S TA N D U P A R C H I T E C T U R E ROBERT FRANSEN KEVIN VERMEULEN D AT E : 0 8 . 0 4 . 2 0 1 1
4030958 4030494
XXL WORKSHOP THE NEW KUIP _ ROTTERDAM
00. INTRODUCTION 0.1 Assignment PROBLEM STATEMENT & ACTION PLAN – XXL AS P1 The focus points of the XXL-workshop are mainly orientated at working together multidisciplinary in a team. Each team has different roles, which can be chosen individually per team (architect, structural design, cladding design and digital manager). This assignment is in our case part of the graduation, the P1. Our opinion about the P1 is to do a total research / developments of the project, in this case a multifunctional stadium.
DIGITAL MANAGER The digital manager is responsible for the strategic approach of the project. By creating an open workspace in which information can be exchanged and edited for both of the group members. The digital tools available are a support during the development of the design and have to become an integral part of the strategy. During this process, the digital manager is responsible for the integration of the different digital models from the various disciplines into one core model during the entire design process.
In performing a task within a group, will specifically focus on one direction, which will lead to limiting the research of other roles of the project. For that reason we have decided to perform this project as duo, with consultation of the tutors; Michela Turrin, Rudi Stouffs and Andrew Borgart.
• Conception and development of a digital and computational strategy to support the design conception, exploration and development • Structure and management of the file archive and exchanges • Integration of specific digital models from the different disciplines into a core model • Customization of digital tools • Rapid prototyping by using CNC machines
To organize this project clearly, there has to be made a clear problem statement and action plan which the various roles of the project will capture. Hereby for each role a clear division of tasks and list of problems we will have to solve this project. ARCHITECTURE The architectural part of the design will mainly match with the original assignment. The main difference is the responsibility of the design, both of the students are responsible for the design en the decisions which will be made.
As program of requirements we maintain the same program, which is used at the design of KCAP Architects. We assume the same Urban Plan and place of the stadium. The architectural part will be focussed on the design of the stadium itself with the additional functions of the program. Program of Requirements:
• Analysis and understanding of the whole architectural program of the project • Conception and development of design concepts • Iteratively looped assessment/evaluation and review of the design considering the architectural performances (visual/aesthetic, functional, adaptable, sustainable, etc.) • Integration of interdisciplinary aspects into the whole design from the very early conceptual phase and during the entire design process STRUCTURAL DESIGN The main task for the structural designer is creating a structure, which fits the building, can capture all forces and has also an additional architectural value. In his role in the interdisciplinary team his priority is the cohesion of the structure combined with the architecture of the total stadium. Besides structure this person will also take care of the building services as an integrated subject in the total project. • Conception and development of a reconfigurable and sustainable structural system • Analysis driven design, based on numeric performance evaluations o Structural performances o CO2 emissions o Material use and quantities o Fabrication process CLADDING DESIGN The building envelope of the building will be in total hands of the cladding designer. During his conceptually design there are a few topics, which have to be taken in account. These topics, based on the environmental effect and the adaptability of the façade will have to be taken care of during the total project.
• 65.000 – 70.000 seats • 10.000 parking places • Public circulation • Corridors (Connection) • Corridors Public (Connection) • Sanitary • Storage • Soccer housing • Media • Offices • Permanent kitchen facilities • Catering • Hospitality • SUP (Supporters distribution) • Technical space • Security • Commerce • First Aid
ca. 40.000 ca. 7.750 ca. 6.775 ca. 5.500 ca. 3.750 ca. 3.200 ca. 650 ca. 3.750 ca. 2.250 ca. 2.500 ca. 15.500 ca. 4.250 ca. 4.250 ca. 1.250 ca. 2.500 ca. 350
Total
ca. 115.000m2 excluding stands and camera positions, including traffic)
m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2 m2
• Conception and development of a per formative envelope (analysis driven design), based on numeric performance evaluations o Solar performance o Energy production, and also reduction o CO2 emissions o Material use and quantities o Fabrication process
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00. INTRODUCTION 0.2 Location On figures 01 and 02 is the location for the New Kuip shown. As can be seen, the New Kuip will be build near the current stadium. The area is well accessible by public transport and by car. Along the current Kuip is a public transport, which will be redeveloped when the New Kuip will be build. At the south side of the current stadium is the sport campus. It is an opportunity to use this part of the area to add more value at the new stadium. Another interesting item of the area is the Maas, which is next to the possible location of the new stadium and could be used. The area is analyzed to be redeveloped in case of the BID for the world championship 2018, the Netherlands and Belgium (Figure 03).
Figure 03 - BID logo
Figure 01 - Photo of area (Google Earth)
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Figure 02 - Area under development (Source: Presentation KCAP
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00. INTRODUCTION TABLE OF CONTENTS 00. INTRODUCTION
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07. DIGITAL MANAGEMENT
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0.1 Assignment 0.2 Location
2 3
TABLE OF CONTENTS
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7.1 Digital process organization 7.2 File management 7.3 Archive structure 7.4 File exchange 7.5 Parametric models and Grasshopper plug-ins
42 42 43 43 44
01. CONCEPT
5
1.1 FIFA requirements 1.2 Configuration grandstands 1.3 The 24/7 use
6 7 8
08. CONCLUSIONS
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8.1 Conclusion / Summary 8.2 Sources
47 47
02. ARCHITECTURE
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09. APPENDIX
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2.1 Urban plan 2.2 Architecture 2.3 Grandstand vs. Cladding 2.4 Architecture vs. Structure 2.5 The New Kuip
10 13 13 13 13
9.1 Floor plans 9.2 Sections 9.3 Elevations 9.4 Section fragments 9.5 Solar study - Roof
03. STRUCTURE
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3.1 Architecture based structure 3.2 Designed structure 3.3 Calculated structure 3.4 Improved structure 3.5 Results improved structure
21 22 23 24 25
04. CLADDING
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4.1 Triangular tessellation 4.2 Horizontal and vertical divisions 4.3 Pyramid shaped elements 4.4 Materialization 4.5 Reference – Unilever Headquarters Hamburg 4.6 Section and details
28 28 28 29 30 31
05. ADAPTABILITY
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5.1 The use of the bowl 5.2 FlexBase 5.3 Stadium is a dock 5.4 Harmonica roof
33 34 35 35
06. SUSTAINABILITY
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6.1 Use the Maas 6.2 Energy 6.3 Collect rainwater
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DO.01 DO.02 DO.03 / DO.04 DO.05 / DO.06
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01. CONCEPT 01. CONCEPT
01. CONCEPT 1.1 FIFA Requirements The start of this project was mainly focused on the FIFA requirements because the reality of the design is an important aspect. The first topic that is explored are the dimensions of the grandstands, because this is the basic of a stadium.
