Studio Morphological Engineering

FACULTY OF I ENGINEERING SCIENCE

MORPHOLOGICAL ENGINEERING DESIGN OF A BRIDGE FOR TINTAGEL CASTLE Tintagel, United Kingdom

Toon Maas Brecht Van de Velde

Academic Year 2015 / 2016

Š Copyright KU Leuven Without written permission of the promotors and the authors it is forbidden to reproduce or adapt in any form or by any means any part of this publication. Requests for obtaining the right to reproduce or utilize parts of this publication should be addressed to dept. Architecture, Kasteelpark Arenberg 1/2431, B-3001 Leuven, +32-16-321361 or via e-mail to secretariaat@asro.kuleuven.be.

A written permission of the promotor is also required to use the methods, products, schematics and programs described in this work for industrial or commercial use, and for submitting this publication in scientific contests.

FACULTY OF I ENGINEERING SCIENCE

MORPHOLOGICAL ENGINEERING DESIGN OF A BRIDGE FOR TINTAGEL CASTLE Tintagel, United Kingdom

Thesis submitted to obtain the degree of Master of Engineering: Architecture Promotors: Prof. ir.-arch. Leo Van Broeck Prof. dr. ir.-arch. Mattias Schevenels Toon Maas Brecht Van de Velde

Academic Year 2015 / 2016

Acknowledgements We would like to express our appreciation to Prof. ir.-arch. Leo Van Broeck and Prof. dr. ir.-arch. Mattias Schevenels, for their patient guidance, enthusiastic encouragement and useful critiques of this work.

We are also grateful of the data provided by English Heritage. Finally we wish to thank our parents for their support and encouragement throughout our studies and likewise our fellow students for their constructive feedback and motivation.

TABLE OF CONTENTS

INTRO MORPHOLOGICAL ENGINEERING

3

HISTORY

8

PROJECT VISION

16

SELECTION PROCESS

20

CONCEPT OF THE FORM

26

PLAN

36

STRUCTURAL CONCEPT

42

C A LC U L AT I O N S

46

STRUCTURAL METHODOLOGY

56

CONSTRUCTION DETAILS

60

REFERENCES

86

A N N E X: S P E C I F I C AT I O N S O F U S E D M AT E R I A L S

D O E S ‘A R C H I T E C T U R E B E G I N W H E R E E N G I N E E R I N G E N D S ’ ? Walter Gropius

TOON MAAS & BRECHT VAN DE VELDE

T

he architect with his creativity, his knowledge of human nature and philosophical mind is considered to be a person working for the people, whereas the engineer is seen in a role in service of the people (designing roads, building bridges, etc.). He is a person looking for a grip in an analytical world, full of data and hard science (exactitude and objectivity) whereas the architect is rather familiar with the soft science (social science).

But when looking back in history, the architect and the engineer – the person who invents, creates, calculates how things can be built were most of the time one and the same person.

A perfect example of this are for example the Gothic churches built in medieval times.

In times of an economic crisis, daring architecture is put numerous times on hold. We fall back on those things we know and think are easier and cheaper to build. In this context it rarely happens that the two fields mentioned above, come together and think about how we could manage to create astounding architecture in times like these.

We must say that the title of this prologue is a contradiction of what we often see today: after the architect designs his building, he goes to the engineer and asks him how it can be built.

The question is: how can we merge those two worlds? This means: looking for a combined action, trying to demolish the barriers between

them and learning each other’s vocabulary or at least trying to understand it.

KU Leuven has provided us a learning platform at an academic level, where we have been schooled for five years in a combined engineering-architectural field of study. We have succeeded to develop an engineering mind-set, and we have tasted richly from the architecture produced in the past.

In this thesis, which carries the name “Morphological Engineering”, we attempt to explore a research field in which the two disciplines are combined in a design project.

The main reason why we have chosen for this thesis, is to try to combine these two disciplines.

It is our aim to show how we can produce quality architecture with a thoughtful structure, which is not just meant to make the design stable but also to add extra value in formal expression of our design. We will implement the design in a parametric program in order to make it easier for us to adjust the form, and to receive immediate feedback about the forces working on it. From this point of view, it is impossible to detach the structure from the design.

Morphological engineering is not a concept that we have invented. The past has already brought numerous achievements within this field. In what follows we show some examples that may or may not be recognised.

