shells only about hyperboloid and paraboloid

1. Fredrick Stephen raj. J 1OQ17AT019
Harshini Subramani 1OQ17AT016
Krithika 1OQ17AT026
Jashwanth 1OQ17AT020

2. 
Single or double
curvature
Single curvature
 Single curvature are
curved on one linear axis
and are a part of cylinder
and cone in form of barrel
vault or conoid shells.
Double curvature
 Double curvature are
either a part of sphere or
hyperboloid revolution.

3. 
 Surfaces with double curvature cannot be developed,
hence known as non developable structures.
 Example :-sphere , hyperbolic paraboloid
 They are mainly classified as Synclastic Anticlastic
 Synclastic shells :- these shells are doubly curved
surfaces and have a similar curvature in each direction.
Non developable
structures

4.  Anticlastic structures are doubly
curved but each of
the two curves have the
opposite direction to the
other.
 Example :- 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.
Anticlastic structures

5. 
 Hyperboloids formed by
rotating a straight line
around a vertical axis.
 Often these are tall
structures such as where the
hyperboloid geometry
structural strength is used to
support and object high off
the ground , but its also
used as decorative element
or structural economy.
Hyperboloids
Kobe tower in Japan

6. 
 Hyperboloids have convex
on along one side and have
concave along the other side.
 Cartesian co ordinates for the
hyperploid can be defined ,
similar to spherical co
ordinates keeping the
azimuth angle θ € [0, 2π) but
changing inflation v into
hyperbolic trigonometry
functions.
hyperboloid

7. 
 The hyperbolic paraboloid form has been used for roofs
at various times since its easily constructed using straight
sections for lumber steel or other conventional materials.
Hyper paraboloid
structure

8. The geometry of HP surface can be
transformed in four basic ways
 By changing the slope of the directrix
one can vary the curvature or twist the
surface and hence change the rise to
span ratio of the principle parabolas
Transformation of surface

9. 
 By varying the angle between the
director plane
 By cutting various segments form a
standard HP surface
 By tilting the Z axis with respect to
the plane of reference

10. 
Hyper paraboloid
structure
 It is usually made up of a
combination of four
intersecting hyper
paraboloids joint together to
form a square plan.
 This form of structure is often
used by architects to roof
large span exhibition halls
and public buildings.

11. 

13. 
 Paraboloids are certain 3D dimensional structure .
 Its an open surface generated by rotating a parabola
 Its is the revolution of parabola along its axis of
symmetry.
 Example:- TWA Terminal
Paraboloids

14. Sydney Opera House

15. 
Sydney opera house

17. 
Method of Construction