The spectators’ distance from the field of play has also requirements. The optimal distance has a radius of 90m from the center point of the field. The maximal distance has a radius of 190m from the corner point of the field (Figure 06).
During designing the grandstand, the starting point is an optimal view. The line of visibility is an important requirement for the view of the spectators. The recommended C-value of the grandstand is 90, with an optimum value of 120 (Figure 04). The main requirement for the seating is the maximum rake angle of 34o (Figure 05).
Figure 04 - Line of visibility
Figure 06 - Spectators’ distance
Figure 05 - Seating
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01. CONCEPT 1.2 Configuration grandstands On the following figures are the results shown of the grandstands, based on the FIFA requirements. An important architectural aspect of the grandstand is the waving part at the third tier. This is the result of following the radius of 190m from the corner of the pitches. The part of the grandstand which is outside these 190m is “cut off� with a waving tier as result (Figure 08).
THIRD TIER Minimal 33,7o Maximal 33,5o C-value: 90
35 ROWS
SECOND TIER Minimal 29,9o Maximal 28,6o C-value: 90
16 ROWS
FIRST TIER Minimal 24,9o Maximal 17,9o C-value: 120
30 ROWS
Figure 07 - Line of visibility
Figure 08 - Waving grandstand
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01. CONCEPT 1.3 The 24/7 use An important aspect of the assignment of designing a stadium is the 24/7 use. To achieve this, there are several functions added to the stadium. The main functions which are added are the cinema and hotel. In the existing location is a cinema, Pathé the Kuip, located. This cinema will be relocated into the stadium (Figure 10). This cinema (Figure 09) is one of the best visited cinema’s in Holland. The added functions will have a striking value in the surrounding, both of the functions need to be recognizable for the people which are visiting the area. Another demand of these functions is the connection with the stadium. When the people are visiting these functions, they need to feel that they are still in a stadium. There need to be a visual connection between the function of the stadium itself and the added functions. Adding the functions of a cinema and a hotel in the stadium, are not the only solutions to design a 24/7 used stadium. The main design aspect is the adaptability of the pitches, and using the Maas for these solution. The pitches will be floating, which results in an adaptable use of the bowl itself. The bowl can be used for several functions, which makes the stadium multifunctional. More details of this subject is reflected in chapter 5 Adaptability - 5.1 Use of the bowl.
PATHE
SPOT OF THE STADIUM
Figure 09 - Pathé the Kuip & Hotel
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Figure 10 - Relocate the Pathé
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02. ARCHITECTURE 02. ARCHITECTURE
02. ARCHITECTURE 2.1 Urban plan As previously stated, there will be added functions (cinema and hotel) into the stadium. The orientation of these functions are based on the urban settings. Because the location next to the river the Maas, this will be an excellent opportunity to use this view for the function of a hotel. The view over the Maas will give the hotel an extra value. The cinema will be located at the south side of the stadium, this is the side of the stadium which is more connected to the surroundings. By designing the two functions as “striking boxes”, these functions are recognizable for the surroundings, which is important to attract people (Figure 11).
Analyzing the area of the stadium, there are four main spots: the public transport, the “old Kuip”, the Sport campus and the new dwelling (+parking) (Figure 12) The stadium will have a connection to these four spots.
View over the Maas
CINEMA
PUBLIC TRANSPORT
HOTEL
Connection with surroundings
SPOT OF THE STADIUM
NEW DWELLING + PARKING
OLD KUIP
SPORTCAMPUS
Figure 11 - Location of Pathé & Hotel
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Figure 12 - Spots in the area
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02. ARCHITECTURE The connection with the four main spots are will be made by creating bridges which will function as main entrance for the spectators. They are orientated in the direction of the spots (Figure 13 & 16 – next page).
As mentioned before, there will be used floating pitches. The different functions will have all their own float (more info in chapter 5 Adaptability). The different floats will be stored on the Maas. When these pitches are not in use in the stadium, they can be used outside for other functions. The soccer pitches can be used for the training of Feyenoord for example. To get connection with the surrounding, there will be made a “harbor” to attract people. This “harbor” will be connected to the public transport and the several floating pitches (Figure 15).
The new dwelling and parking will be at the east side of the stadium. The parking lot will function as kind of barrier between the dwelling and stadium. To make sure the building of the parking will not only in use when there is an event in the stadium, the parking lot can also function as kart track (Figure 14).
CREATE ‘HARBOR’
PITCHES CONCERT / MOTORTRACK
PITCHES SOCCER
PARKI NG & KART
DWELLIN G
Figure 13 - Parking / Kart & Dwelling
Figure 15 - Floating pitches
Figure 14 - Parking & Kart track
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02. ARCHITECTURE 3 Main bridges (entrances) of the stadium Entrances for supporters / spectators Entrances public part of the stadium at west side - Hotel - Cinema - Supporters home - Fan shop Entrances private part of the stadium at east side - Business - Players / Musicians - Press
Figure 16 - The final urban plan
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02. ARCHITECTURE 2.2 Architecture The stadium is kind of separated in two parts: the plinth, which is semi public and semi private, and the top part of the stadium which is public. As mentioned before in the urban plan, the stadium will be accessible by three main entrances, which will be used by the supporters / spectators. These three bridges leads to the 1st level: the promenade of the stadium. The promenade is a large open space which will function as big meeting area for the supporters. From this promenade the grandstands, 1st, 2nd and 3rd tier, are accessible with stairs and elevators. The promenade will function as the separation between the bottom part and the top part. By using the promenade as public entrance, the plinth can be used for the more private functions in the stadium. The functions which are located in the plinth are the entrance for the players, business / VIP, the museum of Feyenoord, the cinema, the hotel, the offices of Feyenoord, the supporters home and the fan shop. The entrances of the players are located at the east side of the stadium, because this is the most quiet part of the stadium (the west side is the main square) and it is the nearest place for the trainings facilities (the floating soccer pitches). The floor plans and sections of the stadium can be found in the appendix: 9.1 DO-01Floor plans. 2.3 Grandstand vs. Cladding Because the grandstand is the starting point of the stadium, the grandstand needs to be seen from outside the stadium. That is the reason to use a cladding which is transparent and has less structure. More details about the cladding is reflected in chapter 4 - Cladding. The elevations, which shown clearly the lower part (plinth) and the upper part (the grandstands and the cladding) separated by the promenade can be found in the appendix: 9.3 DO-03 Elevations. 2.4 Architecture vs. Structure The big bridges which function as main entrances for the spectators needs to have a structure. Especially the bridge over the roundabout will have a striking structure. Because the roundabout, it’s not possible to use several columns below the bridge, this results in a suspension structure. A reference of these structure is shown in figure 17. To create a unity between the structure of the bridge and the stadium, the structure method of the bridge will be return in the stadium. More details about the structure is reflected in chapter 3 - Structure. 2.5 The New Kuip To get a good impression of the final design of the stadium, the next pages appears several impressions from several views.