3

Eladio Dieste / Church of the Christ Worker / Atlรกntida, Uruguay

Localarchitecture / Chapel Of Saint-Loup / Pompaples, Switzerland

4

Felix Candela / Hyperbolic Paraboloid Experiment

Sefar Architects / Medina Haram Piazza / Medina, Saudi Arabia

5

HISTORY PROJECT VISION

HISTORY

TINTAGEL ISLAND

T

intagel, a small dot in the county of Cornwall situated on the Atlantic coast, lying in the Cornwall Area of Outstanding Natural Beauty is of huge importance in English Heritage. This importance was induced by the Arthurian legend by the scholar Geoffrey of Monmouth. In his History of the Kings of Britain he claimed Tintagel Island as birthplace of the legendary King Arthur.

Nevertheless, the history of Tintagel didn’t start with King Arthur, but had a notice of existing much earlier in the Iron Age. In these times, the typical jagged headland of the Atlantic coast was used for safe settlements above the seaways, secure from any danger by the mainland. On the Island itself no conclusive evidence was found for those settlements, due to the fact that later buildings obliterated all evidence of early settlements. But existing examples were found not far from Tintagel. This is why the presumption of the habitation remains affirmable. The isthmus, the narrow passage to the Island, gave this refuge its name: ‘Din Tagel’, composed from the Cornish words ‘din’ or ‘tin’ and ‘tagell’, meaning the Fortress of the Narrow Entrance.

8

In later centuries evidence - though it was not much - was found of a Roman presence in the area of the Island. During the Dark Age the commercial links with the Mediterranean, made Tintagel Island an important networkbase for the trading of luxury goods such as olive oil, wine and fine tableware, in exchange for raw materials such as tin. Although thousands of pieces of pottery were found at Tintagel, it is not clear if Tintagel was either a primary trading site, where the imported goods were landed and exchanged, or if the goods were brought to Tintagel for use.

After an intense period of high activity on the Island itself and in its surroundings, there was a downswing. Assumptions were made that the political, administrative and trading importance Tintagel once had, didn’t correspond with the changing contemporary politics.

The place regained international attention through an important piece of work in the 12th century: History of the Kings of Britain by Geoffrey of Monmouth. He marked Tintagel Island as the place where King Arthur was born.

Monmouth’s veracity was taken up to the sixteenth century.

Since the seventeenth century there was more and more doubt about the exactness of some of his stories. Furthermore there is no scientific proof that the Arthurian legend is welded to Tintagel. It was due to the imagination of people who were thinking about knights, medieval warlords and the old ruins on the site, that one thought one of these heroes had to be King Arthur.

11

12

1260

1337

1390

1540

Maybe driven by The History of the Kings of Britain, Richard, Earl of Cornwall, younger brother of Henry III, builds his castle on the isthmus during the 1230s and 1240s. At this time the peninsula and the mainland were already tormented with erosion as a result of a pounding Atlantic sea. The landslips in the subsequent centuries took many parts of the castle and courtyard deep down into the Atlantic sea.

After the death of Richard’s son, Edmund in 1300, leaving no heir, the Earldom of Cornwall returned to Edmund’s cousin Edward I. However, in the beginning of the fourteenth century the castle fell into disrepair. It was until the Black Prince - sun of Edward III - that the decay came to an end. New building activities on the site were established by the new restoring regime in Cornwall. Later, in the 14th century, the castle was used as a prison, where state prisoners were held under custody. Around the shift of a new century the site started to undergo a fluctuation of decay and fortifications against French and Spanish invasions.

From the 17th until the 19th century the mining industry pushed the attention to the castle in a distant memory. However at the end of the 19th century, Tintagel Castle was being saved from oblivion by an upcoming interest of tourists in the history of the site. Stairs were carved in the steep cliffs by the local quarryman and later on, a bridge was placed to improve the accessibility. Today with 200.000 visitors a year, Tintagel Castle forms one of English Heritage’s most popular sites.

15

PROJECT VISION

TINTAGEL CASTLE BRIDGE DESIGN COMPETITION

T

16

intagel Castle is an extraordinary historical site in South West England. With its thirteenth-century ruins, surrounded by nature and balanced on sea-bitten precipices, it is one of the most spectacular historic sites in Britain.

The elemental power and beauty of the site, combined with a rich history and mystery, makes Tintagel Castle a popular attraction for tourists. For many years, people have been coming to Tintagel to be immersed in its romance and literary mystery.

