Shells ppt
- 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.
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- 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