Figure 17 - Reference Bridge structure - Suspension / Tensile
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02. ARCHITECTURE
Figure 18 - Aerial view perspective
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02. ARCHITECTURE
Figure 19 - Perspective from the sport campus
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02. ARCHITECTURE
Figure 20 - Perspective from the public transport / square
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02. ARCHITECTURE
Figure 21 - Perspective from the Maas
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02. ARCHITECTURE
Figure 22 - Perspective from the pitch
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02. ARCHITECTURE
Figure 23 - “Section” perspective
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03. STRUCTURE 03. STRUCTURE
03. STRUCTURE 3.1 Architecture based structure At the start of this project, one of the preconditions was an opening in the roof, with the width of the soccer pitch, over the whole stadium. This all had to be carried by a structure, which was not visible in the opening of the roof. During the design process the urban plan caused a few troubles. The roundabout in front of the New Kuip had to be crossed, so the spectators are able to reach the stadium directly from the new station. Without placing columns at the roads around the stadium and the roundabout a bridge was needed to access the New Kuip.
Grasshopper usage for structural design For the structural part of this project there has been worked a lot in Rhino and Grasshopper. This was mainly because of the fact that ArchiCAD is unable to create truss systems out of lines with several curvatures. By using Grasshopper and different plug-ins it was possible to create easily numerous truss systems and had the ability to export them to Oasys GSA in which these systems could also be calculated.
During the search for a bridge with a footprint as small as possible, the ‘tension bridge’ appeared. The reference image where it all started can be seen in figure 24. This bridge became normative for the entire stadium, and the roof structure was determined. Based on a architectural decision, the structure was chosen, the only thing left, was calculating it and make it suitable.
Besides truss systems, Grasshopper is also used to determine the amount of columns. But instead of doing this from a structural point of view, it was done in a architectonic point of view. The layout of the floor plans were decisive for the amount of columns in the stadium and with the help of Grasshopper it was easily to make this clear. In figure 25 is shown some animated views of the sliders in Grasshopper which were used to determine the amount of columns.
The urban plan caused a lot of problems, because the columns which were needed to carry the roof had to be placed next to the stadium. Those columns needed a cable-stayed structure, one side to the edge of the roof, the other side away from the stadium.
Figure 25 - Column configuration
The use of Geometric Gym plug-ins was a big help during the structural process, because a lot of operations are needed in Grasshopper and are combined in one single command in Geometric Gym commands. This makes designing and adapting structural parts a lot easier. More information about these plug-ins can be found in chapter 7.5 - Parametric models and Grashopper plug-ins. The communication between Grasshopper and GSA was quite easily made. By using the Geometric Gym Plug-in, the lines created in Grasshopper were ‘baked’ in GSA. Nevertheless there were several problems by doing this.
This cablestayed structure could not be placed on the roads around the stadium, so the location of these base constructions was not determined from structural view.
Following were the main problems: - The scale and units (Rhino and Grasshopper in mm) failed during the export, while the GSA unit settings were filled in correctly - Curves sometimes had to be exploded or GSA would convert them to straight lines. - This would end up in very small segments and a lot more elements and nodes. - Double nodes because of different polylines. - Lines which connected in Rhino/Grasshopper, were detached in GSA, causing a lot of problems.
Figure 24 - Tension based bridge
From this moment on, it was quite a task to make this structure work in a proper way. Designing a structure based on surroundings and possibilities turned out not to be the logic order, but solutions had to be found within those boundaries. On the next page, the structure as it was architectonically designed will be reviewed en clarified. This will also show the problems and shortcomings.
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03. STRUCTURE 3.2 Designed structure The original designed structure had some problems, but most of the structure was designed well. In chapter 3.3 will be discussed which elements are not functioning as they should and how this will be solved. In this chapter the most important parts of the structure will be explained, the structural and the architectural aspect. Figure 26 shows al the structural elements which will be treated.
5
1. Columns inside the stadium Around the entire stadium, columns are placed, to carry the weight of the grandstands and cladding. These columns are constructed out of concrete. As mentioned before, the amount of columns is based on the architectonic value and the possibilities in the floor plans. As can be seen by number 6, the columns stop on top of this space frame. This makes it possible to remove the pitch. This subject will be further explained in chapter 5 - Adaptability.
4 3
2 5
2. Ring(s) around the stadium On top of the columns a truss shaped ring will connect all the columns. This ring is based on the hoop forces to keep the stadium together. More rings are added, based on the cladding principle but these rings have less structural function.
1
6
As shown on the image, these rings will be interrupted on the north and south side of the stadium, where the cinema and hotel comes out of the stadium and through the cladding. For this reason, the additional rings are not calculated as structure, but will provide extra reinforcement.
Figure 26 - Total structure of the New Kuip
3. Roof structure The roof structure is based on a large span, made by an enormous truss. This truss is connected to the stadium rings with roof beams to provide the stiffness of the roof itself and will be carried by a cablestayed structure. The truss itself has an asymmetric section, what makes it quite difficult to calculate it by hand. The height of this truss was based on approximately 10 meters high and 7 meters wide. During the process these measures changed a couple of times, but as shown on figure 26 are the final measurements.
5. Tension cables From the roof structure, cables will be brought on tension from a base structure to the top of the pillars, connected with the truss. These steel cables don’t have a huge size because they are in tension, steel’s main ability. Very important is the angle of those cables to the base structure and to the roof structure. As will be discussed in next chapter, the system does not function when the cables are not complete in tension. 6. Water span To be able to remove the field out of the stadium, a column free span has to be made at the waterside of the stadium. This span, approximately 80 meter has to carry the entire grandstands and hotel on top of it. Additional fact is that this space frame has to be placed under the promenade, and the space underneath also needs a certain height. Combining this facts gives us a 25 meter wide, 4,5 meter high space frame supported by extra columns placed in the water.
