Page 164 - Pressure Vessel Design Manual

142 Pressure Vessel Design Manual
/ -I---. f f

f f

f f

e At Loads Between Loads f f

Kr C, Id Cr e At Loads Between Loads
1" +0.619 -0.01 7 -0.365 -1 .oo
2" +0.601 -0.041 -0.366 -0.999 Id C, K, cr
3" +0.584 -0.052 -0.363 -0.998 1" + 0.254 -1.018
4" +0.566 -0.071 -0.362 -0.997 -0.143 -1.411
5" +0.550 -0.087 -0.360 -0.996 2" + 0.238 - 1.040 -0.143 -1.410
6" f0.532 -0.105 -0.359 -0.995 3" + 0.221 - 1,050 -0.142 - 1.409
7" +0.515 -0.122 -0.357 -0.992 4" + 0.206 - 1.066 -0.140 - 1 A08
8" +0.498 -0.138 -0.355 -0.990 5" +0.194 - 1.079 -0.136 - 1.407
9" +0.481 -0.1 55 -0.352 -0.986 6" +0.178 - 1,095 -0.135 - 1.406
10" +0.466 -0.171 -0.348 -0.985 7" +0.165 -1.108 -0.133 - 1.405
15" +0.387 -0.250 -0.329 -0.966 8" f0.153 -1.117 -0.130 - 1.404
20" +0.315 -0.321 -0.303 -0.940 9" +0.141 -1.130 -0.124 - 1.397
25" +0.254 -0.383 -0.270 -0.906 10" +0.130 - 1.141 -0.119 - 1.393
15"
30" +0.204 -0.433 -0.229 -0.866 + 0.090 -1.183 - 0.093 - 1.366
35" +O. 1 67 -0.469 -0.183 -0.819 20" + 0.069 - 1.204 - 0.056 - 1.329
40" +o. 144 -0.492 -0.1 29 -0.766 25" +0.069 - 1.204 - 0.008 - 1.282
45" +O. 137 -0.500 -0.070 -0.707 30" + 0.090 -1.183 + 0.049 - 1.225
35" +0.132 - 1.141 +0.115 -1.158
40" +0.194 - 1.079 +0.190 - 1.083
Figure 3-24. Coefficients for rings. (Signs in the table are for loads as 45" + 0.273 - 1 .ooo + 0.273 - 1 .ooo
shown. Reverse signs for loads are in the opposite direction.)
Figure 3-25. Coefficients for rings. (Signs in the table are for loads as
shown. Reverse signs for loads are in the opposite direction.)
a Internal moment in rings, MI and M2.
Upper ring: a Required section modulus of upper ring, Z.
M
Mi = k,fR1 COS 8 Z=1
S
Lower ring:
Note: It is assumed the lower ring is always larger or of
Mz = k,fRzcos 8 equal size to the upper ring.
Note: cos 0 is to be used for nonradial loads. Disregard if
load f is radial.