Architecture/Civil Engineering: Shell Structures

1. Shell Structures
Presented by Melissa Martinyak, Nelson Perello and Kelsey BakerAmsterdam Maritime Museum. Dok Architecten

2. Exploring Shell Forms
“Shell Structures are constructed systems described by
three-dimensional curved surfaces, in which one dimension is
significantly smaller compared to the other two. They are
form-passive and resist external loads predominantly through
membrane stresses.”
“Shell structures for architecture : form finding and optimization”
● Freeform
- Free-curved or sculptural shells
● Mathematical
- Geometrical or analytical shells
● Form-found
- Natural, hanging shapes, strained gridshells
“The shell designer seeks forms to carry the applied loads in
axial compression with minimal bending forces.”
“Shell structures for architecture : form finding and optimization”
Figure 1
Figure 2
Figure 3

3. Forms of Shell Curvature
● Singly Curved Shells (Developable)
- Curved on one linear axis
❖ Ex. Barrel Shells
- Uses arch or beam action to transfer stresses
● Doubly Curved Shells (Non - Developable)
- Synclastic: same sided curvature
❖ Ex. Domes use hoop stresses and arch lines to transfer
forces, under compression
- Anticlastic: opposite sided curvature
❖ Ex. Hyperbolic Paraboloids (Hypars) have simultaneous
tension and compression
Figure 10
Figure 11
Figure 12 Figure 13

4. Materiality of Shell Structures
MasonryTimber Concrete Steel
Figure 4 Figure 5 Figure 6 Figure 7

5. Construction Techniques & Manufacturing
Continuous surface
● Thin concrete
- Traditional timber formwork
- CNC moulds
- Fabric formwork
- Inflatable structures
Discrete elements following that surface
● Gridshell
- Prefabricated elements
Figure 8
Figure 9

6. Structural Premise & Basic Structural Formulas
● Membrane Theory of Shells
- Loads distributed through in-plane axial and moment
forces known as Membrane Stresses
- Three Partial Differential equations describe membrane
stresses, require shape and boundary conditions
- Shell roofs, have compressive stresses following convex
curvature and tensile stresses following concave curvature
- Arch action often involved in structures with convex
curvature
● Bending Theory of Shells
- Bending stiffness necessary to prevent buckling
- Different from form-active tensile systems
- Inextensional deformations introduce undesirable
bending stresses
Figure 14
Figure 14

7. Pros Cons
● Very lightweight and efficient
● Dead load can be reduced economizing
foundation system
● Uses geometries that can span longer
distances, allows for large open spaces
● Aesthetic
● Double Parabola shape allows for large
stresses using thin shapes
● Sudden collapse for shell structures
● Great labor, supervision, and skill necessary
due to complexity
● Environmental issues such as sealing,
leaking, condensation
● Efficient structures may fail
catastrophically
Pros and Cons of Shell Structures

8. Mannheim Multihalle
Frei Otto and Architects Carlfried Mutschler and Winfried Langner
Structural Engineers Edmund Happold and Ian Liddell
1974
Gridshell Structure
Figure 1

9. "two kinds of artificial hill - one of earth, one of grid shell"
Material: Hemlock
Span: 60m x 60m
Lath Size: 50 x 50mm at 0.5m
Bracing: Twin 6mm cables every 6th node
Definition: “a double curved surface
formed from a lattice of timber laths
bolted together at uniform spacing in
two directions”
Gridshell or Lattice Shell
Structure
Figure 2

10. Essen Shell + Multihalle Plan + Section
Figure 5
Figure 4Figure 3

11. Hookean principle of inverting a hanging net
Form Finding
Figure 6

12. Construction
Equal mesh square grid readily bent into shape
Deformation of grid squares into rhombi created a doubly curved surface
Continuous Shell: resists normal and shear forces
Lattice Shell: only resists forces in direction of the lath
Figure 7
Figure 9
Figure 8

13. Structure + Aesthetic Solution
Figure 12
Figure 11Figure 10
Figure 13

14. Load Testing
Figure 15Figure 14

15. Other Gridshell Structures
Savill - LarchGeodesic Dome - Steel
Japan Pavilion - Cardboard Tubes
Figure 18
Figure 17
Figure 16

