## Sphere

Circumferential load in the wall of all the spheres under internal pressure is equal to the pressure dmes the internal cross-sectional area, and the hoop stress, using the previous engineering assumption, is found to be:

It will readily be seen that no matter which section is chosen, provided the plane of the section passes through the center of the sphere, the condition will be the same, and it can be said that the hoop stress will be the same in all directions.

When it is assumed that:

it is determined that for wall thicknesses up to approximately 3 inches, the error is negligible. It can also be determined that the percent of error decreases as the ratio r/t increases. Table 4.6 provides size vs. weight of RP spheres.

 Capacity, Outside Nominal Maximum Overall cubic diameter, weight, weight, length, inches inches pounds pounds inches 50 5'/4 1.50 1.60 55/8 100 6'/2 2.50 2.63 615/16 200 8'/s 4.44 4.62 8^2 300 9'/4 6.25 6.56 95/8 400 10'/8 8.06 8.48 109/16 500 10,5/l6 9.87 10.35 115/16 650 11,5/16 12.56 13.18 125/i6 880 13'/,6 16.00 16.80 133/s 1,070 14 20.06 21.07 143/8 1,325 15'/8 24.50 25.73 157/i6 1,575 157/s 28.75 30.15 16'/4 1,800 165/s 32.75 34.42 16,5/I6 2,500 18'/2 44.81 47.06 187/S 3,200 20 56.50 59.32 207/i6

For a sphere with the stresses uniform in all directions, it follows that the fibers require equal orientation in all directions. The problem of orientation resolves itself purely into one of practical application of the fibers. In the cylinder, the fibers are specifically oriented to meet any condition of stressing. The simplest method of doing this is to employ a single helical pattern.

Theory shows that this is highly sensidve to variadons in the longitudinal hoop-stress rado and also the accuracy of the angle wound. The addidon of pure hoop windings to the helix gives a theoretical gain in stability with no loss of strength or efficiency. In order to develop the most satisfactory orientation, the winding is performed so those two different helix angles are used.

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