However, the current situation of circulation is far from ideal to fully enjoy the visit. In summertime, queuing is an important part of visiting the castle, since the only access point to the peninsula is a narrow opening in a wall of the Island Courtyard. This passage is currently only accessible by taking a very steep staircase, which also prevent a part of the visitors to enter the Island. Furthermore the mainland’s courtyard is now often neglected by the route chosen by most of its visitors.

Steep Stairs

Queueing in October

Old circulation pattern

New circulation pattern

English Heritage, the organization in charge of Tintagel Castle, therefore proposed a competition to build a bridge linking the headland to the mainland, just like the original state of the isthmus. This brings solutions to all the problems of the site, but also provides opportunities to bring extra qualities to the visit, making Tintagel Castle an even more popular destination. By having this many values in one place, it is only logical that there are boundary conditions imposed. The goal of these boundary conditions is to maintain the historic values and romantic atmosphere of the peninsula. English Heritage describes the aim of this bridge as follows, making it a perfect study object for a morphological engineering thesis:

The bridge will transform the visitors experience, opening up exhilarating views of the Island, coastline and Atlantic seascape. It will also create a direct route to the Island, relinking the castle with it original entrance. More than just a practical passage, the bridge should exemplify design at its most assured. English Heritage envisages an elegant, even structurally daring, concept, both beautiful in its own right and sensitively balanced with the landscape and exceptional surroundings – the site lying within an Area of Outstanding Natural Beauty.

17

SELECTION PROCESS CONCEPT OF THE FORM PLAN

SELECTION PROCESS

GETTING STARTED

T

o get started with designing, we decided to draw some different standard types of bridges. Bridges which are known to be popular, much in use and likely to endure in time. After a selection, nine bridges remained. We used those nine bridges as ‘representatives’ of nine different classes of a - self proclaimed - taxonomy of pedestrian bridges. The representatives of the classes of pedestrian bridges are: the arch bridge [1], the multiple arch bridge [2], the bow bridge [3], the cable-stayed bridge [4], the beam bridge [5], the hanging bridge [6], the suspension bridge [7], the bow-string bridge [8] and the cable-stayed bridge without backstays [9].

By analyzing the competition’s expression of interest, we chose seven key objectives. This way we could balance their properties against each other [table 1]. We rated each of the bridges with our gut feeling and hereby gave them scores from one to three.

If a bridge seemed to be handling this key objective well, we gave it a two. If we thought the bridge achieved this key objective exceedingly well, it got a three and when the property of the bridge appeared to be insufficient to us, the bridge got a score of one.

Analyzing the total score for each bridge type, being the sum of the assigned values, we were able to make a first - raw conclusion for the design of the bridge: To meet the requirements for designing a pedestrian bridge in this specific location, we prefer not to have any construction elements above the level of the bridge deck. The purpose of this first ‘rule’ for designing this pedestrian bridge, is to lessen the impact on the local vernacular and to maintain a peaceful view at and from the bridge.

20

1

2

3

4

5

6

7

8

9

-1-

-2-

-3-

-4-

-5-

-6-

-7-

-8-

-9-

respect for local vernacular

3

3

2

1

2

3

1

1

1

allowing innovation

2

3

2

2

3

1

2

2

3

build-ability

3

2

3

3

2

3

2

3

2

- archeology

2

2

2

2

3

3

1

3

1

- landscape

3

2

3

1

3

3

1

1

1

- access

3

2

3

2

3

3

2

3

2

low maintenance & safe upkeep

3

3

3

1

3

3

1

1

1

19

17

18

12

19

19

10

14

11

minimal construction impact:

- table 1 -

21

22

1

2

3

4

5

6

SELECTION PROCESS

DESIGN KICK-OFF

After establishing our first ground rule, we started producing little models, placing them in the environment and then evaluating them in terms of the visual impact, concept of the design, originality and beauty in structure.

1. Upside-down conventional tensegrity bridge The bridge deck is supported from underneath by a tensegrity structure. Variation is possible in length and number of supports. Compression elements are thick and the tension elements are slender cables.

2. Two intersecting bridges Two arches working separately and intersecting in the middle of the span, providing an opportunity to create places to rest and enjoy the panorama. Variation is possible in the shaping of the arches.

3. Asymmetrical two-span bridge This is a very simple construction, and attention must be paid in regard to simplicity and details.

Slenderness is a very important element of this design.

4. Staggered Arch Bridge This bridge consists of two rows of arches, each with a different origin, 180째 out of phase, connected by pendentives. Variation is possible in number of supports and overall geometry.

