Shell structures are thin, curved membranes or slabs made primarily of reinforced concrete, characterized by their strength and rigidity derived from their shape. They find applications in various fields, including architecture, engineering, and vehicle construction, utilizing single or double curvature forms to maximize structural efficiency. While offering advantages like lightweight construction and aesthetic appeal, they do present challenges such as the need for precise formwork and potential issues with insulation and labor requirements.

1. SHELL STRUCTURES

2. INTRODUCTION
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 STRENGHT AND RIGIDITY DUE TO ITS
THIN,
NATURAL AND CURVED FORM SUCH AS SHELL OF EGG, A NUT, HUMAN SKULL, AND SHELL OF TORTISE.

3. TYPES OF CURVES

4. APPLICATIONS
Architecture and building.
The development of masonry domes and vaults in the Middle Ages made
possible the construction of more spatious buildings. In more recent times the
availability of reinforced
concrete has stimulated interest in the use of shells for roofing purposes.
Power and chemical engineering.
construction of suitable boilers. These thin shells were constructed from plates
suitable formed and joined by riveting.
Structural engineering.
An important problem in the early development of steel for structural purposes
was to design compression members against buckling. A striking advance was
the use of tubular members in the construction of the Forth railway bridge in 1889:
steel plates were riveted together to form reinforced tubes as large as 12 feet in
diameter, and having a radius/thickness ratio of between 60 and 180.
Vehicle body structures.
The construction of vehicle bodies in the early days of road transport involved a
system of structural ribs and non-structural paneling or sheeting. The modern
form of vehicle construction, in which the skin plays an importatnt structural
part, followed the introduction of sheet-metal components, preformed into thin
doubly curved shells by large power presses, and firmly connected to each other by
welds along the boundaries. The use of the curved skin of vehicles as a load bearing
member has similarly revolutionized the construction of railway carriages and aircraft.
In the construction
Composite construction.
The introduction of fiberglass and similar lightweight composite materials has
impacted the construction of vehicles ranging from boats, racing cars, fighter and
stealth aircraft, and o on. The exterior skin can be used as a strong structural shell.
Miscellaneous Examples.
Other examples of the impact of shell structures include water cooling towers for
power stations, grain silos, armour, arch dams, tunnels, submarines, and so forth.

5. 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 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.
CONOID
DOME
HYPERBOLOID
PARABOLOIDBARREL VAULT

6. TYPES OF SHELL STRUCTURES:
FOLDED PLATE SHELLS:
THE DISTINGUISHING FEATURE OF THE FOLDED PLATE IS THE EASE IN FORMING PLANE
SURFACES. A FOLDED PLATE MAY BE FORMED FOR ABOUT THE SAME COST AS A
HORIZONTAL SLAB AND HAS MUCH LESS STEEL AND CONCRETE FOR THE SAME SPANS.
THE PRINCIPLE COMPONENTS IN A FOLDED PLATE STRUCTURE CONSIST OF :
1) THE INCLINED PLATES
2) EDGE PLATES WHICH MUST BE USED TO STIFFEN THE WIDE PLATES
3) STIFFENERS TO CARRY THE LOADS TO THE SUPPORTS AND TO HOLD THE PLATES IN LIN
4) COLUMNS TO SUPPORT THE STRUCTURE IN THE AIR.
FOLDED PLATE TRUSS
Z SHELL
TAPERED FOLDED PLATES
CANOPIES
THREE SEGMENT FOLDED PLATE

7. TYPES OF SHELL STRUCTURES:
CYLINDRICAL BARREL VAULTS:
BARREL VAULTS ARE PERHAPS THE MOST USEFUL OF THE SHELL STRUCTURES BECAUSE THEY CAN SPAN UPT O 150 FEET
WITH A MINIMUM OF MATERIAL. THEY ARE VERY EFFICIENT STRUCTURES BECAUSE THE USE THE ARCH FORM TO REDUCE
STRESSES AND THICKNESSES IN THE TRANSVERSE DIRECTION.
MULTIPLE BARRELS -
CORRUGATED CURVES UNSTIFFENED EDGES OUTSIDE STIFFENERS THE LAZY S