16. Los Manantiales Restaurant
1958
Groined Vault Shell Structure
Félix Candela
Figure 1

17. Groined Vault Shell Structure
Definition: Groins formed at the convergence of the
intersecting hypar shells, or hyperbolic paraboloid
Structure
Material: Concrete
V-beams reinforced with steel
Shell Diameter: 42.5m (139 feet)
Shell Span: 32.4m (121 feet)
Shell Thickness: 4cm (1 ½ inches)
Figure 2

18. Groined Hypar Vault + Symmetry
allowed for expression of thinness
Structure + Expression
Groined hypar vault
Bolsa de Valores/Mexican Stock Exchange
“the only warped surface whose equation is simple enough
to permit stress calculation by elementary mathematics”
-Candela
4CM
Figure 3
Figure 4

19. Structure + Expression
Hypar shell generate large normal forces at edges
Proper design renders analysis insignificant
Figure 5
Figure 8
Figure 7
Figure 6

20. Structure + Construction Umbrellas
...prevent sinking
...create straight lines
Figure 10
Figure 9
Figure 5

21. Construction + Formwork
Figure 13
Figure 12
Figure 11

22. Constructed Form
Figure 15Figure 14

23. Structure
- Hyperbolic Paraboloid shapes transfer
loads and create symmetry
- V beams transfer membrane stresses
from shell to points of supports
- Arch action is common in shell
structures in order to transfer forces to
supports
- Stresses in thin shells low compared to
strength of materials

24. Louvre Abu Dhabi
2017
Metal Dome Shell Structure
Ateliers Jean Nouvel
Burro Happold Engineering
Figure 1

25. Metal Dome Shell Structure
Modern Dome Proposal
● 7,000 tonnes
● 180 meters in diameter
Design Idea
● Emphasis on light and shadow, reflection and
calm
● Aesthetic matches its role as a sanctuary for
works of art
● A shelter of light
● Geometric design that relates to the local
culture
● Floating atmosphere
Figure 2
Figure 3

26. Filtering Light
● Superimposed layers of repeated pattern at
various sizes
● Four outer layers clad in stainless steel and
four inner layers clad in aluminum separated
by a steel frame five meters high
● 10,000 structural components pre-assembled
into 85 supersized elements
Construction Assembly
Figure 4
Figure 5

27. Structure
● Supported by four symmetrically spaced,
nine-meter high concrete piers topped by a
single steel bearing
● Bearing allows movement when the dome
expands and contracts during temperature
fluctuations
● Dome shape allows forces to be
transferred to concrete piers through
combination of hoop stresses and arch
action in dome
Figure 6
Figure 7

28. Other Applications of Shell Structures
Aircraft
Fuselages
Cars Ship hull
Drinking
Cans
Figure 8 Figure 9 Figure 10 Figure 11

29. Shells in Nature
SeashellsEggshells Flower Petals Tree Leaves
Figure 12 Figure 15Figure 13 Figure 14

30. Beyond the Built Environment | Progressive Fabrications
Funicular ShellsLa Voûte de
LeFevre
Cut-foam Pavilion Thin-tile Vault
Figure 16 Figure 17 Figure 18 Figure 19