5. Different route bridge In our project, we also tried another approach than provided by the competition, connecting the Higher Courtyard with the Island with a promenade over the Atlantic.

6. Maillart revisited Trying to reinterpret the typical slender and elegant bridge of Maillart, now revisited with new possibilities, new materials and new computing techniques.

By discussing the possibilities to develop these types of bridges and comparing them to the criteria provided by English Heritage, we decided that the next 3 bridges are worth developing in the context of the thesis: 1. Upside-down conventional tensegrity bridge.

4. Staggered Arch Bridge.

6. Maillart revisited.

23

SELECTION PROCESS

C O M PA R I S O N O F T H E T H R E E B R I D G E S

T

here are three bridges left in this selection process: the tensegrity bridge, the Maillart bridge and the Staggered Arch Bridge. In the previous step, we used the competition’s key objectives as selection guide to go from 9 types of bridges to 3 implementations. To compare the remaining 3 bridges, we will use verifiable engineering values in this section to decide with which bridge we will proceed.

Step one: In a first step we designed the 3 bridges in Grasshopper (parametric software and plugin for Rhino) which gave us a 3D model, that made it easy to adjust, by changing the parameters. An example of an implementation in Grasshopper can be found adjoined in calculations / parametric design.

Step two: In the following step we defined the models in more detail. We added materials and material properties and defined the boundary conditions etc. The outcome of this step was a 3D model for each bridge that we could use in GSA (structural design analysis software).

Step three: The possibility to import the 3D models in GSA gave us the ability to add loads on the bridges.

The live load we used equals 500 kg/m 2 and the dead load of the bridge was calculated by GSA (each of the loads are multiplied with the proper factors of safety). Then, GSA provided us an outcome regarding the deflection, the strength and the strain energy. We used these parameters to optimize our three different bridges. Eurocode 2 limits the deflection by L/500. The total span of the bridge is 72 m, thus this gives us a maximum deflection of 14,4 cm, which we will use as a design parameter. Step by step we adjusted the different types of bridges, by adding and removing material at the critical points, without crossing the limitation set by the strength of the materials.

When the maximum deflections fitted L/500, GSA calculated the strain energy and the total use of material, presented in table 2.

Step four: In this last step, we chose one bridge that is used in this thesis to be discussed, analysed and designed in detail. When we look at table 2, we see that the tensegrity bridge and the Maillart bridge are more or less comparable concerning the cost of this bridge, something we can not say about the Staggered Arch bridge. The reason for the high cost is logically linked to the high volume of used material. Nevertheless, we see in this bridge the challenge to reduce the amount of material and cost. Beside this challenge, we are attracted by the architectural form and the aesthetic qualities of this bridge and eager to define and detail its design. So we conclude this section with the decision to go on with the Staggered Arch Bridge.

24

strain energy [kJ]

material [m3] concrete steel

cost** [â‚Ź]

tensegrity

115

51

2,7

70 000

Maillart

73

124

/

93 000

staggered arches

46*

760

/

570 000

* For the strain energy of the Staggered Arch bridge we had to make an assumption, due to the fact that GSA is not able to analyse volume elements. We calculated the stain energy by discretising the bridge and multiplying the deflection with the corresponding force. The deflections in this bridge were provided by Scan and Solve (structural analysis plug-in in Rhino). Now we have an estimation, showing in table 2. ** We used 750 EUR/m3 for reinforced concrete and for steel we used 1,5 EUR/kg (11 700 EUR/m3)

- table 2 -

25

CONCEPT OF THE FORM

10 STEPS - HISTORY TOWARDS DESIGN

I

n the following drawings we will show the process of the shaping of the bridge. In the first three drawings we show the process of erosion over the years and manners to overcome the void between the mainland and the peninsula.

A drawbridge was a first solution to this void in the thirteenth century [1]. After collapsing and erosion of the edifice, the void became bigger in the sixteenth century and a wooden bridge was built [2]. The third drawing shows the current state, two steep staircases and a small wooden bridge connect the two lands over the isthmus [3].

1

26

2

3

27

4

5

28

As explained in the selection process, the option of an arch bridge was a basic typology chosen for this site, due to its vernacular value and respect to the surrounding heritage site. Furthermore the arch bridge is a well represented typology in Cornwall, this design will relate to those bridges in a contemporary and refined way [4]. Firstly we refine the structure by duplicating the arch bridge into two rows of arches [5].