4. Columns/Pillars next to the stadium To make use of a cable-stayed structure, columns are needed to connect the cables to. As shown, these pillars are a lot higher then the stadium itself, mostly because the fact the cables need to have a certain angle, otherwise they will not function properly. This was also one of the problems in the first designed structure.
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03. STRUCTURE 3.3 Calculated structure Not every part as described in last chapter will be calculated in the GSA model. The span over the water will be disregarded in the model, and the main focus is on the roof structure. When the model was finally imported correctly in GSA (problems are described in Grasshopper usage for structural design) it was ready to be calculated. During the calculation a couple design problems occurred: Lack of tension As shown on figure 27 there is no tension in the cables. This means that the cables don’t function the way they should. There are a few reasons why this problem occurs: - The location of the columns/pillars and base structure of the cable-stayed structure was based on the urban plan. The location was determined and the calculation would have shown which material properties are needed. The problem is that the calculation shows that there is no tension in the cables, so the location is the biggest problem. - Because of the wrong location of the base structure and the height of the pillars, the angle of the cables is too low. A cable in tension should make an angle of at least 50 degrees. In this configuration this is not possible. - The pressure on the cables is mainly caused by its immense length and the deflection of the cable based on its own weight. Figure 27 - No tension in the cable structure
Big displacements Figure 28 shows the deflections in the truss system of the roof structure. The deflections at the center prove to be maximum 8 meter, an impermissible value. A few reasons why the deflections are so big: - The cable-stayed structure is not in tension, so the cables don’t carry any part of the truss. The truss deflects this much because it was intended to be carried by the cables, next to its own stiffness. - The stiffness of the truss system seems to be to low. By making the truss more rigid, the deflections can be decreased. Errors in the GSA File Different errors in the GSA file occurred. The program was able to calculate the structure, but there were a lot of double nodes and not connection elements. This caused high stresses and big deflections.
Figure 28 - Very high vertical displacements
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03. STRUCTURE 3.4 Improved structure Afterwards the presentation, several adjustments had to be made to the structure. There could be chosen for different scenario’s: Scenario 1 - Remove the columns Removing the columns would be a drastic solution, but is a realistic option. By making the truss system more rigid, the cable-stayed structure becomes superfluous. The big concession which has to be made is the derogation of the architectural value of the total stadium. Scenario 2 - Relocate the columns By relocating the column, the architectural image will not be affected but the urban plan has to be redefined. The angle of the steel cables have to become more steep, so the columns will have to be relocated, become higher, and less steep. Besides this, an ideal location for the base structure has to be found, based on the structural function. This will affect the urban plan, but this has to be accepted to keep the architectonic value. As can be seen on figure 29 there has been chosen for scenario 2. The image which was created proved to be a good one, and removing the columns would affect the stadium too much. Based on GSA values, the columns were relocated until the following values were provided: - The cable-stayed structure has to be in tension before it will fully function. - The location of the columns has been changed compared to the first version. The columns are placed closer to the stadium to shorten the cables. - The columns made more steeper. - The base structure was relocated to their optimal location, based on tension.
Figure 29 - Improved structure of the New Kuip
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03. STRUCTURE 3.5 Results improved structure After improving the structure and calculations in GSA, this are the new results. Figure 30 - Axial Stress As can be seen in the figure, the cables are all in tension. By adding a cable between the trusses over the stadium, the rotation of these trusses decreases, as can be seen on figure 30. As visible the outer cables don’t take a lot of tension, but without those cables, the cable structure wouldn’t be symmetric. Figure 31 - Combined stresses As shown in the figure, the largest stresses occur in the cables. The cables are capable to deal with those stresses, because they are pre-stressed. The roof beams and the trusses are also subjected to tension, but this stress is so small, it may be neglected. Figure 32 - Cable deformation As mentioned before, the deflection of the cables turns out to be very big. By pre-stressing the cables, the deflection decreases. The length of the cables is not a beneficial for this structure, but as the calculations proof, it can be handled.
Figure 31 - Combined stresses
Figure 30 - Axial stress
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Figure 32 - Cable deformation
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03. STRUCTURE After improving the structure and calculations in GSA, these are the new results. Figure 33 - Nodal deformations The deformation in the truss system has made visible with the Uz displacements. When this is compared to the first version of this structure, in which the cables were not in tension, the deflection is halved. Figure 34 - Torsion stress Because of the asymmetric shape of the truss, it wants to rotate over its own axe. By using a more rigid material, en oversize the steel dimensions a rigid truss can be created.
Figure 33 - Nodal deformations
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Figure 34 - Torsion stress
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04. CLADDING 04. CLADDING
04. CLADDING 4.1 Triangular tessellation
4.3 Pyramid shaped elements
The cladding around the total stadium is based on different curves. The stadium has an ellipse form and is on top wider than below. Besides this curved shape, the surface has it’s own vertical curvature. This makes the total cladding double curved.
To accentuate the 3D shape of the elements, and add an extra dimension to the flat panels, each rectangular division was tessellated diagonal in which the center had some extra height. In this way, pyramids are being shaped and the 3D shape of the façade gets some extra accent. Besides the accentual function of these pyramids, it is also a opportunity to use different materials on each side of the pyramid.
To avoid extremely high costs of double curved panels, there has been chosen to tessellate the entire surface. This can be done in many forms, but to stay as close as the original double curved shape it’s wise to use triangular based forms as triangles and hexagons.
Grasshopper usage for tessellation For the tessellation of the façade, Grasshopper was used. The Grasshopper file automatically recognizes the intersections between the lines and creates new surfaces. In figure 36 is shown a screenshot of the grasshopper tessellation file.
Based on a horizontal and vertical division there was almost immediately chosen for a triangular tessellated cladding system. As can be seen on figure 35 a triangular tessellated façade can look like a double curved surface. This is the main goal to achieve during this project. Create a optional double curved surface, which is simplified to a cladding system, based on flat panels. This will decrease the costs and will be optional nearly the same as a double curved façade.