31. Questions?

32. References
Adriaenssens, Sigrid, Philippe Block, Diederik Veenendaal, and Chris Williams. 2014. Shell structures for architecture : form finding and optimization. n.p.: Abingdon,
Oxon : Routledge, 2014., Print.
Burger, N., & Billington, D. P. (2006). Felix Candela, Elegance and Endurance: An Examination of the Xochimilco Shell. Journal of the International Association for Shell
and Spatial Structures: IASS. Retrieved September 7, 2018, from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.545.4812&rep=rep1&type=pdf
Chenjie, Yu, et al. “Moments Due to Concentrated Loads on Thin Shell Structures .” Heron Journal, vol. 61, no. 3, 2016, pp. 153–166., heronjournal.nl/heron.html.
Garlock, M. E., Billington, D. P., & Burger, N. (2008). Félix Candela: Engineer, builder, structural artist. New Haven: Yale University Press.
Evolution of German Shells: Efficiency in Form. (2013). Princeton University Website. Retrieved September 7, 2018, from http://shells.princeton.edu/Mann1.html
Farnsworth, David B. “Behavior of Shell Structures.” Https://Pdfs.semanticscholar.org/66d4/248ff0d27cf61ab69de3ccefc072384efd9a.Pdf, Massachusetts Institute of
Technology , June , 1999, pp. 1–58.
“La Voûte De LeFevre, a Study in Stereotomy.” Archpaper.com, 7 Sept. 2012, archpaper.com/2012/09/la-voute-de-lefevre-a-study-in-stereotomy/.
Body-tu-delft.
Liddell, Ian. (2015). Frei Otto and the Development of Gridshells. Case Studies in Structural Engineering, 4(20) Aug. 2015, 39–49. doi:10.1016/j.csse.2015.08.001
“Louvre Abu Dhabi / Ateliers Jean Nouvel.” ArchDaily, 8 Nov. 2017, ww.archdaily.com/883157/louvre-abu-dhabi-atelier-jean-nouvel.
Williams, Chris J.K. “Shell Structures.” University of Bath, people.bath.ac.uk/abscjkw/LectureNotes/what-is-a-shell.pdf.
Mele, Tom Van. “Free-Form Catalan Thin-Tile Vault, Zurich, Switzerland.” Block Research Group, block.arch.ethz.ch/brg/project/free-form-catalan-thin-tile-vault.
Mele, Tom Van. “Funicular Funnel Shells.” Block Research Group, block.arch.ethz.ch/brg/research/funicular-funnel-shells.
Mele, Tom Van. “MSc2 Studio at Hyperbody TU Delft, Netherlands.” Block Research Group, block.arch.ethz.ch/brg/teaching/msc2-studio-at-hyper
“The Engineering Behind the Louvre Abu Dhabi's Striking Geometric Dome.” ArchDaily, 28 Dec. 2017,
www.archdaily.com/886180/the-engineering-behind-the-louvre-abu-dhabis-striking-geometric-dome.

33. Slides 1-6 Image References
Figure 1. Catalan Tile Vault [Image]. https://archpaper.com/2011/12/block-research-groups-freeform-catalan-thin-tile-vault/
Figure 2. Candela Diagram [Scanned Drawing]] http://pc.blogspot.com/2006/11/restaurant-at-xochimilco-felix-candela.html
Figure 3. Heinz Isler Model [Image] https://n0310093.weebly.com/blog/heinz-isler
Figure 4. Mannheim Multihalle [Image] https://www.archilovers.com/projects/151389/roof-for-the-multihalle-in-mannheim.html
Figure 5. Pines Calyx Masonry Dome [Image] https://www.structuremag.org/?p=2046
Figure 6. Los Manantiales [Image] https://www.archdaily.com/496202/ad-classics-los-manantiales-felix-candela
Figure 7. Amsterdam Maritime Museum [Image] https://ascelibrary.org/doi/10.1061/%28ASCE%29AE.1943-5568.0000074
Figure 8. Concrete Shell Scaffolding [Image] https://archinect.com/tacos/fun-things-to-do-with-concrete
Figure 9. Gridshell Construction [Image] https://www.slideshare.net/whysodumbdotcom/understanding-gridshell-structures-mannheim-multihalle-case-study
Figure 10,11,12,13. Shell Structures - Advanced Building Construction [image] https://www.slideshare.net/shwetamodi23/shell-structures-advanced-building-construction
Figure 13. BEHAVIOR OF SHELL STRUCTURES BY DAVID B. FARNSWORTH JR [image] https://pdfs.semanticscholar.org/66d4/248ff0d27cf61ab69de3ccefc072384efd9a.pdf
Figure 14. Arch formulas [image] http://structx.com/Arch_Formulas_001.html