29

The next step is to make the structure as slender as possible, both the columns as the upper parts of the bows. We try to achieve a tension between mass and slenderness, as it is present in “The Elephants”, painted by Salvador Dalí [6]. By placing the two identical rows of arches 180° out of phase, an interaction between the rows arises. The careful positioning of the arches results in interesting configurations at both ends of the bridge. In addition to this, the bases of the columns will not disturb the walking trail over the staircase, but instead they will create more quality on the walking trail by playfully seeking support besides it [7].

30

6

7

31

8

9

32

10

In drawings [8] and [9], we will connect the rows of staggered arches firstly by a bridge deck and secondly by shells, almost pendentive-like. For example, a shell will start from a column in row A and will connect with two columns in row B. The goal is to resemble a normal arch bridge at a first glance, but when looking closer, the more complex structure will appear.

In the last step of shaping the bridge we lower the bridge deck 1,2 meter to form a balustrade out of the structure instead of having one on top of the structure. This way, the slenderness of the upper part of the arches is retained and a new relation with the bows and shells give character to the walk along the bridge over the isthmus [10].

33

1 500

STRUCTURAL CONCEPT C A LC U L AT I O N S STRUCTURAL METHODOLOGY CONSTRUCTION DETAILS

STRUCTURAL CONCEPT

PRINCIPLES

T

he principles of the structural concept are divided into three parts [fig. 1, 2 & 3]. The first two parts, vertical and horizontal, are essential for transferring loads. The third one will talk about the vaults.

1. Vertical Two rows of arches will transfer vertical loading to the columns and to both ends of the bridge. This vertical loading consist of dead load, live load and snow load. As mentioned in concept of the form, we will try to transfer these forces onto the environment with very slender columns.

Buckling, an instability that will easily lead to failure, will obviously be an issue. By changing the boundary conditions at both endpoints of a column to stiff connections, the critical buckling load will be four times larger then the original load. In this case, the lower end of the column is easily clamped into the foundation in the mountainside. The upper end will not be completely clamped, but will be in as rigid as possible connected to row of arches.

2. Horizontal The next step to reduce buckling effects is to transfer the forces exactly along the axis of the column, perfectly vertical in this case. We do this to avoid bending in the column. At every column two arches start, this symmetry will keep the column in balance along its axis. However in the other direction, wind forces will load the bridge horizontally. These forces would have a negative influence on the critical buckling load, hence we will transfer them to the mountainsides by using the bridge deck as a large overturned beam, clamped at its ends.

3. Vault This third part is of minor structural importance. The shells added to the structure will connect the two rows of arches and will transfer together with the rows of arches the wind loading to the bridge deck. The shells will also pierce the bridge deck and support the openings they create.

42

1

2

3

43

deflections [mm] -1733,0 bending moments [kNm] -28251,6

1

1

1

1

deflections [mm] -3,3

-3,3

bending moments [kNm] 1513,5

1513,5

-1087,8

0,8

1

1

0,8

-1087,8

deflections [mm] 2,1

2,1

bending moments [kNm] 1468,3 -774,2

deflections: max 1,2 mm

deflections: max 6,1 mm

44

-774,2

STRUCTURAL CONCEPT

EQUIVALENT BEAM

T

o gain a better understanding of the final deflections of the structure, we here try to explain, step-by-step, how the final deflections are related to those of a simple beam.

From step 1 to 5, every case is loaded with its own weight and a distributed load of 10 kN/m. The material in this conceptual note is C30/37 concrete.

1. First, we design a simply supported beam with the same mass per running meter as the row of arches. The width of this beam has the same value as the width of the arches: 0,3 m. Therefore the corresponding height of the bridge for an equivalent use of material will be 2,35 m. The maximum deflection is 1733 mm.

2. We then add 3 supports in the span, dividing the beam into five equal spans. The deflection is logically greatest, 3,3 mm, at the spans located at the ends of this continuous beam.

3. In this next step we limit the outside spans to 80 percent of the inner spans of the continuous beam. This gives roughly the same deflection in the four spans, being 2,1 mm.

4. Now we shape the same volume of material in the more logical shape of a row of arches, following from the bending moments in step 3. To be clear, the shape of this structure is closer to an optimised shape for stresses, not deflections.

However, these two are of course related. This results in a maximum deflection of 1,6 mm.

5. This final step is the same row of arches, but now supported by the columns that reach to the valley underneath the bridge.

