Cubierta Hiperbólico-parabólica

T Y Linn,Felix Kulka

doi:10.3989/ic.1963.v15.i147.4765

Abstract

Spokane Church in the State of Washington has been attractively roofed with a parabolic-hyperbolic pre-stressed concrete shell. According to the author, this type of shell structure, normally accepted to be of simple analysis, can present certain difficulties as regards stability. Theories deriving from the study of a membrane are not enough because, if the shell is large enough certain secondary stresses appear which quickly affect stability. In this case the shell, which is symmetrical along one axis only, has two overhangs of 15 and 31 meters respectively, which required a special study. In an attempt to smooth out the difficulties of an exact calculation the author tried as far as possible to even up the bending moments of the whole shell, thus allowing the indetermination conditions to be lessened. To do this he gave the shell a 7.5 centimeter thick overhang of light concrete at the back and a 12 centimeter thickness of ordinary concrete at the front. The front walls are strengthened by the shell, which they support. The light supports at the back will not take any load over the normal design load. To calculate the stress of the shell and around the rim, the membrane theory was applied, and it was assumed that the shell was symmetrical about two axes; this analysis gave a maximum stress of 14 kg/cm 2 . Considering that the boundary area was subject to axial compressive stresses, in principle, it was thought that only normal reinforcement would be needed over the whole shell, without needing it to be pre-stressed; but it was realised that the secondary stresses would be decisive in the general behaviour of the shell. The shrinkage of the concrete would be another cause of these secondary stresses, and likewise the differential shrinkage and elastic shortening of several parts of the structure. The object of the pre-stressing was to apply uniform pressure on the whole shell. To achieve this a stress of 16 tons was applied on each 1-meter wide band of the shell. In the direction of the two stirrups the pre-stress was 10 tons per meter, to avoid the possibility of cracks.

Highlights

La iglesia de Spokane, del Estado de Washington, se h a cubierto, graciosamente, con una, lámina parabólico-hiperbólica, de hormigón pretensado
No son suficientes las teorías que el estudio de u n a membrana proporciona, ya que, si las dimensiones de estas láminas alcanzan ciertas proporciones, aparecen esfuerzos secundarios que rápidamente surgen al intervenir en la estabilidad de la lámina
Con objeto de allanar dificultades de un cálculo exacto, intentó igualar, en la medida de lo posible, los momentos flectores en toda la lámina, admitiendo, con ello, que las condiciones de indeterminación se verían reducidas

Summary

Introduction

La iglesia de Spokane, del Estado de Washington, se h a cubierto, graciosamente, con una, lámina parabólico-hiperbólica, de hormigón pretensado. Para el cálculo de las tensiones de la lámina y de los elementos de borde se aplicó la teoría de membrana y se supuso que la lámina e r a simétrica respecto de los dos ejes, de cuyo análisis resultó u n a tensión máxima de 14 kg/cm^.

Results

Conclusion