Shell Structures

August 14, 2017 | Author: rahul_srikrishna | Category: Beam (Structure), Dome, Vault (Architecture), Bending, Structural Steel
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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.


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









FOLDED PLATES • 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.

Stiffeners – to carry loads to support & to hold plates in line.


Walls continuous with shell

Tapered folded plates

Edge supported folded plates

Folded plates truss

Folded plates rigid frame


Inclined Plates

Columns to support the structure in air.

Folded plates

3-segment folded plate


Edge Plates – to stiffen wide plates

3 segments

3-SEGMENT FOLDED PLATES •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.

Large sloping plate

Window ventilation – reflected south light

Z-SHELL •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.

Roof surface is painted with Al so that sunlight is reflected through windows to the ceiling.


Edge plates

CANOPIES Walls braced on top & continuous with roof plates, so columns not needed.

Walls are of tilt – up concrete, cast on the floor & raised into place by cranes.

•A two segment structure is not desirable because it has very little torsional resistance. 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.

Deep concrete beams with very thin web structures Single barrel vault Stiffeners – to carry loads & to support the vault Edge Plates Columns to support the structure in air.

Use of arch form reduces stress & thickness in transverse direction

Transmission of forces

•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. Arch Structure

Edge beams act like folded plate structures

Long Short shells shells Transmission of forces

•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.

Shell spanning between arches


Edge beams (can be omitted if shell is thickened)


• 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.

Dome formed by using triangular pieces of a cylindrical shell arranged in the form of a square.

Structural action of a short shell Loads are carried by the cross beams

Angle between the components is small

Best type of dome to cover square area. Edge beam – stiffening element

• An intersection of 90 degrees is the optimum value because it gives a stiff rib.

Cantilevered part of the barrel – span should not be large to take the bending forces.

Skylight can be placed at the crown of the dome

4 cylindrical barrels

Architectural advantage – structure appears to Supported by 4 columns at the float in air. intersection


Columns are at the center of each panel not at the ribs.

Form is suitable for large spans – nearly circular in plan

• 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. Suitable for long • 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

Skylights can be used for lighting


Each unit is self supporting


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

Surface is more difficult to form – widths can be more than folded plates

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.

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.


• 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.

British Museum – Norman Foster

Sydney Opera House – John Utzon

• 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.

Venugopal Temple Manipal


Sangath – B.V.Doshi

Hussain – Doshi Gufa

Swiss Re “Gherkin” – Norman Foster


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