9. TYPES OF SHELL STRUCTURES:
DOMES OF REVOLUTION:
A DOME IS A SPACE STRUCTURE COVERING A MORE OR LESS
SQUARE OR CIRCULAR AREA. THE BEST KNOWN EXAMPLE IS
THE DOME OF REVOLUTION, AND IT IS ONE OF THE EARLIEST
OF THE SHELL STRUCTURES. EXCELLENT EXAMPLES ARE STILL
IN EXISTENCE THAT WERE BUILT IN ROMAN TIMES. THEY ARE
FORMED BY A SURFACE GENERATED BY A CURVE OF ANY
FORM REVOLVING ABOUT A VERTICAL LINE. THIS SURFACE
HAS DOUBLE CURVATURE AND THE RESULTING STRUCTURE
IS MUCH STIFFER AND STRONGER THAN A SINGLE CURVED
SURFACE, SUCH AS A CYLINDRICAL SHELL.
HALF SPHERE
SPHERE SEGMENT
DOMES - SQUARE IN PLAN

10. 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.

11. TYPICAL SHELL ROOF FORM
L<S/2
=S/6
=S/9

12. TYPICAL SHELL ROOF FORM
W/8
W/5
R=W S/20
S/7

13. CONTINUOUS CONOID ROOF

14. CONSTRUCTION OF BARREL VAULT
THE BARREL VAULT IS THE MOST STRAIGHT FORWARD SINGLE CURVATURE SHELL CONSTRUCTION. IT IS THE PART
OF A CYLINDER OR BARREL WITH SAME CURVATUREALONG
ITS LENGTH.
ANY NUMBER OF CONTINUOUS BARRELS OR CONTINUOUS SPANS ARE POSSIBLE EXCEPT THAT EVENTUALLY
PROVISION IS MADE FOR THE EXPANSION OF THE JOINTS IN A LARGE STRUCTURES.
THE BARREL VAULTS ARE USED AS PARKING, MARKET PLACE, ASSEMBLY HALL ,ETC.
TYPES OF BARREL VAULTS
1. SHORT SPAN BARREL VAULTS
2. LONG SPAN BARREL VAULTS

15. BARREL VAULT SHELL ROOF
SHORT SPAN BARREL VAULT
SHORT SPAN BARREL VAULTS ARE THOSE IN WHICH SPAN IS SHORTER THAN ITS WIDTH. IT IS USED FOR THE WIDTH
OF THE ARCH RIBS BETWEEN WHICH THE BARREL VAULT SPAN.
LONG SPAN BARREL VAULT
LONG SPAN BARREL VAULTS ARE THOSE IN WHICH SPAN IS LARGER THAN ITS WIDTH.
STRENGTH OF THE STRUCTURE LIES AT THE RIGHT ANGLES TO THE CURVATURE TO THAT SPAN IS LONGITUDINAL TO
THE CURVATURE.
USUAL SPAN OF THE LONGITUDINAL BARREL VAULT IS FROM 12-30 M WITH ITS WIDTH BEING ABOUT 1/2 THE SPAN
AND RISE IS 1/5 OF THE WIDTH.
TO COVER LARGER AREAS MULTIBAY ,MULTI SPAN ROOFS CAN BE USED WHERE THE ROOF IS EXTENDED ACROSS THE
WIDTH OF THE VAULT AS A MULTIBAY .

16. ROOF LIGHTS:
TOP LIGHT CAN BE PROVIDED BY DECK LIGHT
FORMED IN THE CROWN OF VAULT OR BY DOME
LIGHT. THE DECK LIGHT CAN BE CONTINUOUS OR
FORMED AS INDIVIDUAL LIGHTS.ROOF LIGHTS
ARE FIXED TO AN UPSTAND CURB CAST
INTEGRALLY WITH THE SHELL.
ADVANTAGE OF THE SHELL IS THAT ITS CONCAVE
SOFFIT REFELECTS AND HELPS TO DISPERSE
LIGHT OVER AREA BELOW. DISADVANTAGE IS
THAT TOP LIGHT MAY CAUSE OVER HEATING AND
GLARE.
ROOF COVERING:
SHELLS MAY BE COVERED WITH NON-FERROUS
SHEET METAL, ASPHALT, BITUMEN FELT, A
PLASTIC MEMBRANE OR A LIQUID RUBBER BASE
COATING.
ROOF INSULATION:
THE THIN SHELL OFFERS POOR RESISTANCE TO
TRANSFER OF HEAT. THE NEED TO ADD SOME
FORM OF INSULATING LINING ADDS
CONSIDERABLY TO COST OF SHELL. THE MOST
SATISFACTORY METHOD OF INSULATION IS TO
SPREAD A LIGHT WEIGHT SCREED OVER THE
SHELL.
DIFFICULTIES OF PROVIDING INSULATION AND
MAINTING THE ELEGANCE OF CURVED SHAPE
MAKES THESE STRUCTURES LARGELY UNSUITED
TO HEATED BUILDINGS IN TEMPERATE CLIMATE.

