reference notes

1. MMBC – V
MODULE – III
SHELL STRUCTURES & FOLDED PLATES
Lecture by
Ar. Poornima Magesh

2. EVOLUTION OF STRUCTURES
A structure is something that will support an object or a load. A structure must be strong enough to support its own weight and whatever load is put on it !
A structure is a group of elements somehow united to support a load with stability. Everything has a structure. For example: humans have skeleton, bicycles
have a frame, houses have columns, beams and a roof.

3. There are four types of structure :
 Mass Structures
 Frame Structures
 Shell structures.
 Suspension structures
CLASSIFICATION OF STRUCTURES
Solid structures which rely on their own weight to resist loads.
Components and various membranes to carry and resist load
A thin, curved plate structure shaped to transmit applied forces by compressive, tensile,
and shear stresses that act in the plane of the surface. .
A suspension structure holds an elements by cables that are held from the top of
a tall column. The space between one column and the next is called the span.

4. Shell structures are by no means a modern invention.
Evidence of the earliest vaulted structures comes from Mesopotamia in 3000BC: a 5000-year-old Mesopotamian burial chamber with
a barrel vault of approx. 1m span is on display at the Berlin Museum of Prehistory and Ancient History
HISTORICAL BACKGROUND OF SHELL STRUCTURE
Nubian vaulting technique

5. If we tried to stiffen it from its primary state, it couldn't support its own
weight.
However, if we bend it, the sheet achieves a new structural quality.
The shells act in the same way. "You can't imagine a form that
doesn't need a structure or a structure that doesn't have a form.
Every form has a structure, and every structure has a form. Thus,
you can't conceive a form without automatically conceiving a
structure and vice versa".
The importance of the structural thought that culminates in the
constructed object is then, taken by the relationship between form
and structure. The shells arise from the association between
concrete and steel and are structures whose continuous curved
surfaces have a minimal thickness; thus they are widely used in
roofs of large spans without intermediate supports.
Working of shell structure with paper

6. SHELL
STRUCTURES
Introduction
Concept
Function
Structure
Materials
Construction
Techniques
• A shell is a thin structure composed of curved sheets of
material, so that the curvature plays an important role in
the structural behaviour, realizing a spatial form
• A thin curved membrane or slab usually of reinforced
concrete that functions both as structure and covering
• The essential function of a shell structure are continuity
and curvature
• Their continuity transmit forces in a number of different
directions in the surface of the shell
• Open shell structure is deformable

7. Tree structure spider web conch shell Spine bone
SHELL STRUCTURES - CONCEPT FORM:
The sorting of natural
inspiration forms is;
living models and non-
living models.
FUNCTION:
In structural context,
nature’s structures and
forms motivate
architectural innovation
either in aesthetic,
functional or structural
ways for electing optimal
morphology, functional
integration, and
efficiency.
Introduction
Concept
Function
Structure
Materials
Construction
Techniques

8. Introduction
Concept
Function
Structure
Materials
Construction
Techniques
FUNCTION: LOAD TRANSFER Types of Gaussian Curvature
Due to its structural continuity, the shells can transmit the loads in a number
of different directions.

9. STRUCTURAL BEHAVIOUR OF SHELLS
Introduction
Concept
Function
Structure
Materials
Construction
Techniques
• Shells are form based structures where the shape influences the shell’s load carrying capacity.
• This structural geometry largely dictates the development of stresses in the shell elements.
• This has to kept in mind to avoid unwanted deformations and structural failure.
They transfer these loads by generating in-plane membrane forces, a
fact that separates them from plates.
Shells, unlike membranes, stretch and contract without producing
significant bending or changes in local curvature.
Membrane behaviour - Curvature
To secure the high structural efficiency of a thin shell, select a shape,
proportions, and supports for the specific design conditions that come
as close as possible to satisfying the membrane theory

10. CLASSIFICATION OF SHELL STRUCTURE
SINGLE CURVED
DOUBLE CURVED
Surface of revolution
Surface of translation
Synclastic
Anticlastic
Circular cylinders
Conical
Circular or non circular cylinders
Conical
Surface of revolution
Surface of translation
Circular domes
Ellipsoid
Paraboloid
Elliptic paraboloid
Paraboloids
Hyperboloids
Hyperbolic paraboloids
Conoids
Hyperboloids
Monoclastic

11. The terms single and double curvature are used to
distinguish the comparative rigidity of the two forms and
complexity of centering necessary to construct the shell form.
Barrel vault conoid dome hyperboloid paraboloid
CLASSIFICATION OF SHELL STRUCTURE
SINGLE CURVATURE SHELL: are curved on one linear axis
and are a part of a cylinder or cone in the form of barrel
vaults and conoid shells.
DOUBLE CURVATURE SHELL: are either part of a sphere, or a
hyperboloid of revolution.
The terms single curvature and double curvature do not
provide a precise geometric distinction between the form of
shell because a barrel vault is single curvature but so is a
dome.
BARREL VAULT
CONOID
HYPERBOLOID PARABOLOID
DOME

