mm) efficient height [mm] Length plate [mm] Diganonal Length plate [mm] Width [mm] Heigth Difference (dZ) [mm] Moment of Intertia [mm4] Formula:

Force [N] Force [kG] Self-weight [kG]

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69,000.00 0.00

24.00 11.54 5,736.00 6,983.00 2,605.00 125.00 333,440.00 w [mm] =1/3* (F*L^3)/(EI) F= (3EI*w) / (L^3) 25.34 2.58 904

Parameters Case 2 Height plate (3x8mm) efficient height [mm] length plate [mm] Diagonal Length plate [mm] Width [mm] Heigth Difference (dZ) [mm] Moment of Intertia [mm4] Formula:

24.00 11.54 4,652.00 5,554.00 2,881.00 413.00 368,768.00 w [mm] =1/3* (F*L^3)/(EI) F= (3EI*w) / (L^3)

Force [N] Force [kG] Self-weight [kG]

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Calculations Cold Bending Panel under uniform perpendicular Load (snow)

Area load on a plate (maintenance?)

σmax

σmax

a/b β α q t t* a b E

= = = = = = = = =

σmax

=

10.67 MPa

ymax

=

-12.68 mm

Max allowable deformation = 12.7 < 12.84

1.86916 0.5967 0.11394 0.001 24 11.53 6000 3210 69000

[-] [-] [-] N/mm^2 mm mm mm mm MPa

a1 b1 a/b β W t* a2 b2

= = = = = = = =

6000 3210 1.86916 0.60096 1350 11.53 100 100

mm mm [-] [-] N mm mm mm

a2/b1 b2/b1

= =

0.03115 [-] 0.03115 [-]

σmax

=

6.10 MPa

12.84 Approved

Corner panel - Buckling limit σ'

K E v

= = =

0.6306 [-] 69000 MPa 0.21 [-]

σ'

=

2.54 MPa

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Calculations Beam Beam in bending b h l ρ Qweight Qlc qtot E Mmax Z σ

= = = = = = = = 1/8ql^2 (b*h^2)/6 Mmax/Z

50 1000 10000 27.5 1.4 4.0 5.3 69000

mm mm mm kN/m3 N/mm N/mm N/mm MPa

= = =

66.8 kNm 8.33E+06 mm^3 8.02 MPa

1/12*b*h^3 = (5*q*l^4)/(384*p*I) =

4.17E+09 mm^4 2.4 mm

10 m

Deflection I δ

Max allowable deformation: 10000/250 = 40mm 2.4 <40 Approved Beam bending - Buckling check P'

a b d E G l

= = = = = =

P'

=

W'

1.67*P'/l

2.82*b^3*d ((1-0.63)*b/d)*69000*26000 l^2 1- (1.74*500)/10000 69000/((1-0.63)*(50/1000))

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600 50 1000 69000 26000 10000

mm mm mm MPa MPa mm

= =

69000 N/mm^2 26000 N/mm^2

2151.13 kN 359.24 kN/m = = = = =

€ 352,500,000.00 ############### € 100,000,000.00 € 0.91 € 71,244.19

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Calculations Gallow Horizontal part of the 'gallow' Cantilever right part Inputs (dimensions beam, external forces, Young's modulus) q Lbeam P l E b h

= = = = = = =

(q*L)/2

=

5.48 10000 27412.5 3000 69000 50 1000

N/mm mm N mm MPa or N/mm^2 mm mm

Moments in point C Mp Mq

= =

l*P 1/2*q*l^2

= =

Mtot

=

Mp + Mq

=

(b*h^3)/12 (b*h^2)/6 Mmax/Z

= = =

82237500 Nmm 24671250 Nmm

q = 2.9 kN/m, not 5.785

106.9 kNm

Moment of inertia I I Z σ

= = =

4.17E+09 mm^4 8.33E+06 mm^3 12.83 MPa

Deformation in point D vertical direction due to q and P load ωp ωq, 1

= =

(1/3)*((Pl^3)/(EI)) = (1/8)*((ql^4)/(EI)) =

0.9 mm 0.2 mm

Total deformation = 0.8 + 0.2 = 1 mm CAN THE DEFORMATIONS BE ADDED LIKE THIS? Max allowable deformation = 12 1.1 < 12 Approved