The compression in the high central column will result in a shortening of the column and will cause a larger deflection, being 6,1 mm.

45

CALCULATIONS

PA R A M E T R I C D E S I G N

W

e used Grasshopper (a plug-in for Rhinoceros) as a tool to transform the concept from the drawing table to a digital model [fig. A]. The main reason for the use of Grasshopper is the flexibility in changing complex geometry by adjust some parameters [fig. B]. This tool allowed us to implement on a quit easy way the complex vault shapes of the bridge. Once a rough model was drawn, we imported the outline of the model in Diamonds (a finite elements software).

We applied the necessary loads on the model and preformed a first calculation. The first results showed that the bridge was over dimensioned, so we adjusted the model in grasshopper and preformed a new calculation. We repeated this process several times until we reached the structural limit of the bridge.

The result is a structure where engineering and architecture works together to create an optimal design that satisfies our structural and architectural image.

46

fig. A / Rhinoceros model

fig. B / Grasshopper model

47

CALCULATIONS

DIAMONDS

Model dimensions The maximum span between two columns is 19 m, the total span of the bridge is 75,5 m and will have a maximum height of 27,5 m [fig. C]. The model in Diamonds consists of two arch slabs connected by a bridge deck. The vaults are computed as a dead load.

Boundary Conditions The bridge is positioned between two mountainsides; these mountainsides are characterized by very steep hills. The bridge will be clamped at its both ends into those steep mountainsides and will be supported by five columns clamped in to the neck of the site [fig. D].

27,5m

75,5m

fig. C / dimensions

48

fig. D / settle points

Loads Wind: To obtain the most burdensome situation, we applied a load of 1 kN/m2 (sea environment) perpendicular to sides of the bridge. The load was placed in overpressure as well as in under pressure. To be safe and include the total area affected by wind, we applied in Diamonds for practical reasons Âą 2 kN/m2 to each of the arch slabs.

Snow: The Eurocode prescribes a load in function of the height by the following formula: Sk: characteristic snow load A: height of location above sea level = 80m Z: zone number = 0 ďƒ

Sk = 0,2 kN/m2

Live load: We applied 5000 N/m2 perpendicular to the bridge deck.

Safety factors: Own weight and dead loads: 1,35 Live loads: 1,50 Wind and snow loads: 1,50 Combinations: Diamonds automatically generated 52 different load combinations, using the right safety and combination factors.

The following decisions are results of the worst case scenario.

49

Mesh The mesh shown in figure E consists out of two main parts: the columns and the shifted arch slabs. The mesh for the slabs is defined with a maximum element size of 0,75 m. This means that there are no triangular elements with edges larger than the maximum element size. To make sure this discretization will not affect the geometry too much near the edges and sharp corners, the mesh is defined with a reasonable minimum element size of 0,30 m. For a more accurate calculation of the columns we divided them in four parts. The joining of the columns and the slabs is defined in Diamonds as a rigid connection.

fig. E / mesh of the structure

50

Deflections The following figures show the results of our calculations in Diamonds. Figure F and G are the results of the deflection in respectively the Y and the Z direction. The interpretation of these deflection results is already discussed in structural concept. We can conclude that the obtained results are in line with the equivalent beam model.

y z

x

fig. F / deflection along the Y axis [mm]

y z

x

fig. G / deflection along the Z axis [mm]

51

Stresses Figures H until M show the results from the calculations in Diamonds. The maximal compressive and tensile stresses are shown in figures H & I. The compressive stress in the columns is below the strength of the chosen concrete (C30/37 ďƒ sea environment). For the concrete slabs for the arches, we looked at the two principal normal stresses [fig.

J - M]. The compressive stress is represented by negative values, with a maximum of -19,7 N/mm2 and -12,9 N/mm2, the stresses are below the strength of the concrete (C30/37) [fig. J & K]. The tensile stresse, with a max tension stress of 19,8 N/mm2 [fig. L & M], will be handled by the necessary amount of reinforcement bars with steel characteristic BE 500/500. We can conclude that the resulting stresses do not exceed the boundaries of the material characteristics.

fig. H / compressive stresses in the columns [N/mm2]

fig. I / tensile stresses in the columns [N/mm2]

52

fig. J / first principal normal stresses[N/mm2] most stressful situation for compression in the slabs

fig. K / second principal normal stresses [N/mm2] most stressful situation for compression in the slabs

fig. L / first principal normal stresses [N/mm2] most stressful situation for tension in the slabs

fig. M / second principal normal stresses [N/mm2] most stressful situation for tension in the slabs

53

Reinforcements To calculate the necessary amount of reinforcement for the column, we looked at the most critical column (the highest column in the middle of the span). The minimum amount of reinforcement was provided by Diamonds [fig. N]. We chose for 12 reinforcement bars of diameter 25 mm. When we compare the area of the reinforcement bars (5892mm2) to the section of the column (420/420), it results in 3,3% of the area, which fits the maximum of 4% reinforcement steel [fig. O]. The section of the columns is a result of the necessary amount of concrete cover on the reinforcement bars, derived from the environmental class.

