Skeleton or braced frame works are also called latticed structures or space frames. They are categorized based on their Gaussian curvature as having positive, negative, or zero curvature. Braced barrel vaults are a type of skeletal structure with single curvature. Shell structures are thin curved structures that function as both structure and enclosure. They can have single or double curvature and forms include domes, hyperboloids, conoids, and hyperbolic paraboloids. Centering is required to construct shell structures which adds to the cost but shell structures are aesthetically pleasing and efficient due to their light weight. An example is the Sydney Opera House which used precast concrete shell segments and tensioned steel cables to span over 350km and

1. Skeleton or braced frame works
Are also called latticed structures or space frames.
Structure follows regular geometric forms & categorized as structure having
1) +ve Gaussian (synclastic) curvature e.g.. Domes
2) -ve Gaussian (anticlastic) curvature
e.g.. Hyperbolic parabola
3) Zero Gaussian curvature e.g.. Grids.
Braced barrel vaults are special types of skeletal structures having single curvature

2. Surface can be conceptually
Formed by translating a curve
That lies in one plane along a
Curve in another plane or by
rotating the generator about
a line.

3. Gaussian curvature is the
product of the curvature of
the generator & of the line
on the surface perpendicular
to the generator.

4. Saddle like surfaces have –ve Gaussian
curvature because the principal
curvatures correspond to opposite directions.

5. SHELL STRUCTURE

6. INTRODUCTION
A shell is a thin, rigid, three dimensional structural form taken by the enclosure of a volume bounded by a
curved surface.
A shell structure is a thin curved membrane or slab usually of reinforced concrete that functions both as
structure and covering.
The term “SHELL” is used to describe the structures which possess strength and rigidity due to its thin,
natural and curved form such as shell of egg, a nut, human skull, and shell of tortoise.

7. 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.
Double curvature shell: are either part of a sphere, or a hyperboloid of revolution.
The term single curvature and double curvature do not provide a precise geometrical distinction between the
form of shell because a barrel vault is single curvature but so is a dome.
The terms single and double curvature are used to distinguish the comparative rigidity of the two forms and
complexity of centring necessary to construct the shell form.

8. A shell surface may assume virtually any shape.
Common forms include:
Rotational surfaces generated by the rotation of a curve about an axis. (e.g. spherical, elliptical,
conical & parabolic surfaces.)
Translational surfaces generated by sliding one plane curve over another plane curve. (e.g.
cylindrical & elliptical paraboloid surfaces.)
Ruled surfaces generated by sliding the two ends of a line segment on two individual plane curves.
(e.g. conoids & hyperbolic paraboloid surfaces.)
FORMS OF CURVATURE

9. FORMS OF CURVATURE
Rotational Surfaces/ 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, toroid's.

10. FORMS OF CURVATURE
Translational Surfaces/ surfaces of translation are generated by sliding a plane curve along another plane
curve, while keeping the orientation of the sliding curve constant.
The latter curve, on which the 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.

11. FORMS OF CURVATURE
Translational Surfaces/ surfaces of translation
If two parabolas are similar, the surface becomes a surface of revolution, called paraboloid of revolution.

12. FORMS OF CURVATURE
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.

13. FORMS OF CURVATURE
Developable and non-developable surfaces:
Surfaces with double curvature cannot be developed, while with single curvature can be developed.
In other words, 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.

14. FORMS OF CURVATURE
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 behaviour 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 behaviour of long barrels shells:
These are typically supported at the corners and behave structurally as a
large beam.

15. FORMS OF CURVATURE
Non-Developable surfaces (doubly curved):
E.G., Sphere or hyperbolic paraboloid.
They are mainly classified as: 1) Synclastic 2) Anticlastic
Synclastic Shells:
These shells are doubly curved and have a similar curvature in each direction.
E.g. domes.
A dome is a good example of a synclastic shell, it is doubly curved and can be
formed by rotating a curved line around an axis.
A dome can be split up into two different directions; vertical sections
separated by longitudinal arch lines (also called meridians), and horizontal
sections separated by hoops or parallels.
Structural behaviour:
Similar to arches under a uniform loading the dome is under compression
everywhere, and the stresses act along the arch and hoop lines.

16. FORMS OF CURVATURE
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.
Conoids, hyperbolic paraboloid and hyperboloids are all considered to the
anticlastic shell because they are saddled shape with different curvature in
each direction and straight lines can be drawn of the surface.
Conoids: formed by moving a one end of a straight line along a curved path
and the other along a straight path.
Hyperboloids: formed by rotating a straight line around a vertical axis.