Horizontal fin Inputs (dimensions beam, external forces, Young's modulus)

Cantilever left part

q l E b h

Inputs (dimensions beam, external forces, Young's modulus)

Moments M

q l E b h

= = = = =

5.48 1400 69000 50 200

N/mm mm MPa or N/mm^2 mm mm

Moments M Mq, 2

=

1/2*q*l^2

=

5372850 Nmm

Moment of inertia I I

=

=

= = =

2.9 5700 69000 50 1000

1/2*q*l^2= Mq, 1 + Mp= - Mq, 2 Mb / l =

N/mm mm MPa or N/mm^2 mm mm

4.7E+07 Nmm 1E+08 Nmm 17813.3 N

Moment of inertia I I Z σ

= = =

(b*h^3)/12= (b*h^2)/6 = Mmax/Z =

4.17E+09 mm^4 2.88E+07 mm^3 3.53 MPa

Deformation in point C horizontal direction due to q and P load (b*h^3)/12

=

3.33E+07 mm^4

Deformation in point B in vertical direction due to q and P load ωq, 2

Mq, 3 Mb F, b

= = = = =

(1/8)*((ql^4)/(EI)) =

Max allowable deformation 1.1 <

AMS Iceberg

5.6

=

1.1 mm Approved

ωq, 3 ωf

= =

(1/8)*((ql^4)/(EI)) = (1/3)*((Pl^3)/(EI)) =

Max allowable deformation = 5.2 < 22.8

1.3 mm 3.8 mm 22.8 Approved

5.6 mm

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Calculations Pin in Plate Hole in a plate - Stress around Hole Pin in plate

d hole max

σmax

σ,d,max Pd H t Kt dmax

= = = = = =

σ,d,max =

45 28925 1000 50 3.5 955

MPa N mm mm [-] mm

44.99 MPa

Actual hole size σmax

P d D h d/D

= = = = =

58500 170 1000 10 0.17

N mm mm mm [-]

σna Kta σnb Ktb

= = = =

7.05 6.26 34.41 1.26

MPa [-] MPa [-]

σ, max, na= σ, max, nb=

P t D r

= = = =

Kt σnom

= =

2.57 [-] 7.05 MPa

σmax

=

18.1 MPa

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58500 10 1000 85

44.13 MPa 43.37 MPa

N mm mm mm

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Calculations Fin Fin inder axial Load - Conservative Approach b l t n P E

= = = = = =

I Ncr

(b*h^3)/12 (pi^2*E*I)/(n*l)^2

q Mbeam Mq Mtot Z σ

1/8ql^2 (b*h^2)/6 Mmax/Z

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1000 5700 50 0.7 2.74E+04 69000

mm mm mm [-] N N/m^2

= =

1.04E+07 mm^4 44.56 kN

= = = = = =

2.6 8.22E+04 1.06E+07 1.06E+07 4.17E+05 25.5

N/mm kNm kNm kNm mm^3 MPa

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Calculations Facade Panel Panel under uniform perpendicular Load (wind)

Corner panel - Buckling limit

σmax

σ'

a/b β α q t t* a b E

= = = = = = = = =

σmax

=

10.06 MPa

ymax

=

-12.92 mm

Max allowable deformation = 12.9 < 12.84

1.7757 0.56253 0.11605 0.001 24 11.53 5700 3210 69000

[-] [-] [-] N/mm^2 mm mm mm mm MPa

K E v

= = =

0.60817 [-] 69000 MPa 0.21 [-]

σ'

=

2.45 MPa

12.84 Approved

Area load on a plate (maintenance?) σmax

a1 b1 a/b β W t* a2 b2

= = = = = = = =

a2/b1 b2/b1

= =

σmax

=

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5700 3210 1.7757 0.5575 1350 11.53 100 100

mm mm [-] [-] N mm mm mm

0.03115 [-] 0.03115 [-] 5.66 MPa

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Calculations Silicone Minimal area of silicone qwind Center 2 center σmax

= = =

1000 Pa 3210 mm 0.14 MPa

F

=

3.21 N/mm

Lmin

F/σmax

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=

22.9286 mm

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