S H E L L

S T R U C T U R E S

R A H U L S R I K R I S H N AR O L L N O : 3 9 0 6 0 9 0 1 0 6 6

INTRODUCTION

DEFINITION

Shells can be defined as curved structures capable of transmitting loads in more than two directions to supports.

Loads applied to shell surfaces are carried to the ground by the development of compressive, tensile, and shear stresses

acting in the in-plane direction of the surface.

Thin shell structures are uniquely suited to carrying distributed loads and find wide application as roof structures in building.

They are, however, unsuitable for carrying concentrated loads.

SHELLS IN NATURE

Eggshell - The most efficient example as lightness proportion

to its strength is amazingly high.

Bird’s nest is a good example of an inverted dome, results

from bird’s astonishing instinct to capitalize on the efficiency

of the domed geometric shape and on materials that are readily

available

TYPES & FORMS OF SHELL STRUCTURES

FOLDED

PLATES

BARREL

VAULTSDOMES

WARPED

SURFACES

SHORT

SHELLS

SHELL

ARCHES

INTERSECTION

SHELLS

FOLDED PLATE

DOMES

Folded plates

3-segment folded plate

Z-shellWalls

continuous with shell

Tapered folded plates

Edge supported

folded plates

Folded plates truss

Folded plates rigid frame

• Folded plate is the simplest of the shell structures.

• The distinguishing feature of the folded plate is the ease in

forming plane surfaces. Therefore, they are more adaptable to

smaller areas than curved surfaces which require multiple use of

forms for maximum economy.

• 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 structure above may have a simple span, as shown, or

multiple spans of varying length, or the folded plate may

cantilever from the supports without a stiffener at the end.

FOLDED PLATESInclined

Plates

Edge Plates

– to stiffen

wide plates

Stiffeners – to carry

loads to support &

to hold plates in

line.

Columns to

support the

structure in air.

Walls are of tilt – up concrete,

cast on the floor & raised into

place by cranes.

Walls braced on top &

continuous with roof plates,

so columns not needed.

•The dimensions of the plates are dependent on both the width of the barrel and

on the span.

•The depth of the shell should be about 0.10 times the span and the maximum

slope of a plate should not be greater than 40 degrees.

•The slope of the plates is 6/8, which is about 37 degrees and is satisfactory. The

thickness of the plates could be about 3 ½ inches.

3-SEGMENT FOLDED PLATES

•The Z shell is not an efficient structural shape since it is

discontinuous and its effective depth is much less than the actual

vertical depth.

•The spans are limited in comparison to the plates having a large

number of units side by side.

Z-SHELL

3 segments

Large sloping

plateWindow ventilation –

reflected south light

Edge plates

Roof surface is painted

with Al so that sunlight

is reflected through

windows to the ceiling.

WALLS CONTINUOUS WITH SHELL

•A two segment structure

is not desirable because it

has very little torsional

resistance.

CANOPIES

Four segments

BARREL VAULTS

• Barrel vaults are perhaps the most efficient of the shell structures because they can span upto 150 feet with a minimum of material.

• If the span is large in comparison to the width, the form is called a long shell. The span/radius ratio is 5. If the length is short, it is called a

short shell. The span/radius ration less than 1 and shells between these limits are called intermediate shells.

• The thickness of the barrel shell is usually based on the minimum thickness required for covering the steel for fireproofing + the space

required for three layers of bars + some space for tolerance.

• If these bars are all half inch rounds - minimum of 3 1/4 inches. Near the supports the thickness may be greater for containing the larger

longitudinal bars.

• If more than one barrel is placed side by side, the structure is a multiple barrel structure and if more than one span, it is called a multiple

span structure.

• Provision should be made for expansion joints in a large structure.

Single barrel

vault

Edge Plates

Stiffeners – to carry loads

& to support the vault

Columns to support

the structure in air.

Deep concrete beams with

very thin web structures

Use of arch form reduces stress

& thickness in transverse

direction Transmission of forces

SHORT SHELLS

•This structure is a cylindrical shell having a large radius in comparison to the

length.

•The principle structural element is the stiffener, usually a reinforced concrete

arch, although steel arches or trusses have been used.

•Many structures built with short shells, such a large hangars and auditoriums, could

have been built with little more dead load by using a ribbed slab or other lightweight

concrete framing system rather than the shell.

•The curve of the shell is determined by

the proper shape of the arch and may be a

circle for small structures.

•The minimum shell thickness should be at

the top in the center of the span. At the

arch, the shell thickness is increased slightly

for local stresses.

Arch Structure

Shell spanning between arches

Edge beams (can be omitted if shell is thickened)

Edge beams act like folded plate structures

Transmission of forces

Long shells

Short shells

DOMES

INTERSECTION SHELLS

• The surfaces that produce the shell appear to meet at an

intersection.