12. CLASSIFICATION OF SHELL STRUCTURE
Introduction
Concept
Function
Structure
Materials
Construction
Techniques
Classification based on Gaussian curvature
A sphere has positive gaussian curvature, and
so the circumference of a circle drawn on a
sphere is less than ππ times its diameter
The circumference of a circle is longer
than ππ times its diameter, and so, to make a flat
sheet lie along such a surface, you either have to
tear it to increase the circumference, or wrinkle it
in the middle to reduce the radius.

14. CLASSIFICATION OF SHELL STRUCTURE
Introduction
Concept
Function
Structure
Materials
Construction
Techniques
Classification based on Shape Surface of revolution:
Produced by rotating a plane around the axis
MONOCLASTIC
Surface of translation:
Obtained by translating a plane curve parallel to the plane containing
the curve
Ruled surface:
Translating a line along two end curves – Hyperbolic & Hyperboloid
Form of curvature

15. CLASSIFICATION OF SHELL STRUCTURE
Classification based on surface
DEVELOPABLE SURFACES:
Smooth surface with zero Gaussian curvature. It can be reduced to a planer surface without stretching or deforming the surface
Conversely it is a surface that can be deformed by transforming a plane
Eg A cylindrical panel is a developable because it can be unfolded to a rectangular plate.
NON - DEVELOPABLE SURFACES:
It requires stretching, cutting or deforming to collapse it into a planer surface. That requires additional forces to collapse as compared to
developable surface.
Eg – Spherical dome represents a non developable surface

16. Developable surfaces (singly curved):
developable surface is a surface that can be unrolled onto a flat
plane without tearing or stretching it. It is formed by bending a flat
plane, the most typical shape of a developable shell is a barrel, and
a barrel shell is curved only in one direction. Barrel : arch action &
beam action together make a barrel. There are mainly two types of
barrel : - long barrels , arch action is prominent - short barrels,
beam action is prominent structural behavior of short barrel shells:
these shells are typically supported at the corners and can behave
in one or a combination of the following ways: structural behavior of
long barrel shells: these are typically supported at the corners and
behave structurally as a large beam.

17. Surface of translation
Surface of revolution
Ruled surface
CASES OF SHELL STRUCTURE

18. Surface translation
Doubly curved – Anticlastic
Surface translation +Doubly curved + Synclastic

19. SHELL STRUCTURE – MATERIALS & CONSTRUCTION
Compressed earth + Reinforced concrete + Steel + Aluminium alloys + Glass + Timber
Foam Formwork for a Curved Section, This
formwork would be used on ¼ of a hyberbolic
paraboloid, and would then be removed and
reused on the remaining portions. It is a foam
curved shape supported with an inner brace of
wooden 2x4’s.
Span is shorter than its width
Span is 12-30 m with its width ½ of
the span and rise is 1/5 of its width
SPAN
STIFFENING ARCHES

21. TYPES AND FORMS OF SHELL STRUCTURE
• Folded Plates
• Barrel Vaults
• Short Shells
• Domes (surfaces of revolution)
• Folded Plate Domes
• Translational Shells
• Warped Surfaces
• Combinations
• Folded plates are assemblies of flat plates or slabs
inclined in different directions and rigidly joined
along their longitudinal edges that can carry loads
without the need for additional supporting beams
along mutual edges
• Folded plate = Slab action + Beam action
In length direction they act like thin inclined beams
of great depth, stabilized against buckling at the top
and bottom by adjoining plates.

22. • Bending in folded plates cause top compression and bottom tension
• Folded plates tend to flatten out under load that can be prevented by walls or frames at end
supports
• End panel buckling can be resisted by edge beams
Flat paper deforms under its own weight
Folding paper increases strength & stiffness
Paper buckling under heavy load
Secured end support helps resist buckling
STRUCTURE AND THE LOAD

23. STRUCTURE AND THE LOAD
Folded plate concept
Slab action in width direction
Beam action in length direction
Bending as external compression & tension forces
Gravity load
Buckled end panels
End panels stabilised with edge beams
• The external forces are transferred to
shorter end of one folding element
• The axial force is then divided between
adjacent elements
• Later forces are transferred to the
supporting columns

24. TYPES – FOLDED PLATES

25. FOLDED PLATES APPLICATIONS
• Roof structure
• Wall structure
• Floor structure
• Staircase

29. REFERENCE
Shell Structures for Architecture - Form Finding and Optimization
Edited by Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal and Chris Williams
Shell Structures for Architecture [PDF] (pdfroom.com)
Shell Structures for Architecture - PDF Drive