17. STIFFENING BEAMS AND ARCHES:
UNDER LOCAL LOADS THE THIN SHELL OF THE
BARREL VAULT WILL TEND TO DISTORT AND LOSE
SHAPE AND EVEN COLLAPSE IF THE RESULTANT
STRESSES WERE MORE. TO STRENGTHEN THE
SHELL AGAINST THIS POSSIBILITY, STIFFENING
BEAMS OR ARCHES ARE CAST INTEGRALLY WITH
THE SHELL.
THE COMMON PRACTICE IS TO PROVIDE A
STIFFENING MEMBER BETWEEN THE COLUMN
SUPPORTING THE SHELL.
DOWNSTAND STIFFENING RCC BEAM IS MOST
EFFICIENT BECAUSE OF ITS DEPTH, BUT THIS
INTERRUPTS THE LINE OF SOFFIT OF VAULTS, FOR
THIS UPSTAND STIFFENING BEAM IS USED.
THE DISADVANTAGE OF UPSTAND BEAM IS THAT IT
BREAKS
UP THE LINE OF ROOF AND NEED PROTECTIONS
AGAINST
WEATHER.

18. EDGE AND VALLEY BEAMS:
DUE TO SELF WEIGHT AND IMPOSED LOAD THE THIN
SHELL WILL TEND TO SPREAD AND ITS CURVATURE
FLATTEN OUT. TO RESIST THIS RCC EDGE BEAMS
ARE CAST BETWEEN COLUMNS.
EDGE BEAMS MAY BE CAST AS DROPPED BEAMS OR
UPSTAND BEAMS OR PARTIALLY AS BOTH. IN HOT
CLIMATE THE DROPPED BEAM IS USED WHEREAS IN
TEMPERATE CLIMATE UPSTAND BEAM IS USED TO
FORM DRAINAGE CHANNEL FOR RAIN WATER.
IN MULTI-BAY STRUCTURES, SPREADING OF THE
VAULTS IS LARGELY TRANSMITTED TO THE
ADJACENT SHELLS, SO DOWN STAND AND FEATHER
VALLEY BEAM IS USED.

19. EXPANSION JOINTS:
THE CHANGE IN TEMPERATURE
CAUSES THE EXPANSION AND
CONTRACTION IN CONCRETE
STRUCTURES, WHICH CAUSES
THE STRUCTURES TO DEFORM
OR COLLAPSE.
TO LIMIT THIS CONTINUOUS
EXPANSION JOINTS ARE
FORMED AT THE INTERVAL OF
ABOUT 30M, ALONG THE SPAN
AND ACROSS THE WIDTH OF THE
MULTI-BAY AND MULTI-SPAN
BARREL VAULT ROOFS.
LONGITUDINAL EXPANSION
JOINTS ARE FORMED IN A UP
STAND VALLEY.

28. CATENARY SHELL
• Cheesecloth and plaster shells
were dried upside down
creating forms in pure tension.
When flipped, shells rest in pure
compression, resulting in
lightweight forms that could be
built from thin concrete.

33. ADVANTAGES AND DIS-ADVANTAGES OF SHELLS:
ADVANTAGES:
1. VERY LIGHT FORM OF CONSTRUCTION. TO SPAN 30.0 M SHELL THICKNESS REQUIRED IS 60MM
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. FLAT SHAPES BY CHOOSING CERTAIN ARCHED SHAPES
5. ESTHETICALLY 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

34. NUBIAN VAULT

36. GUNA TUBE VAULT