Stirrup: 2  368 mm /m (Diamonds)  diameter 6?/8?/10? requirement diameter stirrup ≥ ¼ diameter reinforcement bars  diameter 8 or 10 area 2*8 = 101 mm2

spacing between stirrups = 275 mm area 2*10 = 157 mm2

spacing between stirrups = 427 mm max spacing

≤ 15*25 =375 mm

≤ smallest section column = 420 mm

≤ 300 mm  diameter 8 Covering:  on the reinforcement bars

≥ thickest bar = 25 mm

≥ environmental class (ES2) = 35 mm 35 + 10 (tolerance) = 45 mm  on the stirrup

≥ thickest bar = 8 mm

≥ environmental class (ES2) = 35 mm 35 + 10 (tolerance) = 45 mm (normative)  total covering on the reinforcement bars 45 + 8 = 53 mm

fig. N / reinforcement columns [mm2]

54

420 45

fig. O / reinforcement scheme [mm] Slabs: For the reinforcement of the upper part of the bridge we use a reinforcement grid of type B1131A [fig. P]. This type of net is banished by Europe out of the list of standard meshes (the weight of the mesh is too high to carry by hand). In our construction methodology we proposed the use of a cable crane to position the construction materials, so the use of the B1131A mesh will be no problem. The concrete cover on the mesh will be the same as calculated for the columns.

12-100

18

12-100

54

fig. P / reinforcement mesh [mm]

55

STRUCTURAL METHODOLOGY

M AT E R I A L S A N D P R I N C I P L E S

construction order

white quartz carpet screed

step 7

polystyrene blocks reinforced concrete lost formwork lost formwork carbon fiber reinforced concrete foundation concrete reinforced concrete reinforced concrete foundation concrete 56

step 8

step 7

step 6

step 5

step 5

step 4

step 1

step 3

step 2

step 1

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he construction of the bridge will go through the following process [fig. Q]: first the foundation will be poured; in a second step the prefabricated columns will be put in place by a helicopter; then the shifted arch slabs will be poured, which will be done in pieces so they could balance each other; step number four is positioning the prefabricated vaults by helicopter; then lost formwork will be attached at the shifted arch slabs; step number six is pouring a reinforced concrete floor on the lost formwork; step seven is providing more height in the floor of the bridge for the plumbing, we use polystyrene blocks in combination with compacted concrete to thicken the floor without gaining too much extra weight; step number eight is putting a quarts carpet on top of the floor, this will function as an anti-slip layer; in the last step the bridge will be painted white.

fig. Q / construction order 57

This structural methodology is based on a combination of examples of bridges on this site, made by the contestants of the Tintagel Bridge Design Competition.

Due to of the complex geometry of the concrete vaults, we opted to prefabricate those elements.

The size of those elements do not allow us to transport them by truck. They will be brought to the construction site by ship. When those elements arrive, they will be put in place by a helicopter.

The prefabricated columns will as well be positioned with this method.

A temporary cable crane will be applied to bring the constructions materials from the mainland to the construction site.

The bridge will be constructed with prefabricated elements (vaults and columns) and in situ pouring concrete slabs (the two shifted arch slabs). A temporary scaffold will be applied, to support the in situ slabs (the passaged to the island will be maintained). The choice for a scaffold is a result of the size and weight of the concrete slaps. This prevented us from prefabricating these elements on the mainland and bringing them with a helicopter or a cable crane to the construction site.