Figure 35 - Triangular tessellated surface
4.2 Horizontal and vertical divisions As mentioned before, the tessellation is based on the vertical and horizontal divisions. This chapter will explain how these divisions are determined. Esthetics were in both horizontal as vertical an important aspect, but also the construction properties are taken into account. Horizontal division For the horizontal division a couple of aspects were very important. The connection to the present floors should be taken in account. Because of the height difference between each floor it is almost impossible to create a universal façade system which would perfectly fit to all the different floor heights. The cinema and hotel box, who will pop out of the stadium on the north and south side will perforate the façade so it is important to have a good connection to both the bottom and top of these boxes. Same problem here, is the different floor height of these floors which makes it impossible to use a universal measure which connect to both floor heights. For this reason there has been chosen for a division as close as possible to both floors, so the connecting can be made with a small extra panel. Besides this argument it was also very important to make as square possible divisions, so the vertical division was also a important factor.
Figure 36 - Façade tessellation
By creating the new surfaces, Grasshopper can also create new end points. By connecting these end points with a polyline, using a Cull including a pattern, the diagonal lines can be created.
Vertical division Vertically, the façade has to connect to the underlying structure. Because of those 40 columns, the vertical division has to be a multiple of 40. As earlier mentioned, it is important to make ‘as square as possible’ divisions, so the final divisions were; Horizontal Vertical
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It was very important that the new lines were drawn as straight lines instead of curves, because the tessellated façade was build up out of all flat elements. The curves which are used as start of the dividing horizontally were divided into 160 parts, and the new control points are connected with a polyline to make sure all lines are straight and not curved.
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04. CLADDING 4.4 Materialization The decision for the tessellation was most of all based on the fact that it is a lot cheaper (factor 10) and easier to build a curved surface out of flat panels. This decision suggest that the material that will be used should be a stiff and hard material. During the process the materialization was determined, and it became clear that a transparent stiff panel (such as glass or plastic) wasn’t ideal for this size and weight. The structure would have to carry a lot more weight, and the stiffness of the material could be a destructive factor. The immense structure could be to flexible for the stiff material and causing it to break. Therefor a new material was chosen, and based on it’s lightweight and high flexibility, this is textile. For the different sides of the pyramids (as determined before and argued in chapter 4.3) the following exact materials will be used.
Figure 39 shows the total image of a part of the façade when it will fully operate. The roof, which has the same structure as the façade will overshadow a part of the grandstand to create a full shell around the entire stadium. As can be seen on the picture the roof of the stadium fully exists out of flexible PV-cells. This is possible because the roof is almost flat. Therefore the orientation of the roof does not have to be taken into account.
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1. PV-cells (mounted on the textile) 2. Translucent textile 3. Transparent textile
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In figure 37 is shown how this distribution is made.
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The upper side of the pyramid is chosen for a textile with several PV-cells mounted on this. There has been chosen for the upper part because this part is the best located to attract as much sun as possible. At the north side of the stadium the PV-cells will be replaced by the translucent textile, because PV-cells won’t work on this side of the stadium due the orientation. Figure 37 - Materialization on the pyramids
The PV-cells which have to be stitched on the textile has to be as flexible as possible, as a second layer of textile. This can impossible been done with the regular PV panels. As can be seen on figure 38 there are flexible PV-cells available such as these, already fixed on a canvas material. For the translucent textile, normal textile will be used. The light will fall through the material, but the view is obstructed. The transparent panels will be made out of textile with an as high as possible transmittance coefficient. In this manner, the view over the Maas and the rest of the location will not be blocked.
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Figure 39 - Façade tessellation
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04. CLADDING 4.5 Reference – Unilever Headquarters Hamburg Tensioned fabric over a pyramid shaped frame isn’t a new form of cladding, it is used before. In this chapter some reference images are shown to clarify the system further before going into detail. As can be seen at figure 40, the size of Unilever’s headquarters is a lot smaller then the New Kuip will be. This will not affect the measurements of the fabric, perhaps only the underlying structure.
Figure 42 shows the main principle of this cladding technique. The cable structure on which the textile is spanned needs one solid element to remain it’s tension. This one solid element keeps all the cables positioned and makes sure there is always tension. This solid element has to be adjustable to make sure the tension on the fabric remains. This adjustability does not have to be automated, but also can be done by hand, every now and than during the maintenance.
Figure 42 - Based on cables, only 1 solid element is needed
At the ‘top of the pyramid’ there will be no textile attached. At this point the steel cables come together and the solid element between the cables has to connect to them. Figure 43 shows how this is constructed. Figure 40 - Unilever Headquarters Hamburg
Even if it was possible for the textile to fully occupy the pyramid, the tension would be to high and the fabric would tear apart. This solution is not water and air tight, but the surface which is open may be negligible.
On figure 41 is clearly visible how the textile is tensioned over the different steel cables and how this cable frame creates a pyramid shape. In this case the textile is the height of the building, so between every pyramid, a steel cable is needed to keep the pyramids in shape.
As earlier mentioned the solid element, which will work as ‘unfolding an umbrella’ has to be adjustable. Figure 43 shows clearly the threat so the steel cables will always be tensioned.
Figure 43 - The ‘top of the pyramid’ is to sharp for textile
The transparency of the façade is quite important for the New Kuip, because of the view outside and vice versa. From the outside it has to be clear what is happening inside of the stadium. In this way there is given a transparent overview at all time. As shown on figure 44, the transparency of the façade can be obtained by using a fabric. Figure 41 - Creating pyramids with a steel cable frame
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Figure 44 - Transparency can be obtained
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04. CLADDING 4.6 Section and details On this page a total section of the stadium is shown. The image is scaled to fit the page. A detailed version, scale 1:50 & 1:20 can be found in appendix 9.4 DO-05 & DO-06 Section fragments.
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Figure 45 - DO-05 & DO-06 Section fragments
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05. ADAPTABILITY 0 5 . A D A P TA B I L I T Y
0 5 . A D A P TA B I L I T Y 5.1 The use of the bowl As mentioned before, the stadium (bowl) will be used for several functions. This will be achieved by using floating pitches. Each float can be used for another functions, even when there is no float inside the stadium, it can be used. On the figure 46, the different possible functions are shown.
Sand / Dirt track ( Monster Jam Events)
Solid floor (Concerts and Events)
Figure 48 - Perspective from the Maas
When empty – Water park >
Soccer Pitch - Feyenoord (main user)
Figure 46 - Several functions of the bowl
The advantage of using floating pitches, is the time to change the function of the bowl. The pitches can be build op outside the stadium. This gives the opportunity to use the bowl of the stadium for several function in one weekend. For example: Friday a Monster Jam Event, Saturday morning and afternoon a water park, Saturday night a concert and Sunday a soccer match. The pitches will be changed by a boat (Figure 47). Not only the pitch is floating, also a part of tier 1 is floating. By making this part also floating, there is a free height around 6 meters, which gives the opportunity to build up the main pitch / float outside the stadium which only has to be entered the stadium. Figures 48 & 49 shows the part of the tier which is floating.
