Since the middle ring has an extensive cut across the midplane on both sides as well as entrance and exit holes and loaded with about 25,000 pds, calculations of the stresses and deformation of the midplane support area of the middle ring and deflection of the window opening were made using the finite element analysis code ANSYS . The work was conducted by a graduate student in the Department of Civil Engineering at the University of Virginia and a REU student. A scaled down model of the middle ring was constructed and then tested by applying forces to it using the Materials Testing Service of the Department of Transportation at the University. ANSYS was first checked by comparing calculations of the test model deflections to the actual data. Agreement was within 10%. Results of ANSYS for the target chamber showed that the maximum deflection of the opening of the window in the middle ring varied from 0.007 in to 0.015 in depending on how the middle ring was loaded. This was decided to be a safe limit. In the final design, several moveable seven inch long, two inch diameter aluminum support rods would be placed in the window for added support. In addition flanges defining the ports and coupling to the spectrometers would be added giving additional support to the middle ring. Compressional stresses, calculated using ANSYS assuming the middle ring were attached to the top hat and loaded with 25,000 pds, were less than 3000 psi most everywhere. However, stresses over small areas rose to levels 6000 psi near the entrance and exit holes. These calculations indicated that we did not exceed the safety limit of 15,000 psi for aluminum. A simple model calculation shown in Appendix A gives the result 1434 psi, which repersents some average value over the midplane contact area.