34. Slides 8-15 Image References
Figure 1. Mannheim Multihalle. [Photo]. https://www.naumer-architekt.de/multihalle/images/slide02.jpg
Figure 2. Mannheim Multihalle. [Photo]. https://stadtbild-mannheim.de/uploads/2012-10-11%20Vortrag%20Multihalle%20Verein%20Stadtbild_Seite_34.jpg
Figure 3. Trial Gridshell Structure at Essen. [Photo].
https://www.researchgate.net/publication/283164806/figure/fig1/AS:407083083157506@1474067578288/Trial-gridshell-structure-at-Essen.jpg
Figure 4. Multihalle Plan. [Digital Drawing]. http://tectonicablog.com/wp-content/uploads/2010/05/img1-10.png
Figure 5. Multihalle Section. [Digital Drawing]. http://tectonicablog.com/wp-content/uploads/2010/05/img6-10.png
Figure 6. Mannheim Multihalle hanging form. [Image of Model], https://payload541.cargocollective.com/1/13/424319/13123954/NILE52_1200.jpg
Figure 7. Mannheim Multihalle grid construction. [Image]. http://tectonicablog.com/wp-content/uploads/2010/05/img2-10.png
Figure 8. Continuous and Lattice Shell elements. [Digital Drawing]. Princeton University. http://shells.princeton.edu/Mann1.html
Figure 9. From Flat to Curved. [Digital Drawing]. Princeton, NJ: Princeton University. http://shells.princeton.edu/Mann1.html
Figure 10. Doubling of Layers. [Digital Drawing]. Princeton, NJ: Princeton University. http://shells.princeton.edu/Mann1.html
Figure 11. Diagram of Multihalle’s Dimensions. [Digital Drawing]. Princeton, NJ: Princeton University.. http://shells.princeton.edu/Mann1.html
Figure 12. Mannheim Joints System. [Digital Drawing]. Princeton, NJ: Princeton University.. http://shells.princeton.edu/Mann1.html
Figure 13. Dokumente zu Frei Ottos Multihalle Mannheim. [Drawing].
https://open-codes.zkm.de/sites/default/files/styles/catalog_full/public/artwork/373-dokumente-zu-frei-ottos-multihalle-mannheim.jpg?itok=eQlQZmM5
FIgure 14. Load testing. [Photo]. https://www.researchgate.net/publication/283164806_Frei_Otto_and_the_Development_of_Gridshells.
Figure 15. SAP2000 Load Diagrams. [Digital]. Princeton, NJ: Princeton University. http://shells.princeton.edu/Mann1.html
Figure 16. Montreal Biosphere. [Photo]. http://workflow.arts.ac.uk/artefact/file/download.php?file=2318882&view=214764&embedded=1&textbox=2319025
Figure 17. Hirai, Hiroyuki. [2000]. Hannover Expo Japan Pavilion. [Photo].
https://cdnassets.hw.net/dims4/GG/c257606/2147483647/resize/850x%3E/quality/90/?url=https%3A%2F%2Fcdnassets.hw.net%2F51%2F6f%2F316b5e434c9084b0600d4e482e25%
2Fe86817af-2f3c-4a4c-a7e7-c74b78f7b515.jpg
Figure 18. Savill Building. [Photo]. http://woodawards.com/wp-content/uploads/2016/02/The-Savill-Building-Glenn-Howells-5.jpg

