Photo-Elastic Determination of Shrinkage Stresses

Stresses due to shrinkage of concrete in masonry dams are of interest and importance, but the determination of these stresses is complex and difficult. In practice, the large masses of concrete used in gravity dams are not homogeneous; nor are they isotropic, as the structure is poured in blocks which present many planes of discontinuity. The indeterminate factors on these planes of discontinuity present such formidable difficulties that an accurate determination of shrinkage stresses is impossible. If the problem is idealized, however, by assuming a homogenous, isotropic, simple gravity dam subject to uniform shrinkage, it becomes possible to predict these stresses with some assurance. Although this idealized case is not truly consistent with actual practice, it creates a philosophical “picture,” nevertheless, of the strained condition that should be of value to the judgment of the de signing engineer.

One approach to the mathematical solution of this problem has been made by J. H. A . Brahtz, of the United States Bureau of Reclamation. Considering the applicability of the solution of this problem, a complete diagrammatic representation of the stress distribution may be of more interest than the mathematical description. The former is herein presented. This problem was studied at the California Institute of Technology in the photo-elastic laboratory of the Guggenheim School of Aeronautics. The writer wishes to express his appreciation for the continued interest in this problem expressed by Theodor von Karman, M. Am. Soc. C. E., who is the Director of the Guggenheim School.