• The structural efficiency depends on the angle of the

intersection of the surfaces. If the angle is small, then a

natural rib is formed by the adjacent elements of the basic

shells which is much stiffer than the adjacent shells on each

side. An intersection for which the angle is very large is

called here a shallow intersection.

• An intersection of 90 degrees is the optimum value

because it gives a stiff rib.

Dome formed by using triangular pieces

of a cylindrical shell arranged in the

form of a square. Angle between

the components

is small

Best type of dome to

cover square area.

Structural action

of a short shell

Loads are carried by

the cross beamsEdge beam –

stiffening element

Form is suitable for large

spans – nearly circular in planColumns are at the

center of each panel

not at the ribs.

Skylight can be placed at

the crown of the dome4 cylindrical barrels

Supported by 4 columns at the

intersection

Cantilevered part of the barrel – span should not be large to

take the bending forces.

Architectural advantage – structure appears to

float in air.

SHELL ARCHES

• Shell arches are somewhat in the same category as short shells in that the

shell action is subservient to the arch action. All the thicknesses can be made

quite small of an arch is used because the stresses will be principally

compression.

• The curve of the arch has to be generally a funicular form, that is, it should

fit the thrust line of the applied loads.

• Shells are not very efficient structures if the bending moments are high, as in

the folded plate rigid frame.

• There are types of shells that fit in several categories. The hyperbolic

paraboloidal dome is really a shell arch.

Long span arches are possible as bending moments are much less in an arch than in a beam

Shearing forces are not very large – larger holes than barrel vaults can be used

Skylights can be used for lightingSurface is more difficult to form –widths can be more than folded plates

Suitable for long spans

Each unit is self supporting

Continuity and Curvature

The essential ingredients of a shell structure in all of the foregoing

examples are continuity and curvature.Thus, a fiberglass hull of a boat

is continuous in away that the overlapping planks of clinker

construction are not. A pressure vessel must be obviously constructed

to hold a fluid at pressure, although the physical components may be

joined to each other by riveting, bolting or welding. On the other

hand, an ancient masonry dome or vault is not obviously continuous in

the sense that it may be composed of of separate stone subunits or

voussoirs not necessarily cemented to each other. But in general domes

are in a state of compression throughout, and the subunits are thus

held in compressive contact with each other. The important point here

is that shells are _structurally continuous in the sense that they can

transmit forces in a number of different directions in the surface of the

shell, as required. These structures have quite a different mode of

action from skeletal structures, ofwhich simple examples are trusses,

frameworks, and trees. These structures are only capable of

transmitting forces along their discrete structural members.The

fundamental effect of curvature and its effect on the stregth and

stiffness of a shell.

EXAMPLES

Santiago Calatrava

L’Hemisfèric (Planetarium)

Valencia, Spain

L’Hemisfèric, the distinctive eye-shaped

construction designed by Santiago

Calatrava, was the first element to be

opened to the public in the City of Arts

and Sciences, in April 1998.

The building’s unique architecture comes

alive as the lids of the colossal “Eye of

Knowledge” opens up to reveal the

fascinating setting.

The globe of L’Hemisfèric (the Planetarium), which also

houses the Omnimax theater, is roofed over by an elliptical

shell structure and placed within an elliptical pod that cradles

it like the pupil of an eye.The L’Hemisfèric is set slightly

below grade to avoid visual conflict with the Science Museum

and Palacio de las Artes

The concrete socket of the eye incorporates elongated

aluminium awnings that differ in length and fold

upwards collectively, or as individual units, to form a

brise-soleil roof that opens along the curved central axis

of the eye shape. The concrete encasement has been

extended upwards, and the brise-soleil narrowed and

replaced by a system of slats mounted on each side of

pivoting, to imitate the structure of a feather.

Conclusion

• The present technology makes it feasible to build long

span roof structures in wood, steel, or reinforced

concrete.

• Cost of wood is the highest + Span limitations.

• Concrete is cheaper than steel as it can be produced

anywhere at a lower cost.

• Steel is more expensive on a world wide basis.

• Therefore, reinforced concrete thin shell should be the

structural system to erect permanent roof structures

enclosing long span buildings.

• But the life span of reinforced concrete thin shells is

less than a century, which is comparatively lesser than the

other systems.

• Concrete domes are becoming increasingly popular.

British Museum –Norman Foster

Sydney Opera House – John Utzon

Swiss Re “Gherkin”

– Norman Foster

Hussain – Doshi Gufa

Venugopal Temple -Manipal

Sangath –B.V.Doshi

Model