35. Slides 16-23 Image References
Figure 1. Los Manantiales Restaurant. [Digital Drawing].
https://userscontent2.emaze.com/images/c1be7888-a41b-46c0-9878-2fb25a11e1e3/43b9478f-405d-4b24-8043-939d262bb84b.png
Figure 2. Princeton University Study Model. [Photo of Model]. https://i.pinimg.com/originals/64/97/c6/6497c651f9ccfe7ecaedcb0fc1786c8b.jpg
Figure 3 Bolsa de Valores de Mexico. [Photo].
https://2.bp.blogspot.com/-uPia9mAJ3Pc/Wn93U556WeI/AAAAAAAAKOw/oJtodkB_CuE9IR7l33UaXk2QtutTAZkXgCLcBGAs/s1600/bolsa%2Bvalores_1.jpg
Figure 4. (1958). Los Manantiales Restaurant. [Photo]. https://archinect.imgix.net/uploads/v2/v2neempg69967gtw.jpg?fit=crop&auto=compress%2Cformat&w=1500
Figure 5. Candela, Felix. Los Manantiales Restaurant. [Drawings].
https://images.adsttc.com/media/images/5340/c233/c07a/8091/a000/0126/large_jpg/LosManantialesDesignDrawing.jpg?1396752938
Figure 6. Obra de Felix Candela. [Digital Stress Model]. Madrid, Spain: Universidad Politecnica de Madrid. http://w3.mecanica.upm.es/~pantolin/img/xochimilcoFE.jpg
Figure 7. Normal Forces. [Digital Drawing]. Princeton, NJ: Princeton University. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.545.4812&rep=rep1&type=pdf
Figure 8. Cubiertas Ala. V-Beam Cross-Section. [Drawing]. Avery Library Archive at Columbia University.
Figure 9. Umbrella. [Photo]. https://std1.bebee.com/br/pb/43169/c976bd56/900
Figure 10. Cubiertas Ala. Umbrella Footing. [Drawing]. Avery Library Archive at Columbia University.
Figure 11. Los Manantiales Restaurant Formwork Construction B&W. [Photo].http://mxcity.mx/wp-content/uploads/2017/08/xochi-7.jpg
Figure 12. Los Manantiales Restaurant Formwork Construction Color. [Photo].
https://images.adsttc.com/media/images/5340/cb28/c07a/8091/a000/0128/slideshow/skyscrapercity.jpg?1396755229
Figure 13. Los Manantiales Restaurant Formwork Construction Workers. [Photo].
https://images.adsttc.com/media/images/5340/cb23/c07a/80d9/e300/00e0/slideshow/skyscrapercity_1_antares.jpg?1396755226
Figure 14. Los Manantiales Restaurant Interior. [Photo]. https://images.adsttc.com/media/images/5349/3e8b/c07a/8005/6100/0057/slideshow/LosManantiales3.jpg?1397309060
Figure 15. Los Manantiales Restaurant Window. [Photo]. https://images.adsttc.com/media/images/5349/3e92/c07a/8073/b400/0067/slideshow/LosManantiales4.jpg?1397309065

36. Slides 24-31 Image References
Figure 1-5. Louvre Abu Dhabi. [Image]. https://www.archdaily.com/883157/louvre-abu-dhabi-atelier-jean-nouvel
Figure 6-7. Louvre Abu Dhabi. [Image]. https://www.archdaily.com/886180/the-engineering-behind-the-louvre-abu-dhabis-striking-geometric-dome
Figure 8. Car shell [Image]. http://www.forgottenfiberglass.com/fiberglass-car-marques/simpson-designed-sports-cars/the-italia-gtc-sports-car-design-extraordinaire/
Figure 9. Aircraft Fuselage [Image] https://link.springer.com/chapter/10.1007/978-981-10-0234-2_6
Figure 10. Ship Hull [Image]. ttps://www.marineinsight.com/shipping-news/first-ship-hull-largest-vessel-royal-netherlands-navy/
Figure 11. Soda Can [Image]. https://www.vecteezy.com/vector-art/197181-realistic-energy-drink-can-mockup-design-template
Figure 12. Eggshell [Image]. https://www.istockphoto.com/photos/eggshell
Figure 13. Seashell [Image]. http://www.seashells4u.com/clam.html
Figure 14. Calla Lily [Image]. https://www.amylamb.com/artwork/white-calla-lily/
Figure 15. Leaf [Image]. https://www.canstockphoto.com/dead-leaf-48728197.html
Figure 16. La Voute [Image]. https://archpaper.com/2012/09/la-voute-de-lefevre-a-study-in-stereotomy/
Figure 17. Funicular shells [Model]. http://block.arch.ethz.ch/brg/research/funicular-funnel-shells
Figure 18. Foam Pavilion. [Image] https://block.arch.ethz.ch/brg/teaching/msc2-studio-at-hyperbody-tu-delft
Figure 19. Tile vault [Image] http://block.arch.ethz.ch/brg/project/free-form-catalan-thin-tile-vault