Shell structures are thin curved surfaces where the thickness is small compared to the radius. Two key developers of analysis for reinforced concrete cylindrical shells were Finsterwalder and Dishinger in the 1930s. Shells provide large column-free interior spaces and are used commonly for roofing. They can be singly curved like cylindrical shells or doubly curved like hyperbolic parabolic shells. Different types of shells include conical, ellipsoid, funicular, conoid, and hyperboloid shells. Membrane and bending theories are often used to analyze shell structures.

1. Topic :
Shells(Overview) : The Stressed Skin Structures
By:
Mohit Sheode
B.E.(Civil)

2.  A Shell from the perspective of structural engineering is a marvelous thin curved
surface.
Its thickness is small compared to its radius.
 Two German Engineers- Finsterwalder and Dishinger were the first to develop a
theoretical analysis applicable to Reinforced Concrete Cylindrical Shells around
1930.
Scharer (1936) was an American contributor via his paper which was an attempt to
simplified analysis.
Until 1940’s ,cylindrical shell analysis and construction was a research oriented
field
Shells are used for roofing purposes providing a designer with large column free
areas
Introduction:
Sheode,M. : Shells (Overview) : The Stressed Skin Structures

3. Sheode,M. : Shells (Overview) : The Stressed Skin Structures
Few Terms used in Shells Analysis:
Gaussian Curvature: It is the product of two principal curvatures at
any point on the surface of a shell.
R= R1 * R2
Where, R= Gaussian Curvature
R1 & R2 = Principal Curvatures.
 Ruled Surfaces: These surfaces can generated entirely by straight lines.
 Generator: The Straight line generating the surface is known as generator.
Directrix: The plane curve that guides the generator is known as directrix.
Chord Width: Projections of the directrix is known as Chord width.

4. Singly Curved (Developable) : Shells Of Translation: Cylindrical Shells
Fig.1: A Finite-Element Model of Cylindrical Shell
Sheode,M. : Shells (Overview) : The Stressed Skin Structures

5. Hyperbolic Parabolic Shells:
These are doubly curved anti-elastic shells of translation i.e. Its Gauss
Surface is definite and negative.
It can be used for roofs as well as foundations where SBC of soil is
very low.
Its surface can be generated by two systems of straight lines so that the
form work is provided by straight boards, warped only slightly over their
length.
Equation of Cartesian coordinates is:
Z= k . x . y
Sheode,M. : Shells(Overview) : The Stressed Skin Structures

6. Other Type of Shells:
Conical Shell
Ellipsoid Shell
Funicular Shell
Conoid
Hyperboloid of revolution
Corrugated
Sheode,M. : Shells (Overview) : The Stressed Skin Structures

7. Analysis types for Shells:
Membrane analysis can be done for Cylindrical Shell roofs.
Bending theory can be used for cylindrical shell roofs too.
Shells of revolutions and translation can be analyzed by membrane
theory.
Note: With the availability of modern software packages , shell analysis is
emerging as great area of research.
Sheode,M. : Shells (Overview): The Stressed Skin Structures

8. Thank you
Sheode,M. : Shells (Overview) : The Stressed Skin Structures