Thin shells — Three-dimensional spatial structures made up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions. Thin shells are characterized by their three-dimensional load-carrying behavior, which is determined by the geometry of their forms, by the manner in which they are supported, and by the nature of the applied load.
Candela did not invent the concrete shell; nor is he the first to make use of the hyperbolic paraboloid... Other people... have contributed more to the theoretical analysis of shell structures. But nobody else can claim credit for such an exciting variety of shell structures... [H]e has concentrated his effort in one particular sphere: the construction of light concrete roofs.
[M]ost of Candela's structures are almost complete in themselves... the forms and proportions bear witness to his artistic sensibility. ...[B]alanced perfection ...makes a... structure into a work of art. ...[T]he whole must take precedence over any of its parts.
The idea of form over mass also developed in Europe in the pioneering work of Dyckerhoff and Widmann... in Weisbaden, Germany. Working in reinforced concrete, the firm experimented with new ways to cover large spaces in the 1920s. The firm built domes and cylindrical "barrel" shells to serve as large roofs of extraordinary thinness. The possibilities... fascinated an Austrian civil engineering student, Anton Tedesko... who joined the firm in 1930.
At the time of construction of the Wyss shell, three-dimensional computer software was not available and it would have been extremely difficult to convey, using only normal engineering drawings, the required form of the concrete at the feet of the shell... To overcome the problems... proposed that, rather than making sketches, drawings, or even a model of the detail, they should resort to modelling it at full-scale on site.
The resistant virtues of the structure that we make depend on their form; it is through their form that they are stable and not because of an awkward accumulation of materials. There is nothing more noble and elegant from an intellectual viewpoint than this; resistance through form.
Nature does not apply the construction principle of a beam supported by two s. Forms developed by nature are following the rational attempt to achieve distinct functionalities with the smallest possible material - and energy consumption. An impressive example is the phenomena of egg shells... The shell principle is adopted by humans... in building construction, in order to achieve wide spanning and material saving 'slender' structures.
The design of shells... implicates the design of internal stress fields of form dependent shapes... meeting the compatabilites of all boundary conditions...
The title of first pioneer of the HP hyperbolic paraboloid or hypar construction] in concrete in the 1930s belongs to Fernand Aimond for the projects that he constructed.., for the formulation of the theoretical structural membrane model, and for his influence both on [Giorgio] Baroni in Italy in the late 1930s and on Candela in Mexico in the 1950s.
The true Mathematical and Mechanical Form of all manner of es for building with the true butment necessary to each of them, a Problem which no Architectonick Writer hath ever yet attempted, much less perform'd. ...Ut pendet continaum flexile, sic stabit contiguum rigidum, which is the Linea Catenaria.
It was the great nineteenth century mathematician, Carl Gauss who proved mathematically that any curved surface, natural or man-made, can be characterized as only one of three different possible shapes: as -like, -like, or saddle-like. All three of these geometric shaped can be used as the basis for thin-shell structures.
Resistance of Spherical Shells to an Internal Fluid Pressure.—An elastic fluid contained in a closed vessel presses each unit of area of the surrounding walls with equal force. The resistance offered by the walls depends on their superficial area, their form, their thickness, and the coefficient of resistance of the material.
The hollow sphere encloses the largest space in proportion to the superficial area of its shell, and all vessels that are not spherical, exposed to an internal fluid pressure, experience distortion on account of their tendency to assume the spherical form. A hollow sphere, having a shell of uniform thickness composed of a homogeneous material, experiences the same tension at all sections of metal formed by diametrical planes.
Resistance of Cylindrical Shells to an Internal Fluid Pressure.—The tension produced in a cylindrical shell by an internal fluid pressure may be considered as being of two different kinds—viz., first, a tension acting in a longitudinal direction, tending to pull the ends of the cylinder apart; and, secondly, a tension acting in a diametrical direction, tending to split the cylinder from end to end.
Resistance of Cylindrical Shells to an External Fluid Pressure.—Thin hollow cylinders exposed to an external fluid pressure never give way by direct crushing, but by collapsing; it may be assumed that, other things equal, the resistance of tubes to collapsing is greater as their form is more truly cylindrical and their shell more perfectly homogeneous.
Fairbairn finds that the collapsing pressure of... an elliptic form of cross-section is found approximately by substituting... for
[P]rinciples as developed by Kelvin and by Love show that it is impossible to bend a nearly flat dish shaped shell about one horizontal axis without at the same time bending it in the opposite direction about a second horizontal axis at right angles to the first.
Any load which is applied to the shell is sustained in general partly by the stretching surface and partly be the surface; and the balance in load-sharing is regulated mainly by the 'interface pressure' between the two surfaces, which varies from point to point over the surface. This interface pressure becomes a prime variable of the problem. In terms of classical it is a variable 'redundancy'.
The of a shell can be of the same sign throughout... In such a case the surface is called synclastic. s are synclastic surfaces... The curvature of a shell can also be of a different sign... both concave and convex... which is known as anticlastic. An example... is the hyperbolic paraboloid.
The great era of thin concrete shells... was an attempt to cover large spans with the most widely used construction material of the Twentieth Century and yielded structures that are now regarded as architectural masterpieces. The design of thin concrete shells also fostered theoretical developments in , in the mathematical theory of shells and in the theory of finite elements.
[A] significant breakthrough was achieved with... two celebrated huge airship hangars built by Freyssinet at Orly in the early 1920s... [whereby] the principle of the corrugated form for the concrete shell was introduced to obtain the necessary stiffness...
Forces present in the structure, shape thin shell concrete. Areas of uniform load present smooth, catenary curvatures, while areas of concentrated force express themselves as sharp bends or spikes in the surface form.
By their very nature all funicular structures, including thin shell, use... less material... By designing only for pure tension or compression these structures experience very little force. These pure forces require less material to resist...
Dieste’s hypar masonry roofs are inexpensive, utilitarian statements about space enclosure...
[T]he second wave of shell building (1940-1960s)... focused almost exclusively on s... [to] include s and hyperbolic paraboloids. ...[T]hey were definable through mathematical formulas, which allowed the designer to understand the forces... Ruled surfaces are... more constructible, because they can be created out of linear elements, such as... boards and pipes...
The most prominent designer to eschew s is the Swiss engineer . In 1954... Isler hit on the idea that a “bubble” (in this case a pillow) takes the optimal shape for its edge boundaries. Isler began to construct models by inflating surfaces or by hanging and then hardening them.
History shows that not all thin shell concrete buildings are funicular—other families... chosen for pragmatic reasons such as their constructability, or because they were geometrically simple enough [that] through calculation... bending... was [found to be] within... tolerances... for the material.
[C]losed surfaces are more rigid than open surfaces. ...Therefore to achieve ...rigidity the openings [are] compensated.
[U]sing concrete shells as roofing provides the possibility of constructing spacious columnless buildings... has enhanced this possibility.
Concrete shells can be built by the assembly of several cast units, or cast in one piece (monolithic). Monolithic concrete shells are structurally stronger...
[D]evelopment of the theory employs (elastic material), equilibrium and compatibility. Hooke’s law relates strains with stresses, equilibrium relates stress resultants with external loading and compatibility relates strains with deformation/displacements. These three sets of equations together with appropriate boundary conditions make up the mathematical aspect of the problem.
[T]he ratio [of] radii of curvature to thickness of the shell, ... greater than 20 can be characterized as thin shells... an egg shell has a ratio of around 55...
[W]e will mainly be dealing with uniform shells. The shells are uniform in the sense that the material properties do not vary through the thickness. (RC) is... regarded as sufficiently uniform... [since] the difference in between steel and concrete is not large...