CONSTRUCTION DETAILS

A - B - C - D

DETAIL A

DETAIL C DETAIL B

DETAIL D

DETAIL A scale 1/50

existing masonry wall

in situ bridge deck

in situ arch slabs

precast vaults

DETAIL B scale 1/100

Sigma Façade Topcoat NPS® Matt

900

1200

aluminium tube

slot gutter (incl. LED stips) ACO rebend connection HALFEN lost formwork carbon fiber reinforced concrete 100 mm shear dowel HALFEN

hollow space

neoprene rubber elastic sealant

scale 1/10

SIDDEC quartz carpet screed (inlc. reinforcement mesh) glued polystyrene blocks reinforced concrete 200 mm lost formwrork (plywood 25 mm)

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DETAIL C1 scale 1/100

Sigma Façade Topcoat NPSŽ Matt

aluminium tube incl. LED

elastic sealant neoprene rubber shear dowel HALFEN

SIDDEC quartz carpet screed (inlc. reinforcement mesh) glued polystyrene blocks reinforced concrete 200 mm lost formwork (plywood 25 mm)

polyethylene tube polystyrene expansion joint carbon fiber reinforced concrete 100 mm

scale 1/10

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DETAIL C2 scale 1/100

shell A

shell B

shell C

precast carbon fiber reinforced concrete shell C shell B shell B

precast reinforced concrete column

neoprene rubber elastic sealant shell A reinforced concrete in situ

scale 1/10

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DETAIL D scale 1/10

stirrup 8 mm reinforcement bar 25 mm

anchor bolts w. possibility to adjust the columns grout reinforced concrete

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CONSTRUCTION DETAILS

ADDITIONAL INFO ON THE DETAILS

Railing, bumps and lighting The railing will be executed as a white powder coated aluminum tube. It will be put at a height of 90 cm, laterally supporting on the balustrade and the bumps. The size of the aluminum tube will be 65 mm, a rather large section, that is still comfortable and allows room for a curved led strip at the bumps to illuminate the information displays. The bumps on the bridge deck form part of the shells and are a result of lowering the bridge deck. A possible way of activating the walking route along the bridge is showing information on enameled information boards on the concrete shells. The information will contain the tale of King Arthur and will explain the history of the heritage site. Also, important elements in the environment, like Merlin’s Cave, can be pointed out on drawings of the skyline.

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Water and lighting Draining the water from the bridge will happen at the sides of the bridge deck. A clean and neat solution of the firm Aco, Sideline Led, will drain the water out of sight and moreover will incorporate OLED lighting strips along the way. The difference in height of the two ends of the bridge ensures that the bridge deck’s slope is 2,8%, wich is a more than sufficient inclination to drain the water. The upper side of the balustrade is slanted towards the innerside of the bridge, this will ensure that all water and filth will not smudge the outside of the bridge, but it will end up in the drain under the bridge deck. This calls for a protection of the inner and upper sides of the balustrades.

The white paint ‘Sigma Façade Topcoat NPS® Matt’ with wich the bridge will be painted, has a certain ‘nanotechnology’. This will make sure that the water absorption of the concrete is reduced and thus will sustain and protect the concrete against moss, algae and efflorence.

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T

he bridge connects with its northwestern end to the peninsula side and with its southeastern end to the lower courtyard on the mainland. The two rows of arches will stop after approximately 1 meter when arriving at the mountainsides, allowing proper foundations and announcing the structure as a self-governing one. The bridge deck on the other hand, will continue for another 2 meters. This has been done to make the clamped connection with the mountain possible but also to translate it to the ones walking over the brigde. By combining those two elements, the bridge also advertises itself to its environment in a subtle and respectfull way.

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scale 1/100

CONSTRUCTION DETAILS

DIMENSIONING THE CONNECTION

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50

37 00

0

20 30 0

00

scale 1/100

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REFERENCES

TEXTS

History & Project Vision Malcolm Readings Consultants, Tintagel Castle: Bridge Design Competition, 2015. Retrieved on 18/05/16 from https:// competitions.malcolmreading.co.uk/tintagel.

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History

English Heritage, Tintagel Castle. Retrieved on 18/05/16 from http://www.english-heritage.org.uk/visit/places/tintagelcastle.

Introduction

Fitzgerald D, Architecture Vs. Engineering: Solutions for Harmonious Collaboration, Lineshapespace, 2015. Retrieved on 18/05/16 from https://lineshapespace.com/architectureawards.

Introduction

Tejerina S, Does the architecture begins where engineering ends?, Interempresas, 2010. Retrieved on 18/05/16 from http://www.interempresas.net/FrontPage/News/43134-Doesthe-architecture-begins-where-engineering-ends.html.

REFERENCES

IMAGES

flickr.com arqred.mx English Heritage Richard Lea 3D model Google Earth

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