Figure 47 - “Pull boat”
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Figure 49 - Perspective from the Maas, floating tier and pitch
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0 5 . A D A P TA B I L I T Y 5.2 FlexBase “FlexBase develops and produces floating foundations that are used for construction projects on water in a broad spectrum of applications for residential occupation and commercial, industrial and leisure use. FlexBase’s design concept is based on the buoyancy of EPS (also known as polystyrene foam) and the structural properties of reinforced concrete.
“Based on the principles of a patented construction method, EPS blocks are used to create a floating grid into which the concrete is cast. The first step is to create a floating work floor directly on the surface of the water. This work floor is made from EPS sheets, which feature a hook-and-butt joint. These sheets are glued to each other in a brickwork bond pattern. The EPS blocks are placed on this floor in a previously determined grid pattern. The total height of this structure depends on the required buoyancy. The structural strength is achieved by casting the joist and floor construction in situ.”
The FlexBase concept is unique in that the foundation is supported directly by the water itself, which makes it possible to construct structures of any dimensions. The use of a long-lasting EPS core makes the floating platform unsinkable. EPS’ excellent buoyancy also results in a low depth of structure below the surface. The fact that EPS is very easy to cut and shape offers enormous design freedom. Additionally, because no special facilities are required during construction, significant cost savings can be achieved.”
“By building directly on the water’s surface, the dimensions of the EPS floating platform are not dependent on transportation by road or by water. The only constraint on the maximum size of a floating platform is the ability to control the concrete when it is prepared and poured. Dimensions of several thousands of square meters are perfectly feasible. Because EPS is easy to process, it is possible to engineer any shape that is required, either square, rectangular, round or u-shaped.”
Source: www.flexbase.eu
1. EPS work floor
2. Hook-and-butt joint
5. Pouring the concrete joints / beams
Source: www.flexbase.eu
3. EPS work floor
4. Install EPS-blocks
6. Placing prefab concrete boundary elements
7. Pouring the concrete floor Figure 50 - FlexBase principal
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0 5 . A D A P TA B I L I T Y 5.3 Stadium is a dock
5.4 Adaptable roof
An important aspect of the floating pitches is the fluctuation of the water level. To reach a verifiable water level, there will be used a lock (Figure 51). This lock will control the water level inside the bowl. The space in the bowl will function like a dock (Figure 52). To ensure that the pitches will fluctuate during the events, the pitches will be supported by a structure in the water. The lock can fluctuate the water level when the pitch needs to be removed.
The second adaptable aspect of the stadium is the â&#x20AC;&#x153;removableâ&#x20AC;? roof of the stadium. The roof of the stadium will open longitudinal, to get ideal daylight into the bowl. The stadium is orientated by the FIFA requirements and the ideal orientation comparing the sun. The shape of the roof is based on a solar study (Appendix 9.5 - Solar Study - Roof) The opening will have the same width as the pitch. The fixed part of the roof will cover the grandstand, which the spectators will always have dry seats.
The advantage of the bowl as a dock, is the possibility to build in the stadium. In the stadium the building conditions are better than outside the stadium.
Figure 51 - Lock
The structure of the adaptable roof is like a harmonica. On figure 53 is a reference shown with a similar structure.
Figure 52 - Dock
Figure 53 - Toyota Stadium Japan - Harmonica Roof
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0 5 . A D A P TA B I L I T Y 5.5 Harmonica roof The harmonica roof will slide along the big trusses of the roof. The mechanism of sliding the roof is like a rollercoaster connection (Figure 54). It is a mechanism which sliding along a rail and will be in motion by using a motor (car) at the topsides of the roof structure. The structure of the harmonica roof are several trusses which span the pitch. These trusses are connected at the rollercoaster connection. Instead of the reference, Toyota Stadium, the harmonica roof consists out of two parts. The reason of the two parts is the requirement of dry seats for every spectator. One of the two parts will span exactly enough to provide dry seats of the grandstand, the other part will span the rest of the roof (Figure 55). The materialization of the roof will be a fabric, to reduce weight of the roof and improve the folding. The principal of the harmonica roof is shown on figure 54.
Figure 55 - Two sliding parts
Figure 54 - Mechanism harmonica roof
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06. SUSTAINABILITY 0 6 . S U S TA I N A B I L I T Y
0 6 . S U S TA I N A B I L I T Y 6.1 Use the Maas The location next to the Maas is an opportunity to use this water in the stadium. The temperature of the water can be used to improve the heating and cooling mechanism through the stadium. The temperature fluctuation of the water is more gradually than the temperature fluctuation of the air. Because the â&#x20AC;&#x153;openingâ&#x20AC;? and the water in the stadium, there is no need of extra pipes because the water is already in the stadium. The airflow will transport the heat or cold to the desired part of the stadium.
Figure 56 - Winter situation
Figure 57 - Summer situation
Winter situation The temperature of the water is warmer than the temperature of the air, these warmth can be used by ventilate the stadium.
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Summer situation The temperature of the water is colder than the temperature of the air, these cold can be used by ventilate the stadium.
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0 6 . S U S TA I N A B I L I T Y 6.2 Energy The stadium will be provided by PV-cells. As mentioned before in chapter 4 – Cladding, the cladding exist out of several “pyramids”. One surface of these pyramids is provides by PV-cells, this is the surface which is directed towards the sun. Not the whole stadium is provided by PV-cells, because the north façade is not useful to add PV-cells. The cladding continuous over the roof, the pyramids of the roof are totally provided by PV-cells. As shown on figure 58 is the materialization based on the sun. The energy which will be generated can be used for the cinema or the lights at the pitch.
SOUTH
Figure 58 - PV-cells on the cladding
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0 6 . S U S TA I N A B I L I T Y 6.3 Collect rainwater The roof of the stadium will be used to collect rainwater. The collected rainwater will be stored and used for the grey-water-system (flush toilets). Because of the shape of the roof, the water will automatically be transported to the lowest part of the roof. The lowest part of the roof is at the â&#x20AC;&#x153;insideâ&#x20AC;? of the stadium. The roof is provided by several beams, thus the surface of the roof will be separated. Each separation is provided by a pump which will pump the collected water to the outside of the stadium. From this point the water will be collected and stored (Figure 59). The principal of using pumps to pump the water from the inside to the outside of the stadium is already used in the current stadium. This proved method can also be used in the new stadium. The stored water will be purified and used for the grey-water-system, mainly to flush the toilets because of the big peak moment during events.
