Basic and simplified introduction of Shell and Dome structures for Architects and Structural Engineer and students of related streams.

1. SURFACE ACTIVE
STRUCTURES

2. PRESENTED BY-
Er.RAJAN GUPTA,
ASSISTANT PROFESSOR,
CSPA,RAJPURA,PUNJAB

3. SURFACE ACTIVE
tending to reduce the surface
tension of a liquid in which it is
dissolved.
OR
Altering the properties and especially
lowering the tension at the
surface of contact between phases.
Reference-https://www.merriam-webster.com/dictionary/surface-active
SURFACE TENSION
The tension of the surface film of a liquid
caused by the attraction of the particles in
the surface layer by the bulk of the liquid,
which tends to minimize surface
area.

4. SURFACE ACTIVE
»PLATE STRUCUTRES
»FOLDED PLATE STRUCUTRES
»SHELL STRUCTURES

5. 1.
PLATE STRUCUTURES

6. 1. STRUCTURAL PLATES ARE FLAT PLANAR GIRDERS WHICH CONTRARY TO THE SLAB ARE
STRESSED BY LOADS PARALLEL TO GIRDER SURFACE
2. WALL GIRDERS LIKEWISE REFFERED TO AS STRUCTURAL PLATES DUE TO THEIR SHAPE
WITH IT MEASURING HALF OF THEIR SPAN, BEHAVES LIKE A BEAM,THEY ARE NOT
PLATES IN STRUCTURAL SENSE.
STRUCTURAL PLATES AND WALL GIRDER

7. PLATE
STRUCT
URES
ONE WAY PLATE WITH
CENTRAL OPENING
ONE WAY PLATE SYSTEM
WALL GIRDER SYSTEM
WITH SHEAR WALL
STABILATION

8. 1.
PLATE STRUCTURES
BIAXIAL PLATE SYSTEM
MULTISTOREY PLATE SYSTEM
WITH ALTERNATING
SPAN DIRECTIONS

9. 2.
FOLDED PLATE STRUCUTURES

10. THE BASIC CONCEPT OF FOLDING

11. Structural Behavior of Folding
 At first, the external forces are
transferred to the shorter edge
of one folding element.
 There, the reaction as an axial
force is divided between the
adjacent elements.
 Then the forces transferred to
the bearings.

12. BASED ON
GEOMETRIC
SHAPE
 Folded plate surfaces structures
 Folded plate frames structures
 Spatial folded plate structures

13. Types of Folded Structure
Classification of folded structures based
on the material they are made of:
 Folded structures made of reinforced concrete
 Metal folded structures
 Folded structures of wood
 Folded structures of glass
 Folded structures of plastic materials
 Folded constructions made in combination
of different materials

14. EXAMPLE
MUNICIPLE STADIUM ,AHMEDABAD ,1965

17. HINDUSTAN LEVER PAVILION

21. Advantages and Disadvantages of Folded-Plate Structure
ADVANTAGES
Very light form of construction. To span 30 m shell
thickness required is 60 mm only.
The use of concrete as a building material reduces
both materials cost and a construction cost.
Longer span can be provided.
Esthetically it looks good over other forms of
construction.

22.  Shuttering is difficult.
 Greater accuracy in formwork is
required.
 Good labor and supervision necessary.
 Rise of roof may be a disadvantage.
Disadvantages

23. 3.
SHELL STRUCTURES

24. »LATTICE AND PORTAL FRAME BUILDINGS CONSIST OF A STRUCTURAL FRAME WHICH
SUPPORTS SLAB, ROOF AND WALL COVERING. THIS FRAME SERVES PURELY AS THE
STRUCTURAL SUPPORT AND PROVIDES PROTECTION AGAINST WEATHER. THE ROOF AND
WALL COVERING ADD NOTHING TO THE STRENGTH THE RIGIDITY OF STRUCTURAL FRAME.
»
»A SHELL STRUCTURE IS A THIN CURVED MEMBRANE OR SLAB USUALLY OF REINFORCED
CONCRETE THAT FUNCTIONS BOTH AS STRUCTURAL SUPPORT AND COVERING.
»THE TERM “SHELL” IS USED TO DESCRIBE THE STRUCTURES WHICH POSSESS STRENGHT
AND RIGIDITY DUE TO ITS THIN, NATURAL AND CURVED FORM SUCH AS SHELL OF EGG, A
NUT, HUMAN SKULL, AND SHELL OF TORTISE.
INTRODUCTION

26. SINGLE OR DOUBLE CURVATURE
SHELLS
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.

27. 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 GEMOETRIC
DISTINCTION BETWEEN THE FORM OF SHELL BECAUSE A BARREL VAULT IS SINGLE CURVATURE BUT SO IS A
DOME.
THE TERMS SINGLE AND DOULBE CURVATURE ARE USED TO DISTINGUISH THE COMPARITIVE RIGIDITY OF
THE TWO FORMS AND COMPLEXITY OF CENTRING NECESSARY TO CONSTRUCT THE SHELL FORM.

