Gravity and Surface-Load Stresses in Spheres

Stresses due to gravity are reported for a solid sphere and for a hollow sphere with an inner diameter one-half its outer diameter. The stresses were obtained using the freezing method of three-dimensional photoelasticity and the immersion technique previously developed by the authors. Epoxy spheres were immersed in mercury to magnify the body forces 11 times. Further results were obtained by applying the gravity solution to various orientations in the spheres. This has the effect of giving the stresses associated with a set of loads applied to the surface of the sphere at these various orientations. In the process, the body force load is automatically eliminated. Thus, the gravity solution can be applied to the determination of stresses associated with any combination of normal loads applied to the surface of the spheres.