SHELL STRUCTURESTHEORY OF STRUCTURES

SHELL STRUCTURESA shell is a type of structural element which is characterized by its geometry, being a three-dimensional solid whose thickness is very small when compared with other dimensions.

It possesses strength and rigidity due to its thin, natural and curved form such as shell of egg ,nut, human skull or of a tortoise.

Made usually of reinforced concrete , it functions both as a structure and covering.

TYPES AND FORMS OF SHELL STRUCTURE

FOLDED PLATES

• Folded plates are the simplest of the shell structures.

• The distinguishing feature of the folded plate is the ease in forming plane surfaces.

                        

The elements of a folded plate structure are similar to those of a barrel shell except that all elements are planar, and the moments in the slab elements are affected by the differential movement of the joints.

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

Domes of RevolutionFolded Plate DomesIntersection Shells

Warped SurfacesCombinationsShell Arches

Folded PlatesBarrel VaultsShort Shells

BARREL SHELLS                                                       The elements of a barrel shell are:(1) The cylinder,(2) The frame or ties at the ends, including the columns, and(3) The side elements, which may be a cylindrical element, a folded plate element, columns, or all combined.For the shell shown in the sketch, the end frame is solid and the side element is a vertical beam.A barrel shell carries load longitudinally as a beam and transversally as an arch. The arch, however, is supported by internal shears, and so may be calculated.The elements of a folded plate structure are similar to those of a barrel shell except that all elements are planar, and the moments in the slab elements are affected by the differential movement of the joints.For the structure shown, the end supports and the side supports are both complete walls The elements of a short shell are the barrel, which is relatively short compared to radius, the element at the base of the cylinder to pick up the arch loads, and the arches or rigid frame to pick up the entire ensemble. In this case it is a rigid frame arch. The size of the arch could have been reduced by horizontal ties at the springings. There may be multiple spans.The short shell carries loads in two ways:(1) As an arch carrying load to the lower elements. and(2) As as a curved beam to the arches.The thickness of the shell can be quite thin due to these properties.

DOMES

Domes are membrane structures, the internal stresses are tension and compression and are statically determinate if the proper edge conditions are fulfilled. In a dome of uniform thickness, under its own weight, the ring stresses are compression until the angle to the vertical is about 57 degrees. If the dome is less than a full hemisphere, a ring is required at the base of the dome to contain the forces.

TRANSLATION SHELLS                                                   A translation shell is a dome set on four arches. The shape is different from a spherical dome and is generated by a vertical circle moving on another circle. All vertical slices have the same radius. It is easier to form than a spherical dome.The stresses in a translation shell are much like a dome at the top, but at the level of the arches, tension forces are offset by compression in the arch. However there are high tension forces in the corner.

Istanbul 2020: Culture and Sports Park The Allianz Arena is a football stadium in the north of Munich, Germany

Kresge auditorium MIT.China national centre for performing arts

SHELL STRUCTURES EXAMPLES-

ADVANTAGES

1. naturally strong structures, 2. allowing wide areas to be spanned without the use of internal supports, giving

an open, unobstructed interior. 3. The use of concrete as a building material reduces both materials cost and

construction costs, as concrete is relatively inexpensive and easily cast into compound curves.

4. The resulting structure may be immensely strong and safe; modern monolithic dome houses, for example, have resisted hurricanes and fires, and are widely considered to be strong enough to withstand even F5 tornadoes.

DISADVANTAGES

1. Since concrete is a porous material, concrete domes often have issues with sealing. If not treated, rainwater can seep through the roof and leak into the interior of the building.

2. On the other hand, the seamless construction of concrete domes prevents air from escaping, and can lead to buildup of condensation on the inside of the shell. Shingling or sealants are common solutions to the problem of exterior moisture, and dehumidifiers or ventilation can address condensation.

SHELLS

SINGLY CURVED DOUBLY CURVED

SURFACES OFTRANSLATION

SURFACES OFREVOLUTION

1.CIRCULAR CYLINDER2.CONES

1.CIRCULAR OR CYLINDER2.CONES

ANTYNCLASTICSYNCLASTIC

SURFACES OFREVOLUTION

SURFACES OFTRANSLATION

SURFACES OFREVOLUTION

SURFACES OFTRANSLATION

1.CIRCULAR DOMES2.ELLIPSOID OF REVOLUTION3.PARABOLOIDS OF REVOLUTION

1.ELLIPTIC PARABOLOIDS2.PARABOLOIDS OF REVOLUTION

HYPERBOLOIDSOF REVOLUTIONOF ONE SHEET

1.HYPERBOLIC PARABOLOIDS2.CONOIDS3.HYPERBOLOIDS OF REVOLUTION OF ONE SHEET

SINGLE CURVATURE SHELLSThey are curved on one linear axis and are part of a cylinder or cone in the form of barrel vaults and conoid shells.

DOUBLE CURVATURE SHELLSThey are either part of a sphere, or a hyperboloid of revolution.

These terms do not provide a precise geometric distinction between the form of shell because a barrel vault is single curvature but so is a dome.They are used to distinguish the comparative rigidity of the two forms and complexity of centring necessary to construct the shell form.

DOME

CONOID

HYPERBOLOID PARABOLOIDBARREL VAULT

FORMS OF CURVATURE

SURFACES OF REVOLUTIONSurfaces of revolution are generated by the revolution of a plane curve called meridional curve,about an axis called the axis of revolution.In the special case of cylinderical and conical surfaces,the meridional curve consists of a line segment.Eg:Cylinder,cones,spherical or elleptical domes,hyperboloids of revolution,toroids

SURFACES OF TRANSLATION

Surfaces of translation are generated by sliding a plane curve along another plane curve,while keeping the orientation of the sliding curve constant.The latter curve on which the original curve slides is called generator of surface.In the special case in which the generator is a straight line,the resulting surface is called cylinderical surface.

ELLEPTICAL PARABOLOID CYLINDERICAL PARABOLOID

HYPERBOLIC PARABOLOID