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  1. Shells Submitted by, S.Supraja - 060138

  2. Shells • Shells are surface structure made out of such inelastic materials as concrete, wood, metal, and synthetics. • They transfer loads by compression, by shear, or even by bending tangentially to their surfaces. • Shells are also called “form-resistant structures” because they are shaped according to the loads they carry. • Load transfer is most effective when the shell’s shape approximates that of the corresponding inverted membrane- the two dimensional antifunicular curve. • Practical considerations limit construction to forms generated by relatively simple geometric laws and shapes; ruled surfaces, developable surfaces, simply or doubly curved surfaces, rotational surfaces, and so on. • The simplest of such forms are cylindrical forms reminiscent of the earliest vault-construction systems.

  3. Shells • These forms are used extensively in contemporary architecture- sometimes as purely decorative elements- often without clearly distinguishing between vault action and shell action. • Hyperbolic paraboloids, which are ruled surfaces albeit with a variable curvature, are used both as building envelopes and as morphological elements. • Shells may be composed of prefabricated (precast) surfaces or linear elements more or less rigidly connected. Taken as integral units, these structures have a surface statical function, whereas their component elements could have a linear, surface, or mass statical function. • In the point of view of statics, the loads must be of the type which is best able to resist. Shells will not carry heavy point loads, specially reinforced. T he inevitable concentrations of loads at supports make it necessary to modify the shell at these points, in order to control the force and transfer them smoothly to the substructure.

  4. Shells • In order to be able to formulate a theory for a shell, a mathematician needs to eliminate al the influences that produce bending of the shell. He would prefer the shell to act like a “membrane”, in which all the forces are tangential to the surface. • In order that the total distribution of forces in the shell may correspond as closely as invisible with assumptions on which the theory is based, the shell is to be made so thin that it is incapable of resisting any forces other than those acting in tangential directions. • Forces and similar considerations restrict the range of forms possible in modern shell construction. • The laws of structural form will be explored with reference to a number of groups of similar, formally related examples. They can be divided into five categories: • Cylindrical shells • Shells of revolution • Conoids • Hyperbolic paraboloids • Free forms

  5. Shells External view of the 50 ft span x 20 ft. wide cylindrical shell roof in the construction of which the new technology was developed. The Soft 50 ft. span x 20 ft. wide concrete shell roof being jacked up. View from above showing the joints between the precast shell in a group of three cylindrical shells at Galle harbor prior to jacking UP. Note the double columns for supporting the edge and valley beams. A study of technical literature at the time showed that these techniques had not been used elsewhere. 100 ft. span x 33 ft. wide shell roofs being jacked up in groups of three roofs for warehouse in Galle harbor. They require no maintenance except periodic paining, even after 35 years.

  6. Cylindrical Shells • Cylindrical surfaces maybe obtained by sliding a horizontal straight line (generator) along a vertical curve (directrix) at right angles to it. • The sliding curve is often a circle, but may be an ellipse, a parabola or any other kind of curve, having in most cases a downward curvature. Moreover, cylinders with curvatures up and down may be joined by the edges to obtain corrugated shells, and cylinders with curvatures up only are used at times. • If a cylinder is cut by planes with different orientations, but all passing through thee normal to the surface at the same point, it will be found that the curvature of the sections thus obtained vary between a minimum (equal to zero) in the direction of the axis of the cylinder, and a maximum curvature at right angels to it, that is, in the plane of the directrix. • The maximum and minimum curvatures of a surface at a point are called its principals curvatures at that point. In the case of the cylinder it is seen that the curvature of any cut has the same sign(is in the same direction) as that of the directrix, except for the curvature in the direction of the generator, which equals zero.

  7. Simple primary forms of cylindrical shell acting like beams spanning between two supports - central market in Budapest and Frankfurt

  8. In collaboration with Nervi the architects Hellmuth, Obata and Kassabaum have prepared a centrally oriented design for the St. Louis Priory in St. Louis. It consist of two superimposed, concentrically arranged rings of conically sliced shells. • Circular arrangement of shell elements in which the cylindrical form has been abandoned, the subsequent development of doubly curved surfaces is suggested.

  9. Cylindrical Shells • Cylindrical shells can be supported in a variety of ways and their behaviour varies depending upon their support conditions. • If a cylindrical shell is supported directly on the ground it will behave like a “frozen inverted catenary” only for a given set of loads, for example, its own weight; but it will not be capable of sustaining other loads without developing a certain amount of bending and twisting stresses. • For this reason, thin cylindrical shells are not usually supported directly on the ground. If instead, a cylindrical shell is hung from two end arches, usually called “stiffeners” it is capable of supporting a variety of loads b means of membrane stress only. • This means that the loads are channeled by the shell to the end stiffeners, and that the stiffenes transfer the loads to the ground by names of direct and bending stresses. A cylindrical shell with stiffeners does not act as an arch, but as a thin piece of material hanging from stiffeners.

  10. Cylindrical Shells • A cylindrical shell of reinforced concrete or steel is capable of taking both tensile and compressive stresses. • Intrestingcylindrical shells are obtained by intersecting cylinders at right angles: these roofs were classical in the middle ages, but a renewed intrest in them is now apparent. Modern intersection roofs are typified by their low rise and could not be built except in reinforced concrete in view of the high stresses developed in them and of the high value of their thrust which must be taken by tensile ties, or buttresses. Building designed as a short shell – Gold-Zack Factory, Gossau, Switzerland,1954, Heinz Hossdorf. Architect: Danzeisen & Voser

  11. Above: Two cylindrical shells interpenetrating at right angles. The result maybe a form similar to that of the cross vault – the St. Louis air terminal. Interior view of the terminal Left: Design employing arched cylindrical shells – Hanger in Marigane, France.

  12. Kresge Auditorium, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts. Architect Eero Saarinen, 1954.  CNIT exhibition hall, Paris

  13. Cylindrical Shells • We shall now summaries the most important characteristics of the cylindrical or segmental shells: • The curvature of the shell is at right angles to the direction in which it spans. • The transverse curvature may take any form; it need not necessarily follow the line of pressure. A parabolic cross section is not typical of the cylindrical shell. • The transverse curvature of the shell should be sufficiently emphatic, not flat or feebly expressed. • The curve of the shell should be bold and harmonious. A succession of ill-matched arcs will never satisfy the eye. • The shell should be a closed unit. Skylights, openings and lands of glazing disrupt the form. • The shell should end decisively. It should not simply peter out. Its form should be exposed at the edges. A curve that dies out feebly is incompatible with the inner tension characteristic of shell construction.