Consequently, some obvious and significant insurmountable inconsistencies between the results obtained from the elastic calculation and the results under real conditions and in tests began to appear. It was always impossible to guarantee that the state of stress obtained in the shell represented the indisputable 'real state' of the structure. All these hypotheses involved either idealising a reality that was impossible to ascertain a priori, or referred to an ideal, homogeneous and isotopic material, when reinforced concrete does not have any of those properties. However, it was practically impossible to apply the elastic theory of shells, as it involved solving complex eighth-order differential equations, based on unreal hypotheses about the surrounding conditions and the structural material used. The mathematical formulation provided by analytical theory, which was at that time widely used and referred too ideal, homogeneous and isotropic materials complying with Hooke's law, was also applied to the structural calculation of long cylindrical reinforced concrete shells, without any consideration being given to the characteristics of the new construction material used. The theory of elasticity began to be implemented in the structural calculation of long cylindrical shells in Germany in the 1930s, as a result of the work by the engineers U. Elastic Theory was applied due to its widespread use in the structural calculations of the time ( Figure 1).įigure 1 Long cylindrical shells on the roof, under construction, in the Dywidaghalle.

In view of the demand for these new types of buildings, it became necessary to establish a mathematical foundation that was able to calculate them before they were constructed.

As a result, a new construction system emerged, with a geometry that was ideal for covering utilitarian spaces, such as stations, warehouses, factories and hangars in short, spaces with large spans which had previously been constructed in steel. Meanwhile, reinforced concrete cylindrical shells became widespread types of structure able to cover large spans with a minimal use of material in construction after the First World War. Reinforced concrete was obviously the material that complied with this mathematical model, due to its moldability, as it contained reinforcements to counteract tensile and shear stresses. The structure therefore no longer solved the resistant problems in terms of a cross-section, but instead did so using the pure form thereby satisfying the principle of economy of material that was so important to engineers and builders at that time. Emperger (Reissner, 1908 Emperger, 1910), found that if the stresses in a thin but sufficiently rigid shell were only compressive, tensile and tangential, were all contained within the shell's thickness and there were no bending stresses at any point, the sheet could be very thin - just a few centimetres thick - in order for its shape and support conditions to meet certain basic conditions. Until the 1920s, and in Germany in particular, the structural behaviour of thin reinforced concrete shells was studied as if they were 'membranes'. The first long cylindrical reinforced concrete shell appeared in Germany in 1924, in the roof of a building that was to be used as a factory by the company Zeiss. Introduction and Description of the problem

Palabras clave: Cáscaras cilíndricas largas cáscaras de hormigón armado Félix Candela Outeriño método de la viga cascarones de hormigón armado Este método, desarrollado anteriormente por otros ingenieros, se expone matemáticamente seleccionando un ejemplo de la obra de Félix Candela, ejecutada por medio de cáscaras cilíndricas largas, y elaborando el proceso de cálculo necesario propuesto. El objetivo de Félix Candela era obtener un método de cálculo seguro y sencillo, respetando la característica de cedencia del hormigón armado y, por tanto, obviando consideraciones de compatibilidad y deformación que pudiera sufrir la estructura. Todo ello, en un momento en el que la teoría elástica de cáscaras cilíndricas resultaba prácticamente inaplicable al implicar la resolución de ecuaciones diferenciales de octavo orden. En el presente trabajo se describe cómo el arquitecto Félix Candela llevó a cabo el análisis de cáscaras cilíndricas largas de cubierta de hormigón armado utilizando un método basado simplemente en ecuaciones de equilibrio.

Felix candela arquitecto