Figure 59 - Principal collection rainwater
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07. DIGITAL 0 7 . MANAGMENT D I G I TA L M A N A G M E N T
0 7 . D I G I TA L M A N A G E M E N T 7.1 Digital process organization
7.2 File management
At the start of this workshop an inventory was made about the software that should be used. By making this inventory a targeted task list could be made. First of all, the software to create the core model was chosen, based on experience and possibilities ArchiCAD has been used. Because of the difficulty to create (double)curved surfaces in ArchiCAD, Rhino has been used as plug-in for these parts of the design. The parameterization of the model has been separated in different parts, which eventually are transferred into the core model.
On figure 60 is a scheme shown of the file management during the process.
1. CORE MODEL
The choice for ArchiCAD instead of Rhino as core model may be called remarkable. The experience and possibilities to create accurate drawings was decisive. The program is based on 2D input, which includes a height value to create a 3D model. Rhino, however, is based on the extensive 3D capabilities but is for a building design a less suitable program to generate drawings with. The possibilities in ArchiCAD to create all drawings, a 3D model and an integrated render program were preferred above the 3D capabilities in Rhino.
2. INPUT PROGRAMS
The parametric part of the workshop is been done in Rhino with the Grasshopper plug-in. The output of these programs is transferred to ArchiCAD to complete the core model. For the extensive 3D modeling Rhino is used and was imported to a suitable exchange file for ArchiCAD. In chapter 7.4 more detailed information will be given about this topic. The following computer programs are used to create the model. Graphisoft ArchiCAD
Core model
McNeel Rhino
3D detailed drawings for faรงade design and parametric design
McNeel Grasshopper
Parametric designing, solar study, creating a structure model
Autodesk AutoCAD
2D schematic drawings, to create import drawings for Rhino Use as conversion tool between ArchiCAD (export) and Rhino (import)
Google Sketch-Up
Conversion software for 3D models between Rhino (export) and ArchiCAD (import)
Oasys GSA
Structural calculation software
Artlantis
Render software for ArchiCAD
Microsoft Word
Text editing
Microsoft PowerPoint
Presentations and reports
Adobe Photoshop
Embellish the renders created in Artlantis
Adobe Illustrator
Embellish 2D drawings
Dropbox
Manage and exchange of files
3. CALCULATION / EDITING OUTPUT
4. TEXT EDITING / PRESENTATIONS
FILEMANAGEMENT / EXCHANGE
Figure 60 - File management
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0 7 . D I G I TA L M A N A G E M E N T 7.3 Archive structure
7.4 File exchange
Following structure has been set up in the Dropbox in order to keep an overview of all the files.
The more difficult 3D parts of the design were made in Rhino with the Grasshopper plug-in. As mentioned before the structure and the façade design had a lot of input from the Grasshopper models. The file exchange between Rhino and ArchiCAD proved to be very difficult. A lot of steps were needed to import a Rhino model into the ArchiCAD core model. As shown on figure 61, several steps has to be made for a successful exchange of the files.
> XXL WORKSHOP (shared folder) > 00 INFORMATION > Information InfoBase > Information FIFA Requirements > Information Municipality of Rotterdam > 01 REFERENCES > Images and information of reference projects > 02 LECTURES > Lectures and readings given > 03 CONCEPTS > Drawings > Images / renders > 04 ARCHITECTURE > Drawings > Images / renders > 05 STRUCTURE > Calculation (GSA files) > Input files (Rhino / Grasshopper files) > Export models ArchiCAD > 06 CLADDING > Rhino / Grasshopper files > Drawings (2D) > Export models ArchiCAD > 07 SUSTAINABILITY > Drawings > Images / renders > References > 08 ADAPTABILITY > Drawings > Images / renders > References > 09 PRESENTATIONS > Pinpoint presentation 11-02-2011 > Concept presentation 17-02-2011 > Final presentation 01-04-2011 > 10 DRAWINGS AND RENDERS > Drawings ArchiCAD > Definitive drawings > Expired drawings > Renders Artlantis > Definitive renders > Expired renders > 11 FINAL REPORT > PowerPoint file > PDF File > 12 FYSICAL MODEL > Laser drawings > Photo’s
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5 Figure 61 - Digital steps
Step 1 – Creating the Rhino file First of all, the Rhino file had to be creating in combination with the Grasshopper plug-in. The information gathered in this step is depending on the subject of the Rhino file. Step 2 – Export the Rhino model to .3ds Because a .3dm file can not be directly imported into ArchiCAD, the file has to be converted to .3ds so it can be opened with Sketch-Up. It is also impossible to import a .dwg or .dxf file into ArchiCAD because the 3D information will be lost during the export. Step 3 – Import to Sketch-Up The .3ds file can be imported in Sketch-Up. During this step the level of details are very important, this can be determined while exporting from Rhino. Rhino can work with nurbs surfaces, while Sketch-Up simplifies the nurbs to surfaces. Depending on the form and level of detail for each object, a different level of detail can be chosen during the exportation from Rhino to .3ds. Step 4 – Upload to Google Warehouse Direct import from .skp files into ArchiCAD is also impossible, so the best option is to upload the .skp file to Google Warehouse so the file is available through the internet. Step 5 – Import in ArchiCAD With a Graphisoft plug-in for ArchiCAD it’s possible to import .skp models from Google Warehouse into ArchiCAD. The file will be read as a .gsm file, which is similar to a object file in ArchiCAD. After these steps the object can finally be used in the core model. Several problems occurred during this exchange of files; - To be able to upload a .skp file to Google Warehouse, the file has to be smaller than 10 Mb. This limits the level of details which is for some parts necessary. The façade elements had to be separated in 40 different parts because of this problem. - Somewhere during this process the scale of the file gets confused. When the object was imported in ArchiCAD it had to be scaled with a factor 0.039 before it was useable. - Different materials were no option in 1 export file. In ArchiCAD it is not possible to change the different material colors and textures of the import model. It’s only possible to change the color of the entire element. The façade for instance had to be separated in 4 different elements because of this problem.
