# Shell (structure)
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{{short description|Thin-walled geometric solid}}
[[Image:08terminal5.jpg|thumb|Shell structure of the [TWA Flight Center](/source/TWA_Flight_Center) Building by [Eero Saarinen](/source/Eero_Saarinen), [John F. Kennedy International Airport](/source/John_F._Kennedy_International_Airport), [New York](/source/New_York_City)]]
[[Image:British Museum Great Court roof.jpg|thumb|upright|[Great Court](/source/Queen_Elizabeth_II_Great_Court), with a lattice thin-shell roof by [Buro Happold](/source/Buro_Happold) with [Norman Foster](/source/Norman_Foster%2C_Baron_Foster_of_Thames_Bank), [British Museum](/source/British_Museum), [London](/source/London)]]
A '''shell''' is a three-dimensional solid [structural element](/source/structural_element) whose thickness is very small compared to its other dimensions. It is characterized in structural terms by mid-plane stress which is both coplanar and normal to the surface. A shell can be derived from a [plate](/source/plate_(structure)) in two steps: by initially forming the middle surface as a singly or doubly curved surface,[{{cite book|title=The finite element method for solid and structural mechanics
|author=O.C. Zienkiewicz and R.L. Taylor.
}}] then by applying loads which are coplanar to the plate's [plane](/source/plane_(geometry)) thus generating significant stresses.
Materials range from concrete (a ''[concrete shell](/source/concrete_shell)'') to fabric (as in ''[fabric structure](/source/fabric_structure)s'').
'''Thin-shell structures''' (also called '''plate and shell structures''') are lightweight constructions using [shell elements](/source/List_of_structural_elements). These elements, typically curved, are assembled to make large structures. Typical applications include aircraft [fuselage](/source/fuselage)s, boat hulls, and the [roof](/source/roof)s of large buildings.
==Definition==
A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. A primary difference between a shell structure and a plate structure is that, in the unstressed state, the shell structure has curvature as opposed to the plates structure which is flat. [Membrane](/source/Tensile_structure) action in a shell is primarily caused by in-plane forces ([plane stress](/source/plane_stress)), but there may be secondary forces resulting from flexural deformations. Where a flat plate acts similar to a beam with bending and [shear stress](/source/shear_stress)es, shells are analogous to a cable which resists loads through tensile stresses. The ideal thin shell must be capable of developing both tension and compression.[{{Cite book|title=Handbook of Structural Engineering, Second Edition|date=2005-02-28|publisher=CRC Press|isbn=978-0-8493-1569-5|editor-last=Chen|editor-first=Wai-Fah|edition=2|location=Boca Raton|language=English|editor-last2=Lui|editor-first2=E. M.}}]
==Types==
The most popular types of thin-shell structures are:
* [Concrete shell](/source/Concrete_shell) structures, often cast as a [monolithic dome](/source/monolithic_dome) or [stressed ribbon bridge](/source/stressed_ribbon_bridge) or [saddle roof](/source/saddle_roof)
* Lattice shell structures, also called [gridshell](/source/gridshell) structures, often in the form of a [geodesic dome](/source/geodesic_dome) or a [hyperboloid structure](/source/hyperboloid_structure)
* [Membrane structure](/source/Membrane_structure)s, which include [fabric structure](/source/fabric_structure)s and other [tensile structure](/source/tensile_structure)s, [cable dome](/source/cable_dome)s, and [pneumatic structure](/source/pneumatic_structure)s.
==See also==
{{div col}}
* [Monocoque](/source/Monocoque)
* [Diagrid](/source/Diagrid)
* [Stretched grid method](/source/Stretched_grid_method)
* [List of thin-shell structures](/source/List_of_thin-shell_structures)
'''Persons related:'''
* [Félix Candela](/source/F%C3%A9lix_Candela)
* [Dyckerhoff & Widmann](/source/Dyckerhoff_%26_Widmann)
* [Wilhelm Flügge](/source/Wilhelm_Fl%C3%BCgge)
* [Eugène Freyssinet](/source/Eug%C3%A8ne_Freyssinet)
* [Heinz Isler](/source/Heinz_Isler)
* [Pier Luigi Nervi](/source/Pier_Luigi_Nervi)
* [Plate](/source/plate_(structure))
* [Frei Otto](/source/Frei_Otto)
* [Ernest Edwin Sechler](/source/Ernest_Edwin_Sechler)
* [Vladimir Shukhov](/source/Vladimir_Shukhov)
** [All-Russia Exhibition 1896](/source/All-Russia_Exhibition_1896)
* [Eduardo Torroja](/source/Eduardo_Torroja)
* [Membrane theory of shells](/source/Membrane_theory_of_shells)
{{div col end}}
==References==
{{reflist}}
==Further reading==
*{{Cite book|title=Innovative Surface Structures: Technologies and Applications|last=[Bechthold](/source/Martin_Bechthold)|first=Martin|date=2008-03-20|publisher=Taylor & Francis|isbn=978-0-415-41967-3|edition=1|location=Abingdon|language=English}}
*{{Cite book|title=VLADIMIR G. SUCHOV 1853-1939; Die Kunst Der Sparsamen Konstruktion|last=Suchov|first=Vladimir G. |editor=Rainer Gaefe |date=1990|publisher=Deutsche Verlags-Anstalt |isbn=978-3-421-02984-3|edition=1st|location=Stuttgart}}
==External links==
{{wikiquote|Thin-shell structure}}
{{commons category|Thin-shell structures}}
* [http://en.structurae.de/structures/stype/index.cfm?ID=1009 Thin-shell structures]
* [http://en.structurae.de/structures/stype/index.cfm?ID=1013 Double thin-shells structures]
* [http://www.recentpast.org/types/hyperpara/ Hypar & Concrete Shells]
* [https://dspace.mit.edu/handle/1721.1/39277 Past and Future of Grid Shell Structures]
* [https://nagoya.repo.nii.ac.jp/record/30513/file_preview/50_1.pdf Shape optimization of Shell and Spatial structure] (PDF)
* [https://web.archive.org/web/20090219230958/http://www.mscsoftware.com/events/vpd2007/emea/presentations/EMEA_VPD2007_Khrunichev-eng_R_2007_12_14.pdf Lattice Shell for Space Vehicles] (PDF)
* [http://www.cedex.es/iass/ International Association for Shell and Spatial Structures]
Category:Solid mechanics
Category:Structural system
{{Civil-engineering-stub}}
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Adapted from the Wikipedia article [Shell (structure)](https://en.wikipedia.org/wiki/Shell_(structure)) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Shell_(structure)?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.