28. FORMS OF CURVATURE
1- Surface of Revolution
2-Surface of Translation
3-Ruled Surfaces

29. 1- Surface of Revolution
SURFACES OF REVOLUTION ARE GENERATED BY THE
REVOLUTION OF A PLANE CURVE, CALLED THE MERIDIONAL
CURVE,
ABOUT AN AXIS, CALLED THE AXIS OF REVOLUTION.
IN THE SPECIAL CASE OF CYLINDRICAL AND CONICAL SURFACES,
THE MERIDIONAL CURVE CONSISTS OF A LINE SEGMENT.
E.G. : CYLINDERS, CONES,
SPHERICAL OR ELLIPTICAL DOMES,
HYPERBOLOIDS OF REVOLUTION, TOROIDS.

30. Surface of Revolution

31. 2-Surface of Translation
(A) ELLIPTIC PARABOLOID (B) CYLINDRICAL PARABOLOID (C) HYPERBOLIC PARABOLOID
SURFACES OF TRANSLATION ARE GENERATED BY
SLIDING A PLANE CURVE ALONG ANOTHER PLANE
CURVE, WHILE
KEEPING THE ORIENTATION OF THE SLIDING CURVE
CONSTANT.
ORIGINAL CURVE SLIDES, IS CALLED THE
GENERATOR OF THE SURFACE
IN THE SPECIAL CASE IN WHICH THE
GENERATOR IS A STRAIGHT LINE, THE
RESULTING SURFACE IS CALLED A
CYLINDRICAL SURFACE.

32. IF TWO PARABOLAS ARE SIMILAR, THE SURFACE
BECOMES A SURFACE OF REVOLUTION, CALLED
PARABOLOID OF REVOLUTION.

33. 3-Ruled Surfaces
RULED SURFACES ARE GENERATED BY SLIDING EACH END OF A STRAIGHT
LINE ON THEIR OWN GENERATING CURVE.
THESE LINES ARE NOT NECESSARILY AT RIGHT ANGLE TO THE PLANES
CONTAINING THE END CURVES.

35. DEVELOPABLE AND NON-DEVELOPABLE
SURFACES
DEVELOPABLE
NON-DEVELOPABLE
SURFACES WITH POSITIVE AND NEGATIVE GAUSSIAN CURVATURE (I.E. SYNCLASTIC AND ANTICLASTIC SURFACES)
CANNOT BE DEVELOPED, WHILE THOSE WITH ZERO GAUSSIAN CURVATURE CAN BE DEVELOPED
(A) POSITIVE GAUSSIAN (B) ZERO GAUSSIAN (C) NEGATIVE GAUSSIAN

36. DEVELOPABLE SURFACES
(SINGLY CURVED)
DEVELOPABLE SURFACE IS A SURFACE THAT
CAN BE UNROLLED ONTO A FLAT PLANE
WITHOUT TEARING OR STRETCHING
IT.
SHORT BARREL STRUCTURAL
BEHAVIOUR
LONG BARREL STRUCTURAL
BEHAVIOUR

37. NON-DEVELOPABLE SURFACES
(DOUBLY CURVED)
SYNCLASTIC SHELLS:
THESE SHELLS ARE DOUBLY
CURVED AND HAVE A SIMILAR
CURVATURE IN EACH DIRECTION.
E.G. DOMES
STRUCTURAL BEHAVIOR :
SIMILAR TO ARCHES UNDER A UNIFORM LOADING THE DOME IS UNDER
COMPRESSION EVERYWHERE, AND THE STRESSES ACT ALONG THE ARCH
AND HOOP LINES.

38. NON-DEVELOPABLE SURFACES
(DOUBLY CURVED)
ANTICLASTIC SHELLS :
ARE DOUBLY CURVED BUT EACH
OF THE TWO CURVES HAVE THE
OPPOSITE DIRECTION TO THE
OTHER. E.G. SADDLE POINTS.

39. Kresge Auditorium

40. NON-DEVELOPABLE SURFACES
(DOUBLY CURVED)
HYPERBOLIC PARABOLOID:
COMPRESSION
STRESSES FOLLOWING
THE CONVEX
CURVATURE AND THE
TENSION STRESSES
FOLLOW THE CONCAVE
CURVATURE.

43. TENSION TIE
WHENEVER THE SHELLS ARE SUPPORTED
VERTICALLY AT THEIR EDGES, A TENSION TIE
IS REQUIRED AROUND THE PERIMETER AT THE
INTERSECTION OF THE DOME AND THE WALL.

44. THE THRUSTS ARE TAKEN BY
SHEAR FORCES THROUGH
THE WIDTH OF THE SHELL,
AND ONLY TENSION FORCES
EXIST IN THE TIE.

48. MOST SUITABLE MATERIAL
THE MATERIAL MOST SUITED FOR CONSTRUCTION OF SHELL STRUCTURE IS CONCRETE
BECAUSE IT IS A HIGHLY PLASTIC MATERIAL WHEN FIRST MIXED WITH WATER THAT
CAN TAKE UP ANY SHAPE ON CENTERING OR INSIDE FORMWORK. SMALL SECTIONS OF
REINFORCING BARS CAN READILY BE BENT TO FOLLOW THE CURVATURE OF SHELLS.
ONCE THE CEMENT HAS SET AND THE CONCERETE HAS HARDENED THE R.C.C
MEMBRANE OR SLAB ACTS AS A STRONG, RIGID SHELL WHICH SERVES AS BOTH
STRUCTURE AND COVERING TO THE BUILDING.

49. SALVACAO CHURCH ,BOMBAY ,1977

50. PLATE STRUCTURES

51. FOLDED PLATE STRUCTURES

52. SHELL STRUCTURES

53. THANKS!