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0 7 . D I G I TA L M A N A G E M E N T 7.5 Parametric models and Grasshopper plug-ins During the project, different Grasshopper models have been made. As earlier mentioned in this report, almost all the different subjects have been determined with a Grasshopper model. In this chapter some extra details about the Grasshopper file itself, and some additional plug-ins which are used.
For an ideal exchange between the Rhino file and calculation program GSA a plug-in was used for this exchange. Geometric Gym has developed different plug-ins such as ssiGSA and StructDrawRhino to connect to GSA and make it possible in Grasshopper to create for instance truss systems easily. As shown on figure 64 the interface is quite extensive.
Grasshopper & Structure In order to design the structure, highly based on itâ&#x20AC;&#x2122;s esthetic value, grasshopper was a useful tool. By adding sliders to manually change the number of columns and their size. On figure 62 is shown the Grasshopper model to determine the amount of columns around the stadium, by animating the output, a decision was made based on esthetics (figure 63).
Figure 64 - Geometric Gym Grasshopper plug-in interface
Using this tool makes it a lot easier to create truss systems because the weave pattern, which should be used in Grasshopper is integrated with a function of different truss systems. By creating a set of curves, the truss system was easily build. Additional information as divisions of the curve and truss pattern can be manually changed in the commands.
Figure 62 - Grasshopper used to determine the structure
Figure 63 - Output of animation made by Grasshopper to compare the different configurations Figure 65 - Output of animation made by Grasshopper to compare the different configurations
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0 7 . D I G I TA L M A N A G E M E N T Grasshopper & Cladding The tessellation of the façade was an operation which could be easily done in Grasshopper. Problem was, there were so many options for performing this operation. Every aspect of the façade could be made parametric, but there was chosen to make only a few aspects parametric. This improved the performance of the model, because otherwise the options would be limitless.
Grasshopper & Sustainable Design In order to create a sustainable as possible stadium, Grasshopper was used to do a solar study. This could also be done in Ecotect, but while making this the Ecotect tutorial was not been given yet. The solar study is used to determine the measurements of the roof. Starting point of this study was the need of maximum sunlight on the pitch during the match.
The shape of the façade was created in a 2D section and ‘sweeped’ around the entire stadium. This surface was tessellated. Parametric values of this tessellation were the amount of divisions, not the exact size of them. Very important was the fact that the amount of divisions should be a multiple value of the amount of columns, as mentioned before. In this way, the structure of the façade could easily connect to the stadium structure behind. The work with sliders to divide the surface was an ideal performing system.
Information about the sun exposure was available on internet as Grasshopper model. Location information had to be indicated (longitude and latitude) of the exact position of the stadium. By creating different roof types (concave and convex) the shadow could be measured. The grandstands were created in the Rhino file so the shadow could be projected on the stands. By animating the different options a decision was made. All output was compared at the same dates and times and an ideal roof height was chosen. The output is included in appendix 9.5 - Solar Study - Roof. Figure 68 shows some examples of this output.
As shown on figure 66 the tessellation of the surface is based on different curves, which were connected by polylines on the control points.
Figure 68 - Output examples of the solar study
As shown on figure 69 the projection of the shadows is depending on the information which is entered manually on the sliders.
Figure 66 - Grasshopper used to determine the façade tessellation
The different divisions were horizontal and vertical connected. By using the control points of each intersection a diagonal pattern could be placed on the surface. In this way the triangular tessellation was formed. On figure 67 is clearly visible how this operation was performed in Grasshopper using the ‘Cull’ command to create the pattern. Figure 69 - Grasshopper used to create a solar study
Figure 67 - Creating diagonal tessellation between divisions
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08. CONCLUSIONS 08. CONCLUSIONS
08. CONCLUSIONS 8.1 Conclusion / Summary
8.2 Sources
During the project of designing a stadium there is created the New Kuip which satisfies the requirements of the FIFA. Combining innovative and proofed methods, a stadium with a combination of all the different disciplines is designed as one complete stadium.
During designing the stadium, there are several sources used: Books: - Football Stadium, Technical recommendations and requirements (FIFA) - 5th edition 2011
A summary of the design: - Stadia, A design and development guide - Geraint John, Rod Sheaard & Ben Vickery - 4th edition
Concept: - FIFA requirements - Waving grandstand
Lectures: - KCAP - Rotterdam - Werner stadionpark New Kuip
Architecture: - Location next to the Maas - Connected to the main spots of the area: public transport, current stadium, sport campus, new dwelling - Use of 3 bridges - main entrances for spectators / supporters - Private entrances in the plinth - Relocate the Pathé into the stadium - 24/7 = cinema + hotel & floating pitches (concerts, events, monster jam, motor cross, soccer, water park) - Parking & Kart track - Recognizable functions = boxes (hotel en cinema) - Big promenade with accessibility to the different tiers - Transparency - see what happens inside the stadium and vise versa - Iconic value in combination with pillars (structure)
Internet: - www.flexbase.eu - www.behnisch.de - www.vector-foiltec.com - www.form-tl.de - www.skyscrapercity.com
Structure: - Pillars - Cable-stay structure - Columns around the stadium - Big trusses (roof structure) - Space frame
- www.rotterdam.nl/gemeenterotterdam
Cladding: - Transparent - see the bowl - Tessellation - “Pyramids” on tension - Materialization: transparent fabric, translucent fabric, PV-cells Adaptability: - Floating pitches & part of grandstand = 24/7 - Removable roof - Harmonica principle Sustainability: - Use the temperature of the Maas - Generate energy by using PV-cells - Collect rainwater and use grey-water-system Digital Management: - Computational parameterization part of the design (Grasshopper, Rhino, Sketchup, ArchiCAD) - Dropbox and InfoBase use as archive
Figure 70 - Perspective from the public transport / square
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09. APPENDIX 09. APPENDIX
09. APPENDIX 9.1 Floor plans
DO-01- Floor plans
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09. APPENDIX 9.2 Sections
DO-02 - Sections A-A & B-B
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09. APPENDIX 9.3 Elevations
DO-03 - Facades North & East
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09. APPENDIX 9.3 Elevations
DO-04 - Facades West & South
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09. APPENDIX
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DO-05 - Section fragment
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9.4 Section fragments
DO-06 - Section fragment
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09. APPENDIX 9.5 Solar Study - Roof
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09. APPENDIX 9.5 Solar Study - Roof
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09. APPENDIX 9.5 Solar Study - Roof
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