17. FORMS OF CURVATURE
Non-Developable surfaces (doubly curved):
Hyperbolic paraboloid:
Formed by sweeping a convex parabola along a concave parabola or by
sweeping a straight line over a straight path at one end and another straight
path not parallel to the first.
Structural behaviour:
Depending on the shape of the shell relative to the curvature, there will be
different stresses.
Shell roof, have compression stresses following the convex curvature and the
tension stresses following the concave curvature.

18. FORMS OF CURVATURE
Tension Tie:
Fig. (A) represents a doubly curved shell with no axis of
symmetry, shows a spherical dome supported on a wall.
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.
However, it is important to note that the tie will be
funicular for any shape of either the plan or elevation.
Fig. (B) the shell has positive curvature and continuous
vertical support.
Tension
ring
Fig. (A)
Fig. (B)

19. FORMS OF CURVATURE
Tension Tie:
The support may be a continuous wall or stiff beams
between adequately spaced columns. It is interesting that
the straight parts of the tie in Fig. (C) do not require ties
across the building.
The thrusts are taken by shear forces through the width of
the shell, and only tension forces exist in the tie.

20. 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 concrete 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.

21. CENTERING OF SHELLS
Centering is the term used to describe the necessary
temporary support on which the curved R.C.C. shell
structure is cast.
The centering of a barrel vault, which is part of a cylinder
with same curvature along its length; is less complex. The
centering of conoid, dome and hyperboloid of revolution is
more complex due to additional labour and wasteful
cutting of materials to form support for shapes that are not
of uniform linear curvature.
The attraction of shell structures lies in the elegant
simplicity of curved shell forms that utilise the natural
strength and stiffness of shell forms with great economy in
the use of materials.
The disadvantage of shell structure is their cost. The shell
structure is more expensive due to considerable labour
required to construct the centering on which the shell is
cast.

22. ADVANTAGES AND DIS-ADVANTAGES OF SHELLS
Advantages:
1. Very light form of construction. To span 30.0 m shell thickness required is 60 mm.
2. Dead load can be reduced economizing foundation and supporting system.
3. They further take advantage of the fact that arch shapes can span longer.
4. Aesthetically it looks good over other forms of construction.
Dis-advantages:
1. Shuttering problem.
2. Greater accuracy in formwork is required.
3. Good labour and supervision necessary.
4. Rise of roof may be a disadvantage.

23. CASE STUDY – SYDNEY OPERA HOUSE

24. CASE STUDY – SYDNEY OPERA HOUSE
System spans and effective spans:
The Sydney opera house spans up to 164 feet.
The arches are supported by over 350 km of
tensioned steel cable.
The shell thickness goes from 3 to 4 inches.
All shells weigh a total of 15 tons.
This involved laying the foundations and building a podium 82 feet (25m) above sea level. More
than 39,239 cubic feet (30,000 m3) of rock and soil were removed by excavators.
The foundation was built at the top of a large rock that sat in Sydney harbour. The second stage saw
the building of the shells, the podium structure, the stage tower, and the necessary machinery.
Cable beams were built and reinforced by steel cables to release the stress of the weight. The
strength of the cables was tested by loading additional weights. When the builders were satisfied
that the cables would support, the beams were made extendable by other beams.

25. CASE STUDY – SYDNEY OPERA HOUSE
System spans and effective spans:
The “shells” were perceived as a series of parabolas supported by precast concrete ribs. The formwork for
using in-situ concrete would have been prohibitively expensive, but, because there was no repetition in any of
the roof forms, the construction of pre-cast concrete for each individual section would possibly have been
even more expensive.
The design team went through at least 12 alterations of the form of the shells trying to find an economically
acceptable form (including schemes with parabolas, circular ribs and ellipsoids) before a workable solution
was completed. In mid 1961, the design team found a solution to the problem; the shells all being created as
sections from a sphere this solution allows arches of varying length to be cast in a common mould, and a
number of arch segments of common length to be placed adjacent to one another, to form a spherical section.

26. CASE STUDY – SYDNEY OPERA HOUSE
Construction:

27. CASE STUDY – SYDNEY OPERA HOUSE

28. CASE STUDY – SYDNEY OPERA HOUSE
Finishes:
Actual clay, brick, and stone veneer
Granite or marble cladding
Exposed aggregate finish
Sand blasted finish
Form linear patterns
The Sydney opera house uses white glazed granite tiles.
10,56,000 tiles were used to cover the massive structure.

29. THANK YOU