The roof of Spokane Church

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 indétermination 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/cm². 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.